VIDEO: Rohit Pappu on Molecular Grammar of Condensates – Part 3

Rohit Pappu (00:02:54):
Let’s start with our stickers and spacers model. How might this be applied to describe the phase behavior of RNA molecules with their protein counterparts? And so to keep life simple, understandable, and potentially relevant, we’ll focus on dipeptide repeats, which many of you are aware of as being quite important in the context of C9orf72 repeat expansion disorders. And particularly in the context of ALS where seemingly toxic dipeptide repeats are generated by these repeat expansions, and they interact in ways that they’re not supposed to with RNA. So this work that I will tell you about today is primarily driven by Steven Boeynaems, who at the time basically, this is science at its very best the way I look at it. Steven had sort of moved from Belgium to Stanford.

Rohit Pappu (00:03:57):
He’d befriended Alex over the years and they developed a very strong connection. And then one day over coffee, Alex started telling me about all these interesting things that were going on. And of course, as any PI would, immediately, I set everything aside and decided to spend all my time at Alex’s desk, virtually speaking of course. So the system of interest that we’ll focus in on is a proline–arginine repeat, this is a dipeptide repeat system. There are GR repeats, there are other repeats, SR repeats in the nuclear speckle, which we’ve also focused on quite a bit recently, but let’s just simply ask the following question. If we were to take a model polycation and we start to think about different homopolymeric RNAs, which actually turns out to be a reasonable way to conceptualize what might happen when we think about naked and folded RNA molecules coming off polysomes, what might be the phase behavior?

Rohit Pappu (00:05:02):
These are experiments done at roughly 1:1 ratios of (PR)30 with different homopolymeric RNAs. The observation that jumped out was that under these conditions, at joint concentrations of modules that are in the low micromolar, one starts to see these fairly well-defined spherical puncta, here it’s the (PR)30 molecule that is being labeled. But interestingly enough, when one has a polyguanine, essentially what one starts to see are these fairly irregular morphologies. And those of you who know your nucleic acid biophysics will appreciate that it is reasonably well established that G-tracts will make G-quadruplexes. And so one hypothesis that started to take root was the idea that RNA structure–and this is not so terribly new because Amy Gladfelter has actually led the charge on this thinking–that RNA structure might actually have a contributing role to dictating the morphology of condensates.

Rohit Pappu (00:06:10):
What was particularly a fun project to work on was Venera Weinhardt’s work at the Lawrence [Berkeley] National Laboratory using soft x-ray tomography where you can actually use anomalous scattering properties of water as a way to image and construct tomograms. And you can actually see these spherical condensates for the adenine, uracil, and cytosine, but you start to see these very irregular morphologies for the guanine-rich systems. So the one question that emerges is, clearly there is a sort of impact of RNA structure on condensate morphology, and that was based on the connections to ideas in the literature that G-tracts make quadruplexes, but you can control RNA structure in a much more defined way.

Rohit Pappu (00:07:03):
And the way to do that was to basically incubate (PR)30 with mixtures of non-base pairing RNA molecules, again, homopolymers. And you can have AC combinations or UC combinations. They don’t form canonical Watson–Crick base pairs. And basically what you start to see, again, here (PR)30 is the entity that is labeled. And you see basically the main tenets of the spherical morphologies. But then when we switch to base pairing RNAs, depending on the ratio of the structure forming entities, so at the limit where you have purely homopolymeric systems, you see essentially purely spherical morphologies, but as we transition through these base pairing mixtures, you start to see much more irregular morphologies. I’m sure at this juncture you’re asking lots of questions in your head about dynamics, et cetera, we’re coming right to that.

Rohit Pappu (00:08:04):
The question on the table for us was, do these structured RNAs or the ability of RNA to engage in structure formation, does that lead to the formation of solids or is what we’re observing something metastable and dynamically arrested? So for that, we essentially turn to simulations, I introduced PIMMS in the last lecture developed by Alex Holehouse who was then a postdoc in the lab. And so essentially what Alex did was he developed PIMMS to be able to do simulations of protein-RNA mixtures. And the type of simulation that one would readily observe based on typical types of interactions for (PR)30 and poly-rA is the formation of these spherical condensates. They become a little hard to fuse past a certain length scale, but that’s largely a move set issue. But then when you look at mixtures of (PR)30 with poly-rA and poly-rU, you start to see these dynamical arrests, but then what Alex had was the thought that, hey, maybe these things are locked in or trapped.

Rohit Pappu (00:09:20):
I’ll give it a thermal kick and then essentially set in an annealing protocol. And indeed what you start to see is the formation of fairly well defined spherical condensates. The picture that emerged was for lack of a better term, this duo funnel model, where if we now project the multidimensional free energy diagram or free energy surface rather onto one coordinate, effectively here by conformation, we really mean morphology of the condensate. You effectively have a metastable trap, so to speak, that can basically be overcome by a sort of thermal kick and an annealing process. Now, for those of you who might think that this is something brand new, let me disabuse you of that because in fact, dating now back to 1993, Francesco Sciortino, then a graduate student in Gene Stanley’s lab postulated this model for gelation as a way of dynamically arresting phase separation.

Rohit Pappu (00:10:23):
So here, the idea would be that the formation of cross-links, be they stacks or hydrogen bonds, but the fact that essentially we are perhaps to the right of the percolation line as far as RNA structure is concerned, leads to this networking phenomenon that can essentially lead to dynamically arrested condensates, which will not necessarily be the equilibrium scenario, at least for this particular case. Steven then went on to basically test Alex’s predictions by taking this mixture and effectively heating it, and then slowly cooling back down and effectively the slow cooling allowed for the reformation of spherical morphologies, essentially leading to the idea that these were actually more dynamically arrested states rather than an equilibrium solid phase.

