Liuba Mazzanti

Sébastien Doutreligne

Cédric Gageat

Philippe Derreumaux

Antoine Taly

Marc Baaden

Samuela Pasquali

What Can Human-Guided Simulations Bring to RNA Folding?

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

It is recognized that the function of many RNA molecules depends crucially on their threedimensional structures. These structures exhibit a wide diversity of architectures, often including non-canonical pairs as well as triplets and quartets with 145 different base-pairs, according to Leontis classification, found experimentally (RNA Basepair Catalog of the Nucleic Acids Database) [START_REF] Berman | The nucleic acid database[END_REF][START_REF] Leontis | The non-watson-crick base pairs and their associated isostericity matrices[END_REF]. Compared to proteins, the number of experimentally resolved RNA structures, is still very limited. In silico predictions can therefore help fill the gap between sequences and structures. In recent years three series of RNA structure predictions competitions (RNA-puzzles [START_REF] Cruz | Rna-puzzles: a casp-like evaluation of rna three-dimensional structure prediction[END_REF][START_REF] Miao | Rna-puzzles round ii: assessment of rna structure prediction programs applied to three large rna structures[END_REF][START_REF] Miao | Rna-puzzles round iii: 3d rna structure prediction of five riboswitches and one ribozyme[END_REF]) have highlighted how computer predictions are best when homology reconstruction is a viable route, when experimental information is available on local base pairing from chemical probing, and when the structure itself is mainly driven by Watson-Crick base-pairings. Predictions of structures stabilized by non Watson-Crick base pairs are still challenging, even when the sequence information is complemented by chemical probing data [START_REF] Miao | Rna-puzzles round ii: assessment of rna structure prediction programs applied to three large rna structures[END_REF].

The best prediction methods currently available are those based on fragment reconstructions [START_REF] Cheng | Modeling complex rna tertiary folds with rosetta[END_REF] and those including predictions of secondary structures first, followed by 3D motif assembly [START_REF] Parisien | The mc-fold and mc-sym pipeline infers rna structure from sequence data[END_REF]. Methods based on secondary structure predictions start by considering canonical base pairs, since they are the most abundant and stacks of canonical base pairs make up A-RNA 3D stems. Canonical base pairs are also the most well characterized for ∆∆G's, and can therefore be used for accurate thermodynamic predictions of duplex formations [START_REF] Turner | Nndb: the nearest neighbor parameter database for predicting stability of nucleic acid secondary structure[END_REF]. However, in a significant percentage of experimental RNA structures, non-canonical base pairs, triplets, quartlets, as well as pseudoknots, increase substantially the complexity of RNA 3D structures (in 28S rRNA 15% of in-stem pairs are non-canonical and ∼20% are long-range pairs or triplets). As a result, the combinatorial complexity of RNA increases sharply with sequence length: O(N 3 ) for secondary structures without pseudoknots [START_REF] Zuker | Optimal computer folding of large rna sequences using thermodynamics and auxiliary information[END_REF][START_REF] Nussinov | Fast algorithm for predicting the secondary structure of singlestranded rna[END_REF], and between O(N 4 ) and O(N 6 ) for secondary structures with pseudoknots [START_REF] Ruan | An iterated loop matching approach to the prediction of rna secondary structures with pseudoknots[END_REF][START_REF] Rivas | A dynamic programming algorithm for rna structure prediction including pseudoknots[END_REF]. All taken into account, RNA secondary structure prediction including pseudoknots has been shown to be NP-complete [START_REF] Lyngsoe | Rna pseudoknot prediction in energy-based models[END_REF].

A complementary strategy to bioinformatics approaches is that of building physical models by simulating the molecule's folding according to a force field. Physical models have the advantage that the base pairing space is naturally restricted by physically accessible conformations, allowing to consider an arbitrarily large set of possible base pairs and to generate all topologies with the same computational complexity. The limitation of physical models resides in the sampling of the conformational space even with the most advanced enhanced simulation techniques. In order to investigate large structural rearangements, like the ones involved in folding, a simplification of the system through coarse-graining is needed [START_REF] Xia | Rna 3d structure prediction by using a coarse-grained model and experimental data[END_REF][START_REF] Ding | Ab initio rna folding by discrete molecular dynamics: from structure prediction to folding mechanisms[END_REF][START_REF] Sulc | A nucleotide-level coarse-grained model of rna[END_REF][START_REF] Pasquali | Hire-rna: a high resolution coarse-grained energy model for rna[END_REF][START_REF] Cragnolini | Ab initio rna folding[END_REF]. Despite the fact that coarsegrained force-fields are still in their infancy, simulations can complement bioinformatic predictions by giving access to the dynamical and thermodynamical behavior of the molecule, and also by identifying possible alternative conformations, metastable states and kinetic traps [START_REF] Stadlbauer | Coarse-grained simulations complemented by atomistic molecular dynamics provide new insights into folding and unfolding of human telomeric g-quadruplexes[END_REF][START_REF] Cho | Assembly mechanisms of rna pseudoknots are determined by the stabilities of constituent secondary structures[END_REF][START_REF] Sulc | Modelling toehold-mediated rna strand displacement[END_REF].

Though more work is certainly necessary to achieve reliable RNA force fields, we present here an application of coarse-grained modeling coupled to interactive molecular dynamics (MD) simulations as a proof of principle of what can be accomplished when a user is given the opportunity to steer the system based on a reasonable force field. For most biomolecular systems, for which it is difficult to identify a limited set of descriptors able to capture the specificity of a given state, justifying why dihedral angle principal component analysis is often used to describe the energy landscape [START_REF] Zhang | Molecular mechanism of the inhibition of egcg on the alzheimer aβ1-42 dimer[END_REF], interactive simulations offer the possibility of exploiting the human ability to recognize patterns. Inspired by the excellent results of Foldit [START_REF] Cooper | Predicting protein structures with a multiplayer online game[END_REF] for predicting protein 3D structures and EteRNA [START_REF] Lee | Rna design rules from a massive open laboratory[END_REF] for predicting RNA secondary structures, which pioneered the coupling between the powers of computer predictions and the intuition of the human intellect, we have developed an open software combining interactive non-equilibrium molecular dynamics simulations with the HiRE-RNA force field for folding, unfolding or deforming structural models. Interactive simulations are performed with the in-house software UnityMol [START_REF] Lv | Game on, science -how video game technology may help biologists tackle visualization challenges[END_REF], which allows for the visualization of a MD trajectory in real time, allows the user to change the temperature, and to apply forces to selected particles through a variety of hardware devices, including the ubiquitous computer mouse.

As a first test of the effectiveness of our approach, we set up a participative experiment where 141 participants were asked to make RNA folding predictions using interactive simulations for 4 molecules of increasing length (22-47 nucleotides) and 3D complexity. The experiment was carried out in two successive rounds, with slight variations as detailed below. In this manuscript we present the basic ideas of the HiRE-RNA model and of interactive simulations, the setup of the experiment, and the prediction results comparing also with the performance of fully automatic computer simulations. The software and benchmark molecules used in the experiment are freely available on the HiRE-RNA contest page (https://hirerna.galaxy.ibpc.fr/).

Materials and Methods

We carry out interactive simulations by coupling UnityMol, a molecular visualization software for chemistry and biology, and the simulator MD engine implementing the HiRE-RNA force field [START_REF] Doutreligne | Unitymol: interactive and ludic visual manipulation of coarse-grained rna and other biomolecules[END_REF][START_REF] Sterpone | The opep protein model: from single molecules, amyloid formation, crowding and hydrodynamics to dna/rna systems[END_REF][START_REF] Chebaro | The coarse-grained OPEP force field for non-amyloid and amyloid proteins[END_REF][START_REF] Nguyen | Communication: Simulated tempering with fast on-the-fly weight determination[END_REF].

The HiRE-RNA coarse-grained RNA model

This description of the HiRE-RNA model corresponds to the explanations that all participants received prior to carrying out the experiment. The full presentation of the model can be found in [START_REF] Pasquali | Hire-rna: a high resolution coarse-grained energy model for rna[END_REF][START_REF] Cragnolini | Coarse-grained hire-rna model for ab initio rna folding beyond simple molecules, including noncanonical and multiple base pairings[END_REF]. HiRE-RNA is an implicit solvent, implicit ion model where each nucleotide is represented by 6 or 7 beads (see fig. 1 of SI) corresponding to the backbone heavy atoms P, O5', C5' and C4, C1' of the sugar, and to the center of mass of each of the aromatic rings of the bases (G1, G2, A1, A2, C1, U1). The force field of the model is composed of local interactions accounting for the local stereochemistry and an excluded volume interaction giving a physical size to the beads, and non-local interactions accounting for base pairing, base stacking and electrostatics. Local interactions are composed of an harmonic potential for bond lengths and for angles amplitudes, and a sinusoidal potential for dihedral angles. A fast-decreasing exponential function describes the excluded volume potential. Phosphate beads carry one negative charge each and have a repulsive interaction with each other. Both base pairing and stacking crucially depend on the relative positions and orientation of the bases. In order to recover the anisotropy of a base, from the model's isotropic particles, base planes are identified by the particles C1'-B1-B2 for purines and C4-C1'-B1 for pyrimidines. Both stacking and base-pairing can occur between any two bases of the system. The stacking potential is minimized when the distance between bases is close to an equilibrium distance, and when the planes are parallel and vertically aligned (see fig. 2 of SI). Base pairing occurs when two bases are side-by-side on the same plane and depends on the relative distance and orientation. To account for the multiple pairing possibilities of each base, equilibrium values depend on the bases' species and on their orientation. In the current model we account for 22 different possible pairs, including the two canonical pairs A-U and G-C, 8 pairs occurring between Watson-Crick sides of any two bases (all possibles with the exception of G-G), and 12 other pairs representing interactions involving also the Hoogsteen and Sugar edges of the base. The energy of each base pair is proportional to the number of hydrogen bonds forming the pair, that is 3 for G-C, and two or one for the other pairs according to the table in [START_REF] Cragnolini | Ab initio rna folding[END_REF]. The HiRE-RNA force field, as any coarse-grained force field for RNAs, is still evolving and suffers from the limitations of not having an explicit description for ions, of a parametrization yet to be extended to include thermodynamical and dynamical quantities and it has to be put to the test on larger and more complex systems than benchmark molecules. However, for the the experiment we present here, the goal was to have a plausible physical coarse-grained model, to which HiRE-RNA seemed adequate. Given the modular set-up of interactive simulations, the molecule's representation and force-field can be easily changed.

