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VIDEO: Rohit Pappu on Molecular Grammar of Condensates – Part 1

On July 29, Dewpoint, in partnership with Condensates.com, kicked off a 3-part series of talks featuring condensate pioneer Rohit Pappu. Rohit’s three lectures present the molecular grammar of biomolecular condensates. In this first part, he covered the basic physics of associative polymers, the stickers-and-spacers model, and the insights that emerge from the application of this model to describe the phase behavior of linear multivalent proteins.

Rohit is the Edwin H. Murty Professor of Engineering and the Director of the Center for Science and Engineering of Living Systems at Washington University in St. Louis. Rohit has made seminal contributions to the field of biomolecular condensates, in particular the drivers of phase transitions that lead to the formation of protein and RNA condensates, and the role that disordered regions play in these cellular processes. Rohit is also a member of Dewpoint’s Scientific Advisory Board and a wonderful advisor, collaborator, and friend.

See the first of this fascinating set of lectures below. And Rohit graciously provided written answers to all of attendee’s questions; those are below as well. To watch the full series, you can find part two here and part three here. Rohit’s talks are part of our Kitchen Table Talk series.

Rohit Pappu on Molecular Grammar of Condensates - Part 1


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TRANSCRIPT
Mark Murcko (00:00:00):
Today, we’re kicking off a three part lecture series today from Rohit Pappu. Rohit, who obviously is one of the pioneers of the whole field of condensates. Rohit’s lectures are the latest installments in our series of what we’re calling Kitchen Table Talks, in which we invite prominent researchers in the condensate field to share their thinking about their recent work with the entire global community. And all of those lectures can be found on condensates.com and we’re adding more all the time.

Mark Murcko (00:00:30):
Rohit’s three lectures in that series, he’ll be presenting on the molecular grammar of biomolecular condensates. And today in part one, he’ll cover the basic physics of associated polymers, the stickers and spacers model, and also the insights that are emerging from the application of this model to describe the phase behavior of linear multivalent proteins. And lectures two and three in the series will be next Wednesday, August 5th, and then the following Wednesday, August 12th. And they’ll be at the same time as this lecture, 10 o’clock Eastern time. Lecture two will cover phase transitions of IDRs, Intrinsically Disordered Proteins and domains, while lecture three will cover phase transitions in multi-component systems, which is a fascinating topic in itself.

Mark Murcko (00:01:22):
Just a little bit more background on Rohit. He’s the Edwin H Murti Professor of Engineering, and the Director of the Center for Science and Engineering of Living Systems at Washington University in St. Louis. Rohit has made seminal contributions to the field of biomolecular condensates, in particular, the drivers of phase transitions that lead to the formation of protein and RNA condensates and the role that disordered regions play in these complex cellular processes. Rohit is also a member of Dewpoint’s scientific advisory board. And he’s a wonderful advisor to us at Dewpoint and a great collaborator and a friend. Rohit, we really want to thank you in advance for what all of us know will be a wonderful series of lectures. The floor is yours.

Rohit Pappu (00:02:12):
Thank you very much, Mark. And thank you to Jill and Rebecca for suggesting this idea and for doing all the leg work to make what will, I think, be a seamless operation. I have learned a lot from my conversations with colleagues at Dewpoint and particularly from Mark. I think it’s a wonderful thing to put together, this Kitchen Table Talk series that is also not for profit, which is really, I think, appreciated by the community.

Rohit Pappu (00:02:46):
As Mark pointed out, today what I’m going to do is sort of focus on this general topic of what I refer to as molecular grammar, and really what this refers to is being able to read information that is written into protein and RNA sequences and connect this information to the driving forces for condensate formation, regulation, dissolution, and so on.

Rohit Pappu (00:03:13):
In today’s talk, I’ll focus primarily on what I’ll refer to as linear multivalent proteins, and in the interest of sort of telling you exactly what they are right from the get go, this will be a combination of folded domains and disordered regions. We make sure that we don’t start off with the notion that it’s just about intrinsically disordered proteins or regions…
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Rohit Pappu (00:03:42):
For all of you who are aficionados of condensates, this slide is, I think, a well-known one since this comes from the review paper that Salman Banani, Tony Hyman and Mike Rosen wrote back in 2017 highlighting the fact that there are lots of bodies that sometimes go by the name of membraneless organelles or compartments or granules, that have been known now for well over 120 plus years, depending on which body we’re talking about, to accumulate material, cellular material, primarily in the form of certain types of protein and RNA molecules either in the cytosol, as shown here, in terms of things like the Balbiani body, stress granules, processing bodies, or within the nucleus where in fact there now is a growing interest in recognition in the possibility that pretty much all of gene regulation might involve these membraneless bodies, which now go by the name of biomolecular condensates.

Rohit Pappu (00:04:57):
At the get go, it’s worth pointing out that Tony and Mike and Salman were very clear in trying to ascribe this name to imply one thing and one thing alone, a condensate is something that concentrates bio-molecules and the concentration of these molecules is evocative of the idea of condensation. And since it’s bio-molecules that are being condensed into some body, these are referred to as biomolecular condensates.

Rohit Pappu (00:05:36):
I bring this up because that particular definition is agnostic about the mechanism by which a condensate will form. Now, of course, that is being mildly glib because of course the working hypothesis, based on a lot of the extant data, not all of it, but a lot of the data, is that membraneless biomolecular condensates form via some form of phase transitions. And I distinguished spontaneous versus driven to recognize the very real possibility and also throw a shout out to observations that there are active processes inside the cell, which may well control a variety of things, including the sizes of condensates, whether or not threshold concentrations pertaining to phase transitions are indeed crossed and so on.

Rohit Pappu (00:06:36):
While the precise mechanism may well be condensate specific and context specific, I think where all parties have converged upon is the realization that a hallmark of molecules– macromolecules, be they proteins or nucleic acids–that end up in condensates or seem to be important for driving the formation of condensates, have the feature of being multivalent macromolecules. And that’s our launching pad for today’s discussion.

Rohit Pappu (00:07:09):
It turns out that while of course a lot of the condensate field is very much fixated on the pioneering and shape-shifting ideas of Flory and Huggins and Flory and Stockmayer, dating back to the 1940s, starting in the 1970s with work of Lundberg followed by the work of Mike Cates and Tom Witten, and then moving on to the work of [Alexander] Semenov and Michael Rubinstein, there’s been this recognition that you can make a polymer that essentially is a generic polymer, but you can sprinkle along the polymer some so-called attractive groups. And these types of polymers go by the name of associative polymers. And the name that we have co-opted, the sort of the term stickers interspersed by spacers is not something that we coined. We have been extraordinarily good thieves in sort of co-opting the language that has taken root in the polymer physics literature.

