Ben Chi Chen

Liang Corry

Niko Hildebrandt Huang

Fret-Modulated

Lijiao Chi Chen

Yu-Tang Ao

Vjona Wu

Marcelina Cifliku

Dos Cardoso

Emmanuel Santos

Martina Bourrier

David Delbianco

Jurriaan M Parker

Zwier

Liang

Pengfei Chi Chen

Li Zhang

Duyang Zhang

Guanhui Gao

Yong Gao

Wenjun Yang

Ping Li

Lintao Gong

Cai

Long-Decay

Clyde Chi Chen

Shashi Midelet

Martinus H V Bhuckory

Niko Hildebrandt Werts

Oral presentations 1

Keywords: Lanthanide energy transfer donors on nanoparticles surfaces: from fundamental mechanisms to multiplexed biosensing quantum dots, terbium, multiplexing, fluorescence, barcoding, FRET

Titre : Transfert d'é nergie entre lanthanides et nanoparticules: des mé canismes fondamentaux aux biosenseurs multiplexé s Mots clé s : points quantiques, terbium, multiplexage, fluorescence, code à barres, FRET Ré sumé : Le multiplexage optique basé sur des nanoparticules offre de nombreux avantages pour la biodé tection et l'imagerie à multiparamè tres. Toutefois, les modifications apporté es à un paramè tre entraî nent é galement la modification d'autres paramètres. Par consé quent, la couleur, la duré e de vie ou l'intensité ne peuvent pas être utilisées, respectivement, comme paramè tre indé pendant. Cette thè se peut ê tre divisé e en deux aspects. Le premier concerne le dé veloppement d'un multiplexage à une seule nanoparticule avec un temps ré solu, basé sur le transfert d'é nergie par ré sonance de type Förster (FRET) des complexes de lanthanides aux points quantiques (QD) et ensuite aux colorants fluorescents. Une investigation systé matique de toutes les diffé rentes combinaisons avec une large gamme de donneurs et d'accepteurs sur le QD est pré senté e, et les ré sultats expé rimentaux sont comparé s à la modé lisation thé orique. Le ré sultat ne contribue pas seulement à une compré hension complè te de ces voies de transfert d'é nergie compliqué e entre multi donneurs / accepteurs sur des nanoparticules, mais offre é galement la possibilité d'utiliser les modè les pour dé velopper de nouvelles straté gies permettant de preparer le QD avec une couleur, une duré e de vie et une intensité ré glables de maniè re indé pendante. Le deuxiè me aspect porte sur le mé canisme de transfert d'é nergie du Tb à la nanoparticule d'or (AuNP). Le transfert d'é nergie par nanosurface (NSET) s'est ré vé lé ê tre un mé canisme opé rationnel pour l'extinction des PL par les AuNP, une information importante pour le dé veloppement, la caracté risation et l'application de nanobiocapteurs basé s sur l'extinction des PL par les AuNP.

compared with theoretical modelling. The result do not only contribute to a full understanding of such complicated multi donor-acceptor energy transfer pathways on nanoparticles but also open the opportunity to use the models for developing new strategies to achieve the QD with independent tunable color, lifetime and intensity. The second aspect focuses on the energy transfer mechanism from Tb to gold nanoparticle (AuNP). Nanosurface energy transfer (NSET) proved to be an operational mechanism in PL quenching by AuNPs, which is important information for the development, characterization, and application of nanobiosensors based on PL quenching by AuNPs.

To my beautiful, talented, and curious wife Xin Geng.

Acknowledgment

First and foremost I would like to express my special appreciation my supervisor Prof. Niko Hildebrandt, who provided many precious opportunities and constant support during my PhD and acted as a role model to me not only academically but also in life. There are many things Niko has taught me, but nothings was more precious than his enthusiasm to pursue pure science and push the boundaries of human knowledge (e.g., FRET). I still remember one day we discussed a huge and complicated work, and he said: "I know all of this takes a long time but this is what science is actually about. We need to remember that we are primarily making science for science and not for our career. " I thank Prof. Adriana Zaleska-Medynska and Prof. Thomas Just Sørensen for being the reviewers of my PhD thesis.

I also want to thank our collaborators Dr. Liang Huang, Dr. Martinus H. V. Werts, Dr. Jurriaan M. Zwier, and Prof. Ben Corry for their kindness, availability and scientific support, and all the co-authors of my publications.

Many thanks to all former and current members of the NanoBioPhotonics group.

My special thanks to Dr. Shashi Bhuckory, Dr. Yu-Tang Wu, and Dr. Xue Qiu for their continuous guidance, patience and valuable time devoted in sharing their technical and scientific knowledge with me. I also thank Dr. Marcelina Cardoso Dos Santos, Vjona Cifliku, and Meryem Sennad for cell culture.

I also want to thank Carlos Mingoes and Tudor Haruta for translating in hospital when I was injured, Dr. Xavier Zambrana Puyalto for suggesting the funny book "Surely You're Joking, Mr. Feynman!", Dr. Akram Yahia-Ammar for translating in CPMA, Dr. Mariia Dekaliuk for helping to find a nice apartment near our lab, Jiajia Guo and Jingyue Xu for providing real hot food when I first came to France, and Bilguissou Diallo for her help with translation of my abstract, I thank the IDEX Paris-Saclay (Investissements d'avenir) for my PhD fellowship.

Of course, thanks must go to my parents. They do not speak English and have no idea what nanophotonics is, but they always try their best to support and encourage me in every possible way.

Last but not least, my deepest gratitude goes to my wonderful wife Xin Geng.

Although she is not a scientist, she always listens curiously to me for sharing my research ideas. The idea of single-nanoparticle barcoding is inspired from a talk in which I want to explain her the spectroscopic ruler. Without her companionship and encouragement, it would have been impossible for me to go through the last three years with full of enthusiasm.

These days in Paris were the happiest three years I have had. Not only FRET theory from "Captain FRET", I also learned a lot of art and culture knowledge from the museums. Thanks to everyone I have met along the way. This sentence is from a book called "The Story of Philosophy". Or we also can call it "The beauty of Philosophy". We know the natural philosophy is considered to be the precursor of natural science. But why every science ends as art? What is art?

In my opinion, art is the expression of imaginative, conceptual, original ideas with technical skill and emotional power, or we can say beauty is art. Euler's Identity shows a profound connection between the most fundamental numbers in mathematics and exhibits the mathematical beauty. Maxwell's Equations establish unified electromagnetic theory. They bring together electricity, magnetism, and light as different manifestations of the same phenomenon, and show the physical beauty. I also want to discovery the beauty in my research field, and I believe it has been there. The aim of this thesis is to study the Förster resonance energy transfer (FRET) mechanism in lanthanides-quantum dot (QD)-fluorescent dyes systems and utilize the FRET modulated multi-hybrid nanoparticle for time-resolved multiplexing, and the study of energy transfer mechanism from long lifetime Tb donors to gold nanoparticles (AuNPs). Time-resolved multiplexing has many advantages, and we also find the beauty of time based multiplexing. The three temporal optical detection windows can be regarded as metaphor of the three clocks in Dali's "The Persistence of Memory" (Figure 1.1 right). Inspired by this painting, we designed this picture (Figure 1.1 left), in which the three clocks with red, green, and blue color perfectly represent the idea of that were used for RGB (red, green, blue) barcoding. Other elements in this painting have also been replaced by the materials using in our study, including a single-nanoparticle assembly (orange clock covered by ants in the original) on the bottom left, a microscope objective (the "monster" in the original) in the center (below the blue clock), and a microscope slide with encoding cells (the platform or pool in the original) on the top left. The first study (Chapter 3) demonstrates the possibility of single-nanoparticle cell barcoding based on lanthanides complex to QD FRET. In order to obtain the optical encoding with higher capacity, the majority of principle was mixing of different luminescent molecules or nanoparticles in microbeads or cells. Designing different concentration-independent codes without mixing various nanoparticles and by using single-wavelength excitation and emission for multiplexed imaging is extremely challenging. As illustrated in Figure 1.2, we report the synthesis of QDs coated with SiO2 of different shell thicknesses (6 and 12 nm). Attachment of lanthanide (Ln) complexes (Tb and Eu) with long photoluminescence(PL)-lifetimes on the SiO2 shells resulted in different Ln-to-QD distances, which, in turn, led to different PL decay times due to distance-dependent FRET. Thus, four specific QD PL decays (all at 640 nm upon excitation of the Ln complexes at 349 nm) were designed with Tb-QD (SiO2-6nm), Tb-QD (SiO2-12nm), Eu-QD (SiO2-6nm), and Eu-QD (SiO2-12nm) and used as well-defined single-particle codes to label live cells.

To recognize the live-cell codes, time-gated fluorescence microscopy was employed and four different cell types could be distinguished by a single measurement. The information density of the single particle encoding can be further enlarged by using donors with various Ln complexes and QD acceptors with different colors. Thus, our time-gated Ln-to-QD FRET concept has the potential to significantly advance fluorescence cell-encoding. However, one important drawback of this strategy is the significant variation in brightness of the different codes. We will address this issue in the second study. The second study (Chapter 4) focuses on multiple donor-acceptor FRET systems with QDs. QDs are the most versatile fluorophores for FRET because they can function as both donor and acceptor for a multitude of fluorophores attached to their surface. However, a complete understanding of multi-donor-acceptor FRET networks on QDs and their full employment into advanced fluorescence sensing and imaging have not been accomplished. In this chapter, we provide a holistic photophysical analysis of such multi-donor-QD-multi-acceptor FRET systems using time-resolved and steady-state PL spectroscopy and Monte Carlo simulations. Multiple terbium-complex (Tb) donors (1 to 191 units) and Cy5.5 dye acceptors (1 to 60 units) were attached to a central QD and the entire range of combinations of single and multiple FRET pathways was investigated by Tb, QD, and Cy5.5 PL. Experimental and simulation results were in excellent agreement and could disentangle the distinct contributions of hetero-FRET, homo-FRET, and dye-dimerization. The FRET efficiency was independent of the number of Tb donors and dependent of the number of Cy5.5 acceptors, which could be used to independently adapt the PL intensity by the number of Tb donors and PL lifetime by the number of Cy5.5 acceptors. As shown in Figure 1.3, we used this unique tuning capability to prepare Tb-QD-Cy5.5 conjugates with distinct QD PL lifetimes but similar QD PL intensities. These brightness-equalized multi-hybrid FRET nanoparticles were applied to optical barcoding via three time-gated PL intensity detection windows, which resulted in an encoding of the distinct PL decay curves into simple RGB ratios. Direct applicability was demonstrated by an efficient RGB distinction of different nanoparticle-encoded microbeads within the same field of view with both single-wavelength excitation and detection on a standard fluorescence microscope. In addition to imaging and biosensing, controlled photophysical tuning of FRET-modulated multi-hybrid QDs for single-wavelength PL encoding has the potential to advance other photonic applications, such as data storage, security labeling, optogenetics, or molecular computing. In the third study (Chapter 5) we attempt to understand the energy transfer mechanism from long lifetime Tb donors to AuNPs. The application of PL quenching by AuNPs has expanded the applicability of optical probe methodologies in biochemistry, biodiagnostics, and biomolecular imaging. Understanding the energy transfer mechanism plays a fundamental role in developing optical ruler methodologies. Both Förster resonance energy transfer (FRET, ~R-6 distance dependence) and nanosurface energy transfer (NSET, ~R-4 distance dependence) have been considered as the correct theory for the quenching mechanism. However, the significant differences of the distance dependence of both resonance energy transfer mechanisms can lead to strong variations in the energy transfer process.

In this chapter, we investigate PL lifetime quenching of terbium complexes (Tb) conjugated to streptavidin when bound to biotinylated Au-NPs of different diameters [START_REF] Corry | A Flexible Approach to the Calculation of Resonance Energy Transfer Efficiency between Multiple Donors and Acceptors in Complex Geometries[END_REF][START_REF] Mattoussi | Self-Assembly of CdSe-ZnS Quantum Dot Bioconjugates Using an Engineered Recombinant Protein[END_REF][START_REF] Lu | Self-Assembled Donor Comprising Quantum Dots and Fluorescent Proteins for Long-Range Fluorescence Resonance Energy Transfer[END_REF], and 80 nm)(Figure 1.4). The binding of Tb-labeled streptavidin (Tb-sAv) to biotinylated AuNPs (biot-AuNPs) was studied using lightscattering spectroscopy. Quenching of the PL of Tb-sAv upon binding to biot-AuNPs of different diameters (5, 30, 50, 80 nm) was studied by time-resolved PL spectroscopy. Energy-transfer efficiencies were found to be practically independent of the AuNP size. Analysis according to FRET theory yielded donor-acceptor distances that were inconsistent and far beyond the expected Tb-AuNP distance.

In contrast, the NSET model yielded a good agreement between the Tb-to-AuNP surface distance estimated from the geometry of the Tb-sAv/biotin-AuNP assembly (4.5 nm) and those calculated from PL lifetime analysis, which range from 4.0 to 6.3 nm. Our findings strongly suggest that NSET (and not FRET) is the operational mechanism in PL quenching by AuNPs, which is important information for the development, characterization and application of nanobiosensors based on PL quenching by AuNPs. QDs, luminescent lanthanides, fluorescent dyes, AuNPs, and time-resolved measurement will be presented (Chapter 2). Three experimental studies will follow in a paper-style with an introduction, materials and method, results and discussion, and a conclusion. A summary addressing the results obtained from the experimental studies will be discussed and an outlook on future research.

Appendix and bibliography follow at the end of the thesis.

Background

This chapter will introduce basic knowledge of Förster resonance energy transfer (FRET) mechanisms, quantum dots (QDs), luminescent lanthanides, fluorescent dyes, gold nanoparticles (AuNPs), and time-resolved (TR) measurement in an attempt to understand how to design and perform lanthanides-to-QDs D-A pairs based FRET and lanthanides-to-AuNPs pairs based NSET experiment. In particular, we are interested in studying the multiple donors and acceptors based FRET model for calculating desired photophysical properties adapted to advanced fluorescence biosensing and imaging applications. The understanding of such a model will be facilitated by a deep understanding of such complicated multi donoracceptor energy transfer pathways on nanoparticles. This chapter will be organized by first examining in Section (2.1) FRET mechanism in terms of FRET theory, multiple donors and/or acceptors FRET. Section (2.2) will examine optical properties and surface functionalization of QDs, and how QDs can server as donor, acceptor, or relay. The next Section (2.3) will examine photophysics of luminescent lanthanide complexes and nanoparticle, and the advantage of lanthanide complexes in donor based FRET. Section (2.4) will focus on dye aggregates and homo FRET of fluorescent dyes. Section (2.5) will focus on the surface plasmon resonance (SPR) and nanosurface energy transfer (NSET) of AuNPs. Finally, Section (2.6) will examine the TR measurement and TR based optical multiplexing.

Förster resonance energy transfer

Resonance energy transfer (RET) is based on the concept of a fluorophore as an oscillating dipole, which can exchange energy with another dipole with a similar resonance frequency. [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF] The best known RET mechanism is Förster resonance energy transfer (FRET), which is considered to occur when the donor and acceptor can be reasonably approximated as point dipoles. For the observation of FRET, the following conditions should be met: [START_REF] Hildebrandt | FRET -Förster Resonance Energy Transfer[END_REF] (i) The donor must be a fluorophore and has a reasonably large quantum yield.

(ii) Spectral overlap must exist between the emission of donor and the absorption of acceptor.

(iii) Donor and acceptor must be close, but not too close.

(iv) The orientation factor should not be zero.

In addition, when the excited state donor is created through a chemical reaction or enzyme-catalyzed biochemical reaction, the RET phenomena are referred to as bioluminescence or chemiluminescence resonance energy transfer (BRET or CRET), respectively. In general, Förster theory applies equal well to both of them.

The FRET mechanism does not generally apply in cases where the donor or acceptor cannot be approximated as a point dipole, which frequently occurs with energy transfer to metal surfaces. The latter are more appropriately described as nanosurface energy transfer (NSET). The discussion below will present some very basic knowledge and mathematics needed of FRET theory (2.1.1), multiple donors and/or acceptors based FRET (2.1.2) to design and perform FRET based experiments, and is mainly extracted from reference [START_REF] Hildebrandt | FRET -Förster Resonance Energy Transfer[END_REF].

Förster resonance energy transfer theory

Förster resonance energy transfer (FRET) is an electrodynamic phenomenon, and the theory behind resonance energy transfer was mainly contributed by Theodor Förster in 1940s. [START_REF] Hildebrandt | FRET -Förster Resonance Energy Transfer[END_REF] FRET is a nonradiative energy transfer process between a donor (D) molecule in the excited state and an acceptor (A) molecule in the ground state with an efficiency that is dependent on the distance R -6 between D and A.

FRET occurs without the appearance of a photon and is the result of long range dipole-dipole interactions between the donor and acceptor. It can be represented by Coulombic coupling (coupling of two charges) VCoul. VCoul should be dominant at the distance range of 1-20 nm, which is usually considered FRET distance. In this case, orbital overlap-related mechanisms and radiative mechanisms play minor roles. The FRET rate can be represented by Fermi's golden rule (Equation 2.1):

𝑘 FRET = 2𝜋 ℏ |𝑉| 2 𝜌 (2.1)
Where ℏ is the reduced Planck constant, V is the electronic coupling between D and A, and ρ is the density of the interacting initial and final energetic states, which is related to the spectral overlap integral J (the overlap of D emission and A absorption, defined in the wavelength or wavenumber scale). In Equation 2.1, V can be replaced by the R -3 distance dependent 𝑉 Coul (Equation 2.2):

𝑉 Coul = 𝜅|𝜇 ⃗ ⃗ D ||𝜇 ⃗ ⃗ A | 4𝜋𝜀 0 𝑛 2 𝑅 3 (2.2)
Where 𝜇 D and 𝜇 A are the transition dipole moments of D and A, 𝜅 is the orientation factor between them, 𝜀 0 is the vacuum permittivity, n is the refractive index, and R is the distance between D and A.

After substituting Equation 2.2 into Equation 2.1, the FRET rate can be descripted as following Equation 2.3: In the Jablonski diagram (simplified energy level scheme), the donor is excited by hv from an electronic ground state (D) to an excited state (D*), and then goes to an excited electronic ground state by inner relaxation (vibrational and rotationaldotted arrow), and finally goes back to ground state by radiative decay (𝑘 R ), nonradiative decay (𝑘 NR ), or FRET (𝑘 FRET ). The FRET process happens when the difference between the respective energy levels are equal, in other words the donor and acceptor share the same electronic transitions (horizontal lines with dots on each end). After FRET, the acceptor is in an excited state (A*), then goes to its ground state (A) by radiative or nonradiative decay. (Right) The overlap (gray area) of the area normalized emission spectrum of D (cf. Equation 2.6) and the molar absorptivity spectrum of A (𝜀 A ) defines the overlap integral J (cf. Equation 2.5). (Adapted from reference [START_REF] Hildebrandt | FRET -Förster Resonance Energy Transfer[END_REF].

𝑘 FRET = 9 (
Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA)

Basic principle of FRET is presented in a simplified Jablonski diagram in Figure 10 2.1 (left), electronic transitions from a higher to a lower energy level in D lead to electronic transitions from a lower to higher energy level in A, if these transitions are in energetic resonance.

Förster distance (R0), at which energy transfer and spontaneous decay of the excited donor are equally probable (𝑘 FRET = 𝑘 D R + 𝑘 D NR = 𝜏 D -1 ), the FRET efficiency 𝐸 FRET is 50%, can be calculated by Equation 2.4 (replace 𝑘 FRET with 𝜏 D -1 and R with R0):

𝑅 0 6 = 9 (ln10)𝜅 2 Φ D 128𝜋 5 𝑁 A 𝑛 4 𝐽 (2.4)
The spectral overlap integral 𝐽 (defined in wavelength scale) is shown in Where 𝜀 A (𝜆) is the acceptor molar absorptivity (or extinction coefficient) spectrum, 𝐼 D ̅ (𝜆) is the donor emission spectrum normalized to unity and is given by Equation

2.6:

∫ 𝐼 𝐷 ̅ (𝜆) 𝑑𝜆 = 1 (2.6) The orientation factor 𝜅 2 can be calculated using the different angles and the unit vectors of 𝜇 𝐷 , 𝜇 𝐴 , and 𝑅 ⃗ (Equation 2.7):

𝜅 2 = [𝜇D • 𝜇̂A -3(𝜇̂D • 𝑅 ̂)(𝜇Â • 𝑅 ̂)] 2 = [cos 𝜃 DA -3 cos 𝜃 D cos 𝜃 A ] 2 (2.7)
where 𝜇̂D, 𝜇̂A, and 𝑅 ̂ represent the unit vectors of 𝜇 D , 𝜇 A , and 𝑅 ⃗ , respectively. As show in Figure 2.2, 𝜃 DA is the angle between the donor and acceptor transition moments, 𝜃 D and 𝜃 A are the angles between the donor and acceptor transition dipole moments and the donor-acceptor connecting vector 𝑅 ⃗ . According to the Equation 2.7, 𝜅 2 can range from 0 to 4 depending on the relative orientation of donor and acceptor transition dipole moments. For instance, 0 can occur for the perpendicular transition dipole moments, 4 for head-to-tail parallel transition dipoles moments, and 1 for the parallel transition dipole moments. Generally, 𝜅 2 is assumed equal to 2/3, which is the value for D and A that are free to rotate any possible orientation during the FRET time ( 1/𝑘 FRET ), which means that the average rotation rate is much higher than the average FRET rate.

Combination of Equations 2.3 and 2.4 leads to the relation between the FRET rate, the luminescence decay time of the donor, and the distances (R -6 distance dependence of the FRET rate, Equation 2.8):

𝑘 FRET = 𝜏 D -1 [ 𝑅 0 𝑅 ] 6 (2.8)
Then the FRET efficiency is given by Equation 2.9: 6 (2.9)

𝐸 FRET = 𝑘 FRET 𝑘 FRET +𝑘 D R +𝑘 D NR = 𝑘 FRET 𝑘 FRET +𝜏 D -1 = 1 1+(𝑅/𝑅 0 ) 6 = 𝑅 0 6 𝑅 0 6 +𝑅
As shown in FRET efficiency can also be calculated by the measurable PL properties including intensity (I), lifetime (τ), and quantum yield (Φ) using Equation 2.10:

𝐸 FRET = 1 - 𝐼 DA 𝐼 D = 1 - 𝜏 DA 𝜏 D = 1 - Φ DA Φ D (2.10)
where D is the donor in absence of the acceptor, and DA is the donor in presence of the acceptor.

FRET with multiple donors and/or acceptors

Nanoparticles (e.g., QDs) possess nontrivial surface areas, and usually can assemble multiple donors and acceptors on their surface. The D/A and A/D ratio can influence the FRET properties (sensitization and FRET efficiency). However, theoretical model for FRET system with multiple (m) donors and multiple (n) acceptors was only considered by a few studies. [START_REF] Berney | FRET or No FRET: A Quantitative Comparison[END_REF]- [START_REF] Raicu | Efficiency of Resonance Energy Transfer in Homo-Oligomeric Complexes of Proteins[END_REF] According to Raicu's theoretical model for FRET with m donors and/or n acceptors, FRET efficiency is solely dependent on the number of acceptors and the efficiency of a single D-A pair. [START_REF] Raicu | Efficiency of Resonance Energy Transfer in Homo-Oligomeric Complexes of Proteins[END_REF] The relation between FRET efficiency and the number of acceptors also has been shown in an experimental study by Mattoussi's group using n Cy3 acceptors around a QD donor, [START_REF] Clapp | Fluorescence Resonance Energy Transfer Between Quantum Dot Donors and Dye-Labeled Protein Acceptors[END_REF] which was the same as the theoretical model and can be descripted by the following Equation 2.11: 𝑛𝐸 FRET 1+(𝑛-1)𝐸 FRET (2.11) An increasing FRET efficiency with an increasing number of n (acceptors per donor) is logical, because acceptors provide n possible FRET pathways to the excited donor, and therefore, the probability of de-exciting via FRET increases.

𝐸 FRET multi =
For m donors around a QD acceptor, as mentioned above, the FRET efficiency does not change with an increasing number of m. [START_REF] Raicu | Efficiency of Resonance Energy Transfer in Homo-Oligomeric Complexes of Proteins[END_REF] However, the probability of acceptor FRET-sensitization will increase with an increasing number of m and can be given by the following Equation 2.12.

𝑃 A = 1 -(1 -𝐸 FRET ) 𝑚 = 1 -( 𝑅 6 𝑅 0 6 +𝑅 6 ) 𝑚 (2.12) Based on a Monte Carlo simulation model, [START_REF] Berney | FRET or No FRET: A Quantitative Comparison[END_REF] Corry and co-workers considered the influence from different excitation intensities and designed a model to calculate FRET efficiencies between m donors and n acceptors in complex geometries. [START_REF] Corry | A Flexible Approach to the Calculation of Resonance Energy Transfer Efficiency between Multiple Donors and Acceptors in Complex Geometries[END_REF], [START_REF] Deplazes | Flexible Tool for Understanding FRET in Complex Geometries[END_REF] It is significant because high excitation intensities may lead to many excited donors and/or acceptors, and as a result the already excited acceptors will be unavailable for FRET and decrease the FRET efficiency. This means that Equation 2.11 is valid only for the FRET system with low excitation intensities, in which all donors and acceptors have already gone back to ground states before the excitation. It is the same in the case of the probability of acceptor FRETsensitization. So the Equation 2.12 is invalid for the FRET system with high excitation intensities or excited state of A is much longer than the one of D.

However, Equation 2.11 and 2.12 is valid for cases in which the excited state lifetime of D is much longer than the one of A (e.g., lanthanide D and QD). When there are enough photons to excite several Tb (on the QD) and the QD, sequential FRET (all with the same FRET efficiency) from each Tb to the QD can occur due to the extremely long exited state lifetime of the Tb. For example: 10 Tb and the QD are excited, in the very beginning after the pulsed excitation (several 100 ns) the QD is excited and FRET cannot occur. After ca. 100 ns, the QD decays back to its ground state and can then become an acceptor (within these 100 ns, the probability of Tb de-excitation is small due to the ms lifetime). The QD will get FRET-sensitized by one Tb and then directly give away that energy (fluorescence within ns) and can be excited again. As the probability that the other 9 Tb are still excited is high due to the ms lifetime, the QD can be FRET sensitized again, and thus the FRET efficiency of this system will be constant but the probability of acceptor excitation increases with high intensities pulsed excitation. These FRET processes were studied in this thesis.

Quantum dots

Quantum dots (QDs) are luminescent inorganic semiconductor nanoparticles mainly composed of II-VI (CdS, CdSe, CdTe, ZnS, ZnSe, ZnTe), III-V (GaAs, GaN, GaP, InAs, InP), IV-VI (PbS, PbSe), I-VI(Ag2S, Ag2Se, Ag2Te), and I-III-VI (AgInS, AgInSe, CuInS, CuInSe) groups of the periodic table, and also composed by alloyed structure, core/shell structure, and doped structure of these materials. represents the spectral range of emission for the most widely studied types of semiconductor nanocrystals. The size of these nanoparticles that is usually between 1-10 nm in diameter (zero-dimensional nanomaterials) is smaller or close to their Exciton Bohr Radius. In 1982, Efros et al. [START_REF] Efros | Interband Light Absorption in Semiconductor Spheres[END_REF] and Ekimov et al. [START_REF] Ekimov | Quantum Size Effect in the Optical Spectra of Semiconductor Microcrystals[END_REF] demonstrated that the ultra-small size of particle has a decisive effect on its optical and electrical properties. In 1983, Brus and colleagues at Bell Laboratories first reported colloidal QDs. [START_REF] Rossetti | Quantum Size Effects in the Redox Potentials, Resonance Raman Spectra, and Electronic Spectra of CdS Crystallites in Aqueous Solution[END_REF] From then on, QD began to attract scientists' attention.

In 1993, Bawendi et al. synthesized nearly monodisperse QDs in the high temperature organic solution. [START_REF] Murray | Synthesis and Characterization of Nearly Monodisperse CdE (E = Sulfur, Selenium, Tellurium) Semiconductor Nanocrystallites[END_REF] Since the synthesized product was soluble in the organic phase, main application fields of QDs were focused on high density memory and photovoltaic equipment. [START_REF] Alivisatos | Perspectives on the Physical Chemistry of Semiconductor Nanocrystals[END_REF], [START_REF] Yoffe | Semiconductor Quantum Dots and Related Systems: Electronic, Optical, Luminescence and Related Properties of Low Dimensional Systems[END_REF] Until 1998, Chan et al. [START_REF] Chan | Quantum Dot Bioconjugates for Ultrasensitive Nonisotopic Detection[END_REF] and Bruchez et al. [START_REF] Bruchez | Semiconductor Nanocrystals as Fluorescent Biological Labels[END_REF] pointed out that the water solubility and biocompatibility of QDs can be [START_REF] Reiss | Synthesis of Semiconductor Nanocrystals, Focusing on Nontoxic and Earth-Abundant Materials[END_REF]. Copyright 2016 American Chemical Society)

Optical properties

QDs possess electronic properties that are intermediate between those of bulk semiconductors and discrete molecules. When a bulk semiconductor is excited by photons, an electron is promoted into the quasi-continuum conduction band (CB) leaving a positively charged hole in the valence band (VB). The electron and the hole can bind to each other to form an exciton, and the distance in electron-hole pair is referred to as the exciton Bohr radius. Since the size of QDs is on the same order as the size of the exciton Bohr radius, when an exciton is created, the density of electronic states is not enough to form complete band structures and quantization of the energy levels can be observed at the band edges. The spatial confinement of excitons in QDs leads to a phenomenon known as quantum confinement, which has a direct effect on the boundaries of the bandgap. As illustrated in Figure 2.5, the inter-bandgap energy of QD can be tuned by the size of the nanoparticle. Due to the quantum confinement effect, the band gap of QD will increase as the particle radius decreases, and therefore a series of different emission wavelengths from the ultraviolet (UV) to the near-infrared (NIR) region can be obtained. [START_REF] Algar | Semiconductor Quantum Dots in Bioanalysis: Crossing the Valley of Death[END_REF] From the perspective of fluorescent labeling, QDs possess many desirable photophysical properties. [START_REF] Resch-Genger | Quantum Dots versus Organic Dyes as Fluorescent Labels[END_REF] (i) Broad and continuous absorption spectrum allows free selection of excitation wavelength. (ii) Both high molar absorption coefficient (10 5 -10 6 M -1 cm -1 at first excitonic absorption peak, increasing toward UV wavelengths) and quantum yields (up to 100%) lead to high brightness, which is essential for single particle tracking. (iii) Narrow, size-dependent, and symmetric emission spectra spanning from UV to NIR region are ideal for multi-color experiment. Generally, high quality and monodisperse QDs yield emission profiles with (full-width at half-maximum) FWHM which are typically in the range of 25-35 nm. It has been reported high-quality core-shell CdSe/CdS QDs with narrow emission line widths (FWHM ~20 nm) can be achieved through a slow growth rate of the shell. [START_REF] Chen | Compact High-Quality CdSe-CdS Core-shell Nanocrystals with Narrow Emission Linewidths and Suppressed Blinking[END_REF]

Surface functionalization

The surface functionalization of QD is a major issue for biomedical applications because most of high quality QDs are synthesized using hydrophobic surface ligands at high temperatures, therefore, as-prepared QDs are not directly soluble in aqueous media. For the purposes of making them stable in aqueous solution, as illustrated in Figure 2.6, there are mainly three different strategies: (i) ligand exchange, (ii) encapsulation, and (iii) silica coating.

Ligand exchange is the strategy by which the original hydrophobic surface ligands on the QD surface are replaced with hydrophilic ligands. Essentially these hydrophilic ligands consist of two functional components: the anchoring group(s) and hydrophilic group(s). Thiol based molecules (mercaptoacetic acid (MAA), [START_REF] Kim | Bioconjugation of Hydroxylated Semiconductor Nanocrystals and Background-Free Biomolecule Detection[END_REF]- [START_REF] Wilson | Highly Stable Dextran-Coated Quantum Dots for Biomolecular Detection and Cellular Imaging[END_REF] mercaptopropionic acid (MPA), [START_REF] Kongkanand | Interfacial Water Transport Measurements in Nafion Thin Films Using a Quartz-Crystal Microbalance[END_REF]- [START_REF] Mitchell | Programmed Assembly of DNA Functionalized Quantum Dots[END_REF] mercaptoundecanoic acid (MUA), [START_REF] Hoshino | Physicochemical Properties and Cellular Toxicity of Nanocrystal Quantum Dots Depend on Their Surface Modification[END_REF], [START_REF] Hering | Energy Transfer between CdSe/ZnS Core/Shell Quantum Dots and Fluorescent Proteins[END_REF] and dihydrolipoic acid (DHLA) [START_REF] Mattoussi | Self-Assembly of CdSe-ZnS Quantum Dot Bioconjugates Using an Engineered Recombinant Protein[END_REF]) are the most frequently used ligands due to their reasonably strong affinity for Cd and Zn, which are the most common metals on the surface of QD. However, the colloidal stability of QD coated with these ligands relies on deprotonation in of the carboxyl groups, limiting the usable pH range of QD. In order to solve the poor colloidal stability of thiol ligands, the thiol ligands were modified with poly (ethylene glycol) (PEG) to expand the usable pH range of QD. [START_REF] Kang | Preparation of Water-Soluble PEGylated Semiconductor Nanocrystals[END_REF], [START_REF] Akerman | Nanocrystal Targeting in Vivo[END_REF] It has been reported that PEG-appended DHLA derivatives have been developed to enhance colloidal stability across a pH range from weakly acidic to strongly basic aqueous media. [START_REF] Susumu | Multifunctional Ligands Based on Dihydrolipoic Acid and Polyethylene Glycol to Promote Biocompatibility of Quantum Dots[END_REF]- [START_REF] Uyeda | Synthesis of Compact Multidentate Ligands to Prepare Stable Hydrophilic Quantum Dot Fluorophores[END_REF] The advantage of ligand exchange is that QD with small hydrodynamic diameter can be prepared, which is essential for FRET based biosensing applications. them for both in vitro and in vivo imaging. [START_REF] Dubertret | In Vivo Imaging of Quantum Dots Encapsulated in Phospholipid Micelles[END_REF] Since these encapsulation techniques do not modify the original ligand on the QD surface and prevent water interacting with this surface, QD almost preserve their original QY after encapsulation. However, this strategy often results in large hydrodynamic diameter, which is not optimal for FRET applications.

Silica coating is a method by which to form nucleation sites on the surface through ligand exchange using (3-mercaptopropyl) trimethoxysilane, followed by further shell growth with silane molecules such as tetraethoxysilane via hydrolysis and condensation, [START_REF] Nann | Single Quantum Dots in Spherical Silica Particles[END_REF], [START_REF] Gerion | Synthesis and Properties of Biocompatible Water-Soluble Silica-Coated CdSe/ZnS Semiconductor Quantum Dots †[END_REF] or a water-in-oil reverse microemulsion method. [START_REF] Darbandi | Single Quantum Dots in Silica Spheres by Microemulsion Synthesis[END_REF]- [START_REF] Selvan | Synthesis of Silica-Coated Semiconductor and Magnetic Quantum Dots and Their Use in the Imaging of Live Cells[END_REF] The silica shell is quite robust and makes QD highly stable. Moreover, the silica shell is nontoxic and can be easier to functionalize with bioconjugation reagents. Despite significant advances in uniformity and size control of silica coating, the silica shell is still relatively thick compared to materials prepared with ligand exchange methods. Even so, there are fewer energy transfer and bioimaging studies by using silica shell coated QD. [START_REF] Gao | Efficient Fluorescence Energy Transfer System between CdTe-Doped Silica Nanoparticles and Gold Nanoparticles for Turn-On Fluorescence Detection of Melamine[END_REF], [START_REF] Wu | Highly Sensitive Multiplexed Heavy Metal Detection Using Quantum-Dot-Labeled DNAzymes[END_REF] Recently, we developed lanthanide complex doped QD/SiO2 system and demonstrated them for FRET based living cell barcoding. [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF] We assembled the Tb-Lumi4 or Eu-1 on the QD surface with different thickness of silica shell (6 nm and 12 nm), and observed strong FRET signals due to large Förster distance (up to 12.2 nm) of Ln-QD FRET pairs.

QD as FRET donor/acceptor/relay

QD as FRET donor

QDs can act as FRET donor, acceptor or relay. Most often, QDs are used as FRET donor due to their unique photophysical properties. As illustrated in Figure 2.7, compared with organic dye donors, the broad absorption spectra of QD donors can be excited in the blue/UV range, hundreds of nanometers from their emission maximum. This property leads to significant minimization of direct acceptor excitation and can enhance the FRET sensitivity. QD donors can be regarded as nanoantenna due to their high extinction coefficients (>10 7 M -1 cm -1 ), which increase sensitivity of FRET assay. The emission spectra of QDs are quite narrow and symmetrical, which means the donor emission does not leak into the acceptor detection channel. The surface area of QDs can assemble several acceptors around a single donor, which can allow "tuning" of FRET efficiency. [START_REF] Medintz | Self-Assembled Nanoscale Biosensors Based on Quantum Dot FRET Donors[END_REF] They used the MBP terminal His6-tag to conjugate proteins on the QD surface directly, which allow to precisely control the number and orientation of MBP. The number of QDs as FRET donor-based sensors has increased considerably since these early contributions. In particular, we are interested in QD donor-to-multiple dyes acceptors based FRET mechanism and their application. The studies about this system are listed in Table 2.1, which open the opportunity to use this system for fabricating desired photophysical properties for biosensing applications. (A555, Cy3.5 or At594, A647.)(L,M,N) L = 0, 2, 5, 8 (or L = 0, 3, 6, 9); M = 0, 2, 5, 8; N = 0, 2, 5, 8.

QD

quantitative tracking the proteolytic activities of trypsin, chymotrypsin, and enterokinase yes [START_REF] Massey | Expanded Quantum Dot-Based Concentric Förster Resonance Energy Transfer: Adding and Characterizing Energy-Transfer Pathways for Triply Multiplexed Biosensing[END_REF] 21

QD as FRET acceptor

In 2005, Clapp et al. studied dye-to-QD configuration and found no evidence for FRET with both steady state and time-resolved spectroscopy, even when the dye/QD ratio was increased up to 10. [START_REF] Clapp | Can Luminescent Quantum Dots Be Efficient Energy Acceptors with Organic Dye Donors?[END_REF] They assumed that the direct QD excitation and excited-state lifetime difference should be responsible for this result. When organic dyes are excited, QDs are always directly excited at the same time due to their broad absorption spectra. Moreover, the relatively long excitedstate lifetime of a QD (usually tens to hundreds of ns) compared to that of a typical organic dye (usually a few ns) leads to a very high probability that the dye will decay back to its ground state before the QD and therefore they cannot effectively serve as acceptors for a proximal excited dye. [START_REF] Algar | Emerging Non-Traditional Förster Resonance Energy Transfer Configurations with Semiconductor Quantum Dots: Investigations and Applications[END_REF] They tested a Ru-based dye as donor (with several hundreds of ns lifetime) and observed significant lifetime quenching in the presence of a QD acceptor. This was the first indicator that long excited-state lifetime donors may unlock QD acceptor based FRET.

Although dye-to-QD based FRET configurations are generally unfavorable, QDs acceptor-based FRET has gradually been established using some non-traditional donors such as lanthanide complexes, chemiluminesent and bioluminescent molecules, and upconverting NPs (UCNPs). [START_REF] Algar | Emerging Non-Traditional Förster Resonance Energy Transfer Configurations with Semiconductor Quantum Dots: Investigations and Applications[END_REF] The main issue of QDs as FRET acceptors is their broad and intense absorption, which means there are efficient excitation at all wavelengths shorter than their emission wavelength. In order to inhibit or decrease direct excitation of the QDs, there are three different strategies: analysis. [START_REF] Huang | A Resonance Energy Transfer between Chemiluminescent Donors and Luminescent Quantum-Dots as Acceptors (CRET)[END_REF] (iii) UCNP with higher energy visible PL can be excited using low energy NIR by sequential absorption of two or more photons. Therefore, direct QD excitation can also be avoided by using upconverting NPs as donors. It should be noted that FRET between UCNPs and QDs is not the most advantageous situation since the NPs usually possess relatively large size as compared to the usual FRET range of ca. 1 to 10 nm. Thus, in UCNP-to-QD FRET, only the lanthanide ions close to the surface can participate in FRET to the QD, whereas the ions close to the center of the UCNP usually remain unquenched. [START_REF] Mattsson | Upconverting Nanoparticle to Quantum Dot FRET for Homogeneous Double-Nano Biosensors[END_REF] In order to generate efficient FRET, it is necessary to design UPNCs with efficient surface-emitting lanthanide ions.

QD as FRET relay

QDs can serve as relay. In this case, the QD is used simultaneously as a donor and an acceptor, and can transfer energy provided by an initial donors to an acceptor.

The advantage of QD as relay is that the color multiplexing can be achieved with a single QD. Figure 2.8 presents a full FRET relay cycle (e.g., mTb-QD-nA647) after a pulsed excitation. Both Tb and QD can be excited by pulsed UV light directly, whereas the A647 (assuming no direct excitation) remains in its ground state. In this situation, FRET2 (QD-to-A647) occurs and followed by A647 PL emission, while the FRET1 is forbidden. Then Tb still remains in excited state due to the long lifetime (~ms), in which the QD and A647 decay to their ground states.