Rohit Pappu (00:11:22):
The other thing that we introduced in the second lecture was the concept of specificity in the form of different types of stickers, wanting to make different types of cross-links. Does that concept of sticker grammar transfer over into thinking about the nucleic acids? So here, of course, we’ve got a choice of the nucleobase, and of course the amino acid, namely the cation. And so these are experiments that Steven did, which are the microrheology experiments where you’re basically quantifying the fusion of condensates. And the inverse capillary velocity is such that the higher the value, the more slowly these condensates will fuse. And in fact, what you see is a very interesting distinction between purines, the double ring systems, versus the pyrimidines emerging, whereby the purines, which of course now have a higher intrinsic valence basically ends up retarding the fusion dynamics. And so that was one conclusion.

Rohit Pappu (00:12:30):
The second conclusion or the second test was to ask, well, okay, if we keep the nucleobase fixed and we now change the cation type, what sort of fusion dynamics might we observe? And again, you start to see this very interesting distinction, and these are essentially on log scales. The inverse capillary velocity with arginine now, which as I pointed out in the last lecture has this delocalized electron cloud, is considerably less like a point charge. And so from the vantage point of its intrinsic quadrupole moment will allow for more interactions, if you will, and hence more cross-linking per sticker. And you essentially see that manifest here, where when you substitute the arginine with the lysine, the inverse capillary velocity drops implying more efficient and rapid fusion of condensates. That trendline, so the relative trendline is preserved as we switch from purines to pyrimidines, and you notice this.

Rohit Pappu (00:13:33):
And so basically the idea then is that the anion type matters in the form of, is it a purine or is it a pyrimidine? The tract mesh matters, is it a G-tract versus not? And also the cation type matters, is it an arginine versus a lysine? What’s good for the fusion dynamics of condensates is also good for the internal dynamics of molecules inside of these condensates. And so here, what one is doing is basically fluorescently labeling the (PR)30 and basically watching the recovery upon photo bleaching of the (PR)30 in the context of these different condensates. And if you do the exact same experiment with the PK system, so where the arginine is substituted with the lysine, the recovery is mostly complete and also essentially shows an insensitivity to the purine type or to the nucleobase type.

Rohit Pappu (00:14:38):
The last thing that came to us was to ask these questions about spatially organized condensates, because we touched upon this in the first lecture. And those of you who have seen images of protein RNA granules will of course recognize that these are not just bags of molecules. There’s always a spatial organization to these condensates. And the question is, was that evident in these fairly simple systems? And the answer was actually yes, so here the fluorophore is on the (PR)30, and you can actually see that there’s a core and a shell type of architecture that was manifest. One can get at this again using soft x-ray tomography, and you can again, see the electron density is indicative of the fact that there is a core-shell architecture, which led Alex to then go back and ask the question of, what would be the simplest model that will lead us to a core-shell architecture?

Rohit Pappu (00:15:34):
So here we’ve got the polycation is modeled as being repulsive for itself. The purine is modeled as having a stronger interaction with the polycation. The pyrimidine in this case, the cytosine tract has a weaker interaction. And then basically there are RNA-RNA interactions that are of modest affinity, and I should point you to these scales, and these are not gigantic interaction strengths. And basically what emerges pretty much spontaneously is a poly-rA core essentially dressed by a poly-rC shell. And that just gets completely abrogated if we were to argue that the cation-anion interactions don’t show any specificity as far as the nucleobase is concerned. And basically now you don’t get any delineation of a core versus a shell.

Rohit Pappu (00:16:31):
So basically what emerges from this is that there appear to be clear rules that dictate the driving forces for local complexity domains interacting with RNAs and driving condensate formation, what might dictate their morphologies. And hopefully what I’ve tried to persuade you here is of the idea that if you see something irregular, if you see something aspherical, it does not have to mean that it is purely a solid phase. It turns out that RNA structure, purine versus pyrimidine content and their patterning will also contribute as does the valence of arginine versus lysine. And there’s in fact, a very interesting story about the molecular grammar that distinguishes IDRs that go into speckles, which basically have very few lysines versus let’s say IDRs that make up euchromatin or heterochromatin. So in the histones where you seldom see arginines. And conversely in the nucleolus, depending on the state of the nucleolus, there is a very interesting interplay between arginine versus lysine richness.

Rohit Pappu (00:17:46):
In ongoing work, what we’ve actually been doing is working very closely with Amy Gladfelter to now ask how these simple rules actually contribute to the organization and dynamics of a variety of really interesting and sophisticated RNP granules. I urge you to stay tuned. But what I will do next is switch to the topic of essentially the elephant in the room, which is that up until this point, I’ve shown you essentially one and two component systems. But what we’ve ignored is the fact that condensates typically encompass hundreds of distinct types of molecules. This has led to the classification of molecules as scaffolds versus clients and all kinds of interesting architectures like core-shell architectures. What we set about to do was to ask a question where we say that, well, a molecule that is not driving phase separation, is not required for phase separation, we’ll call it a non-phase separating ligand if it can bind to the scaffold molecule that undergoes phase separation.

Rohit Pappu (00:18:54):
And so the obvious question that arises is what happens if we were to add an non-phase separating ligand to a solution of scaffold molecules that undergoes phase separation. So a cartoon might actually help us understand what’s going on. So if in this high resolution picture I have a scaffold that is a triangle, a red triangle, basically what I’m saying is that when we realize phase separation by way of equalizing the chemical potential across two phases, a dilute phase A, a dense phase B of the scaffold molecule, and it’s the equalization of the chemical potential, which of course, as all of you know, is the partial molar free energy that controls the concentrations of our scaffold in the dilute phase A versus the dense phase B. Now let’s add a ligand. We’ll make it blue. What do I need now?

