VIDEO: Magnus Kjærgaard on Tethered Enzymes, Multivalent Interactions—and Tigers

Magnus Kjærgaard (00:04:43):
So if we take that thought experiment and then we change one parameter. So we’ll keep the concentration of tigers in Denmark constant and then we introduce one change. So what if I was holding a tiger on a leash, so how would that affect my risk of being eaten by a tiger. We can probably agree that the risk goes up by many orders of magnitude and the reason for this is that now we’re not dealing with a bimolecular reaction anymore, we’re dealing with a unimolecular reaction, which is concentration independent. So it doesn’t how matter tigers there are in Denmark, so there is really only one tiger I need to worry about and that is tiger at the other end of the leash. So instead of being regulated by the concentration, then the probability of being eaten is regulated by the connection between me and the tiger. So is this a rigid rod that I could use to keep it at bay? I probably couldn’t anyway. Or is it a soft tether where it can easily turn around and eat me? And this situation is actually very similar to something we often encounter in biochemistry. So imagine that the tiger was instead an enzyme and I was its substrate. Then we have introduced what the topic is of today’s talk, namely the intramolecular reactions that occur that are dominated not by the concentration of the reactants, but how they are connected.

Magnus Kjærgaard (00:06:27):
And this is a very, very common case throughout molecular biology, we have signaling enzymes that, in some way, are tethered to their substrates. So a good example is the protein kinase A, which has more than 50 different targeting subunits. So that is another protein that binds to the kinase and binds to a subset of its substrates, thereby bringing them together. Lots of kinases also have protein interaction domains, so in addition to the catalytic domain that does the actual action, then we have a tethering domain that attaches it to its substrate. And finally many kinases, they are also own substrates so they regulate their activity by autophosphorylating parts of their own molecule. A good example is, for instance the kinase, calmodulin-dependent kinase II, which can both activate and become calcium independent by phosphorylating itself and the activity of these processes is dependent on the linker, which is regulated by alternative splicing.

Magnus Kjærgaard (00:07:59):
So a lot of signaling reactions, they actually occur inside these tethered complexes and if you look at the proteins, or the regions of proteins, that are responsible for this tethering then you’ll find that in many cases they are intrinsically disordered. And the reason for that is that an intrinsically disordered region is uniquely suited for acting as a linker, so this is really a function that couldn’t in a way be carried out by a folded protein, because the crucial thing for the enzyme is that the catalytic domain can search space and adapt to its substrate, and this one of the hallmarks of an IDP.

Magnus Kjærgaard (00:08:44):
So I’ll just return to the tigers and then I’ll ask you to consider two questions and then think about which one you think is the more interesting. So one question, which is a valid question, is to consider how many people can a tiger eat today? Another related question is how likely am I to be eaten by a tiger today? So these two questions are related, but they are also quite different. So I would argue that the latter question, namely about my probability of being eaten by a tiger today is at least from my perspective more interesting. So it doesn’t really matter how many people it eats, the main thing is whether the one who is first in line, which is me, gets eaten.

Magnus Kjærgaard (00:09:40):
So these two scenarios correspond to two different ways of studying enzyme kinetics. So the “how many people a day” is how we normally characterize enzymes, so this is a steady-state reaction and this is a very useful way of describing many metabolic enzymes. But for signaling enzymes, this latter scenario where you are considering the probability of the first substrate, that’s much more interesting, because many signaling enzymes don’t have to process a lot of substrates in order to carry out their biological functions and also they’re rarely constitutively active. Instead they are activated by, for instance, a stimuli which is often transient. So you, for example consider, a calcium-dependent kinase that’s activated by a burst of calcium influx that lasts on the order of milliseconds and then it dissipates again. So the question that’s relevant for calcium-dependent kinases is then not how many substrates they process, but the probability of going through the first catalytic cycle that will autoactivate the kinase.

Magnus Kjærgaard (00:11:11):
Great. So I started out by mentioning that tethered reactions are concentration independent and that also affects how we study the reaction quantitatively. So for an untethered reaction, that’s concentration dependent, the way we would do this is we would do Michaelis-Menten kinetics, where we are investigating the rate of the reaction as a function of the substrate concentration. But what are we going to do then for a concentration-independent reaction, so the question is not just the question that we normally face, namely that of what shape does the curve have? So we have a deeper question, namely what are we going to put on the x-axis of this. So when we are going to study systematically a tethered reaction, what is the parameter we are going to vary if it’s not concentration.

Magnus Kjærgaard (00:12:11):
So the goal of what I’ll tell you about today is to develop a quantitative framework for thinking about these tethered kinase reactions, in terms of how the linking architecture affects the reaction. So we need to have some way of quantitatively describing the linker. And I think that this could help us answer some open questions. First of all, is there a generalizable mechanism that we could use to study different kinases, so is every case, case by case? There’s the question of regulation; can the architecture of the linker, can it regulate the output of a signaling pathway? And then finally, I think it’s also relevant to ask whether tethering will change the substrates that a kinase will use. So I think it’s pretty well established that tethering can accelerate the reaction, but the question is: does it accelerate all reactions equally or will some be boosted relative to others? So these are some of the questions I would like to answer and before we start, I would like to make my predictions for what the answer would be before we set out on this project. And luckily I have the advantage of knowing what comes later in the talk, which makes it easier to make predictions.

