Christophe Morell

Dr Christine Mottet

Florent Barbault D'

Corinne Lacaze

Dr Jean-Luc Ravanat

Dr Thierry Douki

Dr Antonio Monari

Dr François Dehez

Pr Cecilia Hognon

Dr Floriane Michaël Beuve

Dr Ricardo Poignant

Ramos

Dr Emmanuelle Je

Bignon

Edwige Royboz

Marie-Françoise Guiot

Damien Seon

Merci

Dr Tao Jiang

Christian Melkonian D'

Wei Kiat

Wei Shyon

Hie Ming

le Labex Primes pour avoir

Loffreda pour m'avoir guidé tout

Résumé

Le potentiel des nanoparticules pour améliorer l'efficacité de la radiothérapie est démontré par de nombreuses études expérimentales in vivo et in vitro. Ces particules métalliques mettent en jeu des atomes de numéro atomique élevé qui augmentent l'effet de la radiosensibilisation. La réaction en jeu est la radiolyse de l'eau: une fois excitées par un rayon X, elles génèrent des électrons secondaires et des espèces réactives oxygénées (ROS) qui amplifient les dégâts d'ADN et mènent à une plus grande destruction des cellules cancéreuses.

Les nanoparticules d'or (AuNPs) sont le radiosensibilisateur le plus étudié aujourd'hui car elles sont généralement peu toxiques et elles ont une longue durée de circulation sanguine grâce à la fonctionnalisation des ligands hydrophiles. Pour une efficacité thérapeutique plus optimale, plusieurs propriétés des AuNPs doivent être prises en compte lors de la synthèse comme leur taille, leur forme et leur surface qui sont suspectibles d'influencer ses effets catalytiques (sites actif) et son interaction avec le rayonnement dans l'environnement biologique (majoritairement de liquide d'eau). Ces aspects structuraux ne sont pas encore examinés dans l'état de l'art, ni expérimentalement ni théoriquement.

Ce travail de thèse a pour but de rationaliser le comportement et la stabilité de AuNPs dans un environnement chimique ou biologique avant l'irradiation par des outils de modélisation théorique. Dans un premier temps, nous nous sommes intéressés à la stabilité des polyèdres d'or dans la gamme de 1-3.4 nm, une gamme ou l'effet radiosensibilisant est intéressant en fonction de leur taille et leur morphologie. Nous comparons nos résultats obtenus à l'aide de la théorie de la fonctionnelle de la densité (DFT) qui tient compte de la correction de dispersion semiempirique (DFT-D3) avec d'autres résultats issus de la littérature obtenus principalement par les méthodes d'optimisation globale. Nous étudions ensuite le comportement de ces nanoparticules dans un environnement biologique (hydratation) et chimique modèle (PEGylation), et la combinaison des deux environnements. Quand les nanoclusters de 0.9-1.8 nm sont en interaction avec une couche de molécules d'eau à saturation, nous avons montré qu'il y a une transformation de NPs métastables (dans le vide) telles que l'ino-décaèdre en NPs métastables plus favorables telles que l'icosaèdre. Alors qu'en présence d'une couche de ligands PEG, la liaison forte Au-S et les liaisons hydrogène entre les ligands entraînent une déformation significative de la morphologie de la nanoparticule, à savoir une stellation du décaèdre Au 54 . La déformation induite par la PEGylation est encore plus forte en présence de molécules d'eau co-adsorbées. Par ailleurs, nous avons montré que les ligands PEG promeuvent le confinement de quelques molécules d'eau à proximité des AuNPs. Nos conclusions ouvrent des perspertives intéressantes pour la modélisation théorique de la radiolyse de l'eau. Les résultats DFT obtenus à partir de nos modèles permettront aussi d'affiner les simulations Monte-Carlo mises au point par les collègues de l'Institut de Physique Nucléaire de Lyon (Pr. M. Beuve).

Parallèlement à ces études, nous nous sommes intéressés à la caractérisation de différents types de lésions d'ADN induites par les ROS et aussi par le rayonnement ultraviolet, plus spécifiquement sur la formation et la réparation difficile de certaines lésions observées expérimentalement, qui seraient à l'origine de la mutation de l'ADN. Deux projets ont été menés dans ce contexte, pour lesquels la méthode de dynamique moléculaire classique a été utilisée.

Premièrement, nous démontrons l'interaction d'un peptide trilysine (KKK) avec un oligonucléotide qui pourrait conduire à la formation de pontage d'ADN-polyamine. Ensuite, le deuxième projet porte sur la rationalisation de differents taux de réparation de dimères de cyclobutane pyrimidine (CPD): T<>T, T<>C, C<>T, et C<>C en présence de l'enzyme de reconnaissance DDB2 à l'échelle atomique.

To date, cancer remains a difficult disease to cure, and it is expected that the number of new cases of cancer in human beings will be risen by 70% in the next two decades, according to World Health Organization (WHO). Radiotherapy is the most commonly used approach in cancer treatment, with 50 to 60% of cancerous patients being treated by radiotherapy, alone or combined with others treatments. However, within such technique, the killing of cancerous cells is not selective, since ionizing radiation can damage as well the healthy tissues surrounding the tumors. An effective way to improve radiotherapeutic outcomes is the use of metallic nanoparticles based on heavy atoms, which can act as both radiosensitizers and radical dose-enhancing agents. Indeed, water radiolysis (an indirect reaction of ionizing radiation which generates highly reactive free radicals) can be enhanced when the nanoparticles are irradiated in aqueous media (biological natural environment), leading to an increased production of ROS responsible for cancerous cell death.

Due to many exciting chemical and physical properties, high Z gold nanoparticles (AuNPs) have been studied extensively for their radiosensitizing ability. With the incredible progress of nanotechnology, gold nanomaterials with diverse size and shape, such as sphere, rod, and star can be synthesized. Nevertheless, the synthesis of AuNPs with well-defined geometry, optimal and cost-efficient for radiotherapy applications, requires in part the knowledge of their relative stability in vacuum or in the presence of synthesis environment. This can be investigated experimentally by using high-angle annular dark-field imaging (HAADF-STEM) measurements, or explored theoretically by Heuristic approaches using accurate predictions from density-functional theory (DFT) or by global optimization methods based on well-parametrized and effective semi-empirical potentials. 3 Although many efforts have been devoted to advance on this question at the atomic scale, the relative stability of AuNPs is still a debate due to controversies regarding the results available in the literature.

The surface of metallic nanoparticles can be further functionalized by thiolated ligands in order to improve their stability and biocompatibility. Poly-ethylene glycol (PEG) is the most widely used ligand in experiments, despite the fact that the strong Au-S bond and high grafting density may have a strong effect on the NP structures. The size and morphology of those PEGylated AuNPs can tune significantly their catalytic properties and dose-enchancement, especially when the AuNPs are in the fluxional regime (below 4 nm). 4 Furthermore, the uptake of AuNPs by cancerous cell membrane, is an important process which determines the rate of radiosensitization, and it is also dependent on NP size and morphology. 5 Therefore, for radiotherapy applications, the design of functionalized AuNPs with an optimal therapeutic property is highly desired.

Up to date, little is known about the mechanisms of water radiolysis occurring at the proximity of the AuNPs, from both experimental and theoretical standpoints. The role of the synthesis ligands decorating the nanoparticles, as well as their synergy and interaction with the biological environment (mainly water) are open questions. The mechanisms of internalization of the AuNPs inside the targeted cancerous cells are also the subject of difficult scientific questions, apart from the understanding of the DNA lesions and damages caused by free radical and reactive oxygen species.

The exploration of NPs properties as radiosensitizers is one of the main areas of research within the framework of LABEX PRIMES (Physics, Radiobiology, Imaging and Simulation). This work was supported by the LABEX PRIMES (ANR-11-LABX-0063) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). Some of the multidisciplinary research activities include on the one hand, the synthesis, characterization of metallic-based (iron, gadolinium and gold) nanoparticles, and the evaluation of their radiosensitization efficiency in vitro and in vivo. On the other hand, as a predictive tool complementary to experiments, Monte Carlo (MC) simulations are performed in the framework of LABEX PRIMES to examine the enhancement of ROS dose and the physico-chemical processes which are radio-induced in the presence of nanoparticles. However, to include the effect of water environment in contact with heavy element, the lack of accurate parameters provided at the atomic scale is a limitation in MC simulations since information concerning the electronic structures at the AuNPs/water interface are scarce.

The purpose of the present thesis is to provide at the theoretical level, dynamical and mechanical features of damaged DNA which contribute in many biological processes linked to cancer. Simultaneously we aim to evaluate AuNPs stability in the presence of biological and chemical environment in the context of radiotherapy by using theoretical approaches at the atomic scale. By developing theoretical models, one key objective of this thesis is also to open the scientific discussion and exchanges between three communities of theoreticians working on the topic of radiotherapy at various scales (from the atom to the cell scale). One outcome is the generation of a set of ab initio results to improve the parametrization and predictive power of MC simulations and related code developed by colleagues at IPNL. This re-parametrization is expected to improve their relevance with respect to experiments. This thesis has been developed in the Theory group of Laboratory of Chemistry of Ecole Normale Supérieure de Lyon. Most of the calculations were performed using the data center and cluster of the Pôle Scientifique de Modélisation Numérique (PSMN) at Lyon. The research works have been effected in close collaboration with Dr. Jean-Luc Ravanat and Dr Thierry Douki (experimentalists at CEA de Grenoble), Dr. Antonio Monari and Dr François Dehez (theoreticians at University of Nancy), and Pr Michaël Beuve and Floriane Poignant (theoreticians at Institut de Physique Nucléaire in Lyon).

The outline of the manuscript is organized as follows. In Chapter 2, the state-of-the-art and the corresponding limitations are exposed. Chapter 3 introduces the computational methods employed throughout this thesis. The following three Chapters 4-6 of results are devoted to the investigation of the relative stability of AuNPs at three levels of description by using DFT: i) AuNPs in vacuum; ii) AuNPs in the presence of water monolayers (biological natural environment) and iii) AuNPs in the presence of an organic coating composed of monolayers of hydrated PEG ligands (chemical synthesis environment). The last chapter deals with the use of molecular dynamics simulations to study the association of small trilysine with DNA, and the interaction of different cyclobutane pyrimidine dimers (CPD) photo-lesions with DDB2 enzyme. The general conclusion and perspectives are finally addressed at the end of this manuscript.

Introduction

Cancer is currently the second cause of death in the world after cardiovascular diseases.

Data from the Global cancer statistics (GLOBOCAN) estimated that 18.1 million new cases and 9.6 million death was diagnosed due to cancer in 2018. 1 About 1 over 6 deaths is caused by cancer-related diseases. Among patients, lung cancer is the most frequent for men, followed by prostate and colorectal cancer, whereas for women, breast cancer is the most commonly diagnosed one, followed by colorectal and lung cancer. 1 According to World Health Organization (WHO), tobacco use, alcohol consumption, unhealthy diet, high body mass index and lack of physical activity are the main factors contributing to this deleterious disease.

DNA lesions, defined as alternations of the chemical structures of the DNA double helix, are an important cause of cancer. 2 Indeed, even though DNA is tremendously important as it acts as genetic information storage, their structures are labile and have a limited chemical stability upon exposure to different carcinogenic agents (whereas photostability is remarkable) DNA is a polymer containing a phosphate backbone, 2-deoxyribose sugar, and a nitrogenous base. The molecule exhibits a double helix structure with two polynucleotide strands running in antiparallel directions held together by hydrogen bonds between the bases of the nucleotides. 3 There are four different bases within DNA: adenine (A), guanine (G), cytosine (C) and thymine (T). A always pairs with T and G always pairs with C, which is referred as the Watson-Crick pairing. The double helix interacts with small coiling protein called histones to form nucleosome 5 , as shown in [4]. b) a structure of nucleosome at 1.9 resolution taken from Protein Data Bank: 1kx5 [5] Just like any molecule, DNA can be involved in various chemical reactions that undergo structural changes of its structure and form lesions. It has been estimated that lesions can occur 10 3 to 10 6 times per cell per day. 6 To maintain genome integrity, human body possesses multiple most efficient repair systems that operate at the rate of 10 16 -10 18 per day to cope with such huge amount of lesions. However, if these repair machinery fails to identify and fix the different type of lesions, the accumulation of DNA lesions lead to genomic mutations and promote cell death, neurodegeneration, aging and tumor development. [7].

A large variety of endogenous and exogenous damaging agents results in DNA lesions.

Endogenous damage is generated from natural molecules present in cells that spontaneously react with the DNA, and exogenous damage are resulting from the activity of external chemical and physical agents onto the DNA macromolecule. Figure 2.2 provides a summary of the most common sources that leads to DNA damage, the lesions formed, and the corresponding repair pathway.

Endogenous DNA Lesions

The majority of the DNA damage are endogenous in origin. 8 Indeed, the endogenous damages occur naturally during the cellular and hydrolytic processes. Normal cellular metabolism produced reactive oxygen species (ROS) such as superoxide anion (O 2 -), singlet oxygen ( 1 O 2 ), hydroxyl radical (HO • ), hydroperoxyl radical (HOO • ) and hydrogen peroxide (H 2 O 2 ), whereas hydrolysis cleaves chemical bonds between bases and deoxyribose in DNA.

ROS react readily with heterocyclic bases of DNA and generate over 100 oxidative products. 9 8-oxoguanine (8oxoG) is the most common oxidative adducts. It is produced by or oxidation of guanine at C8-position. 8oxoG is highly mutagenic because it can cause G•C to T•A transversion mutation during replication. 10 Apurinic/apirimidic (AP) sites are another ubiquitous endogenous lesions produced upon spontaneous hydrolysis of N-glycosylic bond linking the nucleobases to the sugar-phosphate backbone or during the removal of damaged bases by N-glycosylases. 11 The absence of nucleobase, meaning that the loss of the genetic coding information lead to mutation during replication. 12 AP sites can also lead to single strand break via beta-elimination of the phosphate residue on the 3'-side of the abasic site, or react with the exocyclic N2-amino group of guanine or aldenine on the opposite strand to form interstrand cross-link cytotoxic lesions. 13 Spontaneous deamination of DNA nucleotide bases carrying exocyclic amino groups results in the formation of highly mutagenic uracil, hypoxanthine and xanthine. 15 DNA-protein cross-links (DPCs) cover another oxidatively generated DNA lesions, more recently characterized, that can cause deleterious biological effects such as cellular aging, mutagenesis, and carcinogenesis. 14 Polyamines have proved to react with guanine cation radical and induce such bulky lesions. Indeed, free polyamines are compounds that can be extensively found in different cell compartments, showing particular accumulation in the nuclei. 16,17,18,19 Low-mass polyamines are widespread in different living organisms, spanning as varied organisms as bacteria, plant and superior animals. Even though they biological role has not been fully characterized yet, there are evidences suggesting their involvement in regulatory signaling, plant development, or even cancerogenesis. 20 In addition to the presence of ubiquitous free polyamines, DNA interacts non-covalently with many proteins which implies that the presence of some amino acids with amine functional groups in their side chain, such as lysine or asparagine. Furthermore, DNA coiling proteins such as histones in eukaryotes or histone-like DNA binding proteins (HU) in bacteria present a large density of ammonium groups in the DNA contact region, necessary to induce coiling by promoting favorable electrostatic interactions with the negatively-charged DNA backbone, an observation also coherent with the action of free polyamines in promoting DNA condensation. 21 The formation of covalent DNA-proteins cross-link adducts 22 has been recently evidenced in nucleosomes 23 at the cellular level, which have been traced back to the involvement of amine groups from lysines of the histone tails (but also from arginine).

The chemical and biochemical stability of guanine-amine cross-link adducts has been explored 24 . Their repair is difficult 25 as these lesions prevent a good recruitment and the optimal operating conditions of the enzymatic repair machinery. Hence, since they lead to bulky adducts that significantly distort the DNA helical structure and induce the replication block, they result in a high cytotoxicity. The high-yield formation for DNApolyamine cross-links adducts has been quantified for the three most prevalent free natural polyamines 26 (spermine, putrescine and spermidine), and for a trilysine peptide 27 , interacting with the TGT trioligonucleotide or a 15-bp double-stranded DNA sequence with the central TGT motif (see Figure 2.3). The formation of a covalent carbon-nitrogen adduct (Figure 2.3-c, pathway B) leading to a guanine-lysine cross-link at the C8 position, 8-N-Gua, has been detected and quantified owing to tandem mass spectrometry 28 . Whereas the structure of KKK interacting with oligonucleotides is still unknown, the characterization of the resulting guanine-lysine adducts suggests a spatial proximity for the stabilization of the prereactive complex.

To rationalize those observation a mechanistic pathway involving the nucleophilic addition of the ε-amino group of a neutral polyamine onto the radical cation G•+, i.e. one of the most common DNA oxidative lesion intermediate 29 , has been proposed 30 , based on density functional theory (DFT) calculations on methylamine small model systems 30,31,32 .

Other pathways have also been delineated, involving the participation of the ethylenic C4 and C5 positions 30 , and a mechanism that can possibly proceed through 1 O 2 photosensitization or radical coupling 32 . However, these DFT investigations have been mostly performed considering the neutral -NH2 form of amine groups, while, given its pKa, at physiological conditions, the former ought to be predominantly protonated (NH3+). Furthermore, one has also to consider that at physiological pH G•+ rapidly deprotonates to give the guanine radical G•. An equilibrium between the N1 and the N2 deprotonated form of G• has also been evidenced 33 . Hence, some questions remain open mostly related to the high efficiency of the process, that is even more competitive than water addition despite the larger abundance of the former 27 . This requires to consider from the one side the structural and dynamical properties of DNA-polyamines or DNApolypeptides non-covalent adducts (i.e. the prereactive complexes) and on the other side taking into account the equilibrium of protonated and deprotonated species involving the guanine radical cation and the amines.

Exogenous DNA Lesions

Besides the various endogenous sources of DNA damage exposed in the previous section, DNA is also continuously subject to exogenous or environmental DNA-damaging agents.

Example of external source are ionizing radiation (IR) and ultraviolet (UV) radiation from sunlight.

Ionizing Radiation

Ionizing radiation (IR) is an external source of DNA damage and can be in the form of electromagnetic radiation (eg. X-rays or gamma rays) or in the form of subatomic particle (eg. alpha and beta particles). IR consists of using these electromagnetic waves to produce high energy for ionizing a molecule by removing an electron and generate ions and free electrons. IR can directly affect DNA structures during its passage and induce various types of DNA lesions including cluster of damaged bases, single-strand breaks (SSBs) and double-strand breaks (DSBs). 34 The latter is difficult to repair and considered as the most relevant lesion for mutation and carcinogenesis. 35 In addition, IR interact with the molecules surrounding the DNA (particularly of water) which undergoes radiolysis reaction, resulting in the production of reactive oxygen species (ROS) that are able to diffuse over distance and interact with DNA and then cause damages. This is called the indirect action of IR. Despite of the harmful effect, IR can be use in radiotherapy to kill cancer cells, as explained in section 2.2.

UV Light

Overexposure to the sunlight is recognized as a cause of the insurgence of malignant skin lesions that may evolve to skin cancer. 36,[START_REF] Rünger | Mechanisms of mutation formation with long-wave ultraviolet light (UVA)[END_REF][START_REF] Cadet | Photoinduced damage to cellular DNA: Direct and photosensitized reactions[END_REF][START_REF] Cadet | Oxidatively generated damage to cellular DNA by UVB and UVA radiation[END_REF][START_REF] Drouin | UVB-induced Cyclobutane Pyrimidine Dimer Frequency Correlates with Skin Cancer Mutational Hotspots in p53[END_REF][START_REF] Sage | Mutagenic specificity of solar UV light in nucleotide excision repairdeficient rodent cells[END_REF][START_REF] Sage | Distribution and repair of photolesions in DNA: Genetic consequences and the role of sequence context[END_REF][START_REF] Pfeifer | Mutations induced by ultraviolet light[END_REF] Indeed, it is well established that, despite the global photostability of DNA [START_REF] Gustavsson | DNA/RNA: Building blocks of life under UV irradiation[END_REF] , UV light can induce the formation of DNA photolesions mostly present in the form of cyclobutane pyrimidine dimers (CPD) upon direct absorption of UVB light (in the spectrum of 290-300nm) by the DNA nucleobase. [START_REF] Bhagavan | Structure and Properties of DNA Photoproducts[END_REF] CPDs are formed upon dimerization at the four possible sequences harboring two adjacent pyrimidine bases located on the same strand, namely CC, CT, TC and TT. [START_REF] Cadet | Oxidatively generated damage to cellular DNA by UVB and UVA radiation[END_REF][START_REF] Cadet | Photoinduced damage to cellular DNA: Direct and photosensitized reactions[END_REF][START_REF] Cadet | Ultraviolet radiation-mediated damage to cellular DNA[END_REF][START_REF] Banyasz | Electronic excited states responsible for dimer formation upon UV absorption directly by thymine strands: Joint experimental and theoretical study[END_REF][START_REF] Rauer | Cyclobutane Thymine Photodimerization Mechanism Revealed by Nonadiabatic Molecular Dynamics[END_REF] UVB radiation also triggers the formation of pyrimidine (6-4) pyrimidone photoproducts (6-4PP) present in a 3-fold lower yield than CPDs [START_REF] Cadet | Ultraviolet radiation-mediated damage to cellular DNA[END_REF][START_REF] Epe | DNA damage spectra induced by photosensitization[END_REF][START_REF] Cuquerella | Benzophenone photosensitized DNA damage[END_REF][START_REF] Dumont | Resolving the benzophenone DNA-photosensitization mechanism at QM/MM level[END_REF] . These two lesions are most harmful for the cell [START_REF] Sinha | UV-induced DNA damage and repair: a review[END_REF] for two opposite reasons. Indeed, while CPDs are characterized by a low repair rate hence leading to accumulation of these defects in cells, 64-PPs although extremely mutagenic are much faster repaired than CPDs. 36 The differential effects have been correlated to the relate change produced in the DNA mechanical properties and in particular flexibility [START_REF] Kim | B-S Contrasting structural impacts induced by cis-syn cyclobutane dimer and (6-4) adducts in DNA duplex decamers: Implication in mutagenesis and repair activity[END_REF][START_REF] Kim | B-S The Solution Structure of DNA Duplex-Decamer Containing the (6-4) Photoproduct of Thymidylyl (3′→5′)Thymidine by NMR and Relaxation Matrix Refinement[END_REF][START_REF] Jing | Thermodynamic and base-pairing studies of matched and mismatched DNA dodecamer duplexes containing cis-syn, (6-4) and Dewar photoproducts of TT[END_REF][START_REF] Fujiwara | hermodynamic studies of the hybridization properties of photolesions in DNA[END_REF][START_REF] Park | Functional insights gained from structural analyses of DNA duplexes that contain UV-damaged photoproducts[END_REF] CPDs tend to rigidify the whole oligonucleotide with minor structural differences as compared to the native B-DNA, whereas 64-PP on the contrary exhibits an extended polymorphism characterized by the simultaneous presence of very different conformations, and their rapid interconversion over the microsecond time-scale [START_REF] Dehez | Conformational polymorphism or structural invariance in DNA photoinduced lesions: implications for repair rates[END_REF] . Hence, while CPDs may efficiently escape the recognition by the repair machinery, nucleotide excision repair (NER), 64-PPs is easily recognized, but its flexibility induces a much lesser replication resistance or fork blockages. [START_REF] Sedletska | Replication fork collapse is a major cause of the high mutation frequency at three-base lesion clusters[END_REF][START_REF] Lee | Solution structure of the DNA decamer duplex containing a 3'-T x T basepair of the cis-syn cyclobutane pyrimidine dimer: implication for the mutagenic property of the cis-syn dimer[END_REF][START_REF] Johnson | Role of DNA polymerase eta in the bypass of a (6-4) TT photoproduct[END_REF][START_REF] Pfeifer | Formation and Processing of UV Photoproducts: Effects of DNA Sequence and Chromatin Environment[END_REF] Indeed, keratinocytes show a globally better repair rate than fibroblasts. In addition, T<>T undergo a slow repair and may persist up to a level of 70%, in drastic contrast in both cell types with C<>T that may reach level of less than 10%. T<>C and C<>C exhibit intermediate repair rates. Therefore, by the analysis of the data reported in Figure 2.5, it is possible to sketch a repair efficiency performance order that can be summarized as follows:

T<>T < T<>C << C<>C < C<>T Indeed, T<>T is the slowest repaired lesion, followed by T<>C that is only slightly less refractory. On the contrary, C<>C shows a definitive improvement in the repair rate and finally C<>T is by far the best repaired lesion. Hence it is apparent that the presence of a cytosine at the 5' position results in a net increase of the repair efficiency. Interestingly, this order of repair rate is reminiscent of mutation frequency in skin tumors and UVirradiated cells [START_REF] Ziegler | Mutation hotspots due to sunlight in the p53 gene of nonmelanoma skin cancers[END_REF][START_REF] Brash | A role for sunlight in skin cancer: UV-induced p53 mutations in squamous cell carcinoma[END_REF] . Indeed, the most frequent mutations are observed at the 3'-end of T<>C sequences and to a lesser extent at C<>C sites. Conversely, C<>T sequences are very rarely mutagenic. These mutation frequencies follow the increasing rate of CPD removal. [START_REF] Mouret | Differential repair of UVB-induced cyclobutane pyrimidine dimers in cultured human skin cells and whole human skin[END_REF] Mutation at T<>T are also quite rare but this is explained by the fact that the two thymines in a T<>T CPD preserve their coding properties without inducing mutations upon replication. 67,68

Cancer Therapy

Types of Cancer Treatment

Different approaches are available nowadays and continuously under development to treat cancer and to prolong patient survival. The choice is depending on the type and stage of cancer. The three conventional therapeutic methods that have been employed clinically include surgery, chemotherapy, radiation therapy and their combinations.

Surgery was considered as the most effective methods to kill local tumor completely (cancerous cell that are not been widespread yet) because surgery operates by zero-order kinetics and excise 100% of the malignant cells. [START_REF] Urruticoechea | Recent advances in cancer therapy: an overview[END_REF] This approach become conservative since the arrival of radiotherapy in the 1920s and chemotherapy after 1940s.