Rohit Pappu (00:19:51):
What I need of course is to ask the following question, which is in the presence of the ligand, what is the concentration of the scaffold in the dilute versus the dense phase? It turns out that the beauty about thermodynamics is just because you changed the underlying composition, you didn’t change the thermodynamics. You essentially still maintain the equalization of chemical potentials as our constraint. And so in fact, to ask this question of what will be the concentration of scaffold in the dilute versus the dense phase, you basically do exactly the same thing. So you say either out or the dilute phase A, or in the dense phase in, basically what you’re doing is you’re now equalizing the chemical potentials of scaffold but now in the presence of ligand. Okay? What this does is it says that the concentrations are now going to be set by the interactions of the ligand with the scaffold in both phases.

Rohit Pappu (00:20:48):
You don’t get to just measure the affinity in the dilute phase and hope that that transfers over. What that leads to is this formalism of polyphasic linkage, which is simply the idea that given now a degree of freedom for binding, so the ligand has a choice between binding to the scaffold in the dilute phase or binding to the scaffold in the dense phase. There is no requirement that that binding has to be equivalent. And so if there is binding favorably, more favorably to the dilute phase, that’s preferential binding to the dilute phase. And if there’s favorable binding to the scaffold in the dense phase, that’s preferential binding to the dense phase. So what this leads to is the saturation concentration, or a concentration of scaffold in the dilute phase, in the presence of ligand. That’s what all this spinach means, equals the intrinsic saturation concentration times a ratio of the binding polynomial.

Rohit Pappu (00:21:51):
So what is the binding polynomial for the ligand to the macromolecule or to the scaffold in the dilute phase A versus the dense phase B? What this says to us that in the presence of a ligand, our driving force for phase separation of the scaffold is actually going to change. It can only be the same if the ratio of the binding polynomials is one, otherwise there is going to be a change, which is great. So now we can go back and ask the question of, given a phase diagram, and here is a system under scaffold, some particular scaffold concentration phase separating to form a coexisting dilute phase here and the dense phase here, a preferential binding to the scaffold in the dilute phase will basically now shrink the width of the two phase regime. Because essentially what it’s saying now is that you need more molecules to be thrown into solution in order to drive phase separation.

Rohit Pappu (00:22:58):
And so basically that is quantified or pictured here in terms of the left arm of this binodal or the coexistence curve shifting to the right, meaning that we need a higher concentration. The polyphasic linkage theory is actually silent largely about what happens to the dense phase. Here we schematize this, but I’ll show you that this is indeed what can happen. Conversely, if the ligand likes the scaffold more so in the dense phase, now what will happen is that you’re basically stabilizing phase separation. And then in contrast to what happens here now, the blue curve basically represents the two phase regime or two phase boundary in the presence of the ligand and that widens.

Rohit Pappu (00:23:46):
Essentially, this is a very, very important point. Preferential binding means that our scaffold is exhibiting some kind of an asymmetry across the phase boundary. This can be due to the very obvious thing, which is that we have differences in concentrations of the scaffold across the phase boundary. That’s a sort of duh, type of point. There could be a difference in accessibilities of binding sites. There could be a difference in cooperativity of ligand binding to scaffold sites. And of course, the big elephant in the room, which is we’ve all worked on the assumption and interpreted certain results to imply that there are no conformational changes of scaffolds across phase boundaries, but this is not a done deal by any sense of the word. And in fact, it turns out that these differences in scaffold conformations across the phase boundary can enable this type of preferential binding.

Rohit Pappu (00:24:43):
And by the way, I should point out that this is, I was basically a seventh grader when Wyman and Gill wrote about this. And I’m fairly old, so these are well-renowned concepts. I think they’re just bare repetition at this point. But what we’re going to do is go beyond the linkage theory to ask, can we uncover certain general rules of polyphasic linkage to now make things a bit more practical to help us think about how we will regulate phase separation by way of ligands, because that’s the theme that’s emerging. And this is the work of Kiersten Ruff, currently a research scientist in the lab working closely with Furqan Dar, a graduate student in the lab. What Kiersten and Furqan did was they said, well, it gets really unwieldy to start thinking about lots and lots of pen and paper theory to write all these linkage relationships for fairly sophisticated scaffolds and ligands.

Rohit Pappu (00:25:40):
So let’s turn to LaSSI, our simulation engine that I introduced in lectures one and two, where we’ll basically put down archetypal multivalent systems on lattices and ask what happens. So here is the model for this part of the talk. This is our scaffold. It has stickers shown as blue PacMan. Some stickers are connected by implicit zero excluded volume spacers. So we are connecting back to lecture one. And then instead of implicit spacers, a couple of the spacers are modeled explicitly as red PacMan. Our ligand can essentially come in different flavors, but the key point is that we could have ligands that bind to sticker sites or ligands that bind to spacer sites. And then these sticker-sticker interaction in units of reduced temperature will be, let’s say minus two. And then we can titrate the strength of the ligand-to-scaffold interactions to be either half of the sticker-sticker interactions, equivalent to the sticker-sticker interactions, or stronger.

Rohit Pappu (00:26:55):
Okay. So what we’ll do is start to look at different types of ligands. So the first thing we’ll do is look at what happens when we have monovalent ligands that interact with stickers or monovalent ligands that interact with spacers. The gray phase boundary is in the absence of ligand. And I’m showing you here for one particular ligand concentration and the orange phase boundary is basically what happens in the presence of ligand. And so when we have monovalent ligands interacting with sticker sites, depending on the strength of the interaction between the ligand and the sticker, you effectively either destabilize phase separation or basically abrogate phase separation. No big surprise here. You’re competing with sites that are actually driving phase separation.

