Jaber Al

Rashid Laris

Sfr Mathstic

Laurent Saintis
email: laurent.saintis@univ-angers.fr

Mohsen Koohestani
email: mohsen.koohestani@eseo.fr

Mihaela Barreau
email: mihaela.barreau@unive-angers.fr

High Temperature Accelerated Ageing Influence on the Conducted Immunity Modelling of the Commonly Used Voltage Regulator ICs

Keywords: ICIM-CI, IB, PDN, SSADT, thermal stress, immunity drift

This paper aims to develop and compare the integrated circuit conducted immunity (ICIM-CI) models of two different voltage regulator ICs with similar functionality (i.e., UA78L05 and L78L05) under the combined influence of two different electrical overstress (i.e., 9 and 12 V) and high temperature (i.e., 70-110 °C) stresses ageing conditions for a total stress duration of 950 hours.

Step-stress accelerated degradation tests (SSADT) are performed on two samples of UA78L05 (i.e., T1 and T2) and L78L08 (i.e., S1 and S2) manufactured by Texas Instrument and STMicroelectronics, respectively. Direct power injection (DPI) test was conducted in nominal conditions (i.e., 7.5 V and 25 °C) on these selected ICs according to IEC 62132-4 standard before and after the accelerated ageing test. For the studied cases, it was found that the passive distribution network (PDN) models extracted before and after ageing test for the ICIM-CI model of UA78L05 and L78L05 remained unaffected. However, the ageing process affected the internal behavioral (IB) block of the ICIM-CI model significantly due to noticeable reduction in the conducted immunity level characterized by the extracted IB look-up table data in terms of power transmitted and frequency. Both fresh and aged samples of L78L05 demonstrated higher conducted immunity profile compared to those of UA78L05.

I. INTRODUCTION

Electromagnetic robustness (EMR) of integrated circuit (ICs) is usually affected by ageing under the influence of harsh external environmental stress conditions (i.e., high temperature and electrical overstress) [START_REF] Barreau | Electro-magnetic robustness of integrated circuits: from statement to prediction[END_REF]. Accelerated life tests can be performed on integrated circuits (ICs) by applying stress conditions to activate and accelerate the rate of degradation due to intrinsic failure mechanisms induced by ageing [START_REF] Ben Dhia | Characteristics of electromagnetic compatibility drifts of nanoscale integrated circuit after accelerated life tests[END_REF]. For example, hot carrier injection (HCI) and negative bias transistor instability (NBTI) are known to degrade the electromagnetic compatibility (EMC) performance of ICs [START_REF] Li | Characterization of the electromagnetic robustness of a nanoscale CMOS integrated circuit[END_REF]. Those internal degradation mechanisms modify different transistor parameters by lowering the electron mobility and increasing the threshold voltage (V th ) of the aged ICs, causing significant impact on electromagnetic emission under the applied electrical stress conditions [START_REF] Boyer | Experimental investigations into the effects of electrical stress on electromagnetic emission from integrated circuits[END_REF]. Likewise, the influence of ageing can also affect the functionality (e.g. noise, saturation current, signal propagation delay) due to the variation of the physical parameters of the transistors in both digital and analog ICs, resulting significant reduction in the conducted immunity to electromagnetic interferences (EMI) [START_REF] Fernandez | Effect of oxide breakdown on RS Latches[END_REF], [START_REF] Li | Ageing effect on immunity of a mixed signal IC[END_REF].

Accelerated life tests methods, such as, high temperature operating life (HTOL) and low temperature operating life (LTOL), are usually performed on the ICs to evaluate the influence of ageing on the conducted immunity to EMI. According to the AEC-Q100-Rev-F standard, HTOL test is performed by applying constant thermal stress at 150 °C for 450 hours, whereas LTOL test requires applying thermal stress at -40 °C for the same stress period [START_REF]Stress test qualification for integrated circuits[END_REF]. In [START_REF] Li | Ageing effect on immunity of a mixed signal IC[END_REF], HTOL ageing test was performed to characterize the evolution of the ageing induced immunity drift of analog circuit structure (i.e., variable controlled oscillator) designed in 0.25 µm CMOS technology. In [START_REF] Wu | Characterization of Changes in LDO susceptibility after electrical Stress[END_REF], accelerated ageing conditions (i.e., electrical overstress) was applied for a specific stress period on the low-dropout voltage regulator (LDO) circuit implemented on a test IC chip to accelerate relevant wear-out degradation mechanisms until the tested chip fails. The changes in the LDO immunity was characterized during the ageing process using the DPI measurements according to the IEC 62132-4 standard [START_REF]Integrated circuits-Measurement of Electromagnetic Immunity 150 kHz to 1 GHz-Part 4: Direct RF Power Injection Method[END_REF] prior and after the accelerated life tests, which showed an increase in the electromagnetic immunity drift [START_REF] Wu | Characterization of Changes in LDO susceptibility after electrical Stress[END_REF]. Moreover, the longterm conducted immunity of different analog circuit blocks of the phase-locked loop was analyzed by performing the accelerated life tests, and the results revealed that the ageing reduced the immunity profiles of the tested structures across the whole DPI frequency range [START_REF] Boyer | Prediction of a long-term immunity of a phase-locked loop[END_REF].

IC designers and manufacturers need to predict the the conducted immunity of ICs prior to the manufacturing phase. ICIM-CI model has been proposed and published in the IEC 62433-4 standard [START_REF]integrated circuit-EMC IC modeling-Part 4: Models of Integrated Circuits for EMI behavioral simulation, Conducted Immunity Modeling (ICIM-CI). IEC standard proposal[END_REF]. This standard model can be extracted from simulations based on the knowledge about the internal structure of the IC under test. In [START_REF] Khan | Validation of IC conducted emission and immunity models including aging and thermal Stress[END_REF], the effect of ageing and external thermal stress conditions on the proposed ICIM-CI model of a custom-designed integrated oscillator was studied, demonstrating significant reduction of the conducted immunity level with better accuracy that can be taken into account in the future revised version of the ICIM-CI standard. In [START_REF] Airieau | Multi-port ICIM-CI modeling approach applied to a bandgap voltage reference[END_REF], multi-port conducted immunity model was proposed and compared with the measurements to validate accuracy of the simulation model to estimate the EMC performance of the bandgap reference circuit designed and implemented in the test chip. In [START_REF] Wu | LDO EMC susceptibility modeling with on-chip sensor measurements[END_REF], the LDO susceptibility model was proposed based on the MOSFET models to extract the ICIM-CI model, which was then validated using the DPI measurements. In [START_REF] Huang | Investigation on EFT effects in a low dropout voltage regulator[END_REF], the ICIM-CI modeling process was presented by extracting individual models for both linear passive and non-linear active elements of the LDO regulator in order to compare the conducted electric fast transient (EFT) immunity measurement to the proposed simulation model. In [START_REF] Wu | Modeling and simulation of LDO voltage regulator susceptibility to conducted EMI[END_REF], a white-box modeling approach was presented for the LDO regulator mounted on a test chip to demonstrate the methodology required to extract the ICIM-CI model. The model was then validated by comparing the simulation results to the DPI measurements. However, the impact of ageing on the ICIM-CI models of ICs should be investigated in order to predict long-term EMR and lifetime reliability. In [START_REF] Rashid | Coupling simulation and accelerated degradation model for reliability estimation: application to a voltage regulator[END_REF], an electrical simulation model for the voltage regulator as well as an accelerated degradation model were proposed to predict various reliability parameters based on functional performance under different thermal and electrical overstress conditions.

Here, we showcase that the standard ICIM-CI model might be updated and modified to analyze the EMC performance, while taking into account of the influence of accelerated ageing on the conducted immunity model of ICs.

II. MATERIALS AND METHODS

This section presents the test conditions for accelerated aging applied to the chosen voltage regulator ICs. Furthermore, it also introduces the experimental test setup used to conduct high temperature SSADT as well as the DPI test on the ICs to characterize the ageing impact on the developed ICIM-CI models.

A. The Accelerated Ageing Test Plan

The accelerated ageing test plan was designed to investigate and compare the high temperature ageing impact on the EMC performance degradation and the ICIM-CI models of the selected ICs (i.e., UA78L05 and L78L05). includes the number of IC test samples, total ageing stress duration, electrical overstress and thermal stress conditions applied on the samples. The table demonstrates that identical thermal step-stress conditions were applied to each of the four DUT samples. Two samples (i.e., T1 and S1) of UA78L05 and L78L05, were respectively subjected to a low arbitrary electrical overstress voltage of 9 V (20% higher than nominal voltage). In contrast, high supply voltage stress condition (60% greater than nominal voltage) was chosen for the T2 and S2 samples, ensuring the aged samples remain operational at the end of the ageing test.

B. Measurement Test Setup and Procedures

Four fresh DUT samples were placed inside the climatic chamber (Climat2) to perform high temperature accelerated ageing test for 950 hours. The accelerated ageing test setup is shown in Fig. 1. The test setup consists of high temperature cables (Amphenol-RF 095-902-466-004) to withstand high temperature within the climatic chamber as well as external DC power supply sources for providing electrical overstress above the nominal voltage (i.e., 7.5 V) into the input voltage supply (V in ) pin 8 (Fig. 1a) of the tested ICs. Those temperature cables are used to inject the DC input voltage signal to the V in pin of these ICs. The Spirale V software interface integrated with the climatic chamber was used to develop a program for regulating and maintaining the thermal step-stress conditions inside the chamber. The latter consisted of varying the temperature from 70 °C to 110 °C with a linear step increment of 10 °C after every 200 hours, reaching the maximum ageing temperature at 800 hours, and the SSADT was continued for the remaining 150 hours. It should be noted that the maximum temperature stress and total stress duration were chosen based on the operational characteristics of the selected ICs so that the aged samples remain functional avoiding permanent failure throughout the SSADT.

The above-mentioned ageing plan was applied to all the four DUTs in the controlled environment condition for the complete duration of the SSADT induced ageing. The aged samples were removed from the thermal ageing climatic chamber at the end of the process, and the DPI immunity test was performed at the nominal condition (i.e., 7.5 V and 25 °C) in accordance to the IEC 62132-4 standard. The standard DPI test bench was used to perform the DPI experiment, and the relevant measurement data (i.e., power injected and frequency) were recorded on both fresh and aged IC samples in order to analyze the influence of the aging process on the conducted immunity of the tested ICs.