Rohit Pappu (00:08:25):
And the idea of stickers interspersed by spacers is intended to convey two very important concepts. Stickers shown here in blue are, for lack of a better way of thinking about this, best thought of as being akin to hotspots on protein surfaces, where you will get stereospecific or particular types of specific interactions. These will be characterized by a hierarchy of interactions, possibly hydrogen bonds, ionic interactions, a range of sort of specific hydrophobic types of contributions, et cetera. But the key point is that irrespective of the specific physical chemistry, what we can use to delineate a sticker is the fact that there will be physical cross-links that will form between pairs of stickers, and these stickers, these physical cross-links will have finite lifetimes based on the strengths of these interactions, the ranges of these interactions, the directionality of the interactions.

Rohit Pappu (00:09:33):
Now, of course, as depicted in this cartoon, which is courtesy of Alex Holehouse, what is depicted here is that the regions that are interspersed between stickers are essentially enabling a huddling or the bringing together of these stickers into spatial proximity. And therefore the spacers themselves are unlikely to be major players in terms of engaging in physical cross-links, but they are enabling the physical cross-linking of the sticker.

Rohit Pappu (00:10:08):
That might sounds a little esoteric. Let’s try to actually map the stickers and spacers formalism directly onto biological systems. And so here, what we’ve got is an instantiation, and I’m starting with folded domains mainly to try to, pretty much from the get go, dispense with the idea that condensate formation, proteins that drive condensate formation, is somehow the sole purview of intrinsically disordered regions. In fact, sort of concomitant with the development of the associative polymer literature, in the physics world was the literature on so-called patchy colloids.

Rohit Pappu (00:10:50):
In fact, folded domains with interaction hotspots maybe thought of as patchy colloids, where essentially what we’ve got is the valence, i.e, the number of specific binding sites, their interaction ranges, and their intrinsic affinities contributing to the overall phase behavior. And for those of you who are interested, it’s certainly worth going into the physical literature and looking up the term patchy colloids and sort of learning the fact that this field is so mature. It’s now about 30 years old. That people can sort of design nano-materials and all kinds of interesting synthetic materials based on sort of a direct tuning of the valence and the interaction strength and the interaction ranges of patches on patchy colloids.

Rohit Pappu (00:11:45):
There is no doubt, and in fact, I should throw a shout out here to the work of Daniel Colón-Ramos from Yale, who has done some beautiful work with glycolytic enzymes. And in fact, there’s not an IDR to be had in that system, but it undergoes this sort of oligomerization transition as a way to generate the requisite multivalence. And in fact, the regulation of, let’s say, the delivery of material across synapses seems to be governed by glycolytic enzymes forming condensates.

Rohit Pappu (00:12:17):
Here are the more sort of notorious or well-known exemplars of biomolecular condensate formation particularly phase transitions driven by multivalent molecules. And here what we have are intrinsically disordered regions where the valence, i.e, the number of short linear motifs and the properties of the disordered linkers or spacers contributes directly to the overall phase behavior. And this will be the topic of lecture two.

Rohit Pappu (00:12:50):
And then we’ve got the topic for today’s discussion, linear multivalent proteins, and simply highlighted here are the types of sort of polyvalent systems that we we’ll come across in signaling primarily, where you’ll have multiple SH3 or SH2 or PDZ or PHD or bromodomains, et cetera, concatenated by disordered linkers. And again, here, the valence of the number of domains, but really it’s the valence of hotspots or specific binding sites. And what we’ll focus on today, the properties of the disordered linkers that actually determine the overall phase behavior.

Rohit Pappu (00:13:33):
Now, I made the point that stickers engage in physical cross-links, and so you can sort of imagine that if you’ve got molecules that have sticky Velcro patches, they come together and essentially make a network. And again, if those of you who are interested in sort of more formal parlance, these are supposed to form what are called non-affine networks, which is just a fancy way of saying nonlinear networks.

Rohit Pappu (00:14:00):
And that nonlinearity here refers to the fact that the combinatorial set of options that I have when I have multivalent systems will give rise to these physically cross-linked networks. The first message that I would like you to take home right at this slide is that, let us not think about these condensates as molecules randomly diffusing around one another like so-called billiard balls, which is what we would refer to as simple liquids, but really these are very much networked liquids or networked molecules. And the key determinant of the overall rheological properties is going to be the timescale of the making and breaking of these physical cross-links.

Rohit Pappu (00:14:47):
Now, this is the topic that we’re going to discuss, and we’re motivated here actually by the beautiful and sort of pathbreaking work that came from the Rosen lab published in Nature in 2012. Here is a very sort of simplified version of the various systems that they studied, a system of poly-SH3 domains. Essentially, we’ve got a linear multivalent protein, where we’ve got multiple SH3 domains, shown in this very high resolution as PacMan, connected by disordered linkers that can make, at the binding site, complimentary interactions with the proline rich modules designated as PRMs. And again, these are poly-SH3 molecules interacting with poly-PRMs.

Rohit Pappu (00:15:39):
Based on what I just told you, you can see that there should be a cross-linking possibility essentially now, where a PRM can make an interaction, let’s say, with one SH3 domain here, but this PRM needn’t make a cross-link with this SH3 domain, but it could make a cross-link with an SH3 domain from a different polymer. So now you start to grow the network.

Rohit Pappu (00:16:05):
That leads us to the idea then that if I have got these linear multivalent proteins, let’s say poly-SH3, poly-PRMs, I throw them into solution, I start to crank up the concentration making sure that I maintain, let’s say, the one-to-one ratio of poly-SH3 to poly-PRM. What I’ll end up with, at some concentration, which we we’ll refer to as the percolation threshold, is the ability to form a network that essentially takes over the entire system. And as a sort of simple way to think about this, this is very much along the lines of asking the following question, which is, how many Kevin Bacon’s, let’s say, separate a pair of Hollywood actors, right? And the answer is everybody has a Kevin Bacon number, and that number typically, because he’s one of these actors who kind of shows up in every random movie, and so everybody has a Kevin Bacon number of, let’s say, between four and seven or something like that.

Rohit Pappu (00:17:07):
And what that is essentially asking is, if I go from, let’s say, one end of my cuvette volume to another end, how many sort of connections do I sort of traverse, right? The fact that I can go from one end of the system to the other without so-called getting my feet wet, essentially means that I now have a system spanning network. Okay?

Rohit Pappu (00:17:28):
Now, let’s go to Mike’s system. What he observed was that as he changed the valence of the SH3 domains, i.e, the number of SH3 domains, there seemed to be a robust formation of droplets, i.e, system, which he referred to as system spanning networks, and the concentration at which these droplets formed dropped as you increase the valence. Okay.