Magnus Kjærgaard (00:13:57):
But in order to answer these questions we need to have some sort of model system where we can systematically manipulate with the parameters of the reaction. So we have built a synthetic model system to study tethered catalysis. The parameters that we tried to design into the system are, first of all, the main thing is, we need to have a variable connection between the enzyme and the substrate. Second, we want to vary the properties of the substrate. And finally, and most importantly, we want to have some sort of way of quantifying the tightness of the linkage and I’ll get back to how we do this.

Magnus Kjærgaard (00:14:44):
So the design we ended up with is what I’ve sketched here, where we have the catalytic subunit of protein kinase A, then we have a linker that we can exchange with another linker, then we have a heterodimerization domain. Then we have another protein that contains the substrate and again another linker. The reason we make it as a two component system is to prevent phosphorylation before we want it to start. So we’ve made a bunch of different variants where we can change the length of the linker, so we are working with the simplest and most neutral linker that we could think of. So this is a glycine-serine repeat which forms a disordered chain with as little sequence specific interactions as we could realistically hope for. And we have variants for both the enzyme and the substrate and then we can mix and match and get different combinations.

Magnus Kjærgaard (00:16:01):
So in order to measure the tethered catalysis we mix the enzyme and the substrate, then we start the reaction by adding radioactive ATP and then we let it react for a while and then we quench it with acid using a Quench-Flow apparatus. So this is necessary because the reactions, as we will see soon, take place of the millisecond timescale. So this is what the reaction time-course looks like. So this is amount of the radioactive ATP as a function of time and I compare two different reactions here, one where it’s tethered and one where we have removed one of the tethering domains, so it’s untethered. And what you’ll see, what we’ll be quantifying is the rate at which this occurs. So this is actually an exponential decay, but it looks a bit funky because we used a logarithmic timescale here. So the first thing to notice is that we have a really big acceleration of the reaction. So in this case it’s 300-fold, so it varies how big this is compared to the conditions of what linker we’re using and the conditions of the untethered reactions, but we consistently see a large acceleration of the phosphorylation reaction.

Magnus Kjærgaard (00:17:35):
Then we wanted to ensure that what we are seeing is actually a concentration-independent reaction. So we did the reaction at different concentrations, over a tenfold concentration range, and different compared to how we would normally do enzyme kinetics. So we’re changing the enzyme concentration and the substrate concentration at the same time. So this is the whole system that we’re changing the concentration of. And what you can see here is that they’re similar. So actually it decreases the reaction rate, it decreases slightly with increasing concentrations, which is the opposite of what we would expect for an untethered reaction. So we’re not actually sure why this happens, but at least it suggests that it’s not occurring as a bimolecular reaction, it is occurring as a unimolecular reaction. Great.

Magnus Kjærgaard (00:18:38):
So now we have set up the system, we can measure the reaction and we are sure that we’re seeing an intramolecular reaction. So now we can get to what we really want to test. We want to test how the length of the linker between the kinase and the substrate changes. So we test various combinations of these two linkers and then we get results that look like this. So you can see again they all fit a single exponential decay and we see as we increase the linker, so this is the combined length of the two linkers, the longer the effective linker is, the slower the phosphorylation reaction is. This is more-or-less as we expected.

Magnus Kjærgaard (00:19:31):
So this was just for one substrate, but how does the substrate properties affect the scaling of the, with the linker? Will all substrates behave equally or will we see a different behavior for different substrates? So the way we tested this is simply by testing point mutants. So the substrate we’re starting out with is a substrate called Kemptide, which is the optimal substrate for PKA. So we wanted to start out with the best possible substrate, because we could always make it worse, but it’s hard to make something a better substrate. So the way we’re changing the substrate properties is to knockout the arginines; we’re changing the arginines to lysines in the substrate motif. So when we test these in Michaelis-Menten mode, in untethered format, we can see that we have perturbed the kinetic parameters by quite a bit and so we have three different substrates with different substrate quality. Great.

Magnus Kjærgaard (00:20:55):
So we want to test how that affects the length scaling, the linker-length scaling. So we repeated the Quench-Flow experiments with different linker lengths for these three different substrates and this is what we see. So this is a slightly different representation of the data before, where we have the rate constant for the reaction on the y-axis and we use a logarithmic axis here to be able to compare the very different reaction rates that we see and then we see the total linker length as the x-axis. So we can see that for all three substrates we see that the longer the linker is, the slower the reaction is. So we see a universal decrease in these rates, but the extent of the scaling is actually quite different. For the wild-type substrate we only see a twofold decrease for the shortest to the longest linker, whereas for the worst substrate we something like a tenfold decrease.