The DPI measurement setup is similar to that in [START_REF] Rashid | Combining obsolescence and temperature stress to evaluate the immunity of voltage regulators to direct power injection in long lifespan systems[END_REF]. The harmonic disturbance signal was injected into the V in pin of each considered sample ICs. Two independent power meters were utilized to record relevant measurement data (i.e., forward power and reflected power). The LabView interface, which is incorporated with the DPI test bench, is programmed to measure the injected power (P inj ) when the defined failure threshold criterion is observed at various frequency values. Based on the forward and reflected power measured from the power meters, the minimum P inj required to cause IC malfunction was recorded at each corresponding frequency values over the entire DPI frequency range between 10 and 1000 MHz. The DPI failure criterion of ±4% deviation from the nominal DC output voltage (V out ) was considered on all the test samples. The DC offset voltage (i.e., ±0.2 V) variation from the nominal V out at the pin 1 (Fig. 1a) of the DUT was considered as the failure threshold. The DPI failure threshold was chosen with a fixed arbitrary value to ensure the ICs remained operational throughout the SSADT, taking into account of various functional performance parameters (i.e., maximum operating temperature, maximum current and operating voltage) of the regulator ICs. It is worth to mention that the input current remained unchanged during the ageing process.

III. RESULTS AND DISCUSSION

This section presents the experimental results to analyze the combined effect of applying thermal and electrical ageing stress conditions on the conducted immunity to EMI. Moreover, several ageing-induced immunity drift parameters (i.e., mean power injection drift, maximum and lowest ageing drift, and standard deviation) for these tested samples were analyzed and compared based on those EMC measurements recorded before and after aging.

A. Accelerated Ageing Impact on Conducted Immunity

The conducted immunity profile for both fresh and aged ICs under two different electrical overstress (i.e., 9 V and 12 V) and identical thermal stress conditions is depicted in Fig. 2.

The ageing impact on the conducted immunity of the samples S1 and T1 subjected to low electrical overstress and high thermal step-stress conditions is displayed in Fig. 2a. Across the whole DPI frequency range, it was found that the fresh L78L05 sample (i.e., S1) was more immune than that of UA78L05 (i.e., T1). Although the conducted immunity profiles for both of these fresh DUT samples showed a gradual increasing trend, the P inj into the V in pin of the S1 sample varied from 12.5 to 25 dBm between 10 and 1000 MHz, while the T1 required lower P inj (i.e., 8 dBm at 10 MHz and 24 dBm at 1000 MHz) to induce the DPI failure. The influence of ageing caused by high temperature and low electrical overstress (i.e., 9 V) conditions resulted in a significant degradation of the conducted immunity level of the tested samples S1 and T1 at both low and high frequency values, ranging from 10 MHz to 200 MHz and 450-1000 MHz, respectively. Conversely, ageing induced by the SSADT and electrical overstress (i.e., 9 V) improved the conducted immunity level of both the aged samples (S1 and T1) in the mid frequency range (i.e., 200-450 MHz). Furthermore, it could be observed that the immunity profile waveform produced for the aged S1 sample needed larger P inj throughout the whole DPI test frequency spectrum than that of the aged T1 sample.

Fig. 2b illustrates the effect of ageing on the conducted immunity level of the test samples (S2 and T2) for the L78L05 and UA78L05, respectively, subjected to both high electrical overstress (i.e., 12 V) and identical thermal stress conditions as outlined in the Table I. Under the effect of the high electrical overstress, both the tested S2 and T2 samples demonstrated a significantly higher difference in the P inj between the aged and fresh states at each corresponding DPI frequencies compared to those of the S1 and T1 samples depicted in the Fig. 2a. Between 10 and 1000 MHz, the sample S2, both in fresh and aged states, could endure greater P inj compared to that of the fresh and aged T2 sample. As a result of this immunity behaviour, it was possible to conclude that the S2 was more immune to the harmonic disturbances than that of the the considered T2 sample.

It is worth mentioning that the observed change of the conducted immunity level could be due to the degradation of the associated CMOS transistors within the tested ICs. Depending on the stress magnitude and duration, the SSADT would activate and accelerate intrinsic degradation mechanisms that could modify the electrical properties (i.e., threshold voltage and charge carrier mobility) of several aged CMOS transistors. Numerous internal CMOS transistors of the aged DUTs could be degraded due to high positive biasing voltage and the biasing current caused by the electrical overstress condition, which would increase the V th and reduce the charge carrier (i.e., holes and electrons) mobility [START_REF] Barreau | Electro-magnetic robustness of integrated circuits: from statement to prediction[END_REF]. Thus, a clear relationship between the variations of the physical features of CMOS transistors induced by aging and the conducted immunity level could be established. The influence of ageing on the observed dispersion of the conducted immunity level between the fresh and aged states of the tested samples under the DPI measurements can be a result of the variability of the DUT characteristics and the measurement uncertainty of the DPI test bench equipment.

B. Ageing Induced Conducted Immunity Drift of ICs

The P inj measured for both fresh and aged ICs (i.e., L78L05 and UA78L05) under the nominal conditions were used to evaluate the ageing induced immunity drift threshold, also known as the power injected drift (∆P inj ), by subtracting the measured P inj of the aged from that of the fresh sample. The ageing induced immunity drift of the test samples at each corresponding frequency value is shown in Fig. 3. Negative EMC immunity drift was observed for both aged samples of L78L05 and UA78L05 at the high frequency range (i.e., 650-1000 MHz). Throughout the whole DPI frequency range, both the aged T1 and T2 samples showed slightly higher mean immunity drift than those of the aged S1 and S2. Moreover, positive ∆P inj of the immunity threshold was observed within the specific frequency range (i.e., 250-450 MHz) due to the fact that the measured P inj of the aged sample was higher than that of the fresh IC, highlighting an improvement in the conducted immunity level of all the tested samples. The impact of the high electrical overstress condition on the aged S2 and T2 samples could be noticed in their respective ageing immunity drift waveforms, which are shown in the Fig. 3. The aged S2 sample showed greater ∆P inj immunity drift than the aged S1, indicating higher conducted immunity drift due to the significant influence of the electrical stress observed on the EM immunity of the aged DUT. Likewise, the aged sample T2 demonstrated higher conducted immunity drift level compared to that of the T1 due to observing noticeable difference in the ∆P inj evaluated throughout the whole frequency range.

Table II summarizes ageing induced EMC drift parameters computed for all the distinct samples of ICs (i.e., L78L05 and UA78L05). The absolute mean EMC ageing drift (∆M P inj ) over the entire frequency range is evaluated as the ∆P inj for both the UA78L05 and L78L05 varied at every corresponding frequency value. The ∆M P inj for the aged S1 and S2 samples of was 6.97% and 6.4% lower than those of the aged T1 and T2, respectively. Thus, the L78L05 showed more EM robustness and immunity than the UA78L05 under the indicated accelerated ageing conditions. Due to the effect of the high electrical overstress and the defined identical thermal stepstress external factors, the aged S2 and T2 samples exhibited greater immunity drift than the other two aged (S1 and T1) samples. The ∆M P inj of the S2 sample was found to be 9.2% greater than the other DUT of the same IC (i.e., L78L05), with a higher mean standard deviation (σ) of the immunity drift. Similar immunity behaviour was observed for the aged samples of UA78L05, with a 7.9% increase in ∆M P inj for the T2 sample and an 18% higher σ compared to the other aged T1 sample.

IV. EFFECT OF AGEING ON THE ICIM-CI MODEL OF ICS

The ICIM-CI model was developed for both fresh and aged DUT samples in order to compare and analyze the effect of ageing on the conducted immunity of the selected ICs (i.e., UA78L05 and L78L05). To investigate influence of ageing on these ICIM-CI models, both PDN and IB blocks models were extracted from experimental results obtained before and after accelerated ageing tests for each individual DUT of L78L05 and UA78L05. The passive PDN block for each DUT was developed by S-parameter measurements using the vector network analyzer (VNA) similar to that in [START_REF] Rashid | A State-ofthe-Art Review on IC Reliability[END_REF]. The measured reflected coefficient (S 11 ) was used to determined the input impedance (Z 11 ) between the V in and ground (GND) pins of the IC samples before and after accelerated ageing. The PDN block was then modeled by extracting the unknown parameters of the lumped passive components (e.g. resistor, inductor and capacitor) from the Z 11 profile to investigate the contribution of the ageing effect on the PDN block of the ICIM-CI model. Fig. 4 displays the Z 11 profile curves versus frequency (i.e., 1-1000 MHz) for both the fresh and aged S1 and T1 test samples. It was found that the impedance profiles of both new and aged ICs remained comparable, with the exception of the aged L78L08 sample (i.e., S1), which exhibited a higher impedance compared to the UA78L05 below and above the resonant frequency, that could be due to higher resistance (R2), lower coupling capacitance (C2), and parasitic inductance (L2) values. As observed in Fig. 4, the extracted RLC values of the PDN model for the aged T1 sample were 35.5 Ω, 19.8 µH and 41.2 pF, whereas the overall RLC values for the aged L78L05 were found to be 49.2 Ω, 21.6 pF and 16.8µH. The conducted immunity could be similar for both of these tested IC at high frequency due to the small difference in the Z 11 values dominated by the extracted L1 and L2 values of the PDN block. Note that, the input impedance profiles of the other two IC samples remained constant after being aged at high electrical overstress condition. Thus, it can be concluded that the PDN block of these studied IC samples was unaffected by ageing.