FRET1 (Tb-to-QD) will then occur followed by another FRET2 (FRET-sensitized QD to A647). Such kind of QD as relay based FRET systems have already been developed for enzymatic and hybridization assay or for the design of molecular logic gates. [START_REF] Algar | Quantum Dots as Simultaneous Acceptors and Donors in Time-Gated Förster Resonance Energy Transfer Relays: Characterization and Biosensing[END_REF]- [START_REF] Afsari | Time-Gated FRET Nanoassemblies for Rapid and Sensitive Intra-and Extracellular Fluorescence Imaging[END_REF] In this thesis, we are interested the mechanism and application of QD as relay based system, and previous studies about these systems are listed in

Luminescent lanthanides

Lanthanides are a series of 15 metal elements located at the sixth period and IIIB group in the periodic table, ranging from lanthanum to lutetium, with the electronic configuration of [Xe]4f 𝑛-1 5𝑑 0-1 6s 2 (n = 1-15), and are also referred as the f-block elements. where radiative transition between the energy levels occurs to give rise to luminescent lanthanide ions. As it can be observed for the Ln 3+ ions on the periphery (Ce 3+ , Pr 3+ , Nd 3+ , Pm 3+ , Ho 3+ , Er 3+ , Tm 3+ , and Yb 3+ ), the energy gaps are relatively small between adjacent levels, while the central metals (Sm 3+ , Eu 3+ , Gd 3+ , Tb 3+ , Dy 3+ ) exhibit larger energy gaps. As a result, f-f emission lines cover the entire spectrum from UV (Gd 3+ ) to visible (e.g., Pr 3+ , Sm 3+ , Eu 3+ , Tb 3+ ) and NIR (e.g., Pr 3+ , Nd 3+ , Er 3+ , Yb 3+ ). [START_REF] Eliseeva | Lanthanide Luminescence for Functional Materials and Bio-Sciences[END_REF] In addition, Ln 3+ ions possess significant paramagnetic properties due to unpaired electrons in 4f orbitals (except La 3+ and Lu 3+ ). Unlike their chemical properties, the magnetic moments and magnetic susceptibilities of Ln 3+ differ dramatically along the series. [START_REF] Sherry | Alternatives to Gadolinium-Based Metal Chelates for Magnetic Resonance Imaging †[END_REF] The studies on lanthanide elements date back to the 18th century. With the development of lanthanide chemistry for more than two centuries, these elements have found a wealth of applications, ranging from high-tech products to health and medical utilization. [START_REF] Eliseeva | Rare Earths: Jewels for Functional Materials of the Future[END_REF], [START_REF] Bünzli | Taking Advantage of Luminescent Lanthanide Ions[END_REF] Particularly, there has been a steady increase in the theoretical and experimental studies of luminescent lanthanide complex and lanthanide nanoparticle over the past decade, principally due to an increasing demand for photoluminescence and related applications, including electronic display, document security, optical data storage, biological labeling, and imaging. [START_REF] Eliseeva | Lanthanide Luminescence for Functional Materials and Bio-Sciences[END_REF], [START_REF] Debroye | Towards Polymetallic Lanthanide Complexes as Dual Contrast Agents for Magnetic Resonance and Optical Imaging[END_REF]- [START_REF] Liu | Lanthanide-Doped Luminescent Nanoprobes: Controlled Synthesis, Optical Spectroscopy, and Bioapplications[END_REF] The discussion below will review the luminescence

Luminescent lanthanide complexes and nanoparticles

Luminescent lanthanide complexes (LLCs)

The unique luminescence properties of lanthanides come from transitions involving a redistribution of electrons within 4f orbitals because of the effective shielding by 6s and 5p orbitals. Since the transitions within 4f orbitals are in violation of the Laporte rule which states that electronic transitions that conserve parity, either symmetry or antisymmetry with respect to an inversion center are forbidden, lanthanide ions display extremely long luminescent lifetimes and very small molar absorption coefficients (<10 M -1 cm -1 ). [START_REF] Zhang | Long-Lived Emissive Probes for Time-Resolved Photoluminescence Bioimaging and Biosensing[END_REF] In order to get more excited, lanthanide ions usually require indirect excitation, which means the emissive states of lanthanides are populated through energy transfer from a sensitizing antenna. As illustrated in The overall quantum yield, Φ Ln L , of a lanthanide complex is given by Equation 2.13:

Φ Ln L = 𝐼 Ln (E) 𝐼 L (A) =  sens Φ Ln Ln (2.13)
Where 𝐼 Ln (E) is the number of photons emitted by the Ln metal ion, 𝐼 L (A) is the number of photons absorbed by the ligand, Φ Ln Ln is the intrinsic quantum yield of the Ln metal ion,  sens represents the sensitization efficiency.

Based on Equation 2.13, the Φ Ln L can be improved by tuning the following two factors:  sens and Φ Ln Ln . A higher 𝜂 sens value can be achieved by the antenna ligand with a higher intramolecular energy transfer rate, and a higher Φ Ln Ln can be improved by optimized Ln 3+ ion carrier chelate which protect the ions from the quenching effects of the aqueous matrix, and thus minimizes the non-radiative processes. (Reproduced from reference [START_REF] Heffern | Lanthanide Probes for Bioresponsive Imaging[END_REF]. Copyright 2014 American Chemical Society)

Upconverting nanoparticles (UCNPs)

Luminescence usually follows Stokes' law which states that emitted photons have a smaller energy than excitation photons. In 1966, Auzel suggested that energy transfer can take place between neighboring Ln 3+ ions that are both in their excited states by sequential energy transfer process, which is more efficient than excitedstate absorption (or 2-step absorption). In this process, two (or more) low-energy photons are combined resulting in the emission of one higher-energy photon, known as upconversion emission.

[86]

Lanthanide complexes as FRET donor

LLCs-based donors have many advantages, and the most important property of lanthanide-based donors for FRET is their long luminescence decay time reaching up to several milliseconds [START_REF] Hildebrandt | Energy Transfer with Semiconductor Quantum Dot Bioconjugates: A Versatile Platform for Biosensing, Energy Harvesting, and Other Developing Applications[END_REF], [START_REF] Cardoso Dos Santos | Recent Developments in Lanthanide-to-Quantum Dot FRET Using Time-Gated Fluorescence Detection and Photon Upconversion[END_REF], [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF], which means that the excited-state lifetimes Therefore, by choosing an acceptor with emission at a wavelength region void of donor emission, and using pulsed excitation and time-gated detector for a short delay time and gate width (time-gated measurement, detail in Section 2.4.1), the acceptor detection channel becomes a "FRET-proof" channel, which means the sensitized acceptor signal completely arises from FRET pairs, and is independent of concentration effects and incomplete binding. In addition, multiple narrow and well-separated PL spectra of LLCs provides the possibility of multiplexing with several different FRET acceptors. [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF] And some of LLCs PL spectra (e.g., luminescent Tb complex (LTC)) are in a wavelength region where many fluorophores are excellent absorbers and therefore lead to relatively large spectral overlap integrals. For example, Förster distances of up to 11 nm can be achieved by using LTC-to-QD D-A pairs. [START_REF] Geißler | Lanthanides and Quantum Dots as Förster Resonance Energy Transfer Agents for Diagnostics and Cellular Imaging[END_REF] is that they most often possess unpolarized emission, which can greatly reduce the uncertainty of the orientation factor 𝜅 2 . Due to their multiple transition dipole moments, LTC can server as randomized donors and the orientation factor 𝜅 2 will be limited to values between 1/3 and 4/3 even with an acceptor having a fixed orientation. [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF] In this situation, simply assuming 𝜅 2 = 2 3 ⁄ results in error in 𝑅 0 less than 12% due to the sixth root dependence.

𝐸 FRET = 1 - 𝜏 DA 𝜏 D = 1 - 𝜏 AD 𝜏 D (2.14)

Fluorescent dyes

Fluorescent dyes are widely used in fluorescent labelling of biomolecules because of their high quantum yields, solubility, and particularly commercial availability.

Fluorescent dyes functionalized with N-hydroxysuccinimide (NHS) ester, maleimide, hydrazide, or amine group are available from commercial sources and easy for bioconjugation. [START_REF] Sapsford | Materials for Fluorescence Resonance Energy Transfer Analysis: Beyond Traditional Donor-Acceptor Combinations[END_REF] Figure 2. [START_REF] Chan | Quantum Dot Bioconjugates for Ultrasensitive Nonisotopic Detection[END_REF] shows the fluorescence spectra regions of commercial dye families that cover the UV-vis-IR range. However, they usually have a high rate of photobleaching, are sensitive to environment and can selfquench at high concentration (self-aggregation). All dye families are typically characterized by closely spaced, broad absorption/emission profiles (small Stokes shift), [START_REF] Sapsford | Materials for Fluorescence Resonance Energy Transfer Analysis: Beyond Traditional Donor-Acceptor Combinations[END_REF], [START_REF] Dsouza | Fluorescent Dyes and Their Supramolecular Host/Guest Complexes with Macrocycles in Aqueous Solution[END_REF] which usually lead to direct excitation of the acceptor for FRET application. Since fluorescent dyes as FRET acceptor/multi acceptors have been discussed in Section (2.2.3), this section will focus on the dye aggregates (2.5.1)

and homo FRET of fluorescent dyes (2.5.2).

Dye aggregates

For FRET application, large surface area of nanoparticle based donor enable to assemble multiple acceptors, and also can facilitate the formation of aggregates of acceptor organic dyes. In general, dye aggregates are classified on the basis of the spectral shift. For some dye aggregates, the absorption maximum is blue-shifted and bandwidth increases as compared to the monomer, termed as Haggregates. [START_REF] Sauer | Handbook of Fluorescence Spectroscopy and Imaging[END_REF] In contrast, the absorption maximum is red-shifted and exhibits very narrow peak with respect to that of the monomer, termed as Jaggregates.

[100] J-aggregates possess a bent or head-to-tail structure and usually show higher fluorescence intensity than that of the monomer, while H-aggregates exhibit non-fluorescence with the exception of a few examples. [START_REF] Rösch | Fluorescent H-Aggregates of Merocyanine Dyes[END_REF] It can be explained by exciton theory of Kasha, as illustrated in Figure 2.16, the dye molecule is regarded as a point dipole and the excited state of the dye aggregate splits into two levels through the interaction of transition dipoles. For Haggregates, molecular dimers stacked "side-by-side" exhibit a blue-shifted absorption maximum and suppressed radiative decay rate, while for J-aggregates, molecular dimers stacked "head-to-tail" exhibit a red-shifted absorption maximum and enhanced radiative decay rate. [START_REF] Hestand | Molecular Aggregate Photophysics beyond the Kasha Model: Novel Design Principles for Organic Materials[END_REF] the n increased in a QD-multiple (n) dyes FRET system. The formation of nonfluorescent dimers led to two hetero-FRET pathways: from the QD to fluorescent monomeric dyes or non-fluorescent dimeric dyes. [START_REF] Conroy | Self-Quenching, Dimerization, and Homo-FRET in Hetero-FRET Assemblies with Quantum Dot Donors and Multiple Dye Acceptors[END_REF] As a result, the sensitized dye PL did not correspond to the QD donor quenching. Bawendi and co-workers reported the QD/J-aggregates can combine the broad UV absorption of QDs with the ultra-narrow emission band of J-aggregates due to efficient FRET from the QDs to the J-aggregates with essentially complete quenching of the QD and sensitizing of the J-aggregates fluorescence, [START_REF] Halpert | Electrostatic Formation of Quantum Dot/J-Aggregate FRET Pairs in Solution[END_REF]- [START_REF] Walker | Narrow-Band Absorption-Enhanced Quantum Dot/J-Aggregate Conjugates[END_REF] which could be potentially applied for biological multiplexing. Consequently, the formation of such aggregates can strongly modify optical absorption and the fluorescence spectra, which is both a limitation and an opportunity for FRET application.

Homo FRET

FRET does not necessarily require two different fluorophores as a D-A pair. In particular, fluorescent dyes usually have a significant overlap of their absorbance and emission spectra due to their small Stokes shift. In principle, such a fluorophore can transfer its excitation energy to a neighboring molecule of the same species, which is referred as homo-FRET. [START_REF] Sauer | Handbook of Fluorescence Spectroscopy and Imaging[END_REF] Typically, this phenomenon does not lead to changes in PL lifetime, the steady-state intensity or a shift in the emission spectrum, and such a bi-directional energy transfer can be monitored only by fluorescence anisotropy. [START_REF] Levitt | Fluorescence Lifetime and Polarization-Resolved Imaging in Cell Biology[END_REF]- [START_REF] Yan | Analysis of Protein Interactions Using Fluorescence Technologies[END_REF] Fluorescence anisotropy (A) can be calculated using Equation 2.15:

[1] 𝐴 = 𝐼 ∥ -𝐼 ⊥ 𝐼 ∥ +2𝐼 ⊥ (2.15)
Where 𝐼 ∥ and 𝐼 ⊥ represent the intensities of emission polarizer that is oriented parallel and perpendicular to the direction of the polarized excitation, respectively.

For randomly oriented transition dipoles in the absence of FRET, A equals 0.4.

When homo-FRET occurs, A will decrease and close to 0 due to depolarization process. [START_REF] Sauer | Handbook of Fluorescence Spectroscopy and Imaging[END_REF] FRET efficiency based on fluorescence anisotropy can be calculated using Equation 2.16:[99]

𝐸 FRET = 1 - 𝐴 FRET 𝐴 0 (2.16)
Where 𝐴 FRET and 𝐴 0 are the fluorescence anisotropy in the presence and absence of energy transfer, respectively.

However, in multi-dye systems (dye aggregates) the increased homo-FRET (more random migration steps) leads to a higher probability that the exciton encounters a trap state (dark dye or H-dimer), which resulted in both PL intensity and lifetime quenching. [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF], [START_REF] Conroy | Self-Quenching, Dimerization, and Homo-FRET in Hetero-FRET Assemblies with Quantum Dot Donors and Multiple Dye Acceptors[END_REF], [START_REF] Zhegalova | Minimization of Self-Quenching Fluorescence on Dyes Conjugated to Biomolecules with Multiple Labeling Sites via Asymmetrically Charged NIR Fluorophores[END_REF]- [START_REF] Song | Rapid Assay for Avidin and Biotin Based on Fluorescence Quenching[END_REF] In this thesis, we also observed quenching of Cy5.5

PL intensity caused by combination of the formation of non-fluorescent H-dimers and multiple homo-FRET steps between Cy5.5 dyes, which increased the probability of the migrating exciton to get dissipated in the Cy5.5 dimer "trap states".

Gold nanoparticles

Gold nanoparticles (AuNPs) possess unique physical and chemical properties that make them excellent candidates for fabricating biosensors. [START_REF] Saha | Gold Nanoparticles in Chemical and Biological Sensing[END_REF] (i) AuNPs with high stability can be synthesized under mild condition. (ii) Similar to other nanoparticles, large surface area of Au NPs offer a suitable platform for multifunctionalization. [START_REF] Daniel | Gold Nanoparticles: Assembly, Supramolecular Chemistry, Quantum-Size-Related Properties, and Applications toward Biology, Catalysis, and Nanotechnology[END_REF] (iii) The properties of AuNPs can be tuned by varying their size, shape, and the surrounding chemical environment (e.g., ligand, magnetic fields and electrolyte ions). [START_REF] Subramaniam | Flow-Induced Transverse Electrical Potential across an Assembly of Gold Nanoparticles[END_REF], [START_REF] Schmid | Gold Nanoparticles: Assembly and Electrical Properties in 1-3 Dimensions[END_REF] (iv) Small AuNPs (or Au clusters diameter ≤ 3 nm) exhibit broad absorption and distinct fluorescence due to quantum confinement effects, while lager AuNPs have strong plasmon absorption bands and non-fluorescence. In this section, we will focus on surface plasmon resonance (2.5.1) and nanosurface energy transfer theory (2.5.2).

Surface plasmon resonance

The SPR is the result of the collective oscillation of the conduction electrons across the nanoparticle due to the resonant excitation by the incoming photons. [START_REF] Saha | Gold Nanoparticles in Chemical and Biological Sensing[END_REF] For AuNPs, the resonance condition is satisfied at visible wavelengths, therefore leading to its deep-red color in water. [START_REF] Halas | Plasmons in Strongly Coupled Metallic Nanostructures[END_REF] The main characteristics of SPB are including: (i) The surface plasmon band (SPB) decreases with decreasing size and is absent for AuNPs with core diameter less than 2 nm. (ii) the SPR is influenced not only by size but also by solvent, ligand, interparticle distance, and temperature. [START_REF] Saha | Gold Nanoparticles in Chemical and Biological Sensing[END_REF] (iii) The SPR frequency is sensitive to the proximity of other nanoparticles. Therefore, the aggregation of nanoparticles results in significant red-shifting (from ∼520 to ∼650 nm) and broadening in the SPB, changing the solution color from red to blue due to the interparticle plasmon coupling. [START_REF] Su | Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles[END_REF] For application of energy transfer, large AuNPs can serve as excellent acceptor, because they have strong SPB that can overlap with the donor (e.g., QD) emission.

For biosensing based on QD quenching by AuNP, emission of QD is often tuned to align with absorption of AuNP to increase quenching efficiency. [START_REF] Dyadyusha | Quenching of CdSe Quantum Dot Emission, a New Approach for Biosensing[END_REF] However, it should be noted that this strong absorption can also lead to inner filter effects (reabsorption of QD emitted light by the AuNPs or absorption of QD excitation light by the AuNPs).[3]

Nanosurface energy transfer theory

Metal nanoparticles (e.g., Au nanoparticles (AuNPs) ) provide strong fluorescence quenchers when paired with dyes, [START_REF] Chen | A Surface Energy Transfer Nanoruler for Measuring Binding Site Distances on Live Cell Surfaces[END_REF]- [START_REF] Seelig | Nanoparticle-Induced Fluorescence Lifetime Modification as Nanoscopic Ruler: Demonstration at the Single Molecule Level[END_REF] QDs, [START_REF] Samanta | Fluorescence Quenching of Quantum Dots by Gold Nanoparticles: A Potential Long Range Spectroscopic Ruler[END_REF]- [START_REF] Vaishnav | Long-Range Resonance Coupling-Induced Surface Energy Transfer from CdTe Quantum Dot to Plasmonic Nanoparticle[END_REF] fluorescent proteins, [START_REF] Saraswat | Energy Transfer from Fluorescent Proteins to Metal Nanoparticles[END_REF] or lanthanide complexes, [START_REF] Chen | Nanosurface Energy Transfer from Long-Lifetime Terbium Donors to Gold Nanoparticles[END_REF] and the extent of energy transfer quenching exceed the range stipulated by FRET. [START_REF] Kapur | Self-Assembled Gold Nanoparticle -Fluorescent Protein Conjugates as Platforms for Sensing Thiolate Compounds via Modulation of Energy Transfer Quenching[END_REF] The energy transfer mechanism to AuNPs has been discussed within the concepts of nanosurfaces.

Nanosurface energy transfer (NSET) is a dipole-surface energy transfer process involving molecular dipole and nanometal surface, which can be distinguished from FRET by the efficiency equations. In addition, there is no overlap integral to calculate. Persson has been a leader in advancing theories of molecular deexcitation by metal surfaces. [START_REF] Persson | Electron-Hole-Pair Quenching of Excited States near a Metal[END_REF] Based on the model suggested by Persson, the NSET model was proposed by Strouse and coworkers. [START_REF] Singh | Involvement of the LSPR Spectral Overlap for Energy Transfer between a Dye and Au Nanoparticle[END_REF]- [START_REF] Jennings | Fluorescent Lifetime Quenching near d = 1.5 nm Gold Nanoparticles: Probing NSET Validity[END_REF], [START_REF] Jennings | LETTERS NSET Molecular Beacon Analysis of Hammerhead RNA Substrate Binding and Catalysis[END_REF], [START_REF] Yun | Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier[END_REF] They suggested a R -4 distance dependence for the energy transfer rate, which significantly increases (about two fold) the distance range of FRET. In detail,

Persson's surface damping model was applied to molecular dipole quenching of NSET model, which was based on the conservation of momentum during electronhole pair formation via the near field of an electric dipole. [START_REF] Persson | Electron-Hole-Pair Quenching of Excited States near a Metal[END_REF] Basically, the electric field of a separate dipole does not provide the required momentum for direct exciton formation, so the process must occur simultaneously with the electron scattering process. Persson recognizes two main sources of scattering: the bulk scattering (electron-electron, electron-phonon, electron-defect etc.) process involves interactions on the over the integrated volume of the crystal, resulting in a R -3 distance dependence. However, scattering from surface potential involves integration on the plane and produces R -4 distance dependence.

NSET transfer rate is given by Equation 2.17: [START_REF] Jennings | Fluorescent Lifetime Quenching near d = 1.5 nm Gold Nanoparticles: Probing NSET Validity[END_REF] 𝑘 NSET = 0.225

𝑐 3 𝜔 D 2 𝜔 F 𝑘 F 𝑅 4 Φ D 𝜏 D (2.17)
where c is the speed of light, 𝜔 D is the angular frequency (𝜔 = 2𝜋𝑐𝜆 NSET has emerged as an energy transfer principle that can measure biomolecular interactions over distances up to 50 nm and thereby more than double the range of FRET. [START_REF] Samanta | Fluorescence Quenching of Quantum Dots by Gold Nanoparticles: A Potential Long Range Spectroscopic Ruler[END_REF] Research showed that NSET model was in good agreement with the experimental data of small size AuNPs (below 3 nm) by using dyes and quantum dots (QDs) as donors because they do not have any plasmon bands. [START_REF] Jennings | Fluorescent Lifetime Quenching near d = 1.5 nm Gold Nanoparticles: Probing NSET Validity[END_REF], [START_REF] Jennings | LETTERS NSET Molecular Beacon Analysis of Hammerhead RNA Substrate Binding and Catalysis[END_REF], [START_REF] Yun | Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier[END_REF] NSET behavior with energy transfer efficiencies independent of the NP size or number of donors was also demonstrated for larger size

AuNPs. [START_REF] Chen | A Surface Energy Transfer Nanoruler for Measuring Binding Site Distances on Live Cell Surfaces[END_REF], [START_REF] Zhang | Distance Dependence of Nonradiative Energy Transfer to a Plane of Gold Nanoparticles[END_REF], [START_REF] Saraswat | Energy Transfer from Fluorescent Proteins to Metal Nanoparticles[END_REF], [START_REF] Kapur | Self-Assembled Gold Nanoparticle -Fluorescent Protein Conjugates as Platforms for Sensing Thiolate Compounds via Modulation of Energy Transfer Quenching[END_REF] However, NSET studies have focused on the interaction of AuNPs with organic dyes and QDs. In this thesis, we will investigate the interaction of AuNPs with luminescent lanthanide complexes.

Time-resolved measurement

Time-resolved (TR) measurements are widely used in fluorescence spectroscopy, particularly for studies of biological macromolecules and cellular imaging because they contain more information than steady-state data. [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF] For instance, the precision of the imaging and quantification analysis are influenced by the variation of excitation laser power and probe concentration in steady-state measurement, while fluorescence lifetimes of probe are typically independent of the probe concentration. [START_REF] Becker | Fluorescence Lifetime Imaging--Techniques and Applications[END_REF] Moreover, when there is spectral overlap between probes and autofluorescence or the emission from two or more probes, it is difficult to recognize the signal of interest based on the steady-state data. In contrast, time-resolved measurement can distinguish these probes from autofluorescence or each other based on their different decay rates. [START_REF] Zhang | Long-Lived Emissive Probes for Time-Resolved Photoluminescence Bioimaging and Biosensing[END_REF]

Luminophores Maximum lifetimes

lanthanide chelates [START_REF] Bünzli | On the Design of Highly Luminescent Lanthanide Complexes[END_REF] µs~ms lanthanide-doped nanocrystals [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF] µs~ms transition-metal complexes [START_REF] Baggaley | Long-Lived Metal Complexes Open up Microsecond Lifetime Imaging Microscopy under Multiphoton Excitation: From FLIM to PLIM and Beyond[END_REF] hundreds ns ∼ µs doped-QDs (e.g., Mn, [START_REF] Gan | Fluorescence Lifetime of Mn-Doped ZnSe Quantum Dots with Size Dependence[END_REF] Cu, [START_REF] Chen | Near-Infrared-Emitting Two-Dimensional Codes Based on Lattice-Strained Core/(Doped) Shell Quantum Dots with Long Fluorescence Lifetime[END_REF] Ni, [START_REF] Jana | Multifunctional Doped Semiconductor Nanocrystals[END_REF] and Yb [START_REF] Martí N-Rodrí Guez | Incorporation and Luminescence of Yb 3+ in CdSe Nanocrystals[END_REF]) hundreds ns ∼µs lattice-strained QDs [START_REF] Smith | Tuning the Optical and Electronic Properties of Colloidal Nanocrystals by Lattice Strain[END_REF], [START_REF] Zhang | Living Cell Multilifetime Encoding Based on Lifetime-Tunable Lattice-Strained Quantum Dots[END_REF] hundreds ns carbon dots [START_REF] Jiang | Activating Room Temperature Long Afterglow of Carbon Dots via Covalent Fixation[END_REF] ∼s metal nanoclusters [START_REF] Stamplecoskie | Size-Dependent Excited State Behavior of Glutathione-Capped Gold Clusters and Their Light-Harvesting Capacity[END_REF], [START_REF] Chen | Fluorescent Gold Nanoclusters: Recent Advances in Sensing and Imaging[END_REF] ∼µs persistent nanoparticles [START_REF] Abdukayum | Functional near Infrared-Emitting Cr 3+ /Pr 3+ Co-Doped Zinc Gallogermanate Persistent Luminescent Nanoparticles with Superlong Afterglow for in Vivo Targeted Bioimaging[END_REF] ~days

Time-gated measurement

Standard luminescence analysis and microscopy techniques are based on variation of PL intensity with specific wavelength bands, which is indicative of the presence of a specific analyte or the occurrence of an event. However, for applications such as analyte in low concentration and rare-event detection, the luminescence signal is difficult recognized from naturally occurring autofluorescent substances. [START_REF] Jin | Time-Gated Luminescence Microscopy Allowing Direct Visual Inspection of Lanthanide-Stained Microorganisms in Background-Free Condition[END_REF] Time-gated (TG) measurement in combination with luminescent probes with relatively long emission lifetimes can efficiently solve this problem. As shown in Figure 2.17, in a typical TG measurement, the luminescent probe is excited by a pulsed light, and exhibits relatively long decay time. The detector starts to work after a delay time in which short-lived autofluorescence fades. Thus, only longlived events will be detected in the signal collection window. These signals can be distinguished from short-lived background even if they are low intensity, which significantly enhances the detection sensitivity. [START_REF] Zhang | Long-Lived Emissive Probes for Time-Resolved Photoluminescence Bioimaging and Biosensing[END_REF] Recently, the application of TG microscopy imaging has been expanded in bioimaging and sensing for different purposes. As mentioned in Section (2.3.2), in a FRET system with a long lifetime LLCs-based donor, time-gated measurement efficiently suppressed the fluorescence from directly excited acceptors. [START_REF] Afsari | Time-Gated FRET Nanoassemblies for Rapid and Sensitive Intra-and Extracellular Fluorescence Imaging[END_REF], [START_REF] Geißler | Lanthanides and Quantum Dots as Förster Resonance Energy Transfer Agents for Diagnostics and Cellular Imaging[END_REF] And the decay time of FRET-sensitized acceptor PL can be precisely tuned and designed as single nanoparticle barcoding. [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF][150] Combination of TG measurement with stimulated emission depletion (STED) microscopy opened up new approaches for designing probe of STED microscopy. [START_REF] Byrne | Precision Targeted Ruthenium(II) Luminophores; Highly Effective Probes for Cell Imaging by Stimulated Emission Depletion (STED) Microscopy[END_REF] In addition, TG measurement can be extended to the second biological window (1000-1350 nm), [START_REF] Del Rosal | Overcoming Autofluorescence: Long-Lifetime Infrared Nanoparticles for Time-Gated In Vivo Imaging[END_REF]- [START_REF] Fan | Lifetime-Engineered NIR-II Nanoparticles Unlock Multiplexed in Vivo Imaging[END_REF] which could provide much higher signal-to-noise ratio and penetration depth in vivo imaging than that within the first biological window (700-950 nm). [START_REF] Smith | Second Window for in Vivo Imaging[END_REF], [START_REF] Welsher | A Route to Brightly Fluorescent Carbon Nanotubes for Near-Infrared Imaging in Mice[END_REF] In this thesis, TG measurement was employed to regionalize the lifetime codes. Where 𝐼 is the luminescence intensity, 𝐴 𝑖 is the amplitude for different I, and 𝜏 𝑖 is the different decay times. It should be noted that the shape of the excitation pulse and how this pulse is detected by the instrument are not negligible in the case of short lifetime sample (in the nanosecond range), and a deconvolution of the instrument response function (IRF) to the measured fluorescence decay curve is necessary in order to extract the "true" lifetime. [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF] For the frequency domain method, as illustrated in Figure 2.18 b, the sample is excited with intensity-modulated (typically sinusoidal modulation) light (e.g., 𝐼 = 𝐼 av (ex) + 𝐼 p (ex) cos(𝑡) ) with a frequency, which is typically in the same range as the reciprocal of the luminescence decay time of the sample. Then the emission light (e.g., 𝐼 = 𝐼 av (em) + 𝐼 p (em) cos(𝑡 -𝜙) ) will have the same frequency, the phase shift (𝜙) between excitation and emission lights is used to calculate the luminescence decay times and can be descripted as Equation 2.20:

𝜙 = tan -1 ( ∑ (𝛼 𝑖 𝜔𝜏 𝑖 2 ) (1+ 𝜔 2 𝜏 𝑖 2 ) ⁄ 𝑖 ∑ (𝛼 𝑖 𝜏 𝑖 ) (1+ 𝜔 2 𝜏 𝑖 2 ) ⁄ 𝑖 ) (2.20)
Moreover, the lifetime of the fluorophore also causes a decrease in the peak-to-peak intensity of the emission relative to that of the excitation. The demodulation is usually expressed as modulation ratio (𝑀 = [𝐼 p (em)/𝐼 av (em)]/[𝐼 p (ex)/𝐼 av (ex)]), and can also be used to calculate the lifetime. The relation between modulation ratio and luminescence decay times can be descripted as Equation 2.21:

𝑀 = √ [(∑ (𝛼 𝑖 𝜔𝜏 𝑖 2 ) (1+ 𝜔 2 𝜏 𝑖 2 ) ⁄ 𝑖 2 + ∑ (𝛼 𝑖 𝜏 𝑖 ) (1+ 𝜔 2 𝜏 𝑖 2 ) ⁄ 𝑖 2 )] (∑ 𝛼 𝑖 𝜏 𝑖 𝑖 ) 2
(2. [START_REF] Yu | High-Resolution Three-Photon Biomedical Imaging Using Doped ZnS Nanocrystals[END_REF] In this thesis we chose to use the time-domain method for temporal characterization. Depending on the lifetime of the fluorophore, the photons arriving at the detector can be counted by several techniques such as steady-state photon counting, gated photon counting, multichannel scalers (MCS), and time correlated single photon counting (TCSPC). [START_REF] Becker | Advanced Time-Correlated Single Photon Counting Techniques[END_REF] Based on the TCSPC, fluorescence lifetime imaging microscopy (FLIM) maps lifetime spatial distribution in cells, tissues, and small animal modes, where all photons are collected for calculation of lifetimes and signals of probe and autofluorescence are distinguished based on their different decay rates in each pixel. [START_REF] Becker | Advanced Time-Correlated Single Photon Counting Techniques[END_REF] FLIM is mainly used to image viscosity, temperature, pH, refractive index, ion and oxygen concentrations at the cellular level [START_REF] Suhling | Fluorescence Lifetime Imaging (FLIM): Basic Concepts and Some Recent Developments[END_REF] or fabricate two dimensional codes. [START_REF] Chen | Near-Infrared-Emitting Two-Dimensional Codes Based on Lattice-Strained Core/(Doped) Shell Quantum Dots with Long Fluorescence Lifetime[END_REF] Recently, the application of FLIM has been expanded to tissues, organs, and laboratory animals. [START_REF] Wu | Tracking the Engraftment and Regenerative Capabilities of Transplanted Lung Stem Cells Using Fluorescent Nanodiamonds[END_REF]- [START_REF] Yaghini | In Vivo Biodistribution Studies and Ex Vivo Lymph Node Imaging Using Heavy Metal-Free Quantum Dots[END_REF] Both TG measurement and lifetime measurement can obtain high quality imaging with minimized autofluorescence interference. TG measurement is more suitable for long lifetime probes with significant intensity response to analyses, while lifetime measurement has higher resolution in time domain, and suitable for relatively short lifetime (ns~µs), because lifetime measurement requires a very long photon acquiring duration.

Time to multiplex

Optical multiplexing typically requires a matrix of optical codes, ideally carried by nano/micro-sized objects, such as nanoparticles or microbeads. It provides many advantages for biomedicine, optical data storage, document security. [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF], [START_REF] Fan | Lifetime-Engineered NIR-II Nanoparticles Unlock Multiplexed in Vivo Imaging[END_REF], [START_REF] Zijlstra | Five-Dimensional Optical Recording Mediated by Surface Plasmons in Gold Nanorods[END_REF], [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF] In biomedicine, multiplexing refers to highthroughput technologies, which can simultaneously identify and quantify multiple distinctive species. [START_REF] Pregibon | Multifunctional Encoded Particles for High-Throughput Biomolecule Analysis[END_REF], [START_REF] Cao | Nanoparticles with Raman Spectroscopic Fingerprints for DNA and RNA Detection[END_REF] In optical data storage, multiplexing is aim to increase the storage capacity within spatially limited memory elements. [START_REF] Zijlstra | Five-Dimensional Optical Recording Mediated by Surface Plasmons in Gold Nanorods[END_REF], [START_REF] Li | Three-Dimensional Orientation-Unlimited Polarization Encryption by a Single Optically Configured Vectorial Beam[END_REF] In document security, the purpose of multiplexing is to prevent forgery, tampering or counterfeiting. [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF] Luminescent nanoparticles based encoding is an important technology for optical multiplexing, and the most commonly used encoding principle is based on color, polarization, lifetime, and intensity. In 2001, Nie et al.

fabricated a diverse array of barcoding by mixing different color and intensity levels of QDs in microbeads. [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF] Since then, the spectroscopic encoding of microbeads based on QD color and intensity has been regarded as one of the most promising approaches due to its flexible encoding and convenient decoding. [START_REF] Leng | Suspension Arrays Based on Nanoparticle-Encoded Microspheres for High-Throughput Multiplexed Detection[END_REF] However, intensity-bases encoding requires the precise control of concentration.

In

Introduction

Optical encoding has great potential for nanomedicine, diagnostics, biosensing, document security, and optical data storage. [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF], [START_REF] Zijlstra | Five-Dimensional Optical Recording Mediated by Surface Plasmons in Gold Nanorods[END_REF], [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF], [START_REF] Leng | Suspension Arrays Based on Nanoparticle-Encoded Microspheres for High-Throughput Multiplexed Detection[END_REF] Such barcoding has exploited both the emission color [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF], [START_REF] Andreiuk | Fluorescent Polymer Nanoparticles for Cell Barcoding In Vitro and In Vivo[END_REF] and the excited-state lifetime [START_REF] Chen | Near-Infrared-Emitting Two-Dimensional Codes Based on Lattice-Strained Core/(Doped) Shell Quantum Dots with Long Fluorescence Lifetime[END_REF], [START_REF] Zhang | Living Cell Multilifetime Encoding Based on Lifetime-Tunable Lattice-Strained Quantum Dots[END_REF], [START_REF] Lu | On-the-Fly Decoding Luminescence Lifetimes in the Microsecond Region for Lanthanide-Encoded Suspension Arrays[END_REF] components of PL. The majority of encoding approaches applied mixing of different luminescent molecules or nanoparticles in microspheres [START_REF] Chen | Near-Infrared-Emitting Two-Dimensional Codes Based on Lattice-Strained Core/(Doped) Shell Quantum Dots with Long Fluorescence Lifetime[END_REF], [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF], [START_REF] Lu | On-the-Fly Decoding Luminescence Lifetimes in the Microsecond Region for Lanthanide-Encoded Suspension Arrays[END_REF] or cells. [START_REF] Zhang | Living Cell Multilifetime Encoding Based on Lifetime-Tunable Lattice-Strained Quantum Dots[END_REF], [START_REF] Andreiuk | Fluorescent Polymer Nanoparticles for Cell Barcoding In Vitro and In Vivo[END_REF], [START_REF] Rees | Nanoparticle Vesicle Encoding for Imaging and Tracking Cell Populations[END_REF] Using individual dyes or nanoparticles (e.g., QDs) [START_REF] Jennings | Reactive Semiconductor Nanocrystals for Chemoselective Biolabeling and Multiplexed Analysis[END_REF], [START_REF] Wegner | Quantum Dots: Bright and Versatile in Vitro and in Vivo Fluorescence Imaging Biosensors[END_REF] for optical encoding is limited by the spectral overlap of their PL spectra and the concentration-dependence of PL intensity.

Concentration-independent PL lifetime-multiplexing with individual

nanoparticles has also been demonstrated. One concept used upconversion nanoparticles (UCNPs) with varying co-doping concentrations of Yb 3+ and Tm 3+

ions, but only for proof-of-concept biosensing and security printing, [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF] most probably due to the limited brightness of UCNPs. [START_REF] Gorris | Photon-Upconverting Nanoparticles for Optical Encoding and Multiplexing of Cells, Biomolecules, and Microspheres[END_REF] Individual QDs were also used for PL lifetime tuning through bandgap engineering, including increasing the particle size, [START_REF] Rogach | Aqueous Synthesis of Thiol-Capped CdTe Nanocrystals: State-of-the-Art[END_REF] introducing various dopants, [START_REF] Chen | Near-Infrared-Emitting Two-Dimensional Codes Based on Lattice-Strained Core/(Doped) Shell Quantum Dots with Long Fluorescence Lifetime[END_REF], [START_REF] Chen | Long-Decay near-Infrared-Emitting Doped Quantum Dots for Lifetime-Based in Vivo PH Imaging[END_REF] and fabricating the nanostructure with lattice-strain. [START_REF] Smith | Tuning the Optical and Electronic Properties of Colloidal Nanocrystals by Lattice Strain[END_REF], [START_REF] Zhang | Living Cell Multilifetime Encoding Based on Lifetime-Tunable Lattice-Strained Quantum Dots[END_REF] Unfortunately, these methods led to the change of PL wavelengths and thus, color could not be used as an independent parameter, which is a prerequisite for combining both color and lifetime into higher-order multiplexing. A facile and robust strategy to prepare lifetime-tunable QDs that are independent of PL color would significantly advance this endeavor.

Förster resonance energy transfer (FRET) is a strongly distance-dependent interaction within a luminescent donor-acceptor pair and the donor-acceptor distance defines the PL lifetime of the donor. A FRET pair of lanthanide (e.g., Eu 3+

or Tb 3+ ) donors and QD acceptors is of particular interest for multiplexed biosensing, because lanthanides possess very long PL lifetimes and QDs provide color-tunability and narrow PL emission. [START_REF] Hildebrandt | Energy Transfer with Semiconductor Quantum Dot Bioconjugates: A Versatile Platform for Biosensing, Energy Harvesting, and Other Developing Applications[END_REF], [START_REF] Cardoso Dos Santos | Recent Developments in Lanthanide-to-Quantum Dot FRET Using Time-Gated Fluorescence Detection and Photon Upconversion[END_REF], [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF], [START_REF] Faklaris | Multicolor Time-Resolved Förster Resonance Energy Transfer Microscopy Reveals the Impact of GPCR Oligomerization on Internalization Processes[END_REF] Due to the large difference between the PL lifetimes of lanthanides (~ms) and QDs (~ns), the FRETsensitized lifetime of the QD acceptor is the same as the FRET-quenched lifetime of the lanthanide donor. [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF] Therefore, shorter (or longer) lanthanide-QD distances lead to shorter (or longer) PL lifetimes of both lanthanide and QD. In this Chapter, we demonstrate that such a distance tuning approach can be used within one single nanoparticle by direct attachment of the lanthanides to QDcoatings with different thicknesses and that these individual lanthanide-coated QD nanohybrids can be used for encoding of different cells via TG temporal multiplexing. As a prototypical system for FRET lifetime encoding via individual nanoparticles (Figure 3.1a), SiO2-coated QD with tunable shell thicknesses (6 and 12 nm) was synthesized. Then, lanthanide complexes (Tb-Lumi4 or Eu-1) [START_REF] Xu | Octadentate Cages of Tb(III) 2-Hydroxyisophthalamides: A New Standard for Luminescent Lanthanide Labels[END_REF], [START_REF] Delbianco | Highly Water-Soluble Triazacyclononane Europium Complexes to Detect Ligand Binding with Time-Resolved FRET Microscopy[END_REF], [START_REF] Butler | EuroTracker® Dyes: Design, Synthesis, Structure and Photophysical Properties of Very Bright Europium Complexes and Their Use in Bioassays and Cellular Optical Imaging[END_REF] with long PL-lifetimes (~ms) were attached on the surface of

Materials and methods

Materials

Synthesis of QD embedded silica nanpspheres

The QDs embedded silica nanospheres were synthesized by a reverse microemulsion approach. Typically, the glass bottlecontaining 30 mL of cyclohexane was added with 3.95 mL of NP-5 and stirred for 15 min. The above solution was mixed with 300 μL of ammonia aqueous solution followed by stirring for another 15 min to form the reverse microemulsion. The mixture was subsequently added to 200 μL of QDs chloroform solution (10 mg/mL), followed by the injection of TEOS to start the silica encapsulation. After stirring at room temperature for 18 h, the QDs embedded silica nanospheres were precipitated by adding ethanol followed by centrifugation. The products were washed with ethanol for several times and finally dispersed in 20 mL of ethanol. To form the silica shell thickness of 6 nm and 12 nm, TEOS volumes of 60 μL and 260 μL were employed, respectively.