Rohit Pappu (00:17:59):
Now, what I showed you here is a test tube spanning network, what I’m showing you here are real data, which are showing sort of spherically confined droplets. And so then the obvious question that arises is, what’s going on here, right? I mean, where is the system spanning network? It turns out that what you can do is everything about the networking focuses exclusively on the stickers–the number of stickers and the affinity of the stickers for one another. But to make a multivalent molecule, of course, I need to concatenate these stickers together. And the way I do that is with the so-called spacers.

Rohit Pappu (00:18:45):
And these spacers can actually enable what I will refer to colloquially as a huddling transition. It can sort of collect up the, enable, for example, stickers, to find one another in a confined volume, right? That means that the spacers and their particular properties are going to enable a density transition where the percolation is a networking transition, giving rise to two co-existing phases, whereby you can have a dense network of molecules co-existing with a dilute solution of largely un-networked molecules, right?

Rohit Pappu (00:19:27):
What does this do? What this does is it effectively says the network becomes confined to the spherical droplet. But more importantly, it’s enabling this networking transition to happen at concentrations that are well below the sort of bulk percolation threshold. In fact, the way to think about this is that, our co-existing sort of dilute phase concentration is at sort of one end, the concentration of macro molecules inside of our dense phase is at the other end. And if the percolation threshold is crossed inside of this confined volume, you end up with essentially what looks like a sort of droplet spanning network, which means that depending on the timescales for the making and breaking of these physical cross-links, this droplet will behave like an elastic material on some timescales. And in fact, we see this quite often in all of condensatology, where we start to see all kinds of interesting differences in the recovery of, let’s say, fluorescence after photo-bleaching and so on.

Rohit Pappu (00:20:42):
Essentially, the way we like to think about this is that this is not simply a phenomenon of liquid-liquid phase separation, but in the lab, at least, we have taken to referring to this as phase separation and percolation. The reason being that in almost all of these multivalent systems, these are not pure homopolymers. We probably almost always have this type of an inequality satisfied. For there to be gelation or percolation without phase separation, it must be the case that the spacers really aren’t doing their thing and you basically make a test tube spanning network at some ridiculously high concentration.

Rohit Pappu (00:21:24):
And of course, there is the possibility of precipitation without making networks. And so in that case, the percolation threshold should be larger than the concentration that you realize inside of the dense phase. That’s a highly unlikely scenario, unless one is looking at the formation of amorphous precipitates. Our biased thinking is that all of condensatology, at least that’s functionally relevant, really belongs into this AND gate, phase separation and percolation. Okay.

Rohit Pappu (00:21:58):
That brings us then to the key point that I’ve alluded to already, which is that the spacers are really the culprits here, right? Their physical properties are determining whether or not percolation is driven by phase separation, namely, I get a spherical droplet inside of which I get a droplet spanning network. Or if I essentially go around phase separation and then eventually at some ridiculously high concentration, make a gel or a percolated network.

Rohit Pappu (00:22:29):
This is the work of Tyler Harmon, which is what I’m going to focus on throughout this talk. He’s a former graduate student, currently a postdoc in the lab of Frank Jülicher and Tony Hyman. Contributions of the intellectual variety from Mike Rosen and of the enabling variety from Alex Holehouse, a former graduate student and a postdoc, are not to be sneezed at because they were super important in helping us think.

Rohit Pappu (00:23:00):
I made the point about physical properties of spacers or linkers, here’s the only math slide that we’ll have. There is a way, it turns out, to sort of summarize the effect of linkers. And that will be in the parlance of polymer physicists, excluded volume, but in the interest of making this a bit more accessible to a general audience, we’ve taken to referring to this as the effective solvation volume.

Rohit Pappu (00:23:29):
And really what this refers to is, if I’ve got a disordered region connecting a pair of folded domains, there is something that I can quantify, which is the volume per residue that is set aside for interactions with the surrounding solvent. And that will be predicated entirely on the nature of the solvent mediated inter-residue interactions. And that’s what this W of r is actually doing.

Rohit Pappu (00:24:01):
Let’s say I set that to zero. That’s my ideal chain, right? Essentially, what that’s saying is that the residue-solvent and the residue-residue interactions are perfectly counter-balanced. What I will basically get back is one minus one, and I’ll get an effective solvation volume of zero.

Rohit Pappu (00:24:18):
If these interactions are repulsive, what that is saying is that the residues in the linker really want to be solvated. What I will now get back is essentially an effective solvation volume that is large and positive, reflective of the fact that the inter-residue interactions are on balance repulsive.

Rohit Pappu (00:24:39):
Conversely, if the linker really doesn’t like to make interactions with the solvent, it becomes super sticky for itself. These interactions as modeled by the W of r are going to be predominantly negative or attractive. And the effective solvation volume referenced to the ideal chain will become negative.

Rohit Pappu (00:25:00):
It’s easier to show that here in a movie, where basically I’ve got between two SH3 domains linkers of different categories, and you can see here that the high effective positive solvation volume linkers are in fact going to be quite expanded. The ones that are agnostic are essentially making rapid fluctuations into and out of expanded and compacted conformations, whereas, the very sticky linkers basically are pretty much like forming folded domains.

Rohit Pappu (00:25:34):
Alex and Tyler went through the human proteome of IDRs focused on IDRs that connect folded domains as linkers. And what we were expecting to find was, “Oh, look, all linkers are sort of exactly the same.” And in fact, that’s not the case, right? And it turns out that about 68% of linkers have sort of either a close to zero or positive excluded volume or effective solvation volume, but there are, in fact, a whole host of linkers that tend to be high in sort of very sticky for one another. What’s interesting though, is that a lot of the linkers that are in the zero or positive effective solvation volume category are the ones that are prevalent in polyvalent molecules, whereas the ones that are super sticky are sort of in things like dimers or trimers, so low valence molecules.

Rohit Pappu (00:26:29):
What that means, we can discuss at the end of the talk. But what we decided to do was to say, “Well, okay, there seems to be this preference for sort of effectively zero effective solvation volume or a positive effective solvation volume.” What would, let’s say, titration of the effective solvation volume of linkers do for us? And that’s the question, how does the effective solvation volume of disordered linkers influence the phase behavior of linear multivalent proteins?

Rohit Pappu (00:27:00):
Now, you can try to do these calculations analytically. In fact, Dan Deviri and Sam Safran have actually published a recent paper in Soft Matter, where they have actually done precisely that. We weren’t that clever, so we decided to take a much more brute force computational approach. And so here, what we’re going to do is include in our simulation hundreds to thousands of poly-SH3 and poly-PRM molecules. These poly-PRMs are going to be modeled as polymers with blue beads. The poly-SH3s are going to be modeled as polymers with red beads.

Rohit Pappu (00:27:42):
And what we’re going to do is fix the interaction strength between a single SH3 and PRM to be sort of governed by the intrinsic dissociation constant. We’ll also require that each SH3 can make an interaction with only one PRM. That’s making sure you’re respecting the stoichiometry. And then we start with is linkers that have zero effective solvation volume, which on a lattice you can actually be extremely slick about, and simply model them as just phantom chains that provide distance restraints between the SH3 domains or between the PRMs.