Chemotherapy use chemical agents such as antimetabolites, plant alkaloids, alkylating agents, antitumor antibiotics to stop cell growth and cell division, with the objective of killing tumor cells. [START_REF] Chabner | Chemotherapy and the war on cancer[END_REF] However, the effectiveness of these compounds are limited due to non-selectivity and inability to control metastasis or secondary growth. [START_REF] Urruticoechea | Recent advances in cancer therapy: an overview[END_REF] Radiotherapy is the third conventional method of cancer treatment which relies on the use of ionizing radiation (described in section 2.1.3.1) aimed at shrinking the tumor cells.

There are two classes of RT depending on the radiation sources : brachytherapy and external beam radiation therapy (EBRT). [START_REF] Laprise-Pelletier | Gold nanoparticles in radiotherapy and recent progress in nanobrachytherapy[END_REF] Brachytherapy relies on the irradiation of radioisotope materials (eg. 131 I, 125 I, 188 Re and 177 Lu) placed nearby the tumor to destruct solid tumor. While EBRT can be divided into proton therapy, heavy ion therapy, and Xray therapy, the latter being the most widely used in clinical applications. Indeed, half of patients diagnosed with cancer receiving the X-ray radiotherapy treatment.

Other treatments such as phototherapies including photothermal therapy (PTT) and photodynamic therapy (PDT), are still-emerging cancer-treatment techniques. [START_REF] Cheng | Functional nanomaterials for phototherapies of cancer[END_REF] PTT use photothermal agent to absorb light in the near-infrared (NIR) region and convert the corresponding optical energy into heat for thermal ablation of cancerous cells. PDT, on the other hand, relies on the use of photosensitizer, light and oxygen to produce singlet oxygen and ROS, both extremely cyctotoxic and leading to cancerous cell death via apoptosis or necrosis. 72,73

Nanoparticles as Radiosensitizers

In the previous section, we have shown that most of the cancer therapies available nowadays failed to kill tumor cells selectively and as a consequence, most of the patients suffer from serious side effects or even secondary cancer which may be develop. More attention has been given particularly to improve conventional radiotherapy performance as it is the leading choice of cancer treatment. The use of direct ionizing radiation in this method lead to severe damage of surrounding healthy tissues. On the other side, limiting the dose results in poor treatment. Some cancer needs even a greater amount of radiation to kill tumors that are resistant to long-term radiotherapy. [START_REF] Huang | Rational design of cancer-targeted BSA protein nanoparticles as radiosensitizer to overcome cancer radioresistance[END_REF] The development of a more precise and effective radiotherapy thus becomes an urgent priority. To this aim, a variety of radiosensitizers (radiosensitizing agent), molecule/materials that are able to target cancer cells and reduce radiation dosage have been proposed. [START_REF] Wang | Cancer radiosensitizers[END_REF] Some common radiosensitizer including halogenated nucleosides and cispatin derivatives, but in the last decade, metallic nanoparticles, with a diameter of 100 nm or less have been extensively studied in the researches domain as promising radiosensitizing agents. [START_REF] Wang | Cancer radiosensitizers[END_REF][START_REF] Schürmann | The Physico-Chemical Basis of DNA Radiosensitization: Implications for Cancer Radiation Therapy[END_REF] The first experiment evidence come from Hainfield et al, [START_REF] Hainfeld | The Use of Gold Nanoparticles to Enhance Radiotherapy in Mice[END_REF] in which small gold nanoparticles (1.9nm) combined with x rays were used to irradiate mice' tumors. A significant increase of one year survival rate was reported, 86% compared to 20% with radiotherapy alone. Starting from this pioneering work, a vast amount of experimental works have been proposed to improving radiotherapy performance by testing on silver (Z= 47), [START_REF] Xu | Ag nanoparticles sensitize IR-induced killing of cancer cells[END_REF] gadolinium (Z= 64) [START_REF] Detappe | AGuIX nanoparticles as a promising platform for image-guided radiation therapy[END_REF][START_REF] Duc | Toward an image-guided microbeam radiation therapy using gadolinium-based nanoparticles[END_REF] platinum (Z=78) [START_REF] Carter | Nanoscale energy deposition by X-ray absorbing nanostructures[END_REF]83 , gold, [START_REF] Laprise-Pelletier | Gold nanoparticles in radiotherapy and recent progress in nanobrachytherapy[END_REF][START_REF] Bobyk | Photoactivation of gold nanoparticles for glioma treatment[END_REF]84 and bismuth nanoparticles. 85 Indeed, these high Z nanoparticles are able to emit, absorb and scatter ionizing radiations energy thus, increase the radical production due to the photoelectric effect. 86,87,88,89 . They contribute to radiosensitization effects making tumor cells more responsive to ionizing radiation, 90,91 since they preferentially accumulate in tumor tissues over healthy tissues thanks to the enchanced permeability and retention (EPR) effect exhibited by solid tumors. 92

Gold Nanoparticles in Radiotherapy

Among the various high Z materials being proposed as radiosensitizer, functionalized gold nanoparticles (AuNPs) have received a significant attention to be employed in cancer diagnosis and treatment due to their facile synthesis, excellent biocompatibility and long circulation time. [START_REF] Laprise-Pelletier | Gold nanoparticles in radiotherapy and recent progress in nanobrachytherapy[END_REF]87,93,94,95,[START_REF] Her | Gold nanoparticles for applications in cancer radiotherapy: Mechanisms and recent advancements[END_REF] Another unique physical property exhibited by AuNPs is the surface plasmon resonance (SPR) which is defined as the collective oscillation of free electrons (conduction band electrons) when exposed to light. 88 The excitation of the plasmonic AuNPs induces high temperature and can be used in photothermal therapy for the destruction of cancerous cells. [START_REF] Cheng | Functional nanomaterials for phototherapies of cancer[END_REF]88 The size of AuNPs can affect significantly its radiosensitization effect. Indeed, when the size of a particle decreases, its surface area to volume ratio increase severely and this leads to the prevalence of surface atoms. The latter have a lower coordination number, and these low-coordinated surface atoms (eg, edge, kink, or corner sites) are known to influence strongly nanoparticle properties, so small size of NP exhibits unique sizedependent chemical reactivity. For example, the radiosensitizing effect in water under irradiations of X-ray and UV light was performed on AuNPs in the range 5-250 nm. [START_REF] Misawa | Generation of reactive oxygen species induced by gold nanoparticles under x-ray and UV Irradiations[END_REF] Smaller AuNPs (size below 5nm) with larger surface area showed a greater production of hydroxyl radical and superoxide anion, leading to a stronger radiosensitizing effect. Other ultrasmall size of AuNPs have been proposed in this context: Au 10-12 (SG) 10-12 , [START_REF] Zhang | Ultrasmall Au10-12 (SG)10-12 nanomolecules for high tumor specificity and cancer radiotherapy[END_REF] and GSH-Au 25 NC 100 , both containing both several atoms embedded inside a glutahione peptide.

They can be efficiently cleared by the kidney after the treatment and thus minimizing the potential side effects due to the accumulation in the body.

Isolated AuNPs in Model Condition

The physicochemical and catalytic properties of AuNPs are highly dependent on their size and morphology. Therefore, structure determination of nanometer-size of AuNPs with both crystalline and non-crystalline geometry is critical in order to have a NP design having an optimal performance in radiotherapy. Various experimental and numerical tools have been developed to sample their configuration space as a function of size and temperature. [START_REF] Baletto | Structural properties of sub nanometer metallic clusters[END_REF] A few of theoretical investigations have been proposed in the literature by using different computational tools on the basis of AuNPs modeled in vacuum by explicit 3D structures 101,102 103,104,105,106,107,108 Density functional theory (DFT) is a powerful atomic scale simulation method to find energy minima, but rather limited to small size of the particle due to computational cost. The size restriction may be overcome by using other approaches based on empirical potentials, simulated annealing and genetic algorithms.

Interaction of AuNPs with Water

In radiotherapy, the ionizing radiation can damage DNA directly or other part of the cells such as mitochondria, but the main pathway of DNA damage is through the indirect reaction of water radiolysis (see illustration in Figure 2.9) due to the fact that water is the main constituent of human body (65% approximately). 118 The yield of the secondary products (such as hydroxyl radicals HO The interaction of AuNPs with water can be investigated by theoretical modeling. For instance, interfacial chemical and physical processes happening at the vicinity of functionalized AuNPs can be explored by atomistic calculations while water radiolysis can be studied by continuous models and Monte Carlo simulations like LiQuiD code. 119,120 These two complementary approaches may provide a better understanding of interfacial properties while Monte Carlo simulations may benefit from useful atomistic information.

Concerning the modeling of the interface between AuNPs and water solvation at the atomic scale, DFT is a powerful method to predict optimal geometries and energetics. In DFT studies, static approaches are often considered to describe water adsorption on Au surfaces, 121,122,123,124,125,126 and nanoclusters up to 20 atoms, 127 although the explicit interface between metallic nanoparticles and liquid water can be described by ab initio molecular dynamics simulations. 128 To date, a few studies based on parametrized force fields and classical molecular dynamics simulations have been reported in the literature for gold/water interfaces. Studies have also performed on AuNPs in a water vapor environment described by extended metallic surfaces calculated by DFT and Wulff construction for predicting thermal properties. 131 The water vapor effect on Au nanoparticle shape is rather small by comparison with other metals, and consists of a progressive transformation of {100} facets in favor of {111} ones becoming larger in truncated octahedra.

The size effect on the adsorption mechanism of water molecules was investigated on icosahedral AuNPs using molecular dynamics simulation. 129 The authors showed that the average interaction energy increases when the size increases concomitantly (-0.174, -0.259 and -0.295 eV for Au 13 , Au 55 , and Au 147 respectively). The authors showed that for larger AuNPs (Au 55 , and Au 147 ) , the hydrogen bonding between adsorbed water molecules lead to an arrangement on the surface in a two-dimensional structure. In the case of Au 13 , the hydrogen bonding of the water molecules generates a three-dimensional structure (see

AuNPs functionalized by PEG ligands

Uncoated AuNPs are toxic and unstable in the biological fluid, therefore their surface must be functionalized by organic ligands to preserve their integrity and to improve their biocompatibility. Various ligands have already been examined to date for this purpose, such as citrate ions 132 , poly-ethylene glycol (PEG), 133,134,135 undecane-thiols and amine derivatives, 136 DNA strands 137 as well as uncoated GNPs as references. 138 Indeed PEGbased ligands have been often considered for applications in imaging and therapy 139,140 because of their high stability, biocompatibility, low cytotoxicity, and interesting antibacterial activity. 141,142 The morphology of AuNPs can be modulated by the chemical nature of the organic coating. For instance, thiol-terminated monomethoxy PEG ligands have been considered

for synthesizing gold nanostructures with different shapes (gold spherical nanoparticles GNPs, nanospikes GNSs and nanorods GNRs) around 50nm (Figure 2.12). 143 The use of other synthesis ligands can yield branched nanoparticles by maximizing the surface to volume ratio and leading to star polyhedral gold nanocrystals or nanostars. 144 For instance, the influence of alkylamine ligands has been demonstrated several times on the morphology of gold nanostars. 145,146,147 A long chain amine ligand promotes rounded nanostars whereas shorter chain amine favors pointed nanoclusters. 145 The grafting density of the ligands can be evaluated precisely experimentally. 148,149,150 According to the models, it decreases with the diameter of the nanoparticle and the ligand molecular weight. As shown in Figure 2.13 (a), for small AuNPs (below 5 nm), grafting densities exceed 1.6 chains/nm 2 . 149 Moreover, for short chain ligand (below 1000 g/mol), the densities become larger than 2.5 chains/nm 2 (see Figure 2.13 (b)) (3.2-3.9 chains/nm 2 for specific PEG ligands 148,150 ). The molecular weights and number of ligands on the AuNPs have also a significant influence on their orientations around gold, 150,151 giving rise to a transition from disorganized "mushroom" orientations to more rigid "brush" configurations. Regarding the theoretical models of coated AuNPs, classical molecular dynamics is one possibility to describe the coordination of alkane-thiols and PEG ligands. 152,153,154 According to these models, the thickness of the coating is only weakly dependent on the surface ligand density, whereas the degree of water penetration in the coating increases for a smaller number of attached ligands. Hybrid approaches combining force-field molecular dynamics simulations, CGMD and DFT allow the investigation of bicomponent self-assembled monolayers (SAM) on gold.

Endocytosis of PEGylated AuNPs

The mechanisms of AuNPs internalizations by cancer cells (endocytosis) is still unclear, despite several studies have shown that internalized AuNPs are able to produce more ROS to induce cell apoptosis and necrosis. 162,163,164 At the cell scale, the pathways of endocytosis can be either investigated experimentally by optical and microscopic techniques. 137 or modeled theoretically by coarse-grained molecular dynamics (CGMD) simulations. 165 At the molecular scale, the interaction modes between naked or coated AuNPs with membrane lipidic bilayers can also be described by atomistic classical forcefields or CGMD. 166 Among the key factors influencing endocytosis, the morphology and the size of AuNPs are of prime importance.

According to recent measurements, 143 the cellular uptake is increased in the order of gold spherical nanoparticles (GNPs) > nanospikes (GNSs) > nanorods (GNRs) (see Figure 2.12 for the structures) in agreement with previous measurements 167 and dissipative particle dynamics (DPD) simulations. 168 All the PEGylated AuNPs induce enhanced cancerous cell death rates upon X-ray irradiation. However, sensitization enhancement ratios determined by the amount of internalized gold atoms have been found larger for spherical GNPs than other shapes, thus showing the impact of nanoparticle morphology on cancer radiotherapy. At larger sizes (80-90 nm) or alternate shapes, other uptake measurements have shown different trends between PEGylated gold nanotriangles (nanoprisms), nanorods and nanostars. 169,170 CGMD simulations of water-solvated AuNPs with various shapes in the range 2-10 nm demonstrate also alternative conclusions for the cellular uptake efficiency. 171 In particular, DPD simulations show that the anisotropy of a copolymer coating improves the cell penetration, with a maximum uptake for Janus-type nanoparticles. 172 PEG-functionalized dithiolane ligands terminated by either methoxy or carboxy group have been used to synthesize AuNPs in the range 2.4-89 nm. 173 Up to 16 nm, these AuNPs have been found to localize in the cell nucleus, whereas larger NPs have not entered the cell and have been located at their periphery.

From a mechanistic point of view, experimental ESEM/TEM and theoretical CGMD approaches 137 have recently shown that the cellular uptake occurs through the ligand exchange at the nanoparticle/membrane interface. The physisorbed ligands on the nanoparticle surface have a larger ability to exchange with membrane lipidic molecules depending on their adsorption a nity and chain length. In these experiments, AuNPs ffi typically aggregate into an ordered monolayer on the lipid bilayers, hence a ecting the ff cell membrane integrity, the uptake e ciency, and the endocytosis pathways. For ffi PEGylated AuNPs, the measurements of height and diameter demonstrate their lower propensity to agglomerate at the interface with the membrane and lower capacity to internalize with respect to citrate ligands and DNA strands.

The chemical nature of the PEG-based ligands (varying with alkyl chains, length and pH)

and their surface grafting density have also a significant impact on the endocytosis.

PEGylated AuNPs terminated with long alkyl chains (up to C 18 ) present larger cell uptake than classical PEG coronas, 174 while smaller chains presenting two thiol functions can reduce the uptake as the surface coverage increases. 175 The pH-reversible cell affinity and photothermal therapeutic efficiency have been measured by synthesizing PEGylated mixed-charge gold nanostars. 176 By tuning the pH gradient around neutrality with mixed ammonium/carboxylate terminal functions, the authors have demonstrated the concomitant higher uptake for ammonium enriched gold nanostars.

Due to the difficulty to observe experimentally the interaction between the nanoparticle and the cell membrane, 166 a few theoretical studies based on DPD, 168,172 CGMD 177 and on free energy calculation continuum models 178 have been reported to model these interfaces approximatively.

Limits of the State-of-the-art and Objectives of My Thesis

Although AuNPs have been proven as promising radiosensitizers since the last two decades, there are only very few clinical trials that combine radiotherapy with AuNPs. 95,89,179 Several properties of AuNPs such as size, shape and functionalization, and the impact on radiosensitization are still poorly understood. To date, there is a lack of studies at the atomic scale describing the effect of chemical and biological environment on the relative stability of AuNPs, before the irradiation takes place.

As exposed in section 2.2.4, the stability of AuNPs in model conditions (vacuum) as a function of size and morphology is still an open question although experimental measurements and theoretical studies are compared as much as possible. This will be discussed in Chapter 4 and the stability order of AuNPs in the range 0.9-3.4 nm will be tackled by using three theoretical descriptors.

Before describing the photocatalytic processes of water radiolysis at the atomic scale, a first understanding of the stability and the competitive forms of AuNPs in the biological natural environment is required. Therefore, the morphology, structure, and energetics of AuNPs in contact with liquid water will be examined in Chapter 5. In particular, an explicit static or atomistic model describing the interaction of water monomers and solvation shells (first solvation shell around the nanoparticle) with gold nanoparticles in the range 1-2 nm will be presented. We aim to probe the water effect on AuNPs morphology and size as a first model describing the influence of the biological environment. In particular, we will examine, in a comprehensive and systematic study, the adsorption energetics of water, especially for decahedral gold shapes, a competitive form which has been rarely considered in the theoretical literature at the DFT level to date. To this end, in the framework of LABEX PRIMES, we propose to generate DFTbased electrostatic potentials and provide them to our collaborators at IPNL, so that these parameters will be incorporated into their Monte-Carlo simulation code for a better estimation of free radicals in the presence of AuNPs.

In the previous sections 2.2.6 and 2.2.7, we have shown that although numerous experimental studies have investigated the shape of PEGylated AuNPs, only few information is available today regarding the relationship between the PEG coating and the nanoparticle stability, the impact of the PEG coating on the uptake ability of AuNPs and the radiosensitization and associated radiolysis mechanisms. For instance, an accurate description of the stability depending on the size and the morphology is missing for gold nanoclusters around 1 nm, where the fluxionality is predominant. Moreover, the concomitant role of water (biological environment) on this stability, its localization around the nanoparticle and its synergy with the PEG corona, are also poorly understood at this atomic scale, although water radiolysis promoted by AuNPs is a key element of radiotherapy. Regarding the help of theory, as previously exposed, DFT studies explore mainly the interaction between PEG and alkanethiol-based molecules with Au extended surfaces (a relevant model for really large nanoparticle facets). To date the organic coating of dry or hydrated PEGylated AuNPs has not been modeled accurately for nanoclusters. In Chapter 6, we will then explore the influence of PEGylation, the grafted ligand density and the simultaneous hydration on the stability of gold nanoparticles (1.1-1.3 nm). Our objective is the determination of the role of the PEG ligand on the nanoparticle stability and on the confinement of water molecules at the proximity of gold, in order to discuss the cellular uptake of the AuNPs and water radiolysis for therapeutic applications.

In this thesis, we will also try to bridge the gap between the theoretical description of nanomaterials for radiotherapy applications with the modeling of the DNA damages caused by the IR, once the ROS have been generated. The characterization of DNA lesions structures is crucial to understand the possible mechanisms leading to mutagenesis and carcinogenesis. Indeed, the structural information of DNA lesions allow the quantification of the induced distortion, and their impact on processing by repair enzymes. Classical molecular dynamics (MD) simulations can describe in detail the dynamics of these systems that are often difficult to access by experimental methods, due to the difficulty to isolate such complex lesions and the small involved length and time scales. In Chapter 7, we will present our works based on MD simulations to study the structural and dynamical properties of trilysine peptide interacting with a trioligonucleotide TGT and with the same TGT motif embedded within an 15-bp oligonucleotide. A mechanistic pathway after one-electron oxidation of the central guanine is proposed at the DFT level. Finally, by using MD simulations coupled with free energy methods, the repair rate of different cyclobutane pyrimidine dimers (T<>T, T<>C, C<>T, C<>C) will be rationalized, and the recognition of the four lesions by the DDB2 protein moiety will be analyzed precisely at the atomic level. Exploring the formation of symmetric gold nanostars by liquid-cell transmission electron microscopy. Nano letters, 17 (7), 4194-4201.

Introduction

Theoretical modeling has known significant advances over the last decades and is becoming an essential approach to investigate many chemical, physical and biological properties at the atomic level. Furthermore, as computers continue to increase in speed and capacity, larger and more complex three-dimensional structures can be studied. In practice, there are two main approaches to compute the total electronic energy of a

Ĥ Ψ = EΨ [Eq 3.1]
where Ĥ is the Hamiltonian operator, Ψ is the multi-electron wave function describing the quantum state of the system and E is its energy. For a system with n electrons and M nuclei, the Hamiltonian can be decomposed in different components:

Ĥ= T e + V eN + V ee + T N + V NN =-∑ i electrons Δ i 2 -∑ i elec . ∑ k nuclei Z k r ik + ∑ i elec . ∑ j>i elec. 1 r ij + ∑ k ∑ l>k Z k Z l R kl -∑ k nucl . Δ k 2 M k [Eq 3.2]
where T e and T N represent the kinetic energy of the electrons and nuclei, respectively,

V eN stands for electron-nuclei attractive electrostatic interaction , V ee for the electron-electron repulsion , and the last term

V NN for the nuclei-nuclei repulsion.
Solving this equation is incredibly complex due to the coupling between electrons and nuclei. However according to the the Born-Oppenheimer (BO) approximation 1 , the electron mass is roughly a factor of 1000 smaller thann the one of the nuclei, and the electrons are moving much faster than the nuclei. The wave function of the nuclei is neglected, so only the Hamiltonian related to electrons is considered. Despite this first step in the simplification of the problem, the Schrödinger equation can not be solved analytically, and additional approximations have to be introduced. In this context, Hartree-Fock (HF) theory 2 is proposed in 1928 to describing the total wave function as a Slater determinant. However this approach does not take into account the electronic correlation (the correlation energy which is defined as the difference between the HF energy and exact energy) and thus can lead to a wrong description of chemical bonding and reactivity.

Density Functional Theory

Density Functional Theory (DFT) is a widely used approach to solve the many-body Schrödinger equation. DFT is based on two theorems. The first theorem introduced by Hohenberg and Kohn 3 in 1964 states that the energy of the ground state of an electronic system is a unique functional of the electron density ρ(r). This means that the ground state electron density determines the Hamiltonian Ĥ, which determines the set of solutions/states {Ψ i }, which determines all the properties of the system. Meanwhile, according to the second theorem, introduced by Kohn and Sham, 4 the exact electron density is the one which minimizes the energy functional and it can be obtained from the variational principle which involves only the density. The ground-state energy according to this theorem is separated into four distinct parts:

E[ρ(⃗ r)]=T e KS [ρ(⃗ r )]+ E H [ρ(⃗ r )]+ E ext [ρ(⃗ r )]+ E xc [ρ(⃗ r )] [Eq 3.3]
where

T e KS [ρ( ⃗ r )] is the electronic kinetic energy, E H [ρ(⃗ r )]
is the energy resulting from electronic repulsion, E ext [ρ(⃗ r)] is the energy of attraction between electrons and nuclei and E xc [ρ(⃗ r )] is the exchange-correlation energy account for the quantum- chemical interaction between the electrons.

Exchange-Correlation Functional

The only unknown in the Kohn-Sham theorem is the exact form of the exchange-

correlation function E xc [ρ( ⃗ r )]
. However there several approximations for

E xc [ρ( ⃗ r )
] such as the local density approximation (LDA) 5 and the generalized gradient approximation (GGA) 6 . LDA is a class of exchange-correlation functional which depends only on the local values of the electronic density based on the homogeneous electron gas model. The energy is written as : 4] where ϵ XC is the exchange-correlation energy per electron for an homogeneous electron gas of density ρ(r ) . GGA includes a gradient expansion of the density as an additional variable at the same coordinate in order to represent better the inhomogeneous electron density. 5] Several GGA functionals are available such as Becke 7 , Perdew and Wang (PW91) 8 and Perdew, Burke and Enzerhof (PBE) 9,10 . In this thesis, we use PBE functionals for all the DFT calculations.

E XC LDA [ρ(r )]= ∫ ρ(r )ϵ XC (ρ(r ))dr [Eq 3.
E XC GGA [ρ(r )]= ∫ ρ(r )ϵ XC (ρ(r )) dr+ ∫ F XC [ρ(r ) , ∇ ρ(r )] [Eq 3.
LDA and GGA are the first two classes of exchange-correlation functionals present in the Jacob's ladder 11

Dispersion Correction

At the standard LDA and GGA levels in DFT, London dispersion or van der Waals (vdW) weak interactions are not described yet. Dispersion is a long-range, weak interaction coming from the response of electrons in one region to instantaneous charge density fluctuations in another one. 12 Indeed, dispersion force is particularly important since it can contribute significantly to the stability of weakly bonded systems such as adsorption of water on metallic surface or nanoparticles. However, standard DFT exchange correlation functionals (LDA, GGA or hybrid) often fail to provide a proper description of the asymptotic behavior of dispersion interactions. Several dispersion corrections have been proposed in order to improve the overall accuracy of GGA functionals. For instance, DFT-D3 13,14,15 , optB86b-vdW 16,17 , and dDsC 18,19 .