Synthesis of mercapto-terminated silica nanospheres

For the grafting of mercapto-groups onto silica surface, the above QDs embedded silica nanospheres in 20 mL of ethanol was added 500 μL of ammonia and 100 μL of MPS, followed by vigorous stirring at room temperature for 12 h. The final product was harvested by centrifugation, washed thoroughly with ethanol and redispersed in 2 mL water.

Estimation of molar concentration of QD/SiO2

We assume that the nanonaterials have the same density as the according bulk materials. For the CdSe/CdS/ZnS QD, the density of CdSe, CdS, and ZnS are 5.816 g/cm 3 , 4.82 g/cm 3 , and 4.09 g/cm 3 , respectively. The radius of QD is about 3.5 nm according the HRTEM. We assume the radius of CdSe core is 1.8 nm, the thickness of CdS and ZnS shell are 1.16 nm and 0.54 nm, respectively. Then we can obtain the density of the QD, which is nearly 5.223 g/cm 3 (Equations 3.1 and 3.2).

According the density and volume of single QD and Avogadro constant, we can obtain the molecular weight of QD, which is nearly 570000. The yield of synthetic QD/SiO2 can be estimate to 70%. Finally, the molar concentration of QD/SiO2 should be nearly 1.23 μM. Lumi4: QD/SiO2 (6 nm) = 100:75:1 and Tb: Lumi4: QD/SiO2 (12 nm) =100:87:1).

𝑉 = 4 3 𝜋𝑟 3 (3.1) 𝜌 = 𝑚 𝑉 (3.2)

Formation of mTb-QD/SiO2 donor-acceptor assemblies

Formation of Eu-QD/SiO2 donor-acceptor assemblies

Eu

Cell culture

Human cervical carcinoma (HeLa) cells were purchased from American Type Culture Collection (CCL-2). Cells were grown in Dulbecco's modified eagle medium (DMEM, Sigma-Aldrich, D6546), supplemented with 10% fetal bovine serum (FBS, Sigma-Aldrich, F0804), 1% antibiotics (Pen Strep, Sigma-Aldrich, P4333) and 2 mM L-glutamine (Sigma-Aldrich, G7513) at 37°C and 5% CO2. The cells were passaged with trypsin-EDTA 0.05%.

Living cell encoding.

HeLa cells were seeded at 3x10 5 cells in 8-chamber glass slide (Nunc® Lab-Tek® II Chamber Slide™, 155409) and incubated at 37°C and 5% CO2 overnight. The following day, the cells were washed with 1xPBS (Sigma-Aldrich, P4417) and incubated with a complete culture medium (10% FBS, 1% Pen Strep and 2 mM Lglutamine). Solution of Tb-QD/SiO2 (6 nm), Tb-QD/SiO2 (12 nm), Eu-QD/SiO2 (6 nm), and Eu-QD/SiO2 (12 nm) in Tris-HCl buffer at pH 7.5 (50 mM) were sonicated for 15 minutes and added at 20 nM into previously prepared slide with cells. Cells were incubated at 37°C and 5% CO2 for 2h. For mixing, the cells which incubated with Tb-QD/SiO2 (6 nm), Tb-QD/SiO2 (12 nm), Eu-QD/SiO2 (6 nm), and Eu-QD/SiO2 (12 nm) were washed by 1XPBS, trypsinized then seeded on the Poly-Llysine (Thermofisher, P4707) coated slide. Images of living cell encoding were acquired using a wide-field, TG luminescence inverted microscope (Olympus IX71) that uses a UV laser (349 nm, 100 Hz, Nd:YLF, Triton, Spectra Physics) for pulsed excitation and an intensified CCD camera (ICCD, PI-MAX3, Princeton Instruments) for gated detection. QD PL signals were detected using a 639±10 nm bandpass filter. Acquisition settings (Winview software controlling the camera)

were adjusted to optimal conditions regarding RGB ratio and were fixed to a delay time of 50 μs (after the excitation pulse) and a gate width of 450 μs (red window -R), a delay time of 500 μs and a gate width of 500 μs (green window -G), and a delay time of 1 ms and a gate width of 2 ms (blue window -B). ImageJ was used to assign red, green, or blue color to the three detection windows and define a common intensity range (same minimum and maximum values for all windows).

Cytotoxicity Measurements

The cytotoxicity of QD/SiO2 (6 nm and 12 nm) were evaluated by MTT viability assay on various cells. Both tumor cells (HeLa, MDA-MB231) and normal cells (293T) were cultured in DMEM medium supplemented with 10% (v/v) FBS, 1%

(v/v) penicillin, and 1% (v/v) streptomycin under 37 °C within a humidified atmosphere of 5% CO2. The HeLa, MDA-MB231 and 293T cells were seeded in 96well plates with a seeding density of 5×10 3 cell/well, respectively. After 24 h incubation, the medium was removed and replaced with fresh medium containing QD/SiO2 with various concentrations (0, 25, 50, 100, 200, 400, 800 nM). After 24 h incubation, the standard MTT assay was carried out to evaluate the cell viability.

Analytical methods

Structural characterization of the QD/SiO2 was carried out using a FEI Tecnai G2

FRET calculation

For FRET model, the overlap integral (J) and Förster distance (R0) were calculated using Equations 3.3 and 3.4:

52 𝐽 = ∫ 𝐼 ̅ D (𝜆)𝜀 A (𝜆)𝜆 4 d𝜆 (3.3)
where 𝐼 ̅ D (𝜆) is the area-normalized emission spectrum of donor, 𝜀 A (𝜆) is the molar absorptivity spectrum of the acceptor in M -1 cm -1 , and  is the wavelength in nm.

𝑅 0 = 0.0211[𝜅 2 Φ D (𝑛) -4 𝐽(𝜆)] 1/6 (in nm) (3.4)
where 𝜅 2 is orientation factor (κ 2 =2/3 due to dynamic averaging of Tb/Eu-NP donor-acceptor systems), Φ D is quantum yield of the donor, and n=1. [START_REF] Uyeda | Synthesis of Compact Multidentate Ligands to Prepare Stable Hydrophilic Quantum Dot Fluorophores[END_REF] is the refractive index of the surrounding medium. The molar extinction coefficients 𝜀 QD/SiO 2 (𝜆) for QD/SiO2 with different shell thicknesses were calculated with estimated molar concentration and absorbance spectra.

Due to the strong difference in their intrinsic PL lifetimes in Ln-to-QD FRET, the FRET-sensitized PL decay time of QD adapts to the FRET-quenched PL decay time of Ln (𝜏 AD =𝜏 DA ). Thus, the FRET efficiency (𝐸 FRET ) can be determined by Equation 3.5:

𝐸 FRET = 1 - 𝜏 AD 𝜏 D (3.5)
The Ln-to-QD distance (R) was calculated using Equation 3.6:

𝑅 = 𝑅 0 ( 𝜏 DA 𝜏 D -𝜏 DA ) 1/6 (3.6)

Multi-exponential PL decay analysis.

We analyzed the data with multiexponential decays. This analysis has been shown to lead to a coherent picture of FRET in Tb-nanoparticle assemblies. It is based on fitting the decay curves were fitted using a multiexponential PL intensity decay function (Equation 3.7).

𝐼 = 𝐴 [∑ 𝛼 ADi * exp (-𝑡/𝜏 ADi )] + 𝐵 exp (-𝑡/𝜏 D ) (3.7)
where A is the total amplitude and 𝛼 ADi * are the amplitude fractions (∑ 𝛼 ADi * = 1)

of the different FRET contributions with FRET-sensitized PL decay times 𝜏 ADi .

Amplitude B and decay time 𝜏 D correspond to the contribution of unquenched Tb donor PL (due to spectral crosstalk in the QD detection channel). The amplitudes must be further corrected by FRET rates (Equation 3.8) to take into account the FRET efficiency-dependent excitation of the acceptor (Equation 3.9).[2] PL decay time averaging was then performed using amplitude weighted average decay times (Equation 3.10).

𝑘 FRETi = 1 𝜏 ADi - 1 𝜏 D (3.8) 𝛼 AD𝑖 = 𝛼 AD𝑖 * 𝑘 FRET𝑖 ⁄ ∑( 𝛼 AD𝑖 * 𝑘 FRET𝑖 ⁄ ) (3.9)
𝜏 AD = ∑ 𝑎 ADi 𝜏 ADi (3.10) Photophysical and FRET parameters for the different single luminophores and the donor-acceptor combinations are listed in Table 1. Although the PL emission wavelength of QDs before and after SiO2 coating did not change (Figure 3.3a), the extinction coefficient of QD/SiO2 significantly increased with increasing shell thickness due to a better protection of the QD from the environment. The spectral overlap integral (J) and Förster distance (R0) of each individual FRET-pair were calculated. The R0 was increasing from 9.7 nm and 8.6 nm to 10.7 nm and 9.2 nm for Tb-QD and Eu-QD, respectively (Table 3. with average decay times (ave) between 0.61 ms and 1.82 ms (Table 3.1) for the four lanthanide-QD FRET nanoparticles. Steady-state PL spectra also showed increased lanthanide PL quenching with decreasing shell thickness (Figure 3.6).

Results and discussion

Based on the PL decay curves, we also calculated FRET efficiencies and donor acceptor distances. With the fixed component of donor contribution, the average lifetime of acceptors in Tb-QD/SiO2 (6 nm), Tb-QD/SiO2 (12 nm), Eu-QD/SiO2 (6 nm), and Eu-QD/SiO2 (12 nm) were 0.75, 1.27, 0.52, and 0.74 ms, respectively. The energy transfer efficiencies were calculated as 0.72 (Tb-QD/SiO2 (6 nm)), 0.53 (Tb-QD/SiO2 (12 nm)), 0.53 (Eu-QD/SiO2 (6 nm)), and 0.33 (Eu-QD/SiO2 (12 nm)). With the R0 for each FRET-pair as calculated above, Tb-to-QD distances of R = 8.6 nm (6 nm SiO2 shell) and R = 10.5 nm (12 nm SiO2 shell), and Eu-to-QD distances of R = 8.4 nm (6 nm SiO2 shell) and R = 10.4 nm (12 nm SiO2 shell) were obtained, respectively. The results from Ln-to-QD with 6 nm SiO2 shell were in very good agreement and very well in line with the estimated average distance of the lanthanide complex conjugated randomly over the surface of SiO2 shell. However, the results from Ln-to-QD with 12 nm SiO2 shell led to the deduction that a significant fraction of Tb and Eu must be positioned inside the 12 nm SiO2 shell. This conclusion is not unrealistic because both the porosity of the outer SiO2 layers and the non-spherical shape on the entire QD can lead to closer and further distances than estimated by the ideal spherical model.

Living cell encoding

The To demonstrate the actual application for live cell imaging, HeLa cells were incubated with Tb-QD/SiO2 (6 nm), Tb-QD/SiO2 (12 nm), Eu-QD/SiO2 (6 nm), and Eu-QD/SiO2 (12 nm), respectively. Although adequately coated and biocompatible

QDs have been used in many biological imaging applications in vivo and in vitro, their toxicity remains an important subject of discussion. [START_REF] Wegner | Quantum Dots: Bright and Versatile in Vitro and in Vivo Fluorescence Imaging Biosensors[END_REF] Cell viability tests (MTT assays) with QD concentrations up to 800 nM (the concentration used for imaging experiments was only 20 nM) for both QD/SiO2 (6 nm) and QD/SiO2 60 (12 nm) revealed no significant cytotoxicity (Figure 3.8b). To encode the cells incubated with a specific nanoparticle, we used a TG microscopy imaging system with pulsed laser excitation at 349 nm and time-gated detection of the QD PL by an intensified CCD camera. [START_REF] Cardoso Dos Santos | Autofluorescence-Free Live-Cell Imaging Using Terbium Nanoparticles[END_REF] In general, TG microscopy in the micro and millisecond range can be realized on any standard fluorescence microscope that is equipped with pulsed excitation (e.g., LEDs, lasers, flash lamps, mechanical choppers) and time-gated detection (e.g., intensified cameras, scanning photon detectors, mechanical choppers). [START_REF] Gahlaut | Time-Resolved Microscopy for Imaging Lanthanide Luminescence in Living Cells[END_REF], [START_REF] Zwier | Time-Gated FRET Detection for Multiplexed Biosensing[END_REF] As defined before in the PL decay experiments, TG windows of 0.05-0.5 ms (R), 0.5-1 ms (G), and 1-3 ms (B) were selected for TG image encoding (Figure 3.9). After merging the images from the three TG detection windows (overlay), the RGB color images were obtained. Each code was determined according to RGB color selection and was consistent with the previously calculated results obtained by PL decays. Noteworthy, the different RGB colors could be readily distinguished by the naked eye (Figure 3.9).

To emphasize the capability of these codes to distinguish cells in more complex environments, four differently encoded HeLa cells were mixed and cultured on the

Conclusion

In summary, we have developed and applied a single-wavelength, single- [START_REF] Qiu | Three-Dimensional FRET Multiplexing for DNA Quantification with Attomolar Detection Limits[END_REF] or for the design of sophisticated molecular logic gates [START_REF] Claussen | Complex Logic Functions Implemented with Quantum Dot Bionanophotonic Circuits[END_REF], [START_REF] Claussen | Biophotonic Logic Devices Based on Quantum Dots and Temporally-Staggered Förster Energy Transfer Relays[END_REF] Taking into account that lanthanide-to-QD FRET can be applied to many different QD colors, [START_REF] Cardoso Dos Santos | Recent Developments in Lanthanide-to-Quantum Dot FRET Using Time-Gated Fluorescence Detection and Photon Upconversion[END_REF], [START_REF] Qiu | Rapid and Multiplexed MicroRNA Diagnostic Assay Using Quantum Dot-Based Förster Resonance Energy Transfer[END_REF]- [START_REF] Morgner | A Quantum-Dot-Based Molecular Ruler for Multiplexed Optical Analysis[END_REF] our single nanoparticle encoding strategy shows the potential of extending to higher-order spectrotemporal PL barcoding and thereby significantly advancing the possibilities of fluorescent encoding.

FRET-modulated multi

Introduction

The combination of unique photophysical properties and large surface-to-volume ratios have made semiconductor quantum dots (QDs) to one of the most versatile types of donors and acceptors for FRET. [START_REF] Hildebrandt | Energy Transfer with Semiconductor Quantum Dot Bioconjugates: A Versatile Platform for Biosensing, Energy Harvesting, and Other Developing Applications[END_REF] Although QD-FRET biological applications range from in-vitro diagnostic assays over molecular logic gates to invivo imaging with various combinations of donors and/or acceptors interacting with many different QDs, the full extent of how the number of donors and acceptors assembled or co-assembled to a single QD regulate the different FRET pathways

has not yet been investigated and understood. Different types of multiple acceptors attached to a central QD have been used for showing the increasing FRET efficiency with the number of acceptors, and such concepts have been frequently exploited for various biosensing applications. [START_REF] Yu | High-Resolution Three-Photon Biomedical Imaging Using Doped ZnS Nanocrystals[END_REF], [START_REF] Charbonnière | Lanthanides to Quantum Dots Resonance Energy Transfer in Time-Resolved Fluoro-Immunoassays and Luminescence Microscopy[END_REF] , [START_REF] So | Self-Illuminating Quantum Dot Conjugates for in Vivo Imaging[END_REF]- [START_REF] Jiang | Cascaded FRET in Conjugated Polymer/Quantum Dot/Dye-Labeled DNA Complexes for DNA Hybridization Detection[END_REF], [START_REF] Algar | Concurrent Modulation of Quantum Dot Photoluminescence Using a Combination of Charge Transfer and Förster Resonance Energy Transfer: Competitive Quenching and Multiplexed Biosensing Modality[END_REF]- [START_REF] Moore | From Antenna to Assay: Lessons Learned in Lanthanide Luminescence[END_REF] The investigation and application of multiple donors interacting with a central QD for an increased probability of QD-sensitization via FRET but unchanged FRET efficiency has been limited to lanthanide complexes. [START_REF] Charbonnière | Lanthanides to Quantum Dots Resonance Energy Transfer in Time-Resolved Fluoro-Immunoassays and Luminescence Microscopy[END_REF], [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF], [START_REF] Geißler | Quantum Dot Biosensors for Ultrasensitive Multiplexed Diagnostic[END_REF], [START_REF] Dí Az | Quantum Dots as Förster Resonance Energy Transfer Acceptors of Lanthanides in Time-Resolved Bioassays[END_REF]- [START_REF] Annio | Sensitivity Enhancement of Förster Resonance Energy Transfer Immunoassays by Multiple Antibody Conjugation on Quantum Dots[END_REF] Few studies have also investigated and applied the co-assembly of several lanthanide FRET donors and dye FRET acceptors, [START_REF] Algar | Quantum Dots as Simultaneous Acceptors and Donors in Time-Gated Förster Resonance Energy Transfer Relays: Characterization and Biosensing[END_REF]- [START_REF] Afsari | Time-Gated FRET Nanoassemblies for Rapid and Sensitive Intra-and Extracellular Fluorescence Imaging[END_REF], [START_REF] Claussen | Biophotonic Logic Devices Based on Quantum Dots and Temporally-Staggered Förster Energy Transfer Relays[END_REF] or the combination of FRET to dyes and charge transfer with ruthenium complexes on one QD. Optical multiplexing or barcoding based on nanoparticles, FRET, or their combination provides many advantages for biological sensing and imaging, optical data storage, and document security. [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF], [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF], [START_REF] Zijlstra | Five-Dimensional Optical Recording Mediated by Surface Plasmons in Gold Nanorods[END_REF], [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF], [START_REF] Dagher | Ensemble Multicolour FRET Model Enables Barcoding at Extreme FRET Levels[END_REF] Encoding based on QDs attracted considerable attention due to their unique optical properties. [START_REF] Algar | Quantum Dots as Simultaneous Acceptors and Donors in Time-Gated Förster Resonance Energy Transfer Relays: Characterization and Biosensing[END_REF], [START_REF] Chen | Near-Infrared-Emitting Two-Dimensional Codes Based on Lattice-Strained Core/(Doped) Shell Quantum Dots with Long Fluorescence Lifetime[END_REF], [START_REF] Han | Quantum-Dot-Tagged Microbeads for Multiplexed Optical Coding of Biomolecules[END_REF], [START_REF] Rees | Nanoparticle Vesicle Encoding for Imaging and Tracking Cell Populations[END_REF], [START_REF] Qiu | Rapid and Multiplexed MicroRNA Diagnostic Assay Using Quantum Dot-Based Förster Resonance Energy Transfer[END_REF], [START_REF] Geißler | Quantum Dot Biosensors for Ultrasensitive Multiplexed Diagnostic[END_REF], [START_REF] Xing | Bioconjugated Quantum Dots for Multiplexed and Quantitative Immunohistochemistry[END_REF] QD emission spectra are narrow and tunable throughout the visible and near-infrared wavelength range. Moreover, their absorption spectra are extremely broad and thus, several QDs with different emission colors can be excited with the same wavelength for spectral multiplexing. [START_REF] Reiss | Synthesis of Semiconductor Nanocrystals, Focusing on Nontoxic and Earth-Abundant Materials[END_REF], [START_REF] Wegner | Quantum Dots: Bright and Versatile in Vitro and in Vivo Fluorescence Imaging Biosensors[END_REF], [START_REF] Reiss | Core/Shell Semiconductor Nanocrystals[END_REF]- [START_REF] Smith | Semiconductor Nanocrystals: Structure, Properties, and Band Gap Engineering[END_REF] An important drawback for quantitative biosensing and imaging is the significant difference in brightness when exciting different QDs by the same wavelength. [START_REF] Lim | Brightness-Equalized Quantum Dots[END_REF] Smith et al. [START_REF] Arppe-Tabbara | Luminescence from Lanthanide(III) Ions Bound to the Glycocalyx of Chinese Hamster Ovary Cells[END_REF] used distinct core/shell/shell structures to overcome the mismatch of extinction coefficients of different QDs and to equalize their brightness over a wavelength range between ca. 500 and 800 nm. [START_REF] Lim | Brightness-Equalized Quantum Dots[END_REF] Despite the similar brightness of these QDs, they still require the detection of different wavelengths for multiplexing or barcoding.

One way to use only a single emission wavelength is the exploitation of PL lifetimes for multiplexing. [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF], [START_REF] Lu | Tunable Lifetime Multiplexing Using Luminescent Nanocrystals[END_REF], [START_REF] Zhang | Living Cell Multilifetime Encoding Based on Lifetime-Tunable Lattice-Strained Quantum Dots[END_REF], [START_REF] Lu | On-the-Fly Decoding Luminescence Lifetimes in the Microsecond Region for Lanthanide-Encoded Suspension Arrays[END_REF], [START_REF] Qiu | Three-Dimensional FRET Multiplexing for DNA Quantification with Attomolar Detection Limits[END_REF], [START_REF] Qiu | Rapid and Multiplexed MicroRNA Diagnostic Assay Using Quantum Dot-Based Förster Resonance Energy Transfer[END_REF], [START_REF] Grabolle | Fluorescence Lifetime Multiplexing with Nanocrystals and Organic Labels[END_REF]- [START_REF] Qiu | Multiplexed Nucleic Acid Hybridization Assays Using Single-FRET-Pair Distance-Tuning[END_REF] Owing to their extremely long PL lifetimes and their multiple narrow emission bands, fluorophores based on lanthanides are particularly well suited for multiplexed detection or optical barcoding. [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF], [START_REF] Qiu | Three-Dimensional FRET Multiplexing for DNA Quantification with Attomolar Detection Limits[END_REF], [START_REF] Qiu | Rapid and Multiplexed MicroRNA Diagnostic Assay Using Quantum Dot-Based Förster Resonance Energy Transfer[END_REF], [START_REF] Qiu | Multiplexed Nucleic Acid Hybridization Assays Using Single-FRET-Pair Distance-Tuning[END_REF]- [START_REF] Kovacs | Photophysics of Coumarin and Carbostyril-Sensitized Luminescent Lanthanide Complexes: Implications for Complex Design in Multiplex Detection[END_REF] The PL lifetimes of lanthanide complexes can be tuned over a broad temporal range and long donoracceptor distances by combination with suitable FRET acceptors, such as organic dyes or QDs. [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF], [START_REF] Qiu | Three-Dimensional FRET Multiplexing for DNA Quantification with Attomolar Detection Limits[END_REF], [START_REF] Qiu | Rapid and Multiplexed MicroRNA Diagnostic Assay Using Quantum Dot-Based Förster Resonance Energy Transfer[END_REF], [START_REF] Qiu | Multiplexed Nucleic Acid Hybridization Assays Using Single-FRET-Pair Distance-Tuning[END_REF], [START_REF] Guo | Amplified, and Multiplexed Detection of MicroRNAs Using Time-Gated FRET and Hybridization Chain Reaction[END_REF], [START_REF] Guo | Conformational Details of Quantum Dot-DNA Resolved by Förster Resonance Energy Transfer Lifetime Nanoruler[END_REF] Moreover the use of such emitting acceptors allows for using the FRET-sensitized acceptor PL as a single-wavelength readout, which we recently applied for single-wavelength optical barcoding in cellular imaging.

Materials and methods

Materials

Synthesis of QDs embedded silica nanospheres

The QDs embedded silica nanospheres were synthesized by a reverse microemulsion approach. Typically, the glass bollte containing 30 mL of cyclohexane was added with 3.95 mL of NP-5 and stirred for 15 min. The above solution was mixed with 300 μL of ammonia aqueous solution followed by stirring for another 15 min to form the reverse microemulsion. The mixture was subsequently added with 200 μL of QDs chloroform solution (10 mg/mL), followed by the injection of 140 μL of TEOS to start the silica encapsulation. After stirred at room temperature for 18 h, the QDs embedded silica nanospheres were precipated by adding ethanol followed by centrifugation. The products were washed with ethanol for several times and finally dispersed in 20 mL of ethanol.

Synthesis of mercapto-terminated silica nanospheres

For the grafting of mercapto-groups onto silica surface, the above QDs embedded silica nanospheres in 20 mL of ethanol was added with 500 μL of ammonia and 100 μL of MPS, followed by vigorous stirring at room temperature for 12 h. The finally product was harvested by centrifugation, washed with ethanol thoroughly and redispersed in 2 mL water.

Estimation of molar concentrations of QD/SiO2

We assumed that the nanomaterials have the same density as the corresponding bulk materials. For the CdSe/CdS/ZnS QD, the density of CdSe, CdS, and ZnS are 5.816 g/cm 3 , 4.82 g/cm 3 , and 4.09 g/cm 3 , respectively. The radius of QD is approximately 3.5 nm according HR-TEM. The radius of the CdSe core and the thicknesses of the CdS and ZnS shell were estimated to 1.8 nm, 1.16 nm, and 0.54 nm, respectively. These assumptions led to a QD density of 5.22 g/cm 3 (Equations

Photoluminescence quantum yield determination

The PL QY of as-prepared QD/SiO2 was determined using Qdot™ 605 ITK™ Streptavidin Conjugate Kit (Invitrogen™) as a standard (λex=480 nm, Φs=0.76).

The PL QY was calculated according to the following Equation 4.3:

Φ x = Φ s ( 𝐴 s 𝐴 x ) ( 𝑙𝑛𝑡 x 𝑙𝑛𝑡 s ) ( 𝜂 x 𝜂 s ) 2 (4.3)
Where Φ is the PL QY, lnt is the area under the emission peak, A is the absorbance at the excitation wavelength, and η is the refractive index of the solvent. The subscripts s and x denote the respective values of the standard and QD/SiO2.

Determination of Tb 3+ to Lumi4-ligand ratio for ~100% coordination

For the titration experiment, the initial solution contained 4 μL of Lumi4-Mal (0.38 mM) and 0.5 μL of TbCl3 (0.6 mM) in 1.5 mL of water (Lumi4-Mal/Tb = 1/0.2). Then 0.5 μL of TbCl3 (0.6 mM) were added stepwise to the solution while stirring until at Lumi4-Mal/Tb ratio of 1/4 was reached. The PL intensity of each point was recorded at 550 nm.

Formation of FRET system 1 (mTb-QD)

For

Microbeads encoding

For brightness-equalized microbeads encoding, solutions of 10Tb-QD, 30Tb-QD-

Analytical Methods

Structural characterization of the QD/SiO2 was carried out using a FEI Tecnai G2

FRET calculation

The overlap integral (J) and Förster distance (R0) were calculated using where 𝐼 ̅ D (𝜆) is the area-normalized emission spectrum of the donor, 𝜀 A (𝜆) is the molar absorptivity spectrum of the acceptor in M -1 cm -1 , and λ is the wavelength in nm.

𝑅 0 = 0.0211[𝜅 2 Φ D (𝑛) -4 𝐽(𝜆)] 1/6 (in nm) (4.5)
where κ 2 is orientation factor (κ 2 =2/3 due to dynamic averaging within all FRET pairs as justified by the flexible attachment of Tb and Cy5.5 to the SiO2 coating, the isotropic emission of Tb and QD, and the long PL lifetimes), ΦD is quantum yield of the donor, and n=1. [START_REF] Uyeda | Synthesis of Compact Multidentate Ligands to Prepare Stable Hydrophilic Quantum Dot Fluorophores[END_REF] is the refractive index of the surrounding medium.

The molar extinction coefficients for QD/SiO2 were calculated using molar concentration (known from the synthesis) and measured absorbance spectra. The molar extinction coefficients for Cy5.5 and Tb were provided by the suppliers.

Relative energy transfer rates were calculated using Equation 4.6, where τD is the unquenched donor lifetime, R0,n is the Förster distance for the FRET pathway, and the donor-acceptor distance R was assumed to be constant between different pathways.

𝑘 1 𝑘 2 = 𝜏 D,1 -1 [ 𝑅 0,1 𝑅 ] 6 𝜏 D,2 -1 [ 𝑅 0,2 𝑅 ] 6 = 𝜏 D,2 𝜏 D,1 [ 𝑅 0,1 𝑅 0,2 ] 6 (4.6)
In the case of Tb-to-QD FRET (due to the strong difference in their intrinsic PL lifetimes -cf. Table 4.1), the FRET-sensitized PL decay time of QD adapts to the FRET-quenched PL decay time of Tb (AD = DA). Thus, the FRET efficiency can be determined by Equation 4.7.

𝐸 FRET = 1 - 𝜏 AD 𝜏 D (4.7)
where AD is the average PL decay time of the mTb-QD FRET system and D is the average PL lifetime of Tb alone. [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF] The Tb-to-QD distance was calculated using Equation 4.8.

𝑅 = 𝑅 0 ( 𝜏 AD 𝜏 D -𝜏 AD ) 1/6 (4.8)
The theoretical probability of FRET-sensitized emission from one QD sensitized by m equidistant Tbs on its surface can be calculated by Equation 4.9

.[94]

𝑃 = 1 -(1 -𝐸 FRET ) 𝑚 (4.9)

In the case of QD-to-Cy5.5 FRET, the FRET efficiencies were calculated using PL decay times (Equation 4.10) and intensities (Equation 4.11).

𝐸 FRET = 1 - 𝜏 DA 𝜏 D (4.10)
where DA is the average PL lifetime of the QD-nCy5.5 FRET system and D is the average PL lifetime of QD alone.

𝐸 FRET = 1 - 𝐼 DA 𝐼 D (4.11)
where IDA is the PL peak intensity of the QD-nCy5.5 FRET system and ID is the PL peak intensity of QD alone.

In the case of FRET from one QD to n equidistant Cy5.5 dyes on its surface, the FRET efficiency can be calculated by Equation 4.12.

𝑘 FRETi = 1 𝜏 ADi - 1 𝜏 D (4.14a) 𝛼 ADi = 𝛼 ADi * 𝑘 FRETi ⁄ ∑( 𝛼 ADi * 𝑘 FRETi ⁄ ) (4.14b
)

𝜏 AD = ∑ 𝑎 ADi 𝜏 ADi

Results and discussion

Design and preparation of the multi-hybrid FRET nanoparticles

The central nanoscaffold of the multi-hybrid nanoparticles were SiO2-coated QDs (the entire QD/SiO2 is denoted as "QD" throughout the manuscript -cf.

Photophysical characterization of the multi-hybrid

FRET nanoparticles

The absorption and PL emission spectra of Tb, QD, and Cy5. 7.5), which was in good agreement with the average donoracceptor distance found for FRET system 1 (R = 8.5±0.6 nm), as expected due to the similar attachment of Tb and Cy5.5 to the SiO2 shell of the QD. The somewhat longer distance for system 1 could be caused by the slightly larger structure of the Lumi4 complex compared to the Cy5.5 dye (cf. on macromolecules, [START_REF] Kang | Prevention of H-Aggregates Formation in Cy5 Labeled Macromolecules[END_REF] proteins, [START_REF] Zhegalova | Minimization of Self-Quenching Fluorescence on Dyes Conjugated to Biomolecules with Multiple Labeling Sites via Asymmetrically Charged NIR Fluorophores[END_REF] or QDs [START_REF] Conroy | Self-Quenching, Dimerization, and Homo-FRET in Hetero-FRET Assemblies with Quantum Dot Donors and Multiple Dye Acceptors[END_REF] was already related to selfquenching of dyes. Similar to these studies, the Cy5.5 absorption spectra showed an increase of the hypsochromic shoulder with increasing n ( both PL intensity and lifetime quenching were found. [START_REF] Lakowicz | Principles of Fluorescence Spectroscopy[END_REF], [START_REF] Conroy | Self-Quenching, Dimerization, and Homo-FRET in Hetero-FRET Assemblies with Quantum Dot Donors and Multiple Dye Acceptors[END_REF], [START_REF] Zhegalova | Minimization of Self-Quenching Fluorescence on Dyes Conjugated to Biomolecules with Multiple Labeling Sites via Asymmetrically Charged NIR Fluorophores[END_REF]- [START_REF] Song | Rapid Assay for Avidin and Biotin Based on Fluorescence Quenching[END_REF] Our MCS approach, which simulated exciton per exciton, included the possibility of Cy5.5to-Cy5.5 homo-FRET and an increasing probability of energy dissipation (or trap state encounter) with an increasing amount of Cy5.5-to-Cy5.5 FRET events. The MCS model accounted for two additional properties of our FRET system. First, the Cy5.5 distance from the QD center was 8.5±1.5 nm whereas the average QD-Cy5.5

donor-acceptor distance was 7.9±0.6 nm (vide supra). Thus, the actual Cy5.5-to-Cy5.5 distance was larger than on the simulated 7.9 nm sphere, which was taken

FRET system 3: mTb-QD-15Cy5.5

The full versatility of a QD-based FRET system can be exploited when both Tb donors and dye acceptors are conjugated to the same QD. In this case, predictions of how the different FRET pathways (Tb-to-QD, QD-to-dye, Tb-to-dye, dye-to-dye) interact and how varying amounts of Tb donors and dye acceptors can be used to tune the PL properties (PL lifetimes and intensities at different emission wavelengths) are even more difficult than for the systems with only one FRET pair (systems 1 and 2). As a first possibility of a central QD with multiple donors and acceptors on its surface, we investigated a system with a variable amount of m Tb donors and constant amount (15) of Cy5.5 acceptors. Experimentally, this FRET One interesting feature of this FRET system is the possibility to study it from three independent perspectives, namely the Tb, QD, and Cy5.5 PL. When comparing the PL decays for these three detection channels for varying amounts of Tb (Figures were used to calculate the FRET efficiencies of the subsequent FRET steps (Figure 4.16d). Tb PL led to a constant value of EFRET = 0.79±0.01 for all m, which is circa 10% higher than for system 1 (cf. 4.1) when they are both attached to the same QD. The FRET efficiency in the QD channel was also constant with EFRET = 0.71±0.02, which was only 2% higher than for system 1. In this case, the average FRETsensitized lifetime could be corrected by the FRET-rates of the two contributing FRET lifetimes (Equations 4.14a and b), which suppressed the additional quenching effect by FRET from QD-to-Cy5.5. Indeed, if only the apparent FRETquenched lifetimes were taken into account (without kFRET correction), the FRET efficiency would be around 81% (Figure 4.17), as expected from the additional QDto-dye FRET pathway. Analyzing the Cy5.5 time-resolved PL led to a constant FRET efficiency of EFRET = 0.70±0.07 for all m, which was in good agreement with FRET system 2 (EFRET~0.7 for n = 15, cf. sensitization from end-to-end (Cy5.5/Tb ratio) followed by the second (Cy5.5/QD ratio) and the first (QD/Tb ratio) FRET steps, which provides another possibility for adapting and/or optimizing sensitivities or limits of detection for multiplexed biosensing applications. Although the experimental results of FRET system 3 make sense when taking into account the findings for system 1 and 2, it would have been interesting to use MCS for comparison. Unfortunately, our current MCS model cannot properly account for long lifetime donors because it (and other MCS codes) tests for available acceptors at the time of excitation rather than at the time of de-excitation. This is due to the fact that the time of de-excitation is itself dependent of the number of locations of available acceptors. The simplification is valid for short lifetime donors and can be accounted for in system 1 by appropriately choosing the laser irradiance, but does not lead to reasonable results in this situation, in which the number of donors varies and dye acceptors are coassembled. One of our future objectives will be the adaption of the MCS model to the complicated properties of this long lifetime multi-donor-acceptor QD FRET system. In contrast to system 3, for which m (amount of Tb) was varied and thus the FRET efficiency did not change, the increase of n (amount of Cy5.5) led to an increasing FRET efficiency, as expected from system 2. This behavior can readily be witnessed in the PL decay curves of all three detection channels, which change significantly in lifetime and intensity (

4.16a

Brightness-equalized barcoding

The importance of such multi-donor-multi acceptor FRET QDs is not limited to a better fundamental understanding of the underlying FRET pathways. In fact, the knowledge of how to adjust the PL lifetimes and intensities in the three different detection channels can be exploited to design powerful tools for optical barcoding. To demonstrate the capability of brightness-equalized PL barcoding, we selected the three NP systems "10Tb-QD", "30Tb-QD-10Cy5.5", and "60Tb-QD-40Cy5.5" and the three TG PL detection windows 0.05-0.5 ms, 0.5-1 ms, and 1-4 ms, which were decoded as red (R), green (G), and blue (B) (Figure 4.24a). This approach did not only allow us to accomplish three distinct RGB codes but also to reduce the brightness mismatch to 1.2 fold between code1 and code2 and 2.

Conclusion

We

Introduction

The application of excitation energy transfer has expanded the applicability of luminescent probe methodologies in biochemistry, clinical diagnostics, and biomolecular imaging. [START_REF] Selvin | The Renaissance of Fluorescence Resonance Energy Transfer[END_REF]- [START_REF] Weiss | Measuring Conformational Dynamics of Biomolecules by Single Molecule Fluorescence Spectroscopy[END_REF] The understanding of energy transfer mechanism between donors and acceptors plays a fundamental role in developing and optimizing biosensing technologies. Förster resonance energy transfer (FRET)

is the best-known energy transfer mechanism and has been confirmed for pairs of small donor and acceptor molecules. It predicts the energy transfer efficiency to be inversely proportional to the sixth power of the distance between the donor and acceptor. [START_REF] Clapp | Fluorescence Resonance Energy Transfer Between Quantum Dot Donors and Dye-Labeled Protein Acceptors[END_REF] This energy transfer occurs at intermolecular distances in the small window between approximately 1 and 20 nm, [START_REF] Hildebrandt | FRET -Förster Resonance Energy Transfer[END_REF] a range that is ideally suited for observing dynamic biomolecular interactions, involving proteins, nucleic acids, cell membranes, and other biological systems. [START_REF] Sekar | Fluorescence Resonance Energy Transfer (FRET) Microscopy Imaging of Live Cell Protein Localizations[END_REF] However, many biomolecular processes take place over longer distances and their dynamic interactions are difficult to follow by FRET. Thus, investigating and understanding longer-range energy transfer processes and using them for biosensor development is highly desirable.

Theorized by Persson and Lang, [START_REF] Persson | Electron-Hole-Pair Quenching of Excited States near a Metal[END_REF] nanosurface energy transfer (NSET) has emerged as an energy transfer mechanism that can measure biomolecular interactions over distances up to 50 nm and thereby more than double the range of FRET. [START_REF] Samanta | Fluorescence Quenching of Quantum Dots by Gold Nanoparticles: A Potential Long Range Spectroscopic Ruler[END_REF] Similar to FRET, NSET is a nonradiative dipole-dipole energy transfer but in contrast to FRET (in which both donor and acceptor are considered as point dipoles) the acceptor is a nanometric surface modeled as a collection of many dipoles. In NSET, the efficiency is inversely proportional to the fourth power of the distance between the donor and the acceptor surface of a metallic nanoparticle (in most cases AuNPs). [START_REF] Pons | On the Quenching of Semiconductor Quantum Dot Photoluminescence by Proximal Gold Nanoparticles[END_REF], [START_REF] Yun | Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier[END_REF] Research showed that NSET model was in good agreement with the experimental data on small size AuNPs (below 3 nm) in combination with organic dyes and quantum dots (QDs) as donors. [START_REF] Jennings | Fluorescent Lifetime Quenching near d = 1.5 nm Gold Nanoparticles: Probing NSET Validity[END_REF], [START_REF] Jennings | LETTERS NSET Molecular Beacon Analysis of Hammerhead RNA Substrate Binding and Catalysis[END_REF], [START_REF] Yun | Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier[END_REF] NSET behavior with energy transfer efficiencies independent of the NP size or number of donors was also demonstrated for larger size AuNPs. [START_REF] Chen | A Surface Energy Transfer Nanoruler for Measuring Binding Site Distances on Live Cell Surfaces[END_REF], [START_REF] Zhang | Distance Dependence of Nonradiative Energy Transfer to a Plane of Gold Nanoparticles[END_REF], [START_REF] Saraswat | Energy Transfer from Fluorescent Proteins to Metal Nanoparticles[END_REF], [START_REF] Kapur | Self-Assembled Gold Nanoparticle -Fluorescent Protein Conjugates as Platforms for Sensing Thiolate Compounds via Modulation of Energy Transfer Quenching[END_REF] However, in other studies reporting about biosensors that use PL quenching by AuNPs, the underlying energy transfer mechanism is assumed to be FRET [START_REF] Li | Size-Dependent Energy Transfer between CdSe/ZnS Quantum Dots and Gold Nanoparticles[END_REF], [START_REF] Guo | Nanostructure and Corresponding Quenching Efficiency of Fluorescent DNA Probes[END_REF] or is not specified. [START_REF] Li | A Multicolor Nanoprobe for Detection and Imaging of Tumor-Related MRNAs in Living Cells[END_REF], [START_REF] Vilela | Sensing of Vimentin MRNA in 2D and 3D Models of Wounded Skin Using DNA-Coated Gold Nanoparticles[END_REF] Studies of the NSET mechanism have focused on the interaction of AuNPs with organic dyes and QDs but have as yet not used luminescent lanthanide complexes as the energy donor. Whereas hybrid nanomaterials incorporating luminescent lanthanide ions and plasmonic AuNPs have been reported in the literature, [START_REF] Zhong | Modulation of Fluorescence of a Terbium-Complex-Containing Polymer by Gold Nanoparticles through Energy Transfer[END_REF]-

Materials and methods

Materials

The biot-AuNPs were purchased from Sigma-Aldrich (5, 30, 50, and 80 nm diameter, biotin-terminated PEG mol. wt. 5000, dispersion in H2O). For the measurements of 5 nm, 30 nm and 50 nm Au NPs, 2 mM Tris-HCl (pH 8.

