that it's bad news. So... Okay.
But apparently now the complete... We are on YouTube right now. From now on everything is online.
Ah, okay. I'll be quiet. Can I share this slide?
Can you see it? Yeah? Yes, very much so.
yeah let me rewire my brain now yeah shall we let people in now? we can yeah i guess yeah we can start let's turn the timer on So whenever I start recording on YouTube, everybody stops talking. It always happens in all the lectures.
Gilad, we can talk. We can talk. Gilad, don't worry.
I knew that Roi will come to help. Some Israeli will come to help. That's good. Well, I cannot miss another Roi giving a talk. That's good.
That's good. Yeah, so we'll wait until, I don't know, one, two minutes at least after the hour, so that people can settle in. So, Roy, I saw that you also started a webinar series now.
Yes, this is the... condensate colloquium series because it was the one group that seemed to not have organized itself so yeah that was a obvious gap very good yeah maybe you want to make some advertisements oh gosh i think we're okay At least on first, the first one went off reasonably well. Yeah, that was a great combination of talks.
I enjoyed it very much. And you know what we've tried to do is blend sort of established and junior people in every session, especially because I think in this field. There's so much going on with the young blood, so I think it'd be good to...
Yeah, I mean, this field is moving so rapidly. That's the point. So initially we thought we'd just go with one talk per colloquium. And then we realized by the time we actually got to, you know, the people we wanted to hear, it would be like four years down the road.
So we should have it as two talks per session. And then we came up with this formula of, you know, sort of established, paired with, you know, young and up and coming. Well, that's a good combination. Okay, so it's too past the hour. I think the numbers are sort of starting to asymptotically stabilize.
And so I would suggest we get going. And so I have the enormous pleasure to welcome Rohit Papu for our webinar on protein folding and dynamics today, and I'm very glad to welcome many of you again today. And so Rohit, of course, as all of you know, is very well known for his work on the molecular driving forces behind protein interactions, be it protein conformations, folding, aggregation, or face separation. And so just to give you some brief background about his career.
Rohit did his undergraduate degree in physics, mathematics, and electronics that he did in Bangalore, and then turned to biological physics with his move to Tufts University, where he did his PhD with David Weaver, and where he entered the field of protein folding. He then did postdocs with Jay Ponder and George Rose. And this was also the time when he started getting interested in the properties of unfolded proteins and their role for protein folding. And then in 2001, he started his own group at Washington University in St. Louis, where he is now.
And he's in the Department of Biomedical Engineering. He's the Edwin Murthy Professor of Engineering and the Director of the Center for Biological Systems Engineering. And there he's been developing an enormously strong research program, and both from the method side and from the conceptual side.
On the method side, I guess one of the key developments was absent and is absent, an implicit salvation model for very efficient Monte Carlo simulations, which turned out to be particularly well suited for unfolded proteins and IDPs. And so some of his early successes were classification of IDPs based on the polymer physical principles, relations, some sort of sequence ensemble relations. in IDPs.
The role of patterning, for instance, is something that he really spearheaded. But he's also interested in biomedical problems like aggregation, in particular Huntington's disease has been a topic that he's been investigating heavily, elegantly combined with experimental work in his lab. And more recently, an increasing focus of Rohit's research has been on face separation, again, using a close integration of of experiment and simulation.
And so his current key interests, I would say, are IDPs, face separation, especially their role in cellular organization, but also for neurodegeneration. All of these aspects are, of course, closely linked. And he always also takes the view from the engineering side, so both in terms of method developments and simulations, but also in terms of designing new sequences, biomaterials with specific... properties and this turned out to be an extremely powerful combination and Rohit's work has had a huge impact on the IDP and face separation fields and so his work has of course been widely recognized and for instance he's a fellow of the American Association for the Advancement of Science of the American Institute of Medical and Biomedical Engineering of the Biophysical Society.
And so it's wonderful to have you here today, Rohit. You'll talk about an exciting topic, how highly charged IDPs lead to emergent structure functions and face separation. But before you start, just the usual technical points, just briefly.
I mean, most of you probably know by now, but maybe there are a few people who don't. So please switch off your microphones now so we can minimize noise and functions. If you have questions, Just put them into the chat or just write, I have a question and we'll call you in the end to ask your question in person for the discussion. And a few minutes after the start of the talk, we will probably lock the meeting to avoid any Zoom bombing.
And as you see or notice, the meeting is recorded. And in case you miss it or any of the future talks or any of the past talks, you can look at them on our YouTube channel as well. And in case you will not be here until the end of the discussion, let me also mention that our next lecture, two weeks.
From now on July 22nd, 26th, sorry, will be by May Hong. She'll talk about the structure and dynamics of membrane proteins. You can always see all of these on our website, Protein Folding and Dynamics.
But now, without any further ado, Rohit, thanks for joining us today. Wonderful to have you here, and the screen is yours. Thank you, Ben, and let me go to sharing my screen here. So that was an unwarrantedly generous introduction. Thank you so much, Hagen, Gilad, and Ben for this opportunity.
It does feel like a homecoming for me when I come to hang out with old friends. So, and hence, we'll also sort of revisit some old problems. And as the title suggests, the focus today is going to be on charge-rich intrinsically disordered proteins.