Rohit Pappu (00:28:22):
I’ll show you a movie where we start these molecules off fully dissociated, and pretty much within a few Monte-Carlo moves what you start to see are essentially these spherical structures forming. And I should point out that the only information in here is the intrinsic association constant, the valence, which in this case has seven SH3 domains and seven PRMs, and the specification of the property of the linkers as being zero effective solvation volume. I’ll play that again. The molecules effectively huddle together and give us what looks like a surface tension, minimizing spherical droplet, right?

Rohit Pappu (00:28:59):
What we then asked was, let’s quantify this percolation idea, which we can quantify in terms of the fraction of molecules that belong to the single largest cluster. And we can do concentration titrations in much the same way that the Rosen lab did this. And all data are shown in concentrations of modules, so that way we can compare molecules of different valence to one another. And so along the abscissa, we have the concentration of PRM modules, along the ordinate, we have concentration of SH3 modules. And what you can see is that above some threshold concentration, pretty much all of the molecules are being collected into a network. Okay? Here we ask the question irrespective of whether or not they’re in a droplet or they’re taking over the entire simulation volume.

Rohit Pappu (00:29:54):
What we can do is use theory to estimate, for this particular system, what is the percolation threshold actually? And it turns out that having 17% of the molecules cross, be part of a single largest cluster, is sufficient to make a system spanning network. It doesn’t require that all of your molecules go in there. That’s actually an important point because it starts to get to the idea that depending on how far one is, with respect to the percolation threshold, the connectivity inside of these condensates will be quite different.

Rohit Pappu (00:30:27):
Then we can quantify phase separation by essentially looking at the relative densities of protein modules with respect to the bulk. And what you can see is that at concentrations of PRM and SH3 modules, where we have crossed the percolation threshold, we also are making a very dense assembly.

Rohit Pappu (00:30:47):
One of the things you can actually do is go back and ask, quantify the organization of these modules with respect to one another using the radial distribution function. A liquid would be sort of highlighted, or hallmark of a liquid is short range, ordered long range disorder. And in fact, you see that here. Of course what we’re doing here is looking at sort of the SH3, SH3 organization, that should look just like an ideal gas. Whereas the SH3, PRM, there is a sort of first coordination shell, and eventually you sort of get the long range disorder.

Rohit Pappu (00:31:28):
And then what we do is we basically look at the comparative analysis here. On the left is how when we change the valence are we changing the fraction of molecules that are incorporated into the single largest cluster? Let’s go along the diagonal. You get back exactly what Mike observed, which is that the fraction of molecules that are incorporated into the single largest cluster will be realized at lower concentrations as you increase the valence. Okay. This is purely networking theory.

Rohit Pappu (00:32:02):
But then we can also track the density transition. And you start to see that for these higher valencies, essentially at the juncture, when you’ve crossed the percolation threshold, you’ve essentially also started to form these dense droplets that are co-existing with dilute bulk phases, on network bulk phases.

Rohit Pappu (00:32:25):
We now have this concomitance, as postulated, of the networking transition and the density transition. The density transition is phase separation. The networking transition is typically known as gelation, but I think in our literature, it gets conflated with the term hardening, so we have taken to referring to it simply as percolation, which refers to forming a system spanning network, which in this case is a droplet spanning network.

Rohit Pappu (00:32:54):
Now, let’s go to the other end. We’ll now say that our linkers have a mind of their own. They’re not just going to enable the huddling transition of these stickers. They’re actually going to exert certain preferences in terms of their solvation properties. And so let’s model what happens when we have high effective solvation volumes. And in this case, basically we model each linker site as occupying a lattice site, which means that they have very high, positive, excluded volume. What is this going to do?

Rohit Pappu (00:33:30):
Essentially, think about it this way, right? You’re going to try to stick your elbows out whilst you’re trying to get the tips of your elbows together and make sticker cross-links. So clearly the fact that now your elbows have forearms have girth is going to come in the way. And indeed that’s what you find.

Rohit Pappu (00:33:48):
Essentially, these are two simulations of two different systems above the percolation threshold. Low effective solvation volume, you get spherical droplets co-existing with the dilute phase. But with the explicit linkers, essentially what you get is this ability to form a fully volume spanning network but they never make droplets. Right?

Rohit Pappu (00:34:14):
This led us to basically now start to think in terms of what the spacers are doing, they are essentially imparting cooperativity, and this is something we can formally quantify. It turns out that if you go to the classic theories of Flory and Stockmayer, you can analytically, given the valence and the intrinsic dissociation constant, on a pen and paper calculate what the percolation threshold will be for whatever system you’re interested. 1941, right?

Rohit Pappu (00:34:50):
You have to do the hard work to do the simulation to calculate what the percolation threshold will be in the simulation, where of course the simulations we account for the effects of these spacers. What we realized is that a simple order parameter that quantifies this ratio as a function of linker length will give us a sense of two things: One is, when is phase separation aiding percolation? And when his percolation happening independent of phase separation?

Rohit Pappu (00:35:24):
Well, if c*, this ratio, is less than one, we are now realizing percolation at concentrations that are quite a bit lower than what Flory and Stockmayer would have decreed, which means that phase separation is providing this positive cooperativity. Some people like to refer to this as avidity. To me, that is something of an ill-defined term. We’ll refer to this as positive cooperativity whereby the density transition enables the networking.

Rohit Pappu (00:35:56):
If c* is just one, then we’re in the Flory Stockmayer limit. But if c* is greater than one, what we’re actually getting now is the linkers are coming in the way of the networking transition and certainly obliterating phase separation. Let me orient you. We now basically plot c* against linker length for three separate systems, the 3-3, 5-5, the 7-7 system. The 7-7 system is basically seven SH3 domains in one polymer, seven PRMs in the other polymer, and we’ve got hundreds of these.

Rohit Pappu (00:36:31):
Let’s look out in the long linker limit. If my linker is long enough, and by the way, here on the bottom axis, we plot number of linker sites in terms of number of lattice sites. We’ve worked out the mapping. And so effectively when we go out to this, we’re talking about linkers that are about 70, 80, 100 residues long.

Rohit Pappu (00:36:52):
What is really beautiful is that if you go back and look at a lot of these linear multivalent proteins, typically linker lengths are in this sort of 20 to 35 range. Okay. And they have, of course, certain compositional biases. In the long linker limit, of course, what we will get is that c* is one because the linkers really don’t play any role here. Essentially, the only thing that matters is the translational diffusion of the stickers with respect to one another, you get back the Flory Stockmayer limit.

