 Thank the organizer for inviting me to present my work. And I am going to talk about the non-equilibrium dynamics of RNA packaging in viral capsules. So let me first present the viral system that I use. So this is the CCMV, which is a plant virus with a capsid T equal 3, comprising 90 dimers, which I will call subunits. The diameter is about 28 nanometers. And the genome is made of about 3,000 nucleotide per particles. So the capsid is made of these proteins, which I depict like this. I should have represented maybe one subunit. But this is one protein with here hydrophobic patches, hydrophobic sites. And the body is negatively charged, which can be tuned by the pH. And the flexible arms is actually cationic and makes the interaction with the genome. So you have actually two types of interaction. You have the protein-protein interaction, which is controlled by this hydrophobic interaction, which is attractive. And the electrostatic repulsion, which is controlled by the pH. And this subunit genome interaction, which is controlled by the flexible arm, which is cationic. Interestingly, we can draw a phase diagram of this virus. So here, this is the phase diagram for empty capsids. At physiological pH, you can get only subunits free in solution when you lower the pH to pH about five. Spontaneously, the subunit self-assembles, and you end up with empty capsids. If you lower the salinity, you can get other structures like tubes and multiple shells. In the presence of genomes, Gilbert's group, in particular, have studied the encapsulation of RNA inside these capsids. And they observe interesting things, especially at physiological pH. When they have a high salt concentration, subunits and genome do not interact very strongly. But when they lower the pH, when they lower the salinity, they get these complexes, which are made of subunits bound to the RNA. But it does not close up. You don't have real viral particles. You just have amorphous complexes. When you lower the pH at this low salinity, you get a really full virus with the RNA fully encapsulated inside the shells. So it's interesting because it shows you that you can actually control this interaction, the subunit-subunit interaction through the pH, and the subunit-genome interaction through the salinity. So it can help you to understand a little bit better how the virus can be formed and can be assembled. So this is particularly interesting to study the dynamics, which is the topics of my talk, the dynamics. And I will explore this interesting feature for this system. So in terms of dynamics, two pathways, mainly pathways, have been identified, especially by numerical simulation in the Mike's-Igan groups. Here you have this cooperative pathway, and here the nucleation and growth. In the cooperative pathway, you mix the subunit with the genome. Here this is more polyelectrolyte. The subunits bind very quickly to the polyelectrolyte and later on the complex actually reorganized slowly and make a full virus with a closed shell. In the nucleation and growth, it's a little bit different. The subunits self-assembled with each other. And at the same time, it packaged the polyelectrolyte inside. And what controls these two pathways, kinetic pathways, is actually precisely the interaction between subunit, subunit, and subunit genome. In this cooperative pathway, you have a strong subunit genome interaction while compared to the subunit, subunit interaction. So that's why the subunit likes to bind first to the polyelectrolyte and then reorganize and make a closed shell. In this nucleation and growth pathway, the subunit-subunit interaction is much stronger than the subunit polyelectrolyte. That's why the shell will form first and package at the same time the polyelectrolyte. So my goal is precisely to study these kinetic pathways and to find whether we can identify it for the CCMV. Any of these pathways, by controlling precisely, as I said, with the pH and the salinity, the interaction between the two components. More precisely, I try to identify, as I said, the mechanism and the composition and the structure of the intermediate, which are formed along the kinetic pathway. By composition, I mean how many subunits are bound to the genome as a function of time, and what is the structure, the size of this intermediate, these complexes. And also, more interestingly, what are the timescales, the typical timescale over which the process takes place? To do so, I use a small-angle scattering technique. So you might not be all familiar with it. Basically, you have a sample. You illuminate your sample with a wave, which can be x-ray or neutron, in my case. The wave is scattered. And you collect on a detector the scattered intensity as a function of scattering angle, theta, here. More practically, we use the wave number q, which is closely related to the scattering wave number. So we do our experiment on the large-scale facilities, synchrotron and nuclear reactor here, because we need high flux, high brilliance to be able to detect, to have a decent signal-to-noise ratio. So I must also emphasize that these experiments take sometimes because we have only usually a few days