Rohit Pappu (00:27:48):
The spacers, on the other hand, they also have a weakening and abolishing effect, but what they’re doing here, again, remember back to lecture one, they’re adding to the effective excluded volume, and remember that our spacers enable this cooperativity of phase transitions that enables the phase separation. And basically we are, by increasing the effective excluded volume or effective solvation volume, we’re basically destabilizing. So this will be true for monovalent ligands. Let’s ask what happens with divalent ligands. As the title basically tells you, you have divalent ligands that are going to interact with these sticker regions and so essentially we start to see a destabilization of phase separation with the divalent ligands. But the extent of the destabilization is not as pronounced as the monovalent ligands.

Rohit Pappu (00:28:45):
And you’re probably wondering why, because there is a cross-linking ability that’s coming about from the divalent ligands because they can actually also add to the valence. So there is a destabilizing, but not an abolishing effect. Now, when you have divalent or bipartite ligands that interact with spacers or spacers and stickers, now what you actually see is the orange curves are wider than the gray curves. So you’re actually seeing an increase in the driving force for phase separation. So you get this enhancement of phase separation. So let’s go back and ask, to what amount? And so basically we focused on the divalent ligands, and this is one of the central issues that comes up, which is that if I have the endogenous concentration of a scaffold that is lower than its intrinsic saturation concentration, can I have a suitable ligand or collection of ligands that can actually drive phase separation by basically lowering the threshold concentration?

Rohit Pappu (00:29:52):
And the answer is yes, in that here, what we’re doing is plotting the concentration in the dilute phase in the presence of ligand and the ratio rather to the intrinsic saturation concentration. If that value is one, then the driving forces are not changing. But if that value is decreasing, we’re actually increasing the driving forces for phase separation. And in fact, what you can see is that in this particular case, as you titrate ligand concentration and you have these divalent ligands that are basically interacting with the spacers, you can increase the driving force by an order of magnitude. So now you have a ligand mediated additional driver. In other words, it’s a bit simplifying to say, the components of condensates will either be clients or scaffolds. These ligands can actually be regulators.

Rohit Pappu (00:30:53):
Now, let’s go back and then ask the question that was left unanswered in the polyphasic linkage formalism, which is what do ligands do to the dense phase? And it will turn out that ligands will actually have a diluting effect on the concentration of scaffold in the dense phase no matter what. So we’re doing the same thing. We’re measuring the concentration of scaffold in the dense phase in the presence of ligand and its ratio when compared to the absence of ligand. And I’ll walk you through these slides. So essentially, divalent ligands that interact with stickers, they are destabilizing phase separation. And so what is the effect on the dense phase? We’re diluting the dense phase. We seldom, these are basically statistical issues, essentially finite sized systems, but really, you never see an increasing of the concentration of the scaffold in the dense phase.

Rohit Pappu (00:31:49):
So even with ligands that are actually enhancing the driving forces for phase separation, what we’re seeing is we’re either maintaining the scaffold concentration, or rather strikingly, we’re even diluting the concentration of the scaffold in the dense phase. If you stop and think about this, this makes perfect sense. Because essentially what you’re doing is you are enhancing the driving forces for phase separation. The ligands are not just passively partitioning in, they are actually coming in and contributing to the driving force. So there has to be a make room for the regulator that’s actually enabling the driving force. And so in fact, if we go back and then quantify the total concentration, not just of the scaffold, but if the ligand and scaffold, what we actually find now is that in cases where the ligand is enhancing the driving force for phase separation, you can actually see that the total concentration has gone up now, so essentially what happens if there’s a linkage, the scaffold has made room for the ligand.

Rohit Pappu (00:32:56):
The ligands have come and bound to the scaffold in the dense phase, for whatever reason, they have enhanced the driving force for phase separation by dropping the saturation concentration required of the scaffold but they’ve also made the condensate more dense overall. But of course, the total concentration goes down when we have destabilizing ligands. Very cool. So now comes the, I’d say the billion dollar question in this field, because I’m fairly confident that one of the things that we all think to do to measure is the partition coefficients of whatever client molecules we want to measure. And so the question is, can I read out the stabilizing or destabilizing, i.e, regulatory effects of ligandsm by just measuring partition coefficients? Okay?

Rohit Pappu (00:33:54):
So let’s define our partition coefficient. It’s basically the ratio of the concentration of the ligand in the dense phase B to the concentration of the ligand in the dilute phase A. Partition coefficient greater than one. We basically say that our ligand is accumulating more preferentially or favorably in the dense phase. If you’ve got macromolecular crowders, for example, the partition coefficient will be less than one. It’ll say that it’s being excluded from the dense phase. So the value of PC is something that we use a lot. What is particularly important is that it’s not out of the realm of possibility that we’ll find a paper where PC equals one is taken to mean that the ligand is essentially agnostic for the scaffold in the dense versus the dilute phase.

Rohit Pappu (00:34:44):
So what Kiersten did was she visited this question and basically asked, does this have merit? And what this plot shows here is that when we consider ligands that these stabilize phase separation, that means that they’re basically increasing the saturation concentration, we can get partition coefficients that are all greater than one. In fact, we can get partition coefficients that are as large as 100. Okay. This is a ligand that is ostensibly destabilizing phase separation. We can look for ligands that do not change phase separation at all, i.e, this ratio is one. The partition coefficient is still in this gray zone, somewhere between 10 and 100. So it’s still accumulating, but it’s not doing anything to the driving forces. And really strikingly, you can actually have ligands that, of course, promote phase separation. And this is much more intuitive, some would argue in that you would get partition coefficients that are actually quite large.