Magnus Kjærgaard (00:22:06):
So this brings us back to the question that I started out with, what should we actually put on the x-axis if we want to study tethered catalysis in a systematic way? So here we have an x-axis that sort of works for linker length, but it’s not very generalizable, right? So this will be specific for the linkers that we use and it’s not actually that useful, because most of biology doesn’t use glycine-serine linkers. So we want to find a way to generate a generalizable x-axis that we can use to compare these different substrates.

Magnus Kjærgaard (00:22:59):
So that brings us back to one of the other previously published papers, where we suggest that the general framework that we want for describing the linker architecture, the best candidate, would be the effective concentration. The effective concentration, in order to define that you have to imagine two different reactions, or basically the same reaction where you have changed the reaction by tethering one of them with a disordered linker. The effective concentration of the tethered system corresponds to the concentration of free ligand that would encounter the binding site as often as the tethered linker. So basically, we’re forcing the ligand to stay in close proximity to the binding site and this is a measure of the equivalent concentration that that causes. And this is the framework that we want to use going forward. And the convenient thing about this is that, at least to a first approximation, the effective concentration will be independent of what you link and may be a property of the linker. And those certain conditions is mainly to do with linker length, so this is only true for relatively longer linkers, whereas for shorter linkers, then you will start to get system-specific effects. But the reason that this is convenient for us is that we don’t actually have to measure the system, or the effective concentration in our kinase system. We can generate a more convenient system for measuring effective concentrations of linkers and then we can extrapolate back to the kinase system.

Magnus Kjærgaard (00:25:04):
So this is what we have developed. We have developed a fluorescent biosensor that allows us to measure effective concentrations conveniently. And the way it works is that we have a pair of protein interaction domains that we have tethered with a linker that we can exchange and then we have attached fluorescent domains that form a FRET pair. So when the two tethered protein-interaction partners, when they bind to each other, the fluorescent proteins get into close proximity and we’ll see FRET between them. If you then do a titration experiment where you titrate with the free ligand then gradually, as the concentration increases, then you will displace the intramolecular reaction with an intermolecular reaction. And that can be read from the FRET efficiency, as a decrease of the FRET efficiency.

Magnus Kjærgaard (00:26:09):
In practice, we have constructed it this way, so it doesn’t really matter. The main thing you need to know is that the interaction pair we’re using is an antiparallel coil-coil. Then we’ve done a lot of these titration experiments where we use competitor peptide to compete with the interaction. And what you can see is that we can read out the effective concentration as the halfway point of the titration reaction. There’s actually a correction factor that we need to apply first, but this is a technical matter. So the main conclusion from this slide is that you can see that the shorter the linker is, the higher the effective concentration is, and then it drops gradually with longer linkers. And these are the same glycine-serine linkers as we used in the other study.

Magnus Kjærgaard (00:27:10):
So, we want to have some sort of physical model for explaining the scaling and luckily lots of other people have been working to describe IDPs from using concepts from polymer physics. And it’s generally well-described that if you look at measures of the length or the dimension of an intrinsically disordered region, then you can to a good approximation describe it using this polymer scaling law, where you have the number of residues here. And then you have a scaling exponent that depends on the sequence of the protein. So we’ll get back to that. So in terms of the effective concentration, so if we just imagine the simplest physical model for what the effective concentration is. If we place one protein interaction pair at the center of our coordinate system, then the linker defines a diffusion volume, in which the tethered ligand can search. And the volume will then be proportional to the cube of the linker length. And then the effective concentration is then one over the volume. So we expect from the simplest toy model that we can generate is that the effective concentrations should scale with the number of residues to the minus three. And then we have the scaling exponent that we normally see for polymer scaling laws. And this is actually also what we see.

Magnus Kjærgaard (00:29:02):
So we see a pretty good relationship here, so if it follows a power law dependence then we’d expect to see a straight line in a log-log plot. And this what we do. And crucially if we look at the scaling exponent, then we know that sort of a neutral IDP should have a scaling exponent of about 0.5. So this is actually in pretty good agreement with what has previously been found. But importantly, this gives us this generic quantification of the connection that we need in order to use it as the x-axis for our kinase kinetics. So I would like to return to the tethered kinase system, where you remember we had this plot, we had the x-axis and we didn’t like that it was the linker length. So now we have this equation from before that we can use to convert GS-linker length into an effective concentration. And then we get a plot that we hope is more generalizable like this.

Magnus Kjærgaard (00:30:22):
So immediately when we plot it like this, then we can see some interesting features. I think one of the first things that we noticed is that we have this saturation effect that when the effective concentration reaches a certain point, at least for the wild-type substrate, then we see a plateau, suggesting that even if you shorten the linker further we wouldn’t expect to see the reaction to get any tighter or any faster. So we see that for some substrates, but we don’t see it for others. And then we see for the intermediate substrate, we see something that approaches saturation. So if start out playing with the equations for what we would expect for a system like this, then one of the models under a given set of assumptions that will come out of this, is that the rate of the reaction takes this form, which we can recognize as the same functional form as the Michaelis-Menten equation. Except that the substrate concentration is replaced by the effective concentration and the Km is actually the Kd of the substrate. And the reaction mechanism that produces this model is to have a rapid pre-equilibrium between an open and a closed form and then you have a rate-limiting phosphorylation transfer step, that then transfers over to the reaction here.