In the DFT-D3 approach proposed by Grimme, the total electronic energy is given by:

E DFT -D 3 =E DFT + E disp [Eq 3.6]
where the dispersion energy E disp is calculated as :

E disp =- 1 2 ∑ i=1 N at ∑ j=1 N at ∑ L ( f d , 6 C 6 ij r ij 6 , L + f d , 8 C 8 ij r ij 8 , L ) [Eq 3.7]
The dispersion coefficient C 6 ij is adjusted on the basis of local geometry (coordination number) around atoms i and j. Two fitting forms of f d ,n can be used: zero damping 20 and Becke-Johnson damping 21 . Zero damping method is expressed as :

f d ,n ( r ij )= S n 1+6( r ij /(SR ,n R oij )) -αn [Eq 3.8]
Becke-Jonson damping is expressed as:

f d ,n (r ij )= S n r ij n r ij n +(α 1 R oij +α 2 ) -n [Eq 3.9]
In order to choose the best dispersion corrected functional able to improve the description of the electronic properties of gold systems (bulk, nanoparticle etc) with respect to GGA

VASP Program

For all the DFT calculations performed in this thesis, the Vienna ab initio Simulation Package (VASP) 22,23,24 developped by G.Kresse and J. Furthmüller is used. This code applied DFT to treat systems with periodic boundary conditions (nuclei and electrons are translated in the three directions of the space defined by the vectors of the elementary pattern). In this tridimensional periodic system, VASP uses Bloch theorem 29 for expending the Kohn-Sham wave function. This theorem states that the electronic wave function can be written in the form of a plane wave phase factor:

Ψ i ⃗ k (r )=e i ⃗ k r u i ⃗ k (r ) [Eq 3.10]
where ⃗ k is a vector of the reciprocal space, e i ⃗ k r is the phase equivalent to the equation of plan wave and u i ⃗ k (r ) is a periodic function associated with a band (or 'energy level' for periodic system). The electronic properties are calculated in the first Brillouin zone thanks to Fourier transform techniques. Within the Kohn-Sham method applied to periodic systems, the number of ⃗ k vectors times the set of monoelectronic equations need to be solved. However, this is impossible if the number of ⃗ k vectors is infinite. Monkhorst-Park 25 approach is proposed in this context to sample the Brillouin zone at special sets of k-points. A plane-wave energy cut-off is also introduced in the calculations in order to reduce the basis set to a finite size. This value is fixed at 400 eV because of the regular pseudo-potential of atomic oxygen. The pseudo-potentials which are used for the description of the electron-ion interactions, is approximated using the projector augmented-wave (PAW) method. 26 The precision of the calculations is set to "normal" and the total electronic energy convergence criterion is set to 10 -6 eV. Geometry optimization is performed using the conjugate-gradient algorithm, with a threshold of 10 -2 eV.Å -1 for the residual forces acting on the nuclei.

Classical Molecular Dynamics Calculations

Force Fields

In molecular mechanics, the total energy of the system can be described by mathematical expressions of potential, which are called force fields. Three force fields commonly used for the simulations of protein and DNA biomolecules are CHARMM 30 (Chemistry at HARvard Molecular Mechanics), GROMOS 31 and AMBER 32 (Assisted Model Buildingwith Energy Refinement). The latter force field has been used in this thesis, since specific corrections for DNA backbone important at the microsecond range have been proposed for the parm99 force field. It can be written as:

E tot = ∑ bond K r (r-r eq ) 2 + ∑ angles K θ (θ-θ eq ) 2 + ∑ dihedral ( V n 2 )[1+ cos(n ϕ)-γ ]+ ∑ i< j [ A ij R ij 12 - B ij R ij 6 + q i q j ϵR ij ] [Eq. 3.11]
The total energy ( E tot ) is the sum of bonded (bonds, angles, dihedrals and improper dihedrals) and non-bonded (Coulomb and van der Waals) components. In this equation, the first two terms describe the covalent-bond stretching and angle bending by using harmonic functions; K r and K θ correspond to the force of the energetic penalty imposed for deviations of the bond length and angle from the defined minimum energy positions.

Torsional potentials for valence angles are described with a multiplicity n and a phase δ;

A and B are non bonded atoms, with van der Waals interactions described by Lennard-Jones potential (the repulsion term is represented by the R -12 and the dispersion by the R -6 part of the potential). The electrostatic interactions are described by a charge-charge interaction-term (Coulombic potentials).

The parameterization is based on experimental and/or high-level quantum mechanical calculations. In Chapter 7, we use the parm99 force field with bsc1 corrections 33 for the simulations of DNA. The parameter of DNA lesions have been generated with antechamber and parmcheck subprograms of AMBER, and atom point charges can be computed using the RESP 34 protocol. ff14SB 35 force field is chosen to describe protein and TIP3P 36 model to describe the water environment.

Molecular Dynamics Simulations

First introduced by Alder and Wainwright 27 in the late 50s and their first application to a protein 28 in 1976, molecular dynamics (MD) simulations have become a popular and powerful approach nowadays to study the biological system at atomic level. MD simulations calculate the relative positions of the atoms at small interval of time (1fs, see later), thus the behavior of atoms over a longer time scale can be predicted. This can be achieved by integrating the Newton's equations of motion (Eq. 3.12) iteratively.

F i =m i a i =m i d 2 r i dt 2 [Eq. 3.12]
where m i is the mass of atom i and a i is the acceleration resulting from the force F i acting on atom i .

In order to numerically solve equation 3.12, standard Taylor series can be used to calculate the position after a short time interval ∆t. Various numerical algorithms have been proposed for integrating the equations of motion, such as Verlet algorithm, the velocity Verlet algorithm and the Beeman's algorithm. Among them, Verlet algorithm and its leap-frog alternative are the most widely used which propagates the atomic positions r i and velocity V i at half-time step from time t to t+∆t :

v i (t + Δ t 2 )=v i ( t- Δ t 2 + a i (t) . dt) [Eq. 3.13]
Then the atomic positions are calculated as:

r i (t +Δ t )=r i (t)+ v i Δ t 2 . Δ t [Eq. 3.14]
To avoid instability of the integration, a time step ∆t should not be larger than the fastest molecular movements (1fs of bond vibrations involving hydrogen atoms in the solute). In Amber, SHAKE [START_REF] Rünger | Mechanisms of mutation formation with long-wave ultraviolet light (UVA)[END_REF] algorithm is applied to freeze X-H vibrations, thus this allow the use of ∆t to speed up the calculations. SHAKE algorithm can also combined with Hydrogen Mass Repartionning 38 (HMR). The idea is to repartition the mass of heavy atoms into the bonded hydrogen atoms in order to slow the highest-frequency motions of the macromolecule, the time step of the simulation can be increased by a factor of 2.

General Procedure for Running MD Simulations

Many packages are available for running MD simulations with the most popular being:

AMBER, CHARMM, GROMACS and NAMD. In general, the simulation procedure can be divided into five steps: preparation, minimization, heating, equilibration, and production. The starting coordinates of the system can be obtained in the databases of experimental crystal or NMR structures in Protein Data Bank (PDB). For isolated oligonucleotides, NAB molecular manipulation package (available in AMBER) is developed to facilitate their construction. Then, a topology file which contains all the information required to define the molecule within the simulation (for instance, the bond lengths, bond angles, partial charges and atom masses etc...) is prepared. The next step consists in solvating the system in a water box (explicitly or implicitly), and adding salt ions to neutralize the system and mimic a physiological environment. Various shapes of water box can be used such as cubic, rhombic, sphere, and truncated octahedron. These solvation boxes however, would present undesired boundary effects due to their finite dimensions. This can be avoided by using a larger solvation box and simulating in periodic boundary conditions (PBC). Since PBC is used, a cut-off must be employed for long-range interactions to prevent self-interactions between atoms' images from one box to the other. Particle-Mesh-Ewald 39 method is used at the same time to treat the longrange electrostatic interaction. Now, minimization step is needed to ensure there are no steric clashes after the addition of hydrogens and solvent molecules. After minimization, the system is brought up to the temperature of interest (usually at 300K in physiological conditions). The heating run is performed slowly for short periods of time. Langevin thermostat is used in our simulations in order to control heating and to ensure that the average temperature is the desired one during the remaining simulation steps.

Equilibration step is then performed to ensure the system is in a stable state, which mean that the energy and temperature should remain stable. At this stage, the system is ready for the production run. The simulation time can be up to nano/micro-seconds, depending on the system size and computational resources available.

Free Energy Calculations

Classical MD simulations have prove very helpful and efficient to sample well the regions with low potential energy configuration spaces. However, the regions of higher energy are sampled rarely and can be overlooked. To overcome the drawback of MD simulations, free energy calculations can be performed by adding biases to enforce the sampling of a transition between two states and thus allow to overcome high energy barriers. Different algorithms have been developed to sample such rare events such as umbrella sampling (US) [START_REF] Drouin | UVB-induced Cyclobutane Pyrimidine Dimer Frequency Correlates with Skin Cancer Mutational Hotspots in p53[END_REF] , metadynamics [START_REF] Sage | Mutagenic specificity of solar UV light in nucleotide excision repairdeficient rodent cells[END_REF] , and extended adaptive biasing force (eABF) [START_REF] Sage | Distribution and repair of photolesions in DNA: Genetic consequences and the role of sequence context[END_REF][START_REF] Pfeifer | Mutations induced by ultraviolet light[END_REF] . Recently, meta-ABF [START_REF] Gustavsson | DNA/RNA: Building blocks of life under UV irradiation[END_REF] algorithms have been proposed to cross the freeenergy barriers by incorporating a history-dependent potential term in the eABF method.

The combination of metadynamics and eABF in this algorithm improve significantly the sampling efficiency and convergence rate, with the simulation time also much shorter compared with other importance-sampling algorithms. Meta-ADF has been used by our colleagues from Nancy to calculate the free energy of base flipping in Chapter 7.

Introduction

Before we investigate the effect of chemical (PEG) and biological (water) environment on the relative stability of the competitive morphologies of AuNPs, it is important to have a fundamental understanding of those isolated AuNPs models in vacuum. In Chapter 2,

we have shown that the question of the most stable shapes according to the size of the NP is debatable. 1,2,3,4,5 Most of the theoretical studies available in the literature are based on simulations using effective semi-empirical potential and global optimization methods to explore the potential energy surface and to identify the global minimum of nanoparticle structures. Those based on ab initio calculations are relatively scarce due to computational cost. Consequently, the choice of the theoretical methods as well as the parameters used to develop into the semi-empirical potentials result in different conclusions. Furthermore, even though the two most common descriptors, normalized cohesion energy and excess energy, have been used extensively in the theoretical community to compare the relative stability of metallic NPs, their reliability and their ability to predict the trends observed experimentally are still questioned. One of the key issue is the fact that they are not observables, that one can compare directly with experiments.

In this chapter, we propose to investigate AuNPs stability as a function of size and morphology by using DFT calculations including dispersion forces. Our Heuristic approach offers a good compromise in terms of accuracy and computational cost. A set of nanoclusters with six different morphologies is selected and optimized in the range 0.9-3.4 nm. The relative stability of the optimized structures is then compared by using cohesive energy, excess energy and a new descriptor introduced in this thesis, nanoparticle surface energy. Our DFT results are compared with available measurements.

Methodology

DFT calculations (spin restricted) of Au NPs were performed by using the VASP code 6,7,8 version 5.3.5. PBE 9 with Grimme's D3 10 semi-empirical dispersion corrected functional (zero-damping formalism) was considered to describe electronic exchange and correlation at the generalized gradient approximation with van der Waals interactions.

The core-electrons were described by the projector-augmented wave (PAW) pseudopotentials 11 (11 valence electrons per Au atom), and valence electrons were expanded in plane waves with a kinetic cut-off energy of 400 eV. All the Au NPs were modeled in a cubic box of 5×5×5 nm 3 with a Γ-point only approach for the k-point mesh and related Brillouin zone. For the Au bulk, the fcc crystalline structure was described by using a kpoint grid of 17×17×17. In the geometry optimizations, the Au NPs structures were relaxed completely with 10 -6 eV for the convergence of the total electronic energy and -0.01 eV.Å -1 for the minimization of the residual forces on the nuclei. A Methfessel-Paxton smearing was used for the calculation of the total electronic energy.

NP Models and Optimal Structures

The objective of this chapter is the determination of competitive morphologies in the range of sizes accessible by DFT calculations, from 0.9 to 3.4 nm. In Figure 4.1, the polyhedra considered in this study are defined, including the three key octahedral, icosahedral and decahedral symmetries according to the literature. 3,4

Results and Discussion

After geometry optimizations of theses NPs at DFT-D3 level of calculation, we will use three descriptors: normalized cohesion energy, excess energy and our proposed nanoparticle surface energy to compare the relative stability of AuNPs according to morphology and size.

Cohesion Energy Analysis

The cohesion energy per Au atom ( E coh ) is defined as follows:

Δ E coh = E tot ( AuNP )-N Au * E tot ( Au iso ) N Au [Eq. 4.1]
where N Au is the total number of Au atoms in Au NP, E tot (AuNP ) being the total electronic energy of the relaxed nanocluster and E tot ( Au iso ) being the total electronic energy of an isolated gold atom. The cohesion energy can be further decomposed empirically into four additive terms, where each term corresponds to the different contributions to the NP energetics coming from the positions of atoms 14 :

E coh =a N +b N 2/ 3 +c N 1/ 3 + d [Eq. 4.2]
The first term (a N ) corresponds to volume contribution (internal strain), b N 2 /3 represents contribution from facets, c N 1/3 and d from the edges and vertices, respectively. Since we normalize the cohesive energy by the total number of atoms of AuNP in order to determine its evolutions against N, both sides of Eq. 4.2 is divided by N and give:

E coh / N=a+b N -1/ 3 + c N -2/ 3 + d N -1 [Eq. 4.3]
This equation show that the normalized cohesion energy is roughly proportional to the largest term N -1/3 . This gives:

Δ E coh =⟨E facets surf ⟩ * N -1 /3 + Δ E coh ∞ (bulk ) [Eq. 4.4]
The slope ⟨E facets surf ⟩ (eV) can be identified as the average facet surface energy of the NP (including center, edge and corner atoms) and the offset Δ E coh ∞ (bulk ) (eV) as the cohesion energy extrapolated for the bulk (infinite value of N).

Excess Energy Analysis

In addition, we propose to compare the trends coming from the cohesion energy with those resulting from the calculation of excess energy ( Δ E exc ) introduced by Baletto et al, 3,4 a relevant descriptor which separates more clearly the nanoparticle stability. The formula of excess energy per atom is the following one :

Δ E exc = E tot (AuNP )-N Au * E tot ( Au bulk ) N 2/ 3
[Eq. 4.5] where E tot (AuNP ) is the total electronic energy of the Au NP, N Au is the total number of Au atoms in Au NP and E tot ( Au bulk ) being the total electronic energy of gold bulk (1 atom in the primitive cell). The energetic balance between the Au NP and the bulk is similar to a surface energy. N 2/ 3 is the normalization constant chosen empirically to take into account the proportion of surface Au atoms with respect to the core Au atoms. In Figure 4.9, the calculations show that two shapes compete in the range of 0.9-1. concluding that decahedral shapes are either majority or equivalent in stability to truncated octahedral forms. 1,3,4,5 In addition, the stability of icosahedra tends to slightly increase with the NP size, in contrast with these previous studies. Our global trends are in better agreement with a previous study based on simulations obtained with the Sutton-Chen potential 16 and they also support in part the recent DFT study examining a set of Au NPs with the TPSS functional. 2 Several experimental studies based on HAADF-STEM measurements have been reported for the determination of the structure of gold nanoclusters especially for particular size 309 28 ,561 29 , and 923 30 atoms. (See chapter 3 for experimental STEM images). The reported images in these publications show the preference of defective decahedral and face-centered cubic forms with respect to icosahedral shape. Our DFT results based on excess energy support these conclusions because truncated octahedral and Marks-decahedral forms are found more stable than the icosahedral shape above 300 atoms.

Surface Energy Analysis

Up to date, most of the descriptor used to compare the relative stability of NP are either based on cohesive energy or excess energy. According to Ferrando et al, the stability of nanoparticles depends on their crystallinity and surface energy effects. 15 However, surface energy effects can be captured by another descriptor, named nanoparticle surface energy (Г), which is not so well addressed in the literature, neither experimentally nor theoretically. Experimental determination of surface free energy is rather challenging especially for small metallic NP. To our knowledge, the experimental nanoparticle surface energy has been reported only for copper 17 , silver 18 , gold 19,20 and bimetallic copper-gold nanoparticles. 20 Depending on the experimental approach and the way the evaporation data are fitted, the nanoparticle surface energy can vary significantly (see for example ref 19 for the comparison of AuNP surface energy reported in the literature). We will only focus our analysis on mesurements where Г is calculated based on Kelvin equation 21 which relates the equilibrium vapor pressure to surface curvature. In fact in the Kelvin equation Г is the only free parameter to be extracted from the fitted slope, so the experimentalists conclude to a better reliability for the corresponding measurements.

Thus according to ref [17, 18 and 20] , the surface energy obtained by fitting the Kelvin equation for copper, silver, and gold are 1.70±0.03, 1.13, and 1.12±0.03 J/m 2 , respectively. Theses measurements also showed that from one NP to another one, Г does not change much and poorly depend on the size. These available experimental measurements are crucial in order to validate theoretical approaches. Indeed, there exist a lot of thermodynamics models mostly developed, on Tolman length 22 to predict the NP surface energy. 23,24,25 According to their calculations on different AuNP morphologies, cuboctahedral clusters show a slightly higher Г than the icosahedra in the case of the smaller clusters (Au 309 and Au 923 ). 24 Г for icosahedral shape increases significantly as the size increases, in contrast to regular cuboctahedral and truncated octahedral AuNP. 25 However in these thermodynamic models, their NP structures are not optimized at DFT level, meaning that the surface relaxation depending on NP size and morphology is not determined explicitly at an ab initio level. So, the ability and accuracy of these thermodynamic models to predict the experiment values are still under debate.

In this section, we propose to estimate the nanoparticle surface energy with the structures of AuNPs being optimized at DFT-D3 level of calculation. The surface energy (Г) is defined as the reversible work per unit area involved in creating a new surface at constant temperature, volume, and total number of moles. 26 It is calculated as follows (in J/m 2 ):

Γ= E tot ( AuNP)-N Au * E tot ( Au bulk ) Λ [Eq. 4.6]
where E tot (AuNP ) is the total electronic energy of the optimized Au NP, N Au is the total number of Au atoms in Au NP, E tot ( Au bulk ) being the total electronic energy of gold fcc bulk, and Λ being the surface area of the corrresponding relaxed AuNP. The latter is calculated using the average Au-Au distance of the NP outer-shell ( dsurf ( Au -Au) ) and the analytical formula of the surface area of different morphologies 27 is given in Table 4.2.

Au NP

Λ

Regular truncated octahedron (to)

(6+12 √3)(n d ) 2 Ino-decahedron (ino) 5 (n d ) 2 (1+√3/2) Icosahedron (ico) (5 √3 )(n d ) 2
Cubotahedron (cubo)

(6+2 √3)(n d ) 2
Decahedron (deca) [20] is given for comparison.

(5/2)(√3 )(n d ) 2 Defective decahedron (def) 10[((n-1) 2 d 2 √(3))/4]+10(2d(n-1)-d)d√(3)/ 4+10(d 2 /2) Marks decahedron (marks) 10[((n-1) 2 d 2 √(3))/4]+10(2d(n-1)-d)d√(3)/ 4 +5([(n-1) d-d ] 2 )+5 d 2 (4 √(2))+10(d 2 /2)
Once the average Au-Au distance in the outer shell is calculated on the basis of the relaxed geometries, the surface area ( Λ ) can be evaluated to estimate the surface energy ( Γ ) of the nanocluster. The results are presented in Figure 4.11. Please note that we are comparing six morphologies with different symmetries and crystallinities, but the reference of the surface energy for all AuNPs is the one calculated for fcc-based bulk.

As a matter of fact, Au bulk structures related to D h and I h symmetries do not exist.

Hence, in the following, we can only compare the stability trends of Γ of AuNP having the same crystallinity.

A general remark is that the NP surface energies do not vary much and it tend rapidly to an asymptotic value when the size increases, in fair agreement with a recent experiment that shows that the nanoparticle surface energy is independent of size. 20 According to this descriptor, truncated octahedron is more stable than cuboctahedron in the range 0.9 -3.4

nm, the surface energy varies from 0.726 to 1.083 J/m 2 . The value of the biggest explored size of truncated octahedra (Au 976 ) is very close to the experimental value (1.12 ± 0.03 J/ m 2 ), 20 showing that our estimation of nanoparticle surface energy at DFT-D3 level is very predictive. The surface energy shows that cuboctahedra which are always the least stable polyhedral according to cohesive energy and excess energy analyses, become competitive energetically with other morphologies (icosahedral and ino-decahedral). This clarifies the analysis of the proportion of competitive structural isomers at Au 561 proposed experimentally by HAADF STEM images, where fcc cubotahedra is more stable than decahedra and icosahedra. 29 Then, the absolute stability of

Conclusion

In this chapter, we have compared in a systematic way, the stability of a set of AuNPs in the range 0.9-3.4 nm using three descriptors: cohesive energy, excess energy, and nanoparticle surface energy. All the Au NP structures were fully relaxed at DFT-D3 level.

Our calculations highlight the importance of the computational method (choice of the where E tot ( AuNP -H 2 O ) is the total electronic energy of the complete relaxed system (water monomer adsorbed on the Au NP) , E tot (AuNP ) being the total electronic energy of the isolated relaxed AuNP (with a starting guess for the geometry optimization being the deformed Au structure in presence of water) and E tot ( H 2 O ) being the total electronic energy of the isolated relaxed water molecule.

Energy decomposition analyses (EDAs) are performed to understand the impact of water adsorption and solvation on adsorption energetics. Two different EDAs are developed and discussed throughout this chapter. First, the adsorption energy can be decomposed into pure GGA PBE contribution ΔE cov (eV) and dispersion D3 semi-empirical corrective term ( ΔE disp ) (eV):

ΔE ads =ΔE cov + ΔE disp [Eq. 5.2]
Second, the adsorption energy can be decomposed into interaction and deformation terms 1 :

Δ E ads = ΔE defo ( AuNP)+ ΔE defo ( H 2 O ) + ΔE inte ( H 2 O-Au ) [Eq. 5.3]
The interaction energy represents the energy associated with the formation of the chemical bond between Au and water (Au-O in our case), while the deformation energy is the cost needed to distort the geometry for both interacting species. Such EDA have been used for the past 30 years for quantifying different contributions to chemical bonding of molecular systems. 1,2

Adsorption on Truncated Octahedra (0.9 -3.4 nm)

In the following section, we have studied the adsorption strength of one water molecule on nine truncated octahedra AuNPs as a function of the NP size. Referring to our previous chapter, we showed that in general, the most stable morphologies in the range 0.9-3.4 nm is the fcc truncated octahedra, on the basis of the analysis three theoretical descriptors. For this reason, we have chosen first this morphology to investigate the adsorption properties of water monomer on AuNPs, from Au 38 to Au 976 .

Adsorption on Icosahedral, Decahedral and Octahedral

Morphologies ( 0.9-1.8 nm)

In the second step, we have examined the adsorption properties of a water molecule on different competitive gold polyhedra with different morphologies in the range of 0.9-1.8 nm. A set of 9 nanoclusters has been defined as follows. The truncated octahedra Au 38 , Au 79 , and Au 201 from the previous analysis have been selected for comparison. In addition, regular decahedra Au 54 and Au 105 and other metastable shapes such as icosahedra and ino-decahedra (Au 55 and Au 147 ) have also been considered to explore the impact of water adsorption on their metastability. Because of the large computational cost required to optimize the water solvation shell examined on, the biggest cluster considered is Au 201 .

In As shown in Figure 5.4, as the size of the NP increases, the adsorption site changes (although the adsorption at a corner remains the majority) and the evolution of the adsorption energy is not monotonous, with values in a narrow range: from -0.31 to -0.46 eV. Our results agree with previous DFT values proposed on Au small clusters 4 and Au(111). 5,6 The adsorption of a water molecule is thus a weak chemisorption with a quite long Au-O distance in the range 2.40-2.63 Å. This is consistent with the weak deformation of Au NPs after adsorption. To quantify this, an energy decomposition analysis of adsorption energetics is also proposed in Figure 5. According to this analysis (Figure 5.5), the deformation energy of the Au NPs is positive and weak in general for all the shapes in 0.01-0.14 eV range. In parallel, the deformation energy of the water monomer is also positive and close to zero (below 8 meV). This means that the non monotonous trend of adsorption energy is mainly captured by the interaction energy between the Au cluster and water (same trend observed in the case of adsorption on truncated octahedra 0.9-3.4 nm). Moreover, this interaction, which corresponds to the chemical bonding between both partners, is the strongest one (-0.6 eV) for the ino-decahedral NPs and for the icosahedral shape at least for small size (-0.47 eV). For truncated octahedra and decahedra, the chemical bonding is quite weaker (from -0.32 to -0.47 eV) and it varies less with the cluster size. Then, the adsorption energy E ads (eV) of each water monomer on the 9 different Au nanoclusters (0.9-1.8 nm) has been decomposed into pure DFT GGA PBE term, noted E cov (eV) and dispersion D3 semi-empirical corrective term, named E disp (eV), as shown in Figure 5.6. As a preliminary remark, in the decomposition energy model, the two components are systematically negative and thus stabilizing. They are equivalent in proportion in the range 30-60% for dispersion and 40-70% for the pure GGA PBE term ("covalence"). Both of them globally capture the trends of the adsorption energy.

Water Monoshells Adsorbed on AuNPs (0.9-1.8 nm)

On the basis of the best adsorption structures of water monomers on the Au NPs, we then propose to explore the interaction of a complete shell of water molecules around the metallic clusters by a static approach. The starting geometries of these solvation shells come from an additive principle assuming that the coadsorption of the best sites is an optimal choice for maximizing the overall stability of the solvated nanocluster.

This means that, for the various NPs, all the equivalent sites corresponding to the best adsorption form of monomers are occupied by water molecules. Then, to complete the solvation shells, metastable adsorption sites were considered in such a way that a network of flat co-physisorbed and co-chemisorbed water molecules is built up through hydrogen bonds with reasonable distances (longer than 1.8 Å). Thus, because all the molecules were initially coplanar with respect to one facet, no arbitrary choice related to H-up/H-down configuration has been considered by construction. This starting choice was also guided by a previous molecular dynamics study of immersed Au clusters (13, 55 and 147) in water, showing that the hydrogen bonding of water molecules is arranged in a two-dimensional structure for Au 55 and Au 147 . 7 In the following, all the structures of solvated AuNP and the adsorption energies are illustrated in section 5.3.1, nanoparticle structural deformation induced by water monoshells are presented in section 5.3.2, whereas details of the total number of water molecules per NP, the numbers of chemisorbed and physisorbed molecules, and analyses of hydrogen bonds are presented in section 5.3.3.