of experiment per year. So you need to prepare carefully your samples. And then you take a lot of time to analyze the thousands of data. And if you make a mistake, you have to go back again to these large-scale facilities six months or maybe one year later. So just to show you the kind of data we get by these techniques, here I plotted the intensity that's scattering intensities as a function of the wave number in logarithmic scale. So the first information is the intensity at very low q values, which is basically proportional to the squared volume of the object. So when you measure the intensity here, you can get somehow the volume of the object. And you can get, for example, the composition. If you know, for example, you have an assembly of subunits. You know the volume of one subunit. So you can estimate how many subunits are in your assemblies. The second information is the radius of duration, which is the global size of your objects and which is given by this approximation valid only for very small q values. Here in black, you have an object with a smaller radius of duration than in blue and red. It's given by actually the curvature of the curve. And the rest of the curve gives you information on the structure. Here, for example, a polymer, in log log, you have a straight line because you have no particular structure. And for a sphere, you have this large oscillation which tells you that you have a high symmetry in your object. We performed already time-resolved studies on empty capsid. So basically, we mixed the subunits with a buffer solution which lowers the pH or increases the salinity and spontaneously the capsid that clearly self-assembled. We collect these scattering intensities as a function of time, and we can compute, we can develop the algorithm that allows us to extract the structural information of the intermediate by assuming a certain kinetic model. So we did it, for example, with the norovirus capsids, where we identified an important intermediate. Here, we start from three dimers in solution. And very fast, we have this intermediate made of two pentamers of dimers, which actually finished slowly in the empty capsids. We studied also the disassembly of CCMV capsids. We start from full empty capsids, and we observed that the capsid break in two pieces, two big pieces, maybe almost half a capsid. And these two pieces break in two smaller pieces made of 16 dimers, roughly. And then we end up with three dimers in solution. We start from pH 5. We increased the pH to 7.5, and we kept the salinity, high salinity, and 0.5 molar of salinity, and pH 7.5. Yes, yes, raise the pH. Correct. So what happens in the presence of genome? Just to recall that this is a subunit, a dimer, which has these flexible arms, which are cationic, and which makes the interaction with the genome. So the first experiment we did was in static, at an equilibrium, by neutron scattering. The advantage of neutron scattering is when you work at here, 68% of heavy water, you can contrast match the signal coming from the genome. So you only see the signal coming from the subunit, from the capsule. So at pH 7.5, I recall that the subunit-subunit interaction is weak. And at high salinity, we have basically noise, so we don't observe any signal. But when we lower the salinity, we see a scattering curve like this, which tells us that the subunits have somehow assembled. So the schematic here shows what happens. The electrostatic interactions are actually screened at 0.5 molar, so we expect no subunits bound to the RNA, or at least nothing detectable when we lower the salinity, the subunits bind to the genome. And more importantly, we can estimate how many subunits are bound to each RNA molecule. And from the I0, and in this case, we can estimate that the mean number of the subunits per RNA is 75, plus a large error uncertainty, which is due to the error of experimental error of measurements. And also you must recall that, I didn't say it, perhaps that genome is made of four segments of RNA. So I have included this polydispersity into the uncertainties of a... Yeah, no. But I saw that in polymer physics with Luflitzket, when you are able to... No, but because here I don't detect, I should detect the subunits alone, right? But this is in the noise. The signal is not strong enough to get a decent signal in this case. That's why I couldn't obtain anything. But when the subunits self-assembled, yes, I have a signal and I could deduce something. But in principle, of course, it's definitely possible. What happens in dynamics? So I do it by X-ray scattering this time. This is X-ray, so I get a much better signal. So here you see actually the number, the average number of subunits per genome, per RNA molecules. And you can see that the subunits bind very quickly to each RNA molecule. In the 100 milliseconds, everything is almost finished. I mean, we have about 75 dimers, subunits per genome, per RNA molecules, and it does not change for tens of minutes. But in contrast, here you have the radius of direction of the object, which is shown here. And you can see that it evolves still more slowly than the binding of subunits. By fitting