Optimization of buffer conditions

Optical extinction and light scattering spectra were measured on solutions of the biot-AuNPs in a selection of aqueous buffers. These spectroscopic measurements enabled to determine the long-term stability of biot-AuNPs in these buffers.

Colloidal stability is a requirement for reliable results when forming donoracceptor assemblies. Aggregation of instable AuNPs would lead to clearly observable changes in the optical spectra. Light scattering spectroscopy is particularly sensitive towards even slight changes in the chemical environment of plasmonic AuNPs. [START_REF] Navarro | Resonant Light Scattering Spectroscopy of Gold, Silver and Gold-silver Alloy Nanoparticles and Optical Detection in Microfluidic Channels[END_REF], [START_REF] Loumaigne | Optical Extinction and Scattering Cross Sections of Plasmonic Nanoparticle Dimers in Aqueous Suspension[END_REF] From these measurements (see Figure S1 to S3), it was concluded that 2 to 4 mM Tris-HCl buffer at pH 8.5, and pure water were the most suitable media for the experiments. An alternative buffer, phosphatebuffered saline (10 mM phosphate, pH 7.2, 137 mM NaCl, 2.7 mM KCl) also yielded stable nanoparticle solutions (no shift of the localized surface plasmon resonance maximum) but led to more pronounced "sticking" of the biot-AuNPs to the spectroscopic cell walls.

Formation of Tb/AuNP donor-acceptor assemblies

We

Analytical Methods

Extinction spectra were acquired using a Lambda

Results and discussion

Characterization of Tb-sAv-biot-AuNP assemblies

The number of binding sites for sAv on each nanoparticle is of the same order of magnitude as the number of biotins per particle. In principle, sAv can bind up to four biotins. [START_REF] Geißler | Quantum Dot Biosensors for Ultrasensitive Multiplexed Diagnostic[END_REF] The number of biotins per biot-AuNP were given by the supplier as a number density of approximately 0.5/nm 2 at the AuNP surface. At the same time, the surface areas were given as 78.5, 2830, 7850, and 20100 nm 2 for the 5, 30 nm, 50 nm, and 80 nm AuNPs, respectively, which led to 39 biotins per 5 nm AuNP, 1415 biotins per 30 nm AuNP, 3925 biotins per 50 nm AuNP, and 10050 biotins per 80 nm AuNP. Because no explanation of this estimation was provided, we applied our own estimation based on the number of Au surface atoms, which we calculated to be 500 for 5 nm biot-AuNPs, 18000 for the 30 nm biot-AuNPs, 50000 for the 50 nm biot-AuNPs, and 128000 for the 80 nm biot-AuNPs. Assuming the number of available biotins on the surface to be ca. 5% of the number of Au surface atoms led to 25 biotins per 5 nm biot-AuNP, 900 biotins per 30 nm biot-AuNP, 2500 biotins per 50 nm biot-AuNP, and 6400 biotins per 80 nm biot-AuNP, which were in good agreement with the estimates of the supplier. Taking into account that four biotins from the biot-AuNP will be able to bind one sAv, and ignoring any steric effects, the number of sAv that can bind to one nanoparticle is anticipated to be 6 for 5 nm biot-AuNPs, 225 for 30 nm biot-AuNPs, 625 for 50 nm, and 1600 for 80 nm biot-AuNPs. PL titrations reported below enabled us to refine these estimates.

The interaction of Tb-sAv with biot-AuNPs was investigated by monitoring the light scattering spectra [START_REF] Navarro | Resonant Light Scattering Spectroscopy of Gold, Silver and Gold-silver Alloy Nanoparticles and Optical Detection in Microfluidic Channels[END_REF], [START_REF] Loumaigne | Optical Extinction and Scattering Cross Sections of Plasmonic Nanoparticle Dimers in Aqueous Suspension[END_REF] of the biot-AuNPs and introducing Tb-sAv into the solution. The light scattering spectra consist of the localized surface plasmon resonance of AuNPs, which is sensitive to the environment of the particles. In particular, immobilization of biomolecules at the nanoparticle surface leads to small changes (a few nm) in the position of the maximum of these resonance bands.

Larger shifts of the plasmon maximum (> 10 nm) are in general the result of clustering of AuNPs into aggregates, which leads to strong coupling between the localized plasmon resonances of the individual particles [START_REF] Navarro | Resonant Light Scattering Spectroscopy of Gold, Silver and Gold-silver Alloy Nanoparticles and Optical Detection in Microfluidic Channels[END_REF], [START_REF] Loumaigne | Optical Extinction and Scattering Cross Sections of Plasmonic Nanoparticle Dimers in Aqueous Suspension[END_REF], [START_REF] Englebienne | Use of Colloidal Gold Surface Plasmon Resonance Peak Shift to Infer Affinity Constants from the Interactions between Protein Antigens and Antibodies Specific for Single or Multiple Epitopes[END_REF], [START_REF] Ghosh | Interparticle Coupling Effect on the Surface Plasmon Resonance of Gold Nanoparticles: From Theory to Applications[END_REF]. The particular sensitivity of the resonant light scattering spectrum towards the environment of the AuNPs provides a tool for monitoring the state of the biot-AuNPs when interacting with Tb-sAv. respectively. Using the surface areas of the different AuNPs (vide supra) and the size of sAv in the solid state (5.8 nm x 5.4 nm x 4.9 nm), [START_REF] Hendrickson | Crystal Structure of Core Streptavidin Determined from Multiwavelength Anomalous Diffraction of Synchrotron Radiation[END_REF] which would lead to a surface footprint of 24.6 nm 2 ( x 2.9 nm x 2.7 nm), the possible coverage of sAv per AuNP would be 3 (5 nm AuNPs), 115 (

Time-resolved PL decay analysis

We analyzed the data with multiexponential decays. The multiexponential analysis has previously been shown to lead to a coherent picture of LRET in Tbnanoparticle assemblies. [START_REF] Wegner | Nanobodies and Nanocrystals: Highly Sensitive Quantum Dot-Based Homogeneous FRET Immunoassay for Serum-Based EGFR Detection[END_REF], [START_REF] Wegner | Influence of Luminescence Quantum Yield, Surface Coating, and Functionalization of Quantum Dots on the Sensitivity of Time-Resolved FRET Bioassays[END_REF] It is based on fitting the decay curves using a multiexponential PL intensity decay function (Equation 5.1):

𝐼 = ∑ 𝐴 i exp (-𝑡/𝜏 i ) = 𝐴 ∑ 𝛼 i exp (-𝑡/𝜏 i ) (5.1)
where 𝐴 is the total amplitude and αi are the amplitude fractions (∑ 𝛼 i = 1). The averaging of the PL lifetime for the quenching process was performed using amplitude weighted average lifetimes (Equation 5.

2):[230]-[232]

⟨𝜏⟩ = ∑ 𝑎 𝑖 𝜏 𝑖 (

The decay curve of pure Tb-sAv donor in buffer slightly deviates from monoexponentially (Figure 5.4a), which can be attributed to the multiple Tb (~4) conjugation per sAv. The heterogeneity in the local environments, that the Tb experience at the different sAv sites give rise to a distribution of decay rates. It was better fitted with a double-exponential decay function, which led to the amplitude fractions αD1 and αD2, the PL decay times τD1 and τD2 (with τD2 >τD1) and the average PL decay time of the pure donor (in the absence of the acceptor) ⟨τD⟩.

The quenched decay curves in the donor detection channel were fitted using a triple-exponential decay function, leading to the amplitude fractions αDA*1, αDA*2, and αDA*0 and the PL decay times τDA1, τDA2, and τDA0, for which the third decay time component was fixed to τDA0 = τD2 in order to take into account the emission of unquenched donors. For the calculation of the average donor decay time in the presence of the acceptor ⟨τDA⟩, only the first two amplitudes and decay times were used (as the third component represents unquenched donors). Therefore, the amplitude fractions must be redefined for these two decay times τDA1 and τDA2. As the unquenched donor possesses two decay time components (τD1 and τD2), ⟨τDA⟩ must be corrected for the shorter time component τD1. As this shorter decay time of the "pure" donor falls within the time-range of the quenched decay times, the use of an additional exponential for the fit procedure leads to inconsistent fit results. We therefore applied a correction factor 𝑧 D (the fraction of unquenched donors in the short time components), which is determined by comparing the 116 amplitude fractions of τD2 and τDA0 (τDA0 = τD2) multiplied by the amplitude fraction (Equation 5.3) and which was shown to lead to consistent distance results for many different Tb-to-quantum dot FRET systems. [START_REF] Hildebrandt | FRET -Förster Resonance Energy Transfer[END_REF], [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF], [START_REF] Wegner | Influence of Luminescence Quantum Yield, Surface Coating, and Functionalization of Quantum Dots on the Sensitivity of Time-Resolved FRET Bioassays[END_REF] 𝑧 D = 𝛼 D1 (𝛼 DA * 0 /𝛼 D2 ) (5.

3)

The average quenched decay time is then (with 𝛼 𝐷A1 + 𝛼 𝐷A2 =1, Equation 5.4)

⟨𝜏 DA ⟩ = 𝛼 DA1 𝜏 DA1 +𝛼 DA1 𝜏 DA1 -ᴢ D 𝜏 D1 1-ᴢ D
(5.4) Using this multi-exponential analysis, the average quenched decay times (⟨𝜏 DA ⟩) were 0.81±0.02 ms, 0.31±0.02 ms, 0.47±0.01 ms, and 0.22±0.03 ms, and the energy transfer efficiencies (E) were 0.62±0.01, 0.86±0.02, 0.79±0.01 and 0.87±0.02 for 5 nm, 30 nm, 50 nm, and 80 nm biot-AuNPs, respectively (Appendix 7.4.2). In addition to the multi-exponential analysis, the PL decay curves were also analyzed with a Kohlrausch decay model (Appendix 7.4.3). We found 〈𝜏〉 DA = 0.80±0.01 ms for 5 nm biot-AuNPs, 〈𝜏〉 DA = 0.19±0.01 ms for 30 nm biot-AuNPs, 〈𝜏〉 DA = 0.46±0.01 ms for 50 nm biot-AuNPs, and 〈𝜏〉 DA = 0.14±0.02 ms for 80 nm biot-AuNPs, with energy transfer efficiencies 0.63±0.01, 0.91±0.01, 0.79±0.01, and 0.9±0.02, respectively. The Kohlrausch analysis led to similar results as the multiexponential analysis, indicating the consistency between the two models. The results of two analysis for all AuNP diameters studied are collected in Table 5.1.

Finally, the energy transfer efficiencies, as well as the determined donor-acceptor distances are in close agreement between the multi-exponential and Kohlrausch decay models.

Energy transfer mechanism: FRET vs NSET

The energy transfer efficiencies indicate that PL quenching takes place by nonradiative energy transfer, and also that this quenching is incomplete, leaving some emission to be detected. Gold nanoparticles are known to be efficient quenchers for luminophores very close to their surface [START_REF] Loumaigne | Fluorescence Correlation Spectroscopy Reveals Strong Fluorescence Quenching of FITC Adducts on PEGylated Gold Nanoparticles in Water and the Presence of Fluorescent Aggregates of Desorbed Thiolate Ligands[END_REF]- [START_REF] Huang | Quenching of [Ru(Bpy)3] 2+ Fluorescence by Binding to Au Nanoparticles[END_REF] and the mechanism for this quenching has been attributed to either FRET or NSET mechanisms. [START_REF] Efros | Interband Light Absorption in Semiconductor Spheres[END_REF], [START_REF] Murray | Synthesis and Characterization of Nearly Monodisperse CdE (E = Sulfur, Selenium, Tellurium) Semiconductor Nanocrystallites[END_REF], [START_REF] Chan | Quantum Dot Bioconjugates for Ultrasensitive Nonisotopic Detection[END_REF], [START_REF] Reiss | Synthesis of Semiconductor Nanocrystals, Focusing on Nontoxic and Earth-Abundant Materials[END_REF], [START_REF] Resch-Genger | Quantum Dots versus Organic Dyes as Fluorescent Labels[END_REF], [START_REF] Yu | High-Resolution Three-Photon Biomedical Imaging Using Doped ZnS Nanocrystals[END_REF], [START_REF] Algar | Adsorption and Hybridization of Oligonucleotides on Mercaptoacetic Acid-Capped CdSe/ZnS Quantum Dots and Quantum Dot-Oligonucleotide Conjugates[END_REF], [START_REF] Wilson | Highly Stable Dextran-Coated Quantum Dots for Biomolecular Detection and Cellular Imaging[END_REF], [START_REF] Ha | Single-Molecule Fluorescence Resonance Energy Transfer[END_REF], [START_REF] Weiss | Measuring Conformational Dynamics of Biomolecules by Single Molecule Fluorescence Spectroscopy[END_REF], [START_REF] Loumaigne | Fluorescence Correlation Spectroscopy Reveals Strong Fluorescence Quenching of FITC Adducts on PEGylated Gold Nanoparticles in Water and the Presence of Fluorescent Aggregates of Desorbed Thiolate Ligands[END_REF] We therefore subjected our PL decay time results to both FRET and NSET theory with the aim of contributing to the understanding of energy transfer processes in assemblies of photoluminescent entities and plasmonic nanoparticles, in particular to find out which theory, FRET of NSET, makes the best predictions about energy transfer in these systems. The long-lived PL emission from Tb enables a clear distinction of the Tb signal from other, short-lived background fluorescence, while still being subject to electric dipole-dipole energy transfer. [START_REF] Selvin | Luminescence Energy Transfer Using a Terbium Chelate: Improvements on Fluorescence Energy Transfer[END_REF] For FRET model analysis, the overlap integral (J) and Förster distance (R0) were calculated using Equations 5.5 and 5.6.

𝐽 = ∫ 𝐼 ̅ D (𝜆)𝜀 A (𝜆)𝜆 4 d𝜆 (5.5)
where 𝐼 ̅ D (𝜆) is the area-normalized emission spectrum of donor, 𝜀 A (𝜆) is the molar absorptivity spectrum of the acceptor in M -1 cm -1 , and  is the wavelength in nm. 𝑅 0 = 0.0211[𝜅 2 Φ D (𝑛) -4 𝐽(𝜆)] 1/6 (in nm) (5.6) where κ 2 is orientation factor (κ 2 =2/3 due to dynamic averaging as found for other Tb-NP donor-acceptor systems), [START_REF] Hildebrandt | Energy Transfer with Semiconductor Quantum Dot Bioconjugates: A Versatile Platform for Biosensing, Energy Harvesting, and Other Developing Applications[END_REF], [START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF] ΦD is Tb-centered quantum yield of the Tb donor (0.64), and n is the refractive index of the surrounding medium. The molar extinction coefficients 𝜀 AuNP (𝜆) for gold nanoparticles were obtained from the extinction cross sections calculated with analytic Mie expressions [START_REF] Bohren | Absorption and Scattering of Light by Small Particles[END_REF] evaluated using a Python computer program. [START_REF] Navarro | Resonant Light Scattering Spectroscopy of Gold, Silver and Gold-silver Alloy Nanoparticles and Optical Detection in Microfluidic Channels[END_REF] Förster distances (R0) were 14.1 nm, 34.8 nm, 46.8 nm, and 60.7 nm (for 30, 50, and 80 nm AuNPs, respectively) when using the refractive index of the aqueous buffer (Table 5.2) or 17.1 nm, 43.1 nm, 57.9 nm, and 75.1 nm, when using the refractive index of gold (Table 5.3). To fit the FRET model to different sizes of AuNPs, Wu et al. suggested to subtract the radius of the AuNPs from the R0 values, [START_REF] Li | Size-Dependent Energy Transfer between CdSe/ZnS Quantum Dots and Gold Nanoparticles[END_REF] which would lead to 11.6 nm, 19.8 nm, 21.8 nm, and 20.7 nm when using the refractive index of the aqueous buffer and 14.6 nm, 28.1 nm, 32.9 nm, and 35.1 nm when using the refractive index of gold. All R0 values are far beyond the FRET range, which provides good evidence that the FRET mechanism is not operational here. Within the FRET model, the Tb-AuNP distance (R) was calculated using Equation 5.

7.[2]

𝑅 = 𝑅 0 (

𝜏 DA 𝜏 D -𝜏 DA ) 1/6 (5.7)
As shown in Table 5.4 and 5.5, the calculated distances between Tb and the AuNP surface globally range from 4.2 nm to 54.7 nm (excluding an unrealistic 0.8 nm value). The calculated distances spans a very large distance range with almost all values far beyond a distance that could be attained by the dimensions of the streptavidin-biotin pair separating the Tb donors from the gold nanosurface.

Moreover, these calculated distances do not show much consistency between the results for 5 nm, 30 nm, 50 nm and 80 nm particles.

For NSET analysis, the 𝑅 0 NSET was calculated by Equation 5.8. [START_REF] Jennings | Fluorescent Lifetime Quenching near d = 1.5 nm Gold Nanoparticles: Probing NSET Validity[END_REF], [START_REF] Jennings | LETTERS NSET Molecular Beacon Analysis of Hammerhead RNA Substrate Binding and Catalysis[END_REF] 𝑅 0 NSET = ⌊0.225

Φ D 𝜔 D 1 𝜔 F 𝑘 F 𝑐 3 ⌋ 1/4 (5.8)
Where 𝜔 D is the angular frequency of the donor electronic transition, 𝜔 F and 𝑘 F are the angular frequency and the Fermi vector for bulk gold, respectively, and c is the speed of light. 𝑅 0 NSET was 7.2 nm for all three different sizes of AuNPs (Table 5.6), since it is independent of nanoparticle diameter (energy transfer to a surface). The Tb-AuNP distance (R) was calculated using Equation (5.9). 5

𝑅 = 𝑅 0 NSET ( 𝜏 DA 𝜏 D -𝜏 DA ) 1/4
(5.9) With the PL decay times for the donor and the donor-acceptor assemblies as determined above, and the 𝑅 0 NSET determined using the NSET theory, Tb-AuNP distances R were obtained and are collected in Table 5.7. All the distances found are in the 4.0-6.4 nm range and do not show a strong dependence on the acceptor AuNP diameter. Moreover, these distances are well in line with the estimated average distance of the Tb complexes conjugated randomly to the sAv binding via biotin to the surface of the AuNP (Figure 5.1). When considering the overall uncertainty on the donor-acceptor distances R derived from the experimental luminescence decay measurements, we distinguish two main sources of uncertainty, the first being the experimental error on the experimental decay times and the second being the uncertainty on the value on 𝑅 0 NSET . To separate these two contributions to the overall uncertainty, we have included the ratio 𝑅/𝑅 0 NSET in Table 5.7. This ratio thus depends solely on the uncertainty of the experimental measurements, which is relatively small. The uncertainty on 𝑅 0 NSET was estimated to be 10% and represents a systematic uncertainty. The NSET model afforded a set of donor-acceptor distances that are similar for various AuNP diameters studied and consistent with the expected structure of Tb-sAv/biot-AuNP assemblies.

Conclusion

We have demonstrated efficient energy transfer between Tb donors and AuNP acceptors within different Tb-sAv/biot-AuNPs assemblies for AuNPs of 5nm,

123

When comparing the quenching efficiencies predicted by NSET and by FRET, we find that NSET predicts less quenching for a given donor-acceptor distance, especially at shorter distance. This makes it more likely that fluorescence of fluorophores attached to plasmonic nanoparticles is partially retained and can still be useful for the detection of such assemblies. Moreover, successful design and optimization of biosensors such as "nano-flares" [START_REF] Li | A Multicolor Nanoprobe for Detection and Imaging of Tumor-Related MRNAs in Living Cells[END_REF], [START_REF] Vilela | Sensing of Vimentin MRNA in 2D and 3D Models of Wounded Skin Using DNA-Coated Gold Nanoparticles[END_REF] and molecular rulers [START_REF] Yun | Nanometal Surface Energy Transfer in Optical Rulers, Breaking the FRET Barrier[END_REF] based on AuNP PL quenching is clearly dependent on the understanding of the underlying energy-transfer mechanism, to which our study has contributed important findings in favor of NSET.

Summary and outlook

This thesis presents the successful understanding and application of FRET Brightness-equalized single-color multiplexed imaging.

Due to the independent tunable color, lifetime and intensity in multi-hybrid QDs can be achieved by using different QDs, multiple and different donors, and multiple acceptors, we can fabricate 3D barcoding by combining three parameter and largely increase the information density of barcoding. Moreover, we can also 125 introduce polarization as a 4 th dimension by using quantum rods (QRs).

Furthermore, the enhanced single-nanoparticle barcoding can be functionalized with aptamer or cell-penetrating peptides which can uniquely identify and track targeted cells in different cells mixture.

The third study shows the NSET model provided excellent agreement between the Tb-to-AuNP surface distance estimated by the biotin-streptavidin interaction and calculated by the PL lifetime analysis. However, we only study the energy transfer mechanism in constant distance (~4.5 nm) between Tb and AuNP surface. In the case of large AuNP, the SPR may cause the energy transfer to varying degrees in different distance from the AuNP. In order to deeply understand the energy transfer phenomenon on the surface of AuNP, AuNP can be coated with silica shell before attaching with Tb donors.

Simulation methods

Monte-Carlo simulations were based on a previously published concept [START_REF] Berney | FRET or No FRET: A Quantitative Comparison[END_REF], [START_REF] Corry | A Flexible Approach to the Calculation of Resonance Energy Transfer Efficiency between Multiple Donors and Acceptors in Complex Geometries[END_REF] tailored to our specific system by modifying our exiFRET code, [START_REF] Deplazes | Flexible Tool for Understanding FRET in Complex Geometries[END_REF] most notably to enable FRET to occur between multiple fluorophore types including homo-FRET and to incorporate non-radiative de-excitation. In this approach, the fluorescence coming from a given configuration of fluorophores is calculated by modelling the evolution of a set of ''excitons'' generated by the adsorption of discrete incoming photons. These incoming photons cause the excitation of specific fluorophores for a period of time during which they cannot absorb another photon, but may become de-excited again either through the emission of a photon (fluorescence), nonradiative de-excitation, or else energy transfer to another fluorophore. The acceptor of an energy transfer event also remains excited for a period of time during which it is not available for further excitation, and itself can be de-excited through fluorescence, non-radiative de-excitation or further energy transfer. In the new scheme, all fluorophores can act as acceptors and a single exciton can participate in multiple energy transfer events.

The method proceeds as shown in Figure 7.1, which includes variations on our initially published approach. [START_REF] Corry | A Flexible Approach to the Calculation of Resonance Energy Transfer Efficiency between Multiple Donors and Acceptors in Complex Geometries[END_REF] We begin by generating coordinates of the fluorophores. In this case, the QD was assumed to be at the center of a spherical nanoparticle with the Tb and Cy5.5 distributed randomly on the surface of the sphere. From this, the distance between each pair of fluorophores and the transfer probability can be calculated. Next, a schedule of arrival times and targets of each incident photon are determined. This is based upon the irradiance of the laser specified assuming steady-state excitation. Photons are assumed to be absorbed by only one type of fluorophore chosen for each system to match wavelength of the incident laser, with the specific fluorophore determined randomly. Finally, each of the events following each incident photon are played out and the number of fluorescence, non-radiative de-excitation, and transfer events is recorded.

To do this last step, we first check that the donor is available for excitation of a photon from the laser. Then we calculate the rate of energy release using the lifetime of the fluorophore and the availability of all potential energy transfer partners. Using this, the time at which the fluorophore de-excites can be derived using a randomized Monte-Carlo approach to select a time matching this release rate. Next, we use another Monte-Carlo step to determine if the fluorophore deexcites via non-radiative energy loss (based upon its quantum yield), fluorescence, or energy transfer. If the result is energy transfer, the time and target of transfer is inserted into the excitation schedule along with all the incident photons so that it can be played out in sequence with the others. Once all excitation events from the incident laser of energy transfer have been played out, we repeat the entire process with a new randomly generated configuration of fluorophores. Finally, once the desired number of configurations have been tested, the average number of fluorescence, energy transfer, and non-radiative de-excitation events from each fluorophore type for each configuration are output for analysis.

FRET-modulated multi-hybrid nanoparticles

A B

Note: Average values (and the resulting errors) of both tables were used to calculate the FRET efficiencies presented in Figure 4.12e. The extinction spectra in water (Figure 7.4) remain stable, whereas in Tris-HCl and PBS some loss of nanoparticles occurred, in particular after 24 hours.

E FRET  AD1&2 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.
E FRET  AD1&2 0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.
Interestingly, the shapes of the spectra did not change, indicating that the disappearance is not due to nanoparticle aggregation but rather to nanoparticles sticking to the cuvette windows. We found that some material was lost by adhesion to the walls of the cuvette upon prolonged standing (24h and longer). This effect was most pronounced when using PBS. Tris-HCl buffer then was selected as the best solvent to work with the particles on a time scale of several hours. The average PL decay time of the donor-acceptor assemblies remains constant when excess biot-AuNPs is present, i.e. in the cases where only few Tb-sAv are attached to each biot-AuNP. In contrast, the PL decay becomes shorter when the density of Tb-sAv per biot-AuNPs is higher (conditions of excess Tb-sAv). We tentatively ascribe this to energy transfer interactions between Tb-complexes at the surface of the nanoparticles at high Tb-sAv loading levels. Another, less likely, explanation may be that a dense packing of Tb-sAv at the biot-AuNP surface changes the structure of the PEG-biotin ligand shell in such a way as to reduce the average distance between Tb complexes and AuNP surface. In order to avoid such effects, only the measurements at low loading (higher biot-AuNPs concentrations -where 〈𝜏〉 DA remains constant) are included in energy transfer analysis. In these cases we are approaching the idealized situation where one Tb-complex interacts purely with one AuNP. In all cases, the energy transfer efficiency was larger than 50%, but less than 95%, leaving some Tb(III) luminescence available for detection. In spite of the giant oscillator strengths of the localized plasmon resonance, luminescence quenching is incomplete, and incorporation of photoluminescent entities into assemblies of plasmonic particles for fluorescence tracking and sensing purposes remains feasible.

Synthèse en français

"

  Every science begins as philosophy and ends as art; it arises in hypothesis and flows into achievement." -Will Durant

Figure 1 . 1 .

 11 Figure 1.1. The imitative work of "The Persistence of Memory" (left) and the original painting by Salvador Dali (right).

Figure 1 . 2 .

 12 Figure 1.2. (a) QDs with SiO2 coatings of different thicknesses (x=6 or 12 nm) functionalized with Eu-1 or Lumi4-Tb for single-wavelength temporal PL barcoding. (b) The RGB encoding principle based on three distinct TG PL intensity fractions for each of the four FRET-specific PL decays and four encoded cells.

Figure 1 . 3 .

 13 Figure 1.3. FRET-modulated multi-hybrid nanoparticles for brightness-equalized singlewavelength barcoding.

Figure 1 . 4 .

 14 Figure 1.4. NSET Model using Tb labeled streptavidin (sAv) and biotinylated Au-NPs.

  ln10)𝜅 2 Φ D 128𝜋 5 𝑁 A 𝑛 4 𝜏 D 𝑅 6 𝐽 (2.3) Where Φ D is the luminescence quantum yield of D in absence of energy transfer, 𝑁 A is Avogadro's number (6.023 × 10 23 mol -1 ), and 𝜏 D is the luminescence lifetime of D.

Figure 2 . 1 .

 21 Figure 2.1. (Left) Basic FRET principle. In the Jablonski diagram (simplified energy level scheme), the donor is excited by hv from an electronic ground state (D) to an excited state (D*), and then goes to an excited electronic ground state by inner relaxation (vibrational and rotationaldotted arrow), and finally goes back to ground state by radiative decay (𝑘 R ), nonradiative decay (𝑘 NR ), or FRET (𝑘 FRET ). The FRET process happens when the difference between the respective energy levels are equal, in other words the donor and acceptor share the same electronic transitions (horizontal lines with dots on each end). After FRET, the acceptor is in an excited state (A*), then goes to its ground state (A) by radiative or nonradiative decay. (Right) The overlap (gray area) of the area normalized emission spectrum of D (cf. Equation 2.6) and the molar absorptivity spectrum of A (𝜀 A ) defines the overlap integral J (cf. Equation 2.5). (Adapted from reference [2]. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA)

Figure 2 . 1 (

 21 right) and given by Equation 2.5:𝐽 = ∫ 𝐼 D ̅ (𝜆)𝜀 A (𝜆)𝜆 4 d𝜆 (2.5)

Figure 2 . 2 .

 22 Figure 2.2. FRET dipole orientation factor 𝜅 2 can be calculated by orientation of the D emission transition dipole moment 𝜇 D , the A absorption transition dipole moment 𝜇 A and the D-A connection vector 𝑅 ⃗ ⃗ . (Reproduced from reference [3]. Copyright 2017 American Chemical Society)

Figure 2 . 3 ,

 23 FRET efficiency is most sensitive in a region between ca.0.5-2.0 𝑅 0 (yellow) and exhibits very steep curve in a region between ca. 0.7-1.3 𝑅 0 (green). FRET changes become extremely difficult to measure beyond this region (red).

Figure 2 . 3 .

 23 Figure 2.3. FRET efficiency as a function of the donor-acceptor distance (R) shows R -6 distance dependence and leads to a steep curve around 𝑅 0 . (Reproduced from reference [3]. Copyright 2017 American Chemical Society)

Figure 2 . 4

 24

  solved by attaching thioglycolic acid to the surface of QDs or by coating with hydroxyl group functionalized SiO2 shell, which successfully established a scientific foundation for the application in life science. The discussion below will focus on the optical properties (2.2.1) and surface functionalization (2.2.2) of QDs and examine how QD serves as FRET donor/acceptor/relay (2.2.3).

Figure 2 . 4 .

 24 Figure 2.4. Spectral range of the photoluminescent emission for the most widely studied types of semiconductor nanocrystals. (Reproduced from reference [17]. Copyright 2016 American Chemical Society)

  photobleaching and chemical degradation) provides powerful support for long-term real-time bioimaging. (vi) High multiphoton action cross sections allow excitation with NIR light to have deeper tissue penetration and decrease autofluorescence from the biological matrix. It has been reported high-resolution in vitro and in vivo imaging can be achieved by combining three-photon excitation of ZnS nanocrystals and visible emission from Mn 2+ dopants.[START_REF] Yu | High-Resolution Three-Photon Biomedical Imaging Using Doped ZnS Nanocrystals[END_REF]

Figure 2 . 5 .

 25 Figure 2.5. Top: Cartoon, photograph, and PL spectra illustrating progressive color changes of CdSe/ZnS QDs with increasing nanocrystal size. Bottom: Qualitative changes in QD energy levels with increasing nanocrystal size. Eg represent the bandgaps energies. Continuous conduction band (CB) and valence band (VB) of bulk semiconductor shown as comparison. (Reproduced from reference [18]. Copyright 2011 American Chemical Society)

Figure 2 . 6 .

 26 Figure 2.6. Schematic overview of different strategies for surface functionalization of QD: (i) ligand exchange, (ii) encapsulation, or (iii) silica coating chemistries. The center represents an assynthesized QD in organic solvent with its hydrophobic surface of organic ligands. (Reproduced from reference [3]. Copyright 2017 American Chemical Society)

Figure 2 . 7 .

 27 Figure 2.7. Comparative absorption and emission spectra of a hypothetical QD donor-dye acceptor (top) and dye donor-dye acceptor (bottom) FRET pair illustrating the photophysical differences between a QD donor and a dye donor (black dotted line: putative excitation lines). (Reproduced from reference [3]. Copyright 2017 American Chemical Society)

  (i) Lanthanide complexes usually possess a much longer excited-state lifetime compared to that of QDs, which can be measured by time-gated detection void of contribution of directly excited QDs. Hildebrandt and Charbonniere et al.demonstrated clear evidence for QDs to be used as FRET acceptors by combining them with Tb and Eu-complex donors.[START_REF] Hildebrandt | Quantum Dots as Efficient Energy Acceptors in a Time-Resolved Fluoroimmunoassay[END_REF],[START_REF] Charbonnière | Lanthanides to Quantum Dots Resonance Energy Transfer in Time-Resolved Fluoro-Immunoassays and Luminescence Microscopy[END_REF] Although such lanthanides complex need to be excited in the UV range, which leads to more efficient excitation of QDs, the 10 5 times longer excited state lifetimes of the lanthanide donors proved to be the key to unlocking QD acceptor based FRET. Time-gated detection after a sufficient delay time after the pulsed excitation allowed efficient detection of both lanthanide donor FRET-quenching and QD acceptor FRET-sensitization. (ii) Bioluminescent and chemiluminesent molecules as donors do not require light excitation. If bioluminescent or chemiluminescent molecules are used as donors in FRET, the phenomena are now referred to as bioluminescence or chemiluminescence resonance energy transfer (BRET or CRET), respectively. In 2006, Rao et al. demonstrated QDs acceptor-based BRET. They showed that mutagenically optimized Rluc and QDs can be used as BRET donor-acceptor for multicolor imaging in vitro and in deep tissues in living mice.[62] In the same year, Ren et al. demonstrated an efficient CRET between luminol and QDs and showed potential application of multiple QDs acceptors with different color to multiplex

Figure 2 . 8 .

 28 Figure 2.8. (a) Schematic presentation of FRET (arrows) and radiative (flashes) transitions and excited and ground state situations for a full FRET relay cycle after pulsed excitation. Steady-state (red) and time-gated (green, 55 μs) PL spectra of (b) pure QDs, (c) mTb-QD (time-gated FRET1 from Tb to QD), (d) nA647-QD (steady-state FRET2 from QD to A647), and (e) mTb-QD-nA647 (FRET relay).The black spectra show scaling of the steady-state PL spectrum to fit the time-gated PL spectrum. (Adapted from reference [3],[65]. Copyright 2017 American Chemical Society)

  mechanism and design of luminescent lanthanide complexes (LLCs) (2.3.1) and upconverting nanoparticle (UCNP) (2.3.2), and examine how lanthanide serves as FRET donor (2.3.3).

Figure 2 . 9 .

 29 Figure 2.9. A summary of ground and excited energy levels of Ln 3+ ions series. (Reproduced from reference [72]. Copyright 2009 American Chemical Society)

Figure 2 .

 2 10 (a), the general architecture of luminescent lanthanide complexes (LLCs) consists of the Ln 3+ center surrounded by a moiety that coordinates the central ion (lanthanide ion carrier chelate) and equipped with a sensitizing chromophore moiety (antenna ligand). The chelate serves to prevent the release of free Ln 3+ ions and to protect the Ln 3+ ions from quenching from vibrational energy dissipation by oscillators like O-H of water. For the antenna effect, a simplified Jablonski diagram shows the main energy migration pathways, the antenna harvests energy through high molar absorption to the ligand singlet excited state (S0  S1), and is generally assumed to first undergo intersystem crossing to the triplet state (S1  T1), followed by population of excited states of Ln 3+ through energy transfer from T1 state of the ligand, and finally characteristic luminescent emission from the Ln 3+ ion. A large ligand-induced Stokes shift should exist between ligand absorption and lanthanide emission in order to prevent back energy transfer which results in low quantum yields and short, temperaturedependent lifetimes.[73] Figure 2.10 (b) shows the transitions between the welldefined J-levels (degenerated from the electronic configuration based on Coulomb interaction and spin-orbit coupling) of Tb 3+ and Eu 3+ .

Figure 2 .

 2 11 represents the Tb complex (Lumi4-Tb) based on 2hydroxyisophthalamide ligands we used in this thesis bearing maleimide functional groups and having a molar absorption coefficient of ca. 26000 M -1 cm -1 at 340 nm.

Figure 2 .

 2 Figure 2.10. (a) Simplified Jablonski diagram for the antenna effect and the scheme of lanthanide complexes (the Ln center surrounded by a chelate and equipped with a sensitizing antenna). (b) Commonly observed emission wavelengths of europium (red) and terbium (green) complexes.

Figure 2 . 11 .

 211 Figure 2.11. Cage-like structure of the ligand for photon harvesting of the Lumi4-Tb complex used in this thesis. (Reproduced from reference [85]. Copyright 2011 American Chemical Society)

Figure 2 . 12 .

 212 Figure 2.12. Principal UC mechanisms of Ln 3+ : (a) ESA, (b) ETU, and UC energy transfer diagrams in (c) Yb 3+ -Er 3+ , (d) Yb 3+ -Ho 3+ , and (e) Yb 3+ -Tm 3+ pairs, (f) CET, (g) EMU. (Reproduced from reference [87]. Copyright 2015 American Chemical Society)

Figure 2 . 13 .

 213 Figure 2.13. Time-resolved decay curves of A with 𝜏 A = 0.001, 0.01, 0.1, 0.5, 1, 2, and 5 𝜏 D (black curves from bottom to top) for 𝐸 FRET =50% (a) and 95% (b). Pure donor decays (𝜏 D , dotted gray curves) and FRET quenched donor decays (𝜏 DA , gray curves) are shown for comparison. (Reproduced from reference [2]. Copyright 2013 Wiley-VCH Verlag GmbH & Co. KGaA)

Figure 2 . 14 .

 214 Figure 2.14. LTC as donor based multiplexed FRET. Top: Broad spectral overlap between LTC emission and the absorption of several different acceptors. Bottom: Well-separated PL spectra of LTC emission bands allows the detection of different acceptors with very low LTC background (represented by the shaded bandpass filter transmission spectra). LTC PL spectra in black. Left (organic dyes): Oregon Green (blue), AlexaFluor555 (green), AlexaFluor568 (orange), Cy5 (red) and AlexaFluor700 (wine); right (QDs): QD525 (blue), QD565 (green), QD605 (orange), QD655 (red), and QD705 (wine). (Reproduced from reference [94]. Copyright 2014 Elsevier)

Figure 2 . 15 .

 215 Figure 2.15. Examples of available fluorescent dye families. (Adapted from reference [97]. Copyright 2006 Wiley-VCH Verlag GmbH & Co. KGaA)

Figure 2 . 16 .

 216 Figure 2.16. Simplified schematic of exciton theory to explain the different absorption and fluorescence behaviors of H-aggregates and J-aggregates. (Reproduced from reference [99]. Copyright 2011 Wiley-VCH Verlag GmbH & Co. KGaA)

Figure 2 . 17 .

 217 Figure 2.17. Principle of TG measurement. (Reproduced from reference [83]. Copyright 2015 American Chemical Society)

Figure 2 . 18 .

 218 Figure 2.18. Principles of fluorescence lifetime measurement. (a) Time domain method, (b) Frequency domain method (Adapted from reference [157]. Copyright 2006 Annual Reviews)

Figure 2 . 19 ,

 219 2014, Chen et al. suggested that the lifetime of QDs can be regarded as an excellent parameter for designing optical encoding, and fabricated NIR-emitting two-dimensional(2D) codes based on multi-lifetime and multi-color.[140] As shown in NIR-emitting QDs with long lifetime (up to 1 µs) were synthesized by doping Cu into the lattice-strained core/shell nanostructure, and embedded into microbeads to fabricate NIR-emitting 2D codes. FLIM and multispectral imaging system were employed to recognize the codes. Lu et al. also realized that lifetimes can become a new dimension for optical encoding. They prepared UCNPs with a wide tunable lifetime range (µs-ms) and named them "τ dots".[137] Figure 2.20shows that tunable lifetime of UCNPs were achieved with stepwise varied Tm 3+ concentrations in NaYF4 host nanocrystals. In this case, energy transfer from the sensitizer to the activator ion at varying sensitizer-activator distances provides lifetime tunability. And they also demonstrated that these τ dots can be used in lifetime-encoded document security and photonic data storage. In a traditional luminescence imaging, only a complex picture can be observed, while in timeresolved imaging, the three patterns with different lifetime can be distinguished.Recently, Fan et al. reported that lifetime-engineering nanoparticles can unlock multiplexing in vivo imaging in the second biological window.[START_REF] Fan | Lifetime-Engineered NIR-II Nanoparticles Unlock Multiplexed in Vivo Imaging[END_REF] They shift the wavelength range of lifetime tunable nanoparticles to NIR, enabling them to reach deeper penetration depths.

Figure 2 .Figure 2 . 3 .

 223 Figure 2.19. (a) Synthesis of NIR-emitting QDs with tunable lifetime and principle of 2D encoding based on color(𝜆) and lifetime(𝜏). Large spheres represent microbeads, in which small colored spheres represent QDs (red: short τ, green: long τ, the size of spheres represents the different color). (b) Decoding using FLIM and multispectral imaging system (from top to bottom: FLIM images, lifetime distribution (inset: unmixed FLIM images), merged multispectral images, and emission spectra. Scale bar: 10 µm).(Adapted from reference [140]. Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA)

Figure 3 .

 3 Figure 3.1 (a) QDs with SiO2 coatings of different thicknesses (x=6 or 12 nm) functionalized with Eu-1 or Lumi4-Tb for single-wavelength temporal PL barcoding. (b) The RGB encoding principle based on three distinct TG PL intensity fractions for each of the four FRET-specific PL decays.

  SiO2 shells. Based on the different thicknesses of SiO2 shell, different PL decay times were obtained due to distance-dependent Lan-to-QD FRET. Distance-tuned PL decay times were selected for well-defined single nanoparticle codes. The principle of time-gated RGB encoding was illustrated in Figure 3.1b, based on the crossing of time-resolved decay curve between each single nanoparticle codes, three time-gated ranges were chosen and defined as red, green, and blue color, respectively. With the comparing and analysis of PL time-gated PL integral intensity in each channel, the RGB color images for each single nanoparticle code was obtained. Furthermore, the living cells encoding was demonstrated by incubating as-prepared single nanoparticle codes with the HeLa cells. To recognize the living cell codes, time-gated fluorescence microscopy system was employed. As a result, we could define the encoded cells according to the PL lifetime parameter in the QD acceptor detection channels.