The black box approach was considered to produce the IB block for each individual samples of both UA78L05 and L78L05 by extracting the look-up table from the DPI measurement data. The look-up table data include the actual power transmitted (P trans ) to the V in pin under test (PUT) at each corresponding DPI frequency value, causing the DPI failure on the considered IC samples. This P trans corresponds to the actual power that couples into the PUT of the IC mounted on the printed circuit board (PCB), and it is considered as the relevant parameter for analyzing the conducted immunity level under the influence of ageing. The P trans was evaluated by using the P inj data from the DPI measurements, S 11 measured using the VNA and insertion loss owing to the cables and PCB trace. The insertion loss was considered to be 3 dB which is subtracted from the P inj to obtain the actual incident power (P inc ) at the PUT of the IC. The calculated P inc data was used to evaluate the actual P trans to the IC samples under test

(P trans = [1 -|S 11 | 2 ] × P inc ).
The data from the look-up table, which corresponds to the IB blocks of the ICIM-CI models of L78L05 and UA78L05, was extracted and plotted against the DPI frequency range, as can be seen in Fig. 5. Fig. 5a shows that the P trans of the aged T1 sample decreased by a mean deviation of 4.3 dB and 4 dB for the aged S1 over the whole frequency range. Besides, the maximum P trans deviation between the aged and fresh samples of UA78L05 and L78L05 is 9.9 dB and 9.5 dB, respectively. Similar to the Fig. 5a, Fig. 5b demonstrates that the P trans level of the aged test samples is lower than that of the fresh ones at each corresponding frequency, with the exception between 200 and 400 MHz, which is due to the improvement of the conducted immunity profile due to ageing. Furthermore, the average P trans drift of the aged samples owing to ageing under high electrical stress was 4.4 dB and 4.7 dB for the S2 and T2, respectively. As a result, the reduced P trans level observed in both Figs. 5a and 5b implies that accelerated ageing impacts the extracted IB blocks of the ICIM-CI models of both UA78L05 and L78L05. In order to account for the effect of ageing on the developed ICIM-CI models of the tested IC samples, it is essential to readjust the IB look-up tables with the modified and updated P trans and corresponding frequencies.

V. CONCLUSION

A comparative study was conducted using measurements on the two pin-to-pin compatible voltage regulator ICs (i.e., L78L05 and UA78L05) to examine the effect of thermal and electrical overstress ageing stresses on the developed ICIM-CI models. The DPI experiments were carried out on both fresh and aged ICs. Two different samples of both L78L05 and UA78L05 were aged inside the climatic chamber to accelerate the rate of internal degradation mechanisms (i.e., HCI or/and NBTI) under the combined impact of the defined thermal stepstress and electrical overstress conditions.

The PDN model was developed using the S-parameter measurement and the corresponding input impedance profile of each considered fresh and aged samples. It was found that the PDN model was unaffected by ageing due to observing no variation in the R, L, and C values of the passive elements included in the model.

Before and after the accelerated ageing of the ICs, DPI tests were performed in nominal conditions and measurements were recorded in nominal conditions to extract the look-up table for constructing the IB blocks of individual samples. It was discovered that the ageing reduces the P trans level, resulting in a significant effect on the IB block of both L78L05 and UA78L05 examined samples. Hence, ageing caused by performing the SSADT at the defined stress conditions decreased the conducted immunity of the considered ICs in a given frequency range, with UA78L05 having a higher mean standard deviation of the P trans between fresh and aged samples than the L78L05. To account for the effect of ageing on the IB blocks of the ICIM-CI models of the IC samples under test, the modified P trans values as a function of frequency should be updated in the look-up tables by applying statistical deviations of the ageing immunity drift.

Fig. 1 .

 1 Fig. 1. Accelerated ageing test set-up (a) outside view; (b) inside view of the climatic chamber.

Fig. 2 .

 2 Fig. 2. Ageing impact on the conducted immunity profile of IC samples under same thermal stress and (a) low electrical overstress (i.e., 9 V); (b) high electrical overstress conditions (i.e., 12 V).

Fig. 3 .

 3 Fig. 3. Influence of the ageing on the conducted immunity drift of the tested ICs.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Influence of the ageing on the input impedance profile of V in of the selected ICs.

  Table I provides information on the accelerated ageing test plan, which

TABLE I DESIGN

 I OF THE ACCELERATED AGEING TEST PLAN

ACKNOWLEDGMENT

This work is carried out in the framework of a PhD thesis in collaboration between the LARIS laboratory of the "University of Angers" and the "ESEO School of Engineering". This research is co-financed by the Region Pays de la Loire and the University of Angers.


Tommaso P Fraccia
email: tommaso.fraccia@unimi.it

Nicolas Martin
email: nicolas.martin@crpp.cnrs.fr

Non-enzymatic oligonucleotide ligation in coacervate protocells sustains compartment-content coupling

Modern cells are complex chemical compartments tightly regulated by an underlying DNA-encoded program. Achieving a form of coupling between molecular content, chemical reactions and chassis in synthetic compartments represents a key step to the assembly of evolvable protocells, but remains challenging. Here, we design coacervate droplets that promote non-enzymatic oligonucleotide polymerization and that restructure as a result of the reaction dynamics. More specifically, we rationally exploit complexation between end-reactive oligonucleotides able to stack into long physical polymers and a cationic azobenzene photoswitch to produce three different phases -soft solids, liquid crystalline or isotropic coacervates droplets -, each of them having a different impact on the reaction efficiency. Dynamical modulation of coacervate assembly and dissolution via trans-cis azobenzene photoisomerisation is used to demonstrate cycles of light-actuated oligonucleotide ligation. Remarkably, changes in the population of polynucleotides during polymerization induce phase transitions due to length-based DNA self-sorting to produce multiphase coacervates. Overall, by combining a tight reaction-structure coupling and environmental responsiveness, our reactive coacervates provide a general route to the non-enzymatic synthesis of polynucleotides, and pave the way to the emergence of a primitive compartment-content coupling in membrane-free protocells.

Introduction

Living cells are sophisticated compartmentalized chemical systems. From that perspective, the bottom-up assembly of chemically reactive soft micro-compartments represents a first step to the de novo construction of primitive life-like systems. [START_REF] Szostak | Synthesizing life[END_REF][START_REF] Mann | The origins of life: old problem, new chemistries[END_REF] Due to their membranous structure, lipid-bounded vesicles have been extensively studied as rudimentary cell-like compartments able to host various reactions, [START_REF] Szostak | Synthesizing life[END_REF] from prebiotically relevant templated nucleotide condensation [START_REF] Adamala | Non-enzymatic template-directed RNA synthesis inside model protocells[END_REF] to gene-directed cell-free protein expression. [START_REF] Kurihara | Self-reproduction of supramolecular giant vesicles combined with the amplification of encapsulated DNA[END_REF] Membrane-free droplets produced by complex coacervation between oppositely charged polyions have recently received increasing attention as viable alternative protocells [START_REF] Koga | Peptide-nucleotide microdroplets as a step towards a membrane-free protocell model[END_REF][START_REF] Pir Cakmak | Prebiotically-relevant low polyion multivalency can improve functionality of membraneless compartments[END_REF][START_REF] Martin | Dynamic synthetic cells based on liquid-liquid phase separation[END_REF] and surrogates of intracellular biomolecular condensates. [START_REF] Yewdall | Coacervates as models of membraneless organelles[END_REF] Coacervates assemble from a diversity of species, including prebiotically plausible molecules, [START_REF] Pir Cakmak | Prebiotically-relevant low polyion multivalency can improve functionality of membraneless compartments[END_REF][START_REF] Martin | Fatty acid vesicles and coacervates as model prebiotic protocells[END_REF] guide the interfacial assembly of lipid membranes, [START_REF] Tang | Fatty acid membrane assembly on coacervate microdroplets as a step towards a hybrid protocell model[END_REF][START_REF] Pir Cakmak | Phospholipid membrane formation templated by coacervate droplets[END_REF] can organize into multiple sub-compartments [START_REF] Lu | Multiphase complex coacervate droplets[END_REF][START_REF] Mountain | Formation of multiphase complex coacervates and partitioning of biomolecules within them[END_REF][START_REF] Karoui | Self-programmed enzyme phase separation and multiphase coacervate droplet organization[END_REF] and be formed and dissolved in response to physical and chemical stimuli [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF][START_REF] Aumiller | Phosphorylation-mediated RNA/peptide complex coacervation as a model for intracellular liquid organelles[END_REF][START_REF] Nakashima | Reversible generation of coacervate droplets in an enzymatic network[END_REF][START_REF] Deng | Programmable ATP-fueled DNA coacervates by transient liquid-liquid phase separation[END_REF][START_REF] Donau | Active coacervate droplets as a model for membraneless organelles and protocells[END_REF][START_REF] Späth | Molecular design of chemically fueled peptide-polyelectrolyte coacervate-based assemblies[END_REF][START_REF] Donau | Phase transitions in chemically fueled, multiphase complex coacervate droplets[END_REF] Owing to their lack of a membrane, liquid-like nature, low internal polarity and high local charge density, [START_REF] Yewdall | Coacervates as models of membraneless organelles[END_REF] coacervate microdroplets also spontaneously uptake and accumulate various guest solutes by partitioning, [START_REF] Martin | Selective uptake and refolding of globular proteins in coacervate microdroplets[END_REF][START_REF] Beneyton | High-throughput synthesis and screening of functional coacervates using microfluidics[END_REF] including nucleotides, RNA and divalent ions. [START_REF] Frankel | Polyamine/nucleotide coacervates provide strong compartmentalization of Mg 2+ , nucleotides, and RNA[END_REF] This local up-concentration has been shown to accelerate or enhance otherwise slow or inefficient enzyme reactions, [START_REF] Sokolova | Enhanced transcription rates in membrane-free protocells formed by coacervation of cell lysate[END_REF][START_REF] Crosby | Stabilization and enhanced reactivity of actinorhodinpolyketide synthase minimal complex in polymer-nucleotide coacervate droplets[END_REF][START_REF] Chen | Construction of coacervate-in-coacervate multi-compartment protocells for spatial organization of enzymatic reactions[END_REF] and been exploited to design coacervates capable of supporting ribozyme catalysis, [START_REF] Drobot | Compartmentalised RNA catalysis in membrane-free coacervate protocells[END_REF][START_REF] Poudyal | Template-directed RNA polymerization and enhanced ribozyme catalysis inside membraneless compartments formed by coacervates[END_REF] offering new hypothesis for the RNA world scenario. Yet, whether coacervate droplets can favour or guide simpler chemical reactions without the need of complex catalytic macromolecules and machineries remains elusive, as non-enzymatic reactions in coacervate droplets are still largely unexplored. [START_REF] Abbas | A short peptide synthon for liquid-liquid phase separation[END_REF][START_REF] Wee | Photoswitchable single-stranded DNA-peptide coacervate formation as a dynamic system for reaction control[END_REF] In a recent study, the lower internal polarity of peptide coacervates, in addition to increased local concentration effects, have been suggested to play a role in promoting aldol reactions and hydrazone formation. [START_REF] Abbas | A short peptide synthon for liquid-liquid phase separation[END_REF] However, non-enzymatic polymerisation reactions, which are critically relevant to the abiotic emergence of functional biopolymers such as polynucleotides, [START_REF] Adamala | Non-enzymatic template-directed RNA synthesis inside model protocells[END_REF][START_REF] Ferris | Synthesis of long prebiotic oligomers on mineral surfaces[END_REF][START_REF] Rajamani | Lipid-assisted synthesis of RNA-like polymers from mononucleotides[END_REF][START_REF] Mast | Escalation of polymerization in a thermal gradient[END_REF][START_REF] Attwater | Ice as a protocellular medium for RNA replication[END_REF] have not been demonstrated to date in complex coacervate droplets.