exponential decays, you can estimate that the binding time, typical binding time is 28 milliseconds. But for the relaxation of these complexes, the structural relaxation, it's about 48 seconds, three orders of magnitude higher. And so it tells us that the binding time scale is smaller than the structural time scale. So the subunits bind very quickly to the RNA. And then in a second time, it relaxes more slowly, reorganizes. Probably subunits-subunits will bind to each other, but in a much longer time scale. So it will definitely follow something like a cooperative assembly mechanism as I shown initially in the introduction. Yes, it's the magic ratio, six. This is the mass ratio between protein and RNA. Yes, we did it with precisely different mass ratio. The row is the subunit to genome mass ratio. So from two to seven. And here I represented the number of subunits bound to RNA at long time scale. So close to equilibrium, hopefully. So I can deduce equilibrium constant, which is also related to the critical concentration above which the complex can be formed. So here I found something like 11 micromolar. Typically in my experiment, I worked at 24 micromolar. So I am twice higher than the critical concentration. And we can estimate the binding energy, which is about 7 kT, which is actually surprisingly lower, low for me. I expected a much stronger interaction between of electrostatics. And to illustrate a little bit further, this weak binding, this weak interaction between proteins and RNA. We did this experiment. We start from complexes, these complexes, and we dilute them two times. And upon dilution, we can see that the average number of subunits bound to RNA decreased from 75 to 57, if I remember well. And it decreased slowly in the 204 seconds, typical time scale. So the complexes upon dilution, the complexes just release the subunit into the solution. So the binding, so the entropy has a strong role in this, has a strong role in the formation of the complexes, and they exchange subunit with the bulk solution. Two times, yeah, we dilute twice. Here the radius of gyration did not change significantly. Yes, it was just to show that by molecular dynamic simulation, we try to compute the conformation of the subunits. And we observe that actually the flexible arm could perhaps actually fold under the body of the dimers, which reduce actually the dipole moment. And which can somehow explain why the interaction is smaller than I expected initially. Regarding the kinetics, we have here an experiment where I have tried to fit a kinetic model here where a complex with n subunits reacts with one subunit and end up with a complex with n plus one subunit. We have this reaction constant K plus and K minus. If the process is purely diffusion limited, K plus will be given by this equation with r the size of a complex and d is a diffusion coefficient. So by fitting the experimental data, we find this diffusion coefficient, which is actually two orders of magnitude smaller than what molecular dynamic simulation gives. So the process is not fully diffusion limited. And we can imagine that when the subunit binds to the RNA, at certain point there are too many subunits and there is a barrier to cross to bind more subunits. So this is what gives this apparent diffusion coefficient smaller than purely free diffusion of subunits. What about the relaxation to fully assembled variant? So we start from these complexes and we lower the pH rapidly. The physics depicted here. In that case, the process is much smaller. The binding time is about three, almost one hour. So it evolves from 75 to here after one hour in 84, I think I remember subunits. In this case, this is at room temperature. So the binding is slow. The radius of gyration do not evolve very significantly. But if we look at closely the form factor of the object, here I have represented the form factor and I have just shown a part of the form factor. In blue and, sorry, in red and black, this is the experimental form factor of the complex that evolves as a function of time and you see that the oscillation actually becomes more and more clear. In blue, this is the form factor of a solution of pure virus. So we see that it tends to converge. They are the form factor of a pure solution of virus. So the size of the complexes is already very close to virus form factor. We have already almost the structure of the virus. So the complex must have some piece of shell which are already formed and little by little the shell must close up to form the full virus. So we are very close to it. And to compute the rapidity of the process, I plotted here the value of the form factor at this web number as a function of time and you can see that the structural reorganization of the object actually takes something like 3,000 seconds, almost the binding time scales. So in this case, the binding time scale is close to the structural time scale so I would guess that we have something like a nucleation growth mechanism meaning that the complexes capture subunits and at the same time they slowly reorganize to make fully assembled virus particles. We did it at several temperatures from 10 degree