And the story begins at a place where sort of Ben brought this up, which is that a few years ago, based on a synthesis of efforts, both in our lab and across the world, particularly Ben's lab, Julie Foreman Kay's lab, we started to think a bit about the organizing principles for connecting. sequence-encoded information to the types of conformational ensembles that intrinsically disordered proteins could adopt. And what emerged was what we started to refer to as a diagram of states, whereby the key determinants, first-order determinants of the types of conformations, highly expanded, fairly compact, sort of chimeric conformations, etc., seemed to be governed by the fraction of...
positive and fraction of negative charges and this interplay between these between electrostatic interactions and solvation effects. What stood out of course is that these regions here designated as R2 and R3 which tend to be the regions where the fraction of charge residues is high but the net charge per residue tends to be sort of on the low side corresponds to polyamphalites and they actually tend to make up. roughly 70 plus percent of the intrinsically disordered proteome culled across all organisms. So we'll start with some sort of rules of the game so to speak. So in the context of polyamphylites, what matters is the way the residues are positioned with respect to one another in the linear sequence which polymer physicists will refer to as the quenched disorder.
So on one limit, we have what are called polysviterions. So essentially, we'll have perfect repeats of cations and anions. They can come in different shapes in terms of the way that the types of residues that perhaps interrupt these viterions. One can also get blocky architectures.
So essentially, where all of the positive charges are collected at one end or somewhere in the middle, and likewise with the negative charges. And of course, we can have a whole enormous combinatorial explosion of possibilities, which for lack of a better way of classifying them, we'll refer to as random copolymers, which basically interpolate between these two limits in all kinds of interesting ways. So the key point I want to sort of emphasize before I jump into a lot of the physics is that these classifications that... I just presented to you, are not something that are purely of pedantic or physics interest.
Nature actually cares quite a bit about these classifications, particularly in the way they're used in biology. And I'll focus on specific functional assemblies or membrane-less organelles. So here is an example of a septal pore-associated protein.
These are in fungi that basically connect their cytoplasms through... branches. And essentially the idea is that every time there's an injury, there's a wound healing via the formation of what are called wormen bodies, whereby these proteins self-assemble to make channels that basically plug the holes.
This is a classic wound healing response in these fungi. They're basically cell-to-cell channels. These are viscoelastic materials. And what's beautiful about these is that they're a complex of proteins.
And basically the... dominant players in these proteins are these RD repeats. So these clearly are polysvitar ions.
And this, by the way, is the work of Greg Jed in Singapore, which I'll talk a bit more in some detail. So when we first saw this, Greg and I started talking and we started working together. And what it led to this very interesting observation that these Distinctions between block copolymers versus polysvitarines actually matters in the context of compositional specificity in the nucleus. So here, for example, is an RD repeat. So this is 60 long, has a GFP tagged on it.
And essentially what this picture is showing is two important observations. One is that these RD repeats co-localize with nuclear speckle markers such as SRSZ1, but they also hover outside of the nuclear speckles in the form of these filamentous structures. If one were to look under the microscope, bright field or scanning electron microscopy, one sees these spherulitic structures, basically organized by these RD repeats.
And these, by the way, have nothing but RDs in them. And They are mildly beta sheeted, but really what they are are highly physically cross-linked repeats. And there's a very interesting observation, which is that the enrichment into speckles of these RD repeats basically seems to track with the length threshold above which one sees condensation in vitro.
So this is a condensation that is not of the liquid. with liquid phase separation variety. It is phase separation, albeit of the liquid sort of viscoelastic fluid, really more like a spherulite type of transition. So a lot of beautiful results emerged from this. I'll sort of summarize a few of them which really make the point about the biology.
So one of the things that turned out to be really striking was if one looks at a series of nuclear speckle proteins, here is the E1 protein, they tend to be enriched in arginines. Substituting the arginines to lysines essentially does two things. One is that the enrichment in the speckle now goes down, whereas the enrichment in the nucleolus goes up.
So now here are two nuclear bodies that are juxta one another in space. but they care about whether the proteins have arginines or lysines. These are both, you know, as far as all of us coarse grain modelers, they are spheres of charge plus one, but the speckles seem to care whether the sequences have arginines versus lysines. It gets even more interesting because the speckles, in addition to having a preference for arginine-containing sequences also have a preference for sequences that are well mixed, that are more like polysviterions rather than the more blocky sequences. And here we quantify blockiness in terms of a parameter we refer to as kappa.
There are newer incarnations of this referred to as sequence charge declaration introduced by King-Skosh. For the purpose of this analysis, it doesn't... matter which parameter we use. And the key point is that basically the arginine versus lysine content and the mixing versus segregation of oppositely charged residues seems to determine speckle localization slash enrichment versus nucleolar enrichment.
And in fact, Matt King, a postdoc in the lab who has been quite active in the field of nucleic acid, effectively reconstituting facsimiles of the fibrillar center and dense fibrillar component of nucleoli, made a pretty striking observation. using spatial mass spectrometry data from Emma Lundberg's lab, noticing that within the fibrillar center, what one actually saw are proteins that tend to have very few origins. They also tend to have these lysine and glutamate patches that look rather like this.
So again, this very blocky architecture basically runs of case in with some interruptions that then are followed by runs of ease with interruptions. And these types of proteins basically are avoided from the nuclear spectros. So essentially, what I've given you are a small number of vignettes, but there's been a surge of interest in sort of in the phase separation literature in particular, establishing the point that the phase behavior, spatial localization in cells. the nature of the molecular recognition driven by polyamphilitic intrinsically disordered regions is governed by two parameters.
One that was a huge surprise to us, this distinction between arginine versus lysine, which people who studied protein nucleic acid interactions was not really a surprise. But the other thing that sort of jumped out was that this, the nature of the polyamphalite toggling between the polysvitarion limit versus... the highly blocky limit does seem to matter for function. So in functionally relevant polysvitar ions, we see this preference of arginine over lysine. And in the context of blocky polyamphalites, we see this preference of lysine over arginine in the context of nuclear bodies.