Adsorption Structures and Energertics

The normalized adsorption energy per water molecule in the monoshell is defined as follows:

Δ E ads = E tot ( AuNP -N H 2 O ) -E tot (AuNP )-N H 2 O * E tot ( H 2 O ) N H 2 O [Eq. 5.4]
where

E tot ( AuNP -N H 2 O
) is the total electronic energy of the complete relaxed system (water monoshell adsorbed on the Au NP), E tot (AuNP ) being the total electronic energy of the isolated relaxed AuNP (with a starting guess for the geometry optimization being the deformed Au structure in presence of water) and

E tot ( H 2 O )
being the total electronic energy of the isolated relaxed water molecule. N H 2 O is the total number of water molecules in the monoshells.

The surface coverage of water is addressed in At first glance, these optimal structures are relatively homogeneous regarding the distribution of chemisorbed and physisorbed water and as a function of the NP size; however, no clear arrangement appears, in agreement with a previous MD study. 7 In addition, the solvation shells are quite spherical around the Au NPs, thus meaning that the average interaction between each water molecule and the cluster should not vary much. This can be seen with the average adsorption energy per water (from -0.607 to -0.643 eV/water), which does not change much against the nanocluster size (see Eq. 5.4

for the definition). This contrasts with the adsorption of the monomer discussed before.

The adsorption energy per water is in average 70% stronger for the solvation shell with respect to the isolated adsorption. According to the optimal geometries, this gain is certainly not due to a strengthening of chemisorbed water but rather to the formation of chemical bonds between the molecules (hydrogen bonds). See section 5.3.3 for a detailed analysis of the hydrogen bonds.

Considering now the impact of the water solvation shells on the geometry of the Au NPs after the geometry optimizations, deformations of the clusters are observed in Figure 5.7, even for the most stable case in vacuum, such as Au 38 , Au 54 , Au 79 . This effect is also seen for the less stable icosahedra Au 55 and Au 147 . A quantitative analysis of the structural deformation of the nanoparticle outershells upon water adsorption is addressed in section 5.3.2. Moreover, the metastable ino-decahedra Au 55 and Au 147 in vacuum are transformed into corresponding icosahedra through the interaction with the water shells. This original result is counterintuitive because water chemisorption on Au is quite weak as reported before, and HAADF-STEM images show that gold icosahedral nanoclusters in model operating conditions (in the range 1-3 nm) transform into decahedral structures. 14,15,16 However, the increase of the chemical bond with water obtained for these clusters and the concomitant increase of chemisorbed water coverage discussed previously allow us to explain the origins of such a remarkable phenomenon. Then in this study we demonstrate that water, standing for a model of the biological environment, may have a significant impact on the morphology of metastable NP shapes, although the intrinsic interaction with water is relatively weak.

Nanoparticle Structure : Induced Deformation by Water

Monoshells

In order to evaluate the influence of the water monoshells on the structure of the Au nanoparticles, we introduce the roundness degree S of the nanocluster as follows :

S= R min R max [Eq. 5.5]
where R min (and R max ) are the minimal (maximal) radius (Å) from the nanoparticle center to the nanocluster relaxed outer shell (after geometry optimization with or without water monoshells). This roundness degree is essentially a positive value in the range [0;1] (dimensionless) : the closer to 1 meaning an optimized nanoparticle outershell approaching the geometry of a sphere; the closer to 0 meaning an outershell approaching the geometry of an ellipsoid.

In order to quantify the influence of the adsorption of the water monoshells on the Au nanoparticle structures, we have calculated the variation of the roundness degree ΔS on the basis of the optimized nanocluster outershells with and without the presence of water. The corresponding variation is thus defined as follows :

ΔS=S AuNP -NH 2O -S AuNP [Eq. 5.6] where S AuNP -NH 2 O and S AuNP are the roundness degrees with and without water monoshells, respectively. When ΔS is positive, the water monoshell has induced a significant geometric deformation of the nanocluster outershell from its symmetric structure in vacuum toward a globally rounder shape. At the opposite, when ΔS is negative, the resulting geometric deformation of the nanocluster outershell upon water adsorption is a stretching of the initial symmetric structure along the largest symmetry axis of the nanoparticle. When ΔS is close to zero, the nanocluster may have been slightly distorted upon water adsorption, however, in average, the deformation is negligible.

123

All the corresponding results have been exposed in Table 5 present in the nine considered nanoparticles.

Hydrogen Bonding Model

In this section, a theoretical model is developed to evaluate the part of the total hydrogen bond energy in the adsorption energy of water molecules surrounding the Au nanoclusters.

In being the total number of physisorbed water molecules and N.A. being the nonadditivity of the model.

The first approximation is the neglect of the non-additivity of the model. The second one is that the total interaction energy between the water molecules is identified as the total hydrogen bonding energy:

Δ E int , H 2O -H 2 O tot ≈ Δ E HB tot [Eq. 5.8]
The last approximation is that the sum of total deformation energy and the interaction energy of chemisorbed and physisorbed molecules in the monoshell is expressed as N H 2 O times the interaction energy of one chemisorbed water monomer (best chemisorption form) on the Au NP:

N H 2 O ΔE ads 1 H 2 O ,best ≈ ΔE deform tot + N chem H 2 O ΔE int ,chem 1 H 2O ,best + N phys H 2O ΔE int , phys 1 H 2 O , best [Eq. 5.9]
This means that chemisorbed and physisorbed molecules are initially not differentiated.

As a consequence, the total coadsorption energy reads:

ΔE coads tot =N H 2 O ΔE ads 1 H 2 O ,best + Δ E HB tot [Eq. 5.10]
Hence in our model, the total hydrogen bonding energy between water molecules in the adsorbed monoshell is calculated according to the following formula and associated

Δ E HB tot =E tot ,OPT NH 2 O , GEO 2 -( N chem H 2O E tot , OPT 1 H2 O , GEO 1 + N phys H 2 O E tot ,OPT 1 H 2 O ,GEO 3 +(1 -N chem H 2O )E tot , SPE
1 AuX ,GEO 1 ) [Eq.

5.11]

where

E tot ,OPT NH 2 O ,GEO 2
is the total electronic energy of the complete relaxed system (water monoshell and Au X ) noted "OPT.GEO2 E tot ,OPT 1 H 2 O , GEO1 ", being the total electronic energy of the best chemisorption form of one water monomer on Au X , noted "OPT.GEO1",

E tot ,OPT 1 H 2 O , GEO3
being the total electronic energy of the optimized isolated water molecule in gas phase, noted "OPT.GEO3", and E tot , SPE

1 AuX , GEO1
being the total electronic energy of the deformed and isolated Au X nanocluster (without water) in the geometry "OPT.GEO1" (single point energy calculation noted "SPE.GEO1"). This means that physisorption is neglected in our approximated model. In fact, on the basis of the energetic models presented above, the adsorption energy per water of the solvation shell is mainly due to the formation of two hydrogen bonds in average (from -0.49 to -0.59 eV/water depending on the NP size), the rest being the interaction energy between water and gold (around -0.1 eV/water). In the case of Au NPs, the formation of the water shell occurs at the detriment of chemisorption, because the latter is rather weak. Hence, for Au NPs in the 0.8-1.9 nm range, both the stability of the solvation shell (-0.6 eV/water) and the average number of formed hydrogen bonds (golden rule of 2) are remarkably independent of the NP size and morphology.

By comparison, in bulk water, the cohesion energy per water molecule is known from experiments (-9.9 kcal/mol or -0.429 eV/water). 9 In addition, the two-body contribution of the dissociation energy of water dimers benchmarked by coupled cluster calculations on configurations extracted from ab initio molecular dynamics simulations of liquid water has been evaluated to be -0.137 eV (while it is -0.221 eV at equilibrium in the gas phase). 10 This means that the maximum number of hydrogen bonds per water molecule in bulk liquid can be estimated to be 3.13 bonds, considering that only hydrogen bonding contributes to the cohesion energy in the liquid. This assumption agrees with previous experimental measurements from neutron diffraction 11 The overall shape of the curves become more complexe in presence of water monoshells and less in correspondence with the Au atomic layers since the electrostatic information coming from water is added in the total calculated value. In order to separate the contributions of the Au cluster and water systematically, a radial integration of the electrostatic potential would surely be more convenient.

Conclusion

In this chapter, we have investigated the impact of water adsorption on an extensive set of AuNP morphologies. The study of isolated adsorption of one water molecule on AuNP in the range 0.9-3.4 nm shows that the most stable adsorption forms are similar (corners and edges) regardless of the nanoparticle shape and size, although the adsorption strength differs significantly. When a complete and explicit water solvation shell interacts with gold nanoclusters, metastable in vacuum and presenting a predominance of {100} square facets (ino-decahedra Au 55 and Au 147 ), these nanoparticles are found unstable and transform into the closest morphologies exhibiting mainly {111} triangular facets and symmetries. The corresponding adsorption strength per water molecule becomes independent of shape and size and is enhanced by the formation of two hydrogen bonds on average. Our DFT work opens promising perspectives for a reparametrization of semiempirical potentials and global optimization methods aiming to describe the relative stability between ino-decahedra and icosahedra in interaction with a water solvation shell at larger NP size. In particular, this would allow the study of Au 309 , Au 561 , and Au 923 , both with static and dynamic approaches for Au/water interfaces, and this would show whether the water solvation still induces the transformation between metastable morphologies at larger NP size. Extracted from our DFT models, the average electrostatic potential coming from AuNP in interaction with water molecules are key parameters for future theoretical developments related to radiochemistry in collaboration with colleagues from Institut de Physique Nucléaire in Lyon.

Introduction

In the previous chapter, we have studied the interaction of water molecules with AuNPs without the presence of the synthesis coating. However, AuNPs for biomedical applications are usually synthesized in the presence of organic ligands. Complex organic coatings on the particle surface prevent the sintering of AuNPs and shield them from the biological environment, the required time to reach the targeted cancerous cells. In this context, hydrophilic polyethylene-glycol (PEG) is an excellent choice of ligand as PEG coatings have been shown to increase blood circulation time and reduce toxicity of AuNPs. 1 Nevertheless, despite their widespread use in experiments, there is a current lack of theoretical models able to describe the relative stability of AuNPs in the simultaneous presence of hydration and PEGylation. Moreover, the role of PEG ligands on the water radiolysis and generation of radical species is poorly described in the literature.

In this chapter, we aim to model the PEGylation of AuNPs at the DFT level, first by considering the adsorption of one PEG ligand, and then by decorating the nanoparticles with coadsorbed ligands approaching saturation at the surface. In a further step, the model is hydrated by a large number of explicit water molecules which are mainly in interaction with PEG ligands, through hydrogen bonds. An energy decomposition model is proposed to evaluate the adsorption strength between one PEG ligand and AuNPs at various conditions (isolated PEG adsorption, ligand saturation, hydration effect) and to determine energetics of the hydrogen bonds. Finally, the relationship between the adsorption strength and the cellular uptake of AuNPs as a function of morphology is discussed.

nanoclusters will then be considered in the range 1.1-1.3 nm. Although small, these nanoclusters are not far from the explored experimental range (2.4-89 nm). 3 In Chapter 4, we shown that five typical morphologies are competitive in vacuum in the range 1-3.4nm: Marks-decahedral, regular decahedral, icosahedral, ino-decahedral and regular/irregular truncated octahedral shapes. In this chapter these morphologies are described by Au 49 (marks), Au 54 (deca), Au 55 (ico), Au 55 (ino) and Au 79 (ito), respectively.

By looking at the relative stability order provided by the normalized cohesion energy of the nanocluster per Au atom, the trend is the following one in vacuum: Au 79 (ito) > Au 55

(ico) > Au 55 (ino) > Au 54 (deca) > Au 49 (marks). In the fluxional regime considered here, these highly symmetric polyhedral forms may not be the most stable ones for each size, as previously demonstrated from global optimization methods and semi-empirical potentials. 4,5 The choice of the PEG ligand length is also strongly determined by the restraints of the supercell size. In order to keep a reasonable vacuum space between GNPs decorated by an organic coating and their equivalent periodic images (in the range 1.8-3.2 nm), two ethylene glycol units (2 EG) have been considered in the PEG ligands, leading to transconformer molecules (see Figure 6.15 in Section 6.4.4) of length 1.6 nm and weight 166 Da (much lower than the molecular weights usually employed in radiotherapeutic experiments ranging from 50 to 200 EG units).

Regarding the grafting moiety, thiol functions -SH are hydrogenated in all our models for the following reasons: (1) gold nanoclusters in the fluxional regime (around 1 nm) may be strongly affected by the surrounding environment in terms of stability and shape (see for instance the influence of water solvation in Chapter 5), thus strongly bound dehydrogenated PEG ligands may induce totally amorphous shapes for which there will be no possibility to establish relationships between morphology and ligand exchange; (2) from recent measurements, the mechanism of endocytosis has been explained by the exchange of physisorbed ligands between GNPs and the cell membrane, 2 thus the interaction between the PEG ligand and the nanoparticle has to be moderate; (3) a recent theoretical study demonstrates that long alkyl chain thiols mainly adsorb molecularly (-SH) on Au adatom deposited on Au(111) (-1.54 eV at the PBE-D3 level with VASP code), at the opposite of short alkyl chain thiols which adsorb dissociatively (-S-). 6 Concerning the second terminal function, -COOH moiety is chosen to correspond to experimental synthesis ligands. 2

Energy Decomposition Analysis Model

In the following section, EDA models are presented for an isolated adsorbed PEG molecule (Eqs. dispersion energies, deformation and various interaction energies are also given.

6.4.1/ Isolated adsorption of a PEG molecule

The adsorption energy Δ E ads for one PEG molecule reported on Table 6.1 of section 6.5 is defined as follows:

Δ E ads =E tot ( AuNP-1 PEG )-E tot ( AuNP)-E tot (PEG ) [Eq. 6.1]
with E tot (AuNP-1 PEG) being the total electronic energy of the adsorption structure of one PEG molecule on AuNPs, E tot (AuNP ) being the total electronic energy of the isolated relaxed AuNP (with a starting guess for the geometry optimization being the deformed AuNP in the presence of the PEG ligand), and E tot (PEG ) being the total electronic energy of the isolated relaxed PEG molecule. where the deformation energies read :

ΔE def (AuNP )=E tot ( AuNP /@)-E tot ( AuNP ) [Eq. 6.4] ΔE def (PEG)=E tot (PEG /@)-E tot (PEG ) [Eq. 6.5]
with E tot (AuNP /@) and E tot (PEG /@) being the total electronic energies of AuNP and PEG molecule calculated in the optimal geometry of the complete relaxed system noted "@", respectively.

The interaction energy between AuNP and the PEG molecule is then:

ΔE int (PEG-Au)=E tot ( AuNP-1 PEG )-( E tot ( AuNP /@
)+ E tot (PEG /@) ) [Eq. 6.6]

6.4.2/ Monoshells of PEGylated AuNPs

The

Δ E coads tot = ΔE def tot (AuNP )+ ΔE int+def tot (xPEG )+ΔE int tot (2 B) (xPEG-Au) [Eq. 6.9]
where the deformation energies read : 6.11] with E tot (AuNP /@) and E tot (xPEG/ @) , being the total electronic energies of AuNP and x PEG molecules calculated in the optimal geometry of the complete relaxed system noted "@", respectively. In the case of x PEG, the deformation energy includes also the interaction energy between the PEG molecules, since the reference is the isolated relaxed gas phase system (one PEG in the supercell).

ΔE def tot (AuNP )=E tot ( AuNP /@)-E tot ( AuNP ) [Eq. 6.10] ΔE int+def tot (xPEG )=E tot (xPEG /@)-xE tot (PEG) [Eq.
The total interaction energy between AuNP and x PEG molecules is :

ΔE int tot (2 B)(xPEG-Au)=E tot (AuNP-xPEG )-(E tot (AuNP /@)+ E tot ( xPEG /@
)) [Eq.

6.12]

By normalizing per chemisorbed PEG ligand, the average interaction energy between one PEG and AuNP as exposed in Table 6.2 can then be derived as follows:

ΔE int (PEG-Au)=(ΔE int tot (2 B) (xPEG-Au))/ N chem [Eq. 6.13]
This interaction energy is also illustrated hereafter in Figure 6.1. Alternatively, the total interaction energy ΔE int tot ( MB) (xPEG-Au) between AuNP and

x PEG molecules considered separately (not in one subsystem) can be expressed also as follows :

ΔE int tot ( MB)(xPEG-Au)=E tot (AuNP-xPEG )-( E tot (AuNP /@)+ ∑ i=1 x ( E tot ( PEG i /@ )) ) [
Eq. 6.14] with E tot ( PEG i / @ ) being the total electronic energy of one PEG molecule belonging to the shell composed of x PEG ligands, calculated in the optimal geometry of the complete relaxed system noted "@".

The total interaction energy between PEG molecules belonging to the family of x PEG ligands is then derived as follows :

ΔE int tot (PEG-PEG )=E tot (xPEG/@)-∑ i =1
x

( E tot ( PEG i /@
)) [Eq. 6.15] By combining Eqs. 6.12 and 6.15, one can write easily:

ΔE int tot (MB)(xPEG-Au )=ΔE int tot (2 B)(xPEG-Au )+ ΔE int tot (PEG-PEG ) [Eq. 6.16]
Furthermore, by combining Eqs. 6.11 and 6.12, one can define the interaction energy between x PEG ligands and AuNP including the deformation energy of x PEG :

ΔE def+int tot (MB )(xPEG-Au)= ΔE int+def tot (PEG-PEG )+ ΔE int tot (2 B )(xPEG-Au)
=E tot (AuNP-xPEG )-( E tot (AuNP /@)+ xE tot (PEG ) ) [Eq. 6.17] Finally, the normalized interaction and deformation energy per PEG molecule (given in Table 6.2 and illustrated in Figure 6.2) is obtained as follows:

ΔE def+int (PEG-PEG)=ΔE def+int tot (PEG-PEG)/ x [Eq. 6.18]

6.4.3/ Monoshells of hydrated PEGylated AuNPs

The normalized coadsorption energy Δ E coads per chemisorbed PEG molecule addressed on Table 6.3 of section 6.7 is defined as follows:

Δ E coads tot =N chem PEG Δ E coads =E tot (AuNP/xPEG/ y H 2 O)-E tot ( AuNP)-x E tot (PEG)-y E tot (H 2 O)
[Eq. 6.19] with E tot ( AuNP / xPEG / y H 2 O ) being the total electronic energy of the complete relaxed system (hydrated PEGylated AuNP), E tot (AuNP ) being the total electronic energy of the isolated relaxed AuNP (with a starting guess for the geometry optimization being the deformed AuNP in the presence of hydrated PEGylated monoshells), x being the total number of PEG molecules, E tot (PEG ) being the total electronic energy of one isolated relaxed PEG molecule, y being the total number of water molecules,

E tot ( H 2 O
) being the total electronic energy of one isolated relaxed water molecule, and N chem PEG being the total number of chemisorbed PEG ligands. [Eq. 6.21] where the deformation energies read :

ΔE def tot (AuNP )=E tot ( AuNP /@)-E tot ( AuNP ) [Eq. 6.22] ΔE int+def tot (xPEG )=E tot (xPEG /@)-xE tot (PEG) [Eq. 6.23] ΔE int+def tot ( y H 2 O)=E tot (y H 2 O /@)-yE tot (H 2 O) [Eq. 6.24]
with E tot (AuNP /@) , E tot (xPEG/ @) and E tot ( y H 2 O/ @ ) , being the total electronic energies of AuNP, x PEG and y H 2 O molecules calculated in the optimal geometry of the complete relaxed system noted "@", respectively. In the case of x PEG (y H 2 O), the deformation energy includes also the interaction energy between the PEG (H 2 O) molecules, since the reference is the isolated relaxed gas phase system (one PEG or one H 2 O in the supercell).

The total interaction energy ΔE int tot (3 B)( AuNP /xPEG / y H 2 O) between the three subsystems AuNP, x PEG and y H 2 O molecules is calculated as follows :

ΔE int tot (3 B) (AuNP /xPEG/ y H 2 O )=E tot (AuNP/ xPEG/ y H 2 O)-( E tot (AuNP /@ )+E tot (xPEG/@)+E tot ( y H 2 O/@ ))
[Eq. 6.25] The total interaction energy between AuNP and x PEG molecules is :

ΔE int tot (2 B)(xPEG-Au)=E tot (AuNP-xPEG /@)-(E tot ( AuNP /@)+ E tot (xPEG /@))
[Eq. 6.26] where E tot (AuNP-xPEG /@) is the total electronic energy of the subsystem AuNP with x PEG ligands in the frozen geometry of the complete relaxed system.

By normalizing per chemisorbed PEG ligand, the average interaction energy between one PEG and AuNP (as exposed in Table 6.3 and depicted in Figure 6.3) can then be derived as follows: This total interaction energy between AuNP and x PEG can also be evaluated in the presence of y H 2 O hydrating the PEG coating:

ΔE int (PEG-Au)=(ΔE int tot (2 B) (xPEG-Au))/ N chem PEG [Eq. 6.27]
ΔE int tot (2 B)(xPEG , y H 2 O-Au)=E tot (AuNP/ xPEG / y H 2 O)-(E tot (AuNP /@)+ E tot (xPEG , y H 2 O/@))
[Eq. 6.28] where E tot (xPEG , y H 2 O/@) is the total electronic energy of the frozen geometry of

x PEG and y H 2 O molecules taken from the complete relaxed system, noted "@".

By normalizing per chemisorbed PEG ligand, the average interaction energy between one hydrated PEG and AuNP (as reported on Table 6.3 and illustrated in Figure 6.4) can also be derived as follows: In the same way of the interaction between AuNP and x PEG, the total interaction energy between AuNP and y H 2 O molecules is expressed easily :

ΔE int ((PEG + H 2 O)-Au)= ( ΔE int tot (2 B) ( xPEG , yH 2 O-Au )) / N chem PEG [Eq. 6.29]
ΔE int tot (2 B)( y H 2 O-Au)=E tot (AuNP-yH 2 O/ @
)-(E tot (AuNP /@)+ E tot ( yH 2 O/@)) [ Eq. 6.30] where E tot ( AuNP-yH 2 O/@ ) is the total electronic energy of the subsystem AuNP with y H 2 O molecules in the frozen geometry of the complete relaxed system.

By normalizing per H 2 O molecule, the average interaction energy between one water molecule and AuNP (as given in Table 6.3 of section 6.7 and depicted in Figure 6.5) is then obtained : By following Eqs. 6.26 and 6.30, the total interaction energy between x PEG and y H 2 O molecules reads:

ΔE int ( H 2 O-Au ) = ( ΔE int tot (2 B) ( y H 2 O-Au )) / y [Eq. 6.31]
ΔE int tot (2 B) ( xPEG-y H 2 O ) =E tot ( xPEG-yH 2 O /@ ) -( E tot (xPEG/@ )+ E tot ( yH 2 O /@
) ) [Eq. 6.32] where E tot ( xPEG-yH 2 O /@ ) is the total electronic energy of the subsystem x PEG with y H 2 O molecules in the frozen geometry of the complete relaxed system. In this latter equation, there is no Au in the energetic balance.

There are two ways of normalization for the latter interaction energy : by either H 2 O or PEG molecule. This leads to two additional respective formulas derived hereafter and presented in Table 6.3 for the values and illustrated in Figure 6.6:

ΔE int ( PEG-H 2 O ) = ( ΔE int tot (2 B) ( xPEG-y H 2 O )) / y [Eq. 6.33] ΔE int ( PEG-H 2 O ) = ( ΔE int tot (2 B) ( xPEG-y H 2 O
)) /x [Eq. 6.34]

Figure 6.6. Definition of the normalized interaction energy (two different normalizations) between x PEG ligands and y H 2 O molecules.

There exists a relationship between the "3B" interaction energy and some of the "2B" terms defined hereabove. By combining Eqs. 6.25 with 6.26 and 6.30, one can derive:

ΔE int tot (3 B) ( AuNP /xPEG / y H 2 O ) -( ΔE int tot (2 B )(xPEG-Au)+ ΔE int tot (2 B) ( y H 2 O-Au )) = ( E tot (AuNP/xPEG/ y H 2 O)+ E tot ( AuNP /@) ) -( E tot ( AuNP-xPEG /@)+ E tot (AuNP-yH 2 O /@) )
[Eq. 6.35] The latter term in Eq. 6.35 is equivalent to interaction energy calculated between x PEG and y H 2 O molecules, but in presence of AuNP, all of them calculated in the frozen geometries extracted from the complete relaxed system. This energy is defined as

∆ E int tot (2 B)( xPEG-y H 2 O
) . This leads to the complete equation linking the "3B" term with "2B" ones:

ΔE int tot (3 B)( AuNP/ xPEG/ y H 2 O )=ΔE int tot (2 B)(xPEG-Au)+ΔE int tot (2 B )( y H 2 O-Au )+ ∆ E int tot (2B)(xPEG-y H 2 O)
[Eq. 6.36] Alternatively, the total interaction energy ΔE int tot

( MB) (xPEG-y H 2 O) between x PEG
and y H 2 O molecules, all considered separately (not in two subsystems), can be expressed also as follows :

ΔE int tot ( MB) ( xPEG-y H 2 O ) =E tot ( xPEG-y H 2 O/@ ) -( ∑ i=1 x ( E tot ( PEG i /@ )) + ∑ j=1 y ( E tot ( H 2 O j /@ )) )
[Eq. 6.37] with E tot ( PEG i / @ ) and E tot ( H 2 O j /@ ) being respectively the total electronic energies of one PEG molecule belonging to the shell composed of x PEG ligands, and of one water molecule belonging to the shell composed of y H 2 O molecules, all calculated in the optimal geometry of the complete relaxed system noted "@".