Rohit Pappu (00:35:45):
So what’s the takeaway here? That essentially the partition coefficient has a blindfold as far as a measure is concerned in terms of telling us anything about how the molecule in question, i.e, the ligand, is affecting the driving forces for phase separation. The obvious question is why? And so Kiersten went back to linkage theory and basically was able to derive for a series of systems, but I’ll show you the simplest one, the partition coefficient, when we essentially use a binding polynomial that’s first order across the phase boundary, it is a product of quantities. Here is the ratio of volume fractions in the dense versus the dilute phase. Here is the concentration of scaffold that’s bound to ligand in the dense phase and the dilute phase. And again, that contribution from the volume fraction of the dense and the dilute phase.

Rohit Pappu (00:36:41):
Put in words, the partition coefficient is not just a measure of preferential binding. It is a measure of the contributions from preferential binding and the differences of the scaffold concentration across the phase boundary. And so in effect what’s going on is that the partition coefficient really is our fairly efficient way of saying, I can tell you what the concentration in the dense phase is going to be versus the dilute phase as seen by some molecule. But how that molecule sees it will be contingent upon two things: How is it binding and how much room is available for it, or what is the effective concentration of scaffolds? What Kiersten then did was she said, well, okay, if this is true, I can solve these binding polynomial equation numerically and ask to see if this is actually true, where now what we have is let’s say, beta A over beta B being 10 is essentially saying that our ligand is preferentially binding to the dilute phase.

Rohit Pappu (00:37:48):
It being, if beta B over beta A is 10, then our ligand is preferentially binding to the dense phase. If they are equal, then essentially we should see that there’s no change in the saturation concentration. What happens to the partition coefficient? Two things, it’s always larger than one, and it’s value depends on the ligand concentration. So effectively what this says is that a partition coefficient in and of itself is an easy-to-measure quantity, but quite likely, uninformative. What we will need our partition coefficients as a function of ligand concentration, but more ideally we would think measure this quantity over this quantity. So that’s the takeaway. Ligands can modulate phase separation via preferential binding. I talked about what happens when you have one type of ligand, but of course you can have a whole plethora, a network of ligands.

Rohit Pappu (00:38:49):
Ligands can enable phase separation at lower scaffold concentrations. When you start thinking about at endogenous levels of expression, how might I think about phase separation actually happening, or how might I ask the question of having crossed the threshold concentration, why should I end up with a condensate that dissolves? A ligand can help do that for us. Which of course means that in the cellular sense, controlling the expression levels of ligands will actually afford a multitude of knobs. Because you have one scaffold, let’s say or two scaffolds, or three scaffolds, but you have, let’s say N different ligands that you can start to tune and you can start to imagine what type of combinotorial complexity a cell might have over different cellular states and phase. So to me, this is very exciting.

Rohit Pappu (00:39:45):
That segues, of course, to the real fly in the ointment, which is I made the very simplifying and glib assumption that we essentially had two types of molecules, a ligand that does not undergo phase separation and a scaffold that basically will undergo phase separation via homotypic interactions in the solvent-mediated homotypic interactions. But now when you start adding other molecules into the system, you bring to bear the possibility of heterotypic interactions, which means that new rules will emerge because of the additional degrees of freedom. So I will give you a current working summary of where this work stands. I should point out that this represents contributions actually from two different labs, in this particular case, non-collaborative. This is not that we have developed a feud or anything. It’s just that we were pursuing this independently, which is actually fun sometimes to converge upon similar findings independently.

Rohit Pappu (00:40:44):
Some of you have read the paper that Josh Riback wrote recently published in Nature. This was proceeded by work that Furqan did that was published in PLOS Comput. Biology. So I will talk more about our work, so we don’t use the free energy formalism that Josh prefers, we prefer the formalism of slopes of tie lines because it gives us something extremely visual to be thinking about. So let’s walk into this. I’ll first walk us through the problem of how to think about multi-component phase diagrams in a system where the driving forces for phase separation don’t involve purely homotypic interactions. They actually, if anything, predominantly involve heterotypic interactions. And so this is the system, nucleophosmin1, studied quite beautifully over the years by Diana Mitrea and Richard Kriwacki at St. Jude.

Rohit Pappu (00:41:41):
And those of you who know the system know it well, it’s got this oligomerization domain, these acidic tracts. And then there is a nucleic acid binding domain. The oligomerization domain drives the formation of pentamers. So essentially this is a branched multivalent polymer that has disordered regions tethered onto a beautiful, folded scaffold. It turns out that you can add arginine-rich peptides that will actually turn out to be the regulators of what’s going on with nucleophosmin, so essentially the GC of the nucleolus. And when you’ve controlled the flux of arginine-rich peptides, you essentially either enhance the stability or weaken the stability by a form of complex coarcervation. It’s not purely electrostatic in nature because as we’ve discussed, arginines versus lysines and aromatics, et cetera, bring lots of interesting things to the party.

Rohit Pappu (00:42:38):
So what Richard’s lab has done over the years, driven primarily by Diana,is to demonstrate that you can come up with a sort of parsimonious version of nucleophosmin that essentially has the pentameric core and the acidic tracts. And then you can study the phase behavior as you titrate the concentration of arginine-rich peptides where what you do is you control the valence of arginines, i.e, the number of arginines, or let’s say even the patterning of arginines. So make a super sticker of arginines connected by a flexible linker to another super sticker, which is exactly what this is. Furqan basically visited the problem of calculating phase diagrams, and I’ll use the system to first walk us through some topological features of phase diagrams in multi-component systems that have begun to be appreciated by us, by Cliff’s lab. Richard has always known this. Mike, I think always knew this, Mike Rosen.