Rohit Pappu (00:37:23):
At very short linker lengths, you essentially get the problem that all of the interactions can be made in small-mers, right? You can get network arresting dimers and trimers and things of that nature forming. So c* is actually going to be greater than one because you actually don’t get a network that can grow. But then there is an optimal linker length, and this is the case when we have the effective solvation volume being zero, I should’ve made that clear. When we have effective solvation volumes being zero, there is an optimal linker length where in fact now what you’ll get is c* less than one, indicative of the fact that you get droplets that are percolated co-existing with the dilute phase that is non-percolated.

Rohit Pappu (00:38:11):
Conversely, if we go and sort of ask exactly the same question, but now of these explicit linkers that have these very high, effective solvation volumes, c* is actually greater than one throughout because what’s happening is that this high bulk is basically arresting both phase separation and cranking up the concentration at which the system will sort of cross the percolation threshold. Okay.

Rohit Pappu (00:38:38):
Now, let’s go back and think about, is any of this tuneable? So we can start to think about the phase diagrams for phase separation and percolation. And the way we’ll plot this is we’ll fix the valence, we’ll fix the stoichiometry, we’ll change the concentration of our polymers, that’s along the X-axis. And we’ll pretend that we can make mutations along the SH3 domains or on the PRMs to titrate the affinity. And the type of phase diagram we expect to see is as follows. For some threshold affinity, you’ll start to see phase separation, namely two phase behavior. And what you’ll get is the crossing of the percolation threshold inside of this two phase regime.

Rohit Pappu (00:39:21):
But if the interactions are too weak, then you have to cross some very high threshold and then you’ll sort of get the classic sol to gel or dilute phase to sort of percolate the network transition. What we’ll do is basically titrate these effective solvation volumes of linkers and ask what happens. Here is our two phase regime for effective solvation volumes being zero. I’ll start to crank up the effective solvation volume. You’ll see the two phase regime narrowing. And goes away. I can play this movie backwards. Let’s do this again.

Rohit Pappu (00:40:00):
I’m increasing the effective solvation volume, I’m shrinking or destabilizing the two phase regime. I need to go to higher affinities in order to realize phase separation. And basically now I obliterate, right? You might be thinking, “Well, where is nature’s knob to tune effective solvation volume?” Well, post-translational modifications are the most obvious way in which this happens. And we’ll talk about this.

Rohit Pappu (00:40:25):
It turns out that it’s not just multivalence but it’s actually the properties of the disordered linkers that also contribute to the phase behavior of linear multivalent proteins. For linkers, the key parameter is the effective solvation volume, which is encoded by sequence. And fortunately, we are in a place where so much work has come before this type of work in the intrinsically disordered protein literature of mapping sequence to ensemble relationships from the labs of Julie Forman-Kay, Ben Schuler, Tanja Mittag, Peter Wright, Martin Blackledge, and so on, including us, Robert Best, where now you can actually quantify these properties and sort of directly calculate–with some hard work–the effective solvation volumes from sequence.

Rohit Pappu (00:41:15):
And the key point is that this convolution of phase separation and percolation is what enables these phase transitions to occur at physiologically relevant concentrations rather than in the sort of millimolar ranges. And this is the point that it can be tuned. And that’s the point that I’ll connect to right away. What I should point out is that if you’re interested in doing these types of simulations, Jeong-Mo Choi, a former postdoc, and Furqan Dar, a current graduate student, have actually put together an engine. This is actually engineered almost exclusively by Furqan, an engine called LaSSI, which basically sort of enables these calculations. It’s available free of charge on GitHub.

Rohit Pappu (00:41:59):
I should point out that this is more of a sort of, if you’re a physics nerd and you like to play with things, this would be the perfect tool. There’s a complimentary tool, which we’ll discuss next time, that comes from Alex Holehouse, which is PIMMS, which is much more of a plug and play type of engine.

Rohit Pappu (00:42:15):
Okay. I will actually sort of jump ahead to the concept of multicomponent systems, because I want to keep that in our field of view. If I gave you different numbers of molecules, we took the PRM, SH3 system and we said, well, there were two types. What if I had n different types? The Gibbs phase rule says that I could get n+1 co-existing phases. What does that actually mean?

Rohit Pappu (00:42:41):
Let’s take a simple example. I’ve got a solvent, two types of polymers. Here is my well mixed case, which all the biochemistry has tried to fixate on forever, right? I mean, we don’t want aggregates, we don’t want condensates, we don’t want phase separation. Now I could get two phase behavior where now I have, let’s say, a condensate that forms that’s enriched in polymer p2, and then I have a sort of co-existing phase that’s enriched in the solvent and p1.

Rohit Pappu (00:43:12):
I could have the sort of traditional view that perhaps condensates are just bags, right? That both our macromolecules have ended up in a condensate, and this is coexisting with a dilute phase. There’s the Amy Gladfelter story, which basically is that you can get unmixed condensates that sort of basically coexist with one another, because these p1 and p2 really don’t like one another, but they don’t like the solvent either, they end up in sort of different condensates.

Rohit Pappu (00:43:42):
But the really more interesting case is this situation where you get this type of whetting behavior, where you get this core-shell architecture whereby in the core, you have an enrichment of one type of polymer whetted by a shell that is enriched in another type of polymer that co-exists with a sort of solvent rich phase.

Rohit Pappu (00:44:04):
What Tyler asked was let’s take this ultra simple system and make certain tweaks to the valence, to the affinity, or to the linkers, and generate a sort of spatially organized droplet where we’ll have, let’s say, one protein in the core, one protein in the shell, let’s say. And then we’ll have, let’s say, a protein that exists in sort of both, and then one protein effectively straddling things in a certain way, right?

Rohit Pappu (00:44:35):
Cut a long story short, it turned out that actually the simplest way in which we could make this be realized is simply take half our poly-SH3 molecules and have them connected by high excluded volume linkers. When we do that, essentially what you get is a spatial organization, where the blue molecules are the ones that have the low excluded volume linkers, the PRMs are all low excluded volume linkers, so they’re straddling the core and the shell. And what you get back is a Corona or a shell that’s made up of these high excluded volume linkers that’s basically making up the shell.

Rohit Pappu (00:45:12):
And in fact, the design was achievable quite nicely, where now you get essentially poly-SH3 with our Flory random coil or low excluded volume linkers making up the core. By the time we come out a certain distance from the center, that density has just decayed off to zero, whereas the molecules connected by the high excluded volume linkers are close to zero density near the core. They make up mostly the shell. And then our poly-PRM, which is providing the complimentary interactions, is effectively straddling both the core and the shell.

Rohit Pappu (00:45:48):
And in fact, what we then set about doing was titrating. We said, is it affinity? Is it valence? We did all the titrations. But really the gist of it was that as you crank down the excluded volume. As we basically sort of decreased the effective solvation volume and the high excluded volume linkers, we start to lose the spatial organization. But if we crank that up, we get this core-shell effect.