Carbodiimide-activated oligonucleotide ligation has recently been achieved in concentrated liquid crystalline DNA phases produced by segregative liquid-liquid phase separation (LLPS) with the uncharged poly(ethylene glycol) (PEG) polymer. [START_REF] Nakata | End-to-end stacking and liquid crystal condensation of 6-to 20-base pair DNA duplexes[END_REF][START_REF] Fraccia | Liquid crystal ordering and isotropic gelation in solutions of four-base-long DNA oligomers[END_REF][START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF][START_REF] Todisco | Nonenzymatic polymerization into long linear RNA templated by liquid crystal self-assembly[END_REF] Unlike coacervates, these aqueous two-phase systems only form at elevated concentrations of polymer species (typically 100-400 g.L -1 vs. 1-2 g.L -1 for coacervates), which limits their relevance as protocells, and significantly differ in composition and properties from complex coacervates, in which high concentrations of polyions can drastically affect the hosted reactions. For instance, aqueous two phase systems formed with the neutral PEG and dextran polymers were shown to enhance ribozyme catalysis due to increased local concentrations, [START_REF] Strulson | RNA catalysis through compartmentalization[END_REF] yet, the same reaction was drastically reduced in complex coacervates due to undesirable ion pairing with polycations, which required careful optimization of the coacervate composition. [START_REF] Drobot | Compartmentalised RNA catalysis in membrane-free coacervate protocells[END_REF][START_REF] Poudyal | Template-directed RNA polymerization and enhanced ribozyme catalysis inside membraneless compartments formed by coacervates[END_REF] To elucidate the interplay between associative LLPS and oligonucleotide polymerization, coacervates with different and controllable internal organization are highly desirable. Liquid crystalline coacervates droplets assembled from oligonucleotides and poly-Lysine have recently been reported, 41- 43 but are not compatible with condensation reactions due to cross-reactivity of polyamines with carbodiimide. We also recently designed light-responsive DNA coacervates assembled from random polynucleotide sequences and a cationic photoswitch on which the positive charge was provided by a non-reactive quaternary ammonium. [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF][START_REF] Lafon | Reversible photocontrol of DNA coacervation[END_REF] Building upon these observations, we here aimed at assembling reactive oligonucleotide coacervates with controllable internal order to rationalize the impact of the latter on non-enzymatic DNA ligation. Since the formation and stability of complex coacervates are intrinsically related to the length, flexibility or charge density of their scaffold polyions, [START_REF] Spruijt | Binodal compositions of polyelectrolyte complexes[END_REF][START_REF] Vieregg | Oligonucleotidepeptide complexes: phase control by hybridization[END_REF] we also intended to investigate the effect of in situ polynucleotide elongation on the properties of the coacervate droplets. Dynamically coupling in situ chemical reactivity and coacervate properties would indeed provide invaluable insights into the interplay between abiotic reactions and phase separation. [START_REF] Serrano-Luginbühl | Soft and dispersed interface-rich aqueous systems that promote and guide chemical reactions[END_REF] Here, we show that mixtures of end-stacking oligonucleotides and a molecular azobenzene cation orthogonal to carbodiimide chemistry produce three different phases depending on the ionic strength or light -soft solids, liquid crystalline or isotropic coacervates droplets -that significantly enhance chemical oligonucleotide ligation, with a marked phase-dependent reaction efficiency. We take advantage of light-mediated trans-cis azobenzene photoisomerisation to dynamically modulate the formation and dissolution of coacervate droplets and achieve light-actuated DNA ligation as a demonstration of temporal control over polynucleotide elongation in periodically changing environmental conditions. Excitingly, we last observe that changes in the length distribution of polynucleotides during in situ polymerization induce phase transitions of or within the coacervate droplets that dramatically alter their physical properties and structure. Overall, although the design of our system does not solely involve prebiotically relevant components, our complex coacervation platform offers a general approach to the non-enzymatic synthesis of polynucleotides from shorter oligomers by combining a tight reaction-structure relationship and environmental responsiveness, and paves the way to the emergence of compartment-content coupling in membrane-free protocells.

Results

Phase behaviour of end-to-end stacking oligonucleotides and azobenzene cations with salt and light Our experimental coacervate system was designed to exhibit a diversity of controllable phases while being orthogonal to carbodiimide chemistry. We chose to work with the light-responsive azobenzene cation trans-azobenzene trimethylammonium bromide (trans-azoTAB, Fig. 1a) that we recently used to produce photoswitchable DNA coacervates with polydisperse polynucleotides. [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF] The cationic charge on trans-azoTAB is provided by a non-reactive quaternary ammonium group to prevent any interference with the ligation reaction.

We first investigated the salt-dependent phase behaviour of charge-balanced mixtures of trans-azoTAB (5 mM) and the self-complementary DNA Dickerson dodecamer sequence (DD, 5'-CGCGAATTCGCG-3', 1.5 mg mL -1 , 5 mM nucleobase concentration), which hybridizes into blunt-end duplexes capable of liquid crystal ordering at high concentration [START_REF] Nakata | End-to-end stacking and liquid crystal condensation of 6-to 20-base pair DNA duplexes[END_REF][START_REF] Fraccia | Liquid crystal ordering and isotropic gelation in solutions of four-base-long DNA oligomers[END_REF][START_REF] Smith | Backbone-free duplex-stacked monomer nucleic acids exhibiting Watson-Crick selectivity[END_REF] (> 300 mg mL -1 , Fig. 1a). Optical microscopy images revealed the formation of solid-like precipitates in pure water (Supplementary Fig. 1), while soft solids or liquid-like microdroplets were observed when the ionic strength was gradually increased (Fig. 1b and Supplementary Fig. 2) due to the weakening of attractive electrostatic interactions, as reported for other coacervates. [START_REF] Fraccia | Liquid crystal coacervates composed of short double-stranded DNA and cationic peptides[END_REF][START_REF] Shakya | DNA local-flexibility-dependent assembly of phase-separated liquid droplets[END_REF][START_REF] Wang | The polyelectrolyte complex/coacervate continuum[END_REF] Interestingly, droplets prepared at intermediate salt concentrations exhibited a strong birefringence under crossed polarisers, with textures typical of columnar liquid crystalline phase (Fig. 1b, 200 mM, and Supplementary Fig. 3), while they appeared isotropic (ISO) at higher ionic strength (Fig. 1b, 350 mM). These observations were in line with the saltdependent formation of ISO or LC coacervate droplets recently reported in DD/poly-L-Lysine mixtures, [START_REF] Fraccia | Liquid crystal coacervates composed of short double-stranded DNA and cationic peptides[END_REF][START_REF] Jia | Liquid crystal peptide/DNA coacervates in the context of prebiotic molecular evolution[END_REF] where LC ordering was attributed to the supramolecular assembly of DD duplexes into long linear aggregates via end-to-end stacking. Here, inhibition of end-to-end interactions by the addition of TT overhangs at the 3'-terminus of the DD sequence prevented the formation of LC droplets (Supplementary Fig. 4), which confirmed that LC ordering required the supramolecular assembly of DD duplexes into long linear aggregates via end-to-end stacking (Fig. 1c). This observation also revealed that coacervate phases were intrinsically dependent on the oligonucleotide sequence. Fluorescence recovery after photobleaching confirmed the increase in the internal fluidity of the phases at increasing ionic strength (Supplementary Fig. 5). Coacervate microdroplets disassembled above a critical salt concentration (Fig. 1b and Supplementary Fig. 1, [NaCl] > 520 mM), indicating that electrostatic interactions were a driving force for DD/trans-azoTAB complexation. Addition of the 1,6hexanediol aliphatic alcohol or the water-miscible organic solvent DMSO also resulted in coacervate disassembly (Supplementary Fig. 6), pointing to the additional role of weak hydrophobic interactions for coacervate formation, such as azobenzene π-π self-stacking and trans-azoTAB intercalation between DNA base pairs, as reported previously. [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF] We also explored the influence of the azoTAB trans:cis molar ratio on the phases produced with DD at different salt concentrations. Equilibrium phase behaviour studies revealed that using lower fractions of trans-azoTAB favoured the formation of ISO coacervates at lower ionic strength in place of soft solids or LC coacervates, and resulted in lower critical salt concentrations for coacervate dissolution (Fig. 1d and Supplementary Fig. 7). These observations suggested that cis-azoTAB had a weaker interaction strength for DD compared to trans-azoTAB, as previously observed with longer double-stranded DNA (dsDNA), [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF][START_REF] Ny | Photoreversible DNA Condensation Using Light-Responsive Surfactants[END_REF][START_REF] Sollogoub | Photocontrol of Single-Chain DNA Conformation in Cell-Mimicking Microcompartments[END_REF][START_REF] Diguet | Photosensitive surfactants with various hydrophobic tail lengths for the photocontrol of genomic DNA conformation with improved efficiency[END_REF] which opened the possibility to navigate through the DD/azoTAB phases at fixed salt concentration using light (Fig. 1d). Indeed, when exposed to UV light, trans-azoTAB quantitatively isomerizes into cis-azoTAB, a process that can be reversed with visible light (Supplementary Fig. 8). As a result, we observed that LC and ISO coacervate microdroplets readily dissolved in a few seconds when exposed to UV light due to quantitative trans-cis azoTAB photoisomerisation, and reassembled into ISO droplets under blue light due to partial cis-trans azoTAB reverse photoisomerisation (Fig. 1e, Supplementary Fig. 9 and Supplementary Movies 1,2). This process was reversible and could be repeated several times without any apparent fatigue (Supplementary Fig. 10). In comparison, salt-free solid-like precipitates transformed into liquid-like ISO coacervate droplets under UV light but did not dissolve (Supplementary Fig. 9), as expected from the equilibrium phase diagram and similar to recently reported photo-controllable phase transitions in arylazopyrazole-conjugated oligonucleotide coacervates. [START_REF] Hidaka | Photo-controllable phase transition of arylazopyrazoleconjugated oligonucleotides[END_REF] Taken together, our observations show that charge-balanced mixtures of a selfcomplementary DNA dodecamer and trans-azoTAB produce ordered LC coacervate microdroplets at intermediate salt concentrations, which is attributed to the physical linear aggregation of blunt-ends oligonucleotides into longer stiff polynucleotides, together with possible contributions from azobenzene π-π self-stacking [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF] (Figs. 1a,c). In comparison, an isotropic coacervate phase is produced at higher ionic strength, presumably associated to disordered monomeric or short repeats of DD duplexes bridged together by trans-azoTAB (Fig. 1c). This behaviour is in line with the known concentration dependence for the reversible linear aggregation of end-to-end interacting oligomeric DNA duplexes, which undergoes a sharp discontinuous increase at the ISO-LC transition. [START_REF] De Michele | Self-assembly of short DNA duplexes: from a coarse-grained model to experiments through a theoretical link[END_REF] By changing the fraction of trans-and cis-azoTAB, light can also be used to modulate the internal organization of DD phases and ultimately induce coacervate dissolution.