Visualization and user interaction through the UnityMol application

UnityMol is a molecular visualization software based on the Unity3D game engine [START_REF] Lv | Game on, science -how video game technology may help biologists tackle visualization challenges[END_REF]. It features molecule representations commonly found in the discipline and serves as an experimental platform to propose specialized methods (i.e. custom polysaccharides rendering [START_REF] Pérez | Three-dimensional representations of complex carbohydrates and polysaccharides-SweetUnityMol: A video game-based computer graphic software[END_REF]).

As coarse-grained models are not easily rendered on standard software, UnityMol was modified to generate appropriate and visually appealing representations. For HiRE-RNA, bases can be rendered through ellipsoids whose orientations correspond to those of bases' planes, as explained in the previous section. This makes it easier to visually detect stacking and possible base pairing. When connected to an interactive HiRE-RNA simulation, plots of selected energy terms over time yield a quantitative insight into the molecule's stability (Figure 5 SI). Using the computer mouse direct action on the simulation is possible. Force vectors are computed based on the selected atom and the current cursor displacement. These forces are transmitted to the simulation engine and added to the force field. This scheme offers a direct, almost instantaneous, visual feedback. More details about the functionalities of UnityMol and the web application are given in Supplementary Material.

Setting up an RNA folding challenge as participative experiment

Participants for this study involve two classes of third year college students majoring in biology. During the course of 2015 and 2016 interactive nucleic acids simulations have been integrated as a mandatory lab for the bioinformatics course, at Paris Diderot University. The course was the very first introduction to numerical tools for the study of biomolecules. During the semester, students received a two-hours lecture on the analysis of bimolecular structures including a light overview of structure prediction methods as well as a one-hour lecture on modeling of biomolecules and basic principles of molecular dynamics. All participants were therefore novice users of molecular simulation techniques and RNA structures. Since users were familiar only with the DNA double helix, but ignored the folding capabilities of single stranded nucleic acids, an overview of nucleic acids structures was given as introduction to the lab.

Users learned how to use UnityMol and interactive RNA simulations through two exercises of pulling open a double helix and reforming it, making observations on the different energy terms, with the local harmonic potential governing the response as the molecule is being pulled by an external force, while base pairing and stacking driving and stabilizing folding. Users were then given 3 hours to work on the HiRE-RNA folding challenge, having to fold four molecules of increasing complexity. The starting point of each exercise was a completely stretched conformation. Users could launch an interactive molecular dynamics simulation with Langevin dynamics for friction. The launching applet allowed to choose the temperature, which could then be changed by pausing the simulation and relaunching it with a different T value. Users were given the instruction to select up to five conformations that could correspond to the native structure for the molecule. Their selection was submitted to a server and entered in the competition. In 2015, evaluation of the RMSD structures with respect to the experimental ones was given to the users at the end of the competition, while in 2016 the server was indicating the score of the structure and RMSD, immediately upon submission, giving users a real-time assessment of the validity of their structures while performing the experiment. We will refer to the 2015 as the "non-feedback experiment" and to the 2016 as the "feedback experiment". Since the strategies adopted for the non-feedback experiment and the feedback experiment were different, we have analyzed both rounds separately. For our subsequent analysis, all submitted structures were recovered from the server as well as the full trajectories, that were physically recovered from each machine.

Four RNA molecules of increasing complexity

The four molecules consist of a simple hairpin, a hairpin with an asymmetric bulge, an Hpseudoknot, and a triple helix pseudoknot (fig. 1). 1F9L is a hairpin of 22 nucleotides including 6 canonical base-pairs, one Hoogsteen G-U pair, and two A-G pairs [START_REF] Rudisser | Solution structure of cobalt(iii)hexammine complexed to the gaaa tetraloop, and metal-ion binding to g.a mismatches[END_REF]. According to Leontis classifications all pairs are cis Watson-Crick/Watson-Crick (see SI for detailed list). 1N8X is a 36 nucleotides hairpin including one asymmetric bulge [START_REF] Lawrence | Structure of the intact stem and bulge of hiv-1 psi-rna stem-loop sl1[END_REF]. The native conformation is stabilized by 14 cis Watson-Crick/Watson-Crick base pairs, including one A-G pair adjacent to the bulge and one G-U pair in proximity of the hairpin loop. 2G1W is a 22 nucleotides simple pseudoknot composed of 7 canonical G-C base pairs [START_REF] Nonin-Lecomte | Nmr structure of the aquifex aeolicus tmrna pseudoknot pk1: new insights into the recoding event of the ribosomal trans-translation[END_REF]. 2K96 is a 47 nucleotides triple helix pseudoknot [START_REF] Kim | Solution structure and dynamics of the wild-type pseudoknot of human telomerase rna[END_REF]. It consists of a Watson-Crick double helix and of an A-rich dangling strand inserting into the WC helix groove and forming several stacked triplets. Overall, 21 base pairs, canonical and non-canonical, stabilize the native structure, including six triplets (five A-U-A and one C-G-A). These four sequences, starting from fully elongated states, were previously folded [START_REF] Pasquali | Hire-rna: a high resolution coarse-grained energy model for rna[END_REF][START_REF] Cragnolini | Ab initio rna folding[END_REF] by long non-biased simulated tempering (ST) and by replica exchange molecular dynamics (REMD) simulations coupled to HiRE-RNA. The simulation on 1F9L found the global free energy minimum at 3.2 Å from the experimental state, for 1N8X the deviation is 3.8 Å for 2G1W the deviation is 4.3 Å and for 2K96, the deviation is 4.3 Å.

Analysis of the participants' performance

We carried out two separate analyses to study the usefulness of interactive simulations in addressing the question of RNA folding. The first focuses only on the structures submitted by the users to the online server and wants to answer the question if a "naive" user is able to produce correctly folded structures and recognize them as such. The second analysis focuses on the full trajectories generated by each participant and wants to investigate how the molecule's conformational space is explored.

The two quantities used to compare submitted structures and trajectories to the native conformation are the RMSD, computed on all beads of the coarse-grained representation, and basepairing. For RMSD we have used a cutoff of 6 Å to detect structures corresponding to the native state. This value comes from our experience of previous simulations with HiRE-RNA at physiological temperatures where the RMSD can fluctuate of about 6 Å while preserving all correct base-pairs and fold. This criterion gives only a rough estimate of the correspondence between two structures, as even lower RMSD values do not necessarily imply correct stack or pairs. Base-pairs were considered formed if they have at least 10% of the maximal interaction energy between the two bases. For all trajectories we analyzed structures from frames taken every 4ps. We monitored the total internal energy given by the HiRE-RNA potential, which we then normalize with respect of the energy of the native structure, the overall number of base pairs as well as native base pairs. In order to better detect base pairs, we smoothed fluctuation using a moving window over several subsequent frames as described in [START_REF] Stadlbauer | Coarse-grained simulations complemented by atomistic molecular dynamics provide new insights into folding and unfolding of human telomeric g-quadruplexes[END_REF]. To give a more accurate, yet concise, description of the molecule's architecture we also looked at its topology starting from the list of detected base pairs, as defined in [START_REF] Gan | Exploring the repertoire of rna secondary motifs using graph theory; implications for rna design[END_REF][START_REF] Fera | Rag: Rna-as-graphs web resource[END_REF]. Details of the analysis procedure are given in Supplementary Material.

Results and Discussion

Participants predict a significant proportion of native folds

Overall participants submitted between 80 and 200 structures, depending on the molecule and on the year. Not all participants used all the 5 attempts at their disposal. A summary of the results of submitted structures is reported in Table 1 in which we present also, as reference, the predictions by two commonly used programs McSym [START_REF] Parisien | The mc-fold and mc-sym pipeline infers rna structure from sequence data[END_REF] and Vfold [START_REF] Xu | Vfold: a web server for rna structure and folding thermodynamics prediction[END_REF]. For each molecule, in SI we report the base pairing of the lowest RMSD structure proposed by the students next to the details of the base paring of the experimental structure.