Magnus Kjærgaard (00:32:04):
I think one of the interesting findings from this is that actually when you compare the Michaelis-Menten parameters to the parameters from the tethered system, when we do this fit with this equation that I just showed you, is that the Michaelis-Menten parameters don’t really describe the tethered system very well. So for instance, for these substrates we can see that our wild-type substrate and then the first mutant, they have very similar Vmax values. And actually when you do the fit for the worst mutant, it’s Vmax value is somewhere around here, so it’s not that different. But when you compare the tethered reaction, then you can see that if you just look at the scale of the y-axis that there’s a huge difference in the plateau value. And if we do it in a more systematic way, we can see that the maximum tether rate is something like eightfold higher for the wild-type than for the R-2K substrate, whereas the Kcat value in the untethered system is only maybe 10% higher.

Magnus Kjærgaard (00:33:32):
So this suggests that the order of tethered reactions might be quite different. You can’t predict their properties solely from untethered reaction systems. And the reason for that is that under steady-state conditions, then the reaction becomes limited by product dissociation. So this is very important if you need to go through multiple cycles of catalysis. But if all you care about is the first cycle, how does it take for the kinase to phosphorylate the first substrate, then you don’t need to worry about product dissociation. So instead, the tethered reaction is limited by the actual chemistry of the reaction. So if we simulate what this looks like, we can see, so we have used, just made-up, some different product dissociation rates that we vary and then we calculate, for these product dissociation rates, what would we expect that Kcat would be and the single turnover of our reaction would be.

Magnus Kjærgaard (00:34:59):
So you can see that we have this plateau. When the reaction is limited by the product dissociation, then you can actually have very different rates of the tethered reaction that will look the same in the steady-state reaction. So similar Michaelis-Menten parameters can disguise very different behavior in a tethered system. So I think that probably shows if what you want to study is a tethered reaction, then you have to study it in a tethered setup; you can’t extrapolate from the Michaelis-Menten parameters. And the reason for that is that for most tethered reactions, this is actually what a steady-state would look like. And if we care about the probability of being eaten by a tiger, then it doesn’t really matter how long the tiger sleeps to digest after it has eaten you, this is irrelevant. But this is important if you want to calculate the total death count for tigers in your area.

Magnus Kjærgaard (00:36:17):
Great, so that brings us to one of the last questions that I asked in the introduction about tethered reactions. Namely does tethering also affect the relative substrate use? So we know that it will boost reactions, we probably already knew that ahead. But does it boost all reactions equally? So let’s do a thought experiment. So we have a kinase that’s tethered to its substrate through some sort of anchoring protein. And then we have some sort of regulatory effects; it can be a protein interaction, I’ve drawn it as a protein interaction; it can be post-translational modification; it could be alternative splicing, anything that changes the architecture of the kinase-substrate connection. So let’s just make up some very nice numbers. So we have before the change, we have an effective concentration of 100 micromolar, and then affects of binding then we have an effective concentration of 1 millimolar. So this corresponds to realistic values for different signaling complex architectures.

Magnus Kjærgaard (00:37:35):
So if we just consider the wild-type and the R-3K substrate, then we can see that these two substrates are affected differently by the change from the low effective concentration to the high effective concentration. So the worst substrate is boosted by ninefold. Whereas the best substrate is close to saturation, so there isn’t that much room for improvement, so it’s only boosted twofold. So this suggests that if you have some sort of regulatory change of the linker between the kinase, then you will also see a change in the relative substrate usage, and that will generally be towards the lower affinity substrates. Great.

Magnus Kjærgaard (00:38:25):
So this was the first part of the seminar about the kinases. So I hope that I have convinced you that the effective concentration is a very useful concept to think about in terms of predicting the behavior of biological systems. The trouble is, however, that for most cases it’s not really something you can measure in your favorite biological system. So instead what we think should be the solution is that we want to have some sort of system where we can predict that. So we take a description of our linker, for disordered proteins this could be the sequence, we put it into a computer and then we want it to spit out an effective concentration. So this the long-term goal of where we want to go with this. And for a lot of reasons these linker architectures can be very complex. The simplest sort of case study to start out with is a fully disordered linker. And the reason for that is that we have a good physical model for how the effective concentrations scale with the length of a disordered protein. We have a good model system for doing these measurements. So the system is designed to work in a parallel fashion, so you can do the titration experiments in 384-well plates. So we can do it quite efficiently.