The total interaction energy between PEG molecules belonging to the family of x PEG ligands is then derived as follows :

ΔE int tot (PEG-PEG )=E tot (xPEG /@)-∑ i=1 x ( E tot ( PEG i /@
)) [Eq. 6.38] And the total interaction energy between H 2 O molecules belonging to the family of y H 2 O is obtained in a similar way:

ΔE int tot ( H 2 O-H 2 O ) =E tot ( y H 2 O/@ ) -∑ j=1 y ( E tot ( H 2 O j /@
)) [Eq. 6.39] By combining Eqs. 6.32 with 6.38 and 6.39, one can then write:

ΔE int tot (MB) ( xPEG-y H 2 O ) =ΔE int tot (2 B) ( xPEG-y H 2 O ) + ΔE int tot (PEG-PEG)+ ΔE int tot ( H 2 O-H 2 O ) [Eq. 6.40]
Moreover, by combining Eqs. 6.23, 6.24 and 6.32, one can define the interaction energy between x PEG and y H 2 O molecules including the deformation energies of x PEG and y

H 2 O: ΔE int+def tot (MB ) ( xPEG-y H 2 O ) =ΔE int+def tot (PEG -PEG )+ΔE int+def tot ( H 2 O-H 2 O ) + ΔE int tot (2 B) ( xPEG-y H 2 O ) [Eq. 6.41]
In addtion, the normalized interaction and deformation energies per PEG and per water molecule (given in Table 6.3 and depicted in Figures 6.7 With these definitions, the interaction energies between x PEG ligands and H 2 O molecules of each family normalized by the corresponding number of water molecules y 1 for (F1), y 2 for (F2) and y 3 for (F3) (y = y 1 + y 2 + y 3 ) can then be easily derived (as given in Table 6.3 and illustrated in Figures 6.9, 6.10 and 6.11):

ΔE int (xPEG-y 1 H 2 O)= ( E tot (xPEG-y 1 H 2 O/@)-(E tot (xPEG /@)+ E tot ( y 1 H 2 O/@)) ) / y 1 [Eq. 6.44]
ΔE int ( xPEG-y 2 H 2 O ) = ( E tot ( xPEG-y 2 H 2 O/@ ) -( E tot (xPEG /@)+E tot ( y 2 H 2 O/@) )) / y 2 [Eq. 6.45]
ΔE int ( y 2 H 2 O-Au ) = ( E tot ( AuNP-y 2 H 2 O/ @ ) -( E tot (AuNP /@)+E tot ( y 2 H 2 O/@) )) / y 2 [Eq.

Due to the terminal -SH and -COOH moieties of PEG and the various adsorption sites on

Au nanoclusters (kink, edge, facet), there exist many adsorption structures. Since S atom is more strongly bound to Au(111) than COOH, 7 the adsorption of PEG on Au nanoclusters has been built mainly through -SH moiety (with a short distance in the range 2.39-2.46 Å, see Figure 6.16 b). However, for isolated chemisorption, an additional stabilizing interaction between -COOH (via -C=O) and Au is obtained in all cases (with a longer distance in the range 2.47-3.16 Å).

According to the best adsorption structures, SH terminal group is always bound on a nanoparticle kink, while COOH moiety can interact with a nanoparticle kink or an edge.

The most stable adsorption form is found on Au 54 (deca) (-1.736 eV, Table 6.1), for which the distortion of the gold nanocluster is significant with an extraction of the interacting Au kink atom from its epitaxial position and a beginning of stellation for the nanoparticle (Figure 6.16 b). The adsorption strength magnitude (1.358-1.736 eV) is compatible with previous theoretical works for alkane-thiols on Au 20 (-1.16 eV) and Au(111) (-1.54 eV). 6,8 The adsorption of PEG on Au 55 (ino) is the second best form (-1.623 eV) which results in a strong deformation of the nanorod shape (ino-decahedron) where the (100) facets transform into (111)-type orientations (icosahedron), see Figure 6.16 b. In this latter case, the extraction of the kink interacting Au atom is as spectacular as the one discussed before for Au 54 (deca). For the three other Au nanoclusters, the adsorption energy is weaker and the gold shape resembles the initial symmetric morphology. Due to the simultaneous bonds between the two terminal functions and gold, the PEG ligand tends to bend over the Au nanocluster, in order to optimize the van der Waals forces. This can be understood by the energy decomposition of the adsorption energy into pure-GGA (covalence) and dispersion energetic terms (Table 6.1 and Eq. 6.2). The dispersion energy is predominant over pure-GGA contribution, except for the most stable PEG-Au nanocluster (Au 54 (deca)). In this latter case, the stabilizing effect of the beginning of nanocluster stellation results in a pure-GGA term almost twice larger (-1.104 eV) than the dispersion energy (-0.63 eV). An alternative way to analyze the trend of adsorption energies is their decomposition into destabilizing (positive) deformation energies (PEG ligand and Au nanocluster) and stabilizing (negative) interaction energies between PEG and Au (chemical bonding). The adsorption energy is essentially due to the chemical bonding between PEG and Au (from -1.874 to -1.526 eV), although its variation does not capture really the one of the adsorption strength. The minority deformation energies are negligible for Au clusters and more significant for PEG, especially on Au 49 (marks) (0.178 eV) and Au 55 (ico) (0.125 eV) where the chain bending is the largest one.

For the deformation of Au, the energetic terms are also weak for Au 54 (deca) and Au 55 (ino), although the geometric distortion is large with respect to the initial symmetric clusters. These deformation energies have been calculated from the optimal deformed Au nanoclusters (those obtained from adsorption forms). Indeed, those distorted particles are more stable than their equivalent symmetric shapes. The deformation of AuNPs structures upon adsorption are presented later in section 6.5.4.

Monoshells of PEGylated AuNPs

Once the most stable chemisorption forms of one PEG molecule are known, the organic coating composed of monoshells of PEG ligands surrounding GNPs can be built more easily. In the next step, the five typical morphologies of Au nanoclusters have been decorated by a surface density of PEG molecules approaching saturation (Figure 6.22).

Due to the difference of surface area and accessible surface Au atoms between all these clusters, the molecule surface (grafting) density varies from one cluster to another one.

The explored range is 2.7-5.1 molec.nm -2 (Table 6.2), in fair agreement with the litterature. 9,10,11 Although the molecule surface density changes significantly, the surface coverage normalized to the number of surface Au atoms, is equivalent for all the GNPs, in the range 0.40-0.45 ML (less than half monolayer).

In order to reach a complete monoshell of ligands on GNPs, the clusters have been decorated by maximizing the best adsorption forms found previously for isolated PEG, and by completing the organic coating with metastable structures. The optimal PEG monoshells on GNPs have been addressed in Figure 6.22 and corresponding energetics in Table 6.2. From a geometrical point of view, the PEGylated GNPs exhibit different ligand organization from one cluster to another one. In the case of the decahedral shapes (Au 49 (marks) and Au 54 (deca)), the ligand arrangements are more symmetric "brushed-type" (Figure 6.22 a,b), whereas the icosahedral and octahedral clusters (Au 55 (ico) and Au 79 (ito)) are decorated by a more disordered "bushy-type" coating (Figure 6.22 c,d,e).

AuNP (non normalized), of PEG summed with the PEG-PEG intermolecular interaction energy, ∆E def+int PEG-PEG (eV per PEG ligand) and into interaction energy between PEG and Au, ∆E int PEG-Au (eV per chemisorbed PEG).

The deformation of the metallic nanoclusters has significantly increased with respect to the isolated adsorption. In the case of Au 55 (ino), the nanorod initial morphology of ino-decahedron is entirely lost in favor of an icosahedron (Figure 6.22 d). In addition, the stellation induced by the PEG coating on Au 54 (deca) is remarkably strong (Figure 6.22 b). The PEG ligands separate during the geometry optimizations in two different adsorption families : majority chemisorbed molecules bound through -SH groups to gold and minority physisorbed ligands inside the organic coating bound with other ligands via hydrogen bonds and van der Waals interactions (Figure 6.22 b). The hydrogen bonds can also stabilize cochemisorbed PEG molecules and help the brushed configuration as depicted in Figure 6.22b for Au 54 (deca).

From an energetic standpoint (Table 6.2), the coadsorption energy per PEG molecule of the PEGylated GNPs is globally similar to the previous adsorption energy values for isolated chemisorption. However, it can be either larger (Au 49 (marks) and Au 55 (ico)) or smaller (Au 54 (deca), Au 55 (ino) and Au 79 (ito)) due to the lateral interactions between ligands (lateral effect) and the competition for interacting with the electronic density of gold nanoclusters (coverage effect). For the case of Au 55 (ino) and (ico), the coadsorption energy per PEG is identical since the ino-decahedron is transformed into icosahedron as explained before. Likewise the isolated system, this energy can be decomposed into pure GGA and dispersion energy terms. Close to ligand saturation, the dispersion energy is slightly more stabilizing than the pure GGA contribution, except, once again, for the systems having the largest coadsorption energy (Au 49 (marks) and Au 54 (deca)).

According to the energy decomposition analysis (EDA) in terms of deformation and interaction energies, the interaction energy between PEG and Au nanoclusters per PEG ligand (Eq. 6.13 and Figure 6.1) is globally weakened in the monoshells by comparison with the isolated adsorption (from -1.053 to -1.269 eV). This is clearly a coverage effect linked to the competition between the molecules (gold atoms sharing their electronic density). Surprisingly, the deformation energy of the Au clusters is very large (from 0.884 to 2.479 eV). In order to maximize the interaction with the PEGylated monoshell, all the gold atoms in the cluster undergo a significant deformation with respect to their initial symmetric positions (Figure 6.22). This means that the distorted geometry of Au in the optimal structures including the PEG ligands is not stable anymore, at the opposite of the isolated chemisorption. The distortion of these clusters is maximal for Au 54 (deca) (2.362 eV) and Au 79 (ito) (2.479 eV). In the case of Au 54 (deca), a stellated cluster is obtained with the five corners of the pentagonal structure extracted from their initial symmetric positions. The global energetic loss coming from the concomitant weakened PEG-Au interaction energy and increased Au deformation energy is balanced by the stabilizing intermolecular interaction energy between the PEG ligands (from-0.382 to -0.506 eV per molecule). This energetic term (Eq. 6.18 and Figure 6.2) is the resulting contribution of weak destabilizing PEG deformation energy and significantly stabilizing dispersion forces and hydrogen bonds between molecules. Hence the apparently unstable stellation (in vacuum) and other deformations of gold structure are promoted by the monoshells of PEG ligands, especially by the lateral molecular interactions.

Hydration of PEGylated AuNPs

In order to further approach realistic conditions for GNPs in the context of radiotherapy, the consideration of the chemical environment of synthesis protecting the metallic nanoparticle (PEGylation) is not enough. The presence of water as a first model of the biological environment is required. Hence in the following, the coadsorption of PEG and water molecules at the surface of gold clusters is described, as well as the solvation of GNPs through the interaction of water molecules with PEG chains.

The corresponding models have been built starting from the optimized monoshells of PEGylated GNPs exposed before, where a large number of water molecules have been positioned around the PEG adsorbates (in average 2 water per PEG chain according to the available free space) through hydrogen bonds and a small number of water molecules have been coadsorbed with PEG (around 10), through oxygen-Au bonds, each time there was enough free space at the surface of the Au nanoclusters. Hence, since PEG adsorption energy is by far larger than water value, the possibility of expelling PEG by water has not been considered. This leads finally to a water/PEG ratio in the range 2.2-2.4

in the hydrated PEGylated GNP structures. In order to keep the analysis as complete as possible, each of the three typical morphologies (decahedral, icosahedral and octahedral) has been retained by solvating the stellated Au 54 (deca) GNP (interesting for experiments)

and the more spherical Au 55 (ico) and Au 79 (ito) stable GNPs. The optimal structures and associated energetic analysis are reported on Figure 6.23 and Table 6.3. Regarding energertics (Table 6.3), the coadsorption energy per chemisorbed PEG for hydrated PEGylated GNPs is globally larger (from -2.88 eV to -3.767 eV) than the values calculated before without water (Table 6.2). This gain is in part due to the significant number of stabilizing additional hydrogen bonds provided by water solvation. This strengthening is also visible on the pure GGA contribution to the coadsorption energy which is now predominant with respect to the dispersion term, as shown in Table 6.3, by comparison with the previous non-hydrated PEGylated GNPs. By decomposing the coadsorption energy in terms of deformation and interaction energies between the three partners (Au, PEG and H 2 O), the first remark is related to the equivalent large distortion energy of the metal in the range 1.357-2.122 eV, and the negligible summed deformation and interaction energy for PEG and water alone. For PEG ligands, this is correlated to the cleavage of the hydrogen bonding between -COOH moieties, while for water, this result means that the majority of the molecules form hydrogen bonds with PEG chains (not with themselves), as demonstrated by the interaction energy between H 2 O and PEG (from -0.581 to 0.668 eV in average per water molecule, corresponding to 1.71-1.97 hydrogen bonds, or from -1.270 to -1.618 eV in average per PEG, corresponding to 4.3-5.6

hydrogen bonds (Eq. 6.50 and Figure 6.15).

Regarding the interaction energy between water and gold, the calculated values are close to zero and negative, thus meaning that water interacting with gold is physisorbed. For the interaction energy between PEG molecule and Au nanocluster, a positive effect of water solvation is found since they are increased (from -0.94 to -1.14 eV) with respect to the non hydrated cases (from -1.09 to -1.20 eV). 5). Same thing for the interaction between H 2 O (F1, F2, F3) and Au.

PEG

Deformation of AuNPs Structures Upon Adsorption & Roundness

Degree Analysis

In the following section, the energetics and geometrical properties of the relaxed uncoated GNPs coming from the adsorbed systems are presented. In Figure 6.24, the structures corresponding to the most stable uncoated GNPs after geometry optimizations have been addressed. In the case of the isolated PEG adsorption, there are many possibilities for considering a starting geometry for each nanoparticle (Au 49 (marks), Au 54 (deca), Au 55 (ico), Au 55 (ino) and Au 79 (ito)). They come from the various possibilities of stable and metastable adsorption forms reported in section 6.5.1. In the analysis presented here, only the most stable clean GNPs are discussed. For the cases corresponding to monoshells of PEG molecules and for the ones associated with hydrated and PEGylated configurations, there is only one possibility (in our study) to optimize the uncoated GNPs after adsorption. where R min (and R max ) are the minimal (maximal) radius (Å) from the nanoparticle center to the nanocluster relaxed outer shell (after geometry optimization with or without chemical environment). This roundness degree is essentially a positive value in the range [0;1] (dimensionless) : the closer to 1 meaning an optimized nanoparticle outershell approaching the geometry of a sphere; the closer to 0 meaning an outershell approaching the geometry of an ellipsoid.

In order to quantify the influence of the adsorption of the PEG molecules and their hydration on the AuNP structures, we have calculated the variation of the roundness degree ΔS on the basis of the optimized nanocluster outershells with and without the presence of PEG adsorbates (with or without water). The corresponding variation is thus defined as follows depending on the chemical environment : The corresponding results are exposed in Figure 6.26 hereafter. Most of the nanoclusters are weakly perturbed by the chemical environment in terms of variation of roundness degree, except for Au 55 (ino) with either isolated PEG adsorption (ΔS << 0), due a significant distortion of the cluster along the adsorption axis (Figure 6.24), or with a monoshell of PEG molecules, due to the transformation of its ino-decahedral shape in favor of a distorted icosahedral form (ΔS >> 0).

ΔS=S AuNP-1 PEG -S AuNP [Eq. 6.52] ΔS=S AuNP-xPEG -S AuNP-1 PEG [Eq. 6.

Discussion

Once the structural and energetic properties of hydrated and PEGylated GNPs have been described, the next steps are the understanding of the role of the PEG ligand on the stability and the morphology of Au nanoclusters and the determination of the relationship between the coated GNP stability and their use in radiotherapy.

According to the energetic analysis of hydrated PEGylated GNPs, PEG ligands promote the stellation of regular decahedral shape (Au 54 (deca)). In order to quantify this result and to compare the overall stability of all the coated GNPs, another energetic descriptor is introduced to evaluate the absolute stability of each system. This corresponds to the formation energy obtained by generating the Au nanocluster from isolated Au atoms and by coadsorbing PEG molecules in an aqueous environment (Figure 6.27). This formation energy normalized by the relaxed surface areas of the Au clusters becomes unitary (formation surface energy Г form ).

In Figure 6.27, the absolute stability of all the coated GNPs is then plotted against the molecule surface density calculated by dividing the number of adsorbed PEG ligands by the nanoparticle area. According to this new analysis, the stellated decahedral-based Au 54 cluster is by far the most stable one in all the considered cases (isolated PEG adsorption, of the molecule surface density. In addition, the number of PEG ligands is constant also due to the defects which do not allow to adsorb more molecules. Hence the stellation process can be linked to a stabilizing structuring ligand effect, since this strongly distorted morphology is unstable in vacuum as explained before. The energy loss related to this metallic deformation is compensated by a small weakening of the interaction energy between PEG and Au and also by a significant stabilizing contribution of the lateral intermolecular interactions (hydrogen bonds). This analysis agrees with experiments showing the high propensity of gold nanoparticles to stabilize in nanostar and nanospike shape. 12,13,14 Regarding Au 55 (ico) and Au 79 (ito) (our models of spherical GNPs), the PEG ligands (hydrated or not) globally keep the shape of the nanoclusters also observed experimentally, 12,13 although they are less stable than the stellated Au 54 (deca) system.

Concerning Au 55 (ino) (our model of nanorod), the PEGylation has a strong destabilizing effect on this metastable morphology since it transforms into icosahedral shape at this size, in agreement with previous results obtained with a water solvation shell ( see Chapter 5). A relationship between the stability of GNPs and their ability to internalize in the cell (endocytosis) for radiotherapeutic applications can be established since the cellular uptake has been recently correlated with the ligand exchange at the nanoparticle/membrane interface. 2 The physisorbed ligands on the nanoparticle surface can be exchanged more easily with lipidic molecules depending on the adsorption affinity and ligand size. According to other measurements, 12 the cellular uptake varies with the nanoparticle morphology and increases in the order of nanospheres > nanospikes > nanorods. By assuming that the ligand exchange is driving the internalization, an explanation of the change of the uptake performance can be proposed on the basis of our theoretical study, at least for spherical and starred GNPs, since our model of nanorod is unstable at the nanometer size. The energy cost to desorb one ligand from the GNPs can be evaluated by the opposite of the coadsorption energy per PEG ligand, in case of a nonactivated process. This energy cost is a good approximation of the ligand exchange with the lipidic membrane since the final state (ligand grafted on the membrane) does not really depend on the nature of the GNP. For non-hydrated GNPs (Table 6.2), the coadsorption energy is the largest one for the stellated Au 54 (deca) system (-1.719 eV), then come the more spherical systems Au 55 (ico) and Au 79 (ito) (-1.565 and -1.471 eV, respectively). Hence the energy cost to desorb one PEG ligand is maximal for the starred Au 54 (deca) GNP, thus meaning that the ligand exchange will be easier for the more spherical Au 55 (ico) and Au 79 (ito) GNPs. As a consequence, according to our analysis at the nanometer scale for gold, the cellular uptake will then be larger for more spherical morphologies such as icosahedral (Au 55 ) and octahedral (Au 79 ) shapes than for the stellated decahedral one (Au 54 ).

Looking at the EDA for non hydrated GNPs (Table 6.2), the reason for the increase of coadsorption energy in the case of Au 54 (deca) (larger energy cost for exchange) is the larger interaction energy between one PEG ligand and Au (-1.20 eV) with respect to the two other nanoclusters Au 55 (ico) and Au 79 (ito) (-1.092 and -1.053 eV, respectively). This theoretical result agrees with measurements 12 and brings a first element of explanation. In the case of hydrated and PEGylated GNPs (Table 6.3), the trend is identical with systematically larger coadsorption energies (-3.767 eV for Au 54 while -2.88 and -3.138 eV for Au 55 and Au 79 , respectively) and interaction energies between PEG and Au (-1.34 eV for Au 54 while -1.11 and -0.95eV for Au 55 and Au 79 , respectively), by comparison with the previous case, due to a stabilizing solvation effect. The corresponding energy costs are large since in our energetic balance for calculating the coadsorption energy does not include the solvation effect for the references (isolated water and isolated PEG molecules which are considered in the gas phase). The interaction energy (around -1 eV) calculated between PEG and Au (effective chemical bonding without the environment) is more realistic for evaluating the ligand exchange cost.

The concept of physisorbed ligand (less bound to the GNPs) evoked experimentally 2 is not straightforward. Inside the organic coating, all the PEG molecules are not equivalent as explained in the previous section. In the case of Au 54 (deca), there is a marked difference between chemisorbed PEG ligands at the spikes of the stellated nanocluster (more outside the ligand monoshell or at its periphery) and the other ones, either physisorbed (lying inside the coating with no direct interaction with Au) or chemisorbed on Au inside the organic coating. A detailed analysis of the ligand extraction (Table 6.4)

indicates that the energy cost to remove one chemisorbed PEG molecule at the spike of the stellated GNP is however smaller than the one related to a physisorbed PEG lying in the organic coating. Due to all the possible stabilizing interactions (Table 6 6.27) and the simultaneous ordering of the ligand monoshell (from "bushy" to "brushed-type"). This stabilizing effect leading to the confinement of a few water molecules at the proximity of the Au nanocluster is quantified by the EDA in terms of interaction energy between adsorbed PEG ligand and H 2 O, bonded mainly through hydrogen bonds (Table 6.3).

By defining three subgroups of water molecules in interaction with PEG ligands in the organic layer, depending on the type of hydrogen bonding and location all along the PEG chains, a remarkable trend results from the analysis of interaction energies between PEG and H 2 O. The first and majority family of water molecules (F1) interact with the -COOH terminal groups of PEG ligands by two asymmetric hydrogen bonds (Figure 6.28). These molecules are located at the periphery of the organic coating, mostly outside the organic coating, thus explaining the zero interaction with Au clusters (Table 6.3). The average interaction energy between H 2 O(F1) and PEG is moderate (-0.735, -0.689 and -0.673eV per water for Au 54 (deca), Au 55 (ico) and Au 79 (ito), respectively) and close to the same energetic term calculated for all the water molecules. However, this interaction energy increases significantly when water diffuses inside the organic layer to interact with the oxygen atoms of the ethylene glycol chains (see the interaction energy between H 2 O(F2)

and PEG, from -0.904 and -1.107 eV per water). This means that the PEGylation can promote also the diffusion of water inside the organic coating progressively. This analysis is also supported by the stability of PEG-H 2 O gas phase dimers through hydrogen bonds (Figure 6.15). When water molecules approach the surface of the nanoparticle, they position in a "H-down"-type configuration because of the stabilizing interaction between water (F2) or (F3) with Au (from -0.096 to -0.235 eV per water of each family). For the stellated Au 54 cluster, the further diffusion closer to the metal (via a hydrogen bonding with the thiol group) is also possible although the interaction energy (between H 2 O(F3)

and PEG, -0.716 eV per water) is slightly weaker than the value at the periphery of the PEG chains (-0.735 eV per water). At the opposite, for the more spherical Au 55 icosahedral GNP, which has a larger propensity to internalize the targeted cell, the interaction energy (between H 2 O(F3) and PEG, -0.817 eV per water) is again larger than the one calculated outside the ligand monoshell (-0.689 eV per water). As a consequence, the PEGylation promotes the confinement of water molecules at the vicinity of gold, especially for the spherical morphologies which exhibit the largest ability to exchange ligands with the membrane and penetrate the cell. This last result opens the discussion of the location of water molecules around the GNPs at the moment of the X-ray irradiation during the radiotherapeutic treatment. Due to their higher stability and vicinity toward the metallic particle, confined water molecules belonging to families (F2) and (F3) can be considered as good candidates for photoexcitation and radiolysis. In

Conclusion

The PEGylation of several sizes and morphologies of gold nanoparticles has been explored on the basis of density functional theory calculations in the range 1.1-1.3 nm.

The role of the PEG chains on the stability and on the shape of the nanoparticle has been discussed in terms of structural and energetic elements.

The stellation of the decahedral nanocluster Au 54 has been demonstrated and explained by the particular stability of the PEG ligands through stabilizing interactions energies between PEG and Au and between PEG chains (hydrogen bonds). These interactions compensate the large deformation energy required to distort the geometry of the nanocluster. The promoter effect of PEGylation on the starred morphology is also preserved when the gold nanoparticles are hydrated. In this case, the multiple stabilizing interactions between water molecules and PEG chains (mainly via hydrogen bonds) explain the stellation.

A relation could have been established between the stability of the coated gold clusters and their uptake inside the cell. Due to the larger stability of the PEG chains in the case of the stellated hydrated and PEGylated Au 54 cluster, the energy cost to exchange a PEG ligand with the membrane is expected to be higher than the one predicted for more spherical icosahedral Au 55 and truncated octahedral Au 79 clusters. In absolute value, these latter spherical nanoparticles are less stable than the starred Au 54 cluster in this mixed chemical and biological environment, in favor of a higher propensity to be internalized in the cell. This counterintuitive result is in fair agreement with measurements provided for much larger gold aggregates.

Finally, the stabilized confinement of a few water molecules close to gold has been shown and explained by a second promoter effect of the PEG chains which tend to form stronger hydrogen bonds with water inside the organic coating than outside. This remarkable property of the hydrated PEGylated layer surrounding gold questions the role

Introduction

In previous Chapters 4-6, a significant advance has been reported on the theoretical modeling of AuNPs in the context of radiotherapy for cancer treatment. On the basis of DFT models of AuNPs in the range 0.9-3.4 nm, several models have been proposed to describe the stability and the morphology of AuNPs decorated by an organic coating composed of a monolayer of hydrated PEG ligands (around 1 nm). The confinement of a few water molecules inside the organic shell has opened an interesting discussion related to water radiolysis promoted by AuNPs. The description of the reaction pathways and associated mechanism of such a photo-excited process exceeds the scope of the present work since other theoretical methodologies (TDDFT for instance) would be required to explore these properties in a relevant and accurate way. Hence the keys explaining the generation of reactive oxygen species at the proximity of AuNPs will not be given in the context of this thesis. However, first theoretical models of formation and repair of DNA lesions occurring also at the atomic scale can be explored once the radical species have been produced and have diffused from the nanoparticle to another part of the targeted cells (nuclei and DNA). This will be the subject of the last and following chapter of results of this PhD manuscript.