Rohit Pappu (00:46:15):
What that says is that a simple precept is differential solvation of disordered linkers can actually give you these spatially organized droplets. And in fact, if you think back to some of Mike’s recent work in collaboration with the Vale Lab, you see this type of behavior, where essentially you have exactly the same polymer but it’s a mixture of molecules where the linkers are, let’s say, phosphorylated, and the linkers are not phosphorylated. And although they didn’t focus on this, what you can bet your cotton socks on is that there is a sort of core-shell architecture actually for them.

Rohit Pappu (00:46:56):
What I will do is end on a note that we can go well beyond synthetic systems because these concepts transfer over quite beautifully. And in fact, when Tyler was putting this work together, Cliff Brangwynne visited us and he said, “Hey guys, let me give you something more concrete and practical to think about rather than your poly-SH3, poly-PRM system, because we have this observation of the nucleolus.” Which, of course, many of you know is essentially the nuclear reactor, if you will, of the nucleus and that’s where you actually assemble ribosomal subunits. But what is sort of also well-known is that the nucleolus actually has several layers to it. And it’s best illustrated in this movie, where what Marina Feric did, when she was in Cliff’s lab, was she took the oocytes and she effectively inhibited the actin network using latrunculin A. And what you now start to see is this core setting behavior where all of the nucleoli basically condense into one gigantic nucleolus.

Rohit Pappu (00:48:03):
Even more important than that, I call your attention to the staining here. Nucleophosmin is in red, fibrillarin is in green, and then polar E1, which is the marker for the fibrillar center is in blue. The DFC, which is the Dense Fibrillar Center, and fibrillar center, they’re sort of inter-mixed, but you clearly see this core-shell architecture, right? Nucleophosmin on the outside, fibrillarin on the inside.

Rohit Pappu (00:48:32):
And then Marina went on to do some beautiful work, where she basically reconstituted this behavior with a simple three component system involving ribosomal RNA, nucleophosmin and fibrillarin. Cliff basically said, “Okay guys, if you think you know this is really a differential solvation and multivalence effect, you ought to be able to recapitulate this using the very simple model.” And so that’s what Tyler Harmon did, was he basically came up with a very simple architecture for fibrillarin, the RGG domain and the methyl-transferase domain instantiated in this sort of very high resolution description.

Rohit Pappu (00:49:14):
Ribosomal RNA, basically described as a polyelectrolyte high excluded volume. And the key ingredient here was the oligomerization, that Richard Kriwacki has taught us a lot about, of nucleophosmin, where you have the oligomerization domain, the acidic tracts, and then an RRM. But of course it makes a pentamer, so that gives you this pentavalence, right? And so again, we put this on the lattice, there is an interaction model that turns out to be absolutely key and the data that Marina and Cliff had collected turned out to be super important in helping us with this, because it turned out that the model required attractive interactions between the RGG domain, a stronger attraction between the RGG domain and the methyl-transference domain. This inter-RGG-domain attraction was actually something of a prediction, both from the experiments and the model.

Rohit Pappu (00:50:07):
Then of course you will have the RGG domain, of course, interacting with the ribosomal RNA, absent that, you wouldn’t get the core-shell architecture. And really the only thing that the nucleophosmin was doing was interacting with the RNA through the RRM, everything else was excluded volume, and the multivalence. And what we got back, rather trivially, it turns out, was a beautiful sort of spatial organization where you get fibrillarin in the core, the ribosomal RNA straddling the core and the shell and nucleophosmin basically making the shell that’s shown in this very clean movie here, where we actually essentially end up with the coarsening behavior that you also see in the oocytes, which was quite striking for us and very exciting. Rather simple models, simple physics, differential solvation.

Rohit Pappu (00:51:02):
We haven’t given up on the nucleolus because there are so many beautiful questions to ask. I will simply give you a teaser that Matt King, who is something of a champion biochemist, who came to us from Sabine Petry’s Lab, has actually succeeded in sort of reconstituting elements of the dense fibrillar center and the fibrillar center on its own, so now we got to start sort of actually doing all the experiments in cohesion with Cliff, which is going to be really exciting to ask all kinds of design questions.

Rohit Pappu (00:51:34):
Before I stop, I’ll tell you that next week what we’ll do is sort of go beyond what we’ve just talked about, build on these concepts, try to see how well they transfer over to describing the phase transitions of intrinsically disordered proteins. And before I end, let me thank, I think I’ve sort of thrown shouts out to people as I’ve gone along, but just a reminder, this is the team as of today. Tyler, as I pointed out, is the person who did all the work that I described. Next week, I’ll tell you a lot about what Jeong-Mo has done. He’s now starting off his independent position in [Daejeon] in Korea.

Rohit Pappu (00:52:09):
Alex, a former postdoc, is a colleague of mine across the park in the biochemistry department. The work that I described today, basically intellectually inspired by a very close collaboration with Mike. I should point out that Tyler’s designs have actually been tested and stay tuned. It turns out to work out quite beautifully, with some added nuances of some interesting salt effects. And I’ve been very fortunate to interact with Cliff from sort of the get go. We’re starting to sort of reboot our collaboration as we start to think about the nucleolus. I’ll take Jill’s orders, leave this slide up. Hopefully, you got up to no shenanigans. I’m very happy to take any questions you might have.

Mark Murcko (00:52:57):
Thanks Rohit. Thanks very much. Now, I know we’re at the top of the hour, but we definitely want to take some questions. We realize that some people may have to jump off, but hopefully many of you can hang on. In the chat, we had a few questions come in that I think have already been answered about how the excluded volume was calculated and how the length of the spacers is factored in. I think those have already been addressed.

Mark Murcko (00:53:26):
But there were a couple of very interesting questions from Pinaki Swain. I apologize if I’m butchering your name. But if you’d like to go ahead and ask some of your questions, I think that would be a good place to start, if you were still on. If Jill, if you can unmute Pinaki. And then we have also a question from Bede that we could cover as well if Pinaki is not available.

Pinaki Swain (00:53:57):
Hi, this is Pinaki.

Mark Murcko (00:53:57):
Great.

Pinaki Swain (00:54:01):
Yeah. I’d like to know if homopolymers which do not have the sticker spacer heterogeneity whether they would only go LLPS, in a poor solvent, and won’t form gelation at all, at any concentration? Is that true?

Rohit Pappu (00:54:20):
That’s a very good question. And so of course, that will depend entirely on what type of homopolymer one has. One of the things that I think is really valuable to remember is that if you go and dig deep into the sort of homopolymer phase separation literature, it’s kind of taken on this idea that it largely is LLPS, but in fact, if you go back and think about those types of systems, what they will do is actually make, away from the critical point, a dilute solution that is described primarily as being a gas of globules, that will coexist with a dense phase that some polymer physicists will actually refer to as a sediment. And in that dense phase, the molecules will essentially behave like they’re in a melt where now because there isn’t a driving force for the chains to be compacted on one another, they will essentially behave like Gaussian chains. The radius of gyration will go something like n to the one half, where n is the number of repeating units. So you’re absolutely right: This networking ability, this type of phase separation and percolation, shouldn’t be realizable for your garden variety homopolymers.