Non-enzymatic oligonucleotide ligation depends on the internal coacervate structure

Quantitative measurements of the oligonucleotide concentration in the LC and ISO coacervate droplets revealed that ~90 mol% of DD strands were sequestered within the coacervate phase, corresponding to a local oligonucleotide concentration of ~480 ± 190 mg mL -1 in the ISO microdroplets (Supplementary Note 1). In comparison, the oligonucleotide concentration in the supernatant was 0.72 ± 0.3 mg mL -1 , so that a ~670-fold enhancement of DD local concentration in the ISO coacervates compared to the supernatant was observed. We sought to utilize this strong enrichment of DNA oligomers within coacervate phases to achieve in situ non-enzymatic oligonucleotide polymerisation, and study the influence of each phase on the ligation reaction. For this purpose, DD strands were functionalized with a 3' terminal phosphate group to produce end-reactive DDp oligonucleotides (5'-CGCGAATTCGCG-p-3') able to undergo covalent ligation, via a phosphodiester bond, upon activation with the water-soluble coupling agent 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride [START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF] (EDC, Supplementary Fig. 11). Due to its sensitivity to hydrolysis, a large molar excess of EDC compared to the reactive phosphate groups is typically required. [START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF][START_REF] Todisco | Nonenzymatic polymerization into long linear RNA templated by liquid crystal self-assembly[END_REF] Here, the contribution of EDC salt to the total ionic strength of the solution produced a similar solid-to-liquid transition as NaCl, and was therefore taken into account to produce the desired oligonucleotide/trans-azoTAB assemblies (Supplementary Fig. 12).

The outcome of the ligation reaction was first monitored after 24 hours in four representative DDp/trans-azoTAB samples prepared at varying NaCl but fixed EDC concentrations (soft solids: 80 mM EDC; LC coacervates: 100 mM NaCl + 80 mM EDC; ISO coacervates: 200 mM NaCl + 80 mM EDC; single phase: 400 mM NaCl + 80 mM EDC) using polyacrylamide gel electrophoresis (PAGE), and compared to the supernatant solution of the LC sample. The dense coacervate phase and supernatant were separated by centrifugation before PAGE analysis (see Methods). Our results revealed that oligonucleotide ligation occurred more efficiently in DDp-rich phases (soft solids and both types of liquid-like coacervates), as manifested by the appearance of a large distribution of oligomer bands in the polyacrylamide gels, compared to the diluted phases (single phase and supernatant) where it was very limited (Fig. 2a and Supplementary Fig. 13). Notably, the maximum degree of polymerisation, nmax, observed in the gels was significantly higher in DDp-rich phases (nmax, soft solids = 9; nmax, LC droplets = 12; nmax, ISO droplets = 6) compared to the single phase (nmax, single phase = 2) and dilute supernatant solution (nmax, supernatant = 2). More extensive investigations confirmed that ligation was also ineffective in samples prepared at higher salt (NaCl + EDC) concentrations (Supplementary Fig. 14), as expected from the lower coacervate volume phase produced near the critical coacervation salt concentration. We attributed such differences in reaction efficiency mainly to differences in the nature of DDp/trans-azoTAB phases, since NaCl addition has been shown to have minimal effect on EDC-activated DNA ligation. [START_REF] Obianyor | Towards efficient nonenzymatic DNA ligation: comparing key parameters for maximizing ligation rates and yields with carbodiimide activation[END_REF] Fluorescence intensity profiles of the gel scans were analysed more quantitatively by exploiting the approximate proportionality between electrophoretic mobility and logarithm of chain length [START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF][START_REF] Maniatis | Chain length determination of small double-and single-stranded DNA molecules by polyacrylamide gel electrophoresis[END_REF] (Fig. 2b). The cumulative weight fraction distribution, C(n), extracted from these profiles was well described by a simple Flory model for linear polymer condensation [START_REF] Flory | Molecular size distribution in linear condensation polymers[END_REF] (Fig. 2b and Supplementary Note 2), despite uncertainties in the quantitative information carried by the fluorescence profiles of the gels. This model allowed us to quantify and compare the polymerization yield, p, and the mean degree of polymerization, <n>, for the different conditions tested (Supplementary Note 3). We observed that both the polymerization yield and average degree of polymerization were the highest for LC coacervate droplets (p = 0.55 ± 0.01, <n> = 3.40 ± 0.10), then decreased for soft solids (p = 0.47 ± 0.01, <n> = 2.77 ± 0.07) and ISO coacervate droplets (p = 0.29 ± 0.01, <n> = 1.82 ± 0.04), and were the lowest for the dilute phase (p = 0.11 ± 0.01, <n> = 1.25 ± 0.01) and the supernatant solution (p = 0.06 ± 0.01, <n> = 1.13 ± 0.02). The same tendency for p and <n> was observed at different reaction times (Fig. 2c and Supplementary Fig. 15). The characteristic reaction time, τ, extracted from fitting of p vs. time using a catalysed step-growth polymerization model (Supplementary Note 4) was 9.0 ± 0.7 h, 4.5 ± 0.9 h, and 22 ± 4 h for soft solids, LC coacervates, and ISO droplets, respectively, corresponding to a 2-or 5-fold acceleration in LC coacervates compared to soft solids or ISO droplets, respectively. In addition, the products distribution gradually moved toward longer DNA sequences as a function of time while the fraction of unreacted DDp oligonucleotides (n = 1) decreased (Supplementary Fig. 16), so that different DNA populations were obtained after 24 hours in the different DDp-rich phases (Fig. 2d). On the contrary, in the dilute single phase the reaction produced only dimeric products, whose formation took place at early stages (τ = 2.9 ± 0.9 h) due to non-zero probability of a 5'-3' covalent bonding of an activated oligonucleotide with its hybridized strand.

Overall, these analyses confirmed that DD ligation was most enhanced in LC coacervates, followed by soft solids and ISO droplets. The enhanced reaction efficiency in the dense complexes compared to the supernatant was attributed to the higher local concentration of oligonucleotides in the condensates. Additional mechanisms contributing to the increased ligation efficiency in LC coacervates compared to soft solids or ISO droplets included stabilization of end-to-end supramolecular association of DNA oligonucleotides into organized repeats characteristic of the already ligated bases, [START_REF] De Michele | Self-assembly of short DNA duplexes: from a coarse-grained model to experiments through a theoretical link[END_REF][START_REF] Mangalath | Supramolecular assembly-enabled homochiral polymerization of short (dA)n oligonucleotides[END_REF] maintenance of stable proximity of the reacting termini, [START_REF] Maffeo | End-to-end attraction of duplex DNA[END_REF] and provision by the LC phase of a still fluid environment for transport and reaction. [START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF] Importantly, ligation experiments in coacervates assembled with non-stacking TT-terminated reactive DD duplexes (TT-DDp, Supplementary Table 1), which are unable to form LC droplets due to the non-pairing dangling ends (Supplementary Fig. 4), showed a poor reaction efficiency (Supplementary Fig. 17). In comparison, sticky end CG-terminated duplexes (12-CG, Supplementary Table 1), which end-to-end stacking propensity is favoured by base pairing, showed a similar coacervation and ligation behaviour as DD strands (Supplementary Fig. 18). These results indicated that ligation enhancement seemed to depend on the capacity of DNA duplexes to undergo linear aggregation, which we attributed to the associated proximity of the reactive groups. It is also worth noting that reaction yields in LC droplets were constantly higher than those observed in soft solids (Fig. 2c), confirming that the suppressed fluidity in the latter affected EDC diffusion and DDp reorganization, in turn reducing ligation efficiency, despite the likely higher concentration of oligonucleotides in such low-salt phase (Supplementary Note 1). Our results also reveal that DD oligonucleotide ligation was almost as effective in LC coacervate droplets as in segregated pure LC DNA phases, [START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF] suggesting that the reaction was not disrupted by ion pairing with azobenzene cations.

Oligonucleotide ligation is reversibly controlled with light

UV light-mediated dissolution of LC and ISO coacervate droplets resulted in the quantitative release of DD strands in the aqueous solution to give an oligonucleotide concentration of 1.50 ± 0.04 mg mL -1 (Fig. 3a), so that a ~320-fold enhancement of DD local concentration in the dark-adapted ISO coacervates compared to the UV-adapted homogeneous solution was observed. Reversibly, exposure to blue light led to the recapture of more than 80 mol% of oligonucleotides within the reassembled coacervate phase (Fig. 3a). These photoswitchable coacervates thus appeared as a viable platform to reversibly up-or down-regulate the local concentration of oligonucleotides using light, and in turn modulate the ligation reaction.