Celsius to 40 degree Celsius so I plotted here the logarithm of binding time scale as a function of the inverse of the temperature and I tried, my goal was to try to estimate some activation energy controlling the process of this relaxation and I could estimate an activation energy which is actually something like 20 KT T0 is the room temperature again 20 KT which is rather high I would say so we have activation energy which is quite high and it explains why the process is slow and when we actually do the experiment at 40 degree Celsius it's, we end up almost with assembled particles. Just to give you some images of the species we observed by cryo electron microscopy so we have seen that before I think at pH 7.5 when we mix subunits and RNA we have this aggregate, these complexes which have no particular structure, amorphous complexes when we lower the pH we end up with these spherical particles and here I show just a three dimensional reconstruction of the complexes from the form factor that I measured by x-ray and here I compared with the crystal structure of the CCMV capsid you can see that this aggregate, these complexes are a little bit bigger but they are maybe slightly more elongated but the size is already quite comparable with the size of a virus particle the last experiment was with synthetic polyelectrolyte we have PSS which is a flexible polyelectrolyte negatively charged in that case very interestingly I find, at least me I find it very interesting is that at pH 7.5 we have already spherical particles we mix PSS with subunits and we end up with spherical particles why with RNA remember we have only this amorphous complexes so we have these spherical particles and the kinetics show so I did not have time to the work is unfinished so I did not have time to compute the number of subunits bound to the polyelectrolyte so I show you here directly I0 so I computed the binding time scale which is 42 milliseconds so very fast also the subunit binds very fast to the polyelectrolyte for RNA it was 28 so it's quite comparable and the radius of duration evolves more slowly than the binding time scale I found 3.1 seconds but anyway it's faster than with RNA RNA was 48 seconds if I remember it's 10 times more so we have in this case again a cooperative assembly mechanism but in this case the subunits bind quickly to the polyelectrolyte and also I said slowly it's reorganized but it's anyway quite fast I mean in 10 seconds let's say in 1 minute the particles are formed and the process do not evolve significantly and this is probably due to the fact that the polyelectrolyte first it's very flexible and it has a hydrophobic backbone so it collapse on itself much more easily than the RNA so it helps the process it helps to form the capsule and to maintain it quite stable to summarize so the binding energy between subunit and genome is moderate I found about 7 kT so I expected something higher but obviously when you dilute the subunits are released and this can be probably explained by the fact that the dipole moment is actually low in this case and the overall subunit is negatively charged the complexes are formed by a cooperative mechanism the subunits bind to the RNA and relaxes slowly to this complex and the relaxation into a viral variant follows a nucleation growth mechanism meaning that the complexes capture the subunit and at the same time they're organized into a fully assembled virus in the case of polyelectrolyte we can form capsids with a low subunit-subunit interaction thanks to the hydrophobicity of the polyelectrolyte and again it's formed by a cooperative mechanism so I try to summarize all these on a diagram so this is maybe preliminary so here I plot the number of subunit-subunit contact which is driven by the interaction between them controlled by the pH polymer hydrophobicity I would say and here the number of subunit-genome contact and which is also controlled by the salinity and the polymer charge of course in this case so as I said so you can imagine on this diagram free energy landscape which will somehow control the kinetics which tells us the equilibrium state of your system so when you travel on this axis you have initially a diffusion-limited process the subunits bind very quickly to the RNA but at some point it becomes reaction-limited because you have already a lot of subunit on RNA so it's somehow crowded and on this direction you have definitely a reaction-limited process which is slow and which accounts for the relaxation of the complexes into a fully-assembled virus here you have a cooperative assembly and nucleation growth mechanism are more in this direction so let me thank the contributor of this work especially Marilyn Chevroy and Jiglin Chen who are a PhD student with me who are Constantin and Médizégal who are colleagues with whom we do a lot of X-ray scattering and Neutron scattering Stéphane Bressanelli is a virologist with whom I work and I have a lot of feedback regarding the structure of the virus and the mechanism that comes into play large-scale facilities ESRF in Grenoble for X-ray scattering and LLB in SACLE for Neutron scattering and I thank you for your attention