In radiotherapy, ionizing radiation (IR) is used to generate reactive oxygen species (ROS) and induce clustered of DNA lesions of the exposed tumor tissues, leading to apoptosis or necrosis. On the other hand, exposure to IR or the radiation coming from sunlight can be harmful to normal tissues since it cause genetic modifications and promotes carcinogenesis if the DNA lesions are not repaired. Recently, DNA-polyamines crosslinks caused by oxidation of hydroxyl radical or singlet oxygen have been characterized in cellular DNA 1 , opening the question of the chemical pathway leading to these deleterious lesions. In a recent work, we have characterized owing to classical all-atom molecular dynamics (MD) the interaction between a 16-bp oligonucleotide and three short, most prevalent natural polyamines (putrescine, spermine and spermidine). In particular, we reported a good correlation of binding free energies between isothermal titration calorimetry (ITC) measurements 2 and our MD simulations. This work has been done in collaboration with Dr. Emmanuelle Bignon and has been published in Chemistry-A European Journal. 10 In this chapter, we extend our simulations to propose representative structures for the association pattern between the tris-lysine peptide KKK and i) the trinucleotide TGT and ii) the 15-bp self-complementary oligonucleotide whose sequence d(GCGCGCTGTCGCGCG). In collaboration with Dr. Antonio Monari from University of Lorraine, we also corroborate a mechanistic pathway involving a fast deprotonation of the guanine radical cation followed by hydrogen transfer from the ammonium leaving as a result a nitrogen reactive species that can subsequently cross-link with guanine.

On the other hand, cyclobutane pyrimidine dimers (CPDs), a typical UVB-induced DNA lesion, can formed in four bipyrimidine sequences: T<>T, T<>C, C<>T, C<>C; indeed, due to the strand orientation, C<>T and T<>C are not equivalent. HPLC-mass spectrometry revealed that the fours CPDs are not repaired at the same rate, T<>T are removed more slowly than those containing cytosine. 3 Together with our collaborators from University of Lorraine, we have investigated the dynamic behavior of an oligonucleotide containing the four different CPDs in order to rationalize the experimental observed repair rate by using MD simulations. Specifically, the interaction between a damaged DNA strand and the nucleotide excision repair enzyme DDB1/DDB2, responsible for photolesions recognition is considered. The flipping of CPD lesions from intra-helical to an extra-helical position with or without the presence of repaired enzyme is examined by using the combined metadynamics and extended adaptive biasing force method (meta-eABF). In this project, I have been implied in a first assessment of the collective variable for the extrusion angle, which turns out to be a delicate one. I spend one-month stay in Nancy in March 2018 to become familiar with NAMD and explicit free energy calculations. The MD simulations and free energy calculations are mainly performed by Cecilia Hognon using the local computing resources of the LPCT Laboratory, I stayed in touch with her when she was re-running the series of MD simulations.

Methodology

Computational ethods for the project related to guanine-lysine cross link

Explicit solvent, full atom molecular dynamics simulations were performed by using Amber12 software package 4 to explore the conformational landscape of KKK interacting with the a) trioligonucleotide TGT and b) the DNA duplex sequence. The system are build using both tleap and Nucleic acid builder (NAB) package available within Ambertools 4 . Standard Amber force field was applied: ff14SB 5 for KKK and parmbsc1 6 for TGT and 15bp oligonucleotide. For a meaningful description of the system, both macromolecules are explicitly solvated using TIP3P water in a truncated octahedron box with 12 Å buffer. 25 K+ ions were added into KKK-15bp systems, while one chorine Cl - ion was added into KKK-TGT system to ensure neutrality of the solvation box and obtain a realistic salt concentration. Minimization is performed on those systems including 5000 steps of steepest decent and 5000 steps of conjugate gradient. Then, the temperature was increase from 0 to 300 K in a 30 ps thermalization run, followed by a 1 ns equilibration performed in NTP conditions. During the rest of the simulation, the temperature was kept constant at 300K using the Langevin thermostat with a collision frequency γln equal to 1ps -1 . Particle Mesh Ewald method was used to treat long range interaction by employing a cut off of 9 Å. For KKK-TGT system, four independent trajectories of 500ns were run (thus 2 μs in total): trajectories 1 and 2 was run using a time step of 2fs, where as trajectories 3 and 4 was run using a time step of 4fs thanks to Hydrogen Mass Repartitioning (HMR) 1 . Whereas for KKK-15bp, four independent trajectories were run for 200 or 500ns (see table 7.2 in section 7.3.2, thus 1.4 μs in total): trajectories 1 and 3 was run using a time step of 2fs, whereas trajectories 2 and 4 was run using a time step of 4fs. Cpptraj module was used to perform cluster analysis. It was also used to calculate the free binding energy based on Molecular Mechanics Generalized Born Surface Area postprocessing (MM-GBSA) 9 (same protocol re-adapt from our previous work 10 ).

Computational methods for the project related to the repair rates of CPDs

To model the interaction with the repair machinery, we considered the complex crystallized by Scrima et al. 11 (PDB code 4a09). The crystal structure consists of the DDB1-DDB2 complex bound to a 15-bp oligonucleotide containing a T<>T lesion (see In what follows, we focused on the interaction between DDB2 and DNA, while the DDB1 moiety was removed. This choice is justified by the low resolution for the DDB1 unit 11 , due do its greater flexibility, and by the fact that it is not directly involved in DNA recognition and binding 12 . In addition to the T<>T CPD, we also Following the same computational protocol described above, the protein/nucleic acid complexes were solvated in a cubic box of water, to which 24 K+ ions were added to ensure electrical neutrality. The protonation states of the DDB2 enzyme were assigned using the Propka program 13 . Standard nucleic acids and amino-acids were modeled using the parm99 force field including the bsc1 correction to the nucleic acids potential 6 , while water molecules were treated with the TIP3P potential energy function 7 . The force-field parameters for each CPD have been optimized following the usual Amber antechamber procedure. The atomic point charges were obtained by fitting the quantum-chemical restricted electrostatic potential (RESP) 14 . To that end, calculations at the HF level, using the 6-31G* basis set, were performed following the RESP protocol. All MD simulations were conducted using the NAMD 2.13 code, 15 using the following protocol: 10,000 steps of energy minimization, including 5,000 steps of steepest descent and 5,000 steps of conjugate-gradient steps were first performed. Next, the temperature was increased from 0 to 300K in a 30 ps thermalization run, using a Langevin thermostat. The computational assays were then equilibrated during 9 ns in the isobaric-isothermal ensemble (300 K, 1 atm), followed by 200 ns of production run. Particle Mesh Ewald (PME) conditions with a cut off of 9.0 Å were used consistently. The Shake-Rattle-Settle algorithms were employed to constrain bonds containing hydrogens to their equilibrium length. A time step of 2 fs was used to integrate the Newton equations of motion. The DNA global deformation and behavior were analyzed using the Curves+ code 16 to post-process the MD trajectories.

The free-energy profiles along the pseudo-dihedral angle (φe) defining the extrusion of the CPD from the DNA helix 17 were obtained using the combination of the extended adaptive biasing force (eABF) and metadynamics algorithms, coined meta-eABF. 18 The potential of mean force (PMF) calculations were performed scanning the region of the pseudo dihedral between 0 to 140 degrees in a single window. The PMF was calculated for the complex between DDB2 and the four CPD, as well as for the isolated oligonucleotides. Convergence of the PMF was achieved after 100 ns.

The Association and Chemical Bond Formation

Mechanisms of Guanine-Lysine Cross-linking

In the following, the structures and interactions of the trilysine peptide KKK with a TGT trinucleotide and with the TGT-embedded 15-bp oligonucleotide will be presented in section 7.3.1 and 7.3.2, respectively, whereas the mechanistic pathway of deprotonation of the guanine radical cation leading to the formation of nitrogen reactive species is presented in section 7.3.3.

Association Modes between KKK and TGT

First, we investigate the supramolecular association between the tris-lysine peptide KKK (charged +3) and the doubly negatively-charged TGT trinucleotide. This KKK:TGT system has been chosen for performing experiments by one of us 19 , with the underlying hypothesis that the structure of this adduct will correspond to the association of the two phosphate groups with the terminal N of lysine K1 and K3 (as schematized in Figure 2.3 in Chapter 2). The central side chain of K2 will then remain free to interact closely with the central guanine of the trinucleotide. This working hypothesis was tested along four independent, unbiased molecular dynamics simulations spanning 500 ns each. Our simulations reveal a much more dynamical and complex behaviour underlying the coexistence of competitive association patterns. Hence, one can surmise a rather complex and rough free energy landscape with the coexistence of a number of local minima separated by easily accessible barriers, and as a consequence an extended sampling reaching the microsecond scale was performed. Four dominant structures can be identified based on cluster analysis of the four independent trajectories and are represented in Figure 7.2, the percentage of prevalence are given in Table 7.1.

Prevalences range between 61% and 69%, denoting a rather complex structural evolution and the co-existence of other structures. To gain insights into the strength of the binding between KKK and TGT, we estimate binding free energies ∆G with the MMGBSA procedure 9 , obtaining the values reported in Table 7.1. They range between -5.5 and -12.2 kcal.mol -1 also suggesting the competitive population of different conformations.

Importantly, all the structures exhibiting a closer distance between the positively-charged amino groups and the phosphates are found to interact more strongly. However, purely electrostatic interactions are not the only factors regulating the KKK-TGT association.

For instance, the ketonic oxygens of thymines T1 or T3 can develop hydrogen bonds with lysines side chain. It is interesting to note that the TGT oligonucleotide can adopt a conformation where T1 lies perpendicularly to T3 (T-shaped orientation shown in Figure 7.2 c) hence a situation in which the stacking of two aromatic nucleobases has been broken, whereas in absence of KKK and in the same conditions of simulations, the isolated TGT system remains in a stacked conformation (see Figure 7.3). The T-shape orientation in Figure 7.1-c is stabilized by a CH ...  interactions and a short electrostatic hydrogen bond between the oxygen atom of the phosphate G2 and the amino hydrogen of 3'-end T3 (2.17 Å). most probably this additional barrier should not exceed very few kcal.mol -1 , as also highlighted by the structurally rich landscape explored by the KKK:TGT complex.

Assembly between KKK and an Oligonucleotide

Molecular dynamics were performed using the same computational protocol as in the former case, to investigate the association of KKK to a guanine-rich 15-bp oligonucleotide, hence considering a case in which the oligonucleotides adopt a B-helix conformation in which some moieties such as the ketonic groups of thymines are less accessible to bind with external agents. This situation was sampled with four independent unbiased trajectories spanning a total time of 1.4 s. The initial configuration is shown in ranging between 200 and 500 ns (see Table 1) for KKK interacting with a 15-bp oligonucleotide.

In agreement with the scenario evidenced for the trinucleotide, KKK presents several stable interaction modes with the double-stranded oligonucleotide, as expected from purely electrostatic considerations. The side chain of lysine is flexible enough to develop interactions with several moieties: first and foremost the phosphate groups, but also the ketonic oxygens of cytosine and guanine. We recently reported the same behaviour and non-covalent interaction patterns for other ubiquitous polyamines 10 , such as putrescine, spermine and spermidine.

Over the 13 guanines, affinity towards KKK differs significantly, as can be seen from the representation given in Figure 7.5. Almost no interaction is found with the central guanines G8 and G11 (in red), even though KKK has been placed nearby the center of the duplex in the beginning of all the simulations (see Figure 7.4). Other guanines G15, G17 and G19 are cold spot for interaction with KKK. On the contrary, the 5'-end block of six guanines from G1 to G29 presents the highest affinity. Indeed we found along our four simulations that the -NH 3 + terminus of lysines K1, K2 and K3 lies in proximity of only three guanines per strand, namely the guanines G25, G3, G5, G25 and G27 by order of affinity, based on the distance criterion defined previously (also see Table 7.2).

Furthermore, the estimated binding free energies, reported in Table 7.2, obtained for the representative structures reported in Figure 7.5 are coherent with the ones of the smaller trinucleotide even if the interaction tends to be more stable. The binding free energy can also be compared with the one estimated for the three biogenic polyamines for a very similar 16-bp DNA sequence with the same computational protocol. 10 Even with a total charge of +2, that happens to be equal to the charge of putrescine but lower than the charges of spermidine and of spermine, KKK develops a stronger interaction with the 15bp sequence.

On the other hand no clear preference for either the major or minor groove can be clearly pointed out, as can be seen from Figure 7.5. Globally, it is apparent that when interacting with double stranded DNA, KKK still span a relative complex conformational space, Furthermore, one should also take into account the different flexibility evidenced by different DNA double-helix sequences that may strongly influence the interaction with KKK and overcome the electrostatic effects evidenced here. We also note that the most stable structure obtained with 500ns of sampling and which is also associated to the highest binding energy (-18.67.3 kcal.mol -1 ) features two ammonium ... phosphate salt bridges (Figure 7.5-c).

Reactive Nitrogen Species Production from Guanine Repair by Primary Amines

As it was shown by the classical MD trajectories, the interaction between the DNA and the positively-charged polyamines leads to stable adducts and appears as preferential, on the other hand the deprotonation of the guanine radical at physiological pH is supposed to be favourable and fast. Hence the question arises on the specific chemical mechanisms leading to the formation of guanine-amine cross-links. Even if a full description of the entire mechanism would be out of the scope of the present contribution we focus here on the possibility of the production of reactive species arising from the protonated primary amine (Scheme 7.1). We considered here the possible repair of the G• moiety by hydrogen transfer from the protonated amine group, that will in turn lead to a RNS that could induce the cross-over. This has been done studying by means of static QM and ab initio molecular dynamics (AIMD) methodologies a minimal systems composed of G• and the smallest primary amine, i.e. CH 3 NH 3 + . The situation is however, completely different when considering the N2 deprotonated G• isomer. In this case the spontaneous hydrogen transfer from the ammonium -NH3+ group leading to the repair of the guanine lesion is observed. This in turns produces a nitrogen centered radical that can be considered as a RNS and hence potentially leading to the attack at the C8 position. Interestingly enough, the hydrogen transfer is extremely fast and happens in the sub-ps scale, this point out to the fact that the former reaction is basically barrierless. This situation can be appreciated from the results presented in

Repair Rates of Different CPD Sequences and Their

Recognition by Repair Enzymes

In the following, I will first present the results of MD simulations and free energy calculations for isolated CPD-containing (T<>T, C<>T, T<>C, or C<>C) oligonucleotides, following by the investigation of the same DNA sequence in the presence of DDB2 repair enzyme.

Isolated CPD-containing Oligonucleotides

In a first step we investigate the structural distortion of damaged oligonucleotides, featuring T<>T, C<>T, T<>C, or C<>C defects. All the simulations show a global common pattern pointing towards a structural stability and a similar behavior of the damaged strands. In particular, no significant difference either in the structure or in the dynamics of the four damaged-DNA, also compared to undamaged B-DNA 20 , was evidenced. In Table 7.3, the DNA bending associated to each CPD lesion is reported, as this descriptor can capture global structural distortion 16 . All the strands experience a relatively moderate average bending, consistent with previous experimental 21 and theoretical works 22,23 and in line with the values measured for undamaged oligonucleotides of the same length. Furthermore, as far as this parameter is concerned the differences between the four lesions do not appear statistically significant and the CPD-containing strands globally behave as the undamaged DNA. The same conclusions can be drawn regarding the analysis of the extrusion angle (φe) of the four CPD lesions (see Figure 7.8 for the definition of reaction coordinate), reported in Table 7.3. Neither significant extrahelical character, nor spontaneous extrusion is observed despite the quite large values of the standard deviations; even though and not surprisingly, in the CPD lesions (φe) spans wider intervals compared to the undamaged oligonucleotide. Free energy profile is also calculated along the flipping reaction coordinate illustated in Figure 7.8 for the damaged-oligonucleotides, the results are presented in Figure 7.9. Indeed, while the minimum energy is previewed for angles centered in between 15 and 20°, the free-energy penalty for spanning the 0-140° region does not exceed 3 kcal/mol. Hence, the analysis of the structure and dynamics of the damaged DNA strands alone does not allow to rationalize the marked differences in the experimental repair rates. In Figure 7.11, the four different CPD give similar free energy profile along the φe coordinate leading to the extrusion of the lesion. Interestingly enough for the four considered cases the free energy profile can be represented by a quasi harmonic function of the pseudo dihedral variation. The free energy spanned during the extrusion process are also quite similar among the different CPDs and are of the order of 10 kcal/mol, which represent a considerable increase compared to the values observed for the isolated nucleic acids. Also a considerable shift of the equilibrium position of φe for the DDB2bound as compared to the solvated DNA structures can be highlighted with the protein definitively stabilizing the extruded position of the lesion. However, subtle but significant, differences can be observed for the strand bearing a thymine or a cytosine in 5' position. Indeed 5'-C oligomers, i.e. C<>T and C<>C, show minimum free energy for larger values of φe at around 90°, while in the case of T<>T and T<>C the minimum in the free energy profile is observed at around 65°-70°. Hence, we shown that the presence of a cytosine at the 5' end of the lesion induces a more extruded configuration, in consistent to the one observed in the crystal structure of the DNA/DDB2 complex.

In order to rationalize the results of the PMF, and in particular the role played by the 5'-C, a analysis of the non-covalent interactions taking place between the protein and the CPD defect in the binding pocket is performed. In Figure 7.12, one can recognize a pattern of favorable interactions that can lock the CPD lesion, and whose strength can vary considerably depending on the 5'-residue. Specifically, the arginine R214 is involved in the stabilization of the DNA/protein interactions. In particular, one can notice that the interaction with the arginine's extremity may be favored by the presence of an exocyclic amino group -NH 2 on the 5'-cytosine that results in a more favorable interaction than the one with the methyl group of Thymine. In Figure 7.12 we report the correlation between the extrusion angle φe and the distance between the NH2 group of R214 and the DNA base counterpart. φe at 20°, i.e. at the free DNA equilibrium R214 is quite distant from the nucleobase and both T<>T and C<>T lesions behave similarly.

222

However, when the CPD is extruded significant differences between the two lesions are evidenced, and in particular C<>T shows the population of shorter distances than T<>T, indicating stronger and more stabilizing interactions. Moreover, the spread of the distances for T<>T is more important than for C<>T with in addition the former also presenting a double branched profile. All those factors once more correlate well with the observed repair rate.

Conclusion

In this chapter, we have examined the formation, damage recognition and/or repair of two types of DNA lesions by mean of theoretical modeling, mostly based on classical molecular dynamics with insights from implicit or explicit free energy calculations. In the first project, the binding of KKK towards a trioligonucleotide TGT and towards a 15-bp double-stranded DNA sequence has been fully investigated owing to molecular dynamics simulations. Our study reveals a more complex interaction pattern than for relative small amines. Indeed, and unlike aromatic drugs and photosensitizers, the conformational landscape of aliphatic or peptidic amines interacting with DNA is more delicate to capture, and leads to the coexistence of different structures and competitive binding modes that could be show significant binding free energies and may be separated by barriers of different magnitudes. In any case, and coherently with the results obtained for natural occurring polyamines, it appears that the binding driving force is mostly due to electrostatic interactions, and hence the positive protonated ammonium form, that is also the most abundant one at physiological pH conditions, is required to induce a strong binding. Furthermore, even if no clear preference is observed for minor or major groove binding, our results indicate that the KKK polypeptide is not exploring the DNA space uniformly. Instead it clearly shows a preference for some hot spots suggesting non trivial sequence effects guiding the association and thus the overall reactivity. Globally our results, while confirming the possible interactions also stress out the structural differences between KKK interacting with TGT or with a B-DNA oligomer. Even though the polyamines tails are flexible enough to induce specific interactions with the selforganized helical DNA including ketonic oxygen of cytosine and guanine.

The results of the classical MD, unequivocally point out that charged primary amine leads to favourable interactions with both model oligonucleotides and B-DNA sequences.

Hence, this consideration raises the question of the reactivity leading to the formation of cross-links upon guanine oxidation. While the fast deprotonation of the guanine radical cation is nowadays unambiguous, the outcome of the deprotonated radical is still a matter of more debate. In this study we clearly show that the guanine radical, especially for the N2 deprotonated isomer, can be readily repaired by hydrogen transfer from a primary ammonium group through a favourable and intrinsically barrierless reaction. This occurrence will however lead to the production of a reactive radical cation centered on the primary amine that will then be able to react to the G8 position of the nucleobase and determine the cross-link.

Our results also allow to clarify the experimental preference for the reaction with nitrogen derivatives, leading to cross-link, compared to the reaction with water, leading to the formation of 8-oxoG. Indeed, and despite the obvious predominance of water compared to amines, not only we have shown that the latter form rather protective arrangements leading to a possible water exclusion, but also that the cross-link reactivity is favoured by the preliminary repair of oxidized guanine that is indeed not possible for water.

In the second project, we have performed MD simulations combined with meta-eABF free energy calculations to rationalize the difference in the repair rates of the four CPDs (T<>T, C<>T, T<>C, or C<>C) evidenced experimentally in different cell types. The impact of the CPD lesions on the intrinsic structural behavior of the isolated DNA strands does not provide any rationale for a differential repair rate. Indeed, all the considered strands containing CPDs exhibit a similar dynamical behavior. On the contrary their interactions with the DDB2 enzyme responsible for triggering the repair processes show marked differences, as evidenced by the different free energy profiles. Indeed, for lesions containing a T in 5' position the extrusion of the CPD is smaller than for the strand presenting 5' C. This behavior, for the 5'-end thymine containing strands can be rationalized in terms of weaker non-covalent interactions with the amino-acids in the recognition pocket due to the lack of amino groups, and the presence of the electron richer methyl groups. As a consequence, the global structure of the DNA strand is less affected, and in particular present a less prominent kink and bulge that are considered as checkpoints for the NER machinery to trigger the subsequent repair.

Note that the difference in the structure observed for the T<>T complex between the crystal structure and the MD may also be due to the close crystal packing that will hamper the CPD from repositioning. This situation is indeed reversed in the case of C<>C and especially C<>T containing strands. In this case the interactions in the pocket become much stronger and the CPD is stabilized in the extruded position, as evidenced by the larger value of φe providing the minimum in the free energy profile.

Our results, thanks to the combination of high-level simulation techniques and enhanced sampling protocols, provide new information on the molecular factors guiding the repair efficiency against DNA photolesions. Indeed, we show that the interaction of C<>T and C<>C strands with the DDB2 enzyme leads to much better recognized clusters, hence correlating with the observation that in skin, as well as in fibroblasts and keratinocytes the fastest removed CPD lesions are the ones presenting a cytosine at the 5'-end.

energetically in the size range of 1-2 nm, above 2 nm, the stability follows the order: to > marks> ico. Apart from these discrepancies, both normalized cohesion energy and excess energy are not observable, therefore their predictive power with respect to the experiments is questionable. In the end of Chapter 4, we have proposed a new descriptor, nanoparticle surface energy, which is observable and has been measured, with a model to determine nanoparticle surface area at DFT level. The corresponding results have shown that the NP surface energy do not vary much when the size increases, in qualitative and quantitative agreement with recent measurements. Our analysis of AuNPs stability has thus reopened the discussion about the relevance of theoretical descriptors and their validation with respect to experiments.

In Chapter 5, in order to provide a first model describing the influence of the natural biological environment, we have explored the adsorption behavior of water on different size and shape of AuNPs with a static approach. The adsorption of isolated water molecule is first investigated, then the AuNPs are saturated on their surface by a complete and explicit water solvation shell. The most stable adsorption of one water molecule on various morphologies of AuNPs (0.9-1.8 nm) indicates that in general, corner is the preferential adsorption site and the strength of water binding is rather moderate and varies with the nanoparticle size and shape. Similar conclusions can be drawn for the adsorption of truncated octahedra AuNPs of larger size (0.9-3.6 nm). Regarding now the effect of the solvation shell surrounding AuNPs in the range 0.9-1.8 nm, the average adsorption energy per water molecule is quite constant regardless of size and shape of AuNPs, and is approximately twice stronger than the isolated adsorption, due to the formation of stabilizing hydrogen bonds (2 in average) between water molecules. Our static approach is also able to capture the transformation of metastable nanoclusters in A more complex model and a more realistic chemical environment surrounding AuNPs have been further considered in Chapter 6, that is to say the simultaneous explicit hydration and PEGylation on AuNPs at the atomic level around 1 nm. At this NP size, in the case of the Au 54 (deca), the PEG coating can deform significantly the NP geometry and extracts the corner atoms from their epitaxial position, leading to the formation of a stellated nanocluster. The stellation is possible due to the intermolecular stabilizing interactions of hydrogen bonds between PEG ligands or between PEG and water. The average interaction energy of PEG ligands with this stellated Au 54 is relatively larger than the one obtained for more spherical shape of AuNPs (Au 55 (ico) and Au 79 (ito)). In agreement with experimental trends of cellular uptake of nanoparticle, a larger energy cost is thus needed in the case of Au 54 (deca) to desorb PEG ligands and exchanging them with cell membrane, which is an important process responsible for the internalization of AuNPs. Finally, the PEGylation promotes the confinement of a few water molecules, at the proximity of the nanocluster, inside the organic layer. Such confinement occurs via stronger hydrogen bonds with thiol or ethylene glycol groups than those occurring outside the coating on the carboxylic moieties. To conclude, for radiotherapy applications, the PEG coating protects the metallic nanoparticles and makes them biocompatible and stable but also promotes the confinement of water molecules near the NP, which is desirable for photoexcitation and radiolysis to generate free radicals.