Rohit Pappu (00:43:42):
And more recently, Sam Safran and Emmanuel Levy’s lab have done some beautiful work in this area and so has Priya Banerjee. So let’s look at our physicists version of N130 and rpL5. Basically, this is telling us that we have a divalent molecule. So we flood our system with multiple rpL5s. We then essentially can titrate the concentration of N130, note these curious units because we’re doing simulations on a lattice. So our concentrations are measured in units that are per voxel of the lattice. There’s no micromolarity here. And then we’ve got rpL5 that is titrated here. So I’ll walk you through some important features. First and foremost, the purple contour essentially is now our phase boundary or coexistence curve. It’s not a binodal because of course, what we have are the possibility of higher number of nodes, if you will.

Rohit Pappu (00:44:48):
We can also calculate the percolation line as discussed in the first lecture and basically ask, what fraction of the concentration envelope, essentially what would be a networked droplet? And that would be the green contour. And then of course you have the bulk gel that is forming out here. Let’s walk us through some features of this. So let’s now say something like this, we’ll keep the concentration of N130 fixed and basically increase the concentration of rpL5. So we’ll go through the two-phase regime. That means for all points that lie between the purple boundary we’ll end up with phase separation, where basically we’ll get two coexisting phase corresponding to this value here and this value here. But importantly, and similarly, we’ll have the same thing if we keep rpL5.

Rohit Pappu (00:45:42):
But one of the things that you will see of course, is that this closed loop behavior enables something called reentrant phase transitions. So essentially, by controlling the concentration of the second molecule that’s driving phase separation or required for driving phase separation, you can essentially cause these molecules to exit the two-phase regime. And so Priya Banerjee, when he was a postdoc in Ashok Deniz’s lab first introduced this idea to our literature. It’s been prevalent in the phase separation literature for some time. But then there’s also something that Tyler Harmon discovered, and Furqan Dar rediscovered, which is the idea that the percolation line or percolation boundary is going to have this parabolic shape also exhibiting a form of reentered behavior, mainly because essentially what will happen is that above here we have too many N130 molecules. Basically you cannot really network here. You have too many rpL5 molecules, you cannot network. So you essentially get these reentrant features both for phase separation as well as percolation.

Rohit Pappu (00:46:51):
Okay. So what we’ll do is go back and now start to think about some model two-component systems. Furqan designed this, where we’ll say that we have got two systems that require one another to undergo phase separation. So the only way they can undergo phase separation is via heterotopic interactions. Here’s the interaction table. We can have that system to which we add a client, which following Mike Rosen’s schematization will essentially be a reduced valence version of polymer one. We’ll now say we’ll add some homotypic interactions. So now you start to see interactions showing up along the diagonal. And so our blue molecules can interact with themselves.

Rohit Pappu (00:47:37):
And then the final scenario is we say, we have only homotypic interactions, but then we have a crowder. So essentially, the only thing that the black polymer here is going to do is serve to contribute excluded volume effects. And so we ask, what do these phase diagrams actually look like? In the next few slides, there will be two scales that I’ll be using. I’ll be using the linear scale here because that helps us highlight the dense phase arm. And then I’ll show the logarithmic scale because that helps us highlight the dilute phase arm, which basically otherwise makes the phase diagram look like a guitar pick because you don’t really have the concentration resolution down here. It still has this closed loop nature. And so essentially what happens here is with heterotypic interactions, you get a beautiful, perfect closed loop.

Rohit Pappu (00:48:28):
And it’s essentially symmetric about the one to one ratio. Add a client, and since the client interacts with the red polymer and you start to increase the asymmetry, because now in fact there is a sort of bulge that is forming in our phase diagram. If you add homotypic interactions–by the way, the temperature is fixed here–you essentially now start to fundamentally change the shape of the phase diagram. That closed loopness is gone. And in fact, you start to see more of a verticality here. So it’s becoming less sensitive to the red polymer, so to speak. And really basically you’re getting the phase boundary that looks more like what we’ve come to expect with binodals as a function of temperature and the really, really odd ball, which is what happens in the presence of a crowder.

Rohit Pappu (00:49:23):
Essentially, these are depletion mediated attractions. And so essentially what you say is you get what looks like two lobes of a boomerang of some sort. But basically this is the dilute phase. This is the dense phase. And we’ll get to what is going on with the crowders. Now, these types of phase diagrams will have tie lines. They have slopes. They have implications for thresholding behavior. This will sound like a mouth full, in the few minutes that I have left, I’ll explain what I mean here. Let’s go back to the phase diagrams we know and love. Concentration on the X axis, temperature on the Y axis. The two coexisting phases, let’s say I have, my system is at this particular concentration, it separates into these two coexisting phases, gray and green.

Rohit Pappu (00:50:14):
There is a tie line that passes through this black point and joins the two coexisting phases. That basically is the line that connects the two points that are of equal chemical potential. The tie line is horizontal. What is the ordinate here? It’s temperature. That is basically saying that the temperature in the dilute phase and in the dense phase are exactly the same. As a consequence, but that’s going to be different here because in our multidimensional or multicomponent systems, now our tie lines actually have slopes. So in the previous case, the tie line basically was horizontal, zero slope. Here we’re basically going to have some finite slope. And also what’s interesting is that if you convert this from linear space to logarithmic space, essentially our tie lines actually start to have curvature on them.