And so this led us to the question of, the first question I'll try to answer today, what is so different about arginine versus lysine? And for chemists, this, I think, is something of a rhetorical question, because, of course, there's this plainer sort of why aromaticity, Julie Foreman Kay has written about this quite extensively and in beautiful reports, lysine really is sort of an amine that is best mimicked as a point charge. What we reasoned was that since the processes that we're looking at are really about the interplay between solvation and desolvation, might it be the case that the free energies of solvation of these ionizable residues reveal something interesting in terms of differences between arginines versus lysine.
So this then actually opened up rather a large can of worms because as a lot of you will appreciate, direct measurements of free energies of hydration of ionizable groups are basically unavailable, right? You know, classic methods like vapor pressure osmometry simply won't work for these types of systems because the free energies of hydration are so favorable. So Martin Fossa and Xiang Zazeng, the two postdocs in the lab, basically teamed up and said, there is a way around this problem of trying to ask how favorably hydrated is, let's say, arginine versus lysine. or aspartate versus glutamate or the anions versus the cations. And to do so, we can use a extent information about easy to measure quantities, combine these with the monadic cycles and then go back and sort of plug any holes using the high resolution force field.
In this case, we use the polarizable amoeba force field developed by my colleague here, Jay Ponder. with whom, as Ben pointed out, I did my postdoc many moons ago, and Peng Yu Ren, who is now at UT Austin. So the thermodynamic cycle-based approach starts something as follows. So in the gas phase, if you have a base, a protonated base, essentially one can quantify the free energy of dissociation of the base into the neutral molecule plus the proton. That same reaction, and by the way, these quantities are measurable or amenable to calculation using really high level quantum mechanical approaches for all kinds of exotic ions.
So this is a gettable quantity. In the aqueous phase, the free energy of dissociation of the proton is really tied to the pKa of the titratable group, which of course is measurable for model compounds. The quantity we want is the free energy of hydration, which as Ben Naim will point out is basically the transfer free energy associated with transferring the base from a fixed position in the gas phase to a fixed position in the condensed phase or the aqueous phase. This is the quantity we are after.
It turns out that measurements of the ilk that George Makatadze and Peter Privolov pioneered over the years give us numbers for the free energy of hydration for the neutralized. So you can use vapor pressure osmometry, one can use calorimetry to get at these numbers because they are sort of excessively favorable. And then, of course, comes the mystery quantity. So if we knew the free energy of hydration of the proton, then basically we close the cycle and estimate the free energy of hydration of the ionizable group.
This is simply sort of thermodynamic cycle 101. So here's the quantity that we want. Here are the quantities that we ostensibly can get. But, and similarly, this is for the acid.
The key point is that the check marks denote quantities that are either directly calculable, directly measurable, or available in the literature to very high precision. What is missing? The free energy of hydration of the proton is very much like the sighting of the Loch Ness Monster.
It is a value that basically is highly variable. And how variable is variable? Here are, this is fairly updated, 72 different estimates that have been published in the literature. And I'm fairly sure we were not comprehensive. And you can see the spread of values, right?
I mean, many of these In fact, many of these are basically straight up calculations based on different levels of quantum theory. When one is dissecting, let's say, data from whole salts measured across homologous compounds, the consensus estimate tends to be about negative 259 kilocalories per mole. But what we realized was that actually what we... at least to answer qualitative questions, we can do the follow. We can, using our TCPV, thermodynamic cycle-based analysis, at least ask the following question.
If a model generates a particular value of the free energy of hydration for the proton, does it generate consistent estimates that you would expect so you can plug that free energy of hydration back into the this this one of these equations and then ask would the free energy of hydration that we calculate using the model be consistent with what the TCPD would say. So I'll illustrate that using amoeba. So here we know that the free energy of hydration for the proton for amoeba is roughly consistent with what you would expect based on sort of the parsing of experimental data.
So here is the value now for the arginine, so essentially this is propyl guanidinium, about 53.5 kcal per mole. If you use this free energy of hydration for the proton in the TCPB model that Martin developed, you get this value. So they're fairly close.
Now comes the first surprise. Lysine is actually about 12 kcal per mole more favored in terms of its hydration free energy. Immediately, this starts to point in the direction of why arginine would be the residue of choice if one is looking to make a more gooey, and that is a technical term, molecule that basically can sort of drive self-assembly. The other very interesting result, but again, those who've studied electrolytes are not going to be surprised by this. the aspartate and glutamate tend to actually be more favorable in terms of their free energies of hydration by close to 20 kcal per mole vis-a-vis lysine, for example.
So this is a significant asymmetry. So these numbers, what they should translate to in your minds at this point would be something like this. In the primary hydration shell, Each water molecule sitting around an arginine side chain would basically contribute roughly about 3kcal per mole. So to strip that water off costs you about 3kcal per mole.
Conversely, The same number for lysine is about negative 12 kcal. And further, you notice that these delta CPs, so these are heat capacities of hydration, they are large, they're positive, more so for arginine. And in fact, if you remember your hydrophobic effect numbers, these numbers are starting to look very much like those of hydrophobic solutes. And in fact, as... has been pointed out in the literature, positive delta CPs have been taken to mean the hydrophobic hydration, negative delta CPs have been taken to mean hydrophilic hydration.
But as pointed out by Roland Netz and rediscovered by us, that is really a cation versus anion distinction, right? It turns out for whole salts, the delta CP is in fact negative, but that masks the fact that the cations always... generate a positive delta CP. Now look at the same numbers for aspartate and glutamate, and what you can show is that it costs us about 10 kcal per mole per water to strip it off from the first hydration shelf, and again we get these fairly large negative delta CPs for these model compounds.