Finally in the last chapter of results, two projects are performed by using MD simulations in order to gain structural information of DNA lesions and their repair, two properties very difficult to characterize experimentally. In the first project, we have investigated the interaction mode of trilysine peptide with guanine-rich oligonucleotide, in which the binding affinity could provide insight in the initiation of lysine-guanine cross-links, if the guanine of DNA is oxidized into radical cation. Our simulations with a sufficient long sampling have shown that several association modes are possible, with most of the binding driving force being the electrostatic interactions. The presence of neighboring cytosines has been identified as a factor favoring KKK binding with DNA. In the second project, MD simulations and free energy calculations are performed to interpret the experimental repair rate measurements of four CPD photo-lesions: T<>T, T<>C, C<>T, and C<>C. Their interaction with a recognition enzyme is examined at the atomic level.

We have shown that T<>T and T<>C are displaced from the recognition binding pocket, hence hampering optimal repair, in contrast to C<>C and C<>T which experience excellent interaction with the repair protein interface. The free-energy calculations of CPD extrusion also correlate well with the experimental repair rate. Both projects were performed in collaboration with our coworkers from University of Nancy.

On the basis of the theoretical results obtained in this thesis, several perspectives can be considered to further investigate AuNPs models especially for providing a deeper understanding at the atomic level of the contribution of AuNPs to radiosensitizing effects, and of their catalytic role on water radiolysis before the diffusion of ROS into the cell and DNA lesions. The size range of AuNPs accessible by our DFT calculations is limited to 4 nm. The relative stability of AuNPs at larger size could be further evaluated by using Monte Carlo simulations, with a refinement of the parametrization of semi-empirical potentials based on our DFT calculations including dispersion. The interaction of AuNPs with the cell membrane as a function of their size and morphology could also be investigated by using coarse-grained molecular dynamics, not only to better understand the process of ligand exchange and endocytosis, but also to validate our static DFT model. In addition there is a gap between our solvated and PEGylated AuNPs models with the mesoscale Monte Carlo simulations developed by our colleagues at IPNL, in order to provide an accurate description of the photo-excitation of water molecules leading to the production of free-radicals. The use of our DFT based electrostatic potential could improve our understanding at this level. The study of water radiolysis at

Figure 2 .

 2 1 (b).

Figure 2 . 1 .

 21 Figure 2.1. a) Illustration of the DNA double-stranded and the nucleobases of DNA. This schema was adapted from [4]. b) a structure of nucleosome at 1.9 resolution taken from

Figure 2 . 2 .

 22 Figure 2.2. Common DNA damaging agents, type of DNA lesions and the corresponding repair mechanisms. The figure is taken from ref [7].

Figure 2 . 3 .

 23 Figure 2.3. a) Scheme for the postulated KKK-TGT interaction b) scheme of KKK interacting with a guanine-rich 15-bp oligonucleotide (water is omitted) c) Two mechanistic pathways for the formation of a covalently-tethered adduct between guanine at C8 position and a generic amine RNH2 (polyamine or lysine derivative). After oneelectron ionization, the guanine radical cation can direct react with the neutral amine (pathway A), or deprotonates at N1 or N2 positions to generate the guanine radical G•[-H].

Figure 2 . 4 .Figure 2 . 5 .

 2425 Figure 2.4. The two most common UV induced photo-lesions, a) CPD and b) 64-PP.

  Most of the studies focus on the comparison of face-centered-cubic (fcc) gold nanoclusters based on three high point-group symmetry: I h , D 5 h, and O h . For instance, a DFT study (with PBE and TPSS functional) have been performed recently to compare the relative stability of gold nanoclusters with icosahedral, Ino-decahedral and cuboctahedral morphologies in the range of 1.1-3.5nm.106 As shown in Figure2.6, they have plotted the cohesive energy per atom against N -1/3 which exhibits a linear relationship with the size of the particle. In this fluxional regime, the authors have shown that the cohesive energy is very close to each other, with a preference for icosahedral morphology (decahedral and octahedral ones being metastable). However, other morphologies such as truncatedoctahedra and Marks-decahedra, which are competitive energetically are not considered in this study.

Figure 2 . 6 .Figure 2 . 7 .

 2627 Figure 2.6. Structures of (a) icosahedral (I h ), (b) Ino-decahedral (D 5 h), and (c) cuboctahedral (O h ) Au 923 clusters. (d) Cohesive energies of AuNPs versus N -1/3 . This figure was taken from the reference [106]. Another recent study have been proposed to explore more configurations of metallic particles with six distinct morphologies (including octahedron (not truncated), truncated octahedron, cuboctahedron, icosahedron, regular decahedron, and Marks-decahedron) in

Figure 2 . 8 .

 28 Figure 2.8. HAADF STEM images of Au 561 clusters recorded at 20 °C and 500 °C. (a)-(d) HAADF STEM images of Au 561 clusters and (e)-(h) matching multi-slice electron scattering simulations of the cuboctahedron and Ino-decahedron at different orientations.This figure was taken from the reference[115]

Figure 2 . 9 .

 29 Figure 2.9. Schematic of the mechanism of ionising radiation in the presence of AuNPs. Yellow and red stars correspond to the direct and indirect damage, respectively. (a) the incident radiation interact with NPs. b) secondary electrons produced by the radiation or by AuNPs in the water medium to amplify the production of secondary electron. c) the damage of other parts of the cell (like mitochondria). This figure is taken from Reference [118] to simply illustate the damage pathways.

Figure 2 . 10 .

 210 Figure 2.10. Adsorption energies (at PBE and with vdW-DF level) and geometries of one water molecules on Au clusters (N < 20 atoms) for corner adsorption. The upperfigure on the left shows the adsorption energy in eV. The middle figure on the left show the distance between water O atom and the closest Au corner atom in Å. The lower figure on the left shows the adsorption induced change in the average Au-Au nearest-neighbor bond length in Å. This figure was taken from reference [127] .

Figure 2 .

 2 Figure 2.11).

Figure 2 . 11 .

 211 Figure 2.11. Morphologies of water molecules surrounding icosahedra a) Au 13 , b) Au 55 , and c) Au 147 . Dashed line between oxygen and hydrogen indicates the hydrogen bonding. This figure was taken from the reference [129].

Figure 2 . 12 .

 212 Figure 2.12. (left) SEM images of gold spherical nanoparticles GNPs (A), nanospikes GNSs (B) and nanorods GNRs (C) and their size distribution histograms (right). This figure was taken from reference [143].

Figure 2 . 13 .

 213 Figure 2.13. Evolution of the grafting density of SH-PEG ligands on AuNPs against a) diameter of AuNPs and b) ligands molecular weight. This figure was adapted from the reference [149].

  , a metaphor proposed to classify different levels of approximation, as illustrated in Figure 3.1. Climbing the ladder means that the sophistication of the exchange-correlation functional and kinetic energy operator increases and more accurate predictions are expected.

Figure 3 . 1 .

 31 Figure 3.1. Schematic representation of Jacob's ladder of the exchange-correlation approximation. The five generation of functionals are sorted by accuracy and calculation time. Examples of functionals are given in italic.

  functionals, we have compared optB86b-vdW, dDsC and DFT-D3 functionals with zero damping or Becke-Johnson damping on their ability to reproduce bulk property. The cohesion energy of gold bulk calculated with different functionals against the NKPTS (number of K-points) is evaluated in Figure 3.2. The value of ∆E coh for all the functionals becomes constant starting from NKPTS=50. ∆E coh of gold bulk calculated with DFT-D3 (zero damping) functional (-3.695 eV/atom) is the closest one to the experimental value, follow by DFT-D3 (Becke-Johnson damping) (-3.657 eV/atom) and opt-B86b (-3.605 eV/atom). ∆E coh calculated with dDsC functional (-3.424 eV/atom) is very far from experimental value. Based on this analysis, we have thus chosen DFT-D3 functional with zero damping for all the DFT calculations of gold nanoparticles.

Figure 3 . 2 .

 32 Figure 3.2. Cohesion energy of gold bulk ∆E coh in eV/atom against the number of Kpoints. The reference (no dispersion) and the experimental bulk value (-3.81 eV/atom) is also given.

Figure 4 . 1 .

 41 Figure 4.1. Definition of the considered Au NP morphologies in the range of 0.9-3.4 nm (44 NPs): Truncated octahedra (to), cuboctahedra (cubo), ino-decahedra (ino), and Marks decahedra (marks) are composed of mixed facets [hexagonal (HF), triangular (TF), pentagonal (PF) with square (SF) or rectangular (RF) facets], whereas decahedra (deca) and icosahedra (ico) present only triangular facets (TF).

Figure 4 . 2 .

 42 Figure 4.2. Optimized structures of regular (rto) and irregular (ito) truncated octahedral Au NPs in the range 0.9-3.4 nm.

Figure 4 . 3 .

 43 Figure 4.3. Optimized structures of icosahedral Au NPs in the range 0.9-3.4 nm.

Figure 4 . 4 .

 44 Figure 4.4. Optimized structures of ino-decahedral Au NPs in the range 0.9-3.4 nm.

Figure 4 . 5 .

 45 Figure 4.5. Optimized structures of cuboctahedral Au NPs in the range 0.9-3.4 nm.

Figure 4 . 6 .

 46 Figure 4.6. Optimized structures of regular decahedral Au NPs in the range 0.9-3.4 nm.

Figure 4 . 7 .

 47 Figure 4.7. Optimized structures of Marks-decahedral Au NPs in the range 0.9-3.4 nm.

Figure 4 .

 4 8 plots the cohesion energy of the NP in vacuum against N -1/3 . For each polyhedral family among the six key shapes exposed in Figure 4.1, we have quantified the slopes and the offsets of the linear laws obtained in the range 0.9-3.4 nm (38-976 atoms).

Figure 4 . 8 .

 48 Figure 4.8. Normalized cohesion energy per atom ∆E coh (NP) (eV) diagram against N -1/3 , where N is the number of Au atoms in the NP. The parameters (slope, offset and R 2 ) of the linear regressions are defined in the equation 4.4. The six different families of the NPs are reported with different colors defined in the inset where the parameters of the linear regression for each shape family are exposed (the stability for each family being captured in average by the values of the offsets).

Figure 4 . 9 .

 49 Figure 4.9. Excess energy ∆E exc (NP) (eV) diagram against the number N of Au atoms in the NP according to the Equation 4.5 .The six different families of the NPs are reported with different colors , with the same definition shown in Figure 4.8.

  8 nm (38 to 201 atoms): truncated octahedral and decahedral (regular and Marks); the Au 55 icosahedron is also competitive. Above 1.8 nm (201 atoms), the variation is more monotonous and the truncated octahedra become really more stable than the other polyhedra. At 3.4 nm (about 1000 atoms), they predominate while the Marks-decahedra and icosahedra are minority. Cuboctahedron is always metastable according to this descriptor. Our picture differs from previous systematic studies based on global optimization methods, effective semiempirical potentials, and Monte Carlo simulations

Figure 4 . 10 .

 410 Figure 4.10. Evolution of the average surface Au-Au distance ( dsurf (Au -Au) ) in Å against the number of Au atoms N. The six different families of the NPs are reported with different colors , with the same definition shown in Figure 4.8.

Figure 4 . 11 .

 411 Figure 4.11. Surface energy Г (J/m 2 ) diagram against the number N of Au atoms. The six different families of the NPs are reported with different colors, with the same definition as Figure 4.8. The experimental surface energy from ref[20] is given for comparison.

  exchange-correlation functional and dispersion forces), and the need of accurate parametrization for mesoscale Monte-Carlo simulations aiming to evaluate precisely the relative stability of AuNPs. On the one hand, cohesion energy and excess energy which are the two mostly used theoretical descriptors to explore the NP stability, provide different stability trends at the same level of comparison or calculation, thus opening the question about their predictive ability. On the other hand, these two descriptors are not observable, in contrast to calculated nanoparticle surface energy which can be compared straightforwardly with experiments. In this context, we proposed to extend the discussion related to the relative stabilities of Au NPs by introducing nanoparticle surface energy at DFT with D3 dispersion correction level. This functional reproduces quite accurately the measurements, so the nanoparticle surface energy descriptor is relevant to predict precisely energetics and geometrical properties (areas) of AuNPs. The general asymptotic convergence of the properties (average Au-Au length and energies) of the AuNPs demonstrated in this chapter is an indication of our ability to extrapolate easily the chemical and physical properties of these NPs at larger size (above 3.4 nm), and open exciting perspectives for developing in the future much faster ab initio-based global optimization methods aiming to probe the absolute stability of AuNPs with an improved accuracy.In the context of AuNP-enchanced radiotherapy, water which is considered as a model of the biological natural environment, plays undoubtedly a key role. Indeed, the interaction of water with ionizing radiation in the presence of AuNPs generates a huge amount of free radicals through the reaction of water radiolysis. Those radicals interact aggressively with DNA (indirect damage) and produce more DNA lesions, and concomitantly they induce cell death and lead to a better performance of radiotherapy. The generation of free radicals and the initial physico-chemical process upon irradiation of AuNPs can be investigated theoretically by using nanodosimetric Monte-Carlo simulations. However, the interaction of water with AuNPs before irradiation as a function of size and morphology is still poorly understood at the atomic level with first-principle methods. In the literature a few theoretical studies have been devoted to the adsorption properties of water on gold nanoclusters, but for clusters of very small size (less than 20 atoms). Above 1 nm, the available theoretical data is scarce, and even rare for the adsorption of a complete shell of water molecules interacting with AuNPs.In this chapter, we use DFT-D3 calculations to model the water/AuNP interface with an explicit atomistic model. We aim to rationalize the interaction between water molecules and AuNP as a function of the nanoparticle morphology and size. Calculations have been performed to explore the adsorption structures and energetics of water molecules on AuNPs, from single adsorption to a shell of water molecules. Then once the optimized geometries and adsorption energetics of AuNPs in contact with water have been understood, the electrostatic potential of the solvated gold nanoparticles are calculated, aiming to improve the parametrization of the Monte-Carlo simulations in collaboration with Michael Beuve and Floriane Poignant (IPNL).

Figure 5 . 1 .

 51 Figure 5.1. Definition of all the possible adsorption sites for Au 38 .

Figure 5 . 2 .

 52 Figure 5.2. Optimized adsorption structures of a water monomer on nine different truncated octahedra AuNPs, in the range of 0.9-3.4 nm. HF and SF correspond to hexagonal and square facet, respectively. The definitions of the H 2 O adsorption site are given inside parenthesis. The Au-O bond distances are reported in Å (blue characters), whereas the adsorption energies in eV (red characters).

Figure 5 . 3 .

 53 Figure 5.3. Energy decomposition analysis of adsorption energy ∆E ads for water monomer on truncated octahedron, from Au 38 to Au 976 . The equations of EDA are given and the definition of the different contributions is given in different colors.

Figure 5 . 4 ,

 54 for each of the 9 nanocluster, the most stable adsorption structures have been reported (including adsorption energetics, Au-O distance and site), while all the metastable adsorption forms are presented in Appendix A (Figure A.8-A.13).

Figure 5 . 4 .

 54 Figure 5.4. Optimized adsorption structures of a water monomer on nine different Au NPs in the range of 0.9-1.8 nm, including four competitive morphologies : regular and irregular truncated octahedron (rto and ito, respectively), icosahedron (ico), ino-decahedron (ino) and decahedron (deca). The definitions of colors for atoms are given, as well as the location of the surface Au adsorption site with the following possibilities: corner, edge, facet center. The Au-O bond distances are reported in Å (blue characters), whereas the adsorption energies in eV (red characters).

  5 and Figure 5.6.

Figure 5 . 5 :

 55 Figure 5.5: Energy diagram against the number of Au atoms in the NPs, showing the energy decomposition analysis (EDA) of the adsorption energy (E ads , eV) of water monomer on nine different Au clusters with four different shapes (defined by specific colors) in the range of 0.9-1.8 nm (see Figure 2 for the optimal adsorption structures).E ads is expressed in the equation as the sum of the pure binding energy between Au NP and water (E int , energy gain), the deformation energy of water between optimal isolated situation and the geometry in the adsorption form (E def,H2O , energy cost), and the equivalent deformation energy of Au NP (E def,NP , energy cost).

Figure 5 . 6 .

 56 Figure 5.6. Energy decomposition analysis (EDA) of adsorption energy ∆E ads for water monomers on Au NPs. ∆E ads (points in circle) is defined as the sum of pure GGA PBE ("covalence") energy ∆E cov (points in square) and dispersion energy ∆E disp (points in triangle). These energies for truncated octahedral, icosahedra, ino-decahedra and decahedra are differentiated by blue, green, cyan, and brown color, respectively.

Figure 5 . 7 ,

 57 with the ratio of chemisorbed and physisorbed molecules. When the size of the NP increases, this coverage decreases in average progressively from 0.44 to 0.23 ML with two exceptions at sizes 55 and 147 for icosahedral (0.40 ML) and ino-decahedral (0.31 ML) shapes. In a concomitant way, the number of chemisorbed molecules decreases in favor of physisorbed water (the ratio decreasing in average from 0.27 to 0.15), again with two exceptions for Au 55 (0.28) and Au 147 (0.22). At the largest size (Au 201 ), the calculated coverage of 0.23 ML is smaller than the one proposed previously (0.29 ML) for an explicit liquid water/Pt 201 interface investigated by ab initio molecular dynamics at 350 K.8 Our result for Au with a static approach is thus reasonable because the chemical bonding on Au 201 (-0.35 eV) is almost twice weaker than the one found on Pt 201 (-0.54 eV). For the two exceptions of larger coverage of chemisorbed water on Au 55 and Au 147 (icosahedra and inodecahedra), this is only a direct consequence of the stronger interaction energy or chemical bonding discussed before, not the fact that these clusters would present more stable adsorption sites in number.

Figure 5 . 7 .

 57 Figure 5.7. Optimized adsorption structures of a shell of water molecules on nine differentAu NPs in the range 0.9-1.8 nm, including four competitive morphologies: regular and irregular truncated octahedron (rto and ito, respectively), icosahedron (ico), ino-decahedron (ino) and decahedron (deca). The definitions of colors for atoms are given. The adsorption energies in eV per water molecule in total are reported (red), as well as the surface coverage of chemisorbed water molecules in ML (monolayer) and the ratio Nc/Np between chemisorbed water (Nc) and physisorbed water (Np). The complex network of hydrogen bonds is also marked by light gray dotted lines. The strongly distorted facets of icosahedral (and transformed ino-decahedral) shapes are drawn with full gray areas for Au 55 and Au 147 .

Figure 5 . 8 .

 58 Figure 5.8. Evolution of the variation of the roundness degree ΔS (dimensionless) upon water adsorption (monoshells) as a function of the number of Au atoms (N Au )

Figure 5

 5 Figure 5.22:

Figure

  Figure 5.9. Hydrogen bonding model for the water monoshells decorating the various Au

Figure 5 . 10 .

 510 Figure 5.10. Average electrostatic potential [V(Z)] in eV along the direction of Z axis is plotted for the naked AuNP (in black), AuNP with isolated water adsorption (in blue) andAuNPs with adsorption of one shell of water molecules (in green).

Figure 5 . 11 .

 511 Figure 5.11. Average electrostatic potential [V(Z)] in eV along the direction of Z axis and its corresponding with the atomic plane of for the case of Au38 (rto) is plotted for the a) naked NP , b) NP with isolated water adsorption and c) NP with adsorption of one shell of water molecules.

Figure 5 .

 5 Figure 5.10 showed that the curve of the is complexe and different depending on the atomic plane of AuNP. The evolution of for the naked AuNP and with the isolated water adsorption are almost identical for all cases, showing that the perturbation upon the adsorption of one water molecule on the potential energy of AuNPs is negligible. On the other hand, when the AuNPs are saturated coated by with monoshells of water molecules, the extent along Z of the average electrostatic potential increases and the osscilation of potential become wider in dimension along axis Z, due to the expansion and the deformation of the nanocluster in response to the adsorption of these water monoshells.

Figure 6 . 1 .

 61 Figure 6.1. Definition of the normalized interaction energy between AuNP and PEG ligands.

Figure 6 . 2 .

 62 Figure 6.2. Definition of the normalized interaction energy (including deformation energy) between PEG ligands.

Figure 6 . 3 .

 63 Figure 6.3. Definition of the normalized interaction energy between AuNP and PEG ligands.

Figure 6 . 4 .

 64 Figure 6.4. Definition of the normalized interaction energy between AuNP and PEG ligands, in the presence of the hydrated shell.

Figure 6 . 5 .

 65 Figure 6.5. Definition of the normalized interaction energy between AuNP and water molecules.

Figure 6 . 7 .

 67 Figure 6.7. Definition of the normalized interaction energy (including deformation energy) between PEG ligands. ΔE def+int (H 2 O-H 2 O)= ΔE def+int tot

Figure 6 . 8 .

 68 Figure 6.8. Definition of the normalized interaction energy (including deformation energy) between H 2 O molecules.

Figure 6 . 9 .

 69 Figure 6.9. Definition of the normalized interaction energy between x PEG ligands and y 1 H 2 O molecules belonging to family (F1).

Figure 6 . 10 .

 610 Figure 6.10. Definition of the normalized interaction energy between x PEG ligands and y 2 H 2 O molecules belonging to family (F2).

Figure 6 . 12 .

 612 Figure 6.12. Definition of the normalized interaction energy between AuNP and y 1 H 2 O molecules belonging to family (F1).

6. 48 ]Figure 6 . 13 .Figure 6 . 14 .

 48613614 Figure 6.13. Definition of the normalized interaction energy between AuNP and y 2 H 2 O molecules belonging to family (F2).

Figure 6 . 16 .

 616 Figure 6.16. (a) Top and laterals views of optimized clean Au nanoclusters in the range 1.1-1.3 nm with five different morphologies : defective (concave) Marks decahedral (marks) Au 49 , regular decahedral (deca) Au 54 , icosahedral (ico) Au 55 , ino-decahedral (ino) Au 55 and irregular truncated octahedral (ito) Au 79 . The facet types are marked with colored areas: green for (111)-type (triangle, pentagon or hexagon), red for (100)-type (square) and blue for (110)-type (concavity). (b) Best and optimized adsorption structures of one PEG molecule (composed of two ethylene glycol units, thiol and carboxy terminal groups) on the five Au nanoclusters. The adsorption occurs mainly through simultaneous chemical bonds between -SH or -COOH moieties and Au kink and edge atoms, following an  2  2 form. -SH group binds via the S atom, while -COOH through the -C=O carbonyl bond. The colors of atom types are defined and will be kept in all the figures.

Figure 6 . 17 .

 617 Figure 6.17. Optimized adsorption structures of one PEG molecule on different top adsorption sites of Au 49 (marks) (PF meaning pentagonal facet). The Au-S bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure 6 . 18 .

 618 Figure 6.18. Optimized adsorption structures of one PEG molecule on different top adsorption sites of Au54 (deca) (TF meaning triangular facet). The Au-S bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure 6 . 19 .

 619 Figure 6.19. Optimized adsorption structures of one PEG molecule on different top adsorption sites of Au55 (ico) (TF meaning triangular facet). The Au-S bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters(eV) (the most stable structure with bold characters).

Figure 6 . 20 .

 620 Figure 6.20. Optimized adsorption structures of one PEG molecule on different top adsorption sites of Au55 (ino) (SF and TF meaning square and triangular facet, respectively). The Au-S bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure 6 . 21 .

 621 Figure 6.21. Optimized adsorption structures of one PEG molecule on different top adsorption sites of Au79 (ito) (SF and HF meaning square and hexagonal facet, respectively). The Au-S bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure 6 . 22 .

 622 Figure 6.22. Optimized PEGylated Au nanoclusters with monoshells of adsorbed molecules close to saturation : (a) Marks-decahedral Au 49 , (b) stellated decahedral Au 54 , (c) icosahedral Au 55 , (d) initially ino-decahedral Au 55 (transformed into icosahedral Au 55 ) and (e) irregular truncated octahedral Au 79 . Distorted geometries of Au clusters (without PEG) are also presented. For each system the numbers of PEG ligands in the organic coating, of chemisorbed (N c ) and physisorbed (N p ) molecules, the surface coverage  chem

Figure 6 . 23 .

 623 Figure 6.23. Optimized hydrated and PEGylated Au nanoclusters with monoshells of coadsorbed molecules close to saturation : (a) stellated decahedral Au 54 , (b) icosahedral Au 55 and (c) irregular truncated octahedral Au 79 . Distorted geometries of Au clusters (without the hydrated coating) are also presented. For each system the numbers of PEG ligands and H 2 O molecules in the organic coating are mentioned, as well as the number of chemisorbed (N c ) and physisorbed (N p ) PEG and the surface coverage  chem related to chemisorbed PEG (ML). The hydration of the PEGylated monoshell tends to increase the disordering in the coating of the stellated Au 54 cluster.

Figure 6 . 24 .

 624 Figure 6.24. Optimized structures of uncoated GNPs for Au49 (marks), Au54 (deca), Au55 (ico), Au55 (ino) and Au79 (ito) related to (a) isolated PEG adsorption, (b) monoshells of adsorbed PEG molecules and (c) hydrated and PEGylated coatings. The initial geometries for the optimizations are those coming from the relaxed adsorption structures.

Figure 6 . 25 .

 625 Figure 6.25. Stability diagram of optimal GNPs against the chemical environment for the initial starting structures. The cohesion energy ∆E coh per atom (eV/at.) has been plotted

53 ]

 53 ΔS=S AuNP-xPEG -yH 2O -S AuNP-xPEG [Eq.6.54] where S AuNP-xPEG-yH 2 O , S AuNP-xPEG , S AuNP-1 PEG , and S AuNP are the roundness degrees for the complete hydrated PEGylated systems, the saturated PEGylated structures, the isolated PEG adsorption case and the clean GNP, respectively. When ΔS is positive, the variation of the chemical environment (PEG and/or H 2 O) has induced a significant geometric deformation of the nanocluster outershell from its symmetric structure toward a globally rounder shape. At the opposite, when ΔS is negative, the resulting geometric deformation of the nanocluster outershell upon PEGylation and/or hydration is a stretching of the initial symmetric structure along a specific direction (adsorption axis). When ΔS is close to zero, the nanocluster may have been slightly distorted upon PEG and/or H 2 O adsorption, however, in average, the deformation is negligible.

Figure 6 . 26 .