The ratio of predicted structures of RMDS lower than 6 Å ρ, varies significantly with the molecule, with the best predictions, as expected, for the simple hairpin (1F9L), where almost half of the submissions correspond to the native state in the non-feedback experiment and one quarter in the feedback experiment, and for which the lowest RMSD structures in both experiment have base pairing identical to native. Molecule 2 (1N8X) was harder to predict than molecule 1 because of the asymmetric bulge in its middle region. Most submitted structures include 7 correctly paired bases (lower stem). Some structures predicted the correct base pairs but resulted in distorted overall shapes, bringing the RMSD to about 10 Å, and are therefore not included in ρ. Other high RMSD structures exhibit also a high number of non-native base pairs, and were folded into low-energy structures alternatives to the experimental configuration. The lowest RMSD structures have 9/14 native base pairs for the non-feedback experiment, and 10/14 for the feedback experiment. Molecule 3, 2G1W, has a markedly doubly-peaked distribution. The lowest peak corresponds to the formation of the two stems in the pseudoknot configuration, while the higher peak corresponds to only one of the stems being formed. This is in agreement with results from REMD simulations. Most structures predicted the formation of one of the stems and include also some non-native pairs, achieving alternative compact structures. They are mainly mismatched (non-canonical) hairpins. The lowest RMSD structures have 7/7 native base pairs for the non-feedback experiment and 4/7 for the feedback experiment. Given the size and complexity of molecule 4, we did not expect users to be able to fully predict Table 1: Submitted structures' statistics. For each round we report the total number of structures submitted by the participants (str.), the percentage ρ of structures with RMDS below 6 Å, the lowest RMSD among all submissions, and the approximate values of the first two peaks of the distribution in RMSD of all structures (the full distribution is visible in gray in fig. 2, horizontal histograms). * For 2K96 we give a looser definition of the percentage of success and we consider the number of structures exhibiting the native topology. As a reference we report also RMSD values of structures folded with the two bioinformatics programs McSym and Vfold accessible on-line. Values are averages computed over the 10 best structures according to the programs. For the two pseudoknots, McFold/MCSym was not able to predict the correct topology despite having allowed the search for H-shaped pseudoknots. Instead it proposed hairpins. VFold found the correct secondary structure but gave errors when attempting to build a 3D structures based on the pseudoknotted secondary structure, not finding suitable motifs. its structure. We were however interested in testing how far they could come in proposing a plausible structure with the correct topology. Both years 10 structures were submitted with RMSD between 11 and 12 Å and corresponded to the topology of the pseudoknot. Other structures included the WC helix but did not reach the folding into a pseudoknot, leaving a dangling end. The distribution in RMSD exhibits a small peak at 12 Å and is for the rest rather flat, showing how there wasn't an alternative structure found by the users, but all other proposed structures sampled widely the more or less unfolded states. The lowest RMSD structures are also the ones with the most native base pairs, with 9/21 native base pairs for the non-feedback experiment and 12/21 for the feedback experiment.

When we analyze submitted structures based on their internal energy, we systematically find some of the lowest RMSD and highest native base pairs structures among the 15 lowest energy submissions (Table 2). This is an encouraging results as in a blind prediction one would usually focus on the lowest energy structures. The combined results for both experiments show that simple molecules could be folded quickly and easily by a large portion of users, while molecules with more articulate structures are clearly harder to predict. Still, a significant portion of users were able to generate the native conformation and recognize it as such in about 30 minutes of interactive simulation. In addition, it was possible to generate alternative conformations and test them for stability. Even for very complex architectures such as the triple helix, some users were led to the intuition of the correct topology of the molecule. This is particularly remarkable as none of them had any prior experience with RNA structures other than double helices and hairpins.

The users' strategy in the feedback experiment was different than in the non-feedback experiment. Indeed the number of submissions in the feedback experiment is roughly twice as much as in the non-feedback experiment. The number of users being comparable in the two years, one can immediately observe that users in the feedback experiment submitted more structures than their non-feedback experiment colleagues. In the feedback experiment a significant percentage submitted structures have a high RMSD suggesting that users submitted one or two randomly chosen structures just to test how far they were from the correct solution and used this information for the pursuit of the challenge. It is interesting to notice real-time feedback does not seem to give any particular advantage in the prediction of the folded structure as it can be observed by the comparison of all statistical quantities in Table 1 between the non-feedback experiment and the feedback experiment. On the contrary, one can argue that results in the non-feedback experiment are better than those of the feedback experiment. This observation is reminiscent of the observation made with Foldit that players could move from one basin to another through their ability to ignore a quantitative score [START_REF] Cooper | Predicting protein structures with a multiplayer online game[END_REF].

Humans explore phase space more broadly than automated approaches

Having retrieved single trajectories from each user's machine, we have analyzed the full exploration of the conformational space of each simulation with the goal of understanding the contribution of interactive simulations over regular, enhanced sampling, simulations. Results were assessed after merging all trajectories together, keeping the distinction between the non-feedback experiment and the feedback experiment and comparing them to the results from REMD simulation performed on a computer cluster using 32 replicas, spanning from 250 to 500K. For REMD simulation we have analyzed the structures of one low temperature replica, corresponding to a temperature below melting where the native state is present, if not dominant. An example of a participant's single trajectory is presented in Supplementary Material (Figures 5 and6).

Sampling is focused on low energy conformational space

Figure 2 illustrates the distributions of internal energy vs. RMSD. Interactive simulations focus sampling on low energy conformational space. Most of the structures in the full trajectories are well above the native internal energy, however, structures picked by participants have lower energies as shown by the height of the gray peaks in population density (both for RMSD and energy) compared to the blue peaks extracted from full trajectories. For low RMSD structures these energies are close to native. Selected structures' energies are generally low because users spontaneously proceeded in a sort of simulated tempering by restarting the simulation at different temperatures. When they thought a structure was close to native, they stopped the simulation and relaunched it with a lower temperature to reduce fluctuations and perform small adjustments to the structure, with temperature lowered to as much as 10K. They then raised it back to room temperature on the refined structure to test for its stability.

In the non-feedback experiment, users sampled extensively different basins, including the exact native state for all molecules except the triple helix (2K96). In the feedback experiment, users sampled more uniformly the conformational space in RMSD and internal energy. This can be observed by the presence of several, well separated, population peaks in the plots of the non-feedback experiment, while a more uniform diagonal shade is observed for the feedback experiment. It appears that the instantaneous assessment provided in the feedback experiment led to a gradual decrease in RMSD, but prevented from exploring disconnected basins. This can explain why in the feedback experiment users were less successful at folding than in the non-feedback experiment. The details of the results vary from molecule to molecule. For 1F9L, in the non-feedback experiment users sampled extensively at least 3 different basins, as it appears from the three distinct peaks in population density, while they sampled more connected basins in feedback experiment, remaining further away from the native state. For 1N8X, the full trajectories of the non-feedback experiment remain globally at a higher internal energy than those of the feedback experiment, however in the non-feedback experiment users were able to reach lower energy states with a better correspondence to the native structure and select them as candidates for native. The same is true for 2G1W. Interestingly for this molecule, in the feedback experiment users did sample a basin at 6 Å RMSD corresponding to the native state, but they did not select these structures as possible native candidates. In the non-feedback experiment this region was less explored, but recognized as native by a dozen users. As a general trend, in the non-feedback experiment users explored more widely in energy. They seem to have sampled lower energy states than in the feedback experiment and have picked these states for their submission.

For comparison, trajectories from REMD simulations spend most of their time exploring the unfolded states and, despite the presence of low temperatures, do not minimize the energy as effectively as interactive simulations. Still, a peak corresponding to the native structure is clearly visible, even though it represents only a small fraction of the overall population and its internal energy is similar to other states.

Base pairing and topology measure native fold propensity

To assess whether an RNA structure is correctly folded it is important to consider also the base pairing network, and not simply at the RMSD. For the non-feedback experiment, which based on the previous analysis and discussion we consider the most interesting, we have analyzed the details of base pairing. Results are reported in fig. 3. For each molecule we looked at the overall number of base pairs, at the number of native base pairs and at two topological parameters allowing to compare the general features of the base pairing network to that of the native structure.

For all molecules we can observe that trajectories focused on configurations with a relatively high number of base pairs. This is particularly clear for 1F9L and 1N8X where we can observe a peak of the distribution of base pairs at values close to the native number of pairs (first column, vertical histogram in blue). The number of native base pairs however is low. Only a negligible percentage of all trajectories explore conformations with exactly the same base pairs as the native structure (second column), but, interestingly, these structures were chosen for submission and indeed correspond to the best predictions also in terms of RMSD. A possible explanation for the choice of the users comes from the observation of the stability of the molecule, which is not captured by the instantaneous structure they submitted. Indeed, native states are generally more stable than other states, as observed by our previous computer simulation studies for these same molecules, and users had the tendency to submit structures that remained stable for a while in the simulation. We can observe that for 1N8X and 2G1W one native stem is clearly explored in the trajectories. This corresponds to the lower stem for 1N8X, formed by 7 pairs, and one or the other of the stems of 2G1W, which can both be composed of 4 pairs. Trajectories of 2K96 explore configurations with a wide range of base pairs, with the number of native base pairs not exceeding 40%. There is not a clear peak of the distribution, but all options seemed to be explored rather uniformly.

The comparison of topological values (column 3) gives a measure of the extent to which the base pairing organization of generated structures (trajectories or submitted) corresponds to the native secondary structure. For 1F9L and 1N8X the topology explored in the trajectories, and even more so that of selected structures, corresponds well to the native topology, suggesting that most users focused on the hairpin as their prediction for the molecule's architecture. Indeed most trajectories focus on a topological parameter (λ, see SI) equal or close to native, and selected structures are very strongly peaked at the correct eigenvalue. If we consider dual graph topological parameters [START_REF] Fera | Rag: Rna-as-graphs web resource[END_REF], for 1N8X 17% of all trajectories and 33% of selected structures share the native values of number of vertices and second eigenvalue of the Laplacian matrix, indicating that the overall base pair organization and stem-loop organization of the explored configurations correspond to native. For 2G1W analysis of topological parameters shows that full trajectories focused on configurations of topologies different than the pseudoknot (indeed most users tried to form hairpins), however submitted structures were chosen also from conformations of the correct topology, as it is shown by a peak of the distribution for λ/λ 0 ∼ 1. For 2K96 the best predictions have the native value λ ∼ λ 0 , supporting the observation that even though the details of the structures are not predicted correctly the overall organization of submitted structures corresponds to native.

Interactive RNA folding open new opportunities

The fact that participants were quite successful in folding the four molecules and exploring phase space in a broad manner opens the prospect for applications. In research, such interactive simulations on unknown targets may provide complementary means to generate a pool of plausible structures. In combination with experimental data this can be a powerful tool to refine structural models. Teaching is another promising application area, as we noticed that many of the complex concepts associated to RNA conformational flexibility were quite naturally made aware to the participants. The interactive approach is also a wonderful tool for outreach activities.