Rohit Pappu (00:51:09):
Not only do we have to recognize that when we go to multi-component systems, tie lines are not horizontal. We have to recognize that we have to worry about, are we plotting our phase boundaries in linear versus logarithmic space in order to figure out what sort of tie lines are we working on? What are the implications of having non-zero slopes? The canonical expectation is let’s say I were to titrate the concentration of a scaffold molecule that’s driving phase separation. I’ve measured the amount that remains in the dilute phase or in the solution. I’ll come to some threshold concentration, and then that will plateau. That’s our saturation concentration. This is basically the way we think about the problem. But that goes out the window now. So essentially what I’ve done here is basically said, I’m going to fix the concentration of B, vary A, so that means… that’s right.

Rohit Pappu (00:52:08):
So we’re moving up along the ordinate and we’re going to measure how much of A remains in solution. So basically we hit the phase boundary when we come to this point here. We actually see some completely non-trivial behavior. And then of course, when we exit the phase boundary, we catch up back with the dashed line. This is shown in logarithmic scale, which is important. So the key point is that the concentration in solution of molecule A does not saturate, but it’s set by the slope of the tie lines. So let’s return now to our model systems and actually see what sort of behavior we get. Essentially what we’ll find is that the slopes of the tie lines will approach zero. And therefore we’ll start to see this leveling off behavior only when we add homotypic interactions.

Rohit Pappu (00:53:00):
But if we have purely heterotopic interactions, we’re basically going to see variable concentrations in the dilute phase as we change the total concentration of a particular molecule. So here are the tie lines. Again, the bottom part here is showing what happens in linear scale, here what happens in logarithmic scale, and you can actually start to see how these slopes start to shift. They become completely funky when you start to add crowder. And let’s go back and look at what happens to the concentration of component one, let’s say our blue polymer in the dilute phase as we titrate the total concentration here. And this would be of component two. I would basically look at this system here. Notice you never really get any kind of saturating behavior, but instead you start to get this dipping type of behavior.

Rohit Pappu (00:53:52):
In other words, it’s not that the concentration will saturate at some value, it will go below some threshold. And that the value that it falls below will be governed by the strength of the heterotopic interactions. But what’s really fascinating is that in the case of the crowder, you don’t get leveling off behavior either. So in fact, what’s going on is the amount of our scaffold molecule that remains in the dilute phase actually starts to go down and that’s because the crowder is now taking, it doesn’t want to go into the condensate. It’s taking up more and more of the dilute phase. And so basically what this says is that it is really a tricky issue to basically say that, hey, I can unmask the contributions of homotypic interactions by adding crowders because the underlying physics actually changes when you start to add crowders because you’re driving phase separation primarily via depletion mediated interactions.

Rohit Pappu (00:54:52):
Now, of course, if you’re convinced that in the cellular milieu there are bonafide excluded volume based crowders, these experiments will have some merit. But I think if the intent is to unmask the contribution of the homotypic interactions, proceed with caution. Okay? I will stop there, suffice it to say that we’re just starting to sort of, it’s the tip of the iceberg here. There’s a heck of a lot more to understand regarding this complex interplay between spontaneous and driven phase transitions in multi-component systems. There are going to be some very interesting regulators, ligands I talked about, post-translational modifications, post-transcriptional changes are also going to be super important. And thinking about now heterotypic interactions and the complexities of multi-component systems will be absolutely imperative.

Rohit Pappu (00:55:46):
Let me stop there. Let me thank the people who’ve done the work today. I mostly talked about work that Steve Boeynaems did on the protein-RNA side in collaboration with Alex Holehouse. And then the latter two stories were driven exclusively by Kiersten and by Furqan. Thank you for your time and attention.

Mark Murcko (00:56:06):
Thank you, Rohit. Again, just as in the last two weeks, spectacular lecture, lots to chew on, lots of great results to think about. We have a number of questions that have come in, and I know that we’re at the top of the hour, so we don’t have too much time. But why don’t we jump to Charlotte? Charlotte had a very interesting question about post-translational modifications.

Charlotte Fare (00:56:30):
Hi. Yeah. Can you hear me?

Rohit Pappu (00:56:31):
Yes, Charlotte.

Charlotte Fare (00:56:33):
Hi. I guess you alluded to it on that final slide, but I was wondering if, when you discussed how ligands can affect the percolation concentration or saturation concentration of one component in a multi-component condensate, how might one think about post-translational modifications on that same protein modifying the unmodified partners in the condensate?

Rohit Pappu (00:57:07):
You can start to see that there is now going to be quite a bit of an interesting complexity emerging. So let’s start simply with, I’ve got ligands, I’ve got post-translational modifications to think about or post-transcriptional if I have RNA, and then I’ve got our molecules that are driving phase separation either by homotypic or heterotypic interactions. So we’ve got basically at a minimum, three players that we’ve got to think about. Now, of course, there may not be just one ligand, there may not be just one pair of heterotypic interactions, but the question is, are these rules extractable? And the answer is absolutely yes. And so a lot of these intricate phase behavior that I think we’ve come to know and appreciate in the context of condensates is going to become manifest and that will give rise to, for example, the ability to fluidize certain components.

Rohit Pappu (00:58:07):
The ability to realize wetting versus dewetting behavior, the ability to get unmixed condensates. The ability to, let’s say, use ligands that preferentially interact with, let’s say one’s component of the scaffold, and let’s say there are other scaffolds that can engage in homotypic interactions. You can actually dissolve certain, do selective dissolution of condensates, which is actually going to be really interesting, and I rather suspect quite important for biology. I guess the short answer is, yes. The long answer is that there’s going to be a lot more interesting stuff that’s going to come along. And the real challenge, I think here is going to be how we formalize this in terms of both the theory side and also in terms of connecting these two measurements, because fundamentally, how do you measure? The challenge is how do you measure the concentrations of more than a pair of species? That would be the billion dollar challenge. Right?

Charlotte Fare (00:59:13):
Thank you.