Lumi4-

  Mal was dissolved to 3.8 mM in anhydrous DMF. 5.25 μL of Lumi4-Mal (3.8 mM), 162.5 μL of QD/SiO2 (6 nm or 12 nm, 1.23 μM), and 232.25 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in 0.5 mL eppendorf tube (Lumi4: QD/SiO2=100:1). The mixtures in alu foil were incubated for 3 h at room temperature. Intelli Mixer was employed for prewetting tubewalls by rotating the tube. Then the product was harvested by centrifugation (8000 r.p.m, 20 min) and redispersed in 400 μL Tris-HCl buffer at pH 7.5 (50 mM). The number of Lumi4 per QD/SiO2 was confirmed by absorbance spectrum (75 Lumi4 per QD/SiO2 (6 nm) and 87 Lumi4 per QD/SiO2 (12 nm)). For the formation of 100Tb-QD/SiO2 donoracceptor assemblies, Tb 3+ was dissolved to 100 µM in pure water. For the 200 nM 100Tb-QD/SiO2 codes, 80 µL of Lumi 4-QD/SiO2 (500 nM), 40 µL of Tb 3+ , and 80 µL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in 0.5 mL eppendorf tube (Tb:

- 1 -

 1 Mal was dissolved to 0.1 mM in pure water. 100 μL of Eu-1-Mal, 40.6 μL of QD/SiO2, and 359.4 μL Tris-HCl buffer at pH 7.5 (50 mM) were mixed in 1 mL eppendorf tube (Eu-1-Mal: QD/SiO2=200:1). The mixtures were incubated for 3 h at room temperature. An Intelli Mixer (ELMI) was employed to prewet the wall of the tube. Then the product was collected by centrifugation (8000 r.p.m, 20 min) and redispersed in 500 μL Tris-HCl buffer at pH 7.5 (50 mM). The number of Eu-1 per QD/SiO2 was confirmed by absorbance spectrum (175 Eu-1 per QD/SiO2 (6 nm) and 180 Eu-1 per QD/SiO2 (12 nm)).

F20 S -

 - Twin high-resolution transmission electron microscope (HR-TEM) operating at 200 kV. Absorption spectra were acquired using a Lambda 35 UV/Vis spectrophotometer (Perkin Elmer). Steady state PL spectra were acquired using a Xenius fluorescence plate reader (SAFAS). For the measurement of the PL decay curves of the Tb or Eu to QD/SiO2, an EI fluorescence plate reader (Edinburgh Instruments, UK) with 4000 detection bins of 2 μs integration time was used. A nitrogen laser (LTB, Berlin, Germany) was used for excitation (337.1 nm, 20 Hz, 600 flashes). (494/20) nm, (567/15) nm, and (640/14) nm bandpass filter were used for analyzing the Tb, Eu, and QD PL, respectively. For the measurement of the PL decay curves of the pure QD/SiO2 (6 nm) and QD/SiO2 (12 nm), a SuperChrome sources (Fianium, UK) was used for excitation (480 ± 15 nm, 5 MHz, Laser Power: 200). (640/14) nm bandpass filter were used for analyzing. The data were fit with FAST software version 3.1 (Edinburgh Instruments, UK). All assays were measured in black 96-well microtiter plates with an optimal working volume of 150 μL.

3. 3 . 1

 31 Characterization of Ln (Tb/Eu)-QD assemblies High resolution transmission electron microscopy (HRTEM, Figure 3.2) showed nearly monodisperse QDs with clearly defined SiO2 nanoshells of 6 nm and 12 nm thicknesses. Absorption and emission spectra of Lumi4-Tb, Eu-1, QD/SiO2 (6 nm) and QD/SiO2 (12 nm) were presented in Figure 3.3a. Both lanthanide complexes were excitable in the 300 to 400 nm wavelength region and their PL spectra overlapped well with the QD absorption spectra for efficient FRET (Figure 3.3b).

1 ).

 1 The maleimide functional Lumi4 and Eu-1 were conjugated with acceptor through sulfhydryl on the surface of SiO2 shell. UV-vis absorbance spectra were employed to calculate the number of lanthanide donors per QD acceptor. The absorbance spectra (Figure3.4), which presented linear combinations of QD-SiO2 and the lanthanide complexes, resulted in labeling ratios of ~75 Lumi4-Tb per QD/SiO2(6 nm), ~87 Lumi4-Tb per QD/SiO2(12 nm), ~175 Eu-1 per QD/SiO2(6 nm), and ~180 Eu-1 per QD/SiO2(12 nm). Approximate double amounts for Eu-1 were used to account for the lower brightness (lower extinction coefficient at the microscopy excitation wavelength of 349 nm and lower quantum yield) of Eu-1 compared to Lumi4-Tb. Due to the long PL lifetime of lanthanides, one QD can be sensitized by FRET from several lanthanide donors and therefore an increasing number of donors increases the

1 ms)

 1 were quenched to different extents. Because of the much shorter PL lifetime of the QDs (ns) compared to the lanthanide complexes (ms), the FRET-quenched PL decay times of the lanthanides equaled the FRET-sensitized PL decay times of the QDs.[3] Therefore, FRET led to distinct and long-lived QD decays (Figure 3.5)

Figure 3 . 5 .

 35 Figure 3.5. (a) Tb donor PL decay curve, (b) QD acceptor PL decay curve of Tb-QD/SiO2 FRETpairs. (c) Eu donor PL decay curve, (d) QD acceptor PL decay curve of Eu-QD/SiO2 FRET-pairs.

Figure 3 . 6 .

 36 Figure 3.6. (a) Steady-state PL spectra of Tb-QD/SiO2 (6 nm) (red), Tb-QD/SiO2 (12 nm) (blue), Eu-QD/SiO2 (6 nm) (yellow), and QD/SiO2 (12 nm) (green). (Filter green: 490/20 nm, filter yellow: 567/15 nm, and filter red: 640/14 nm). (b) Time-resolved PL decay curves of (left) pure Lumi4-Tb-Mal and Eu-1-Mal (in water) and (right) pure QD/SiO2 (6 nm) and QD/SiO2 (12 nm). (IRF: Instrument response function.)

  principle of TG RGB encoding is illustrated in Scheme 1b. Based on the intersections of the four distinct PL decay curves (Figure 3.7a), three temporally distinct TG PL intensity detection windows were selected and defined as red (R), green (G), and blue (B), respectively. One PL intensity (integrated over the time interval of the detection channel) is recorded for each channel. The different shapes of the decay curves (different PL lifetimes) result in distinct PL intensity combinations of the three detection channels R, G, and B. Thereby, each FRET-nanoparticle can be identified by a unique RGB ratio (ratios of TG PL intensities: R/(R+G+B), G/(R+G+B), and B/(R+G+B); Figure 3.7b and Table3.2). TG imaging uses the same three TG detection windows as de-fined by the decay curves and each camera pixel records three time-dependent intensities (R, G, and B) for each image. ImageJ was used to assign red, green, or blue color to the three detection channels and define a common intensity range (same minimum and maximum values for all channels). The resulting overlay images provide RGB codes (be-tween 0 and 255 for R, G, and B) for each pixel, which can then be transferred into RGB ratios and directly related to the four different FRET-nanoparticles. As a first evaluation of biocompatibility, the stability of the RGB codes was analyzed for the four different nanoparticles incubated in PBS buffer at different pH (5.3, 6.8, and 7.5) for 2h and 4h. TG PL intensity ratios of each code were nearly invariant (Figure3.8a), which provided first good evidence concerning compatibility of our temporal PL encoding approach with live cell imaging.

Figure 3 . 7 .

 37 Figure 3.7. (a) QD acceptor PL decay curves of each single nanoparticle code. (b) TG PL intensity (RGB) ratio of each single nanoparticle code calculated from the TG intensities in the red, green, and blue TG detection windows in a.

Figure 3 . 8 .

 38 Figure 3.8. (a) Stability of RGB color of the single nanoparticle codes in PBS buffer with different pH. (b) Cell viability data of MDA-MB231, 293T, and Hela cells incubated with (left) QD-SiO2 (6 nm) and (right) QD-SiO2 (12 nm) after 24 hours in various concentration (0, 25, 50, 100, 200, 400 and 800 nM).

  same microscopy slide. As shown in Figure 3.10, single-color (one excitation and one emission wavelength) TG imaging could efficiently distinguish the four types of cells within the same field of view. Again, the four RGB codes can be already distinguished by the naked eye (Figure 3.10d). However, for clarity and taking into account the different color impressions from screen to screen and from screen to paper, we retrieved the RGB codes from color selection within the overlay image and marked the different cells with colored arrows in the bright field images (Figure 3.10e). We noted that the RGB color of each code in this rather complex mixing environment exhibited less blue, which we assigned to quenching effects during the 8 h incubation time. Still, we could clearly distinguish the encoded cells via the ratios of TG PL intensities. Finally, to demonstrate the independence of PL intensity and probe concentration, different encoding nanoparticles were incubated at distinct concentration with HeLa cells and afterwards the cells were mixed. Adjusting brightness and contrast within the same field of view also allowed us to distinguish cells with significantly different PL intensities (Figure 3.11).

Figure 3 . 9 . 62 Figure 3 . 10 .

 3962310 Figure 3.9. TG PL images (top panels) and high resolution TG PL images (bottom panels) in different temporal detection windows (time-ranges on top), their overlay, and bright field (BF) images of HeLa cells labeled with individual nanoparticle codes. (a) Tb-QD/SiO2 (6 nm), (b) Tb-QD/SiO2 (12 nm), (c) Eu-QD/SiO2 (6 nm), (d) Eu-QD/SiO2 (12 nm). Scale bar (top right): 20 μm; ex: 349 nm; em: 640 nm.

Figure 3 . 11 .

 311 Figure 3.11. Time-gated PL images of Hela cells labeled with different single nanoparticle codes at different concentrations (red dot-dashed area: Tb-QD/SiO2 (6 nm), yellow dot-dashed area: Eu-QD/SiO2 (6 nm), green dot-dashed area: Eu-QD/SiO2 (12 nm). Scale bar: 20 μm.

  , B. Corry, L. Huang, N. Hildebrandt. FRET-Modulated Multihybrid Nanoparticles for Brightness-Equalized Single-Wavelength Barcoding. Journal of the American Chemical Society 2019, 141, 11123-11141.

  [START_REF] Algar | Concurrent Modulation of Quantum Dot Photoluminescence Using a Combination of Charge Transfer and Förster Resonance Energy Transfer: Competitive Quenching and Multiplexed Biosensing Modality[END_REF] However, none of these studies has systematically investigated all different combinations with a broad range of numbers of donors and acceptors and compared the experimental results with theoretical modelling. Such an extensive investigation would not only contribute to a full understanding of such complicated multi donor-acceptor energy transfer pathways on nanoparticles but also open the opportunity to use the models for calculating desired photophysical properties adapted to advanced fluorescence biosensing applications such as multiplexed or encoded detection.

  [START_REF] Chen | Single-Nanoparticle Cell Barcoding by Tunable FRET from Lanthanides to Quantum Dots[END_REF] Similar to the excitation-dependent brightness of QDs, one important drawback of temporal optical barcoding via time-gated (TG) FRET codes is the significant variation in brightness of the different codes, which can be in the order of 10 to 100 fold, depending on the selection of the distinguishable temporal coding windows. Multiple Tb donors and dye acceptors co-assembled to the same QD and a precise control of PL lifetimes and intensities have the potential to be used for designing multi-hybrid nanoparticles with brightness-equalized singlewavelength PL emission for temporal optical barcoding applied to single-contrast imaging. Thus, an extensive analysis of a multitude of donor-acceptor combinations on the same QD for a precise understanding of how the different FRET pathways lead to controlled photophysical properties is not only of fundamental interest for multi-donor-acceptor FRET on nanoparticle surfaces. It also provides the necessary knowledge of optimizing such multi-FRET nanoparticles for advanced multiplexed biosensing in both fluorescence spectroscopy and microscopy.

Figure 4 . 1 .

 41 Figure 4.1. Concept of FRET-modulated multi-hybrid NPs. (a) Schematic illustration of the four multi-donor-acceptor FRET systems. (b) Design and principle of brightness-equalized multi-hybrid NP for PL lifetime barcoding.

  ~191 Lumi4 per QD, 42 μL of Lumi4-Mal (3.8 mM in anhydrous DMF), 162.5 μL of QD (1.23 μM), and 195.5 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube (molar ratio of Lumi4/QD = 800:1). For ~136 Lumi4 per QD, 10.5 μL Lumi4-Mal (3.8 mM in anhydrous DMF), 162.5 μL QD (1.23 μM), and 227 μL Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube (molar ratio of Lumi4/QD = 200:1). For ~50 Lumi4 per QD, 3.7 μL of Lumi4-Mal (3.8 mM in anhydrous DMF), 162.5 μL of QD (1.23 μM), and 233.8 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube (molar ratio of Lumi4/QD = 70:1). The mixtures were incubated for 3 h at room temperature with the tube covered in aluminum foil and rotating with an Intelli Mixer (ELMI). Then the product was collected by centrifugation (10,000 r.p.m, 10 min) and redispersed in 400 μL Tris-HCl buffer at pH 7.5 (50 mM). The number of Lumi4 per QD was determined by UV/Vis and TG PL spectroscopy. For the formation of mTb-QD FRET assemblies with constant QD concentration, we used two different constant concentrations of Lumi4-QD (0.5 nM and 5 nM). Tb 3+ was used at concentrations of 0.5 µM and 5 µM in pure water. For the 20 to 1000 Tb per QD in solution series, a QD concentration of 0.5 nM (in Tris-HCl buffer at pH 7.5, 50 mM) was used. For the total measuring volume of 150 µL, 15 μL of QD solutions (5 nM) were mixed with 135 µL of solutions containing increasing amounts (3, 7.5, 15, 22.5, 30, 37.5, 45, 52.5, 60, 67.5, 75, 82.5, 90, 97.5, 105, 112.5, 120, 135 μL of Tb 3+ (0.5 µM) and 15 μL of Tb 3+ (5 μM)) in pure water. The mixtures were incubated while slowly shaking for 1 h at room temperature. For the 0 to 300 Tb per QD in solution series, a QD concentration of 5 nM (in Tris-HCl buffer at pH 7.5, 50 mM) was used. For the total measuring volume of 150 µL, 15 μL of QD solutions (50 nM) were mixed with 135 µL of solutions containing increasing amounts (0, 1.5, 3, 7.5, 15, 30, 75 μL of Tb 3+ (0.5 µM) and 15, 22.5, 30, 37.5, 45 μL of Tb 3+ (5 μM)) in pure water. The mixtures were incubated while slowly shaking for 1 h at room temperature. For the 0 to 300 Tb per QD in solution series, a QD concentration of 5 nM (in Tris-HCl buffer at pH 7.5, 50 mM) was used. For the total measuring volume of 150 µL, 15 μL of QD solutions (50 nM) were mixed with 135 µL of solutions containing increasing amounts (0, 1.5, 3, 6, 12, 15, 22.5, 30, 45, 60, 75, 90 μL of Tb 3+ (0.5 µM) and 10.5, 12, 13.5, 15, 22.5, 30, 37.5, 45 μL of Tb 3+ (5 μM)) in pure water. The mixtures were incubated while slowly shaking for 1 h at room temperature.

4. 2 . 9

 29 Formation of FRET system 3 (mTb-QD-15Cy5.5) For the total incubation volume of 400 µL, 6.6 μL of Cy5.5-Mal (0.454 mM), 5.2 μL of Lumi4-Mal (3.8 mM), 162.5 μL of QD (1.23 μM), and 225.7 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube. The mixtures were incubated for 3 h at room temperature with the tube covered in aluminum foil and rotating with an Intelli Mixer. Then the product was collected by centrifugation (10,000 r.p.m, 10 min) and redispersed in 400 μL pure water. The number of Cy5.5 and Lumi4 per QD was confirmed by UV/Vis spectroscopy. For the formation of mTb-QD-15Cy5.5 FRET assemblies, we used constant concentrations of QD-15Cy5.5 (5 nM) for the experiments. Solutions of 50 nM QD-15Cy5.5 and 0.5 µM 5 µM, and 50 µM Tb 3+ in pure water were used. For the total incubation volume of 150 µL, 15 μL of QD-15Cy5.5 solutions (50 nM) were mixed with 135 µL of solutions containing increasing amounts (1.5, 3, 6, 12, 15, 22.5, 30, 45, 60, 75, 90 μL) of 0.5 µM Tb 3+ , (10.5, 12, 13.5, 15, 22.5, 30, 37.5, 45, 60, 75, 90 μL) of 5 µM Tb 3+ and (10.5, 12, 13.5, 15 μL) of 50 µM Tb 3+ in pure water. The mixtures were incubated while slowly shaking for 1 h at room temperature.

4. 2 . 5 )

 25 10 Formation of FRET system 4 (75Tb-QD-nCy5.For the total incubation volume of 400 µL, 5.2 μL of Lumi4-Mal (3.8 mM), 162.5 μL of QD (1.23 μM), and 232.3 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube. The mixtures were incubated for 3 h at room temperature with the tube covered in aluminum foil and rotating with an Intelli Mixer. Then the product was collected by centrifugation (10,000 r.p.m, 10 min) and redispersed in 400 μL Tris-HCl buffer at pH 7.5 (50 mM). The number of Lumi4 per QD was confirmed by UV/Vis spectroscopy. For the formation of 75Tb-QD, 2.44 μL of Tb 3+ (5 mM) were added (molar ratio of Tb 3+ per QD = 150:1). For the formation of 75Tb-QD-nCy5.5 FRET assemblies, the total incubation volume of 200 µL contained 20 μL of 75Tb-QD (500 nM) and

4. 2 .

 2 11 Fabrication of FRET-modulated multi-hybrid nanoparticles for brightness-equalized single-wavelength barcoding. For the total incubation volume of 400 µL of mTb-QD, 2.6 μL of Lumi4-Mal (3.8 mM), 81.3 μL of QD (1.23 μM), and 316.1 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube. For the total incubation volume of 400 µL of mTb-QD-10Cy5.5, 2.2 μL of Cy5.5-Mal (0.454 mM), 2.6 μL of Lumi4-Mal (3.8 mM), 81.3 μL of QD (1.23 μM), and 313.9 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube. For the total incubation volume of 400 µL of mTb-QD-40Cy5.5, 8.8 μL of Cy5.5-Mal (0.454 mM), 2.6 μL of Lumi4-Mal (3.8 mM), 81.3 μL of QD (1.23 μM), and 307.3 μL of Tris-HCl buffer at pH 7.5 (50 mM) were mixed in a 0.5 mL Eppendorf tube. The mixtures were incubated for 3 h at room temperature with the tubes covered in aluminum foil and rotating with an Intelli Mixer. Then the products were collected by centrifugation (10,000 r.p.m, 10 min) and redispersed in 400 μL pure water. The number of Cy5.5 and Lumi4 per QD were confirmed by UV/Vis and TG PL spectroscopy. For formation of mTb-QD-nCy5.5 FRET assemblies with n = 0, 10, or 40, Lumi4-QD-nCy5.5, solutions of 50 nM and Tb 3+ solutions of 0.05 µM, 0.5 µM, and 5 µM in pure water were used. For the total incubation volume of 150 µL, 15 μL of QD-nCy5.5 solutions (50 nM) were mixed with 135 µL of solutions containing increasing amounts (15, 30, 60 μL) of 0.05 µM Tb 3+ , (12, 15, 22.5, 30, 45, 60, 75, 90 μL) of 0.5 µM Tb 3+ , and (10.5, 12, 13.5, 15, 22.5, 30, 37.5, 45 μL) of 5 µM Tb 3+ in pure water. The mixtures were incubated while slowly shaking for 1 h at room temperature.

10Cy5. 5 ,

 5 and 60Tb-QD-40Cy5.5 were selected. For each microbead encoding, 5 µL of microbeads (Pierce Iminobiotin Agarose Microbead, Thermo Scientific) were mixed with 100 µL (50 nM) of each single-nanoparticle code. After purification by centrifugation, the microbeads were dispersed in 200 µL pure water in an 8chamber glass slide (Nunc® Lab-Tek® II Chamber Slide™, 155409) for imaging.Images of microbeads encoding were acquired using a wide-field, TG luminescence inverted microscope (Olympus IX71) that uses a UV laser (349 nm, 100 Hz, Nd:YLF, Triton, Spectra Physics) for pulsed excitation and an intensified CCD camera (ICCD, PI-MAX3, Princeton Instruments) for gated detection. QD PL signals were detected using a 639±10 nm bandpass filter. Acquisition settings (Winview software controlling the camera) were adjusted to optimal conditions regarding RGB ratio and were fixed to a delay time of 50 μs (after the excitation pulse) and a gate width of 450 μs (red window -R), a delay time of 500 μs and a gate width of 500 μs (green window -G), and a delay time of 1 ms and a gate width of 3 ms (blue window -B). ImageJ was used to assign red, green, or blue color to the three detection windows and define a common intensity range (same minimum and maximum values for all windows).

F20 S - 1 (

 -1 Twin high-resolution transmission electron microscope (HR-TEM) operating at 200 kV. Absorption spectra were acquired using a Lambda 35 UV/Vis spectrophotometer (Perkin Elmer). Steady-state PL spectra were acquired using a Xenius fluorescence spectrometer (SAFAS). PL decay curves of FRET system 1 (mTb-QD), FRET system 3 (mTb-QD-15Cy5.5), and FRET system 4 (75Tb-QD-nCy5.5) were recorded in multi-channel scaling mode with a time-resolved fluorescence plate reader (Edinburgh Instruments) with 4000 detection bins of 2 μs integration time. A nitrogen laser (LTB) was used for excitation (337.1 nm, 20 Hz, 600 flashes). 494/20 nm (Semrock), 640/14 nm (Semrock), and 707/16 nm (Delta) bandpass filters were used for analyzing the Tb, QD, and Cy5.5 PL, respectively. For the measurement of the PL decay curves of FRET system 2 (QD-nCy5.5), a SuperChrome supercontinuum source (Fianium) was used for excitation (480 ± 15 nm, 5 MHz, indicated laser power: 255) and the time-resolved fluorescence plate reader (Edinburgh Instruments) was used in TCSPC mode. 640/14 nm and 707/16 nm bandpass filters were used for analyzing the QD and Cy5.5 PL, respectively. PL decay data was fit with FAST software version 3.Edinburgh Instruments). All samples were measured in black 96-well microtiter plates with an optimal working volume of 150 μL.

Equations 4 .4 and 4. 5 .

 45 𝐽 = ∫ 𝐼 ̅ D (𝜆)𝜀 A (𝜆)𝜆 4 d𝜆 (4.4)

[ 2 ],[ 3 ],[ 8 ] 76 4. 2 .

 238762 15 Multi-exponential PL decay analysis PL decay curves of FRET-sensitized QD or Cy5.5 PL were fit using a multiexponential PL intensity decay function (Equation 4.13). 𝐼 = 𝐴 [∑ 𝛼 ADi * exp (-𝑡/𝜏 ADi )] + 𝐵 exp (-𝑡/𝜏 D ) (4.13) where A is the total amplitude and 𝛼 ADi * are the amplitude fractions (∑ 𝛼 ADi * = 1) of the different FRET contributions with FRET-sensitized PL decay times 𝜏 ADi . Amplitude B and decay time D correspond to the contribution of unquenched Tb donor PL (due to spectral crosstalk in the QD detection channel). The amplitudes must be further corrected by FRET rates (Equation 4.14a) to take into account the FRET efficiency-dependent excitation of the acceptor (Equation 4.14b).[2] PL decay time averaging was then performed using amplitude weighted average decay times (Equation 4.14c).

  of FRET-quenched QD PL were fit using a multiexponential PL intensity decay function (Equation 4.15). 𝐼 = 𝐶 [∑ 𝛾 DAi exp (-𝑡/𝜏 DAi )] (4.15) where C is the total amplitude and 𝛾 DAi are the amplitude fractions (∑ 𝛾 DAi = 1) of the different FRET contributions with FRET-quenched PL decay times 𝜏 DAi . PL decay time averaging was performed using amplitude weighted average decay times (Equation 4.16). 𝜏 DA = ∑ 𝛾 DAi 𝜏 DAi (4.16)

Figure 4 . 1 )Figure 4 . 2 ).

 4142 , which consisted of a circa 7 nm diameter CdSe/CdS/ZnS core/shell/shell QD emitting at 620 nm and a 7±2 nm thick SH-functionalized SiO2 shell (cf. Control over the number of Tb donors and/or Cy5.5 acceptors (cf. Figure 4.3 for chemical structures) assembled to the central QD was extremely important for an extensive characterization of FRET over a large range of numbers of Tb and Cy5.5 per QD. Both, Tb and Cy5.5 contained maleimide groups for attachment to the SH-functionalized SiO2 shells of the QDs. The separation of absorption (via the Lumi4 ligand) and emission (via the central Tb 3+ ion) of the supramolecular Lumi4-Tb complex (the entire complex is denoted as "Tb" throughout the manuscript -cf.

Figure 4 . 1 )

 41 Figure 4.1) provided a particular advantage because without the central Tb 3+ ion the ligands were not luminescent and could not contribute to FRET. Thus, we could conjugate a constant number of ligands (between ca. 50 and 190) per QD, which was quantified by UV/Vis absorption and time-gated PL spectroscopy (Figure 4.4), and add the Tb 3+ ions in a second step via addition of TbCl3 to the ligand-coated QDs. The advantage of this two-step procedure was the much simpler control of the number of actual Tb donors (addition of Tb 3+ that coordinates to the Lumi4 ligand) with only one QD-functionalization and separation step (attachment of maleimide-activated ligand to the thiols of the QD SiO2 shell and separation of free ligands). Only a Tb 3+ ion coordinated inside a ligand (and neither the Tb 3+ nor ligand alone) resulted in a functional luminescent Tb donor on the QD and thus, the number of Tb per QD could be simply adjusted and calculated via the concentrations of TbCl3 and QD and taking into account a ratio of ~1.5 Tb 3+ per Lumi4 ligand (because coordination by titration is not quantitative). This ratio of 100% Tb coordination into the ligand was determined by titrating TbCl3 into a solution of Lumi4 ligands and measuring the Tb PL intensity (at 550 nm) upon ligand excitation (at 337 nm). PL saturation occurred at 1.5±0.2 Tb 3+ per ligand (Figure 4.5). Therefore, the amount of m Tb per QD equaled the amount of Tb 3+ in solution divided by 1.5. The amount of n Cy5.5 per QD was calculated by the respective concentrations of Cy5.5 and QD used for fabricating the QD-Cy5.5 assemblies and assuming a ~100 % attachment efficiency (all maleimidefunctionalized Cy5.5 added to a QD solution attached to the QD surface). The ~100% surface functionalization efficiency was confirmed by measuring the Cy5.5 and QD concentrations of QD-nCy5.5 conjugates (after separation of QD-nCy5.5

Figure 4 . 2 .

 42 Figure 4.2. TEM images of QD/SiO2 NPs and determination of SiO2 shell thickness of 7±2 nm (calculated from 96 QD/SiO2 NPs from the right TEM image).

Figure 4 . 3 .

 43 Figure 4.3. Chemical structures of maleimide-functionalized Lumi4-Tb (top left) and Cyanine5.5 (top right) and changes in absorption (dotted) and PL (straight) spectra of Cyanine5.5 in water (black) and attached to QDs in Tris-HCl buffer at pH 7.5 (bottom). The spectra of Lumi4-Tb do not change upon attachment to QDs.

Figure 4 . 4 . 80 Figure 4 . 5 .

 448045 Figure 4.4. Absorption (a) and PL (b to d -TG Tb PL in the top graphs and TG QD PL in the bottom graphs) spectra used to analyze the number of Lumi4 ligands per QD. Absorption spectra use the difference between Lumi4-coated QDs and pure QDs and the extinction coefficients of Lumi4 (at 340 nm) and QD (at 610 nm) to calculate the Lumi4 per QD ratios (given inside the graph). The same samples were used for PL titration experiments (Tb 3+ ions were added to the Lumi4-coated QDs) and the saturation points of the Tb and QD PL curves were divided by 1.5 (saturation of Lumi4 with Tb 3+ -cf. Figure S4) to verify the number of Lumi4 per QD. Both approaches were used to estimate Lumi4 per QD ratios (average ± 10%) of 50±5, 136±14, and 191±19, respectively.

Figure 4 . 6 .

 46 Figure 4.6.Absorption spectra of QD (red) and 52±7 Lumi4 and 15±2 Cy5.5 per QD (purple). We note that Cy5.5 has a weak absorption at 340 nm (εCy5.5≤10,000 M -1 cm -1 ), which was subtracted when calculating the number of Lumi4 per QD on mTb-QD-nCy5.5 nano-hybrids.

5 ( 5 - 4 . 6 ,

 5546 Figure 4.7a) show spectral overlap between the different luminescent components. Thus, spectral overlap integrals (J) and Förster distances (R0) were calculated for each individual FRET pair (Figure 4.7b and Table 4.1). Details and equations concerning the calculations are given in the Experimental Section (Equations 4.1 to 4.5). The large Forster distance for the initial Tb-QD FRET pair (R0 = 9.7±0.7 nm) was caused by the very strong absorption of the QD across the almost entire PL emission range of the Tb donor. However, also the other FRET pairs showed significantly large Forster distances of 5.7±0.4 nm (Tb-Cy5.5), 6.0±0.4 nm (QD-Cy5.5), and 6.2±0.4 nm (Cy5.5-Cy5.5). Even QD-QD (R0 = 7.4±0.5 nm) and Cy5.5-QD (R0 = 1.9±0.1 nm) could function as FRET pairs. However, QDs were not in close enough distance to each other to engage in FRET and the Cy5.5-QD Förster distance was too short for efficient FRET. It is important that the initial FRET step from Tb to QD is much more efficient than FRET from Tb to Cy5.5 (~24-fold higher FRET rate when considering equal distances between Tb and QD and Tb and Cy5.Equation Experimental Section) to avoid significant energy transfer from Tb to Cy5.5 even at high loading ratios. Another FRET pathway to take into account is homo-FRET between Cy5.5 dyes at high loading ratios. Both Tb-to-Cy5.5 and Cy5.5-to-Cy5.5 FRET were taken into consideration for the Monte-Carlo simulations. Other important PL properties of the FRET nanohybrids were the molar absorptivities or extinction coefficients (), PL quantum yields (), PL lifetimes (), and band pass wavelength ranges of the filters used for detecting Tb, QD, and Cy5.5 PL (Table 4.1 and Supporting Figure 4.8 and 4.9).

Figure 4 . 7 .

 47 Figure 4.7. (a) Absorption (dashed lines) and PL (solid lines) spectra of Tb (green), QD (red), and Cy5.5 (blue). (b) Spectral overlap functions for the Tb-QD, QD-Cy5.5, Tb-Cy5.5, Cy5.5-Cy5.5, QD-QD, and Cy5.5-QD FRET pairs.

Figure 4 . 8 .

 48 Figure 4.8. PL decay curves of Tb (left, ⟨τ⟩ ~ 2.7 ms, λex = 337.1 nm, λem = 494±12 nm), QD (center, ⟨τ⟩ ~ 8 ns, λex = 480 nm, λem = 639±10 nm) and Cy5.5 (right, ⟨τ⟩ ~ 1 ns, λex = 660 nm, λem = 708±8 nm). IRF: Instrument response function.

Figure 4 . 9 .

 49 Figure 4.9. Spectra of band pass filters for Tb (green), QD (red), and Cy5.5 (blue) and a representative Tb-QD-Cy5.5 PL emission spectrum (purple).

4. 3 . 3 FRET system 1 :Figure 4 .

 3314 mTb-QDThe unique feature of this FRET system was the ability to first conjugate the antenna ligands to the QD and then add Tb 3+ ions in different amounts, thereby investigating a very large range of Tb donor per QD acceptor ratios (m). To estimate a maximum loading ratio of Lumi4 ligands per QD, we prepared three batches with 70:1, 200:1, and 800:1 molar ratios of ligand per QD, which resulted in 50±5, 136±14, and 191±19 Lumi4 per QD (Figure4.4), respectively. Owing to the strong decrease of labeling efficiencies of 71 % and 68 % for the first two batches to 24 % for the third batch, we did not further increase the initial molar ratio and used these three batches (with 191 Lumi4 per QD as maximum labeling ratio) for the mTb-QD FRET investigations. PL titration experiments (4b to d) of the Lumi4 coated QDs with Tb 3+ ions revealed that the lowest labeling ratio (50 Lumi4 per QD) resulted in complete saturation of the PL upon saturation of the ligands with Tb ions, whereas the samples with 136 and 191 Lumi4 per QD showed a continuous (linear) increase of PL intensities even after saturation. This phenomenon was stronger for the samples with 191 Lumi4 per QD and was attributed to a more difficult complete saturation of the Lumi4 ligands, which were attached at high density to the QDs.

Figure 4 . 10 .

 410 Figure 4.10. FRET system 1 (mTb-QD): Selected PL decay curves (cf. Appendix Figure 7.2 for all curves) of Tb FRET donor (a) and QD FRET acceptor (b) at different Tb per QD ratios (only the curves for 191 Lumi4 ligands per QD are shown). (c) FRET efficiency as function of m for experimental (determined by PL decay times from experiments with 136 and 191 Lumi4 ligands per QD -Appendix Tables 7.1 and 7.2) and simulation (MCS) results. (d) TG (0.1-0.9 ms) intensity ratios (normalized FRET ratio: ym(norm) = [ym -y(min)] / [y(max) -y(min)]) as function of m for experimental (with 50, 136, and 191 Lumi4 ligands per QD) and simulation (MCS) results. Note: m corresponds to "Tb per QD in solution" divided by 1.5, which is the necessary ratio of Tb 3+ ions per Lumi4 ligand to accomplish ~100% Tb 3+ -to-ligand coordination (cf.Figure 4.5).

Figure 4 .

 4 Figure 4.10. FRET system 1 (mTb-QD): Selected PL decay curves (cf. Appendix Figure 7.2 for all curves) of Tb FRET donor (a) and QD FRET acceptor (b) at different Tb per QD ratios (only the curves for 191 Lumi4 ligands per QD are shown). (c) FRET efficiency as function of m for experimental (determined by PL decay times from experiments with 136 and 191 Lumi4 ligands per QD -Appendix Tables 7.1 and 7.2) and simulation (MCS) results. (d) TG (0.1-0.9 ms) intensity ratios (normalized FRET ratio: ym(norm) = [ym -y(min)] / [y(max) -y(min)]) as function of m for experimental (with 50, 136, and 191 Lumi4 ligands per QD) and simulation (MCS) results. Note: m corresponds to "Tb per QD in solution" divided by 1.5, which is the necessary ratio of Tb 3+ ions per Lumi4 ligand to accomplish ~100% Tb 3+ -to-ligand coordination (cf.Figure 4.5).

Figure 4 . 5 )..1 and 7 . 2 )

 4572 Figure 4.5). Although m ranged from 1 to 670, the PL saturated at approximately 1.5 times the number of ligands (Figures 4.4b to d), which means that the actual maximum amount of luminescent Tb (Tb 3+ coordinated to the Lumi4 ligand) on the QD was limited by the number of ligands. Addition of Tb 3+ beyond ligand saturation did not lead to a further increase of the PL intensity (or only small continuous increase due to a more difficult ligand saturation for the two systems with 136 and 191 ligands -vide supra). Because the concentrations of Tb increased and the concentration of QDs was constant, both PL intensities of Tb and QD increased with increasing m. PL decay time analysis (Appendix Table 7.1 and 7.2) revealed a constant FRET efficiency of EFRET = 0.69±0.03 for all m, which was in almost perfect agreement with the MCS results (Figure 4.10c), and an average Tb-QD distance (Equation 4.8) of 8.5±0.6 nm. The independence of EFRET from the number of donors is in agreement with previously proposed theoreticalapproaches.[START_REF] Berney | FRET or No FRET: A Quantitative Comparison[END_REF],[START_REF] Deplazes | Flexible Tool for Understanding FRET in Complex Geometries[END_REF],[START_REF] Raicu | Efficiency of Resonance Energy Transfer in Homo-Oligomeric Complexes of Proteins[END_REF]

Figure 4 . 11 .

 411 Figure 4.11. FRET system 1 (mTb-QD): Time-gated (0.1-0.9 ms) intensity ratios ((normalized FRET ratio: ym(norm) = ym / y(min)) as function of m (with 50, 136, and 191 Lumi4 ligands per QD). Inset shows the region of m<70. Note: m corresponds to "Tb per QD in solution" divided by 1.5, which is the necessary ratio of Tb 3+ ions per Lumi4 ligand to accomplish ~100% Tb 3+ -to-ligand coordination (cf.Figure 4.5).

Figure 4 . 5 .

 45 Figure 4.11. FRET system 1 (mTb-QD): Time-gated (0.1-0.9 ms) intensity ratios ((normalized FRET ratio: ym(norm) = ym / y(min)) as function of m (with 50, 136, and 191 Lumi4 ligands per QD). Inset shows the region of m<70. Note: m corresponds to "Tb per QD in solution" divided by 1.5, which is the necessary ratio of Tb 3+ ions per Lumi4 ligand to accomplish ~100% Tb 3+ -to-ligand coordination (cf.Figure 4.5).

Figure 4 . 3 ).

 43 When taking into account that the optically active CdSe core of the QD (approximated as a sphere) has a radius of 1.8 nm, the total CdSe/CdS/ZnS has a radius of 3.5 nm, and the SiO2 shell has a thickness of 7±2 nm, the Tb donors and Cy5.5 acceptors should be positioned on the surface of a sphere with a radius of 9.4±1.5 nm and 8.8±1.5 nm, respectively (Figure4.13). These distance estimations lead to the deduction that a significant fraction of Tb and Cy5.5 must be positioned inside the SiO2 shell. This conclusion is not unrealistic because both the porosity of the outer SiO2 layers and the non-spherical shape on the entire QD can lead to closer and further distances than estimated by the ideal spherical model.

Figure 4 . 12 .

 412 Figure 4.12. FRET system 2 (QD-nCy5.5): Selected PL decay curves (cf. Appendix Figure 7.3 for all curves) of (a) QD FRET donor and (b) Cy5.5 FRET acceptor. Steady-state FRET-quenching of (c) QD donor PL and (d) FRET-sensitization of Cy5.5 PL (enlargement of Cy5.5 contribution from the spectra in (c)). (e) FRET efficiencies as a function of n calculated theoretically (gray dotted curves), from QD PL decays ((a) and Appendix Table7.3), from QD PL intensities ((c) and Appendix Table7.4), and MCS. (f) FRET-quenched QD PL intensity (blue) and FRET-sensitized Cy5.5 PL intensity (red) as a function of n for experimental (full symbols) and MCS data (hollow symbols). The gray curve presents a reduced MCS model that did not take into account the decreasing spectral overlap with increasing n.

Figure 4 .

 4 14), which is characteristic of H-dimers.[START_REF] Sauer | Handbook of Fluorescence Spectroscopy and Imaging[END_REF] On the other hand, the increase was rather weak, which means that only a small fraction of dyes formed non-fluorescent dimers. This finding is reasonable because the dyes were directly attached to the SiO2 coating of the QDs without further linkers or biomolecules (e.g., peptides or DNA), which should limit dye-dye dimerization and favor monomeric dyes. Therefore, a large fraction of the strong PL intensity decrease of ~95 % from n = 8 to n = 60 must have been caused by homo-FRET. Homo-FRET does not lead to changes in PL lifetime or intensity and such non-directional energy migration between identical dyes can only be detected by fluorescence anisotropy.[START_REF] Levitt | Fluorescence Lifetime and Polarization-Resolved Imaging in Cell Biology[END_REF]-[START_REF] Yan | Analysis of Protein Interactions Using Fluorescence Technologies[END_REF] On the other hand, the migration of an exciton in a random manner over many dye-to-dye homo-FRET steps increases the probability (compared to a stationary exciton) of encountering a dark or trap state (e.g., a non-fluorescent H-dimer), which leads to fluorescence quenching. In multi-dye systems (densely packed or aggregated dyes)

into account by reducing the Cy5. 5 -Figure 4 . 15 ).

 5415 Cy5.5 Förster distance from R0 = 6.2 nm to R0 = 5.8 nm in the MCS model. Second, the blue shift (hypsochromic shoulder increases and bathochromic peak decreases) of the Cy5.5 absorption and red shift of the Cy5.5 emission (Figure 4.12d) with increasing n resulted in a decreasing spectral overlap with increasing n. In the model, each energy transfer event involves some degree of energy loss making future transfer more difficult due to worsening the spectral overlap. The MCS kept track of how many times a packet of energy had undergone homo-FRET and reduced the transfer probability for future homo-FRET by 50 %. Although reduced overlap effect has little influence for small number of n, it is more significant for larger n (gray compared to red simulation curves in Figure 4.12f), for which the chance of multiple homo-FRET events is greater. The MCS results were in excellent agreement with the experimental data (red curves in Figure 4.12f). Förster distance, sphere radius, and probability of trap state encounter per homo-FRET step could be easily changed in the MCS input parameters and allowed to evaluate the influence of these properties on the probability of FRET-sensitized Cy5.5 emission (The comparison of experimental and simulation data for up to 60 dyes per QD explained very well the quenching of FRET-sensitized acceptor PL at high loading ratios by a combination of homo-FRET and non-radiative deactivation by non-fluorescent h-dimers and is an important result for a better understanding of such multiple-acceptor FRET systems.