We therefore proceeded to demonstrate light-actuated ON/OFF oligonucleotide ligation. LC and ISO DDp/trans-azoTAB coacervate droplets prepared under reactive conditions were either stored in the dark for 48 hours, continuously irradiated with UV light, or exposed to cycles of UV and blue light, and polyacrylamide gel scans were performed over time to extract the reaction yield, p, and average, <n> degree of polymerization (Supplementary Fig. 19). Results revealed that UV lightexposed dilute DDp/cis-azoTAB samples exhibited a much lower oligonucleotide ligation efficiency compared to dark-adapted samples (Fig. 3b,c), and similar to that of reaction performed in diluted single phase at higher salt (Fig. 2c). More specifically, we observed that p, and <n> increased monotonously and rapidly for samples kept in the dark, with a stronger increase for LC coacervates compared to ISO droplets, as expected from the enhanced ligation efficiency associated to LC ordering, while UV-exposed samples showed a poor ligation efficiency (Fig. 3b,c and Supplementary Fig. 20). Remarkably, for samples exposed to cycles of UV and blue light, the reaction yield and degree of polymerization only increased under blue light conditions but remained almost constant during UV light exposure (Fig. 3b,c and Supplementary Fig. 20). These results therefore demonstrate that DD oligonucleotide ligation could be periodically modulated with light based on the reversible dissolution of coacervate droplets and the resulting change in the local oligonucleotide concentration. Interestingly, such an environmentally responsive transient compartmentalization could be particularly useful in overcoming the parasite problem. [START_REF] Matsumura | Transient compartmentalization maintains catalytically active RNA replicators and prevents functional collapse due to parasites[END_REF]

Oligonucleotide elongation produces phase transitions and multiphase coacervate droplets

Samples kept in the dark were further observed before and after a 24 hour ligation reaction. Optical microscopy images revealed that soft solids and LC coacervate droplets evolved towards crystallinelike assemblies after the reaction (Fig. 4a), which we attributed to the formation of long covalent polynucleotides that produced less fluid, more ordered complexes. [START_REF] Nakata | End-to-end stacking and liquid crystal condensation of 6-to 20-base pair DNA duplexes[END_REF] More surprisingly, ISO coacervates exhibited a multiphase droplet organization after ligation, as revealed by the presence of a newly formed birefringent coacervate sub-phase (Fig. 4a). Droplets doped with the DNA staining dye SYBR Gold further showed a brighter fluorescence within this phase compared to the surrounding coacervate layer (Fig. 4b and Supplementary Fig. 21), suggesting that the inner phase contained a higher nucleotide density. Time-dependent experiments further pointed to the gradual growth of this coacervate sub-phase over time (Supplementary Fig. 22), which correlated with the gradual advancement of the ligation reaction. After 96 hours, most of the droplets became completely birefringent and less spherical, with typical textures of columnar LC. Similar reaction-induced phase transitions were observed for sticky ends CG-terminated duplexes, with the formation of LC-in-ISO multiphase droplets (Supplementary Fig. 18). In comparison, control experiments using non-reactive DD oligonucleotides (Supplementary Fig. 22) or non-stacking TT-terminated reactive duplexes (Supplementary Fig. 17) did not undergo structural change over time.

These observations suggested that the coexistence of ISO and LC phases in coacervate droplets was driven by the gradual enrichment of the DNA population in long polynucleotides produced by DDp or 12-CG ligation, and their preferential partitioning in the columnar sub-phase (Fig. 4c). Such behaviour is consistent with the higher degree of order expected for long polynucleotides chains compared to shorter ones [START_REF] Nakata | End-to-end stacking and liquid crystal condensation of 6-to 20-base pair DNA duplexes[END_REF][START_REF] Fraccia | Liquid crystal ordering and isotropic gelation in solutions of four-base-long DNA oligomers[END_REF][START_REF] Smith | Backbone-free duplex-stacked monomer nucleic acids exhibiting Watson-Crick selectivity[END_REF] and with spontaneous phase separations predicted and observed in highly polydisperse LC forming DNA solutions. [START_REF] Sollich | Predicting phase equilibria in polydisperse systems[END_REF][START_REF] Bellini | Liquid crystal self-assembly of random-sequence DNA oligomers[END_REF] This hypothesis was corroborated by the observation that boundaries in the phase diagram of trans-azoTAB and the self-complementary 24mer oligonucleotide DD2 (in which the DD sequence was repeated twice: 5'-CGCGAATTCGCGCGCGAATTCGCG-3') were shifted to higher ionic strength compared to DD (Fig. 1d), so that LC coacervates rather than ISO droplets were produced at 350 mM NaCl for DD2/trans-azoTAB, and a higher critical coacervation salt concentration was observed compared to DD/trans-azoTAB. Length-dependent phase transitions are peculiar of the LC nature of this coacervate system, since longer DNA duplexes order at lower concentration, [START_REF] De Michele | Self-assembly of short DNA duplexes: from a coarse-grained model to experiments through a theoretical link[END_REF] while the increase in coacervate stability with polymer length is well established, [START_REF] Spruijt | Binodal compositions of polyelectrolyte complexes[END_REF] and has been observed in oligonucleotide coacervates. [START_REF] Shakya | DNA local-flexibility-dependent assembly of phase-separated liquid droplets[END_REF][START_REF] Vieregg | Oligonucleotidepeptide complexes: phase control by hybridization[END_REF] In addition, multiphase coacervation has been shown to occur when two coacervate systems with sufficiently different critical coacervation salt concentrations are mixed together at lower ionic strength, a condition under which droplets with a sufficient difference in density and surface tension are formed. [START_REF] Lu | Multiphase complex coacervate droplets[END_REF][START_REF] Mountain | Formation of multiphase complex coacervates and partitioning of biomolecules within them[END_REF] Accordingly, mixtures of DD, DD2 and trans-azoTAB produced multiphase LC-in-ISO coacervate droplets containing birefringent columnar sub-domains at 350 mM NaCl (Supplementary Fig. 23), a condition at which DD alone formed uniformly isotropic coacervate droplets. The fact that LC subdomains are prevalently fully engulfed in the ISO coacervate phase indicates that the surface tension of the inner LC phase (γLC) is higher than the surface tension of the outer ISO phase (γISO) and than the surface tension between the two phases (γISO-LC). This in turn can be understood on the basis of the density difference between the interfacing phases ρLC > ρISO >> ρS, corresponding to the density of LC droplets, ISO droplets and supernatant, respectively.

We last undertook microscopy observations of ISO coacervates subjected to cycles of UV and blue light (Fig. 4d). We observed that the coacervate subdomains produced after 24 hours were smaller than those formed in samples kept for 24 hours in the dark, as expected from the lower ligation yield during light cycling. Notably, when the multiphase droplets were re-exposed to UV light, only the outer ISO phase disassembled while the LC coacervate subdomains no longer dissolved (Fig. 4e and Supplementary Movie 3). We attributed this lack of dissolution to the increased stability of phases produced with longer polynucleotides, as suggested by the partial phase diagram of trans-azoTAB and DD2 compared to DD (Fig. 1d). These undissolved domains subsequently acted as seeds to localize the re-growth of the outer ISO coacervate phase when samples were exposed to blue light (Fig. 4f and Supplementary Movie 4). These results open promising perspectives for selecting the most stable subphases and for reshuffling ligation substrates around coacervates seeds during light cycles (Fig. 4g). The survival of the LC core could also allow to establish compartments lineages, if compartment filiation could be performed, which would open new possibilities far beyond transient compartmentalization.

Discussion

In conclusion, we show that charge-balanced mixtures of an end-to-end stacking oligonucleotides, the Drew-Dickerson dodecamer, and an amphiphilic cationic azobenzene photoswitch produce a rich ensemble of phase-separated complexes, including soft solids, LC and ISO coacervate droplets, depending on oligonucleotide length, azobenzene photoisomerisation and ionic strength. These chemically-enriched phases provide a favourable environment for the non-enzymatic ligation of endreactive oligonucleotides via carbodiimide chemistry, so that long polynucleotides are produced in situ, while the condensation reaction is only poorly effective in the dilute supernatant or in the absence of coacervates. Significantly, polymerization yields are strongly correlated with the nature of the phase in which it occurs, with a markedly increased reaction yield in LC coacervates compared to soft solids or isotropic droplets, indicating that a combination of fluidity and order, typical of liquid crystals, is critical for DD oligonucleotide ligation. Reversible modulation of the assembly and dissolution of coacervate droplets based on light-switchable azobenzene isomerization provides temporal modulation over the ligation reaction in periodically changing environmental conditions, which, if extended to other sequences, could open perspectives for the sequential incorporation of different oligonucleotides along the synthesized polynucleotide chain as a first step towards the emergence of sequence-defined DNA strands. Remarkably, the phase-dependent growth of the DNA population towards longer polymers during DD ligation induces structural changes to the compartments themselves, such as the onset of multiphase organization and gradual ISO-to-LC coacervate transition. Such a correlation between compartment structure and in situ reactions offers a promising platform for compartment-content coupling in protocells. Since coacervates composed of longer polymers are more stable than those made of shorter ones [START_REF] Spruijt | Binodal compositions of polyelectrolyte complexes[END_REF] and LC coacervates are more stable than ISO ones upon increase in salt and temperature, [START_REF] Fraccia | Liquid crystal coacervates composed of short double-stranded DNA and cationic peptides[END_REF][START_REF] Jia | Liquid crystal peptide/DNA coacervates in the context of prebiotic molecular evolution[END_REF] a positive feedback may also arise, where oligomer elongation stabilizes the compartment, in turn enhancing elongation. The enhanced ligation and phase transitions reported here strongly depend on the capacity of the model DD sequence to form LC phases. In particular, TT-terminated DD duplexes that are unable to undergo end-to-end stacking due to the nonpairing dangling ends, show poor ligation efficiency in coacervates. In comparison, CG-terminated duplexes, which linear aggregation is favoured by base pairing, exhibit a similar behaviour as DD duplexes. Since many other oligonucleotides with structures compatible with end-to-end linear aggregation, including RNA, replicate the DD phase behaviour, [START_REF] Nakata | End-to-end stacking and liquid crystal condensation of 6-to 20-base pair DNA duplexes[END_REF][START_REF] Fraccia | Liquid crystal ordering and isotropic gelation in solutions of four-base-long DNA oligomers[END_REF][START_REF] Fraccia | Abiotic ligation of DNA oligomers templated by their liquid crystal ordering[END_REF][START_REF] Todisco | Nonenzymatic polymerization into long linear RNA templated by liquid crystal self-assembly[END_REF] it is likely that our results can be extended to other sequences.