A key question for research applications is whether one is able to select the correctly folded structures from the pool of all submissions. The current dataset suggests that structural clustering of the solutions combined with a low energy filter should lead to a good selection of candidate structures. In that context it should also be recalled that in some sense our experiment setup was not ideal, because the participants were only allowed quite basic tools, without 3D visualization of the structures nor use of 3D input devices that would facilitate the manipulation in space. Furthermore, available time for the experiment was limited. In particular for the more complex 2K96 molecule this limitation had an impact on what could be achieved. Another promising avenue for future extension would be to implement collaborative strategies whereby users would not only be able to work individually but also collectively. This is the route successfully taken by Foldit through the use of a scripting tool that allowed players to share their strategies [START_REF] Khatib | Algorithm discovery by protein folding game players[END_REF]. Furthermore, one could imagine several participants working on distinct parts of one molecule at the same time, or cross-checking each others' solutions. These preliminary results on molecular explorations by interactive simulations are encouraging especially if projected onto the direction of the use by the research community, where the average user would already have some prior knowledge of the possible motifs of nucleic acids systems and possibly modeling. One of the main directions of our continuing development of HiRE-RNA and UnityMol is to include different sources of experimental information. In the current simulation software, it is possible to include local restraints such as base-pairs, including information from secondary structure predictions, crystallographic data of subparts of the molecule, and preliminary NMR data. In a new version soon to be released, it will be possible to include the on-the-fly calculation of theoretical SAXS curves and compare them to a target curve as the simulation proceeds. The introduction of indirect experimental data to guide simulations has to be done with the awareness that a successful strategy is to explore very different regions of the conformational space, and not to focus on a restricted region of one single parameter. Indeed, the knowledge of a score with respect to a target structure, such as the RMSD in the feedback experiment appears to limit the conformational space that is explored by the users, which have then the tendency to remain a single region of good scores, instead of exploring more widely.

Conclusions and perspectives

The approach presented here fundamentally builds upon the interactive molecular dynamics family of approaches [START_REF] Delalande | Complex molecular assemblies at hand via interactive simulations[END_REF], yet provides many significant improvements, in particular the introduction of crowd sourcing aspects for harvesting user contributions. To our knowledge, this is the first large-scale participative experiment at a coarse-grained level of representation, whereas alternative approaches such as FoldIt focus on all-atom models. We previously demonstrated that the coarse grained level provides particular opportunities for interactive simulations [START_REF] Delalande | Complex molecular assemblies at hand via interactive simulations[END_REF]. In our approach, the physically sound simulation of the conformational dynamics is at the center of the experiment and it is guided by the user; in other folding challenges the user 3D puzzle is at the center of interest with limited contribution from modeling, mostly through instantaneous minimization. For our purpose, we extend the existing Interactive Molecular Dynamics (IMD) protocol with the possibility to steer simulation parameters such as temperature or to exchange experimental data used as additional constraint on the simulation. We provide several adapted real time analyses, such as live plots of relevant quantities to monitor the simulation, on-the-fly topology and secondary structure graphs as well as generation of experimentally relevant information, for instance a SAXS scattered intensity profile. Overall we propose an open design that others can build on for similar experiments, providing among others a convenient web application to harvest and manage participants' contributions.

The main result of our experiment was that through interactive simulations and a simplified representation of the molecule, "naive" users were able to successfully predict native RNA folds. The use of interactive non-equilibrium MD simulations, with the possibility of monitoring in real time certain features such as internal energies, not only allows the participants to explore the conformational space more widely and in different regions with respect to what is done by standard REMD computer simulations, but lead them to identify native-like structures and to explore more thoroughly their basins. The plurality of proposed structures is an advantage in folding predictions. Given the variability of experimental conditions that cannot be accounted for in simulations, the ability to quickly produce plausible alternative structures is indeed a valuable feature in the context of a real scientific research, in which the target structure is unknown and where possible conformations have to be selected based on their agreement with indirect experimental information. Submission of several different structures is also a winning strategy in RNA and protein folding competitions. Looking at all energy and base pairing plots together from non-feedback experiment, we observe that there is no straightforward correlation between energy and RMSD, nor between the number of base pairs and RMSD, yet the participants could reach a high success rate. Comparing the results from non-feedback experiment and feedback experiment, there is no increase of the success rate. This is surprising but expected since a single parameter is not sufficient to detect the native state. Participants were able, however to guide their molecules to native basins and to select native-like conformations, by acquiring chemical and physical intelligence that standard computer simulations based on the equations of motion, and energy calculations, do not have yet. This observation makes a strong argument for the pursuit of hybrid methods where the power of computers is combined with the creativity of humans.

With the amazing variety of RNA structures, are many more RNA folding challenges than those we presented here, biologically more interesting and more intriguing for predictions. However, our goal here was to demonstrate what naive users, with little background in nucleic acids structures and modeling, in just one day could go from learning to use the software to the proposing solutions in good agreement with experimental structures. Our ultimate goal is to provide this open software to experts in RNA structures and function, who are aware of the complexity of the structural details of single stranded nucleic acids, have a good knowledge of the NDB, and by intuition can test their ideas very rapidly without having to enumerate an excessively large number of conformations.

Figure 1 :

 1 Figure 1: The four molecules proposed to the participants for the folding challenge represented atomistically (left) and in the coarse-grained representation used in the actual experiment with UnityMol (center). The image on the right represents the lowest RMSD prediction made by the participants in the first round. 1F9L and 2G1W correspond well to the native structure with a low RMSD and the correct base pairing organization. 1N8X exhibits some non native base pairs. 2K98 has the correct overall shape, forming a triple helix pseudoknot, but deviates significantly in the local organization. The complete list of base pairs for the 4 molecules (native and predictions) is given in SI.

Figure 2 :

 2 Figure 2: Internal energy vs. RMSD distributions for all interactive simulations as well as for one REMD simulation. The population color coding for full trajectories goes from blue (low) to red (high), while values from individual submitted structures are superposed as gray circles. Internal energy at finite temperature is normalized with respect to the absolute value of the energy of the minimized native structure |E 0 |. RMSD distributions for both full trajectories (blue bars) and submitted structures (gray bars) are presented on the horizontal histogram, while energy distributions are presented on vertical histograms. The pink wedge in each PMF indicates the position of the native structure (RMSD = 0, E/|E 0 | = -1).

Figure 3 :

 3 Figure 3: Base pairs vs. RMSD analysis for the non-feedback experiment: number of detected base pairs (left), percentage of native base pairs (center), molecule's topology as defined by the second eigenvalue of the Laplacian matrix. Eigenvalues are normalized with respect to the second eigenvalue of the Laplacian matrix λ 0 for the native structure. In the central and right columns the pink wedge corresponds to the position of the native structure (RMSD=0, % native pairs = 100, λ 0 /λ 0,native = 1).

Table 2 :

 2 For each molecule we analyze the 15 lowest energy structures submitted by the users and we report the number of structures with low RMSD values and the number of structures with a high percentage of native base pairs. The choice of 15 lowest energy structures is arbitrary but is in the range of what is typically analyzed by prediction methods.

			non-feedback experiment		feedback experiment	McSym	Vfold
	Molecule str. ρ	lowest RMSD ( Å)	RMSD peaks ( Å)	str. ρ	lowest RMSD ( Å)	RMSD peaks ( Å)	RMSD ( Å) RMSD ( Å)
	1F9L	88	50% 2.0		4; 7		203 25% 2.1	6; 12	4.0	3.75
	1N8X	90	10% 4.5		5; 10		207 5%	2.6	8; 12	5.5	3.7
	2G1W	96	13% 3.8		6; 12		168 3%	5.7	8; 12	12.9	na
	2K96	74	13% * 11.4		11; 15		119 8% * 11.2	11; 15	33	na
					non-feedback experiment	feedback experiment
				Molecule	best rmsd		native BP	best rmsd	native BP
				1F9L	10/15 ≤ 5 Å 6/15 ≥ 0.75 12/15 ≤ 5 Å 7/15 ≥ 0.75
				1N8X	7/15 ≤ 6 Å	5/15 ≥ 0.75	4/15 ≤ 6 Å	3/15 ≥ 0.75
				2G1W	3/15 ≤ 6 Å	7/15 ≥ 0.75	2/15 ≤ 8 Å	8/15 ≥ 0.75
				2K96	6/15 ≤ 11 Å 5/15 ≥ 0.40 5/15 ≤ 12 Å 2/15 ≥ 0.40

Acknowledgements

We wish to thank all third year biology majors of 2015 and 2016 at Paris Diderot University for enthusiastically taking part in this experiment. We also wish to thank the first year students of "Frontières du Vivant" curriculum at Paris Descartes University as well as the MOOC students "Bases Moléculaires de la Vie" for also testing our interactive simulations software and folding challenge, helping us properly set up the experiment. L.M. was supported by the "Initiative d'Excellence" program from the French government, project "DYNAMO", ANR-11-LABX-0011-01. S.D. was supported by the French National Agency for Research, proposals "ExaViz" (ANR-11-MONU-003) and "GRAL" (ANR-12-BS07-0017).

Authors contributions

L.M. analyzed data and contributed to writing the paper, S.D. contributed the interactive simulation and visualization tools, developed the website, managed data collection and contributed to writing the paper, C.G. helped setting up the lab, P.D. contributed developing the coarse-grained model, wrote the MD simulation code and contributed to writing the paper, A.T. contributed in designing the in-class experiment, M.B. designed the simulation tools, contributed in designing the research set up and in writing the paper, S.P. designed the coarse-grained model, designed the research set-up and wrote the paper.


Rawan Khalaf

Andrea Viamonte

Etienne Ducrot

Rémi Mérindol

Serge Ravaine

Transfer of multi-DNA patches by colloidal stamping

Patchy particles have received great attention due to their ability to develop directional and selective interactions and serve as building units for the self-assembly of innovative colloidal molecules and crystalline structures. However, synthesizing particles with multiple dissimilar patches is still highly challenging and lacks efficient methods, these building blocks would open paths towards a broader range of ordered materials and their inherent properties. Herein, we describe a new approach to pattern functional DNA patches at the surface of particles, by use of colloidal stamps. DNA inks are transferred only at the contact zones between the target particle and the stamps thanks to selective strand-displacement reactions. The produced DNA-patchy particles are ideal candidates to act as advanced precision/designer building blocks to self-assemble the next generation of colloidal materials.