Pinaki Swain (00:55:40):
Thank you. Another question. The core-shell architecture, observed in the case of the nucleolus, would the phases have different material properties?

Rohit Pappu (00:55:53):
Yes. That’s exactly right. It turns out, of course, that… And this is something that is still a bit of a ways to sort of work out the connection between the thermodynamics and the rheology, but you’re absolutely right, that the core, the fibrillarin core is actually on. And this is an important caveat, when interrogated on exactly the same timescales, the fibrillarin core is classified as a viscoelastic material, whereas the shell has more like a viscous material. But of course that depends entirely on what timescales you are probing these things at, right?

Rohit Pappu (00:56:36):
The underlying moduli, both storage and elastic moduli, are different for one another. And that, to zeroth order you can rationalize as coming about due to two things: One is that the strengths of the interactions are possibly different, but at least in our model, it’s entirely due to the sort of wealth of more interactions that you have characterizing the core when compared to the shell.

Pinaki Swain (00:57:04):
Is there any correlation between the interfacial tension?

Rohit Pappu (00:57:06):
Absolutely. I don’t know if you got to see that. I was slightly mindful of the time getting away from us, but notice that when we were parameterizing this, we use a Flory Chi parameter to parameterize the strengths of the interaction, but of course, for these types of systems, they effectively mean the same thing as the interfacial tension. And so basically what we’re saying, and this, by the way, also was corroborated and actually driven by Cliff’s lab, where they showed that fibrillarin would essentially be effectively more hydrophobic when compared to nucleophosmin, and that you can effectively think about by thinking about the relative surface tensions of let’s say fibrillarin plus RNA in interface with the solvent versus NPM1 plus RNA interface with the solvent. And what should happen in order for this to work out is gamma 1-2 should be smaller than gamma 1-3, but if it is quite a bit larger, then you will just get unmixed condensates, right? The inequality has to A, be satisfied, but there are also bounds on the inequality.

Pinaki Swain (00:58:25):
Okay. From interfacial tension, can you tell something about whether the phase will be viscous or viscoelasticity or?

Rohit Pappu (00:58:29):
As proxies, yes, but there needs to be sort of a much more elaborate because, again, the elasticity versus the viscosity, those depend on the timescale over which you interrogate the material, right? It is then directly tied to the timescale for the making and breaking of the cross-links and the extent of cross-linking. So, yes, those are useful proxies, but they are not one-to-one corresponders.

Pinaki Swain (00:58:58):
Thanks [crosstalk 00:58:59].

Mark Murcko (00:58:59):
Thanks, Pinaki. Thank you. I think I we’ll go to Bede. Bede, you had an interesting question.

Bede Portz (00:59:07):
Rohit, thanks, first of all, for a conversation or a talk that was accessible to biologists. I appreciate that. You juxtaposed these scenarios where you have percolation directly, which you said is unlikely to occur in biology, and then you have percolation sort of mixed with as a function of phase separation. Do you think there are going to be exceptions to this? Are there going to be proteins or systems that gel at physiological concentrations? And I sort of say this as someone who I think might have observed this in a test tube. And if so, how might that difference manifest itself in a cell? Right? I don’t envision a cell spanning system.

Rohit Pappu (00:59:51):
Yeah. Well, it’s interesting that you bring that up because I’m going to put that slide up. Here are three scenarios. I should point out that actually… When I selectively chose the one at the top, I should have clarified that that was a scenario that for my way of thinking was about condensates, but it also turns out that Simon Alberti has shown, Christine Jacobs Wagner has shown, and there are several other data, [Z Stecker? Inaudible 01:00:25] has shown these examples as well, where you can actually get whole cell gelation, right?

Rohit Pappu (01:00:33):
Effectively, if you subject yeast to pH shocks, for example, you can just change the material properties of the entire single cell organism. And of course Christine has been studying bacteria so you see that in bacteria. The answer is yes, you will end up with a full cell wide percolating network. I should also point out that Mike has pointed out to me that when they tune the properties of the linkers, or let’s say they use mutations on the SH3 domains, or they see this with the SUMO-SIM system as well, where there are mutations that are weakening the affinity, now, when they go to high enough concentration, they basically get these test tube spanning networks. And that you can read out, by a variety of things, the scattering goes through the roof. You don’t see any spherical condensates. If you image things, they look like these sort of very irregular, spiny structures that have no bearing or no similarity to spherical condensates.

Rohit Pappu (01:01:40):
The answer is, yes, it’s really about sort of the collective tuning of valence, linker properties, affinities of the stickers for one another, and are the spacers bringing along any other auxiliary sticky interactions, right? In these minimalist systems, that’s what it will take, but in cellular systems, you absolutely can cause a cell to percolate. Right? I hope that answered your question.

Bede Portz (01:02:12):
It’s great. Yeah. Thanks.

Mark Murcko (01:02:12):
That’s great. I think we’ll wrap up with one last question. Let’s see. Let’s say Samrat, if you’re still on. You said you had a question, so go ahead, please.

Samrat Mukhopadhyay (01:02:28):
Thank you. Rohit, beautiful talk. We learned a lot about phase separation. I had a quick question about the disordered linker, which you referred to as contributing to the huddling together to form the system spanning network. My question is, is this disordered linker is also responsible for the breaking of the interactions. It is essentially sort of catching up the weak interactions and trying to sort of break it apart on a characteristic timescale. And the next question is, how does characteristic timescale of the making and breaking of interaction is coupled with the strength of the interaction that governs the phase transition, especially to get to a critical middle scale size of that particular droplet?

Rohit Pappu (01:03:35):
Yeah. Those are excellent questions. And so two comments, first, is that all of my sort of comments about timescales have been super qualitative because this is actually something that we need to start thinking about in greater detail. But that’s simply a writer. Now going directly to your point, you can absolutely see that the excluded volume or the effective solvation volume of the linker will definitely contribute to the timescales over which these cross-links are made and broken, right? Because effectively the barrier to dissociation will be governed by how easily they’re pulled apart versus how cohesively they stick to one another. If the stickers or sort of the spacers bring to the table some isotropic attractions, for example, those will start to give us sort of more long-lived cross-links.

Rohit Pappu (01:04:39):
Conversely, if the spacers start to provide sort of an excluded volume, that will be the way in which you will start to sort of more readily dissociate the sticker-sticker cross-links. And so it is absolutely the case that the spacer excluded volumes will indeed contribute. And so just to sort of put this into perspective. If you go back and look at the way we calculate the excluded volume, you will see that the inter-spacer interaction strength is actually sort of baked into that, right? I mean, that’s what the W of r is, that potential of mean force.