Overall, this work highlights an unexplored approach to the restructuring of coacervate droplets via in situ enzyme-free oligonucleotide elongation, and reveals a strong connection between nucleic acid content and compartment morphology. If generalized to populations of different DNA sequences, these results could be expanded to the emergence of genotype-phenotype coupling in membrane-free protocells, where different DNA sequences (seen as genotype variations) would produce coacervates with different materials properties (seen as a rudimentary form of phenotype differentiation). Combined with self-replication strategies [START_REF] Adamski | From self-replication to replicator systems en route to de novo life[END_REF] and recently reported non-equilibrium coacervate growth-division processes, [START_REF] Ianeselli | Non-equilibrium conditions inside rock pores drive fission, maintenance and selection of coacervate protocells[END_REF] such a system could also open perspectives for a systems chemistry realization of Darwinian evolution in protocell populations with synergistic compartmentcontent reproduction mechanisms. [START_REF] Matsumura | Transient compartmentalization maintains catalytically active RNA replicators and prevents functional collapse due to parasites[END_REF]

Methods

Materials. Oligonucleotides were purchased from Integrated DNA Technologies as HPLC-purified, freeze-dried, annealed double-stranded oligomers (sequences are given in Supplementary Table 1); sodium chloride (NaCl) and water-soluble 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC) were purchased from Sigma-Aldrich; SYBR Gold nucleic acid stain was purchased from ThermoFischer Scientific; azoTAB was synthesized using a three-step reaction by azocoupling pethoxyaniline with phenol, followed by alkylation with dibromoethane then quaternisation with trimethylamine (see Supplementary Methods); denaturing polyacrylamide gels were prepared using gel stock solution from Roth; gel running buffer, 1 Tris-Borate Ethylenediaminetetraacetic acid (TBE) buffer, was prepared from 10 TBE from Roth.

Printed circuit board-mounted LEDs operating at 365 ± 4.5 nm (model M365D2) or 450 ± 9 nm (model M450D3) were purchased from Thorlabs, Inc. and adapted on a custom-made aluminium heat sink. The LEDs were controlled by a T-Cube LED driver that was purchased from Thorlabs, Inc.

Glass coverslips were functionalized with poly(ethylene glycol) brushes to avoid wetting of coacervate droplets. PEGylation was performed by incubation of ethanol-rinsed glass coverslips (0.13-0.17 mm thick) for 48 hours into a 10 mL toluene solution containing 500 μL of 3-[methoxy(polyethyleneoxy)propyl]tri-methoxysilane (90%, 6-9 PE units, abcr GmbH). Coverslips where subsequently rinsed with ethanol and water, and dried with compressed air before being assembled into an observation capillary chamber (as shown in Supplementary Fig. 24). Preparation of stock solutions. Stock solutions of double-stranded oligonucleotides were prepared at 25 mM (nucleobase concentration) by dissolving an appropriate amount of the freeze-dried oligonucleotide powder in nuclease-free Milli-Q water in an Eppendorf tube, and stored at 4°C. A 25 mM trans-azoTAB aqueous stock solution was prepared by dissolving an appropriate amount of the synthesized azoTAB powder in Milli-Q water in an Eppendorf tube, and the pH adjusted to 8 with NaOH (0.1 M) or HCl (0.1 M). The stock solution was stored in the dark at room temperature before use to ensure complete isomerisation to the trans state, and then protected from light during use by wrapping the tube with aluminium foil. Sodium chloride (NaCl) stock solutions were prepared at various concentrations (250 mM, 500 mM, 1 M, 2 M, 4 M); and fresh EDC stock solutions were prepared at 400 mM and 1 M concentration just before use.

Equilibrium phase behaviour studies. Complexes between DD and trans-azoTAB were prepared by mixing in the following order aliquots of aqueous stock solutions of trans-azoTAB (25 mM, pH 8), NaCl (250 mM -4 M), DD (25 mM nucleobase concentration) to reach final concentrations of 5 mM trans-azoTAB, 5 mM oligonucleotide (nucleobase concentration) and 0-800 mM NaCl. For studies at varying trans:cis-azoTAB molar ratio, we first mixed a UV-equilibrated cis-azoTAB stock solution (25 mM, kept under UV light for at least 30 minutes) and a dark-adapted trans-azoTAB stock solution (25 mM) to produce a mixed trans:cis-azoTAB stock solution (25 mM, pH 8) at the desired isomer ratio. This new stock solution was used to prepare samples containing different trans:cis-azoTAB molar ratios. In this case, observations were performed rapidly (< 30 minutes) to limit the spontaneous thermal relaxation of cis-azoTAB to trans-azoTAB in the dark (half-time of ca. 20 hours [START_REF] Martin | Photoswitchable phase separation and oligonucleotide trafficking in DNA coacervate microdroplets[END_REF] ), and make sure that the trans:cis-azoTAB molar ratio did not change during our observations. Samples were imaged ca. 15 minutes after formation by loading an aliquot of the suspension onto a custom-made PEG-functionalized capillary chamber. The complexes (aggregates or droplets) were left to settle for ca. 5 minutes on the glass coverslip before imaging. Optical microscopy imaging was performed on an inverted Leica DMI 4000B microscope using a ×63 oil immersion objective (HCX PL APO, 1.4 NA), images acquired using MicroManager (v1.4); and on an inverted Nikon Ti-U polarized microscope using a ×20 or ×50 objectives, images acquired using Nikon NIS Element AR (v5.30.03). UV or blue light irradiation was performed in situ on the optical microscope by using a CoolLED light source operating at 365 nm (UV) or 450 nm (blue), or a Nikon epifluorescence mercury lamp (OSRAM HBO 103 W/2) and Nikon DAPI and FITC filter cubes for UV and blue light, respectively. Images were processed using FIJI (ImageJ) software (v1.53f).

Turbidity measurements were also used to characterize the salt-and light-dependent phase behaviour of DD and azoTAB. Here, freshly made samples were added to a 384-well plate and incubated for ca. 5 minutes, then the absorbance at 700 nm was measured on a Molecular Device SpectraMax Paradigm microplate reader using SoftMax Pro software (v6.2.2) and a reference value (corresponding to 25 μL of pure water) subtracted. Cycles of UV and blue light were performed by irradiating the samples for 15 min using alternating UV and blue LED (Thorlabs, Inc): the samples were irradiated for 15 min under UV light using a LED operating at 365 nm, then the absorbance was measured and the samples were irradiated for 15 min under blue light with a LED operating at 450 nm, and the turbidity monitored at 700 nm after each irradiation.

Fraction of oligonucleotides in dense complexes vs. supernatant. The fraction of DD sequestered in LC and ISO coacervates vs. supernatant was measured by UV-vis spectroscopy after separation of azoTAB and DD by size exclusion chromatography. Typically, 30 µL of a suspension of trans-azoTAB/DD coacervate droplets was produced in an Eppendorf tube (5 mM nucleobase concentration, 5 mM trans-azoTAB, 200 or 350 mM NaCl for LC or ISO coacervates, respectively), and separated in three 10 μL-aliquots. One aliquot was equilibrated in the dark (10 min), another one was irradiated with UV light (10 min), and the last one was first exposed to UV light (10 min) followed by blue-light irradiation (10 min). Each sample was then centrifuged (10 min, 10 600 ×g), and the supernatant collected, supplied with 2 μL of 5M NaCl, and further irradiated with UV light to induce complete dissociation of any potential DD/azoTAB complexes. 10 µL of 1M NaCl were added to the initial tubes after supernatant removal (we observed that these tubes contained a sedimented bulk coacervate phase, for dark and blue light conditions), and the samples were further irradiated under UV light to induce complete dissociation of DD and cis-azoTAB. All samples were added to a PD10 desalting column (GE Healthcare) equilibrated with Milli-Q water to separate azoTAB and DD. Fractions containing only DD were collected and the concentration of oligonucleotide determined in each of them by UV-vis spectroscopy at 260 nm, using an extinction coefficient of 189,089 L mol -1 cm -1 for double stranded DD. [START_REF] Tataurov | Predicting ultraviolet spectrum of single stranded and double stranded deoxyribonucleic acids[END_REF] The total amount of DD in bulk coacervate phases and supernatant were determined from the concentration of DD in each fraction and the volume of the fractions (measured by pipetting).

Non-enzymatic oligonucleotide ligation conditions. Time-dependent oligonucleotide ligation experiments in the dark were performed in 0.2 mL Eppendorf tubes containing 10 µL of reaction solutions: 5 mM trans-azoTAB, 0.42 mM 3'-phosphate DNA 12-mer, DDp (corresponding to 5 mM negative charge concentration), 80 mM EDC, and 0, 100, or 200 or 400 mM NaCl for soft solids, LC and ISO coacervates formation or single phase, respectively. Before PAGE analysis, samples were centrifuged for 10 min at 5 000 ×g to ensure dense phase sedimentation, then 9 µL of supernatant were extracted by pipetting and transferred to 11 µL stop solution (composed of 1 µL of 4 M NaCl and 10 µL of 50 mM ethanolamine in water), while the remaining 1 µL at the bottom of the tube was diluted with 11 µL of stop solution. The same protocol was followed to perform ligation reaction for DD-TTp and 12-CGp oligonucleotides, except that: i) the initial DD-TTp concentration corresponding to 5 mM negative charge concentration was 0.36 mM; ii) 20, 80, 160 mM EDC were tested; iii) for 12-CGp soft solids, LC and ISO coacervates formation was obtained at 50, 150 and 250 mM NaCl, respectively. For different reaction times, samples prepared from the same initial solution were incubated in different tubes and stopped at decided time intervals. For reactions performed under varying light irradiation conditions (continuous dark, continuous UV or UV/blue cycles), the 10 μL reactive solutions were incubated in non-binding treated plastic surface 384-well plates (Corning 3544). To prevent evaporation in the well plates, samples were covered with 20 µL of mineral oil light (Sigma-Aldrich) and plates were sealed with adhesive PCR plate film (Biorad). UV or blue light irradiation was performed in situ on a Nikon Ti-U inverted optical microscope equipped with a ×2 objective, allowing the illumination of the full well area, by using a Nikon epifluorescence mercury lamp (OSRAM HBO 103 W/2) and Nikon DAPI and FITC bandpass filter cubes for UV and blue light (10 seconds exposure every 2 minutes), respectively. These light sources are far enough from the UV adsorption peak of DNA (260 nm) so that no degradation is expected. Reactions were stopped by addition of 2 μL 4M NaCl, to cause coacervates disassembly, and 20 μL of 50 mM ethanolamine solution. For different reaction times, samples prepared from the same initial solution were incubated in different wells and stopped at decided time intervals.