So what this says is that to zeroth order, the differences between arginine and lysine really come down to the differences in free energies of hydration and hydration structures, right? Further, this asymmetry in terms of the free energies of hydration between the bases and the acids should have important consequences for conformational and binding and phase equilibria. So just to put this in context, Ben's group has been studying molecules like the prothymocene alpha, star maker one, et cetera, these are all acid rich sequences. And so when one thinks about their interactions versus let's say their interacting counterparts, such as the histone H1, et cetera, there is already going to be quite a bit of an asymmetry in terms of how tightly or weakly these side chains are going to hold on to their water molecules.
And that, as Ben has shown, starts to make itself apparent in terms of the entropic driving forces for making these complexes because that's tied to not just the release of ions but also the release of waters. So now we segue from here to another question. So we had to, as you can imagine, backtrack through a variety of our different pronunciations as instantiated, for example, in the diagram of states.
We had sort of never really acknowledged that there was A, this asymmetry, and B, that their arginines and lysines were different in the types of simulations that we did that were absent-based where a key input is the reference-free energy of solvation of these types of model compounds. So we were really intrigued by this beautiful result. As far as the amount of work goes, it's simply...
incomprehensibly deep and rigorous from Charlotte Sorensen and Magnus Schergar. And they developed a very clever approach using this fusion protein as a motivation. So MBD2 that binds to P66A. And essentially what they said was, let's create a fusion protein construct where we basically strip down MBD2 just to its...
motif that binds to the P66A pocket, and then use a FRET-based assay to saturate, essentially, the binding site, but then compete with a peptide that's flown in in trans and effectively ask the following question. What is the concentration of this MBV2 peptide that it would take to displace this particular motif that is stuck here and how does that depend on the linker that tethers the motif to the P66A, right? And the reason this becomes very interesting is that you can essentially use this ratio of the acceptor fluorescence intensity to the sum of the acceptor and donor fluorescence intensity, titrate peptide concentration, back out an effective concentration. but then basically make the point that this must be the linker mediated effective concentration because everything that's peptide intrinsic just becomes the pre-factor. And the thinking that they came up with was that essentially this is a problem of the diffusion of a linker on a sphere, borrowing from Gilad's work.
And essentially the idea is that from polymer physics, depending on the solvent quality, there is an apparent scaling exponent, nu, which I would really refer to as nu-app, that determines how the linker length scales with the number of residues. So if you make measurements... for a series of chain lengths of exactly the same sequence and composition, then one can actually extract these scaling exponents from the measurements of the effective concentration. It's a very nice paper, highly recommended. The datum that I will zero in on is that for the Zwitterionic systems.
that have a particular architecture which is this. So GKE-SKE repeats. They measured this for a series of repeat lengths and then GRE-SRE repeats.
And there's actually a very striking observation here. Yes, the differences between the arginines and lysines are clearly manifest in terms of the apparent scaling exponent, which is essentially one third. for the arginine containing system, perhaps not a surprise given that arginine is considerably less favored in terms of free energy of hydration. And then for lysine, the lysine variant, the apparent scaling exponent was basically one half.
But this started to become a bit of a fly in the ointment for us because the difference between the arginine and the lysine one can reasonably well attribute to the differences in free energies of hydration. But these exponents made little sense to us. So here is a reminder of the type of work we did back in 2013, where we were looking at a series of EK variants. This kappa parameter basically quantifies the linear distribution of oppositely charged recipes with respect to the energy to one another. So the more blocky sequences have values of one, the super well-mixed polysviterion sequences have values very close to zero.
So let's take the polysviterion and ask what we would have predicted. And remember, this is based on absence simulations where we treated all of these residues as being equivalent from a free energy of hydration standpoint. And what we end up obtaining is essentially a distribution of self-avoiding walks, because what we reasoned is that on every length scale where there is an electrostatic attraction to be had that is screened by electrostatic repulsions, because of course the quench disorder of the sequence makes it so. So the only thing left is this ultra high favorable free energy of salvation that basically cranks up. the excluded volume on the chain.
And what we get are apparent exponents that are more like 0.6, those of self-avoiding walks, rather than what Magnus and Charlotte observed, namely exponents of 0.5. So this was definitely a puzzle. And so to sort of start to wrap our heads around this, we went back through the polyamphylite literature.
particularly the pioneering theoretical contributions of Joani, the Kardar groups, etc. Basically, what Higgs and Joani showed, and this is the model that Hagen and Ben and Andreas Serrano have used quite extensively, for random polyamphylites that are, let's say, N residues, and each residue has an excluded volume size of... let's say b, with the fraction of positive and the fraction of negative charges being equal, so we'll set that to f, and we have a Bjarne length of basically lb, then this mean field theory that Higgs and Joani developed, that's basically a scaling theory, will lead to the prediction that the radius of gyration or even some kind of measure of size, be the Hollingsworth size or what have you.
will go as n to the one-third which is the prediction for a compact globule, right? And in fact what they proposed is that these globules would be fairly dilute in terms of their packing density. and would resemble a salty droplet that you could, spherical droplet that you would carve out from the small volume in a simple electrolyte for example that is in solution. So this is one prediction, so that's one limit that comes out of the theory. So we have, there is a precedent for globules which would accommodate the result for the arginine basis.