Figure 4 . 13 . 91 Figure 4 . 14 .

 41391414 Figure 4.13. Estimation of Tb donor and/or Cy5.5 acceptor positions on the SiO2-coated CdSe/CdS/ZnS QD when approximated as an ideal spherical model and taking into account the results from Tb-to-QD and QD-to-Cy5.5 FRET.

Figure 4 . 15 .

 415 Figure 4.15. FRET system 2 (QD-nCy5.5): MCS results showing the probability of FRET-sensitized Cy5.5 PL as a function of n for (a) changing R0 (Cy5.5-Cy5.5 Förster distance), (b) changing sphere radius (sphere on which surface the Cy5.5 dyes are situated), and (c) changing probability of trap state encounter (TS). Only a 0% probability of trap state encounter allows for a constant increase in Cy5.5 sensitization with increasing n.

system 3

 3 was realized by co-labeling 52±7 Lumi4 ligands and 15±2 Cy5.5 on the SiO2 coating of the QDs. Similar to FRET system 1, the varying amount of Tb (m) was accomplished by adding increasing amounts of Tb 3+ ions to the Lumi4-QD-15Cy5.5 conjugates (Tb per QD-15Cy5.5 in solution) and taking into account a 1.5 Tb/Lumi4 saturation to calculate m.

Figure 4 . 16 .

 416 Figure 4.16. FRET system 3 (mTb-QD-15Cy5.5): Selected PL decay curves (cf. Appendix Tables 7.6 to 7.8 for complete data) of Tb FRET donor (a), QD FRET acceptor/donor (b), and Cy5.5 FRET acceptor (c) at different Tb per QD-15Cy5.5 ratios. (d) FRET efficiencies as function of m determined by PL decay times of the Tb initial donor (green), the QD acceptor/donor (red), and the Cy5.5 final acceptor (blue). (e) TG (0.1-0.9 ms) intensities (normalized intensity: ym(norm) = [ymy(min)] / [y(max) -y(min)]) as function of m for Tb, QD, and Cy5.5. FRET ratios of TG PL intensities of QD and Tb (brown), Cy5.5 and QD (magenta), and Cy5.5 and Tb (orange) as a function of m and normalized to unity for the maximum FRET ratio (f) or at the smallest value of m (g).

  to c), it becomes clear that the long PL lifetime of FRET-quenched Tb can be used to FRET-sensitize Cy5.5 via the central QD. The PL decay becomes faster for each step (from Tb to QD to Cy5.5), which shows that the first FRET-sensitization (from Tb-to-QD) is reutilized for a second FRET sensitization (from QD-to-Cy5.5).The average PL decay times of Tb, QD, and Cy5.5 (Appendix Tables 7.6 to 7.8)

Figure 4 . 5 (

 45 10c). This increased FRET efficiency can be explained by the additional quenching of Tb by Cy5.R0 = 5.7±0.4 nm, cf. Table

Figure 4 .

 4 12e). The different FRET efficiencies found for this mTb-QD-15Cy5.[START_REF] Corry | A Flexible Approach to the Calculation of Resonance Energy Transfer Efficiency between Multiple Donors and Acceptors in Complex Geometries[END_REF] FRET system confirmed the findings of FRET systems 1 and 2 and that their FRET properties can be combined into one multi-donor-acceptor QD-FRET approach.Similar to FRET systems 1 and 2, an interesting aspect from the application point of view is the investigation of FRET-sensitized PL intensities and FRET intensity ratios. In addition to the distinct PL decays for Tb, QD, and Cy5.5 (Figures 4.16a

  to c) upon single-wavelength excitation of the initial Tb donor, tunable TG PL intensities of Tb, QD, and Cy5.5 by a varying amount of Tb (m) would present an interesting lever to adapt such multi-hybrid FRET NPs for brightness-equalized spectrotemporal barcoding.

Figure 4 .

 4 16e shows that the TG PL intensity of FRETquenched Tb (as a function of m) was transferred to both FRET-sensitized QD and FRET-sensitized Cy5.5 and could be tuned in the entire range of 1 to 52 Tb (52±7 Lumi4 ligands per QD). The FRET-ratios (sensitized TG PL intensities of QD and Cy5.5 divided by the donor intensities for each m) normalized to the maximum or minimum values (Figure 4.16f and g) showed the strongest relative FRET

Figure 4 . 17 . 5

 4175 Figure 4.17. FRET system 3 (mTb-QD-15Cy5.5): FRET efficiencies calculated with apparent average PL decay time (without correction of amplitudes by kFRET -red) and FRET average PL decay time (correction of amplitudes by kFRET -black) of FRET-sensitized QD acceptor PL (cf. Appendix Table 7.7).

Figure 4 . 18 .

 418 Figure 4.18. FRET system 4 (75Tb-QD-nCy5.5): Selected PL decay curves (cf. Appendix Tables 7.9 to 7.11 for complete data) of (a) Tb FRET donor (time scale 0 to 8 ms), (b) QD FRET acceptor/donor (time scale 0 to 8 ms) and (c) Cy5.5 FRET acceptor (time scale 0 to 4 ms) at different Cy5.5 per 75Tb-QD ratios. (d) FRET efficiencies as function of n determined by PL decay times of the Tb initial donor (green), the QD acceptor/donor (red), and the Cy5.5 final acceptor (blue). (e) Steady-state PL spectra (inset is a zoom into the Cy5.5 PL) of the different 75Tb-QD-nCy5.5 assemblies. (f) Normalized (to unity at the highest value) PL intensities of Tb, QD, and Cy5.5 (from left to right) as a function of n (TG: 0.1-0.9 ms using the PL decay curves in (a) to (c); SS: steadystate using the PL spectra from e; sim: MCS data).

Figures 4 . 7 .9 to 7 . 11 )

 47711 18a to c). When considering all four possible FRET pathways (Tb-QD, Tb-Cy5.5, QD-Cy5.5, and Cy5.5-Cy5.5) independently, the MCS results show a constant FRET efficiency for Tb-QD (as expected from system 1) and increasing FRET efficiencies for the other three pathways (as expected from system 2) with increasing n (Figure4.19). In the experiments, allFRET pathways influenced the PL decays of the different emitters and thus, the FRET efficiencies (as calculated by PL decay time analysis -Appendix Tables became convolutions of those FRET pathways. Because Tb was only FRET-quenched (initial donor), increasing FRET efficiencies with increasing n became most obvious (green data points in Figure 4.18d) and were caused by a constant FRET efficiency for Tb-QD and an increasing FRET efficiency for Tb-Cy5.5 FRET. For QD PL (acceptor to Tb and donor to Cy5.5), the FRET efficiencies also increased but less steep compared to Tb-QD (red data points in Figure 4.18d), which was in agreement with the MCS results that showed a steeper increase for Tb-Cy5.5 compared to QD-Cy5.5 (Figure 4.19). The Cy5.5 is the most complicated case because Cy5.5 is an acceptor for Tb and QD and a donor to other Cy5.5 acceptors (homo-FRET), the latter leading to significant PL quenching at high numbers of n (cf. system 2). MCS results (Figure 4.19) suggested a convolution of increasing FRET efficiencies for all three pathways. Taking into account that two are energy inputs (Tb-Cy5.5 and QD-Cy5.5) and one is an energy output and input (Cy5.5-Cy5.5), predictions of the overall FRET efficiency are difficult. The experimental results (blue data points in Figure 4.18d) did not show a clear trend but rather a more or less constant FRET efficiency around 0.73±0.10 caused by the convolution of the ingoing and outgoing FRET efficiencies for Cy5.5. Although a precise interpretation of the FRET efficiencies as in system 3 was not possible for system 4, the results still confirmed the findings and expectations from FRET systems 1 and 2 and from the MCS for each distinct FRET pathway. Moreover, the modification of n clearly resulted in a significant and tunable change of the PL decays in the different detection channels, which is very advantageous for temporal barcoding (vide infra). Another interesting aspect of this FRET system 4 was the possibility of analyzing the influences of the different FRET pathways on the PL intensities, which should decrease for Tb and QD and increase and then decrease for Cy5.5 (homo-FRET) with increasing n, when taking into account the previous results of system 1 and 2. Experimentally, we analyzed TG PL intensities (0.1-0.9 ms) from the PL decay curves (Figures 4.18a to c) and steady-state (SS) PL intensities (Figure 4.18e) for Tb, QD, and Cy5.5 as a function of n and compared the results to MCS (Figure 4.18f). As expected, both TG and SS experimental and MCS results showed decreasing PL intensities for Tb and QD and an initially strongly increasing followed by a decreasing PL intensity for Cy5.5. While the Tb donor MCS data could be well reproduced by both TG and SS PL intensity data, the more complicated PL cases of QD and Cy5.5, who acted as both acceptors and donors, clearly showed that TG PL was much better suited to analyze the development of PL intensities as a function of n. The reason for the better fit of TG and MCS data for the QD and Cy5.5 channels is most probably related to the selective energy pathway for TG detection. In steady state, both Tb and QD excitation lead to PL because short PL lifetimes (from direct QD excitation) and long PL lifetimes (from Tb excitation and FRET to QD and Cy5.5) cannot be distinguished. In TG detection, only the long-lifetime PL components are taken into account and thus the short-lifetime QD-to-Cy5.5 FRET is not detected. To show that the decreasing PL intensities for high values of n in the Cy5.5 channel (Figure 4.18f right) were really caused by energy loss due to non-radiative decay after each Cy5.5-to-Cy5.5 step (cf. system 2), we recorded the PL intensities of Cy5.5 as a function of n for different excitation wavelengths, such that Tb, QD, or Cy5.5 were selectively excited, and compared the results to MCS (Figure 4.20). The same PL intensity quenching behavior, no matter if Cy5.5 was excited via Tb-to-QD-to-Cy5.5 or QDto-Cy5.5 FRET or directly by the excitation source, for both experimental and MCS results clearly confirmed our results from system 2 and the interpretation that homo-FRET between many dyes with non-unity quantum yield leads to significant PL intensity quenching due to non-radiative decay. The different increases and decreases of PL intensities as a function of n in the different detection channels could also be used for tuning the different FRET ratios both in intensity and direction (increase or decrease with n -Figure 4.21), which could again be very beneficial for designing multiplexed sensing applications or molecular logicgates.[START_REF] Claussen | Complex Logic Functions Implemented with Quantum Dot Bionanophotonic Circuits[END_REF],[START_REF] Claussen | Biophotonic Logic Devices Based on Quantum Dots and Temporally-Staggered Förster Energy Transfer Relays[END_REF]

Figure 4 . 19 .

 419 Figure 4.19. FRET system 4 (75Tb-QD-nCy5.5): Simulated (MCS) FRET efficiencies for each possible FRET pathway. All different FRET pathways were calculated without the influence of the others.

Figure 4 . 20 .

 420 Figure 4.20. FRET system 4 (75Tb-QD-nCy5.5): PL intensities (SS and TG experimental and MCS results) of Cy5.5 upon excitation of Tb (a), QD (b), and Cy5.5 (c). Excitation of QD and Cy5.5 could not be measured with TG detection because of the short PL lifetimes (ns range).

Figure 4 . 21 .

 421 Figure 4.21. FRET system 4 (75Tb-QD-nCy5.5): FRET ratios of different TG (0.1 -0.9 ms) PL intensities (QD/Tb, Cy5.5/QD, and Cy5.5/Tb) normalized between 0 and 1 (a), to unity for the highest FRET ratio (b), or to unity for the lowest FRET ratio (c).

Figure 4 . 22 )

 422 Based on the mTb-QD-nCy5.5 systems, brightness-equalized lifetime-barcoding multi-hybrid FRET NPs can be designed by optimized numbers of Tb donors (m) and Cy5.5 acceptors (n). As our results from the different FRET systems showed, the intensity in the QD channel can be tuned by m without significantly altering the lifetime (cf. Figures 4.10b and 4.16b), whereas the lifetime can be tuned by n (cf. Figures 4.12 and 4.18b). Thus, TG PL intensity barcoding by distinct PL decays, which we previously demonstrated for different lanthanide donors attached to QD acceptors at variable brightness,[44] can possibly advance to a next level, namely single-wavelength barcoding at similar intensity levels. To select the optimal combinations of m and n for distinct codes at similar brightness, we prepared three types of samples with different amounts of Lumi4 ligands and Cy5.5 (60Lumi4-QD, 60Lumi4-QD-10Cy5.5, and 60Lumi4-QD-40Cy5.5and measured the TG PL intensities in the three detection channels as a function of m (Figure 4.23). Because the quenching of both QD PL intensity by the Cy5.5 acceptors could be compensated by increasing amounts of Tb donors without altering significantly the PL lifetime, both lifetime and intensity of the 100 multi-hybrid FRET NPs could be tuned independently.

Figure 4 . 22 .

 422 Figure 4.22. Absorption spectra of QD with different amounts of Lumi4 and Cy5.5. Note that Cy5.5 possesses absorption bands in the UV (cf.Figure 4.7a), which makes a precise quantification of Lumi4 per QD rather difficult. Taking into account a conjugation efficiency of ~70% and the PL results from Figure 4.23, we assumed 60±10 Lumi4 per QD for all three conjugates.

Figure 4 .

 4 Figure 4.22. Absorption spectra of QD with different amounts of Lumi4 and Cy5.5. Note that Cy5.5 possesses absorption bands in the UV (cf.Figure 4.7a), which makes a precise quantification of Lumi4 per QD rather difficult. Taking into account a conjugation efficiency of ~70% and the PL results from Figure 4.23, we assumed 60±10 Lumi4 per QD for all three conjugates.

  2 fold between code1 and code3 (Figure 4.24b). In contrast, lifetime tuning alone, as shown in FRET system 4 with a constant amount of 75 Tb per QD (Figure 4.18b), resulted in up to 12 fold (code1/code2) and 74 fold (code1/code3) TG PL intensity differences. To verify that deviations in the number of Tb donors (m), which could be caused by the uncertainties in Lumi4 ligand conjugation and/or the coordination of Tb 3+ inside the ligands, do not cause deviations in the specific RGB codes, we evaluated the stability of the code as a function of m for the three different multi-hybrid FRET NPs (Figure 4.25). All codes were extremely stable and only deviated significantly for low values of m in system mTb-QD-40Cy5.5. These values were much lower than the selected m = 60 and did therefore not interfere with the code stability.

Figure 4 . 23 .

 423 Figure 4.23. Time-gated intensities (range: 0.1-0.9 ms) of mTb-QD (a and d), mTb-QD-10Cy5.5 (b and e), and mTb-QD-40Cy5.5 (c and f) in the different detection channels (a to c) and in only the QD detection channel (d to e) for estimating the Lumi4 per QD/SiO2 ratio (60±10) and for a better visualization of the sensitivity (slope of the curves) of TG PL intensity as a function of m.

Figure 4 .

 4 Figure 4.24. (a) PL decays of the three multi-hybrid NPs selected for optical barcoding. The TG PL intensities in the detection windows from 0.05 to 0.5 ms, 0.5 to 1 ms, and 1 to 4 ms were used for RGB encoding. (b) RGB ratios of the TG intensities from the different PL decay curves in a. Three codes with distinct ratios and the same order of brightness (maximum of 2-fold difference) were accomplished. (c) TG PL images (single R, G, and B detection channel and RGB code in overlay) of several beads (top) and single beads (bottom -amplification of top images) doped with 10Tb-QD (I), 30Tb-QD-10Cy5.5 (II), and 60Tb-QD-40Cy5.5 (III). Scale bar (top right): 50 µm; λex = 349 nm; λem = 639±10 nm. (d) TG PL images of differently encoded beads mixed on the same microscopy slide and imaged in one field of view. For easier distinction (colors appear different depending on the screen/print version) the codes are also shown in the bright field (BF) images on the right. Scale bars (right): 50 µm; λex = 349 nm; λem = 639±10 nm. Determination and assignment of the codes via RGB analysis is shown inTable 4.2.

Figure 4 . 25 .

 425 Figure 4.25. TG PL intensity (RGB) ratios of each multi-hybrid nanoparticle as a function of m (calculated from the TG intensities in the red (0.05-0.5 ms), green (0.5-1 ms), and blue (1-4 ms) TG detection windows shown in Figure 4.24a). The selected codes for barcoding (highlighted by orange frames) were in regions were the changes with m were negligible. Because the number of Lumi4 ligands per QD was 60, the maximum number of m was also 60 (ligand saturation).

  have extensively analyzed the photophysical properties of a single QD surrounded by up to 191 Tb donors and up to 60 Cy5.5 acceptors in all possible combinations. By separating the mTb-QD-nCy5.5 FRET-modulated multi-hybrid NPs into four distinct systems (mTb-QD, QD-nCy5.5, mTb-QD-15Cy5.5, and 75Tb-QD-nCy5.5) and combining steady-state and time-resolved spectroscopy with MCS, we were able to decipher the single contributions of all FRET pathways. Tbto-QD FRET possessed a constant FRET efficiency and FRET-sensitized QD PL increased with m until a maximum loading of circa 200 Tb per QD was reached.However, this increase was less steep than expected from a purely theoretical estimation, which assumes that all Tb donors can sensitize the QD acceptor in a sequential manner without competition and/or experimental limitations. These restrictions could be very well modeled with MCS, which confirmed the experimental results. The FRET efficiency of QD-to-Cy5.5 FRET increases with n, which confirmed that FRET efficiency depends only on the number of acceptors and not the number of donors. Because of the many Cy5.5 FRET acceptors, we could show a steep increase of FRET-sensitized Cy5.5 PL for small values of n, followed by a constant decrease until n = 60. This decrease was mainly caused by combination of the formation of non-fluorescent H-dimers and multiple homo-FRET steps between Cy5.5 dyes, which increased the probability of the migrating exciton to get dissipated in the Cy5.5 dimer "trap states". The mTb-QD-nCy5.5 systems showed a convolution of Tb-to-Cy5.5 (co-assembled on the QD surface), Tb-to-QD, QD-to-Cy5.5, and Cy5.5-to-Cy5.5 FRET. When n was constant, the FRET efficiency of all FRET steps was independent of m and the sensitization of QD by Tb could be used to further sensitize Cy5.5. When m was constant, Tb-to-Cy5.5, QD-to-Cy5.5, and Cy5.5-to-Cy5.5 FRET efficiencies increased with increasing n. Tb and QD PL intensities decreased with increasing n, whereas Cy5.5 PL increased for small n and then decreased for larger n (due to increased PL quenching caused by increased energy migration via homo-FRET). TG PL intensity detection of the long-lived PL (from the initial Tb donor with > 2 ms PL lifetime) provided more consistent results with MCS because TG could distinguish QD-to-Cy5.5 FRET originating from FRET-sensitized QDs and from directly excited QDs, which was not the case for steady-state PL detection. Knowing the different FRET pathways and their dependence of m and n allowed us to tune both the PL intensity and lifetime of QD PL by adjusting m and n. This lever of independently tuning the intensity and shape (lifetime) of the QD PL decay curves was used to design brightness-equalized long-lifetime QDs with the possibility of RGB-encoded PL by TG intensity detection in three distinct time windows. The encoding strategy was applied to multiplexed imaging with single excitation and emission wavelengths and without the necessity of contrast adjustment for the differently encoded signals in the same field of view. The profound knowledge about multi-donor-multi-acceptor QD FRET and the demonstration of its application for single-wavelength optically-encoded multiplexed imaging demonstrate the level of sophistication such complicated FRET systems can contribute to fluorescence biosensing and imaging in case their properties are well understood. We anticipate that our results will find application in other fields of advanced optical barcoding such as multiplexed in-vitro diagnostics and cellular biology, security labeling, optical encryption, data storage, and molecular computing.

5 .

 5 Energy transfer from Tb donors to AuNPs C. Chen, C. Midelet, S. Bhuckory, N. Hildebrandt, and M. H. V. Werts. Nanosurface Energy Transfer from Long-Lifetime Terbium Donors to Gold Nanoparticles. The Journal of Physical Chemistry C 2018, 122, 17566-17574.

[ 222 ]

 222 a quantitative experimental study on the applicability of NSET versus FRET mechanisms in these materials has not been carried out. Compared with fluorescent molecular energy transfer donors, lanthanide ions offer some distinctive features such as long excited-state lifetimes (in the micro-to millisecond range) and multiple narrow emission bands in the visible region of the spectrum.[START_REF] Hildebrandt | Luminescent Terbium Complexes: Superior Förster Resonance Energy Transfer Donors for Flexible and Sensitive Multiplexed Biosensing[END_REF] Thus, the investigation of lanthanide-to-AuNP energy transfer with AuNPs of different sizes has the potential to provide new insight for the debate on whether FRET or NSET is the cause of AuNP-based PL quenching.In the chapter, we investigated the energy transfer interactions of Tb-conjugated sAv with biotinylated AuNPs with diameters of 5, 30, 50, and 80 nm (Figure5.1).Resonant light scattering spectroscopy (RLS) and time-resolved PL spectroscopy were applied to characterize the different Tb-sAv-biot-AuNP assemblies at various donor/acceptor ratios. PL decays of many Tb-sAv-biot-AuNP assemblies at different concentrations and with AuNPs of all three sizes were studied by multiexponential PL decay analysis and streched-exponential (Kohlrausch law) and the energy transfer efficiencies were found to be independent of the AuNP size. NSET theory provided excellent agreement between the time-resolved PL results and the Tb-to-AuNP distances within the different Tb-sAv-biot-AuNP assemblies, whereas application of FRET theory led to unrealistically long Förster distances and Tb-108 AuNP distances without any correlation between the different AuNP sizes. Our results strongly suggest that energy transfer between Tb and AuNPs is of NSET type, which is a very important finding for understanding and designing AuNPbased biosensors and assemblies of AuNPs with photoluminescent units.

Figure 5 . 1 .

 51 Figure 5.1. Schematic representation (not to scale) of the assemblies of Tb-labeled sAv (Tb-sAv) and biotinylated AuNPs (biot-AuNPs), in which excitation energy transfer occurs. For clarity only 3 biotins are shown. The actual number of biotins attached to the surface of each AuNP was determined to be ca. 25, 900, 2500, and 6400 for the 5, 30, 50, and 80 nm diameter AuNPs, respectively. A distance of 4.5 nm was estimated by a radius of 3 nm for sAv (size of sAv in the solid state: 5.4 nm x 5.8 nm x 4.8 nm in the solid state)[223] plus 1.5 nm for the biotin and linker attached to the AuNP.

  5) was used as a solvent, for the measurements of 80 nm Au NPs, pure water was used as a solvent. Black Costar Half Area 96 well microtiter plates were purchased from Corning Inc. (Corning, NY, USA), and Tb complexes (Lumi4-Tb) functionalized to sAv at a ratio of 4 Tb/sAv were provided by Lumiphore Inc. (Berkeley, CA, USA).

  used different but constant concentrations of Tb-sAv for the experiments with each of the three AuNPs. To these constant concentrations of Tb-sAv, increasing amounts of biot-AuNPs were added, such that the fraction of biot-AuNPs (x) was given per 6 Tb-sAv for 5 nm biot-AuNPs (25/4 = 6; 25 biotins on 4 sAv binding sites), per 225 Tb-sAv for 30 nm biot-AuNPs (900/4 = 225), per 625 Tb-sAv for 50 nm biot-AuNPs (2500/4 = 625), and per 1600 Tb-sAv for 80 nm biot-AuNPs (6400/4 = 1600). Tb-sAv was dissolved to 20.7 µM in anhydrous DMF, which corresponded to 82.8 μM of Tb (conjugation ratio of 4 Tb/sAv). For 5 nm biot-AuNPs, Tb-sAv was diluted to 2.73 nM in pure water. For the total measuring volume of 150 µL, 50 μL of Tb-sAv solutions were mixed with 100 µL of biot-AuNP solutions containing increasing amounts (0, 1, 5, 10, 20, 30, 40, 50, 60, 70, 80 μL) of 5 nm biot-AuNPs (9.09 nM) in 2 mM Tris-HCl buffer at pH 8.5. The mixtures were incubated for 2 h at 37° C. For 30 nm biot-AuNPs, Tb-sAv was diluted to 1.33 nM in pure water. For the total measuring volume of 150 µL, 50 μL of Tb-sAv solutions were mixed with 100 µL of biot-AuNP solutions containing increasing 110 amounts (0, 1, 2, 5, 10, 20, 30, 40, 50, 60, 80 μL) of 30 nm biot-AuNPs (29.6 pM) in 2 mM Tris-HCl buffer at pH 8.5. The mixtures were incubated for 2 h at 37° C. For 50 nm biot-AuNPs, Tb-sAv was diluted to 0.65 nM in pure water. For the total measuring volume of 150 µL, 50 μL of Tb-sAv solutions were mixed with 100 µL of biot-AuNP solutions containing increasing amounts (0, 1, 2, 5, 10, 20, 30, 40, 50, 60, 80 μL) of 50 nm biot-AuNPs (5.3 pM) in 2 mM Tris-HCl buffer at pH 8.5. The mixtures were incubated for 2 h at 37° C. For 80 nm biot-AuNPs, Tb-sAv was diluted to 0.72 nM in pure water. For the total measuring volume of 150 µL, 50 μL of Tb-sAv solutions were mixed with 100 µL of biot-AuNP solutions containing increasing amounts (0, 1, 2, 5, 10, 20 μL) of 80 nm biot-AuNPs (2.24 pM) in pure water. The mixtures were incubated while shaking slowly overnight at room temperature.

  [START_REF] Uyeda | Synthesis of Compact Multidentate Ligands to Prepare Stable Hydrophilic Quantum Dot Fluorophores[END_REF] UV/Vis spectrophotometer from Perkin Elmer or on a modular fiber-based spectrometer system (OceanOptics LS-1 white light source and USB4000-VIS-NIR CCD spectrometer). Resonant light scattering spectroscopy (RLS) of the AuNP and AuNP-Tb-sAv solutions was performed using a fibre-coupled incandescent white light source (AvaLight-HAL-(S)-mini) and an OceanOptics QE65000 spectrograph, at right angle, using our published method,[START_REF] Navarro | Resonant Light Scattering Spectroscopy of Gold, Silver and Gold-silver Alloy Nanoparticles and Optical Detection in Microfluidic Channels[END_REF]-[START_REF] Midelet | Spectroscopic and Hydrodynamic Characterisation of DNA-Linked Gold Nanoparticle Dimers in Solution Using Two-Photon Photoluminescence[END_REF] A 200x diluted Ludox solution[START_REF] Deželić | Determination of Size of Small Particles by Light Scattering. Experiments on Ludox Colloidal Silica[END_REF] in 50 mM aqueous NaCl was used as the reference. The corrected light scattering spectra represent the relative light scattering cross sections as a function of wavelength. In the kinetics experiments probing the stability of the biot-AuNP solutions and the binding of Tb-sAv to biot-AuNP, corrected light scattering spectra were recorded at evenly spaced time intervals (rate typically 1 spectrum per 10 s). The position of the maximum of the resonant light scattering band 𝜆 max RLS in each recorded spectrum was determined by fitting a parabola through the data points in a narrow spectral window (Δ𝜆 = 10 nm) around the numerical maximum. The maximum of the parabola obtained from this first fit was then used as the center point for a second parabolic fit through the measured spectral data points over a narrow window (Δ𝜆 = 10 nm), from which a refined determination of the position of the maximum was deduced. This procedure yielded stable and reproducible measurement of the position of the resonant light scattering maximum 𝜆 max RLS and mitigates problems due to noise on the measured spectrum. For the measurement of the PL decay curves of the Tb to AuNPs, an EI fluorescence plate reader (Edinburgh Instruments, UK) was used. For the multichannel scaler, 4000 detection bins of 2 μs integration time were used. A nitrogen laser (LTB, Berlin, Germany) was used for excitation (337.1 nm, 20 Hz, 600 flashes). 494/20 nm bandpass filter was used for analyzing the Tb PL. The data were fit with FAST software version 3.1 (Edinburgh Instruments, UK). All assays were measured in black 96-well microtiter plates with an optimal working volume of 150 μL.

Figure 5 . 2

 52 Figure 5.2 shows the evolution of the wavelength of the maximum 𝜆 max of the resonant light scattering spectrum of biot-AuNPs (30 nm, 50 nm, 80 nm diameter)over time, before and after adding Tb-sAv to the solution. The light scattering by 5 nm AuNPs is too weak and was not studied. The amount of Tb-sAv added was 25% and 200% of the amount needed to cover all binding sites on the AuNPs. The position of the maximum did not change over time before adding Tb-sAv, which was in line with the stability of the biot-AuNPs in the buffer. A prompt, small wavelength shift was observed in the light scattering resonance of the biot-AuNPs when Tb-sAv was added to the solution. Subsequently, there was virtually no evolution of 𝜆 max at longer times after adding Tb-sAv. The observed evolution of 𝜆 max is consistent with the binding of Tb-sAv to the biot-AuNPs. The absence of changes in 𝜆 max after binding of Tb-sAv to the biot-AuNPs indicates that no significant clustering of Tb-sAv/biot-AuNPs into multi-AuNP aggregates occurred, and that under the experimental conditions the only donor-acceptor assemblies are based on single AuNPs.

Figure 5 . 2 .

 52 Figure 5.2. Wavelength evolution of the maximum of the resonant light scattering band of biot-AuNPs (30, 50 and 80 nm diameter AuNPs) as a function of time. At t = 0, Tb-sAv (a) 25% and (b) 200% with respect to biot-AuNP binding sites was added.

  30 nm AuNPs), 319 (50 nm AuNPs), and 817 (80 nm AuNPs). When taking into account the curved surface of the AuNPs, the hydration layer of sAv, and possible sterical hindrance in sAv binding to biot in very close proximity, the 35% lower values determined by PL titration are in good agreement with the geometrical binding conditions. At [biot-AuNP]/[Tb-sAv] ratios below the equivalence point, biot-AuNPs carried the maximum number of Tb-sAv. At excess of biot-AuNP, the number of Tb-sAv per biot-AuNP decreased.

Figure 5 . 3 .

 53 Figure 5.3. PL titration of Tb-sAv with biot-AuNP (a) Integrated time-gated (0.1 -2 ms) PL intensities of the PL decay curves (black: 5 nm biot-AuNPs; red: 30 nm biot-AuNPs; blue: 50 nm biot-AuNPs; green: 80 nm biot-AuNPs). Crossing of the green dotted lines (at 3 [biot-AuNP]/ [y Tb-sAv] with y = 6 for 5 nm biot-AuNPs, y = 225 for 30 nm biot-AuNPs, y = 625 for 50 nm biot-AuNPs, and y = 1600 for 80 nm biot-AuNPs) indicates the maximum number of Tb-sAv per biot-AuNP (6/3=2 for 5 nm biot-AuNPs, 225/3 = 75 for 30 nm biot-AuNPs, 625/3 = 208 for 50 nm biot-AuNPs, and 1600/3 = 533 for 80 nm biot-AuNP (b-d): Selected PL decay curves detected within the Tb donor channel for increasing ratios of (x biot-AuNPs) per (y Tb-sAv). (b) 30 nm biot-AuNPs with y = 225 Tb-sAv; (c) 50 nm biot-AuNPs with y = 625 Tb-sAv; (d) 80 nm biot-AuNPs with y = 1600 Tb-sAv. Black: x = 0; red: x = 0.2; orange: x = 0.5; green: x = 1; blue: x = 2; violet: x = 3; pink: x = 4.

Figure 5 . 4 .

 54 Figure 5.4. (a) PL decay (λex = 337.1 nm; λem = 490/20 nm) of Tb-sAv in buffer (red) and fit (black) using multiexponential decays; yielding an average lifetime of ⟨τ⟩ = 2.2 ms. (b) Overlap between absorption spectra of 30 nm (black), 50 nm (red), and 80 nm (blue) biot-AuNP acceptors and emission spectrum of the Tb-sAv donor (green) (inset: Overlap between absorption spectra of 5 nm biot-AuNP acceptor (red) and emission spectrum of the Tb-sAv donor (green)).

Figure 5 . 4 b

 54 Figure 5.4 b shows the intensity-normalized (area under the emission spectrum from 450 to 700 nm normalized to unity) PL spectrum of Tb donor and the absorption spectra of the differently sized biot-AuNP acceptors (5, 30, 50, and 80 nm).

30 nm, 50

 50 nm, and 80 nm diameter. Characterization by RLS and time-resolved PL spectroscopy demonstrated the assembly of Tb-sAv to biot-AuNP with ratios up to 2 (5 nm AuNPs), 75 (30 nm AuNPs), 208 (50 nm AuNPs), and 533 (80 nm AuNPs) Tb-sAv per biot-AuNP, in good agreement with expectations based on the surface areas of the particles and the biotinylation density of the AuNPs. The stable Tb-sAv/biot-AuNP assemblies were investigated at different concentrations, Tb-sAv per biot-AuNP ratios, and AuNP sizes in aqueous solutions by time-resolved PL spectroscopy. The resulting PL decay curves were studied using both multiexponential and Kohlrausch (stretched exponential) PL lifetime models, which yielded mutually consistent results. The analyses showed that energy transfer efficiencies were independent of the AuNP size. In contrast to FRET, NSET theory provided a coherent analysis of the experimental energy transfer results. The Tb donor to Au-NP surface acceptor distances determined based on NSET proved in excellent agreement with the structural conditions of the biotin-sAv binding on the AuNP surface. Our results present strong evidence favoring NSET over FRET as the operational energy transfer mechanism for the PL quenching of electric dipole emitters by AuNPs.

  modulated multi-hybrid nanoparticles based time-resolved multiplexing and the study of energy transfer mechanism from long lifetime Tb donors to AuNP. In a holistic approach, extensive spectroscopic analysis with Monte-Carlo simulations are combined to explain the interactions within multiple donor-acceptor FRET network, containing up to 191 lanthanide complexes and up to 60 fluorescent dyes attached to a single QD. And even highly complicated FRET nanosystems with up to four different hetero-FRET and homo-FRET pathways and non-fluorescent dimer formation concerning more than 100 participating donors and acceptors per one QD can be understood by time-resolved and steady-state PL spectroscopy and adequate modeling and simulation. Moreover, two strategies are developed for single-nanoparticle multiplexing. One is achieved by using different lanthanide donor and tunable D-A distance. Thus, tunable lifetime of QD can be obtained by attaching Tb or Eu complexes and well-defined silica shell, lead to single excitation, single wavelength, and single nanoparticle based live-cell barcoding. Another strategy is achieved by using multiple donors and acceptors. Multiple donors can enhance sensitizing QD PL without altering significantly the PL lifetime, while multiple acceptors change PL lifetime of QD, which means both lifetime and intensity of QD can be tuned independently. The control of such FRET-modulated multi-hybrid QDs can be used for designing a novel concept of optical multiplexing or barcoding, which has the potential to significantly advance multiplexed in-vitro diagnostics and cellular biology, security labeling, optical encryption, data storage, and molecular computing. Single-wavelength excitation and single-wavelength detection are employed to distinguish multiple FRETencoded microbeads within a single microscopy image at constant contrast:

Figure 7 . 1 .

 71 Figure 7.1. Flowchart of the steps involved in the Monte Carlo simulation scheme. Processes involving a random number generator are indicated by a shaded background.

Figure 7 . 2 .

 72 Figure 7.2. FRET system 1 (mTb-QD): PL decays of Tb donor (a, b, and c) and QD acceptor (d, e, and f) at different ratios of Tb per QD. To accomplish a sufficient amount of PL photons for PL decay time analysis, excitation laser (337.1 nm) intensities and concentrations were adapted. Conditions are the same for a and d, d and e, and c and f, respectively. The selected curves in Figure 4.10 show normalized PL decay curves from all three conditions (a/d, b/e, and c/f). Normalization was done by comparing the decay curves of overlapping ratios of Tb per QD in solution for the three different conditions.

Figure 7 . 3 .

 73 Figure 7.3. FRET system 2 (QD-nCy5.5): PL decays of QD donor (a) and Cy5.5 acceptor (b) from FRET system 2 (QD-nCy5.5) for increasing n.

Figure 7 . 4 .

 74 Figure 7.4. Extinction spectra of 50nm biot-AuNP at t=0 min, at t=3 hours and t=24 hours in the three different buffers: (a) water, (b) Tris-HCl, (c) PBS

Figure 7 . 5 .(Figure 7 . 6 ).

 7576 Figure 7.5. Normalized extinction (left) and light scattering (right) spectra of 50nm biot-AuNP after 24 hours in buffers.

Figure 7 . 6 .Figure 7 . 7 .

 7677 Figure 7.6. Extinction (left) and light scattering (right) spectra of 80 nm biot-AuNP after 24 hours in buffer.

Figure 7 . 8 .

 78 Figure 7.8. PL decay curves detected in the Tb donor channel for increasing ratios of (x biot-AuNPs) per (y Tb-sAv) for 30 nm biot-AuNPs with y = 225 Tb-sAv. black: x = 0; red: x = 0.1; orange: x = 0.2; dark yellow: x = 0.5; green: x = 1; cyan: x = 2; blue: x = 3; violet: x = 4; pink: x = 5; wine: x = 6; gray: x = 8).

Figure 7 . 9 .

 79 Figure 7.9. PL decay curves detected in the Tb donor channel for increasing ratios of (x biot-AuNPs) per (y Tb-sAv) for 50 nm biot-AuNPs with y = 625 Tb-sAv. black: x = 0; red: x = 0.1; orange: x = 0.2; dark yellow: x = 0.5; green: x = 1; cyan: x = 2; blue: x = 3; violet: x = 4; pink: x = 5; wine: x = 6; gray: x = 8)

7. 4 . 3 1 : 2 )Figure 7 . 11 .

 4312711 Figure 7.11. In presence of increasing biot-AuNP concentrations, the PL decay of the Tb-sAv donor is gradually replaced with a shorter PL decay component. This

Figure 7 . 11 . 2 .

 7112 Figure 7.11. Analysis of PL decays of Tb-sAv (0.22 nM) in the presence of increasing amounts of 50 nm biot-AuNP in buffer. (a) Experimental decay traces (red), with fitted two-component Kohlrausch decay laws (black). The traces were scaled to equal initial amplitude for clarity. (b) Amplitude fraction of the Tb-sAv/biot-AuNP donor-acceptor assembly PL decay in the total PL decay as a function of biot-AuNP concentration, obtained from the curve fits. (c) Average PL decay times for the Tb-sAv/AuNP assemblies. The dotted line indicates the minimal biot-AuNP concentration to bind all available Tb-sAv (i.e. 208 Tb-sAv per biot-AuNP). The error bars indicate 95% confidence intervals.

  Similar behavior was observed with the 5 nm, 30 nm and 80 nm biot-AuNPs (Figures 7.12, 7.13 and 7.14). Using the same analysis procedure based on the Kohlrausch decay law, we are able to find the average decay times of Tb(III) luminescence in the donor-acceptor complex.

Figure 7 . 12 .

 712 Figure 7.12. PL decays of Tb-sAv (0.91 nM) in the presence of increasing amounts of 5 nm biot-AuNPs in buffer. (a) Experimental decay traces (red), with fitted two-component Kohlrausch decay laws (black). The traces were scaled to equal initial amplitude for clarity. (b) Amplitude fraction of the Tb-sAv/biot-AuNP donor-acceptor assembly PL decay in the total PL decay as a function of biot-AuNP concentration, obtained from the curve fits. (c) Average PL decay times for the Tb-sAv/AuNP assemblies.

Figure 7 . 13 .

 713 Figure 7.13. PL decays of Tb-sAv (0.44 nM) in the presence of increasing amounts of 30 nm biot-AuNPs in buffer. (a) Experimental decay traces (red), with fitted two-component Kohlrausch decay laws (black). The traces were scaled to equal initial amplitude for clarity. (b) Amplitude fraction of the Tb-sAv/biot-AuNP donor-acceptor assembly PL decay in the total PL decay as a function of biot-AuNP concentration, obtained from the curve fits. (c) Average PL decay times for the Tb-sAv/AuNP assemblies. The dotted line indicates the minimal biot-AuNP concentration to bind all available Tb-sAv (i.e. 75 Tb-sAv per biot-AuNP).

Figure 7 . 14 . 160 7

 714160 Figure 7.14. PL decays of Tb-sAv (0.24 nM) in the presence of increasing amounts of 80 nm biot-AuNPs in buffer. (a) Experimental decay traces (red), with fitted two-component Kohlrausch decay laws (black). The traces were scaled to equal initial amplitude for clarity. (b) Amplitude fraction of the Tb-sAv/biot-AuNP donor-acceptor assembly PL decay in the total PL decay as a function of biot-AuNP concentration, obtained from the curve fits. (c) Average PL decay times for the Tb-sAv/AuNP assemblies.

  Toute science commence comme philosophie et se termine en art ; elle surgit dans l'hypothèse et coule dans l'accomplissement » . -Will Durant Cette citation est extraite du livre intitulé « Histoire de la philosophie » . Nous pouvons également l'appeler « La beauté de la philosophie » . Nous savons que la philosophie naturelle est considérée comme le précurseur des sciences naturelles. Mais pourquoi chaque science se termine en art ? Qu'est-ce que l'art? À mon avis, l'art est l'expression d'idées originales, conceptuelles et imaginatives, avec une habileté technique et un pouvoir émotionnel, ou on peut aussi dire que la beauté est un art. L'identité d'Euler montre un lien profond entre les nombres les plus fondamentaux en mathématiques et en montre la beauté mathématique. Les équations de Maxwell établissent une théorie électromagnétique unifiée. Ils associent électricité, magnétisme et lumière en tant que différentes manifestations du même phénomène et témoignent de la beauté physique. Je veux aussi découvrir la beauté dans mon domaine de recherche, et je pense que cela existe déjà.