Introduction

Over the past decades, scientists have aspired to fabricate functional materials by colloidal self-assembly. 1 Although many beautiful examples of self-assembled colloidal molecules 2 or colloidal crystals 3 from particles with well-defined shapes and composition have been reported so far, colloidal systems cannot be targeted towards most of the sophisticated structures that Nature built. Indeed, the latter require encoding the building units with information to guide their self-assembly by programming their geometry as well as the directionality, valence, range of their pair interactions. Several strategies have been developed to address this challenge, including the attachment of molecules that recognize one another onto the surface of particles. 4 Among the wide range of binding groups that have been employed, synthetic DNA strands have been proven to be very versatile and promising as a tremendous number of orthogonal interactions can be programmed based on the design of nucleotide sequences, giving access to highly specific programmable interactions. DNA-coated particles have thus been extensively employed as building blocks for the selfassembly of clusters with precise symmetries 5 and crystalline lattices. 6 To further control both the valence of the particles and the directionality of the bonds they form with their partners, a number of groups have recently proposed strategies to regioselectively pattern particles with DNA patches. 7 Sleiman et al. successfully transferred DNA motifs from a parent 3D DNA template to gold 8 and polymeric nanoparticles. 9 Two-10 and three 11 -dimensional DNA origami structures were used as stamping platforms to transfer DNA inks onto gold nanoparticles. In both cases, the printed nanoparticles were released from the frame by a strand displacement reaction. 12 In order to create micron-sized particles with several dissimilar patches, we translate this strategy by using colloidal particles coated with DNA inks as stamps. The colloidal stamps can assemble with support colloids via DNA hybridization. The injection of eject strands allowed us to transfer the DNA inks at the contact zones between support and stamp particles (Fig. 1a) leading to patchy particles. We also take benefit of packing constraints to control the number of stamp particles that can park around the support ones 5a , which finally defines the number of transferred patches.

Experimental Synthesis of DNA-coated particles

Azidated 3-(trimethoxysilyl)propyl methacrylate (TPM) particles were prepared through the azidation of chlorine groups present at the surface of particles previously synthesized according to the protocol developed by Wang et al. 6e (see ESI). After synthesis the particles were imaged by TEM and SEM. Fig. S1 shows that they are spherical and monodisperse in size. Their surface is smooth, which has been shown to be required to allow an homogeneous distribution of DNA strands during the former step. 13 In order to functionalize monodisperse polystyrene (PS) particles with azide groups, we followed the protocol developed by Oh et al.,6d which relies on the physical entrapment of an azidated PS-b-PEO copolymer (PS-b-PEO-N3). For this, the PS particles are swollen with tetrahydrofuran (THF) to allow the PS block of the copolymer to penetrate in the PS particles (see ESI). After evaporation of the THF, the PS block of the copolymer is physically trapped in the PS particles while the PEO block and the terminal azide group form a brush at the surface, swollen by water and exposed to the surrounding media. Azidated particles were further functionalized with DNA following the protocol described by Wang et al. 6e that ensures a dense surface coverage of the colloids with DNA (see ESI). The process relies on the strain-promoted azide-alkyne cycloaddition (SPAAC) to graft DNA strands end-functionalized with a dibenzocyclooctyne moiety (DBCO) onto azide functionalized particles.

Characterization

Transmission electron microscope (TEM) images were taken using a Hitachi H600 microscope operating at an acceleration voltage of 75 kV. The samples for TEM observation were supported on conventional carbon-coated copper grids. Scanning electron microscope (SEM) images were taken using a Hitachi S4500 microscope at an accelerating voltage of 5 kV. Confocal fluorescence microscopy images were taken using a Leica SP2 confocal laser scanning microscope as well as a ZEISS LSM980 equipped with an Airyscan detector.

Results and discussion

DNA strands A and B (Table S1) have first been grafted onto azidated TPM and PS particles, respectively. The coated particles are referred to as TPMA and PSB. We then functionalized/inked the stamp TPMA particles with the Ink565 (see Table S1 for details) by adding a large excess of ink to a suspension of particles (Fig. 1b). The ink consists in two hybridized DNA strands, T-X-A* and X*565-B*, the latter being modified with the fluorescent dye Atto565. As the domain A* is complementary to the sequence A at the surface of the TPM particles, the ink sticks on their surface due to the formation of A/A* duplexes. The particles and strands were maintained in a buffer enriched in magnesium ions and at low temperature in order to strengthen the DNA duplexes and prevent strand migration (see ESI). The excess of ink was subsequently washed away by centrifugation/dispersion steps. As Ink565 is also complementary to strands B, the TPMA~Ink565 stamp particles were mixed with a 40:1 excess of PSB particles to form preferentially small clusters with only one TPMA particle at the core and PSB satellites (Fig. 1c). This ultimately maximizes the number of one-patch PS particles produced in the process. When the assembly is completed, Y*488-B* strands (labelled with Alexa488) are added to hybridize with the remaining B strands available on the PSB particles and passivate their surface (Fig. 1d). Fig. 2a shows that clusters made of one TPMA particle surrounded by PSB particles were obtained. A detailed analysis reveals that the number of PSB particles in the clusters varies from 1 to 7. Their relative amounts have been determined by statistical analysis performed over 100 clusters (Fig. 2c-i). Some rare clusters (~5 %) formed of one PSB particle in contact with two TPMA particles could be observed as well as a large amount of free PSA particles. Thanks to the density difference between TPM (1.2 g.cm -3 14 ) and PS (1.06 g.cm -3 ), we successfully removed most of these free PS particles (Fig. 2b) by sedimentation in a PBS based buffer solution of intermediate density (1.07 g.cm -3 ) prepared by mixing H2O and D2O (see ESI). The relative proportions of the different clusters remained unchanged during this purification stage, as indicated in Fig. 2ci, proving that the clusters are sufficiently robust and do not break during centrifugation. The final step to form patchy particles consists in disassembling the clusters formed by the stamp and support particles leaving the fluorescent part of the ink on the support particle only at the contact point between them. To do so, we injected the EjectX strand which binds to the toehold T of Ink565 and replaces the strand X*565-B*. This breaks the duplex X/X* that was holding the stamp and support particles and results in the release of the support particle, which still carries the red fluorescent strands X*565-B* at the former contact point with the stamp (Fig. 1e andS2). Fig. 2j and Movie S1 show that PS particles with one red fluorescent patch are mostly obtained, validating the developed strategy. Some non-patchy PS particles that were not completely removed by centrifugation and a few two-patch particles (~5 %), which result from the disassembly of the clusters in which one PS particle is in contact with two TPM particles are also observed. We firstly extended our strategy to prepare particles with multiple identical patches precisely located at their surface. To do so, we prepared clusters with different controlled morphologies by the random parking 5a of an excess of large PS spheres functionalized with DNA strands A and Ink565 on smaller TPM particles functionalized with DNA strands B. Due to packing constraints inherent in the ratio of radii between large and small spheres, only a fixed number of large spheres can park, leading to a population of clusters with well-defined coordination. When the assembly is completed, the Y*488-B* strands, complementary to DNA strands B, are added to passivate the surface of TPMB particles. Fig. 3a-c shows confocal images of the DNA-colloidal clusters obtained when TPM particles with a diameter of 1.1, 1.6, and 2 µm are employed, respectively. Different clusters made of one TPM core and different numbers of PS satellites are observed (Fig. 3d-g andS3). The relative proportions of each type of clusters obtained for different values of the size ratio α of PS/TPM, are listed in Table 1. One can note that when α is 4.39, clusters made of one or two PS particles attached to one TPM sphere are mainly formed. Decreasing α to 3.02 and 2.42 led to the formation of higher proportions of clusters containing 3 and 4 PS particles, as expected. Lastly, we further extended our strategy to prepare particles with multiple dissimilar patches. We first divided the PS particles into two batches, and coated one batch with Ink565 and the other with Ink647 (Table S1). The two batches were then mixed together and TPMB particles functionalized with B strands were added in a number ratio TPMB:PSA~Ink565:PSA~Ink647 of 1:20:20. The sample was kept in the fridge at 4 ℃ for 24 h to maximize the formation of clusters. Then, Y*488-B* strands were added to hybridize with the B strands outside of the contact zones and passivate the surface of the TPMB particles. Different clusters made of one TPM core and different numbers of PSA~Ink565 and PSA~Ink647 are observed (Fig. 4a-j). The relative proportions of each type of clusters are listed in Table 2. After injection of the eject strands EjectX and EjectZ in the clusters suspension, non-fluorescent PS particles and TPM particles with red and/or blue fluorescent patches are observed, proving the transfer of the fluorescent DNA from PSA~Ink565 and PSA~Ink647 (Fig. 4k and S6 and Movie S2). When we worked with three batches of PSA particles coated with Ink488, Ink565 and Ink647, respectively, and mixed them with TPMB particles in a number ratio TPMB:PSA~Ink488:PSA~Ink565:PSA~Ink647 of 1:13:13:13, we observed the formation of a few clusters made of one TPM particles surrounded by varying numbers of PSA~Ink488, PSA~Ink565 and PSA~Ink647 particles (Fig. 4l). After injection of EjectX, EjectY and EjectZ, TPM particles with red and/or blue and/or green fluorescent patches are observed, proving once again the efficiency of our approach (Fig. 4m and Movie S3).

Conclusions

In conclusion, we have synthesized micron-sized particles with one or several identical and distinct DNA patches by combining colloidal parking and the transfer of DNA strands at the contact zones with colloidal stamps thanks to strand-displacement reactions. Our strategy is versatile and can be extended to a gallery of hard particles and soft systems whose shape and size could be independently varied, opening the way to the synthesis of new DNA-patchy building blocks and the comprehensive study of their assembly into novel structures, such as alternating polymers or rings, dendrimers or gyroid crystals.