In contrast, In the Joani-Heggs theory, something that we sort of reproduce from a scaling approach, and Kings Gauche has also reproduced using his variational approach, what you would get is either due to finite size artifacts, or because the free energy of salvation is so highly favorable, what you would get is the end to the point six scaling behavior that you would expect for a self-avoiding walk. So these are effectively the two fixed points, if you will, that you can anticipate based on theoretical considerations for a polysvitarion or a polyamphylite, right? So essentially, the way we looked at it was we said that, okay, in the limit of the electrostatic attractions taking over, you can start to get these globular conformations in the limit where this intrinsic favored solvation-free energy takes over, you start to get these self-avoiding walks, neither of which is N to the one half, right? But there is a theory that actually gives you N to the one half, and that's the work of Mehran Kardar and Charlie Cantor, basically showing that there is this important sort of Rayleigh instability that basically says that, you know, in polyelectrolytes, at least, that you cannot sort of simply compact the chain down because you... got a lot of electrostatic repulsions, but in a polyamphylite that instability actually manifests as a push-pull between the electrostatic attractions and the favorable solvation, which can actually lead to an end to the one-half scaling and these types of what are called necklace globule or pearl necklace types of architectures.
And this comes from the mean field theory that Cantor and Cardart developed for random polyamphylites. collection of papers published in the 90s that actually lead to some very interesting findings. So this is where theory sits. Either we have two fixed points or there's a consensus between these two effects and we get the necklace globule.
So what Xiangzi said was that okay so now we have got sort of recalibrated free energies of solvation. We can go back using Magnus'data as a sort of guidepost if you will. and ask the following question, which is, when we sort of adjust our free energies of solvation to be consistent with what we would expect from the revisited calculations, what do we obtain at a temperature where, you know, the exponent is 0.5, for example?
What we find, interestingly enough, is a bistability, right? So we essentially see... for lack of a better way of putting it, a coexistence of the chain in globules and self-avoiding walks.
This is for the GKE-SKE system. And just to sort of walk you through, the free energies of solvation were adjusted so as to make sure that they stay constrained to the asymmetry that we quantified, to the gap between the lysine and the arginine that we quantified. And then we ask the following question, what will it take to get to an exponent of one half at 300 kelvin, which is a simulation temperature not to be taken literally. So here is what that ensemble would look like, self avoiding walks here, and a transition over into fairly compact, but loosely held globules with a lot of sort of holes in between to accommodate interactions both with the solvent and complementary electrostatic interactions. So you really get this sort of bistability, not a necklace globuli.
And in fact, what ends up happening is that this interplay between the electrostatic attractions and the favorable free energies of solvation lead to this bistability whereby the coil-globuli transition now becomes actually a first-order transition. And this is shown sort of non-rigorously here, where what we do is we calculate the potentials of mean force along the normalized radius of gyration as a reaction coordinate. And what one sees is that the globules are favored at low temperatures. we come to a place where the globules and the self-avoiding walks are roughly equivalent in stability, we go above that temperature, and now essentially the system favors the self-avoiding walks.
Whereas, as Gilad has shown beautifully back in 2006, if you were looking at a classic coil-to-globulin transition, you would see a continuous transition whereby the well would basically shift up and shift to the right as we went up in temperature, right? So, okay, now let's go back and ask what happens when we switch the lysine to the arginine. Here's the bistability that I just talked about.
That same bistability is maintained, but in simulation temperature, we have to go to really high temperatures to start to melt away these globules, right? So this favorable free energy of solvation of the lysine essentially enables the transition temperature to be shifted. down so to speak.
So the coil to globule transition remains this pseudo first order nature but the globules now persist over a wider temperature range when we have arginines. So much so that this apparent exponent of 0.5 in terms of simulation temperatures for these constructs would be about 320 Kelvin and remember this is an implicit solvents model so don't have a nutty about things being vaporized. So basically the melting temperature, if you will, shifts by about seven Kelvin per lysine to arginine substitution in constructs that look like what Magnus and Charlotte used.
So now we get to ask, well okay, there's also other sort of aspects of this. So now let's think about the glutamate to aspartate switching. So in this construct, where we now observe this bimodality. Now let's switch the E to a D, a glutamate to an aspartate, and something interesting starts to happen.
Again, the temperatures change where we start to, they shift up. So clearly the aspartate is bringing a bit more glueyness. But now remember, the free energies of hydration are actually very, very similar to one another, right?
In fact, they're basically negligibly different. But what we instead start to observe are some interesting changes to the nature of the transition, whereby we see these metastable intermediates popping up. That, we think, has a lot to do with the fact that the shorter aspartate side chain can make a lot of side chain to backbone hydrogen bonds at different radial gyration.
And in fact, one systematically sees more hydrogen bonding. intramolecularly speaking, with aspartates versus glutamates. And in fact, this metastable state is most readily apparent when we sit at the transition temperature and look at histograms of the energy basins. So here is the globule, here's the self-avoiding walk, and there's really not much going between this for this particular system, which is basically a repeat of R and E. Conversely, what we start to see are these interesting metastable species that are populated at the transition temperature that are distinctive of the RD repeats and those look like the Cardar necklace globules.
So in fact here what's happening is that the ability of the aspartate to make these side chain to backbone hydrogen bonds and also populate some distinctive regions on the Ramachandran map as Reinhard Schweitzer's standard has shown us over the years. Basically what happens is that you start to get these regions that are locally compact. They would be the pearls or the globules in the necklace globules that people have referred to in the past.
And then the solvation now takes over and that sort of stretches itself out. And so effectively the idea is that this local state imparted by the aspartate makes the transition sort of go through these metastable necklace globule confirmations. It is worth noting that the source of this, the stability of this necklace globule has been something of a bone of contention in the polymer literature for a long time.
It largely comes about from bead spring models where basically the solvation is treated using a kind of a variant of Leonard Jones. attractive interactions. Whereas if you had explicit solvent or many body solvation effects, one actually is able to show that these necklace globules are in fact metastable.