Polyacrylamide gel electrophoresis. Ligation products analysis were performed using 15% denaturing polyacrylamide gels (20 cm wide x 16 cm high) containing 8.3 M urea and run in 1× TBE for 3 hours at constant power of 32 W. Equal DNA masses from each sample, 0.5 μg, were loaded in the gels. Gels were stained with 1 SYBR Gold for 20 minutes with gentle agitation. Ladders used in gels were composed by an equal mass mixture of 12-, 24-, 48-and 96-mer DNA sequences, corresponding to 1-, 2-, 4-and 8-times repetitions of the DD sequence, respectively, unless otherwise specified. Uncropped gels are shown in a Source Data file (for gels shown in Figure 2) or at the end of the Supplementary Information (for gels shown in the Supplementary Information file).

Gel images analysis was carried out with FIJI (ImageJ) software (v1.53f) using a custom MATLAB (MathWorks) script. Estimations of the ligation products distributions from gel bands intensities were performed by measuring the profile peaks areas, normalized on the sum of the area of the peaks. Calculations of reactions yield were obtained by fitting the data with the cumulative products distribution obtained from Flory's theory for simple polymerization 57 (see Supplementary Notes 2 and 3) using OriginLab 2019 (v 9.6.0.172).

Sample imaging during ligation. Reactive samples were prepared by mixing 5 mM trans-azoTAB, 0.42 mM 3'-phosphate DNA 12-mer DDp (corresponding to 5 mM negative charge concentration) supplemented with 1× SYBR Gold, 80 mM EDC, and 0, 100 or 200 mM NaCl for soft solids, LC and ISO coacervates formation, respectively. Samples were loaded in a custom-made capillary chamber (Supplementary Fig. 24) that was sealed with UV-curing glue (while protecting the samples from UV light exposure using foil). No evaporation was observed in the sealed chamber for up to 2 weeks. Samples were imaged at different times during the reaction on an inverted Leica DMI 4000B microscope using a ×63 oil immersion objective (HCX PL APO, 1.4 NA). Light cycling during ligation was performed using the in situ-mounted CoolLED and appropriate band pass filters to select the irradiation wavelength (UV, 365 nm; blue, 450 nm). Confocal fluorescence microscopy imaging was performed on an inverted Leica DMI RE2 scanning laser confocal microscope. DD-TTp and 12-CGp samples were prepared following the same protocol, but without SYBR Gold addition, and imaged on an inverted Nikon Ti-E microscope using a ×60 objective (CFI S Plan Fluor ELWD ADL 60XC, 0.7 NA).

Fluorescence recovery after photobleaching.

Fluorescence recovery after photobleaching (FRAP) experiments were performed on a Leica DMI8 scanning laser confocal microscope equipped with a 25× water immersion objective (HC FLUOTAR L, 0.95 NA). Coacervate samples were prepared by doping DD solutions with 1:1000 Cy5-labelled DD oligomers (Integrated DNA Technologies). Images were analysed by the Leica LAS X software (v 3.5.7.23225). The normalized FRAP intensity IFRAP(t) was calculated as [S(t) -B(t)]/[C(t) -B(t)], where S(t), C(t) and B(t) are the fluorescence intensity measured in circular ROIs with same diameter (2-5 μm) inside the bleached coacervate area (sample, S), non-bleached coacervate region (control, C) and nonbleached supernatant (background, B). IFRAP(t) was fitted with a monoexponential growth function A.exp(-t/τ) to extract the fluorescent recovery time constant, τ.

Statistics and Reproducibility

Quantitative comparisons of ligation reactions were performed on samples from the same experiment and derived from analysis of lanes belonging to the same gel, or gels run in parallel when this was not possible. Gels replicas on two independent experiments were performed for all experiments to qualitatively confirm reproducibility. All shown micrographs are representative images of two different field of views of two independent experiments.

Figure 1 .

 1 Figure 1. Salt-and light-dependent phase behaviour of end-interacting oligonucleotides and azobenzene cations. a, Sequence and hybridization of the self-complementary DNA Dickerson dodecamer (DD) used in the study (left), chemical structure of trans-azoTAB and reversible photo-isomerisation to cis-azoTAB (right), and schematic representation of interactions involved in DD/trans-azoTAB complexation (middle). b, Bright-field optical microscopy images of charge-balanced mixtures of DD (5 mM nucleobase concentration) and trans-azoTAB (5 mM) prepared at different NaCl concentrations, as indicated, showing the formation of irregular soft solids (100 mM NaCl), liquid crystal (LC) coacervate droplets (200 mM NaCl), isotropic (ISO) coacervate droplets (350 mM NaCl), or absence of phase separation (550 mM NaCl). Scale bars, 20 μm. Insets show zoomed images of the white squared areas under 90° crossed polarisers. Scale bars, 10 μm. c, Schematic views of the selfassembled complexes produced at the different salt concentrations shown in b. d, Equilibrium phase diagram of charge-balanced mixtures of DD or DD2 (5 mM nucleobase concentration) and azoTAB (5 mM total concentration) at varying trans:cis fraction (for DD) and at 100% trans-azoTAB (for DD2) and at varying NaCl concentration. The complexes produced for each condition were characterized by optical microscopy (as shown in Supplementary Fig. 7) and classified as solid-like aggregates (dark grey), soft solids (light grey), LC coacervates

Figure 3 .

 3 Figure 3. Oligonucleotide ligation is reversibly controlled with light. a, Molar fraction of DD strands sequestered in ISO and LC coacervate droplets in the dark, under UV light, and under blue light (after exposure to UV light). The average value of three independent experiments (shown as black dots) is reported. Error bars represent the associated standard deviation. b,c, Polymerization yield, p, calculated from fitted product distributions (see Supplementary Notes 2 and 3) for reactive LC (b, 100 mM NaCl + 80 mM EDC) and ISO (c, 200 mM NaCl + 80 mM EDC) coacervate droplets kept in the dark (black dots) or under constant UV light (purple dots), or exposed to cycles of UV and blue light (cyan or green dots, solid line; purple regions show when UV light was on). Normalized data for UV/blue cycles (open dots, dotted line) was obtained by subtracting the contribution of ligation occurring during UV exposure measured in dilute samples constantly exposed to UV light. Yields were extracted by analysing samples from the same experiment (n=1) run in the same PAGE gel (except for constant UV exposure, whose gel was run in parallel) shown in Supplementary Fig. 19 using two fitting procedures, as detailed in Supplementary Note 3, and are reported as mean ± SD of the two values obtained from fits. Error bars thus represent errors associated to uncertainties in the fits used to extract the reaction yields. Solid lines for dark and UV conditions are fits using a catalysed step-growth polymerization model; other solid lines are guides to the eye. Source data are provided as Source Data file.

Figure 4 .

 4 Figure 4. Structural transformation of coacervates during DD oligonucleotide ligation. a, Bright-field optical microscopy images of charged-balanced reactive mixtures of DDp (5 mM nucleobase concentration) and trans-azoTAB (5 mM) prepared at different total ionic strength (soft solids: 80 mM EDC (top); LC droplets: 100 mM NaCl + 80 mM EDC (middle); ISO droplets: 200 mM NaCl + 80 mM EDC (bottom)) at t = 0 and after 24 hours, as labelled. Scale bars, 20 μm. Insets show the white squared areas under 90° crossed polarisers. Scale bars, 10 μm. b, Confocal fluorescence microscopy images of reactive ISO coacervate droplets (5 mM DDp nucleobase concentration, 5 mM trans-azoTAB, 200 mM NaCl + 80 mM EDC) doped with 1× SYBR Gold at t = 0 and after 24

Acknowledgements

We thank D. Cuvelier and F. Giavazzi for the use of their microscopes during parts of this study, P. Nghe laboratory at ESPCI for support for gel electrophoresis and M. Todisco for useful discussions. We are indebted to J.-P. Douliez, J.-C. Baret, T. Bellini and A. Griffiths for critical reading of the manuscript and stimulating discussions. T.P.F. is supported by a Junior Research Chair fellowship from IPGG

Data Availability

The data supporting the findings of this study are available within the article and its Supplementary Information. Numeric data underlying all plots and gels in the main publication are available as Source Data files. All other data is available from the corresponding author upon request. Source data are provided with this paper.

Code Availability

The MATLAB code used to analyse the gels can be found at https://github.com/tfraccia/gel_lane_analysis-code.

Author contributions

T.P.F. and N.M. conceived the project, designed and performed the experiments, undertook data analysis and wrote the manuscript.

Competing interests

The authors declare no conflict of interest.

(cyan), ISO coacervates (green) and no phase separation (orange). The fractions of cis-and trans-azoTAB produced under UV or blue light are also indicated (dashed vertical lines). e, Optical microscopy images of DD/trans-azoTAB ISO coacervate droplets prepared at 350 mM NaCl under blue light or UV light, as indicated. Scale bars, 20 μm. ). Solid lines show fits of C(n) data points using Flory's theory for linear polymer condensation (see Supplementary Note 2). c, Timedependent evolution of polymerization yield, p, for the different solutions prepared as in a (grey: soft solids, cyan: LC coacervates, green: ISO coacervates, orange: single phase, black: supernatant). Yields were extracted by analysing samples from the same experiment (n=1) run in the same PAGE gel (except for single phase, whose gel was run in parallel) shown in Supplementary Fig. 13 using two fitting procedures, as detailed in Supplementary Note 3, and are reported as mean ± SD of the two values obtained from fits. Error bars thus represent errors associated to uncertainties in the fits used to extract the reaction yields. Solid lines are fits using a catalysed step-growth polymerization model to estimate the characteristic reaction time, τ (see Supplementary Note 4). d, Weight fraction distributions, P(n), after 24 hours of ligation reaction in the different solutions prepared as in a (black: supernatant, grey: soft solids, cyan: LC coacervates, green: ISO coacervates, orange: single phase). Solid lines show fits of P(n) data points using Flory's theory for linear polymer condensation (see Supplementary Note 2). Source data are provided as Source Data files.