Figure 1 . 1 .

 11 Figure 1.1. Le travail imitatif de « La persistance de la mémoire » (à gauche) et le tableau original de Salvador Dali (à droite)

Figure 1 . 2 . 1 . 2 , 1 . 3 ,

 121213 Figure 1.2. (a) QDs avec des couches SiO2 d'épaisseurs différentes (x = 6 ou 12 nm) fonctionnalisés avec Eu-1 ou Lumi4-Tb pour le codage à barres temporel PL à longueur d'onde unique. (b) Le principe de codage RGB basé sur trois fractions d'intensité TG distinctes pour chacune des quatre durées de vies PL spécifiques au FRET et quatre cellules codées.

Figure 1 . 4 .

 14 Figure 1.4. Modèle NSET utilisant de la streptavidine (sAv) marqués au Tb et des NP-Au biotinylés.

Table 2 .1. QD as donor based multiple (n) acceptors FRET system.

 2

	Acceptors	n	Donors	Application	Mechanism	Ref.
					investigated
	QSY9, (Cy3,	0~10	QD 530	/	yes	[46]
	Cy3.5)
	Cy3	0~10	QD510, 530,	/	yes	[8]
			555
	biot-Au NPs	~9	sAv-QDs	detection for avidin	no	[47]
	(2~3 nm)		(rod shape)
	Rhodamine	0~48	QD545	extracellular matrix	no	[48]
	Red-X,			metalloproteinases
				(MMPs) activity in
				normal and cancerous
				breast cells
	mOrange,	15.7 and 16.5	QD 520	sensing intracellular	no	[49]
	mOrange			pH
	M163K
	EYFP, Atto647	0~18	QD	/	yes	[50]
	(A555, A647)	(0,0)~(7,7)	QD	multiplexed protease	yes	[51]
				sensing
	Cy3-Cy3.5-	1~8	QD525	/	yes	[52]
	Cy5-Cy5.5
	A555/A647	0~16	QD, A488	detection of the activity	yes	[53]
				of nanomolar
				concentrations of
				trypsin
	(A555, A647)	(0,0)~(7,7)	Green-	tracking the activity of	no	[54]
			emitting QD	trypsin and
				chymotrypsin
	(A555, A647)	(0,0)~(12,18)	QD520b,	/	yes	[55]
			QD525a
	A610 or A633.	0~30	QD 525,	/	yes	[56]
	A555 or A647		530a, 540a,
			550, 575,
			600, 650

Table 2 .2.

 2

Table 2 .2. QD as relay based multiple (m) donors and multiple (n) acceptors systems. Acceptor n Donor m Application Mechanism investigated Ref.

 2

	IRD700	/	PDFD(polymer),	/	detection of DNA	yes	[69]
			QD615		hybridization
	A647	0~15	Tb	0~20 monitoring protease	yes	[65]
					activity and nucleic
					acid hybridization
	A647	0~5	Tb	0~10	multiplexed	no	[66]
					protease sensing
	A647	0~25	Tb	0~25	complex logic	yes	[67]
					functions
	A555/Cy3/A594	0~8	Ru-phen	0~12	detection of the	yes	[70]
					proteolytic activity
					of trypsin
	A647	0~20	Tb	0~45 sensitive intra-and	no	[68]
					extracellular
					fluorescence
					imaging

  Trivalent lanthanide ions (Ln 3+ ) are the most stable oxidation state of lanthanide cations, except for Ce 4+ , Tb 4+ , and Yb 2+ , for which the f orbitals are empty, half-, or full-occupied, respectively.[START_REF] Schlücker | Surface-Enhanced Raman Spectroscopy: Concepts and Chemical Applications[END_REF] Due to specific electronic configurations, Ln show similar chemical properties. Ln 3+ ions possess intrinsic

luminescence that originates from f-f electronic transitions, the 4f orbitals do not directly participate in chemical bonding due to shielding by the 5s and 5p orbitals, which minimizes the influence of external ligand fields, leading to sharp-band emissions.

[START_REF] Moore | From Antenna to Assay: Lessons Learned in Lanthanide Luminescence[END_REF]

Figure

2

.9 show the ground and excited states of the Ln 3+ ions,

Figure 2.13, the

  higher the FRET efficiency, the lager the required difference between 𝜏 A and 𝜏 D . For the case of 95% FRET efficiency, 𝜏 A = 0.1𝜏 D already shows clear differences in the slope of decay curve of 𝜏 AD and 𝜏 DA . As a result, the use of donors with 𝜏 D ≫ 𝜏 A allows the replacement of 𝜏 DA by 𝜏 AD , and

	LLCs have been used much as FRET-donors. Depending on the design of FRET
	systems, FRET acceptors such as organic dyes fluorescent proteins, or QDs can be
	paired with LLCs as donor. As mentioned in Section (2.2.3), LLCs/UCNP-to-QD
	based FRET configurations can inhibit or decrease direct excitation of the QDs. A
	clear evidence for LLCs-to-QD based FRET configurations was demonstrated by
	Hildebrandt and Charbonnière.[60],[61] Due to the large difference in D and A
	excited state lifetimes, the FRET-sensitized lifetime of A is the same as the FRET-
	quenched lifetime of the lanthanide donor.[2] As shown in
	of most lanthanide-based donors are several orders of magnitude larger than those
	of any other acceptor. In 1993, Mathis demonstrated LLCs can be used as energy
	donors in a homogeneous FRET immunoassay,[95] and since then Tb and Eu based

Equation 2.10 (Section 2.1.1) can be rewritten as Equation 2.14:

2.4.1), lifetime measurement (2.4.2), and application of time- resolved measurement (2.4.3).

	Furthermore, in order to obtain high-
	quality time-resolved photoluminescence images of biological samples,
	luminophores are required to possess a luminescence lifetime that is sufficiently
	long compared to that of autofluorescence in biological sample. Lanthanides
	complexes and nanoparticles are famous for their long luminescence lifetimes (up
	to ms) and have been mentioned in Section (2.3.1). Other luminophores such as
	transition-metal complexes, doped-quantum dots (d-dots), lattice-strained QDs
	(LS-QDs), carbon dots, metal nanoclusters, and persistent nanoparticles have also
	been reported to exhibit long luminescence lifetimes and be suitable for time-
	resolved luminescence measurements. The lifetime ranges of different classes of
	luminophores are listed in Table 2.3. The discussion below will focus on the time-
	gated measurement (

Table 2 .3. PL lifetime ranges of different classes of long lifetime luminophores.

 2

2.6.2 Lifetime measurement

	following the pulsed excitation, and can be descripted as a function of time
	(Equation 2.19):
	𝐼 = ∑ 𝐴 𝑖 𝑒 𝑖	-	𝑡 𝜏 𝑖	(2.19)
	TG measurement provides the intensity information of the photons collected in
	gate width. In contrast, lifetime measurement analyzes the luminescence lifetime
	of a probe. The time-domain and frequency-domain are two dominant methods for
	measuring time-resolved fluorescence. For the time-domain method, as illustrated
	in Figure 2.18 a, the sample is excited with a pulse of light much shorter than the
	decay time τ of the sample. The time dependent intensity decay is measured

Table 3 .1 Optical characteristics of Tb, Eu, and QD/SiO2 with their FRET pairs.

 3 See Figure3.6a for filter spectra. Lumi4-Tb and Eu-1 filters were selected to measure their bluest emission bands with the least possible overlap with the QD emission band. QD filter was selected to avoid overlap with Tb and Eu PL. (b) See Figure3.6b for PL decay curves. (c) Amplitude averaged decay time that takes into account the complete decay curves, which contain FRET-quenched and unquenched (lanthanide complexes that do not participate in FRET) components. FRET-quenched average decay times, FRET efficiencies, and donor-acceptor distances can be found in Table3.2.

		εmax (M -1 cm -1 ) [λmax]	ΦLn3+	Emission Filter (nm) (a)	τ (b)
	Lumi4-Tb	26,000 [340 nm]	0.79	490/20	2.7 ms
	Eu-1	58,000 [330 nm]	0.48	567/15	1.1 ms
	QD/SiO2 (6 nm)	485,000 [610 nm]	/	640/14	~12 ns
	QD/SiO2 (12 nm)	680,000 [610 nm]	/	640/14	~11 ns
	FRET pair (D → A)	J (M -1 . cm -1 . nm 4 )		R0 (nm)	τave (ms) (c)
	Tb → QD/SiO2(6 nm)	6.1 × 10 16		9.7	0.74
	Tb → QD/SiO2(12 nm)	1.1 × 10 17		10.7	1.82
	Eu → QD/SiO2(6 nm)	4.8 × 10 16		8.6	0.61
	Eu → QD/SiO2(12 nm)	7.3× 10 16		9.2	1.09
	(a)

Due to the different distances (6 nm or 12 nm) and different R0 values (between 8.6 and 10.7 nm, Table

3

.1), the PL lifetimes () of Lumi4-Tb (2.7 ms) and Eu-1(1.

Table 3 .2. PL decay time fitting and analysis parameters, and RGB ratio calculation in QD acceptor channel for four well-defined codes (0.1 ms-8 ms for Tb-QD/SiO2, and 0.1 ms- 4 ms for Eu-QD/SiO2).

 3

	Codes	Tb-QD/SiO2 (6 nm)	Tb-QD/SiO2 (12 nm)	Eu-QD/SiO2 (6 nm)	Eu-QD/SiO2 (12 nm)
	AAD1*	1920	92	850	29
	AD1*	0.555	0.234	0.324	1.000
	τAD1 (ms)	0.19	0.25	0.12	0.74
	kFRET1	4.89	3.63	7.42	0.44
	AD1	0.17	0.03	0.06	1.00
	AAD2*	1540	301	1770	/
	AD2*	0.445	0.766	0.676	/
	τAD2 (ms)	0.86	1.30	0.54	/
	kFRET2	0.79	0.40	0.94	/
	AD2	0.83	0.97	0.94	/
	B	439	346	1234	715
	τD (ms)	2.7	2.7	1.1	1.1
	 2	1.164	1.201	1.138	1.160
	τAD(ms) (a)	0.75	1.27	0.52	0.74
	EFRET (b)	72%	53%	53%	33%
	R(nm) (c)	8.6	10.5	8.4	10.4
	TG intensity(0.05-0.5 ms)	594320	144800	620500	422300
	TG intensity(0.5-1 ms)	289130	116410	307880	305280
	TG intensity(1-3 ms)	419120	250080	333020	450680
	RGB ratio	(46%/22%/32%) (28%/23%/49%) (49%/24%/26%) (36%/26%/38%)

(a) Amplitude-averaged PL decay of only the first two decay components, which were caused by FRETquenching. The third decay component (2.7 ms and 1.1 ms, respectively) results from unquenched lanthanide PL, which is still present (spectral crosstalk) in the QD detection channel. (b) Calculated using Equation 3.5. (c) Calculated using Equation 3.6.

  nanoparticle encoding system composed of QD cores with lanthanidefunctionalized SiO2 shells. Our TG-FRET barcoding technique was accomplished by precise distance control between lanthanide donors and QD acceptors, which, in turn, led to distinct PL decay curves. TG PL detection in three specific time windows allowed us to create distinct RGB codes for each encoding nanoparticle, which were used to label live cells. Individual and mixed cells could be distinguished by the predefined RGB codes in the same field of view using TG PL imaging. Our encoding approach was independent of PL intensity and nanoparticle concentration and was shown to be stable at different pH over several hours of incubation. While our study used two different QD coating thicknesses and two

different lanthanide complexes to create four different codes, more variations could be used to extend the coding range by additional lifetimes. Although a larger lifetime difference will always lead to a better distinction, the curves of Eu-QD/SiO2 (6 nm) and Tb-QD/SiO2 (6 nm) are very similar with an average lifetime difference of only ca. 20% (0.61 and 0.74 ms, cf. Table

3

.1) but can still be distinguished very efficiently. A 20% difference between all lifetimes and a minimum lifetime of ca. 10 % of the one of Lumi4-Tb (2.7 ms) would allow for 14 different codes (lifetimes of 0.25, 0.30, 0.36, 0.44, 0.52, 0.63, 0.75, 0.90, 1.09, 1.30, 1.56, 1.88, 2.25, and 2.70 ms). If the coding system of interest requires more than 20% lifetime difference, the FRET multiplexing range can be extended by other means, e.g., by a combination of the spectral and temporal multiplexing components or by multistep FRET processes, in which the QD is used both as acceptor (to a Tb complex) and donor (to a dye). Such approaches have already been used in solution to quantify multiple DNAs by spectrotemporal multiplexing

  /CdS/ZnS QDs with emission maximum at 620 nm were purchased from Poly OptoElectronics Co., Ltd. Black Costar Half Area 96 well microtitration plates were purchased from Corning Inc. (Corning, NY, USA), and Lumi4 functionalized to maleimide were provided by Lumiphore Inc. (Berkeley, CA, USA).

	CdSe
	Terbium(III) chloride hexahydrate (99.999% trace metals basis), Poly(ethylene
	glycol) nonylphenyl ether (NP-5), tetraethyl orthosilicate (TEOS) and (3-
	mercaptopropyl) trimethoxysilane (MPS) were purchased from Sigma-Aldrich.

Cyanine5.5 maleimide was purchased from Lumiprobe Inc. (Berkeley, CA, USA).

Cyclohexane, chloroform, ethanol, ammonia aqueous solution (28%) were purchased from Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China).

  Using the density and volume of a single QD and Avogadro's constant, we obtained the molecular weight of QDs, which was ~570,000. The yield of synthetic QD/SiO2 was approximately 70%, which resulted in a final molar concentration of 1.23 µM QD/SiO2.

	𝑉 =	4 3 𝜋𝑟 3	(4.1)
	𝜌 =	𝑚 𝑉	(4.2)

4.1 and 4.2).

  .5 donor-acceptor assemblies, we used constant concentrations of QD (50 nM) for all experiments. For the total incubation volume of 200 µL, 20 μL of QD solutions (500 nM) were mixed with 180 µL of solutions containing increasing amounts (2.2, 4.4, 8.8, 17.6, 22, 33, 44, 66, 88, 110, 132 μL) of Cy5.5 (4.54 µM) in

	Tris-HCl buffer at pH 7.5 (50 mM). The mixtures were incubated for 3 h at room
	temperature with the tube covered in aluminum foil and rotating with an Intelli
	Mixer. For the total measuring volume of 150 µL, 150 µL of above mixtures were
	used for steady state PL experiments, while 15 µL of above mixtures mixed with
	135 µL pure water were used for time-resolved (time-correlated single photon
	counting -TCSPC) PL experiments.
	4.2.8 Formation of FRET system 2 (QD-nCy5.5)

Cy5.5-Mal (4.54 mM) in anhydrous DMF was diluted to 4.54 µM in pure water. QD was diluted to 500 nM in Tris-HCl buffer at pH 7.5 (50 mM). For the formation of QD-nCy5

  180 µL of solutions containing increasing amounts (2.2, 4.4, 8.8, 17.6, 22, 33, 44, 66, 88, 110, 132 μL) of 4.54 µM Cy5.5 in Tris-HCl buffer at pH 7.5 (50 mM). The mixtures were incubated for 3 h at room temperature with the tube covered in aluminum foil and rotating with an Intelli Mixer. For the total measuring volume of 150 µL, 150 µL of above mixtures (50 nM) were used for steady state PL experiments, while 15 µL of above mixtures diluted with 135 µL of pure water were used for time-resolved (multi-channel scaling) experiments.

Table 4 .1. Photophysical properties of the FRET compounds within the multi-hybrid FRET NPs.

 4

	Fluorophore	εmax (M -1 cm -1 ) [λmax]	Φ	Filter (nm)	lifetime
	Tb	26,000 [340 nm]	0.79±0.08	494±12	2.7±0.1 ms
	QD	501,000 [610 nm]	0.20±0.05	639±10	7.0±1.2 ns
	Cy5.5	209,000 [694 nm]	0.20±0.05	708±8	~1 ns
	FRET pair	J (M -1 . cm -1 . nm 4 )		R0 (nm)
	Tb → QD	6.0±0.6× 10 16		9.7±0.7
	QD → Cy5.5	1.3±0.1× 10 16		6.0±0.4
	Tb → Cy5.5	2.5±0.3× 10 15		5.7±0.4
	Cy5.5 → Cy5.5	1.6±0.2× 10 16		6.2±0.4
	QD → QD	4.6±0.5× 10 16		7.4±0.5
	Cy5.5 → QD	1.2±0.1× 10 13		1.9±0.1

Notes:  and  of Tb and Cy5.5 were provided by the suppliers.  and  of QD were calculated using Equations 4.1, 4.2, and 4.3. J was calculated using Equation 4.4. R0 was calculated using Equation 4.5.

Table 4 .2.Table 4 .2. Brightness-equalized single-wavelength barcoding: Determination and assignment of the three different codes.

 44

						R %	G %	B %
		SPECTROSCOPY RESULTS		0.40	0.20	0.40
		(Figure 4.24 a/b)		0.45	0.21	0.34
						0.47	0.17	0.36
		MICROSCOPY RESULTS FOR EACH CODE			D
	Figure	Sample Top bead 1	R value 109	G value 54	B value 124	R % 0.38	G % 0.19	B % 0.43	E
	4.24cI	Top bead 2 Top bead 3	110 146	53 73	121 158	0.39 0.39	0.19 0.19	0.42 0.42	T
		Top bead 4 Bottom bead	155 124	77 60	163 134	0.39 0.38	0.20 0.20	0.41 0.42	E
			Code 1		mean SD	0.39 0.005 39±1%	0.19 0.005 19±1%	0.42 0.008 42±1%	R M
	4.24cII	Top bead 1 Top bead 2 Top bead 3 Bottom bead	148 114 166 163	59 43 70 68	117 88 134 131	0.46 0.46 0.45 0.45	0.18 0.18 0.19 0.19	0.36 0.36 0.36 0.36	I N
					mean SD	0.45 0.008	0.18 0.006	0.36 0.002	E
		Top bead 1	Code 2 138	61	89	45±1% 0.48	18±1% 0.21	36±1% 0.31	T
	4.24cIII	Top bead 2 Top bead 3 Bottom bead	192 149 156	86 66 69	119 95 96	0.48 0.48 0.49	0.22 0.21 0.21	0.30 0.31 0.30	C O
	mean SD 0.005 Figure 0.48 0.21 0.30 0.003 0.002 Sample R value G value B value R % G % B %	D E ASSIGN CODE
		Top left	170	74	154	0.43	0.19	0.38	2
	4.24dI	Top right Bottom left	139 157	56 59	121 120	0.44 0.47	0.18 0.17	0.38 0.36	2 3
		Bottom right	184	78	157	0.44	0.19	0.37	2
		Top left	116	47	125	0.40	0.16	0.44	1
	4.24dII	Top right Bottom left	119 169	49 73	108 171	0.43 0.41	0.18 0.18	0.39 0.41	2 1
		Bottom right	206	94	180	0.43	0.19	0.38	2
		Top left	207	102	109	0.40	0.20	0.40	1
	4.24dIII	Top right	217	91	188	0.44	0.18	0.38	2
		Bottom	173	58	130	0.48	0.16	0.36	3

Table 5 .1. Tb donor and Tb-sAv/biot-AuNP donor-acceptor decay times obtained from fits of decay models to the experimental Tb(III) luminescence decay. Uncertainties are reported as 95% confidence intervals.

 5

		Kohlrausch decay model	Multi-exponential decay model
	AuNP diam. (nm)	〈𝝉〉 𝐃 (ms)	〈𝝉〉 𝐃𝐀 (ms)	𝑬	〈𝝉〉 𝐃 (ms) 〈𝝉〉 𝐃𝐀 (ms)	𝑬
	5	2.17(±0.02) 0.80(±0.01) 0.63(±0.01) 2.15(±0.02) 0.81(±0.02) 0.62(±0.01)
	30	2.23(±0.02) 0.19(±0.01) 0.91(±0.01) 2.20(±0.02) 0.31(±0.02) 0.86(±0.02)
	50	2.20(±0.02) 0.46(±0.01) 0.79(±0.01) 2.19(±0.02) 0.47(±0.01) 0.79(±0.01)
	80	1.66(±0.02) (a) 0.14(±0.02) 0.92(±0.02) 1.78(±0.02) 0.22(±0.03) 0.87(±0.02)
	(a) Measurements for 80 nm biot-AuNPs were done in pure water instead of buffer; the donor lifetime is
	slightly shorter in this solvent.

Table 5 .2. FRET model of resonance energy transfer from Tb to AuNPs.

 5

	AuNPs	5 nm	30 nm	50 nm	80 nm
	κ 2 :	2/3	2/3	2/3	2/3
	ΦD :	0.64	0.64	0.64	0.64
	n (refractive index):	1.35	1.35	1.35	1.35
	J(λ) (M -1 cm -1 nm 4 ):	6.9 x 10 17	1.6 x 10 20	9.3 x 10 20	4.4 x 10 21
	R0 (nm):	14.1	34.8	46.8	60.7

Table 5 .3. FRET model of resonance energy transfer from Tb to AuNPs (using the refractive index of Au).

 5

	AuNPs	5 nm	30 nm	50 nm	80 nm
	κ 2 :	2/3	2/3	2/3	2/3
	ΦD :	0.64	0.64	0.64	0.64
	n (refractive index):	0.98	0.98	0.98	0.98
	J(λ) (M -1 cm -1 nm 4 ):	6.9 x 10 17	1.6 x 10 20	9.3 x 10 20	4.4 x 10 21
	R0 (nm):	17.4	43.1	57.9	75.1

Table 5 .4. Calculation of Tb-to-AuNP distance (R) with calculated Förster distances (R0) and measured PL decays (<𝝉 𝐃𝐀 > and <𝝉 𝐃 > obtained from the multi-exponential PL decay analysis).

 5

		AuNP	<𝝉 𝐃𝐀 >	<𝝉 𝐃 >	R0	R	R (in nm)
		diameter	(in ms)	(in ms)	(in nm)	(in nm)	minus
		(nm)					AuNP
							radius
	n=1.35; R0	5	0.81	2.15	11.6	10.7
	with subtracted	30	0.31	2.20	19.8	14.6
	AuNP radius	50	0.47	2.19	21.8	17.5
		80	0.22	1.78	20.7	15.1
	n=0.98; R0	5	0.81	2.15	14.6	13.5
	with subtracted	30	0.31	2.20	28.1	20.8
	AuNP radius	50	0.47	2.19	32.9	26.5
		80	0.22	1.78	35.1	25.6
	n=1.35;	5	0.81	2.15	14.1	13.0	10.5
	full R0 without	30	0.31	2.20	34.8	25.7	10.7
	subtraction	50	0.47	2.19	46.8	37.7	12.7
		80	0.22	1.78	60.7	44.2	4.2
	n=0.98;	5	0.81	2.15	17.1	15.8	13.3
	full R0 without	30	0.31	2.20	43.1	31.8	16.8
	subtraction	50	0.47	2.19	57.9	46.6	21.6
		80	0.22	1.78	75.1	54.7	14.7

Table 5 .5. Calculation of Tb-to-AuNP distance (R) with calculated Förster distances (R0) and measured PL decays

 5 (< 𝝉 𝐃𝐀 > and < 𝝉 𝐃 >

obtained from the analysis using the Kohlrausch decay law).

		AuNP	<𝝉 𝐃𝐀 >	<𝝉 𝐃 >	R0	R	R (in nm)
		diameter	(in ms)	(in ms)	(in nm)	(in nm)	minus
		(nm)					AuNP
							radius
	n=1.35; R0	5	0.80	2.17	11.6	10.6
	with subtracted	30	0.19	2.23	19.8	13.3
	AuNP radius	50	0.46	2.20	21.8	17.5
		80	0.14	1.66	20.7	13.9
	n=0.98; R0	5	0.80	2.17	14.6	13.3
	with subtracted	30	0.19	2.23	28.1	18.9
	AuNP radius	50	0.46	2.20	32.9	26.4
		80	0.14	1.66	35.1	23.6
	n=1.35;	5	0.80	2.17	14.1	12.9	10.4
	full R0 without	30	0.19	2.23	34.8	23.4	8.4
	subtraction	50	0.46	2.20	46.8	37.5	12.5
		80	0.14	1.66	60.7	40.8	0.8
	n=0.98;	5	0.80	2.17	17.1	15.6	13.1
	full R0 without	30	0.19	2.23	43.1	29.0	14.0
	subtraction	50	0.46	2.20	57.9	46.4	21.4
		80	0.14	1.66	75.1	50.5	10.5

Table 5 .6. NSET model of resonance energy transfer from Tb to AuNPs

 5

	c (m/s):	3 x 10 8
	𝚽 𝐃 :	0.64
	𝝎 𝐃 (s -1 ):	3.8 x 10 15
	𝝎 𝐅 (s -1 ):	8.4 x 10 15
	𝒌 𝐅 (m -1 )	1.2 x 10 10
	R0 (nm):	7.2

Table 5 .7. Tb-AuNP surface distances R calculated from the experimental luminescence decay times and the NSET theory. Decay times obtained using the Kohlrausch model can be compared to those obtained using multi-exponential model.

 5

		Kohlrausch decay model	Multi-exponential decay model
	AuNP diam. (nm)	𝑅 𝑅 0 NSET ⁄	R (nm) [a]	𝑅 𝑅 0 NSET ⁄	R (nm) (a)
	5	0.87 (±0.01)	6.3 (±0.6)	0.88 (±0.01)	6.4 (±0.7)
	30	0.55 (±0.01)	4.0 (±0.4)	0.63 (±0.03)	4.5 (±0.3)
	50	0.72 (±0.01)	5.2 (±0.5)	0.72 (±0.01)	5.2 (±0.6)
	80	0.55 (±0.02)	4.0 (±0.4)	0.62 (±0.03)	4.5 (±0.5)
	(a) Using 𝑅 0 NSET = 7.2(±0.7) nm, assuming 10% uncertainty on 𝑅 0 NSET

Table 7 .1. FRET system 1 (mTb-QD):

 7 Results of PL decay fitting (PL decay curves shown in Figure 7.2 d, e, and f for A; decay curves for the fitting results in B and C were similar and are not shown) of FRET-sensitized QD acceptor PL using Equations 4.13, 4.14, and 4.7. Fit range: 0.1 to 8 ms.

A (

191 Lumi4 per QD) B (191 Lumi4 per QD)

	Experi-ment	c(QD)	Tb per QD in solution	A AD1*  AD1*	τ AD1 (ms)	k FRET1	 AD1	A AD2*  AD2*	τ AD2 (ms)	k FRET2	 AD2	B	τ D (ms)	 2	τ AD (ms) E FRET
			1	279	0.546	0.13	7.32	0.14	232	0.454	0.72	1.02	0.86	81	2.7	1.327	0.64	76%
	1	5 nM	2 5	479 906	0.515 0.460	0.16 0.18	5.88 5.19	0.14 0.12	451 1063	0.485 0.540	0.80 0.83	0.88 0.83	0.86 0.88		2.7 2.7	1.250 1.222	0.71 0.75	74% 72%
			10	1965	0.448	0.20	4.63	0.12	2417	0.552	0.87	0.78	0.88		2.7	1.162	0.79	71%
			2	44.3	0.572	0.12	7.96	0.17	33.2	0.428	0.63	1.22	0.83	11	2.7	1.244	0.54	80%
			5	69.1	0.522	0.12	7.96	0.13	63.2	0.478	0.70	1.06	0.87	21	2.7	1.333	0.63	77%
			10	133	0.502	0.16	5.88	0.13	132	0.498	0.82	0.85	0.87	39	2.7	1.393	0.74	73%
			20	178	0.504	0.19	4.89	0.14	175	0.496	0.89	0.75	0.86	50	2.7	1.302	0.80	71%
	2	5 nM	50 100	481 928	0.480 0.461	0.20 0.21	4.63 4.39	0.13 0.13	521 1087	0.520 0.539	0.91 0.90	0.73 0.74	0.87 0.87		2.7 2.7	1.241 1.197	0.82 0.81	70% 70%
			150	1420	0.461	0.20	4.63	0.12	1663	0.539	0.90	0.74	0.88		2.7	1.207	0.82	70%
			200	1646	0.451	0.20	4.63	0.12	2005	0.549	0.89	0.75	0.88		2.7	1.204	0.81	70%
			250	1362	0.475	0.21	4.39	0.13	1503	0.525	0.93	0.70	0.87		2.7	1.162	0.84	69%
			300	2399	0.459	0.21	4.39	0.12	2826	0.541	0.91	0.73	0.88		2.7	1.201	0.82	69%
			20	103	0.472	0.16	5.88	0.12	115	0.528	0.78	0.91	0.88	33	2.7	1.443	0.70	74%
			50	260	0.470	0.20	4.63	0.13	293	0.530	0.89	0.75	0.87	63	2.7	1.303	0.80	70%
			100	482	0.438	0.19	4.89	0.11	618	0.562	0.86	0.79	0.89		2.7	1.278	0.78	71%
			150	848	0.468	0.21	4.39	0.12	963	0.532	0.93	0.70	0.88		2.7	1.184	0.84	69%
			200	731	0.450	0.20	4.63	0.12	893	0.550	0.88	0.77	0.88		2.7	1.204	0.80	70%
			250	1009	0.461	0.22	4.18	0.13	1182	0.539	0.92	0.72	0.87		2.7	1.189	0.83	69%
			300	1027	0.464	0.22	4.18	0.13	1186	0.536	0.93	0.70	0.87		2.7	1.225	0.84	69%
			350	828	0.443	0.19	4.89	0.12	1042	0.557	0.85	0.81	0.88		2.7	1.249	0.77	71%
	3	0.5 nM	400	1228	0.490	0.21	4.39	0.15	1276	0.510	0.87	0.78	0.85		2.7	1.269	0.77	71%
			450	1870	0.451	0.21	4.39	0.13	2275	0.549	0.87	0.78	0.87		2.7	1.248	0.79	71%
			500	1366	0.467	0.22	4.18	0.14	1560	0.533	0.89	0.75	0.86		2.7	1.204	0.80	70%
			550	1367	0.446	0.20	4.63	0.12	1700	0.554	0.87	0.78	0.88		2.7	1.226	0.79	71%
			600	1819	0.457	0.21	4.39	0.13	2165	0.543	0.87	0.78	0.87		2.7	1.257	0.78	71%
			700	1930	0.462	0.21	4.39	0.13	2247	0.538	0.87	0.78	0.87		2.7	1.218	0.78	71%
			800	1534	0.465	0.21	4.39	0.13	1765	0.535	0.90	0.74	0.87		2.7	1.240	0.81	70%
			900	2309	0.459	0.22	4.18	0.13	2719	0.541	0.90	0.74	0.87		2.7	1.206	0.81	70%
			1000	1560	0.474	0.21	4.39	0.14	1733	0.526	0.88	0.77	0.86		2.7	1.184	0.79	71%
																average	0.77	71%
	Experi-
	ment c(

QD) Tb per QD in solution A AD1

  Note: Average values (and the resulting errors) of all three tables (each consisting of different experiments, as indicated by the different background colors) were used to calculate the FRET efficiencies presented in Figure 4.10c in the manuscript. Experiments shown in red font were not used for the calculations of the data in Figure 4.10c because the PL intensities were too low or the background of unquenched Tb PL was too high.

										C (136 Lumi4 per QD)
	Experi-ment	c(QD)	Tb per QD in solution	A AD1	 AD1*	τ AD1 (ms)	k FRET1	 AD1	A AD2	 AD2*	τ AD2 (ms)	k FRET2	 AD2	B	τ D (ms)	 2	τ AD (ms) E FRET
			2	555	0.554	0.14		6.77	0.22	447	0.446	0.78		0.91	0.86	130		2.7	1.632	0.70	74%
	1	5 nM	10		0.546	0.17		5.51	0.24	1068	0.454	0.87		0.78	0.85	299		2.7	1.262	0.78	71%
			20		0.529	0.18		5.19	0.24	2614	0.471	0.87		0.78	0.86	712		2.7	1.287	0.79	71%
			5	106	0.628	0.12		7.96	0.22	62.9	0.372	0.74		0.98	0.83	33		2.7	1.471	0.64	76%
			10	150	0.588	0.14		6.77	0.22	105	0.412	0.82		0.85	0.85	53		2.7	1.311	0.73	73%
	2	5 nM	50	704	0.576	0.17		5.51	0.23	519	0.424	0.95		0.68	0.86	249		2.7	1.230	0.85	68%
			100		0.569	0.19		4.89	0.24	1117	0.431	0.97		0.66	0.85	535		2.7	1.263	0.87	68%
			200		0.554	0.19		4.89	0.24	2141	0.446	0.96		0.67	0.85	962		2.7	1.224	0.87	68%
			20	110	0.593	0.14		6.77	0.22	75.5	0.407	0.83		0.83	0.85	29		2.7	1.149	0.73	73%
			50	506	0.558	0.18		5.19	0.24	401	0.442	0.94		0.69	0.86	172		2.7	1.240	0.85	69%
			100		0.557	0.18		5.19	0.23	864	0.443	0.96		0.67	0.86	370		2.7	1.246	0.87	68%
			150		0.554	0.18		5.19	0.24	1251	0.446	0.93		0.70	0.86	537		2.7	1.247	0.84	69%
			200		0.546	0.19		4.89	0.24	1859	0.454	0.93		0.70	0.85	753		2.7	1.196	0.84	69%
			250		0.537	0.18		5.19	0.23	1851	0.463	0.91		0.73	0.86	785		2.7	1.260	0.82	69%
			300		0.545	0.19		4.89	0.24	2041	0.455	0.95		0.68	0.86	830		2.7	1.216	0.86	68%
			350		0.552	0.19		4.89	0.24	1842	0.448	0.95		0.68	0.85	742		2.7	1.236	0.86	68%
			400		0.539	0.19		4.89	0.24	2189	0.461	0.93		0.70	0.86	898		2.7	1.215	0.84	69%
	3	0.5 nM	450		0.560	0.19		4.89	0.24	1458	0.440	0.96		0.67	0.85	604		2.7	1.200	0.86	68%
			500		0.542	0.19		4.89	0.24	1811	0.458	0.94		0.69	0.86	755		2.7	1.148	0.85	68%
			550		0.546	0.19		4.89	0.24	2290	0.454	0.95		0.68	0.86	940		2.7	1.225	0.86	68%
			600		0.548	0.18		5.19	0.24	1704	0.452	0.92		0.72	0.86	709		2.7	1.149	0.83	69%
			650		0.555	0.19		4.89	0.24	1991	0.445	0.95		0.68	0.85	798		2.7	1.208	0.86	68%
			700		0.534	0.19		4.89	0.24	2554	0.466	0.92		0.72	0.86	1047		2.7	1.222	0.83	69%
			750		0.538	0.19		4.89	0.24	2406	0.462	0.93		0.70	0.86	969		2.7	1.235	0.84	69%
			800		0.546	0.20		4.63	0.25	2396	0.454	0.95		0.68	0.85	971		2.7	1.190	0.86	68%
			900		0.546	0.19		4.89	0.24	2353	0.454	0.94		0.69	0.85	937		2.7	1.230	0.85	69%
			1000		0.546	0.19		4.89	0.24	2546	0.454	0.94		0.69	0.85	1037		2.7	1.197	0.85	69%
																					average	0.82	70%
					 AD1*	τ	AD1	k	FRET1	 AD1	A AD2	 AD2*	τ	AD2	k	FRET2	 AD2	B	τ	D (ms)	 2	τ	AD (ms) E	FRET
						(ms)						(ms)
			1	685	0.525	0.16	5.88	0.23	620	0.475	0.80	0.88	0.86			2.7	1.297	0.72	73%
			2	1080	0.485	0.17	5.51	0.22	1145	0.515	0.83	0.83	0.88			2.7	1.196	0.76	72%
	1	5 nM	5	2467	0.420	0.19	4.89	0.21	3406	0.580	0.85	0.81	0.89	1020		2.7	1.182	0.80	70%
			10	4357	0.355	0.19	4.89	0.18	7919	0.645	0.88	0.77	0.92	2261		2.7	1.199	0.84	69%
			5	706	0.522	0.20	4.63	0.26	646	0.478	0.88	0.77	0.85			2.7	1.190	0.80	70%
			10	1419	0.477	0.19	4.89	0.24	1553	0.523	0.85	0.81	0.87			2.7	1.185	0.78	71%
	2	5 nM	20	2224	0.444	0.20	4.63	0.23	2790	0.556	0.87	0.78	0.88			2.7	1.194	0.81	70%
			50	4879	0.349	0.19	4.89	0.18	9096	0.651	0.90	0.74	0.92	2318		2.7	1.240	0.87	68%
			5	98.5	0.520	0.12	7.96	0.20	90.8	0.480	0.72	1.02	0.88	26		2.7	1.342	0.66	76%
			10	174	0.494	0.15	6.30	0.21	178	0.506	0.80	0.88	0.88	52		2.7	1.400	0.74	73%
			20	242	0.460	0.15	6.30	0.20	284	0.540	0.80	0.88	0.89	83		2.7	1.334	0.74	72%
	3	5 nM	50	732	0.467	0.19	4.89	0.23	837	0.533	0.88	0.77	0.88			2.7	1.166	0.82	70%
			100	1420	0.472	0.21	4.39	0.24	1589	0.528	0.91	0.73	0.87			2.7	1.171	0.84	69%
			150	2014	0.448	0.21	4.39	0.24	2478	0.552	0.89	0.75	0.88			2.7	1.149	0.83	69%
			50	413	0.447	0.18	5.19	0.21	510	0.553	0.87	0.78	0.89			2.7	1.303	0.81	70%
			100	402	0.445	0.18	5.19	0.21	502	0.555	0.88	0.77	0.89			2.7	1.249	0.82	69%
			150	805	0.451	0.19	4.89	0.22	978	0.549	0.89	0.75	0.89			2.7	1.232	0.83	69%
			200	611	0.435	0.19	4.89	0.22	793	0.565	0.87	0.78	0.89			2.7	1.257	0.82	70%
			250	824	0.428	0.19	4.89	0.22	1102	0.572	0.86	0.79	0.89			2.7	1.189	0.81	70%
			300	1284	0.458	0.21	4.39	0.24	1521	0.542	0.90	0.74	0.88			2.7	1.215	0.84	69%
			350	1015	0.432	0.19	4.89	0.22	1335	0.568	0.84	0.82	0.89			2.7	1.218	0.79	71%
			400	1220	0.447	0.21	4.39	0.23	1507	0.553	0.90	0.74	0.88			2.7	1.222	0.84	69%
			450	1232	0.459	0.22	4.18	0.24	1453	0.541	0.92	0.72	0.87			2.7	1.241	0.86	68%
	4	0.5 nM	500	1420	0.455	0.22	4.18	0.24	1698	0.545	0.91	0.73	0.87			2.7	1.194	0.85	69%
			550	1105	0.464	0.22	4.18	0.25	1279	0.536	0.90	0.74	0.87			2.7	1.253	0.84	69%
			600	1806	0.462	0.22	4.18	0.25	2104	0.538	0.90	0.74	0.87			2.7	1.169	0.84	69%
			650	1501	0.453	0.21	4.39	0.24	1813	0.547	0.90	0.74	0.88			2.7	1.247	0.84	69%
			700	1579	0.456	0.21	4.39	0.24	1883	0.544	0.90	0.74	0.88			2.7	1.154	0.84	69%
			750	1851	0.472	0.22	4.18	0.25	2073	0.528	0.92	0.72	0.87			2.7	1.157	0.85	68%
			800	1735	0.451	0.21	4.39	0.24	2112	0.549	0.89	0.75	0.88			2.7	1.243	0.83	69%
			900	2020	0.466	0.22	4.18	0.25	2315	0.534	0.89	0.75	0.86			2.7	1.247	0.82	69%
			1000	2831	0.432	0.22	4.18	0.24	3729	0.568	0.90	0.74	0.88			2.7	1.285	0.85	69%
																					average	0.81	70%
											135 136

Table 7 .2. FRET system 1 (mTb-QD):

 7 Results of PL decay fitting (PL decay curves shown in Figure 7.2 a, b, and c for A; decay curves for the fitting results in B were similar and are not shown) of FRET-quenched Tb donor PL using Equations 4.15, 4.16, and 4.10. Fit range as indicated.

A (

191 Lumi4 per QD) B (191 Lumi4 per QD)

  Note: Average values (and the resulting errors) of both tables (each consisting of different experiments, as indicated by the different background colors) were used to calculate the FRET efficiencies presented in Figure 4.10c in the manuscript. Experiments shown in red font were not used for the calculations of the data in Figure 4.10c because the PL intensities were too low or the background of unquenched Tb PL was too high.