Magnus Kjærgaard (00:40:04):
But we still need to account for the linker sequence. So we cannot just passively assume that all linkers will be well-approximated by glycine-serine linkers. We know that there are sequence features that have a big effect on the compaction of an intrinsically disordered protein. So the way we want to test, or work towards a prediction system is to make synthetic linkers, where we introduce systematic variation into the sequence of the disordered protein. So this is an example where we change the net charge of the linker by introducing glutamates; so we have here 5%, 10%, 20%, third and half of the residues being glutamate. And then for each of these linker architectures, then we do a couple of different lengths; so we do four for almost all of them. And then we can get this polymer scaling relationship. And what we then extract from these plots is the slope, which is the scaling exponent. And we can do this systematically for different systematic variations of the linker architecture.

Magnus Kjærgaard (00:41:32):
So here I’ve shown you the plot for charge, just expanded a little bit. Just to explain what is going on, so what this axis describes is that when this number is high, it means that the effective concentration will drop off rapidly when we make the linker longer. And in all cases the glycine-serine linker is the zero point, so this is the reference point. And when it’s low this means that when we make the linker longer, the effective concentration doesn’t increase as much. So if we think back to the toy model for how the effective concentration depends on the linker length, then you remember that we have this dependence on the scaling exponent. So we also plot the equivalent [inaudible 00:42:32] value for comparison to other studies where this is typically what you quantify for an intrinsically disordered protein.

Magnus Kjærgaard (00:42:40):
So we know that a high value here means that the chain is expanded, whereas a low value means that it’s compact. So for all these series we increased the net charge by introducing different charged amino acids. So we can see that they all expand and they seem to reach some sort of plateau around 20% charged residues. So this suggests that when a chain has expanded to a certain extent, then it will not go any further, even though we increase the charge. And the value that we get here is actually in quite good agreement with other measurements by others, primarily at the Schuler lab and the Pappu lab, who have done a lot of these measurements as well. However, we see that three of the different charged residues behave similarly in terms of expansion, but there’s that’s different and that is arginine. And I don’t think this will come as a surprise for anyone who is used to working with condensates. So this is basically the same phenomenon we see here, where we know that arginine is important for intermolecular interactions, but it’s also important for intramolecular interactions. So these are really two sides of the same coin.

Magnus Kjærgaard (00:44:10):
But in principle we can do this experiment with any sort of physical, chemical feature that we want to systematically test. So we tried to test some of the other features that we know from previous research should have a big effect on IDP compaction. So we tested polyampholyte strength. So here again as in all cases, we’re working with well mixed sequences. And so here when we test the polyampholyte strength and we introduce a positive and a negative residue in equal proportion, and then we have them in different lengths, and we increase the fraction of charged residues. So we can see that at low fractions of charged residues, polyampholyte strength doesn’t seem to have a big effect. Whereas when it reaches a certain, it might be a threshold, we don’t really have enough data points for that, but at least we see a strong compaction for some polyampholytes, not so much for others. And again the difference here is that the strong compaction only occurs if the ampholyte contains arginine, which mirrors what we saw for the charged residues on their own.

Magnus Kjærgaard (00:45:42):
So if you’re wondering about the big error bars here, then you should know that this is actually the only experiment in this talk that I have done. So this is what the error bars look like when Charlotte does the measurement, and this is what the error bars when I do it. So that’s the reason for that. We can do other things. So we also tried to introduce proline residues, which have also been suggested previously to lead to expansion of intrinsically disordered regions. Again, we’re adding a well mixed fraction of prolines and we can see a small expansion, and then there might be a drop, or there might be a plateau, but at least it’s not as dramatic as the charge, which goes up to here. But we definitely see a moderate expansion due to proline.

Magnus Kjærgaard (00:46:39):
We can do it with hydrophobicity. And the way we test hydrophobicity is by introducing leucines. So we see almost no effect of hydrophobicity on its own. Again this is in contrast to some previous studies, but I think the next figure shows the nature of that discrepancy, where that comes from. So we also tested aromatics. And we can see that we actually see that tyrosines drive compaction of the chain. Again this mirrors what we know from liquid-liquid phase separation of IDPs. So I should probably mention that the scaling exponent here of one of the effective concentration of 0.33, this is actually the physical limit for how low it can go, so this means that the IDP is basically a ball. So even though this change doesn’t look like very much, it actually suggests that the IDP region is actually very compact even at relatively low contents of tyrosine.

Magnus Kjærgaard (00:47:55):
So now we have a number of individual contributors, then the question is: how are we going to combine these into one aggregate expansion or scaling coefficient? So we tested the effect of adding two sequence features that both drive expansion of the chain together. So we add net charge and proline. We also did leucine because we started this experiment before we had the single leucine so we actually thought that leucine would drive compaction but it doesn’t appear so, but we have it here as well. So what we can see is that adding proline on top of adding glutamate doesn’t have an additional effect. So glutamate and proline, it follows glutamate only pretty perfectly. So this suggests that the sequence features are not additive. And I think it, to some extent, makes sense that the IDP ensemble will be dominated by the largest effect. So if the chain is already expanded from charge-charge repulsion then you can easily, within that ensemble, you can contain the chain stiffness that the increase in prolines will introduce without leading to any further expansion. I think this is probably the reason that just considering net charge on its own is actually such a good predictor of IDP properties.