Fig. 1

 1 Fig. 1 General scheme and key steps. a) General schematic representation of the preparation of particles with DNA patches by colloidal stamping following sequentially the subsequent steps. b) Inking: the ink, formed by the association of T-X-A* and X*-B*, is hybridized at the surface of the bare stamp particle decorated with an A* DNA brush. c) Assembly: in the contact zone, formation of duplexes between the support particle decorated by B strands and the stamp thanks to the B* domain exposed by the ink. d) Passivation: the surface of the support particle, outside of the contact zone is passivated by hybridization between the B strands of the surface and Y*-B* strands. e) Eject: strand displacement reaction to separate the stamp from the support particle, leading to the formation of a X*-B* patch at the contact zone and the recovery of patchy particles exposing the stand Y* on the surface with patches of X*. f) Schematic representation of the DNA strands and assemblies used in this study.

Fig. 2

 2 Fig. 2 Confocal fluorescence microscopy images of clusters obtained by incubating 1.6 µm TPMA~Ink565 and 1.5 µm PSB particles in a 1:40 ratio a) before and b) after purification. c-i) Zoom on the different clusters containing 1 to 7 PS particles. Their relative amounts (in %) in the sample before/after purification are given at the top right corner of each image. j) Confocal fluorescence microscopy image of the patchy PS particles resulting from the strand-displacement disassembly of TPMA~Ink565~PSB clusters. Scale bar of 10 µm for a, b and j and 5 µm for c to i.

Fig. 3

 3 Fig. 3 Confocal fluorescence microscopy images of the clusters obtained by incubating TPMB and PSA~Ink565 in a 1:40 ratio followed by the addition of the Y*488-B* passivation strand. The diameter of the TPM particles is: a) 1.1 µm (α = 4.39), b) and d-g) 1.6 µm (α = 3.02), c) 2 µm (α = 2.42). h) Confocal fluorescence microscopy images (Alexa488, green channel; Atto565, red channel) with transmission microscopy (grey channel) of PSA~Ink565~TPMB & Y*488-B* (α = 3.02) clusters after strand displacement reaction using EjectX strand. i-l) Zoom on the patchy TPM particles with an increasing number of patches obtained after strand displacement reaction using EjectX (α = 3.02). Scale bar of 10 µm for a to h and 2 µm for i to l.Table1Compositions of the batches resulting from the mixing of TPMB of different sizes with PSA~Ink565 in a 1:40 number ratio determined by statistical analysis of confocal fluorescence images over about 100 clusters.

  the eject strands EjectX in the clusters suspension, non-fluorescent PS particles and TPM particles with red fluorescent patches are observed, proving the transfer of the fluorescent DNA from PSA~Ink565 (Fig.3h and S3). More precisely, Fig.3i-lshow that 1.6 µm TPM particles with one to four patches are obtained. Similar results were obtained with 1.1 µm and 2 µm TPM particles (Fig.S5), validating the strategy based on the combination of colloidal parking and colloidal stamping.

Fig. 4

 4 Fig. 4 Confocal fluorescence microscopy images of the clusters obtained by incubating TPMB, PSA~Ink565 and PSA~Ink647 in a 1:20:20 number ratio followed by the addition of the passivation strand Y*488-B*. The diameter of the TPM particles is 1.6 µm (α = 3.02). k) Confocal fluorescence microscopy image of the patchy particles obtained after injection of EjectX and EjectZ. The inset shows a TPM particle with one red and one blue fluorescent patches. l) Confocal fluorescence microscopy image of a cluster made of one TPM particle surrounded by one PSA~Ink488, one PSA~Ink565 and one PSA~Ink647 particles. m) Confocal fluorescence microscopy image of the patchy 1.6 µm TPM particles obtained after injection of EjectX, EjectY and EjectZ. Scale bar of 10 µm for a, 5 µm for b to m, and 2 µm for k inset.

Table 2

 2 Compositions of the batches resulting from the mixing of TPMB with PSA~Ink565 and PSA~Ink647 in a 1:20:20 number ratio determined by statistical analysis of confocal fluorescence images over about 100 clusters.

	7	22	26	8	19	13	0	2	2	1

Acknowledgements

The authors thank S. Yao and I-S. Jo for the functionalization of the copolymer. R. Khalaf thanks the French Ministry of Higher Education, Research and Innovation and Campus France for her PhD grant. This work was supported by the Agence Nationale de la Recherche (POESY project, ANR-18-CE09-0019). We acknowledge funding from IdEx Bordeaux, a program of the French government managed by the Agence Nationale de la Recherche (ANR-10-IDEX-03-02), and from Région Nouvelle-Aquitaine (AAPR 2020(AAPR -2019-8330510)-8330510).

Author Contributions

Conflicts of interest

There are no conflicts to declare.


Bin Liu

Etienne Duguet

Serge Ravaine
email: serge.ravaine@crpp.cnrs.fr

Solvent-induced assembly of mono-and divalent silica nanoparticles

Keywords: Patchy nanoparticles, assembly, patch-to-particle size ratio, chain stopper

Particles with attractive patches are appealing candidates for use as building units in the objective of fabricating novel colloidal architectures by self-assembly. Here, we report the synthesis of one-patch silica nanoparticles, which consist of silica halfspheres of which the concave face carries in its center a polymeric patch made of grafted polystyrene chains. The multistage synthesis allows a fine control of the patchto-particle size ratio from 0.23 to 0.57. The assembly of the patchy nanoparticles can be triggered by reducing the solvent quality for the polystyrene chains. Dimers or trimers can be obtained by tuning the patch-to-particle size ratio. When mixed with twopatch nanoparticles, the one-patch nanoparticles control the length of the resulting chains, by behaving as colloidal chain stoppers. The present strategy allows the future elaboration of novel colloidal structures by controlled assembly of nanoparticles.

Introduction

Colloidal engineering has become an enormous research effort, with a major focus placed on creating increasingly smart particles scalably, such that desired structures can be assembled in a bottom-up fashion [START_REF] Glotzer | Self-assembly: From nanoscale to microscale colloids[END_REF][START_REF] Damasceno | Predictive self-assembly of polyhedra into complex structures[END_REF][START_REF] Hynninen | Self-assembly route for photonic crystals with a bandgap in the visible region[END_REF][START_REF] Cademartiri | Using shape for selfassembly[END_REF][START_REF] Halverson | DNA-programmed mesoscopic architecture[END_REF]. Among all the existing synthetic routes permitting to imbue functionality into a colloidal suspension, those dedicated to the formation of patchy particles have received particular attention [START_REF] Ravaine | Synthesis and assembly of patchy particles: Recent progress and future prospects[END_REF][START_REF] Yi | Recent progress on patchy colloids and their self-assembly[END_REF][START_REF] Du | Anisotropic particles with patchy, multicompartment and Janus architectures: preparation and application[END_REF][START_REF] Pawar | Fabrication, assembly, and application of patchy particles[END_REF][START_REF] Duguet | Patchy colloidal particles for programmed self-assembly[END_REF]. Indeed, several generic models including the extended Kern and Kern-inspired patchy models [START_REF] Sciortino | Phase diagram of Janus particles[END_REF][START_REF] Giacometti | Phase diagram and structural properties of a simple model for one-patch particles[END_REF][START_REF] Sciortino | A numerical study of one-patch colloidal particles: from square-well to Janus[END_REF],

the spot-like patchy models [START_REF] Zhang | Self-assembly of patchy particles into diamond structures through molecular mimicry[END_REF][START_REF] Bianchi | Phase diagram of patchy colloids: towards empty liquids[END_REF], and the rigid-body patchy models [START_REF] Yan | Self-assembly of Janus nanoparticles in diblock copolymers[END_REF][START_REF] Nguyen | Rigid body constraints realized in massively-parallel molecular dynamics on graphics processing units[END_REF] have shown the great potentiality of patchy particles to serve as building blocks for the assembly of an exotic variety of colloidal structures. Experimentally, depletion interactions have been utilized to drive particles with a spherical cavity and complementary microspheres to form colloidal clusters [START_REF] Sacanna | Lock and key colloids[END_REF]. Colloidal chains have been obtained by the assembly of Janus particles with one face selectively functionalized with DNA having self-complementary sticky end [START_REF] Oh | Colloidal fibers and rings by cooperative assembly[END_REF], particles with two patches functionalized with metal-coordination-based recognition units [START_REF] Wang | Patchy particle self-assembly via metal coordination[END_REF] and by coassembly of block copolymer micelles and hard nanoparticles [START_REF] Cui | Self-regulated co-assembly of soft and hard nanoparticles[END_REF]. Particles with two patches located at the opposite poles have been assembled into a Kagome lattice by hydrophobic interactions [START_REF] Chen | Directed self-assembly of a colloidal kagome lattice[END_REF], into chains by liquid bridging [START_REF] Lyu | Low-symmetry MOF-based patchy colloids and their precise linking via site-selective liquid bridging to form supra-colloidal and supraframework architectures[END_REF] and into a series of structures under AC electric field [START_REF] Wang | Directional and reconfigurable assembly of metallodielectric patchy particles[END_REF]. The linear self-assembly of patchy gold nanorods tethered with hydrophobic polymer chains at both ends has been triggered by solvophobic attractions induced by a change in solvent quality [START_REF] Fava | Evolution of self-assembled structures of polymer-terminated gold nanorods in selective solvents[END_REF]. By using postassembly ligand photo-cross-linking [START_REF] Lukach | Controlling the degree of polymerization, bond lengths, and bond angles of plasmonic polymers[END_REF] or by adding monofunctional nanospheres into a suspension of bifunctional gold nanorods [START_REF] Klinkova | Colloidal analogs of molecular chain stoppers[END_REF], it was shown that the average degree of polymerization of the resulting chains could be controlled. The reduction of the solvent quality may be also employed to induce the assembly of silica/polystyrene dumbbells [START_REF] Li | Clustering of asymmetric dumbbell-shaped silica/polystyrene nanoparticles by solvent-induced self-assembly[END_REF] and silica nanoparticles with two PS patches (2-PSN) [START_REF] Li | Self-assembly of colloidal polymers from two-patch silica nanoparticles[END_REF][START_REF] Liu | Templated synthesis and assembly of two-, three-and six-patch silica nanoparticles with a controlled patch-to-particle size ratio[END_REF][START_REF] Liu | Linear assembly of two-patch silica nanoparticles and control of chain length by coassembly with colloidal chain stoppers[END_REF] into multipod-like clusters and colloidal chains, respectively. We have recently reported that the same strategy can be used to assemble one-patch silica nanoparticles (1-PSN) with a well-controlled patch-to-particle size ratio (PPSR) into dimers, trimers, tetramers and spherical micelles at low incubation time in mixtures of tetrahydrofuran (THF) and ethanol [START_REF] Liu | Solvent-induced assembly of one-patch silica nanoparticles into robust clusters, wormlike chains and bilayers[END_REF]. Here, we extend the study to 1-PSN with smaller PPSR values and to the use of another poor solvent for the PS patch, i.e. salty water. We show that only dimers or trimers can be obtained, due to steric hindrance induced by the large silica cap of the patchy nanoparticles. The present study also extends the insights we gained recently about the capability of using 1-PSN with a PPSR of 0.60 as chain stoppers [START_REF] Liu | Linear assembly of two-patch silica nanoparticles and control of chain length by coassembly with colloidal chain stoppers[END_REF], as we show that the addition of 1-PSN with a lower PPSR value of 0.38 allows us to control the length of 2-PSN chains in a wider range of compositions.