 626 Figure 6.26. Analysis of roundness degree variation (∆S) of AuNPs. squares mean ∆S upon isolated PEG adsorption; circles ∆S upon adsorption of PEG monolayer; triangles ∆S upon coadsorption of PEG-H 2 O monolayer. The colors in purple, marron, green, cyan and blue correspond to Au 49 (marks), Au 54 (deca), Au 55 (ico), Au 55 (ino), and Au 79 (ito), respectively.

Figure 6 .

 6 Figure 6.27 a, non hydrated and hydrated PEG coadsorption, Figure 6.27 b). From a more general standpoint, the intrinsic stability of the cluster increases almost linearly with the molecule surface density, and inversely with respect to the nanoparticle size. The

Figure 6 . 27 .

 627 Figure 6.27. Formation energy Γ form expressed in surface energy per particle unit area (meV.Å -2 ) of GNPs plotted against the PEG molecule surface density (MSD) (molec.nm -2 ). (a) Isolated adsorption of a PEG on five typical Au nanoclusters. (b) (top) PEGylated GNPs (SAM) for the five Au clusters and (bottom) hydrated PEGylated GNPs for the three competitive shapes. The chemical equations are indicated for the corresponding definitions of Γ form .

Figure 6 . 28 .

 628 Figure 6.28. Three families (F1, F2, F3) of water molecules (63 in total) hydrating the optimized PEGylated coating (26 PEG molecules) of the stellated Au 54 decahedral cluster. F1 family (52 molecules) corresponds to water interacting with the carboxylic ending group of PEG ligands at the periphery of the GNP; F2 family (6 molecules) is related to water interacting with the oxygen atoms of ethylene glycol in the PEG; F3 family (5 molecules) gathers water interacting with thiol moiety in the ligands.

  fact, the proximity to Au should enhance the photocatalytic activity and the homolytic dissociation of water leading to •OH and •H radical species. Moreover, these species confined inside the PEG chains could also be stabilized by interacting with either dehydrogenated thiol group or the oxygen atoms of the EG moiety. In this perspective, the PEG chains would ensure a dual role by promoting the confinement of water close to gold, and stabilizing concomitantly H• and OH• reactive oxygen species inside the coating, far enough from the biological environment and liquid water, thus avoiding an immediate reverse recombination.

Figure 7 .

 7 Figure 7.1-a). In what follows, we focused on the interaction between DDB2 and DNA,

  mutated the DNA lesion to include C<>T, T<>C, and C<>C. In the case of isolated DNA and for the sake of simplicity and uniformity, we chose to use the same DNA sequence of the crystal structure, inserting the different CPD lesions (T<>T, C<>T, T<>C, and C<>C ) at the central position (see Figure7.1-b). The sequences were solvated in a TIP3P7 water box. Potassium (K+) cations were then added to ensure electroneutrality of the simulation box.

Figure 7 . 1 .

 71 Figure 7.1. a) Crystal structure of DDB1-DDB2 protein bound to a CPD (T<>T) containing duplex, PDB: 4A09 11 . We only simulated the DNA recognition subunits (DDB2) evidenced with red dashed lines b) DNA sequence containing the CPD lesion (marked as XX).

Figure 7 . 2 .

 72 Figure 7.2. Representative structures for the {KKK:TGT} complex of the four trajectories, obtained as the most prevalent along four 500ns molecular dynamics trajectory after cluster analysis.

Figure 7 . 3 .

 73 Figure 7.3. Representative structure of isolated TGT trinucleotide after 200ns of simulation.

Figure 7 .

 7 Figure 7.4 where KKK was place near the center of the 15-bp oligonucleotide. After simulations, the four representative structures extracted after cluster analysis one per trajectory, are shown in Figure 7.5.

Figure 7 . 4 .

 74 Figure 7.4. Initial configuration of the 15bp oligonucleotide with the KKK peptide placed near the center of the duplex.

Figure 7 . 5 .

 75 Figure 7.5. a) Superimposed representation of KKK interacting with the 15-bp oligonucleotide for the four trajectories (color code below). The guanines in red display a low presence of lysines at 6 Å (<2%), whereas guanines in green present a proximity higher than 5% (higher than 10% for boldfaced guanines) b-e) (Zoom) Cartoon representations of four representative structures obtained upon molecular dynamics

Figure 7 . 6 .

 76 Figure 7.6. A) Time evolution of the distance between the guanine N2 position and the transferable H during the AIMD trajectory. B) Representative snapshots extracted at the reactants (0 fs), transition state (180 fs) and products (700 fs) region.

Figure 7 .

 7 Figure 7.6 where we report the time-evolution of the distance between the G• N2 position

Figure 7 . 7 .

 77 Figure 7.7. Evolution of the spin density during the AIMD showing the transfer to the unpaired electron from the guanine to the primary amine molecules upon the hydrogen transfer.

Figure 7 . 8

 78 Figure 7.8 Definition of dihedral angle taken from Zacharias et al. 17 in order to describe extrusion of CPD. The dihedral angle is formed by center of mass of four group of atoms: four residues situated opposite of CPD dimers (group 1 in cyan), four nucleotide situated at the end-of oligonucleotide (group 2 in red), backbone heavy atoms of CPD (group 3 in green), and heavy atoms of thymine base of CPD (group 4 in yellow).

Figure 7 . 9 . 7 . 4 . 2 Figure 7 . 10 .igure 7 . 11 .

 79742710711 Figure 7.9. PMF giving the free energy profiles along the pseudo dihedral describing the extrusion of the CPD lesion in the case of T<>T, T<>C, C<>T, and C<>C, respectively in free DNA. Representative snapshots at significant value of pseudo dihedral are shown for each with the value of the dihedral yielding the minimum value of the free energy.

Figure 7 . 12 .

 712 Figure 7.12. Correlation between the dihedral angle defining the CPD extrusion and the distance between the guanidium group of the R214 residue and the 5' CPD nucleobase for T<>T (A) and C<>T (B). The specific atoms between which the distance has been calculated are specified in the C and D panel for T<>T and C<>T, respectively.

  vacuum: ino-decahedral NP (Au 55 and Au 147 ) into corresponding icosahedra which are more stable through the interaction with water shells. At the end of this chapter, we have proposed electrostatic potential calculated at the DFT level for these solvated AuNPs model, in order to improve future parametrization of Monte Carlo Simulations developed by our colleagues IPNL (Pr Michël Beuve and Floriane Poignant). The main results of Chapter 4 and 5 were published in the Journal of Physical Chemisty Letters (DOI: 10.1021/acs.jpclett.8b03822).

Figure A. 4 .Figure A. 5 .

 45 Figure A.4. Optimized adsorption structures of water monomers on different top adsorption sites for Au 201 (rto). The Au-O bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure A. 6 .Figure A. 7 .

 67 Figure A.6. Optimized adsorption structures of water monomers on different top adsorption sites for Au 405 (ito). HF and SF correspond to hexagonal and square facet, respectively. The Au-O bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure A. 8 .Figure A. 9 .

 89 Figure A.8. Optimized adsorption structures of water monomers on different top adsorption sites for Au 54 (deca). The Au-O bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure A. 10 .Figure A. 11 .Figure A. 12 .

 101112 Figure A.10. Optimized adsorption structures of water monomers on different top adsorption sites for Au 55 (ino). The Au-O bond distances are reported in blue characters (Å), whereas the adsorption energies in red characters (eV) (the most stable structure with bold characters).

Figure B. 2 .Figure B. 3 .Figure B. 4 .

 234 Figure B.2. Average electrostatic potential [V(Z)] in eV along the direction of Z axis and its corresponding with the atomic plane of for the case of Au55 (ico) is plotted for the a) naked NP , b) NP with isolated water adsorption and c) NP with adsorption of one shell of water molecules.

Table 4 .

 4 -packed isomers composed of the same magic number (Au 55 , Au 147 , Au 309 , Au 561 , and Au 923 ) and form complete symmetrical structures. Truncated octahedra can be regular (rto) (Au 38 , Au 201, Au 586 ) or irregular (ito) (Au 79 , Au 116 , Au 314, Au 405, Au 807 and Au 976 )depending on the hexagonal facets as shown in Figure4.1 (regular meaning having the same length of edges). Please also note that in the case of Marks-decahedron, a concave shape with twin boundaries introduced by Marks,13 there are two possibilites to build the NPs (Please see Figure4.7 for all the optimized structures): by either removing the five corner atoms of the regular decahedra shape to build the {110} re-entrant facet (Au 49 , Au 100, Au 176, Au 282 , Au 423 , Au 604 and Au 830 ), or using theses latter structures and truncate all the atoms of the edges in order to create square facets on the nanoparticles (Au 75 , Au 146, Au 176, Au 247 , Au 383 , Au 559 and Au 780 ). A summary of the six AuNPs morphology and the information of these NP facets are indicated in Figure 4.1 and Table 4.1 while all the optimal structures of the considered 44 NPs are displayed in Figures 4.2-4.7.

	Truncated Octahedra

12

Ino-decahedra (ino), icosahedra (ico) and cubotahedra (cubo) are three close1. For each morphology, the total number of facets N F , the total number of hexagonal N HF , square or rectangular N S(R)F , triangular N TF, pentagonal N PF facets, the total number of vertices N v , and edges Ne are given.

  The corresponding R 2 of the linear regression for the six AuNPs are larger than 0.9990, showing that the linear laws used in our studies are meaningful. The obtained offsets are close to the calculated bulk cohesion energy (-3.695 eV/atom) in good agreement with experiment (-3.81 eV/atom). Our linear models are in better agreement with experiments of previous DFT work 2 (-3.285 eV for the icosahedra with the TPSS functional). However, they differ slightly from one polyhedral family to another one because the examined range of NP size is limited (below 3.4 nm). The truncated octahedral NPs have the most stable offset (-3.736 eV/atom). This is expected since it exhibits the bulk fcc

crystallinity and have a good surface/volume ratio. They compete with icosahedra and Marks-decahedra with bulk cohesion energy of -3.714 eV/atom and -3.711 eV/atom, respectively. In contrast, the decahedral NPs (regular and Marks) show the minimal facet surface energies (3.367 eV). This is expected because these polyhedra exhibit mainly large (111)-facet type. Then come the icosahedra with small (111)-facet type

(3.428

eV in this work, whereas 2.478 eV was proposed previously 2 ). The NPs having the highest average facet surface energy are truncated octahedra, ino-decahedra, and cuboctahedra because they possess large (100)-facet type, well-known to be less stable than (111) type.

Table 4 . 2

 42

. Analytical formula used to calculate the surface area of Au NPs. nd is the length of edge and d is the average distance of the NP outer shell.

Table 5 .

 5 .1 and Figure 5.8. As a first remark (see Figure 5.8), the influence of the adsorption of water monoshells on the nanocluster shape tends to decrease progressively with the size of the nanoparticle. From a general standpoint, the majority of the Au clusters have undergone a slight stretching of their structures (negative ΔS ). Among the nine nanoclusters, only two of them have become rounder (Au 38 (rto) and Au 55 (ino), with positive ΔS ) and two other ones have not been distorted significantly in average (Au 54 (deca) and Au 147 (ino), with ΔS being almost zero).

	Nanocluster	Au 38	Au 54	Au 55	Au 55	Au 79	Au 105	Au 147	Au 147	Au 201
			(rto)	(deca)	(ico)	(ino)	(ito)	(deca)	(ico)	(ino)	(rto)
	R AuNP -NH 2 O min	3.882 4.008 4.645 4.704 5.267 5.101 6.657 6.765 7.201
	(Å)
	R AuNP -NH 2 O max	5.784 6.896 5.727 5.570 6.464 9.339 8.421 8.816 8.982
	(Å)
	S AuNP -NH 2 O	0.671 0.581 0.811 0.845 0.815 0.546 0.790 0.767 0.802
	R AuNP min	(Å)	3.653 3.990 4.810 4.203 5.356 5.244 6.870 6.497 7.329
	R AuNP max	(Å)	5.769 6.900 5.441 5.678 6.424 9.213 8.291 8.570 8.855
	S AuNP		0.633 0.578 0.884 0.740 0.833 0.569 0.828 0.728 0.827
	ΔS		0.038 0.003 -0.073 0.104 -0.019 -0.023 -0.038 0.009 -0.026
										min	and
	maximal	R AuNP -NH 2 O max	radii (Å) from center to surface atom of solvated Au
	nanoparticles ("AuNP-NH2O"), minimal R AuNP min	and maximal R AuNP

In the case of Au 55 (ino) and Au 147 (ino) with the presence of the water monoshells, the final and relaxed metallic geometries (icosahedral shape) are different from the clean initial structures (ino-decahedral shapes). This morphology change is captured in the calculation of ΔS . For Au 55 (ino), the change of morphology from ino-decahedral to icosahedral shape induced by the water monoshell explains the positive value of ΔS (the nanocluster being rounder). For Au 147 (ino), this phenomenon is similar to a lesser extent. 1. Surface atom to center distance analysis: minimal R AuNP -NH 2 O max radii (Å) from center to surface atom of naked Au NP, roundness degree of solvated S AuNP -NH 2 O and naked AuNP S AuNP , and the variation of roundness degree ΔS with and without water (dimensionless).

  our additive model, the total coadsorption energy ΔE coads

							tot	for N H 2 O water
	molecules present in the monoshell surrounding the Au NP is expressed following the
	additive model :
	ΔE coads tot	=ΔE deform tot	+ N chem H 2O ΔE int ,chem 1 H 2 O , best	+ N phys H 2 O ΔE int , phys 1 H 2 O , best	+ Δ E int , H 2 O -H 2 O tot	+ N . A . [Eq. 5.7]
	where ΔE deform tot	is the total deformation energy of Au NP and water molecules induced
	by the adsorption process, ΔE int , chem 1 H 2 O ,best	being the interaction energy of one water
	monomer chemisorbed on Au NP (best chemisorption structure), ΔE int , phys 1 H 2 O ,best	being the
	interaction energy of one water monomer physisorbed on Au NP (best physisorption
	structure), Δ E int , H 2O -H 2 O tot	being the total interaction energy between water molecules
	in the monoshell, N chem H 2 O	being the total number of chemisorbed water molecules,
	N phys H 2 O

Table 6 .

 6 Au 49 (marks) Au 54 (deca) Au 55 (ico) Au 55 (ino) Au 79(ito)

	1 PEG
	Grafting density	0.20	0.19	0.16	0.15	0.08
	∆E ads	-1.589	-1.736	-1.358	-1.623	-1.519
	∆E disp	-0.802	-0.632	-0.783	-0.822	-0.948
	∆E cov	-0.787	-1.104	-0.575	-0.801	-0.571
	∆E def AuNP	0.044	0.045	0.043	0.057	0.066
	∆E def PEG	0.178	0.093	0.125	0.076	0.098
	∆E int PEG-Au	-1.810	-1.874	-1.526	-1.756	-1.683

1. Grafting densities (molec.nm -2 ) and adsorption energetics of the most stable structures for one PEG molecule on five Au nanoclusters (Figure 6.16). Adsorption energy E ads (eV), decomposed into dispersion E disp (eV) and pure GGA E cov (eV) contributions, or into deformation energy of Au,  def AuNP , of PEG,  def PEG (eV) and interaction energy between PEG and Au,  int PEG-Au (eV) (chemical bonding).

Table 6 . 2

 62 stellation (Au 54 ) results in a more organized coating ("brushed-type"), whereas non symmetric deformation (Au 49 , Au 55 and Au 79 ) induces disordered monoshells ("bushy-type").

	PEG sat	Au 49 (marks) Au 54 (deca) Au 55 (ico) Au 55 (ino) Au 79 (ito)
	Grafting density	5.09	4.87	3.44	3.24	2.66
	∆E coads (/PEG chem )	-1.933	-1.719	-1.565	-1.569	-1.471
	∆E disp (/PEG tot )	-0.754	-0.780	-0.815	-0.791	-0.783
	∆E cov (/PEG tot )	-1.180	-0.938	-0.750	-0.778	-0.689
	∆E int PEG-Au (/PEG chem )	-1.269	-1.200	-1.092	-1.224	-1.053
	∆E def AuNP (non normalized)	1.851	2.362	0.884	2.205	2.479
	∆E def+int PEG-PEG (/PEG tot )	-0.506	-0.470	-0.449	-0.382	-0.430

. Grafting densities (molec.nm

-2

) and adsorption energetics of the PEGylated SAMs on five Au nanoclusters (Figure

6

.22). Coadsorption energy ∆E coads (eV per chemisorbed PEG), decomposed into dispersion ∆E disp (eV per PEG ligand) and pure GGA ∆E cov (eV per PEG ligand) contributions, or into deformation energy of Au, ∆E def

Table 6 . 3 .

 63 sat -H 2 O Adsorption energetics of the PEGylated and hydrated SAMs on three Au nanoclusters (Figure3). Coadsorption energy ∆E coads (eV per chemisorbed PEG), decomposed into dispersion ∆E disp (eV per PEG) and pure GGA ∆E cov (eV per PEG)

		Au 54 (deca) Au 55 (ico) Au 79 (ito)
	∆E coads (/PEG chem )	-3.767	-2.880	-3.138
	∆E disp (/PEG tot )	-1.030	-1.050	-1.007
	∆E cov (/PEG tot )	-1.722	-1.701	-1.542
	∆E def AuNP (sans norm)	2.122	1.357	1.953
	∆E int (PEG+H2O)-Au (/PEG chem )	-1.340	-1.110	-1.147
	∆E int PEG-Au (/PEG chem )	-1.114	-0.940	-0.951
	∆E int H2O-Au (/H 2 O tot )	-0.042	-0.040	-0.039
	∆E def+int PEG-PEG (/PEG tot )	-0.033	-0.089	-0.153
	∆E int PEG-H2O (/H 2 O tot )	-0.736	-0.680	-0.656
	∆E int PEG-H2O (/PEG tot )	-1.783	-1.637	-1.436
	∆E def+int H2O-H2O (/H 2 O tot )	-0.084	-0.078	-0.100
	∆E int PEG-H2O(F1) (/H 2 O(F 1 ))	-0.735	-0.689	-0.673
	∆E int PEG-H2O(F2) (/H 2 O(F 2 ))	-0.905	-0.904	-1.107
	∆E int PEG-H2O(F3) (/H 2 O(F 3 ))	-0.716	-0.817	-0.930
	∆E int H2O(F1)-Au (/H 2 O(F 1 ))	-0.004	-0.029	-0.022
	∆E int H2O(F2)-Au (/H 2 O(F 2 ))	-0.217	-0.162	-0.096
	∆E int H2O(F3)-Au (/H 2 O(F 3 ))	-0.235	-0.108	-0.173

  Although the PEG organic layer is relatively dense, a few water molecules are stabilized inside the coating according to our DFT calculations (Figure6.23). The ratio between H 2 O and PEG molecules increases slightly (from 2.19 to 2.42) with the GNP absolute stabilization (from Au 79 to Au 54 (Figure

	PEG sat -H 2 O	Au 54 (deca)	Au 55 (ico)	Au 79 (ito)
	∆E lee (PEG chem )	2.705	2.680	2.310
	∆E lee (PEG phys )	3.139	2.786	2.382
	Table 6.4. Ligand extraction energy ∆E lee (eV) related to the removal of one physisorbed
	or chemisorbed PEG molecule from the hydrated PEGylated GNPs. These energies are
	endothermic and obtained by single point energy calculations of the complete systems
	with a missing ligand.
				.3) associated
	with one PEG ligand (PEG-PEG, PEG-H 2 O, PEG-Au), the concept of physisorption
	should be used cautiously. The ligand extraction energy analysis (Table 6.4) also supports
	the trends previously discussed for the relative order of interaction energies between PEG
	and Au.

Table 7 .

 7

	Bending (in °)	φe (in	°)

Remerciements

Methodology

DFT calculations (spin restricted) of AuNPs and water adsorption have been performed by using the VASP code, version 5.3.5. PBE with Grimme's D3 semi-empirical dispersion corrected functional (zero-damping formalism) has been considered to describe electronic exchange and correlation at the generalized gradient approximation with van der Waals interactions. The core-electrons were described by the projectoraugmented wave (PAW) pseudo-potentials (11 valence electrons per Au atom), and valence electrons were expanded in plane waves with a kinetic cut-off energy of 400 eV.

All the AuNPs were modeled in a cubic box of 5×5×5 nm 3 with a -point only approach for the k-point mesh and related Brillouin zone. In the geometry optimizations, the Au NPs and water adsorption structures were relaxed completely with 10 -6 eV for the convergence of the total electronic energy and -0.01 eV.Å -1 for the minimization of the residual forces on the nuclei. A Methfessel-Paxton smearing was used for the calculation of the total electronic energy.

Isolated Water Adsorption

In the following, we have evaluated the adsorption energetics of one water molecule on AuNPs for two cases: In the first case, the morphology of the NP is kept constant (truncated octahedron), with an explored wide range of size from 0.9 to 3.4 nm. In the second case, the adsorption of water monomer is performed on four morphologies of AuNPs in a more restricted range of size: truncated octahedra, inodecahedra, icosahedra and regular decahedra, in the range 0.9-1.8 nm.

The adsorption energy of one water monomer on the various Au NPs is expressed as follows:

Analysis of Electrostatic Potential

In this section, the electrostatic potential V(x,y,z) for solvated AuNPs is calculated, in order to evaluate the impact of solvation on AuNP and to provide these parameters obtained at ab initio level for our collaborators M. Beuve and F. Poignant. This potential is calculated at any point (x,y,z) of the 3D supercell considered in our study. In order to analyse more easily the results, an average electrostatic potential ( V z ) is integrated along the Z axis of the 3D 5×5×5 nm 3 box (this axis is chosen in such a way that the layers of the Au NP are perpendicular to it, as well as the adsorption structure of water monomers): Chapter 6 : PEGylation of Hydrated Gold Nanoparticles

Methodology

Spin-restricted DFT calculations of PEGylated and hydrated GNPs were performed by using the VASP package, version 5.3.5. PBE with Grimme's D3 semi-empirical dispersion corrected functional (zero-damping formalism) was considered to describe electronic exchange and correlation at the generalized gradient approximation (GGA) with van der Waals interactions. The core-electrons were described by the projectoraugmented wave (PAW) pseudo-potentials (11 valence electrons per Au atom), and valence electrons were expanded in plane waves with a kinetic cut-off energy of 400 eV.

All the GNPs were modeled in a cubic box of 5×5×5 nm 3 with a Γ-point only approach for the k-point mesh and related Brillouin zone. In the geometry optimizations of the complete systems, the coadsorption structures of PEG and water on GNPs were relaxed completely with 10 -6 eV for the convergence of the total electronic energy and -0.01 eV.Å - 1 for the minimization of the residual forces on the nuclei. A Methfessel-Paxton smearing was used for the calculation of the total electronic energy.

Choice of AuNPs and PEG Model

The first important step in the study is the selection of the gold nanoclusters to build the organic monolayers of PEGylated systems. According to the measurements, depending on the choice of the synthesis ligand and the size, GNPs may have several competitive morphologies including nanospheres, nanostars (nanospikes), nanorods, nanotriangles and nanoprisms. In order to tackle the discussion of the internalization of the GNPs and the ligand exchange with the membrane which has been recently proposed, 2 our choice in this work is to elaborate DFT models of gold nanospheres, nanospikes and nanorods. Due to the inherent limit of 3D models (5 nm × 5 nm × 5 nm), the size of the gold

Definition of the normalized interaction energy between x PEG ligands and y 3 H 2 O molecules belonging to family (F3).

Similarly, the interaction energies between AuNP and the water molecules of each family can be expressed with the following formulas (addressed in Table 6.3 and depicted in Figures 6.12, 6.13 and 6.14):

The number of hydrogen bonds between PEG and H 2 O in the case of the hydrated PEGylated GNPs are evaluated by dividing the average interaction energy between PEG and H 2 O (normalized per PEG or per water) by the dimerization energy of the most stable configuration between one PEG and one water (dimer2) as follows:

Various DFT models of PEGylated AuNPs

Isolated PEG Adsorption

Before considering the monoshells of PEG ligands surrounding the Au nanoclusters, the most stable adsorption forms have to be investigated for each shape and size. In Figure 6.16 and Table 6 Interestingly enough, the interaction of TGT with KKK and its three ammonium side chains, does not always rigidify the oligonucleotide by promoting two ammoniumphosphate interactions, as it was thought experimentally (see Figure 2.3 in Chapter 2).

Indeed this case scenario is found only for one of the representative structure extracted from our MD simulation.

The formation of the guanine-lysine cross-link, whose existence was probed experimentally, implies a spatial proximity between the C8 carbon atom of the central guanine G2 and the terminal nitrogen of the central lysine K2. However, along our dynamics, the interatomic distance (G/C8 … K2/NZ) rarely reaches values below 6 Å (see Table 7.1, last column). Interestingly, the most stable structure according the MM-GBSA analysis and corresponding to the T-shaped arrangement (Figure 7.2-c) features a higher proximity (4% of structures with an approaching distance below 6 Å). This indicates that the formation of a guanine-lysine cross-link, in addition to the electronic energy barrier could also imply an additional free energy penalty necessary to adopt a pre-arranged conformation more prone to react. However, the KKK:TGT complex is very flexible and however the structural variability is significantly decreased, and more importantly precise binding site, or more properly guanine hot-spots my be underlined. This preference suggests that cytosines adjacent to guanines favour the binding of the polyamines: a close inspection of the representative structures in Upon deprotonation G• develops an equilibrium between the N1 and the N2 deprotonated forms, hence both possibilities. The repair involving hydrogen transfer to the N1 G• position, while it cannot be entirely ruled out, seems less probable since the reaction is found to be exergonic, as estimated via the rigid rotor approximation. Indeed, at equilibrium geometry the situation in which the radical is centered on guanine has a free energy of about 3.6 kcal.mol -1 lower than the CH3NH2 +• arrangement. Correspondingly AIMD trajectories starting from the reactants or products get trapped in local minima and show that both arrangements are stable enough to give rise to persistent aggregates.

Conclusions and Perspectives

This thesis is devoted to theoretical modeling of the electronic properties of AuNPs (in a