Magnus Kjærgaard (00:49:50):
Yeah. I think I hope to convince that we can estimate effective concentrations by polymer scaling laws, with a scaling coefficient that you can model from a surprising naïve model for how the effective concentration depends on the linker. And this system represents a quite convenient system for systematically testing the relationship between the sequence and the ensemble of the disordered proteins. But that the outcome of all these perturbations is that we basically confirmed what the Schuler lab and the Pappu lab have already shown, that charge is by far the largest contributor to understanding the compaction of disordered proteins. And I think at least for disordered linkers I think we are probably within reach of having this sort of computational predictor of intrinsically disordered linkers. Great. I believe I still have time to talk a little bit longer, is that right?

Avinash (00:51:04):
Yeah, sure. We have about half an hour.

Magnus Kjærgaard (00:51:14):
Okay, great. So I’m just going to change topic a little bit here and talk about multivalency. So multivalency is a very common phenomenon for IDPs. So many intrinsically disordered proteins that interact with other proteins, they have different binding regions that actually work pretty well as independent units. And then when you have two binding regions that can binding to two binding sites then you get the phenomenon of avidity. So to think about that we can make this sort of model system where you have on one side you have one binding site, and then you have another system that’s similar where you have two binding sites between the proteins. So what avidity means is that two interaction sites will give you a much, much tighter binding. So if you consider what it takes to dissociate this guy from his protein interaction here. So if one of the binding sites here let’s go, then he will dissociate, yeah. Whereas in this case over here, even if one of the binding sites let’s go, as long as the other one is bound, then the binding site that dissociates has the chance of re-binding. And then you can see opening and closing of the complex and the effect of that is that you’re going a much tighter total binding than you would from a single binding site. And this is the phenomenon that is called avidity. So what we would like to understand is how the linker affects the interaction.

Magnus Kjærgaard (00:53:10):
I can see the questions coming into the chat so I’ll stop in five minutes time, then we can take the questions afterwards if that’s fine.

Magnus Kjærgaard (00:53:17):
So what we want to understand is how the properties of the linkers affect how much avidity you’re going to get for a bivalent system. So if you consider the simplest multivalent interaction that we can imagine, so this is a bivalent system, we have two binding motifs that are tethered, each of them are tethered by a disordered linker. So what will happen when these two meet? Then they will bind either to one interaction pair or the other, and then this is sort of a normal binding reaction that will have the same kinetic constants more-or-less as the monovalent reactions. Then the second step here is then an intramolecular binding event, so this is very similar to the systems that we have seen before. And theory suggests that it should be governed by the effective concentration. And that means that the total reaction, if you look at the affinity of the total protein, should depend, of course, on the affinity of the individual interactions, but also it should scale with the effective concentration that the linkers enforce.

Magnus Kjærgaard (00:54:31):
So this is what we would like to test. So we have built a model system that allows us to measure both the affinity and the effective concentration at the same time. And the construction of this model system is based on the system, the biosensor we used for measuring effective concentrations, except that here we have two chains and two interaction pairs. Then one of the interaction pairs is much tighter than the other, so in all the measurements that we do, it will always be bound. And then we do a titration experiment where we compete the weaker interaction out and then we see opening and we see a decrease in the FRET efficiency. And then we get a curve like this, where we see similar to before; the shorter linkers will give us a higher effective concentration, this is the shorter linker that will give a higher effective concentration than the longer linkers. And we can do a similar plot. So you can see the error bars here are substantially bigger, so this is mostly a systematic error. So we think that actually the scaling is better than the error bars suggest. But we see that it still follows something that looks like a polymer scaling law.

Magnus Kjærgaard (00:55:55):
Surprisingly however, the scaling of the effective concentrations is much less than we expected. So we think that this has to do with a suboptimal design of the system, so we can get back to that. But for the sake of the avidity, then we’ll continue with the values we have, where we see about an eightfold difference in the effective concentrations between these linker combinations. So then we can use surface plasmon resonance to measure the affinities of these constructs. So we can see that this is what it looks for the bivalent interactions and the corresponding monovalent interaction. And we can see from the off-rate that we have a much slower off-rate in the bivalent interaction, and it’s a much more stable complex. And the avidity enhancement is mainly the difference between the off-rates in these two systems.

Magnus Kjærgaard (00:57:00):
So when we want to express this in a quantitative manner, then we define an avidity-enhancement factor, that’s the ratio between the off-rates. And then we can plot that as a function of linker length. You can see that we’ve done this for both the wild-type and some weakened mutants. And in all cases we see this scaling with linker length as expected, that the longer the linker gets, the weaker the avidity is. But the magnitude of the scaling is actually much, much less than we though it would be. So we only see about a twofold difference. And we see the same difference in all variants it’s just that the linear scale here overemphasizes the largest effect. So we only see a twofold difference in the avidity enhancement between the shortest and the longest linker, where we about an eightfold difference in the effective concentration. So we see a much shallower scaling with avidity with linker length than we expected.