Results and Discussion

Synthesis of one-patch silica particles with well-controlled patch-toparticle size ratio

Figure 1 shows the multi-step approach developed to synthesize 1-PSN with controlled patch size. First, silica/PS monopods consisting of a central silica core attached to one PS nodule (Figure 2 a) have been prepared by seeded-growth emulsion polymerization of styrene, as reported elsewhere [START_REF] Liu | Solvent-induced assembly of one-patch silica nanoparticles into robust clusters, wormlike chains and bilayers[END_REF] (see experimental details). The silica core of the silica/PS monopods was regrown through successive additions of a small amount of TEOS interspersed with centrifugation/redispersion cycles in order to avoid the occurrence of secondary nucleation of silica [START_REF] Liu | Templated synthesis and assembly of two-, three-and six-patch silica nanoparticles with a controlled patch-to-particle size ratio[END_REF]. Figures 2 b-f) show the morphology of the silica/PS nanoparticles after 1, 2, 4, 9 and 14 iterative silica growth steps, with measured diameter of the silica cap of 130, 165, 195, 250 and 315 nm, respectively. The selective dissolution of the physically-entangled PS chains by three centrifugation/redispersion cycles in 20 mL of THF was thus performed to get the 1-PSN with controlled PPSR, which is defined as the ratio of the diameter of the PS patch divided by the diameter of the silica cap. As shown in Figure 3, it led to the formation of silica particles with one circular cavity, at the bottom of which the accessible surface of the initial silica seed is decorated by a PS shell of about 15 nm (as estimated by TEM). The latter is made up of covalently grafted PS macromolecules resulting from the copolymerization of styrene with the methacryloxymethyl groups. As demonstrated previously [START_REF] Fava | Evolution of self-assembled structures of polymer-terminated gold nanorods in selective solvents[END_REF], these PS chains can serve as sticky patches when their solubility is reduced through the addition of a poor solvent. Therefore, the diameter of the patch is about 74 nm and the PPSR of the asobtained 1-PSN varies from 0.23 to 0.57 (Figure 3).

Influence of the patch-to-particle size ratio on the self-assembly behaviour of one-patch silica particles

Our previous work on the assembly of 1-PSN with larger PPSR ranging from 0.69 to incubation time, and that the higher the PPSR value, the more these micelles evolved into larger objects over long incubation periods. They elongated in the form of chains for PPSR = 0.87 or extended into bilayers for PPSR = 1.18 or 1.54 [START_REF] Liu | Solvent-induced assembly of one-patch silica nanoparticles into robust clusters, wormlike chains and bilayers[END_REF]. Here, we first tried to assemble 1-PSN with PPSR ranging from 0.23 to 0.57 in THF/ethanol mixtures.

Figure 4 a) shows all of them were found to be unable to self-assemble in the presence of ethanol, meaning that ethanol is not sufficient as bad solvent for PS to make the patches attractive enough and/or the macromolecular interactions strong enough to maintain the assembly. We performed other series of experiments by using pure water strong influence on their capability to self-assemble. Indeed, when the regrown silica cap reaches a certain size, the PS chains which are grafted onto the initial silica seed surface and whose number-average mass was estimated to be ~500 000 g.mol -1 [START_REF] Hubert | Synthesis of multivalent silica nanoparticles combining both enthalpic and entropic patchiness[END_REF],

(
can no longer interact because they are too far from each other. A closer examination of Figures 4 b-c) shows that water and even more so salty water is more efficient than ethanol to promote the assembly of 1-PSN. This is probably because salty water reduces both the electrostatic repulsions between nanoparticles due to negatively charged silanolate groups at their surface and the solvent quality for the PS macromolecules. Minimization of the free surface energy of the system thus corresponds to the formation of physical bonds between the latter [START_REF] Liu | Step-growth polymerization of inorganic nanoparticles[END_REF][START_REF] Choueiri | Linear assembly of patchy and non-patchy nanoparticles[END_REF], which thus behave as sticky patches. The kinetics of the assembly in a 7/3 (vol/vol) THF/salty water mixture was more deeply investigated. Figure 4 d) shows that the incubation of 1-PSN with a PPSR of 0.57 led to the formation of dimers, trimers and larger aggregates, whose number fraction after 10 days of incubation was 10%, 8% and 74%, respectively. Interestingly, the incubation of 1-PSN with smaller and smaller PPSR progressively led to the formation of assemblies made of fewer and fewer 1-PSN (Figure 4 e-g)). More explicitly, only dimers and trimers were obtained from 1-PSN with a PPSR of 0.45, while only dimers were obtained when PPSR was 0.38. The stickiness of the PS chains in the presence of salty water was further exploited by mixing 1-PSN of two different PPSR. The aim here was not to get heterodimers, i.e.

resulting from the assembly of two different 1-PSN, with a high yield since homodimers could also be formed, but to perform a proof-of-principle experiment to demonstrate that such complex structures could be obtained.

Co-assembly of 2-PSN and 1-PSN acting as chain-stoppers

It was previously shown that monofunctional nanoparticles can act as chain stoppers, as their addition into suspensions of soft patchy nano-particles [START_REF] Gröschel | Guided hierarchical co-assembly of soft patchy nanoparticles[END_REF], gold nanorods [START_REF] Klinkova | Colloidal analogs of molecular chain stoppers[END_REF] or silver nanoplates [START_REF] Luo | Polymerization-like coassembly of silver nanoplates and patchy spheres[END_REF] allowed the control of chain length. We thus studied the capability of the 1-PSN to act as chain stoppers when they are mixed with 2-PSN, whose solvent-induced assembly into colloidal polymers was recently reported [START_REF] Li | Self-assembly of colloidal polymers from two-patch silica nanoparticles[END_REF][START_REF] Liu | Templated synthesis and assembly of two-, three-and six-patch silica nanoparticles with a controlled patch-to-particle size ratio[END_REF].

Indeed, we previously showed that 2-PSN, which exhibit a disk-like morphology with a diameter of 190 nm, formed chains as long as 6 µm (Figure 6 a, bottom row) when 30 vol % of salty water was added into the NP dispersion in THF, thereby reducing both the electrostatic repulsions between NPs due to negatively charged silanolate groups at their surface and the solvent quality for the PS chains [START_REF] Li | Self-assembly of colloidal polymers from two-patch silica nanoparticles[END_REF]. The statistical analysis of the TEM images recorded from samples collected at different incubation times The linear relationship which can be observed at short incubation time (t < 2 h) is characteristic of a reaction-controlled step-growth polymerization, in which the reactivity of the patches is independent of the chain length [START_REF] Yi | Alternating copolymerization of inorganic nanoparticles[END_REF]. At longer times (t > 2 h), on can observe that 𝑋𝑋 � 𝑛𝑛 does not vary linearly with time anymore (Figure 6 b). The polymerization of 2-PSN seems to follow a different pathway, that is, most likely, a "diffusion-controlled" stage, which can be possibly attributed to the fact that the sedimentation of the chains becomes the rate-limiting factor when they become relatively long. We recently reported that the length of the chains made of 105 nm or 130 nm 2-PSN can be controlled by the addition of 1-PSN with a PPSR of 0.60, which act as colloidal analogues of chain stoppers, at several [1-PSN]/[2-PSN] ratios between 0 and 0.5 [START_REF] Liu | Linear assembly of two-patch silica nanoparticles and control of chain length by coassembly with colloidal chain stoppers[END_REF]. Here we decide to further explore this behaviour by expanding the range of [1-PSN]/[2-PSN] ratios from 0 to 1.5. We thus first tried to co-assemble 190-nm 2-PSN with 1-PSN with a PPSR of 0.60. Figure 6 c)

shows that even if a small proportion of chains are capped with 1-PSN, most of these ones are interspersed between the 2-PSN within the chains (red arrows), probably because of their small size. Assuming that the PPSR of 1-PSN should be at least equal to that of the 2-PSN so that they can play the role of chain stoppers, we thus decided to work with 1-PSN with a smaller PPSR of 0.38. Figure 6 a) shows that this time the 1-PSN are effectively located at both ends of the 2-PSN chains. In agreement with our previous results [START_REF] Liu | Linear assembly of two-patch silica nanoparticles and control of chain length by coassembly with colloidal chain stoppers[END_REF] and those reported by others [START_REF] Klinkova | Colloidal analogs of molecular chain stoppers[END_REF][START_REF] Luo | Polymerization-like coassembly of silver nanoplates and patchy spheres[END_REF], Figure 6 a) shows that the chain length depends strongly of the 1-PSN/2-PSN ratio, as the higher it is, the shorter the chains after 120 hours of incubation. The chain stopper strategy allowed us to finely tune the degree of polymerization at any incubation time, as shown in Figure 6 b). For instance, at t = 9 h, the average number of 2-PSN in the chains is 10.7 in the absence of 1-PSN, whereas it is only equal to 3.2, 2.5 and 1.9 when the ratio 1-PSN/2-PSN is 0.5, 1 and 1.5, respectively.