	Experi-ment	c(QD)	Tb per QD in solution	A DA1*  DA1*	τ DA1 (ms)	A DA2*  DA2*	τ DA2 (ms)	B	τ D (ms)	 2	τ DA (ms) E FRET fit range
			1	143	0.290	0.30	350	0.710	1.10	214	2.7	1.345	0.87	68%
	1	5 nM	2 5	288 652	0.263 0.260	0.29 0.34	807 1859	0.737 0.740	1.10 1.10	439 1161	2.7 2.7	1.327 1.269	0.89 0.90	67% 67%	0.05-8ms
			10	1425	0.247	0.27	4338	0.753	1.10	2257	2.7	1.236	0.89	67%
			2	55.2	0.543	0.01	46.4	0.457	0.78	24	2.7	1.333	0.36	87%
			5	30.3	0.233	0.19	100	0.767	0.98	51	2.7	1.569	0.80	71%
			10	69.2	0.220	0.18	246	0.780	0.99	117	2.7	1.425	0.81	70%
			20	91.3	0.199	0.15	367	0.801	0.98	162	2.7	1.403	0.81	70%
	2	5 nM	50	251 614	0.188 0.226	0.18 0.26	1082 2105	0.812 0.774	1.00 1.10	409 731	2.7 2.7	1.314 1.320	0.85 0.91	69% 66%
				1040	0.258	0.33	2991	0.742	1.10	992	2.7	1.260	0.90	67%
				1151	0.238	0.28	3690	0.762	1.10	1242	2.7	1.241	0.91	66%
				925	0.247	0.33	2814	0.753	1.10	953	2.7	1.270	0.91	66%
				1693	0.251	0.27	5048	0.749	1.10	1681	2.7	1.250	0.89	67%
			20	74.4	0.241	0.11	234	0.759	0.94	100	2.7	1.484	0.74	73%
			50	196	0.235	0.21	639	0.765	1.00	186	2.7	1.422	0.81	70%
				421	0.243	0.23	1313	0.757	1.00	391	2.7	1.281	0.81	70%
				582	0.212	0.22	2160	0.788	1.00	692	2.7	1.281	0.83	69%	0.01-8ms
				601	0.232	0.23	1985	0.768	1.00	548	2.7	1.352	0.82	70%
				789	0.231	0.26	2629	0.769	1.10	823	2.7	1.363	0.91	66%
				803	0.227	0.22	2741	0.773	1.00	872	2.7	1.280	0.82	70%
				861	0.270	0.26	2322	0.730	1.00	565	2.7	1.341	0.80	70%
	3	0.5 nM		1206	0.287	0.21	3003	0.713	0.95	639	2.7	1.352	0.74	73%
				1798	0.269	0.24	4881	0.731	1.00	1174	2.7	1.273	0.80	71%
				1204	0.254	0.25	3536	0.746	1.00	788	2.7	1.293	0.81	70%
				1277	0.252	0.26	3783	0.748	1.00	862	2.7	1.319	0.81	70%
				1845	0.282	0.23	4699	0.718	1.00	1129	2.7	1.318	0.78	71%
				1875	0.275	0.25	4943	0.725	1.00	1080	2.7	1.308	0.79	71%
				1384	0.260	0.24	3948	0.740	1.00	1084	2.7	1.243	0.80	70%
				2164	0.275	0.26	5694	0.725	1.10	1398	2.7	1.348	0.87	68%
			1000	1469	0.277	0.24	3836	0.723	1.00	1159	2.7	1.260	0.79	71%
												average	0.82	70%
	Experi-ment	c(QD)	Tb per QD in solution	A DA1	 DA1*	τ DA1 (ms)	A DA2	 DA2*	τ DA2 (ms)	B	τ D (ms)		2	τ DA (ms) E FRET fit range
			1	429	0.256	0.18	1249	0.744	0.99	808	2.7	1.284	0.78	71%
	1	5 nM	2	717	0.235	0.19	2340	0.765	1.00	1431	2.7	1.216	0.81	70%	0.05-8ms
			5	2008	0.241	0.23	6334	0.759	1.10	3521	2.7	1.235	0.89	67%
			10	3528	0.228	0.15	11972	0.772	1.20	7852	2.7	1.216	0.96	64%
			5	387	0.223	0.15	1348	0.777	0.95	720	2.7	1.283	0.77	71%	0.02-8ms
	2	5 nM	10 20	1027 1979	0.253 0.278	0.16 0.21	3034 5137	0.747 0.722	0.99 1.10	1618 2783	2.7 2.7	1.328 1.291	0.78 0.85	71% 68%	0.01-8ms
			50	4984	0.272	0.13	13339	0.728	1.20	7268	2.7	1.212	0.91	66%
			5	44	0.228	0.16	149	0.772	0.95	72	2.7	1.464	0.77	71%	0.02-8ms
			10	89	0.204	0.09	347	0.796	0.88	176	2.7	1.323	0.72	73%
	3	5 nM	20	160	0.228	0.13	543	0.772	0.95	264	2.7	1.353	0.76	72%
			50	434	0.203	0.19	1699	0.797	1.00	772	2.7	1.321	0.84	69%
				913	0.227	0.26	3111	0.773	1.10	1307	2.7	1.250	0.91	66%
				1478	0.247	0.27	4514	0.753	1.10	1847	2.7	1.213	0.90	67%
			50	373	0.240	0.17	1178	0.760	0.96	440	2.7	1.368	0.77	71%
				307	0.218	0.19	1102	0.782	1.00	397	2.7	1.298	0.82	69%
				659	0.243	0.26	2058	0.757	1.10	829	2.7	1.282	0.90	67%
				497	0.220	0.21	1758	0.780	1.00	673	2.7	1.308	0.83	69%
				712	0.238	0.27	2283	0.762	1.10	885	2.7	1.261	0.90	67%
				1157	0.253	0.23	3420	0.747	1.00	1191	2.7	1.264	0.81	70%
				1001	0.261	0.26	2838	0.739	1.00	926	2.7	1.329	0.81	70%	0.01-8ms
				1090	0.252	0.26	3243	0.748	1.10	1189	2.7	1.340	0.89	67%
	4	0.5 nM		1078	0.248	0.25	3267	0.752	1.10	1207	2.7	1.325	0.89	67%
				1223	0.241	0.25	3855	0.759	1.00	1176	2.7	1.274	0.82	70%
				1064	0.265	0.28	2958	0.735	1.10	1063	2.7	1.275	0.88	67%
				1807	0.277	0.24	4710	0.723	1.10	1443	2.7	1.295	0.86	68%
				1192	0.237	0.26	3831	0.763	1.10	1371	2.7	1.267	0.90	67%
				1289	0.246	0.27	3950	0.754	1.10	1476	2.7	1.239	0.90	67%
				1664	0.282	0.25	4235	0.718	1.10	1349	2.7	1.310	0.86	68%
				1511	0.255	0.25	4407	0.745	1.10	1514	2.7	1.271	0.88	67%
				2026	0.286	0.23	5068	0.714	1.00	1384	2.7	1.321	0.78	71%
			1000	2764	0.285	0.26	6949	0.715	1.20	2736	2.7	1.266	0.93	65%
												average	0.85	69%
								137

Table 7 .3. FRET system 2 (QD-nCy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure 7.3a for A; decay curves for the fitting results in B were similar and are not shown) of FRET-quenched QD donor PL in FRET system 2 (QD-nCy5.5) using Equations 4.15, 4.16, and 4.10. Fit range: 0.1 to 8 ms.

	A
	B

Table 7 .4. FRET system 2 (QD-nCy5.5):

 7 FRET efficiencies calculated by steady-state PL intensities (from PL spectra shown in Figure 4.12c for A; PL spectra for the results in B were similar and are not shown) using Equation 4.11.

Table 7 .

 7

	5. FRET system 2 (QD-nCy5.5): Calculation of R using the FRET-efficiencies from
	Tables 7.3 and 7.4 and Equation 4.12 with an R0 = 6.0 nm.
	Note: Values shown in red font were not used for calculating the average distances because of the relatively
	high uncertainties caused by the low values of n, which lead to FRET efficiencies in the very steep part of the
	increasing FRET efficiency curve in Figure 4.12e.

mean) = 7.9±0.6 nm 139Table 7 .6. FRET system 3 (mTb-QD-15Cy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure 4.16a for A; decay curves for the fitting results in B and C were similar and are not shown) of FRET-quenched Tb donor PL using Equations 4.15, 4.16, and 4.10. Fit range: 0.02 to 8 ms.

						A
	Tb per QD-
	15Cy5.5 in	A DA1	τ DA1 (ms)	A DA2	τ DA2 (ms)	B	τ D (ms)	 2	τ DA (ms)	E FRET
	solution
	1	154	0.097	176	0.9	62	2.7	1.622	0.50	81%
	2	286	0.15	333	0.9	120	2.7	1.571	0.57	79%
	4	537	0.13	644	0.9	225	2.7	1.454	0.56	79%
	8	1251	0.14	1489	0.9	499	2.7	1.486	0.56	79%
	10	1566	0.15	1834	1.0	603	2.7	1.508	0.58	78%
	15	2161	0.14	2546	0.9	825	2.7	1.451	0.57	79%
	20	3086	0.15	3489	1.0	1081	2.7	1.524	0.57	79%
	30	4230	0.15	4524	1.0	1357	2.7	1.510	0.57	79%
	40	5240	0.15	5417	1.0	1598	2.7	1.520	0.57	79%
	50	6091	0.15	6156	1.0	6156	2.7	1.565	0.57	79%
	60	6726	0.15	6764	1.0	1888	2.7	1.638	0.57	79%
	70	7348	0.15	7542	1.0	2135	2.7	1.664	0.57	79%
	80	7502	0.14	7791	1.0	2233	2.7	1.710	0.56	79%
	90	7799	0.15	7989	1.0	2333	2.7	1.780	0.56	79%
	100	7888	0.15	8194	1.0	2349	2.7	1.759	0.56	79%
	150	8420	0.14	8937	1.0	2522	2.7	1.801	0.56	79%
	200	8513	0.14	8964	1.0	2541	2.7	1.809	0.56	79%
	250	8746	0.14	9363	1.0	2638	2.7	1.842	0.56	79%
	300	9053	0.13	10035	0.9	2852	2.7	1.928	0.55	80%
	400	9149	0.14	9969	1.0	2796	2.7	1.852	0.56	79%
	500	9346	0.13	10271	0.9	2943	2.7	1.902	0.55	80%
	600	9425	0.13	10433	0.9	2969	2.7	1.943	0.55	80%
	700	9695	0.13	10814	0.9	3029	2.7	1.905	0.56	79%
	800	9580	0.14	10574	0.9	2987	2.7	2.035	0.56	79%
	900	9512	0.13	10675	0.9	3048	2.7	2.003	0.55	80%
	1000	9814	0.13	11063	0.9	3169	2.7	2.051	0.56	79%
									average	79%
						B

Tb per QD- 15Cy5.5 in solution A DA1 τ DA1 (ms) A DA2 τ DA2 (ms) B τ D (ms)  2 τ DA (ms) E FRET

	1	131	0.1	152	0.81	56.8	2.7	1.572	0.48	82%
	2	256	0.12	316	0.83	118	2.7	1.544	0.51	81%
	4	507	0.15	570	0.92	201	2.7	1.473	0.56	79%
	8	1195	0.15	1359	0.93	446	2.7	1.390	0.57	79%
	10	1520	0.14	1787	0.91	598	2.7	1.377	0.56	79%
	15	2103	0.14	2428	0.92	780	2.7	1.371	0.56	79%
	20	2848	0.15	3190	0.93	999	2.7	1.369	0.56	79%
	30	3900	0.15	4141	0.95	1243	2.7	1.409	0.56	79%
	40	4559	0.15	4828	0.95	1421	2.7	1.352	0.56	79%
	50	5143	0.15	5334	0.95	1552	2.7	1.355	0.56	79%
	60	5641	0.15	5767	0.95	1670	2.7	1.402	0.55	79%
	70	6179	0.15	6274	0.97	1771	2.7	1.312	0.56	79%
	80	6420	0.15	6616	0.94	1914	2.7	1.337	0.55	80%
	90	6579	0.15	6673	0.96	1936	2.7	1.366	0.56	79%
	100	6933	0.15	6933	0.96	1999	2.7	1.349	0.56	79%
	150	7402	0.15	7435	0.96	2112	2.7	1.403	0.56	79%
	200	7434	0.14	7745	0.93	2229	2.7	1.331	0.54	80%
	250	7657	0.14	7972	0.94	2241	2.7	1.387	0.55	80%
	300	8055	0.14	8496	0.94	2402	2.7	1.359	0.55	80%
	400	8258	0.14	8735	0.94	2466	2.7	1.381	0.55	80%
	500	8451	0.14	8846	0.95	2489	2.7	1.430	0.55	79%
	600	8423	0.14	8942	0.94	2502	2.7	1.395	0.55	80%
	700	8996	0.14	9733	0.94	2682	2.7	1.419	0.56	79%
	800	8985	0.14	9795	0.93	2740	2.7	1.366	0.55	80%
	900	9026	0.14	9844	0.93	2768	2.7	1.422	0.55	80%
	1000	9111	0.14	9887	0.93	2843	2.7	1.395	0.55	80%
									average	80%
						140

C

  Note: Average values (and the resulting errors) of all three tables were used to calculate the FRET efficiencies presented in Figure 4.16d. Experiments shown in red font were not used for the calculations of the data in Figure 4.16d because the PL intensities were too low or the background of unquenched Tb PL was too high.

Table 7 .7. FRET system 3 (mTb-QD-15Cy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure4.16b for A; decay curves for the fitting results in B and C were similar and are not shown) of FRET-sensitized QD acceptor PL using Equations 4.13, 4.14, and 4.7. Green rows were used for calculating FRET-corrected FRET efficiencies (using Equations 4.14). Yellow rows were used to calculate apparent FRET-efficiencies (without correction for FRET rates). Comparison of both FRET efficiencies is shown in Figure4.17. Fit range: 0.1 to 8 ms.

	A

per QD- 15Cy5.5 in solution A AD1*  AD1* k FRET1  AD1 τ AD1 (ms) A AD2  AD2* k FRET2  AD2 τ AD2 (ms) B τ D (ms)  2 τ AD (ms) τ AD (ms) E FRET E

																		FRET
	1	96.5	0.648	7.96	0.21	0.12	52.5	0.352	1.12	0.79	0.67	43.3	2.7	1.479	0.31	0.56	88%	79%
	2	125	0.592	6.77	0.16	0.14	86.3	0.408	0.90	0.84	0.79	29.2	2.7	1.483	0.41	0.69	85%	75%
	4	191	0.584	5.88	0.16	0.16	136	0.416	0.79	0.84	0.86	48	2.7	1.582	0.45	0.75	83%	72%
	8	349	0.519	5.51	0.13	0.17	323	0.481	0.79	0.87	0.86	97.2	2.7	1.392	0.50	0.77	81%	72%
	10	440	0.520	5.19	0.14	0.18	406	0.480	0.78	0.86	0.87	128	2.7	1.346	0.51	0.77	81%	71%
	15	581	0.501	5.51	0.13	0.17	579	0.499	0.81	0.87	0.85	166	2.7	1.278	0.51	0.76	81%	72%
	20	791	0.514	5.19	0.13	0.18	748	0.486	0.75	0.87	0.89	205	2.7	1.314	0.53	0.80	81%	71%
	30	1087	0.527	4.89	0.15	0.19	976	0.473	0.75	0.85	0.89	266	2.7	1.265	0.52	0.79	81%	71%
	40	1247	0.508	5.19	0.13	0.18	1206	0.492	0.78	0.87	0.87	308	2.7	1.252	0.52	0.78	81%	71%
	50	1453	0.519	5.19	0.14	0.18	1344	0.481	0.77	0.86	0.88	330	2.7	1.258	0.52	0.78	81%	71%
	60	1569	0.523	4.63	0.15	0.2	1432	0.477	0.75	0.85	0.89	351	2.7	1.291	0.53	0.79	80%	71%
	70	1696	0.511	5.19	0.14	0.18	1625	0.489	0.79	0.86	0.86	392	2.7	1.266	0.51	0.77	81%	72%
	80	1824	0.516	5.19	0.14	0.18	1711	0.484	0.79	0.86	0.86	412	2.7	1.280	0.51	0.76	81%	72%
	90	1859	0.513	5.19	0.14	0.18	1766	0.487	0.79	0.86	0.86	423	2.7	1.276	0.51	0.77	81%	72%
	100	1935	0.513	5.19	0.14	0.18	1835	0.487	0.79	0.86	0.86	433	2.7	1.324	0.51	0.77	81%	72%
	150	2135	0.518	5.19	0.14	0.18	1987	0.482	0.79	0.86	0.86	472	2.7	1.264	0.51	0.76	81%	72%
	200	2175	0.517	4.89	0.15	0.19	2029	0.483	0.79	0.85	0.86	474	2.7	1.254	0.51	0.76	81%	72%
	250	2229	0.515	5.19	0.14	0.18	2099	0.485	0.79	0.86	0.86	478	2.7	1.319	0.51	0.77	81%	72%
	300	2373	0.517	4.89	0.15	0.19	2213	0.483	0.78	0.85	0.87	506	2.7	1.314	0.52	0.77	81%	71%
	400	2486	0.519	4.89	0.14	0.19	2303	0.481	0.77	0.86	0.88	513	2.7	1.341	0.52	0.78	81%	71%
	500	2465	0.511	4.89	0.14	0.19	2361	0.489	0.78	0.86	0.87	525	2.7	1.264	0.52	0.77	81%	71%
	600	2509	0.508	5.19	0.14	0.18	2427	0.492	0.81	0.86	0.85	538	2.7	1.281	0.51	0.76	81%	72%
	700	2758	0.511	4.89	0.14	0.19	2642	0.489	0.79	0.86	0.86	571	2.7	1.305	0.52	0.76	81%	72%
	800	2753	0.512	5.19	0.14	0.18	2626	0.488	0.79	0.86	0.86	574	2.7	1.289	0.51	0.77	81%	72%
	900	2814	0.519	4.89	0.15	0.19	2610	0.481	0.78	0.85	0.87	569	2.7	1.260	0.52	0.77	81%	71%
	1000	2830	0.509	5.19	0.14	0.18	2734	0.491	0.81	0.86	0.85	595	2.7	1.328	0.51	0.76	81%	72%
									142

C

  Note: Average values (and the resulting errors) of all three tables were used to calculate the FRET efficiencies presented in Figure 4.16d. Experiments shown in red font were not used for the calculations of the data in Figure 4.16d because the PL intensities were too low or the background of unquenched Tb PL was too high.

Table 7 .8. FRET system 3 (mTb-QD-15Cy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure 4.16c for A; decay curves for the fitting results in B and C were similar and are not shown) of FRET-sensitized Cy5.5 acceptor PL using Equations 4.13, 4.14, and 4.7. Fit range: 0.1 to 4 ms.

	Tb per QD-15Cy5.5 in solution	A AD1*  AD1* k FRET1  AD1	τ AD1 (ms)	A AD2  AD2* k FRET2  AD2	τ AD2 (ms)	B	τ D (ms)	 2	τ AD (ms)	τ AD (ms)	E FRET E FRET
	1	52	0.591 10.50	0.15	0.092	36	0.409	1.32	0.85	0.59	13	2.7	1.348	0.30	0.51	89%	81%
	2	65	0.533	9.63	0.12	0.1	57	0.467	1.14	0.88	0.66	20	2.7	1.350	0.36	0.59	87%	78%
	4	114	0.553	6.30	0.13	0.15	92	0.447	0.79	0.87	0.86	30	2.7	1.390	0.47	0.76	83%	72%
	8	170	0.482	6.77	0.10	0.14	183	0.518	0.85	0.90	0.82	58	2.7	1.350	0.49	0.75	82%	72%
	10	223	0.515	5.19	0.13	0.18	210	0.485	0.72	0.87	0.92	65	2.7	1.339	0.54	0.83	80%	69%
	15	338	0.510	4.89	0.13	0.19	325	0.490	0.69	0.87	0.94	96	2.7	1.328	0.56	0.84	79%	69%
	20	375	0.474	6.30	0.11	0.15	416	0.526	0.83	0.89	0.83	125	2.7	1.402	0.51	0.76	81%	72%
	30	625	0.502	5.51	0.12	0.17	621	0.498	0.75	0.88	0.89	184	2.7	1.267	0.53	0.80	80%	70%
	40	661	0.510	5.51	0.12	0.17	634	0.490	0.74	0.88	0.90	173	2.7	1.303	0.53	0.81	80%	70%
	50		0.522	4.89	0.14	0.19	963	0.478	0.73	0.86	0.91	259	2.7	1.174	0.53	0.81	80%	70%
	60		0.529	4.89	0.14	0.19	1041 0.471	0.69	0.86	0.94	259	2.7	1.240	0.54	0.84	80%	69%
	70		0.516	5.19	0.13	0.18	1117 0.484	0.75	0.87	0.89	288	2.7	1.249	0.52	0.79	81%	71%
	80		0.503	5.51	0.13	0.17	1197 0.497	0.79	0.87	0.86	306	2.7	1.187	0.51	0.77	81%	71%
	90		0.502	5.51	0.13	0.17	1241 0.498	0.79	0.87	0.86	320	2.7	1.241	0.51	0.77	81%	71%
	100		0.508	5.19	0.14	0.18	1457 0.492	0.79	0.86	0.86	348	2.7	1.233	0.51	0.77	81%	72%
	150		0.516	4.89	0.14	0.19	1468 0.484	0.74	0.86	0.90	366	2.7	1.239	0.53	0.80	80%	70%
	200		0.515	4.89	0.14	0.19	1562 0.485	0.77	0.86	0.88	401	2.7	1.273	0.52	0.78	81%	71%
	250		0.524	4.63	0.15	0.2	1501 0.476	0.74	0.85	0.90	379	2.7	1.231	0.53	0.80	80%	71%
	300		0.523	4.89	0.14	0.19	1373 0.477	0.74	0.86	0.90	356	2.7	1.266	0.53	0.80	80%	70%

C

  Note: Average values (and the resulting errors) of all three tables were used to calculate the FRET efficiencies presented in Figure 4.16d. Experiments shown in red font were not used for the calculations of the data in Figure 4.16d because the PL intensities were too low or the background of unquenched Tb PL was too high.

Table 7 .9. FRET system 4 (75Tb-QD-nCy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure 4.18a for A; decay curves for the fitting results in B were similar and are not shown) of FRET-quenched Tb donor PL using Equations 4.15, 4.16, and 4.10. Fit range: 0.01 to 8 ms. Experiments shown in red font were not used for the calculations of the data in Figure 4.18d because the PL intensities were too low or the background of unquenched Tb PL was too high.

	Tb per QD-15Cy5.5 in solution	A AD1	 AD1*	k FRET1	 AD1 τ AD1 (ms) A AD2	 AD2*	k FRET2	 AD2 τ AD2 (ms) A AD3	 AD3* τ AD3 (ms)	 2	τ AD (ms)	QD τ D (ms)	E FRET  AD1&2
	1	37.9	0.35	25.08	0.09	0.037	52.8	0.48	3.31	0.91	0.19	18.6	0.17	0.88	1.095	0.18	0.51	66%
	2	67.4	0.33	35.35	0.08	0.027	96.6	0.48	4.20	0.92	0.17	38.9	0.19	0.82	1.274	0.16	0.59	73%
	4	162	0.42	16.55	0.12	0.056	175	0.45	2.54	0.88	0.26	48.8	0.13	1.1	1.043	0.23	0.76	69%
	8	369	0.48	12.55	0.17	0.072	310	0.40	2.11	0.83	0.29	96.3	0.12	1.1	1.140	0.25	0.75	66%
	10	533	0.52	10.84	0.21	0.083	369	0.36	2.01	0.79	0.31	124	0.12	1.1	1.248	0.26	0.83	68%
	15	897	0.52	11.64	0.19	0.078	639	0.37	1.94	0.81	0.32	193	0.11	1.1	1.364	0.27	0.84	68%
	20	1109	0.55	10.31	0.20	0.086	713	0.35	1.62	0.80	0.34	202	0.10	1.2	1.374	0.29	0.76	62%
	30	1717	0.53	11.10	0.20	0.081	1166	0.36	1.88	0.80	0.32	329	0.10	1.2	1.486	0.27	0.80	66%
	40	1711	0.52	11.92	0.19	0.076	1241	0.38	1.99	0.81	0.31	344	0.10	1.1	1.385	0.27	0.81	67%
	50	2767	0.55	10.53	0.20	0.085	1815	0.36	1.71	0.80	0.34	459	0.09	1.2	1.451	0.29	0.81	64%
	60	2908	0.54	11.00	0.20	0.082	1974	0.37	1.84	0.80	0.33	502	0.09	1.2	1.433	0.28	0.84	66%
	70	2949	0.54	10.65	0.20	0.084	2012	0.37	1.77	0.80	0.33	513	0.09	1.2	1.442	0.28	0.79	65%
	80	3059	0.52	11.21	0.18	0.08	2206	0.38	1.83	0.82	0.32	575	0.10	1.1	1.460	0.28	0.77	64%
	90	3298	0.54	10.47	0.20	0.085	2249	0.37	1.74	0.80	0.33	587	0.10	1.2	1.441	0.28	0.77	63%
	100	3782	0.54	10.60	0.19	0.084	2647	0.38	1.73	0.81	0.33	627	0.09	1.2	1.386	0.28	0.77	63%
	150	3915	0.53	10.52	0.19	0.085	2789	0.38	1.78	0.81	0.33	688	0.09	1.2	1.468	0.28	0.80	65%
	200	4211	0.53	10.21	0.19	0.087	2971	0.38	1.66	0.81	0.34	701	0.09	1.2	1.437	0.29	0.78	63%
	250	4265	0.53	10.51	0.19	0.085	2986	0.37	1.68	0.81	0.34	724	0.09	1.2	1.463	0.29	0.80	63%
	300	3915	0.55	10.38	0.19	0.086	2635	0.37	1.61	0.81	0.35	612	0.09	1.2	1.428	0.30	0.80	62%
																		65%

A B

Note: Average values (and the resulting errors) of both tables were used to calculate the FRET efficiencies presented in Figure

4

.18d.

Table 7 .10. FRET system 4 (75Tb-QD-nCy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure4.18b for A; decay curves for the fitting results in B were similar and are not shown) of FRET-sensitized QD acceptor PL using Equations 4.13, 4.14, and 4.7. Green rows were used for calculating FRET-corrected FRET efficiencies (using Equations 4.14). Yellow rows were used to calculate apparent FRET-efficiencies (without correction for FRET rates). Fit range: 0.1 to 8 ms. Experiments shown in red font were not used for the calculations of the data in Figure4.18d because the PL intensities were too low or the background of unquenched Tb PL was too high.

	Cy5.5 per 75Tb-QD	A AD1*  AD1* k FRET1  AD1	τ AD1 (ms)	A AD2  AD2* k FRET2  AD2	τ AD2 (ms)	B	τ D (ms)		2	τ AD (ms)	τ AD (ms)	E FRET E FRET
	0	313	0.576		4.63	0.16	0.2	230	0.424		0.63	0.84	1.00	110		2.7	1.305	0.54	0.88	80%	68%
	1	252	0.575		5.51	0.15	0.17	186	0.425		0.72	0.85	0.92	90		2.7	1.300	0.49	0.81	82%	70%
	2	201	0.535		5.88	0.14	0.16	175	0.465		0.82	0.86	0.84	85		2.7	1.267	0.48	0.75	82%	72%
	4	144	0.524		5.88	0.12	0.16	131	0.476		0.75	0.88	0.89	56		2.7	1.279	0.51	0.80	81%	70%
	8	90	0.533		5.88	0.14	0.16	79	0.467		0.81	0.86	0.85	28		2.7	1.327	0.48	0.76	82%	72%
	10	92	0.541		5.51	0.14	0.17	78	0.459		0.79	0.86	0.86	27		2.7	1.317	0.49	0.76	82%	72%
	15	54	0.540		7.96	0.12	0.12	46	0.460		0.96	0.88	0.75	12		2.7	1.337	0.41	0.67	85%	75%
	20	35	0.493		7.96	0.15	0.12	36	0.507		1.42	0.85	0.56	11		2.7	1.379	0.34	0.50	87%	82%
	30	22	0.524		7.96	0.17	0.12	20	0.476		1.45	0.83	0.55	6.2		2.7	1.454	0.32	0.48	88%	82%
	40	18	0.600		9.63	0.20	0.1	12	0.400		1.63	0.80	0.50	4.2		2.7	1.253	0.26	0.42	90%	84%
	50	12	0.500 32.96	0.08	0.03	12	0.500		2.86	0.92	0.31	4.7		2.7	1.378	0.17	0.29	94%	89%
	60	1	0.137 28.20	0.03	0.035	6.3	0.863		4.63	0.97	0.20	2.8		2.7	1.405	0.18	0.20	93%	93%
	Cy5.5 75Tb-QD A per AD1*	 AD1*	k	FRET1	 AD1	(ms) τ AD1	A AD2	 AD2*	k	FRET2	 AD2	(ms) τ AD2	B	τ	D (ms)	 2	(ms) τ AD	(ms) τ AD	E	FRET	E	FRET
	0	4383	0.533		4.89	0.13	0.19	3837	0.467		0.66	0.87	0.97	1542		2.7	1.231	0.55	0.87	79%	68%
	1	4671	0.597		5.19	0.18	0.18	3149	0.403		0.79	0.82	0.86	998		2.7	1.308	0.45	0.73	83%	73%
	2	3712	0.602		5.51	0.18	0.17	2450	0.398		0.82	0.82	0.84	789		2.7	1.349	0.44	0.72	84%	73%
	4	2829	0.609		6.30	0.15	0.15	1815	0.391		0.73	0.85	0.91	747		2.7	1.221	0.45	0.79	83%	71%
	8	1854	0.616		5.88	0.19	0.16	1157	0.384		0.85	0.81	0.82	280		2.7	1.271	0.41	0.70	85%	74%
	10	2184	0.612		5.88	0.19	0.16	1386	0.388		0.85	0.81	0.82	346		2.7	1.277	0.42	0.70	85%	74%
	15	1947	0.616		5.88	0.21	0.16	1212	0.384		0.96	0.79	0.75	249		2.7	1.307	0.39	0.63	86%	77%
	20	908	0.623		6.30	0.22	0.15	550	0.377		1.06	0.78	0.70	113		2.7	1.330	0.36	0.58	87%	78%
	30	839	0.647		6.77	0.24	0.14	458	0.353		1.14	0.76	0.66	79.5		2.7	1.421	0.32	0.54	88%	80%
	40	958	0.674		6.30	0.28	0.15	464	0.326		1.17	0.72	0.65	71.8		2.7	1.416	0.31	0.51	88%	81%
	50	423	0.667		7.32	0.28	0.13	211	0.333		1.42	0.72	0.56	46.3		2.7	1.419	0.27	0.44	90%	84%
	60	232	0.652		9.63	0.26	0.1	124	0.348		1.85	0.74	0.45	35.6		2.7	1.402	0.22	0.36	92%	87%

A B

Note: Average values (and the resulting errors) of both tables were used to calculate the FRET efficiencies presented in Figure

4

.18d.

Table 7 .11. FRET system 4 (75Tb-QD-nCy5.5):

 7 Results of PL decay fitting (PL decay curves shown in Figure 4.18c for A; decay curves for the fitting results in B were similar and are not shown) of FRET-sensitized Cy5.5 acceptor PL using Equations 4.13, 4.14, and 4.7. Fit range: 0.1 to 4 ms.

	Cy5.5 per 75Tb-QD	A AD1  AD1* k FRET1  AD1	τ AD1 (ms)	A AD2  AD2* k FRET2  AD2	τ AD2 (ms)	A AD3  AD3*	τ AD3 (ms)		2	τ AD (ms)	QD τ D (ms)

A B Note: Average values (and the resulting errors) of both tables were used to calculate the FRET efficiencies presented in Figure 4.18d in the manuscript. Experiments shown in red font were not used for the calculations of the data in Figure 4.18d because the PL intensities were too low or the background of unquenched Tb PL was too high.

Energy transfer from Tb donors to AuNPs 7.4.1 Stability of the AuNPs in buffer

	7.4 The stability of the biotinylated particles in different buffers was studied for 50 nm
	biot-AuNP and 80 nm biot-AuNP, by measuring extinction and resonant light
	scattering spectra. Two buffers were investigated: PBS (Phosphate-buffered saline,
	10 mM phosphate, pH 7.2, 137 mM NaCl, 2.7 mM KCl) and Tris-HCl buffer (4 mM,
	pH 8.4). A suspension of the same particles diluted in purified deionized water was
	used in comparison.
																	87	\
	1	595	0.40	12.34	0.15	0.073	591	0.40	2.21	0.85	0.28	297	0.20	1.1	1.165	0.25	0.73	66%
	2	799	0.42	10.95	0.17	0.081	728	0.39	2.05	0.83	0.29	361	0.19	1.1	1.166	0.25	0.72	65%
	4	1243	0.41	11.73	0.18	0.077	1184	0.39	2.44	0.82	0.27	579	0.19	1.1	1.218	0.24	0.79	70%
	8	879	0.45	12.08	0.17	0.074	747	0.39	2.13	0.83	0.28	309	0.16	0.99	1.300	0.24	0.70	65%
	10	1077	0.42	12.46	0.16	0.072	1076	0.42	2.41	0.84	0.26	437	0.17	0.95	1.396	0.23	0.70	67%
	15	1257	0.44	12.90	0.17	0.069	1173	0.41	2.41	0.83	0.25	450	0.16	0.89	1.248	0.22	0.63	65%
	20	617	0.44	14.15	0.16	0.063	595	0.42	2.63	0.84	0.23	200	0.14	0.82	1.475	0.20	0.58	65%
	30	534	0.45	13.76	0.18	0.064	488	0.41	2.68	0.82	0.22	160	0.14	0.75	1.376	0.19	0.54	64%
	40	340	0.35	21.30	0.11	0.043	484	0.49	3.93	0.89	0.17	161	0.16	0.64	1.394	0.16	0.51	70%
	50	127	0.33	20.98	0.11	0.043	198	0.52	3.98	0.89	0.16	56.6	0.15	0.59	1.176	0.15	0.44	67%
	60	48.5	0.22 140.06 0.03	0.007	119	0.54	9.25	0.97	0.08	52.9	0.24	0.34	1.262	0.08	0.36	77%
									148

Table 7 .

 7 12. Multi-exponential fits of Lumi4-Tb-sAv-biot-5 nm Au NPs.

	NO.	%	𝝉 𝟏 		A1	DA*1	DA1		𝝉 𝟐	E2	A2	DA*2	DA2
		0							540 0.75 577	0.13	1.00
		10	350 0.84 663	0.18	0.27		940 0.56 1802	0.50	0.73
		50	370 0.83 926	0.26	0.30		990 0.54 2120	0.59	0.70
		100	370 0.83 454	0.15	0.18		990 0.54 2080	0.67	0.82
		200	390 0.82 884	0.26	0.30		970 0.55 2047	0.60	0.70
		300	380 0.82 833	0.25	0.28		960 0.55 2124	0.63	0.72
		400	310 0.86 722	0.20	0.23		920 0.57 2371	0.67	0.77
		500	350 0.84 747	0.23	0.26		940 0.56 2112	0.64	0.74
		600	410 0.81 885	0.27	0.32		990 0.54 1912	0.59	0.68
		700	320 0.85 594	0.20	0.23		940 0.56 1956	0.64	0.77
	10	800	350 0.84 643	0.20	0.24		950 0.56 1984	0.63	0.76
	average 1-10	360 0.83			0.26		960 0.55			0.74
						fraction: 26%					fraction: 74%
	NO.	%		𝝉 𝟎 (fixed)	A0	DA*0			〈𝝉〉	z(D)	𝝉 𝐃𝐀  
		0			2400	3792	0.87			2150
		10			2400	1162	0.32			1300	0.05	790	0.63
		50			2400	555	0.15			1050	0.02	810	0.62
		100			2400	550	0.18			1150	0.03	890	0.59
		200			2400	480	0.14			1020	0.02	800	0.63
		300			2400	430	0.13			1000	0.02	800	0.63
		400			2400	451	0.13			980	0.02	780	0.64
		500			2400	455	0.14			1010	0.02	790	0.63
		600			2400	452	0.14			1030	0.02	810	0.62
		700			2400	486	0.16			1050	0.02	800	0.63
	10	800			2400	512	0.16			1060	0.02	810	0.62
	average 1-10			2400							810	0.62

Table 7 .

 7 13. Multi-exponential fits of Lumi4-Tb-sAv-biot-30 nm Au NPs.

	NO.	%	𝝉 𝟏 		A1	DA*1	DA1		𝝉 𝟐	E2	A2	DA*2	DA2
	0	0									550 0.75 455	0.11	1.00
	1	10	80 0.96 217	0.05		0.29		590 0.73 528	0.12	0.71
	2	20	140 0.94 249	0.06		0.35		640 0.71 468	0.11	0.65
	3	50	140 0.94 454	0.12		0.44		710 0.68 568	0.14	0.56
	4	100	150 0.93 959	0.24		0.61		690 0.69 614	0.15	0.39
	5	200	170 0.92 1726	0.28		0.72		720 0.67 659	0.11	0.28
	6	300	180 0.92 1911	0.51		0.74		690 0.69 686	0.18	0.26
	7	400	180 0.92 1870	0.54		0.74		640 0.71 648	0.19	0.26
	8	500	180 0.92 2176	0.55		0.75		690 0.69 736	0.19	0.25
	9	600	180 0.92 2239	0.56		0.75		680 0.69 735	0.18	0.25
	10	800	190 0.91 2284	0.55		0.75		680 0.69 744	0.18	0.25
	average 4-10	170 0.92				0.65		680 0.69	0.35
						fraction: 65%				fraction: 35%
	NO.	%		𝝉 𝟎 (fixed) A0	DA*0				〈𝝉〉	z(D)	𝝉 𝐃𝐀  
	0	0		2400	3754	0.89					2200
	1	10		2400	3696	0.83					2070	0.10	430	0.80
	2	20		2400	3399	0.83					2060	0.10	460	0.79
	3	50		2400	2922	0.74					1900	0.09	450	0.80
	4	100		2400	2445	0.61					1600	0.07	350	0.84
	5	200		2400	3823	0.62					1600	0.07	300	0.86
	6	300		2400	1171	0.31					960	0.04	310	0.86
	7	400		2400	927	0.27					860	0.03	290	0.87
	8	500		2400	1026	0.26					850	0.03	300	0.86
	9	600		2400	1026	0.26					840	0.03	300	0.86
	10	800		2400	1144	0.27					880	0.03	300	0.86
	average 4-10		2400								310	0.86

Table 7 .

 7 14. Multi-exponential fits of Lumi4-Tb-sAv-biot-50 nm Au NPs.

	NO.	%	𝝉 𝟎 (fixed)	A0	DA*0		〈𝝉〉	z(D)	𝝉 𝐃𝐀  
		0	2400	3847	0.89		2190
		10	2400	3234	0.75		1910	0.09	450	0.79
		20	2400	2053	0.58		1570	0.07	440	0.80
		50	2400	1114	0.29		1030	0.04	460	0.79
		100	2400	726	0.15		750	0.02	460	0.79
		200	2400	484	0.10		660	0.01	470	0.79
		300	2400	321	0.09		640	0.01	470	0.79
		400	2400	283	0.08		630	0.01	480	0.78
		500	2400	299	0.08		630	0.01	480	0.78
		600	2400	283	0.08		650	0.01	490	0.78
	10	800	2400	324	0.10		680	0.01	500	0.77
	average 2-10	2400						470	0.79

Table 7 .

 7 15. Multi-exponential fits of Lumi4-Tb-sAv-biot-80 nm Au NPs.

	NO.	%	𝝉 𝟏 		A1	DA*1	DA1		𝝉 𝟐	E2	A2	DA*2	DA2
	0	0							680 0.62 1818	0.36	1.00
	1 2	10 20	190 0.89 170 0.90	473 519	0.11 0.12	0.27 0.31		830 0.53 1300 780 0.56 1164	0.29 0.26	0.73 0.69
	3	50	160 0.91 2317	0.36	0.62		660 0.63 1403	0.22	0.38
	4	100	170 0.90 1928	0.40	0.69		710 0.60	874	0.18	0.31
	5	200	180 0.90 2501	0.50	0.75		590 0.67	831	0.17	0.25
	average 3-5	170 0.90			0.69		650 0.63			0.31
						fraction : 69%					fraction : 31%
	NO.	%		𝝉 𝟎 (fixed)	A0	DA*0			〈𝝉〉	z(D)	𝝉 𝐃𝐀  
	0	0			2400	3238	0.64			1780
	1	10			2400	2651	0.60			1700	0.34	650	0.63
	2	20			2400	2790	0.62			1720	0.35	540	0.70
	3	50			2400	2682	0.42			1210	0.24	250	0.86
	4	100			2400	2054	0.42			1210	0.24	230	0.87
	5	200			2400	1659	0.33			990	0.19	190	0.89
	average 3-5			2400							220	0.87

Code 3 48±1% 21±1% 31±1% FINAL CODES (Spectroscopy and Microscopy) Code 1 40±2% 18±2% 42±2% Code 2 44±2% 19±2% 36±2% Code 3 48±2% 19±3% 33±3% BARCODING (find codes in unknown samples)

overall brightness of FRET-sensitized QD emission. In this work, we used 100 configurations and 10,000 incident photons for each data point shown in the MCS results. The size of the nanoparticles was determined by fitting the particle radius to match the experimental transfer efficiency for system 1. Because our simulation is designed for steady-state excitation, to emulate pulsed excitation in which all the incident photons arrive almost simultaneously, we fit the intensity ratio in Figure 4.10d at 200 Tb per QD to obtain the equivalent steady-state laser intensity to match the behavior of the pulsed system. An approximation in our method is that we determine all the available acceptors for energy transfer and thus whether the fluorophore de-excites via fluorescence, energy transfer, or non-radiative de-excitation at the time at which the donor fluorophore becomes excited. While this is suitable for the case of short lifetime donors under steady state excitation, it can break down for long lifetime donors as discussed in the thesis. photoniques, telles que le stockage de données, l'étiquetage de sécurité, l'optogénétique ou l'informatique moléculaire.