Magnus Kjærgaard (00:58:10):
So we don’t really have a perfect explanation for this. We have some suggestions that we think might work. So I think one of the key differences between this system and the other systems that we’ve measured is that here we have two disordered linkers, and the way that they interact may add up in a way that is not fully captured by the effective concentration. For instance, the interaction between the two linkers, where normally the interactions inside a single linker will be captured in the effective concentration, the interactions between two different linkers will not necessarily be captured fully in the effective concentration. The other sort of, at least, toy sketch we could come up with is that we could get entanglement of these two linkers, so that even if both the binding sites dissociate, they would still stay together because they are actually entangled into each other, so we would get a slower dissociation than we would expect from just a passive linker. Great. This takes us to the end of the talk. And I would like to end with thanking all the people who have done the work, minus the ugly data point with the big error bars that I have take responsibility for. So again this was Mateusz Dyla, it was Charlotte Sorensen and Agnieszka Jendroszek and the work was funded by these people.

Magnus Kjærgaard (00:59:50):
Great. I think that brings us to some questions, let’s see.

Mark Murcko (00:59:55):
Wonderful talk. Just wonderful. And Avi, of course, is in Dresden and I’ve heard him say similar things about all the data that Tony Hyman generated by hand.

Magnus Kjærgaard (01:00:15):
So I’m in good company.

Mark (01:00:15):
That’s just a joke. I’ve never heard Avi actually say that.

Avinash (01:00:25):
Any questions?

Ben Levin (01:00:29):
If I can raise my hand first, I really enjoyed the change in properties of the linkers. Have you looked at instead of the distributed change actually bunching those changes together like hydrophobicity, or charge, rather than distributed across the linker itself?

Magnus Kjærgaard (01:00:53):
Yeah. So, again the Pappu lab has been leading this, where they have studied the chunkiness of the charges, for instance, and showed that this has a big impact. I think this is a great idea. I think that our model system is actually the wrong way of studying it for the effective concentration, because in order to get the really nice scaling coefficients we need to have the different lengths with the same linker composition. So that means we are really somehow restricted to working with something that can be approximated to a homopolymer. So we are looking at getting into synthetic IDPs with defined and controlled properties, but without having this measurement system. But actually it turns out that they are harder to make without the folded domains actually. So we haven’t quite gotten there yet.

Ben (01:01:58):
Thank you so much. I had one other question, if you don’t mind about your SPR. Does the monovalent actually saturate as you move up in concentration? It didn’t look like the system was saturating there and it could have just been [crosstalk 01:02:15]

Magnus Kjærgaard (01:02:14):
So we’ve done it for both of them, both of the monovalent interactions. So one of them is so fast on and off, so we only see sort of box curves. Those are the ones that I didn’t show you. And they saturate and you can follow a titration curve from the level of binding. I’m pretty sure the other one saturates as well, but we’re generally measuring this at pretty low concentrations, because what can happen is if you have a bivalent system, what we want to see is that they bind like this and then ring closing reaction occurs before you get binding of another protein, so you also could have double monovalent binding. So we usually restrict our concentration ranges to pretty low concentrations in order to avoid that.

Ben (01:03:23):
Thank you. That’s really interesting.

Avinash (01:03:31):
If I may ask, I have a couple of questions.

Magnus Kjærgaard (01:03:33):
Yep. Sure.

Avinash (01:03:35):
That was a beautiful talk, really enjoyed it. So now thinking about, in a condensate perspective, right? So if I imagine that all that you are mentioning about tethering would be true for condensates. So condensates would provide a platform for tethering of most of the kinases. Am I thinking in the right direction, or?

Magnus Kjærgaard (01:03:59):
This is definitely one of the next steps that we want to get into. It would depend on how actually the kinase is targeted to the condensate. So if you have this sort of solvent-like partitioning, then I don’t think we would see this sort of linker-like scaling. The easiest way to target a kinase to a condensate is basically just do as we do, and put a protein interaction domain in the condensate and then one on the kinase, and then the linker will define the accessible volume for how much of the condensate that the kinase can search. So again this will have to be examined properly in a steady-state situation as well. And then binding and dissociation of the targeting interaction also becomes very important. So this is the other thing that we’re investigating as the next step, is that for most cases. Right now we’ve made a system where we can approximate it to static connection, where we don’t see dissociation of the link, but for most kinases that are targeted to protein interaction domains, the strength of the interaction is actually pretty weak. So these protein interactions happen on micromolar affinities so the residence time will not necessarily be that long, and then we’ll have some sort of mixture between steady-state catalysis and single turnover, for both the targeting interaction and the properties of the linker will affect. So this is where we’re going and we’re also hoping to get into condensates as well.

Avinash (01:06:03):
So just a related question, since you mentioned that, right? So one of the obvious first candidates that’s come to my mind is the [Src-kinase that Mathias Bergman, inaudible 01:06:12] has found, how the intrinsically disordered part might be responsible for targeting it to the condensates. Are you thinking of that kinase at all in terms of your view?