This is the work of Govardhan Reddy and Arun Yathiraj from 2006. Why might these metastable necklace globules actually matter for things like RD repeats? If I can remind you of what we observed in collaboration with Greg Jedd, basically the idea would be that these necklace globules can condense, they can cross-link, and in fact there's kind of an interesting sort of generator of these spherulitic structures that already manifest in these necklace globules. And so Xiangzi has actually developed a very nice coarse-grained model that sort of remains faithful to the all-atom details here, and we can start to sort of move in the direction of modeling these phase behavior. So what I've told you is polyamphylites can be globules or self-avoiding walks.
They can switch between these states. this apparent exponent of 0.5 that Magnus Shergaard sort of identified, which is something of a surprise, really seems to point to the system being at a temperature corresponding to a bistability, which of course shifts based on the lysine versus arginine content. Blocky sequences maintain this bistability, but of course the strong electrostatic attractions basically shift them to being much more compact.
And effectively, there are some rules here. Arginine, sphincter, and scolombules, lysines, tilt the balance towards self-avoiding walks. Aspartates enable metastable necklace scolombules, and glutamates preserve this fixed two-state behavior.
So these are some very interesting inferences, and I think the hope is that we would sort of subject ourselves to a lot of scrutiny by experimentalists in particular, and I think fun times lie ahead. In the last five minutes, what I'll do is basically point out one last wrinkle that also forces us as, you know, pseudo physicists to not disregard physical chemical details, right? And this is something that has sort of bugging me, Ben, Robert Best for a long time, which is all our inferences are basically based on fixed charge models, right? And what do I mean by that? Essentially, Everything that I showed you up to this point says, okay, let's consider some intensively disordered creatines with, you know, some number of ionizable residues, let's say like these sequences.
And what we do is simply count up the numbers of lysines, numbers of arginines, numbers of glutamates, numbers of aspartates, and we calculate, you know, pseudo-order parameters that look like this, the fraction of charge residues and the charge per residue and so on. These have turned out to be very helpful organizing. principles. But the key question is, from a sort of complexity in biological systems, are they masking? So here's the question.
What if the actual charge is not the apparent charge that we infer by just reading these sequences, right? Which means that there might be some ways of regulating the charge inside of realistic systems. So here is... some work that Madhavi Krishnan's lab did when she was in Zurich, a work that involved collaboration with Ben. And these are single molecule electrometry measurements where essentially you have trapping fields that set up these electrostatic traps for molecules.
Here's scanning electron microscopy image. One can then use fluorescence at the single molecule resolution and start to do XY tracking of the motions of these molecules. and basically start to get out sort of either dwell times and also sort of amounts to single particle tracking these molecules.
What emerges from sort of back inferencing of the data is that for something like prothymocene alpha and star maker, the actual charge or apparent charge that you would read off from the sequence would say that there the net charge would be minus 46 or negative 102.7 for StarMaker. What one infers from the electrometry measurements is quite good, right? A significant reduction in terms of the net charge. And so what that starts to lead us to is there's possible charge regulation effects, where might they be coming from?
So let's say I... I gave you a sequence that I sort of colored this way where now the red is the negative charge, the blue is the positive charge, and I've got polar and or hydrophobic groups interspersed in between. One route to charge regulation could be context-dependent shifting of PKA's, right?
So essentially now I can imagine that the acidic group is being neutralized or the basic group is being neutralized. There's enzyme-catalyzed ways of regulating the charge, and that would be via post-translational modifications, whereby now essentially what one does is add charge to... serines or threonines or take away charge from lysine via acetylation and things like that.
There's, of course, the well-known stuff from the polymer physics literature, which is, you know, if you have multivalent solution ions, one can essentially decorate these polymers with lots of charge and change the underlying charge. But of interest is A, how to measure and B, how to interpret. So this leaves us with... the point that we need to have actual measurements of the global charge for different conditions.
Electrophoretic or mobility-based measurements are generally a no-go for the simple reason that they need very, very low salt concentrations. And so that becomes a really tricky set of experiments to interpret coherently. So what we've started to do is move back to classical methods, which is essentially proton binding assays, right? pioneered way back by Kyle Anderson Lang and sort of made more fashionable recently by Bertrand Garcia Moreno.
So here's the general idea. You're basically measuring the pH in the solution that contains the peptide. In this case, it's essentially a polyamphlytic peptide as a function of the titration of a strong base. One can then go back and ask if there were no shifted PKA's, what would the pH actually be? which would be B, and that would be the curve shown in blue, clearly indicating that the actual charge has somehow changed when compared to the expected charge.
So what we're doing these days is, and so I'm just going to give you a sneak preview, is Ammon has been pushing quite heavily on doing these potentiometry measurements on a variety of systems, and Martin Posa has developed this. a really elegant way of thinking about how to analyze these potentiometric data. So here basically is the measurement. I won't dwell on it too much, but the key point that Martin made was that when we have so many ionizable groups, we cannot gloss over combinatorial complexities.
And let me illustrate what I mean by that. So let's take a sequence with n ionizable residues. In theory, there are two to the n possible charge microstates.
Let's take this very simple dipeptide, the lowercase e shown in black is the neutralized version. There are actually four microstates to worry about here. So what Martin does is he basically collects these microstates, organizes them by net charge, and groups them into what he calls our mesostates. So where the mesostate designation basically tells us what is the net charge.
and the subscript denotes the degeneracy of microstates per mesostate, right? So the naive approach would be to pick three mesostates and call it quits. What Martin points out is that this combinatorics cannot be avoided. And so when we analyze potentiometry data, essentially what we're doing is trying to back infer the mesostate probability. So we have the net charge from potentiometry.
We know the charge. per meso state, because that's simply writing down the meso states. And what we're trying to do is solve from the measurements for the probability that a particular meso state I will be populated at a given pH. So here are the potentiometry data. The key takeaway here is that simple models that do not account for charge regulation will not reproduce the entire titration. So here's the net charge from potentiometry in orange.