Conclusion

Following a multi-step approach based on the conformational enlargement of the silica core of silica/PS monopods that we recently developed [START_REF] Liu | Templated synthesis and assembly of two-, three-and six-patch silica nanoparticles with a controlled patch-to-particle size ratio[END_REF][START_REF] Liu | Linear assembly of two-patch silica nanoparticles and control of chain length by coassembly with colloidal chain stoppers[END_REF][START_REF] Liu | Solvent-induced assembly of one-patch silica nanoparticles into robust clusters, wormlike chains and bilayers[END_REF], one-patch silica nanoparticles with a controlled patch-to-particle size ratio ranging from 0.23 to 0.57 were synthesized. The decrease of the solvent quality for the PS patch induced by the addition of salty water made it sticky, which induced the assembly of the patchy silica nanoparticles into mostly dimers when the interactions between the PS chains were not annihilated by steric hindrance between the silica parts. We also show that these one-patch silica nanoparticles can act as colloidal chain stoppers when they are mixed with divalent nanoparticles. We expect these results will inspire the fabrication of yet inaccessible colloidal structures by self-assembly. Bridging functionality at the colloidal chain end being now conceivable, their assembly into block-copolymer analogues can for instance be considered.

Experimental details

Materials

We used styrene (Sigma-Aldrich, 99%), methacryloxymethyltriethoxysilane (MMS, ABCR, 98%), sodium persulfate (Sigma-Aldrich, 99%), Symperonic® NP30 (Aldrich), sodium dodecylsulfate (SDS, Sigma-Aldrich, > 90%), tetraethoxysilane (TEOS, Sigma-Aldrich, 99%), L-arginine (98.5 %, Sigma-Aldrich), ammonium hydroxide (28-30% in water, SDS), sodium chloride, (≥99.0%, Sigma-Aldrich), sodium hydroxide (≥98%, pellets, Sigma-Aldrich) as received. We systematically used ultrapure water with a resistivity of 18.2 MΩ•cm at 25°C obtained from a Milli-Q system (Millipore). We purchased absolute ethanol and tetrahydrofuran (THF, >99%) from VWR Chemicals.

Synthesis of the silica/PS monopods and bipods

In a manner similar to the already reported procedure [START_REF] Liu | Solvent-induced assembly of one-patch silica nanoparticles into robust clusters, wormlike chains and bilayers[END_REF], monopods consisting of a central silica core attached to one PS nodule have been prepared by seeded-growth emulsion polymerization of styrene. Briefly, silica nanoparticles with an average diameter of 44±2 nm were obtained by TEOS hydrolysis/polycondensation according to a two-stage protocol. At the end of the synthesis, the silica surface was functionalized with methacryloxymethyl functions by reacting with MMS at room temperature for 3 hours and then one more hour at 90°C under stirring. The added MMS amount corresponded to a nominal grafting surface density of 0.7 funct./nm 2 .

Then, the MMS-functionalized silica NPs (1.8×10 16 part/L) were used as seeds for the seed-growth emulsion polymerization of styrene (100 g/L) stabilized by a mixture (3 g/L) of Symperonic® NP30 and SDS (5 wt.%) and initiated by 1.3 mL Na2S2O8 (0.1 g dissolved in 4 mL water) at 70 °C for 6 h to obtain silica/PS monopods with a PS pod diameter of about 155 nm. The morphological yield was 99%.

Bipods consisting of a central silica core surrounded by two PS nodules with a diameter of about 160 nm were obtained with a yield of 97 % in a similar way from 55±2 nm silica nanoparticles which were functionalized with MMS at 0.5 funct./nm 2 .

Controlled growth of the silica core

According to the procedure reported in [START_REF] Liu | Templated synthesis and assembly of two-, three-and six-patch silica nanoparticles with a controlled patch-to-particle size ratio[END_REF], 9.1 mL of absolute ethanol, 0.7 mL of ammonia and 0.2 mL of the dispersion of monopods (1.8×10 16 part/L) or bipods (1.8×10 16 part/L) were introduced into a 25 mL flask and the mixture was homogenized using a magnetic bar. 200 µL of TEOS were added all at once after 5 min. The reaction was left under stirring at 20 °C for 15 min. The reaction medium was poured into a 50 mL Falcon tube containing 15 mL of absolute ethanol. After 2 cycles of centrifugation (12,000 g / 5 min) and redispersion in absolute ethanol, the nanoparticles were finally redispersed in 10 mL of a previously prepared hydroalcoholic solution (absolute ethanol/ammonia/water volume ratio: 91%/7%/2%). This protocol was renewed to obtain the next generation. The final diameter of the silica core of the bipods is 190 nm.

Dissolution of the PS nodules

For dissolving the PS nodules of the monopods and bipods, three centrifugation/redispersion cycles in 20 mL of THF (12,000 g; 10 min) were performed.

The concentration of 1-PSN and 2-PSN dispersions was adjusted to 1.08•10 15 part/L and the solution was stored at 4 °C.

Assembly of one-patch silica nanoparticles

Incubation of the nanoparticles was carried out in 15 mL tubes under rolling motion at 60 rpm at room temperature. A calculated volume of ethanol, water or salty water (20 mM NaCl aqueous solution) was added drop-by-drop under stirring into the THF dispersion of 1-PSN to reach the targeted volume fraction and a total volume of 1 mL.

It took about 20 seconds for adding 100 µL. Assembled structures were monitored by collecting 50 µL samples at various incubation times and direct deposition on TEM grids.

Co-assembly of one-and two-patch silica nanoparticles

Incubation of the nanoparticles in a 7/3 (vol/vol) THF/salty water mixture was carried out in 15 mL tubes under rolling motion at 60 rpm at room temperature. The composition of the mixtures is given in Table 1.

Table 1. Experimental conditions used for the co-assembly of 2-PSN and 1-PSN.

Figure 1 :

 1 Figure 1: Synthetic route for the preparation of 1-PSN with a controlled patch-toparticle size ratio.

Figure 2 :

 2 Figure 2: TEM images of the silica/PS monopods after (a) 0, (b) 1, (c) 2, (d) 4, (e) 9, (f) 14 iterative silica growth steps.

Figure 3 :

 3 Figure 3: Schemes and representative TEM images of 1-PSN with PPSR varying from 0.23 to 0.57. Scale bars: 100 nm.

Figure 4 b

 4 ) or salty water (Figure4 c) instead of ethanol in different fractions. We observed that, except for 1-PSN with PPSR ≤ 0.3, assembly was possible and led to dimers and possibly to clusters of low aggregation number for the highest PPSR values. These results first indicate that the size of the silica cap of the 1-PSN has a

Figure 4 :

 4 Figure 4: Phase diagrams identifying the main products of self-assembly (1-PSN (light blue squares), dimers (magenta circles) and large clusters (grey diamonds)), as a

Figure 5 a

 5 ) shows that heterodimers were effectively obtained by mixing 1-PSN with a PPSR of 0.45 and 0.38. After 24 hours, the incubation medium consists of 1-PSN (~26%), heterodimers (~30.5%), homodimers made of two 1-PSN with a PPSR of 0.45 (~17.5%), homodimers made of two 1-PSN with a PPSR of 0.38 (~23%), and also heterotrimers (~1.5%), and homotrimers (~1.5%) (Figure5 b).

Figure 5 .

 5 Figure 5. a) TEM image showing some heterodimers obtained after incubation in a 7/3 (vol/vol) THF/salty water mixture during 24 hours of a 1/1 mixture of 1-PSN with a

  plot the time evolution of the number-average degree of polymerization, 𝑋𝑋 � 𝑛𝑛 , defined as:𝑋𝑋 � 𝑛𝑛 = ∑ 𝑛𝑛 𝑥𝑥 𝑥𝑥 ∑ 𝑛𝑛 𝑥𝑥, where x is the number of 2-PSN in the chain and 𝑛𝑛 𝑥𝑥 is the number of chains containing 𝑥𝑥 2-PSN (Figure6b), magenta curve).

Figure 6 :

 6 Figure 6: a) Chain length distribution and representative TEM images of chains for 1-PSN/2-PSN = 0 (magenta), 0.5 (light blue), 1 (green) and 1.5 (blue) at t = 120 h. Scale

  Transmission electron microscopy (TEM) experiments were performed using a Hitachi H600 microscope operating at an acceleration voltage of 75 kV. We prepared the samples by depositing one drop of the colloidal dispersion on conventional carboncoated copper grids. We let the liquid evaporate in the open air at room temperature and placed the grids in a box away from dust. Statistics from image analysis were performed over at least 300 multipods or 200 chains. The ζ potential value of 1-PSN aqueous dispersions (pH ~5.7) was measured using the Malvern Zetasizer 3000 HS setup (Malvern Instruments). The dielectric constant of water was set to 80.4 and the Smoluchowsky constant f(ka) was 1.5.

FundingB.

  Liu was supported by a grant from the China Scholarship Council.

0.23 0.30 0.38 0.45 0.57

	0.23	0.30	0.38	0.45	0.57	Patch-to-particle size ratio
	0.2		0.4	0.5

1.54 in a THF/ethanol mixture has shown that colloids with a low aggregation number, e.g. dimers, trimers, tetramers and spherical micelles could be obtained at low