Magnus Kjærgaard (01:06:34):
So we’re looking at different possibilities for moving forward. So I’m, as you may have figured out a big fan of synthetic model systems, but I think in order to convince people this is biologically relevant I think we are also looking at various more biologically interesting systems. So we’re at a neuroscience research institute so we’re mainly focusing of synaptic kinases, which is also sort of considered a condensate.

Avinash (01:07:11):
Interesting, yeah thanks.

Mark (01:07:14):
Yeah, so actually a similar kind of question — I was thinking about the part of your talk where you were describing what are the rate-limiting steps? What are the slow steps? And I’m think about how every case is different. So how tightly do you want the affinity to be versus what is the time-average sense in which the pieces are finding each other? So you started out looking at the length of the linker, and then you moved to on the x-axis using the effective concentration. But you could also use in some sense the time-average conformational manifold of each linker, as another way, as a surrogate for how often the two ends are finding each other.

Magnus Kjærgaard (01:08:01):
And I think these are different ways of expressing the same thing, right? I think the main thing is that you have find some sort of generic, generalizable metric for describing your linker architecture.

Mark (01:08:20):
Exactly. And how tight you want the interaction to be will also depend on so many other variables. How dynamic is the individual system? What is the Km for the substrates? And what are the kinetics of product release? So all of the usual enzymology questions that we all grew up with, those questions are still relevant. In a much more complicated formalism.

Magnus Kjærgaard (01:08:47):
So I think if you invite me in a year’s time, then I think I will hope to have some answers to some of these questions.

Mark (01:08:57):
Yeah but it’s beautiful work and it’s applicable like you said. It’s not just kinases, it’s anything involving signaling. So it’s interesting to think about which kinases operate inside of kinases that we know of. Which kinases are involved in signaling? Which ones have disordered domains? All of those questions. To your point about finding ways of taking what you’ve learned and then applying it to real systems.

Magnus Kjærgaard (01:09:28):
And probably phosphatases, it will be even more relevant, because they are much more dependent on anchoring proteins for-

Mark (01:09:35):
Absolutely.

Magnus Kjærgaard (01:09:36):
-for regulation.

Mark (01:09:37):
Because there’s fewer phosphatases than kinases.

Magnus Kjærgaard (01:09:39):
Yeah only a tenth right?

Mark (01:09:42):
Yeah, something like that. And then, of course, it’s not limited to those. There’s, of course, other enzymes as well that play critical roles in signaling in different cell types. So I guess what I’m saying is your work feels to me like it applies to just a huge swath of biology.

Magnus Kjærgaard (01:10:01):
That’s what we hope. And I think that’s the beauty of the synthetic model system, even though it’s more abstract, that you’re not answering an immediate biological question, but because it’s abstract then you can also hopefully generalize it to many other systems. At least that’s our goal.

Mark (01:10:24):
Yeah, it seems like a great direction.

Avinash (01:10:29):
Magnus, one quick question I might also want to ask is, you beautifully described the IDP system, right? And since now we know that many of these IDPs inside the cell are mostly associated with RNA right? So how would you imagine that RNA binding would affect such kinetics? Are you thinking to take RNA as an extension of the disordered part as well, in a very simplistic sense, or how would you imagine RNA fitting into this?

Magnus Kjærgaard (01:11:04):
So I think all the sequences that we accidentally made that bound RNA, I think they failed at some point in the protein purification pipeline, so I think that most of these in our experiments, there has been some sort of selection against RNA binding. But many of them, also of the other systems that we engineer, they seem to bind nucleic acids whether we want it or not. So in many cases I think it will make it more compact and this will make the linker scaling much shallower to some extent. And also I think when we also expand into patchy linkers, as Ben mentioned, then we can also get something that doesn’t scale with this polymer scaling law. But what really matters is the distance between the ends and the end-to-end contact probability. So if you imagine that you have a longer linker and you have a patch of positive charges and then a patch of negative charges then it doesn’t matter how much you have between these two if this forces it together and the same applies for RNA. So if you’ve a got an RNA binding motif here and an RNA binding motif here that is then brought together, then that will also give you a very different scaling.

Avinash (01:12:36):
Great. Any-

Mark (01:12:44):
Any other questions? I have the same question you were about to ask, does anybody have any other questions? What often happens is after a seminar we get together and we talk about it and we often come back with additional questions, if that’s okay?

Magnus Kjærgaard (01:13:01):
Yep, so you know my email.

Mark (01:13:04):
Sure.

Magnus Kjærgaard (01:13:06):
Great. But nice meeting you and hopefully we can meet in person at some point when all this mess is over.

Mark (01:13:14):
Well I hope someday in the US are back of semi-normal. It sounds like you guys are heading in that direction already, so congrats on that.

Magnus Kjærgaard (01:13:24):
Yep. Thank you.

Mark (01:13:27):
Beautiful work.

Avinash (01:13:30):
Thank you. Magnus

Mark (01:13:30):
Thanks very much. Okay take care.

Avinash (01:13:32):
Okay thanks

Mark (01:13:34):
Bye-bye.

Avinash (01:13:35):
Bye.