Rohit Pappu (01:05:23):
And so one of the things we can start to do is to go back and effectively do things like bond lifetimes or inter-sticker cross-link lifetimes as a function of either the strength of these spacer-spacer interactions, or in a much more sort of linker-wide readout as a function of the effective solvation volume. And I think what you will start to see are two things: One is that, if the linkers are all the same, then you will get a certain sort of characteristic timescale. But what is beautiful is that the linkers have a lot of heterogeneity. It’s never the case that in biology the linkers are exactly the same between any pair of domains. They’re always quite different. And I think that actually leads to this encoding of a hierarchy of timescales as well.

Mark Murcko (01:06:18):
That’s great. Well, this has been wonderful. We’re already about 15 minutes over, so I think this is probably a good stopping spot. I’m sure to all the other participants, if you have additional questions, just get in touch with Rohit. He’s never unwilling to share his knowledge as he has just done for us today. He’s wonderful in that way.

Mark Murcko (01:06:40):
Rohit, thank you very much. And Jill and Rebecca, thanks for organizing this. And to all the participants, it’s great to see you and hopefully we’ll see all of you and lots more of your friends next Wednesday, same time, same channel. Thank you all very much.

Rohit Pappu (01:06:55):
Thank you, Mark. Thank you, Jill. And thank you all for showing up.

Mark Murcko (01:06:58):
Yeah. Great lecture. Thank you, Rohit. Okay. Bye-bye. Bye-bye.

Rohit Pappu (01:07:04):
Bye.

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EXTENDED Q&A

Question from Bede Portz: Rohit, do you mention that Cdense<Cperc<Cdense is where most biology will be, in contrast to Cperc<Cdilute giving rise to system spanning gels. Do you think there are proteins that will form system spanning gels at physiological concentrations? I think of the earlier work on the Laf1 IDR from Elbaum-Garfinkle. In other words, do you think there are exceptions where proteins will gel at low conc?
Rohit’s Response: The reference you are making is to the Nature Chemistry paper Wei et al., (2017). Note that this was a direct collaboration between the Brangwynne and Pappu labs. Your question raises the intriguing possibility that cperc < cdilute for the LAF1 protein and possibly even the LAF1 IDR…
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Figure S3 shows rather large, micron-sized droplets formed by the full-length LAF1 protein. The network should therefore remain a dropletspanning rather than a system spanning. Our rationalization of the semidilute behavior of the LAF1 protein (less certain about the RGG itself) is that the excluded volume of ca. 75% of the protein that is C-terminal to the RGG domain contributes to the dilution of inter-IDR crosslinks. Accordingly, we think that cdilute  < cperc ≈ cdense for this system. Further, the gap between cdense and cdilute is, we think, reduced by the excluded volume contributions of the non-RGG domains. The jury, we think, is still out on the robustness of the results for the RGG and a plausible explanation for the observations of apparently semi-dilute droplets. One of the trickier aspects regarding the phase behavior of the LAF1 RGG domain is the prospect of preferential accumulation of solution ions within the condensate. We know two things that are pertinent: (A) The critical salt concentration is ca. 325 mM NaCl for LAF1 and ca. 260 mM for the RGG. So, both systems show salting-in behaviors. Interestingly though, the RGG domain appears to have a wider two-phase regime than LAF1. (B) From the polyphasic linkage work we have done recently, and mulling over your question, it would appear to be the case that the dilution of the dense phase derives mainly from the preferential accumulation of solution ions. This would explain two quirks regarding the LAF1 system: First, that there is a clear refractive index mismatch to enable the visualization of droplets even in DIC. Second, the semidilute nature of the condensates might be reflective of the accommodation of solution ions within the dense phase. Notice that we do not have the slopes of tie lines and it is more than likely that these slopes are positive, which would be suggestive of an accumulation of solution ions in the dense phase being required to equalize the osmotic pressure across the phase boundary.

Question from Emily Bentley: How is this excluded volume of linkers calculated? Presumably it’s sequence-dependent?
Rohit’s Response: Yes, the excluded volume will be sequence dependent. For the histogram that was in the talk, we generated a proxy parameter for the excluded volume. For each system, we perform ABSINTH-based simulations and compute internal scaling profiles, which plot the average spatial distance between pairs of residues i and j as a function of the linear sequence spacing |j-i|. We know that for each sequence, we can recapitulate the zero excluded volume behavior by turning off all the interactions. Therefore, for every sequence of interest, we compute a parameter ∆ that quantifies the normalized deviation of the sequence-specific internal scaling profile from of the Flory Random Coil (FRC) i.e., the sequence of interest in a theta solvent. If ∆ is less than zero, then the excluded volume for the sequence of interest will be negative, positive if ∆ > 0 and zero if ∆ ≈ 0. Details may be found in the caption of Figure 3 of this paper published in eLife.

Question from Jeremy Schmit: Did the calculation of the excluded volume parameter ignore the possibility of amino acid stickers?
Rohit’s Response: This question pertains to the quantification of apparent excluded volumes for linkers derived from the human proteome. These sequences were excised from their larger sequence context and simulated as autonomous units. And since all sequences were compared in an equivalent manner, no account was taken of possible stickers within the sequences. Please note that the focus was on linkers between folded domains. Lecture 2 dealt with the issue of how to uncover stickers vs. spacers in an IDR without prior designation of motifs as being stickers or spacers.

Question from Vijay Rangachari: For a homopolymer systems, LLPS promoted by the intramolecular interactions between the stickers must be potentially regulated in part by the length of the spacers, which determines the “effective concentration” of stickers coming together… is this something you tested and observed?
Rohit’s Response: The lengths of spacers do contribute. Please see Figure 8 in this paper published in eLife. Cooperativity is weakened as the length of the spacers increase because we recover the mean-field result of Flory and Stockmayer where only the valence of the stickers matters. For very short linkers, the network cannot grow. So, there is a sweet spot in linker length, for a given linker category where the cooperativity is highest, be it the positive cooperativity or negative cooperativity.

Question from Samrat Mukhopadhyay: I have a question. The linker allows huddling together. The fluctuations in the linker can also break the interactions on a typical timescale. Is that correct?
Rohit’s Response: Absolutely!

Question from Vijay Rangachari: What is the chemistry along the phase boundary? how well is it defined if at all.
Rohit’s Response: This is a really important question. There are two aspects of the interface between the dense and dilute phases that need to be assessed. How thick is the interface? This is going to be governed by the surface energy, which folds in contributions from surface stresses and surface tension. The second question pertains to the organization and dynamics of molecules within the interface. We are starting to wrap our heads around these issues and we are hoping to make some advances in the near future.

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