Here is what all of us in the simulation world would do. Basically assume that there are three mesostates, the plus four at very low pH, the minus four at very high pH, and zero all the way through. That's shown in black. Does a really bad job of reproducing the titration curve.
If Martin takes one step further and says that there are a lot of different mesostates, let's basically say that There are no shifted PKA's, but the mesostates are different from one another in terms of their degeneracies of microstates. The fits get substantially better. But then if we say that we don't fixate on... unshifted pKa's, now the fits basically overlap quite nicely.
The key takeaway is that one shouldn't look at this region and say, oh look, one doesn't really need to worry too much about these things because you know in the pH that I really care about because my cell only cares about this pH range, shifted pKa's don't really matter. Well the easiest thing to do is to calculate the derivative of these titration curves and you find that the derivative is nowhere zero. basically meaning that the net neutral state for this peptide was never really achievable, no matter the pH. Here is what we extract in terms of mesostate populations, which is really cool. And the nice thing is we can actually rethink the way we calculate PKA's now.
But this gets, I'll leave you with one last point, which is that as we increase the combinatorial complexity, we actually start to see that the dominant mesostate starts to become less important or less dominant in terms of the pH range where the population is significant because this combinatorics starts to take over. So even if one doesn't see conformational consequences of pH titration, it may well mean that there is an ensemble of charged states that are sort of in solution. So I'll leave you with that thought. and basically point out that Martin has actually been using this concept of an ensemble of ensemble of description and it's going bringing us down the road of thinking about some broader implications as well but I think I'm over time so I'll stop there and simply thank the people who have done the work.
I think I've thrown shouts out to them as I've gone along the three key people here Martin Fosar, Ammon Posey and Xiang Zetian and I think I have time for questions. Ben, you are somehow muted, Ben. You cannot hear.
Oh, sorry. Does this work now? Yeah, now it works.
Yeah. So then let me say thank you again, Roy, for this beautiful talk and for showing us that there's much more to polyamphylites than most of us would think. Really exciting.
So we already have two questions. The first one. from Roy Beck.
Roy, please. Yeah, hi, thank you. That was really a wonderful talk and very enlightening. So you started the talk with this beautiful, very symmetric phase diagrams, right, of all the possible IVPs and how do they look like.
And somewhat along the way I thought that this very symmetric phase diagram would now look very different, where the positive and negative charges are now. different energy, well, you haven't shown something like that. What I'm thinking about, again, from what I was thinking based on the differences, because of solvations, what happens to an IDP when we put it in the natural, right?
Because then all the solvation effects should somehow, should disappear, in a sense. Would that be something that you would estimate this is something that you think is, I mean, denaturating the denaturated. So what would be the effect of that?
What do you anticipate? Yeah, that's actually a very good question. So I thought you were going to go in the direction of salt because all our simulations are done in the absence of salt.
But that was the second question, but I promised Ben that I would only ask one. Pretend I anticipated it. And so let's answer the salt question first.
which is that you get a combination of effects. So you get this osmotic effect that will sort of swell up the chain. So in effect, what happens is that as salt concentrations increase for a lot of these well-mixed polysviterion type of sequences, we start to move more back into the self-avoiding regime because now you essentially are getting competing screening effects, but you also get the fact that these ions like to absorb onto the chain. And so that sort of creates a swelling effect in and of itself as well.
And I think a similar idea applies in the context of denatureds, right? Because now you could sort of imagine that depending on at least the conventional ones that one uses, you can start to imagine that, you know, the guanidinium group starts to sort of home in on, you know, again, because it's not so favorably solvated, would like to be. can get desolated by hanging out with the aspartates and the glutamates, for example, right? And so that can generate a preferential interaction that enables a swelling transition.
So I think what basically the money point that you've hit on is that the responsiveness of these systems that show these bistabilities will be quite significant when we start thinking about the complex ionic mixture that is a cellular milieu, right? And so we are just at the beginning. So there's a very good reason why I didn't touch the diagram of states because that.
taught me a very important lesson, and maybe also I'm getting older, that we're going to not hang our head out just yet in terms of drawing a diagonal stage because there's quite a bit to sort of sort out here in terms of what happens with solution activity and so on. So maybe can I ask briefly here before we go to the next question in the chat because it directly links to Roy's question. So I mean one thing that I was of course thinking about immediately when I saw your bi-stability result is the question of what will be the dynamics of interconversion between these states and is that something that we could possibly see experimentally?
Absolutely. So the key question or the first question now coming back to what you just said is, is there a chance that this would also be visible at slightly higher salt concentrations or do you think this would be limited to very low salt? No, no, no.
So in fact, I think the barrier my proposal would be would be modulated by salt in two ways, right? So just in terms of the thermodynamic considerations, that barrier is likely to get lower enabling and then you tilt the landscape towards more expanded conformations as you increase salt. But of course you now have the stuff that you and Dima and others have been thinking about, which is the internal friction effect, because now of course you've got adsorbed ions to be worrying about. But I suspect that doesn't happen really at very high until you get to fairly high salt concentrations.
So the answer to your question then would be that if one actually titrates the salt concentration, one is actually changing both the relative well depths but also modulating the barrier. And so from the interconversions, one can actually start to get at the relative preferences for these two conformations but also extract from that apparent barrier. Absolutely.
Thank you. Thank you. Next question was from Hagen.
Hagen, go ahead. Wonderful talk, Rohit. Crystal clear as always. Unfortunately, I had the salt question as well.
So that's good. I didn't hear the other question. And actually, I was really wondering what the entropic effect of salt ions would actually be.