Mark Murcko (00:59:13):
That’s a great discussion. I think, Bede, you had a very interesting question about what can be learned from the simulations about some of the subtleties of these systems.

Bede Portz (00:59:27):
Rohit, with respect to Steven and Alex’s work, can you predict from the simulation that the length of the DPRs will require an elevated amount of energy to overcome this barrier between a dynamically arrested metastable state and the ultimate spherical state. And I ask this question from the perspective of someone who’s tangentially working in neurodegeneration. We tend to think of aggregates as an endpoint emerging from a liquid thing. But what this work suggests is that it might, amorphous thing, an aberrant phase transition might actually be something on pathway to a condensate and energy in the cellular sense isn’t heat but rather helicases and chaperones. And so might we be looking at an endpoint that is really not emerging from a droplet but rather arrested on the way there?

Rohit Pappu (01:00:26):
I have to first do this, because I think I got through. You’re absolutely right, Bede. There, the issue that arises is there are two polymers whose length effects one can start to titrate. And of course, the way to do that would be to titrate the length whilst keeping track of what that’s doing to the sticker valence. So for example, if I start to dope in in predominantly purine-rich regions, some pyrimidine-rich spacers, for example, I have increased the length, but I’ve perhaps not created as much of a problem for entanglements and therefore for the dynamical arrest. Likewise, the experiment that we’re actually setting up to do and think about computationally as well as experimentally is not just think about PR repeats, but then start to dope in the occasional lysine, for example.

Rohit Pappu (01:01:24):
And I should point out here, throw a shout out to Sua Myong and Taekjip Ha at Hopkins. They have a piece of work that I think will see the light of day soon. And I think she’s talked about this, I’m not disclosing privileged information because it’s on bioRxiv as well, because it turns out that she can interpret the effects of particular arginine to X mutation or a glycine to glutamate mutation in FUS as being due to dynamical arrest. Because you can actually demonstrate that given enough time, in this particular case, they didn’t go after the particular question that you asked, but this is precisely the point. I think helicases, energy-driven processes might well be there to enable the traversing of these barriers. So you’re absolutely right.

Rohit Pappu (01:02:23):
We shouldn’t think about, the minute you start to see irregularly shaped condensates, we shouldn’t think that these are solids that came out of liquids as crucibles. They could very well be dynamically arrested phases.

Mark Murcko (01:02:37):
I think that’s a really interesting mental model to think about some more. I love that. We have a question also from Alan who also wondered about how the dynamic properties of proteins affects the behavior of condensates. Alan.

Alan Underhill (01:02:53):
So beautiful talks have been tremendously helpful. I’m just curious, as you actually push to these really high partition coefficients where the protein is effectively only within the condensate, what happens to the dynamic properties within the condensate and exchanging between the dilute and the dense phase?

Rohit Pappu (01:03:12):
One of the missing pieces of the puzzle here that I didn’t write on is the dynamics actually becomes really, really, really, really important. And so one way to step back and think about this is, I think if you connect to lecture one, the first point I would make is that we need to stop thinking about these as purely viscous bodies. These are always viscoelastic, which means that the viscosity and the elasticity are time dependent. And that will mean that as we change both spatial inhomogeneities or local densities inside condensates, we are likely to start seeing time dependent conversions between viscous and elastic properties.

Rohit Pappu (01:04:00):
And just to put this in context, I didn’t show this, but in the experiments that Steven did with the protein-RNA mixtures, there was actually a beautiful coexistence dynamically speaking, whereby from a FRAP standpoint, if all you did was to take the fluorescently labeled RNA and did a FRAP analysis on that, you would conclude that these were solid-like condensates. But if you, in the second channel, because you have two different constructs that are labeled the protein and the RNA, but when you look at the FRAP and the timescales for recovery of the fluorescence, when you look at the protein side, it essentially looks like what we’ve become accustomed to looking at. And so there again, there appears to be, and that gap between the recovery times with the protein and the RNA are again, very dependent on the sticker types on the protein and the RNA.

Rohit Pappu (01:05:01):
So going to your question, I think what we’re going to start seeing is possibly, we’ve been talking about thermodynamic coexistence of phases, but I think we’re probably heading toward also thinking about the coexistence of dynamical phases inside of condensates, which will therefore give rise to a really rich spectrum of timescales, but a time dependence to those properties as well.

Mark Murcko (01:05:34):
That’s a great answer. Okay. I think we’re running a bit late, so I think maybe we’ll call it here. Rohit, again, everyone on the call, everyone who’s come to all three lectures really wants to thank you for all the effort you put into these lectures and how brilliantly you delivered them. So thank you very, very much for all of the hard work.

Rohit Pappu (01:05:55):
And I should say this was inspired by Rebecca Zacks, who has not actually revealed herself on here, at least I haven’t seen her. I know she’s there somewhere, but Rebecca, you are the one who prompted me to do this. I am truly appreciative. And Jill, you’ve basically held me by my finger as I’ve gone through this. So thank you so much. And thank you, Mark, for your support. This has been loads of fun putting it together and I’m happy to… And I should point out one last thing, which is I do have, I think something like 27 questions from the last time. So I collected all of them. What I decided to do was to see what new questions came up and then basically I will be super proactive to make sure that before Jill uploads this last lecture, you get the answers to all questions that came from lectures one, two, and three.

Mark Murcko (01:06:45):
That’ll be wonderful. That’ll help everyone. So thanks again for that too. All right. I think we’ll sign off at this point.

Rohit Pappu (01:06:51):
Yeah.

Mark Murcko (01:06:52):
All right. Thank you all. Thank you, Rohit.

Rohit Pappu (01:06:53):
Thank you, Mark.

Mark Murcko (01:06:54):
Okay. Take care. Bye, bye everybody.