And my initial guess would have been exactly the one that Ben mentioned, that probably the barrier disappears and sort of your first-order transition turns over into second-order transition. But your explanation sort of also makes sense. So is there something that you could possibly check in absinthe simulations?
I don't actually know. Maybe you can remind me, do you have explicit salt ions or you have just deep-ahead screening? No, no, so we have it.
explicit ions. So in this case, we cheated. These are basically what I call the Muthukumar limit of zero excess salt, exactly zero salt. So because they're perfectly charged neutral, so we don't use any additional salt. But we can do exactly what you're proposing, right?
And in fact, to your point, the very interesting effect is going to be when the net charge tilts in a certain direction. you will move in the direction of essentially eliminating that barrier and start to sort of renormalize this condition from being a bistable to more of a continuous transition. What brings up something interesting is that, is that a regime where these necklace globules become apparent, right? So now you could sort of imagine that if we have a long enough chain like star maker, for example, you essentially look at placing a series of threat probes at different sequence separations and start to sort of see the possibility that you get this coexistence of large, low-threat efficiencies, large distances, with high-threat efficiencies, short distances, that would be concordant with the necklace globule.
Whereas the perfect bistable behavior would be that you either see one type of threat efficiency or the other, but never the sort of hybrid under the same solution conditions. And so I think that that sort of comes back down to really what the ions or solution ions are going to do. Because as you point out, there is an entropic cost for hanging around.
But on the other hand, the charged side chains have a lot to give the almonds, right? And so there is definitely this interplay that we'll have to sort out. Thanks a lot.
Then we have a question by Robert Best. Rob, please. Hey, Ruud. Very nice talk. Thank you.
I had kind of just a methodological question about whether you'd looked at, because your absinthe, I guess, parameterization was based on amoeba calculations, whether you look at these peptides directly with amoeba, because I mean there are some amoeba implementations that are fairly respectable in terms of speed these days. So that's possible. I'm not surprised you asked that question because if all the details are available, might as well go for it. There are two issues that I think plague such an approach. Yes, you're right, they are respectable, but for the In order to see this sort of bi-stability, we really need these potential mean force calculations.
So we're actually, we have to go through an entire spectrum of our G values. And even with the fastest implementations on our GPUs, we've not really been able to hit those types of length scales. But let's assume that that's something we can access within a year or so.
We've been working very closely with Tengu to try to see what efficient approaches we can start to deploy. There is, however, one particular wrinkle. which I'll be very cautious in the way I say this, in terms of conformational equilibria, I think amoeba still needs a lot of work. Part of the problem is because it's not really been deployed on a very large number of peptide-based systems. What we often see is a very, very high population, way more so than is reasonable at all in the polyproline 2 basis.
So that preference for polyprolene 2 at the local level essentially covers everything that you can start to sort of quantify for longer length scales, right? And so that, to me, makes me very queasy in terms of deploying at large scale until we've addressed that issue somehow. You know, there are ways to address it, you know, bring around a sort of machine learning type of approach along the ways.
In fact. As you'll remember, we developed what we refer to as this, you know, peptide statistics for Phi Psi, right? And in this JCTC paper, that was actually originally intended to be done with amoeba.
And we started to see thoroughly strange distributions. And so we backed off, right? So this, I think, is a particularly relevant point that needs to be brought up with amoeba developers, because the question becomes, if you go back and compare to the types of peptides, type data that Reinhardt has measured over the years and several others have measured, these local equilibria seem to be badly misrepresented, at least in our experience with amoeba.
I recognize that once this goes on YouTube, the amoeba developer will probably send me very nasty emails. I hope they don't. I apologize guys ahead of time.
Next question is by Kingshokosh. Kings, please. Hi Rohit, very nice talk, very thought-provoking.
So I saw, I think near the end you were mentioning this point, this whole bi-stability business, is it at different scales or is it at the same distance? So what we, you know, so when we put the three-body term, we can actually see this called globule. What we noticed is at a, depending on where you are probing, at what length scale, Yeah.
Some part could be in the coil state, some part could be in the globule state. Absolutely. Yeah.
So what did, so did you look into this internal distance distribution? Yeah, that's a very good point. Because this is an RG.
Yeah. So right now we've not done that fine length scale dissection, but the Higgs and Giovanni theory already makes this point, right, that you can start to see these and actually there's this very nice paper by Yamakov et al that actually goes through this point. saying that you know on local length scales you can start to see more quail-like behavior.
So we've observed that essentially the way I think about this these are like little rods but then you know juxta them that's why you see these these necklace globule architectures as well. But we haven't at this point finally parsed all of the internal scaling plots but that's a ready-made thing we can do. The only thing that we've got to be careful of because in order to sort of get these whole spectrum of PMFs, we've had to do umbrella sampling calculations.
So we need to remove those biases on all observables that we record. And then that's certainly a very, very important question that needs to be answered. But I suspect it would be very much along the lines of what you just presented.
Okay. And quickly for the counter-irons, you said no salt, but did you have the counter-irons? Oh, so these are perfectly compensated, right? Okay, so no iron.
As I showed you, it has... any excess charge whatsoever. Yeah, okay, thank you.
Okay, so I see no further questions in the chat. If anybody else wants to speak up, welcome to just unmute yourself, but that doesn't seem to be the case. I have many more questions, but I will discuss this with Rohit over a glass of panache at some point soon. So thank you very much again.
Rohit for a wonderful talk. Thank you all for joining and joining the discussion. And I hope to see many of you in two weeks when we will hear about the structure and dynamics of membrane proteins from Mayholm.
Have a good morning, afternoon, evening, wherever you are. See you soon. Thank you, everyone.
Thanks a lot, Rohit. Thank you so much. It was wonderful.