 doing research. So our first speaker is Professor Hyun. Please welcome him. Okay, good morning, everyone. So, thanks for introduction. And actually, our chair, I mean, phrase everything I want to say at the beginning. So last week, we had some school basically introducing the basic concept of the statistical physics, but there's no, basically, there's no, I mean, lecture on the life science component. There was nothing about the life science component. So maybe next two days, we can actually hear something about the life science and application of the statistical physics in the life science. And maybe this is the first example. So molecular chaperone, what is a molecular chaperone? Okay, so molecular chaperones are cellular machinery that actually consume large amount of ATP to help protein or RNA to fold into their functionally-competent state, native state. And actually, the history of the molecular chaperone is actually very long, and it feels kind of dominated by the experimentalists, the biochemists or molecular biologists who are very well familiar with the equilibrium chemical thermodynamics. And the, oh, sorry. If you look at the chaperone for protein and RNA, it looks very different, but there are some underlying principles for their action can be described as some unified framework. And I want to, maybe I can actually emphasize the non-equilibrium nature of a chaperone-assisted folding in this talk. Okay. So let me start with the protein and protein folding and protein chaperone. Protein folding is basically defined by the, so three-dimensional sequence, one-dimensional sequence, which includes a three-dimensional, native structure of protein. And for a given sequence, well, if, as long as the sequence is already designed, evolutionarily, it actually defines a unique native state. And the folding passway is kind of smooth, folding landscape is smooth, smooth such that as long as you are sitting in some right condition, let's say low temperature, then you can get to the native states very easily via smooth landscape. Okay. Hydrophobic patches are in the native states, hydrophobic patches in the sequestered, sequestered in the interior of the structure, such that there's a kind of structures that are very compact and that there are low hydrophobic patches exposed to the exterior of the structure, that, so that you don't need to worry about some sort of aggregation kind of stuff. Okay. Or however, not all the protein can be folded nicely. I mean, at least 30% of the entire protein has some problem of the spontaneous folding. It doesn't actually fold into the right structure. So in that case, you can actually imagine the very long in the landscape like this. So in this kind of very long in the landscape, only a fraction of the population can fold into the native state and then rest over them to trap in the kinetic trap. So one minus five over them trapped in the computing base of attraction. So you can actually think about some folding passway in many different parallel passways. So in this kind of scenario, folding kinetic can be described as this kind of kinetic scheme. And the five, which are called the partition factor is defined by the two kinetic rate, cholesterol rate to the native and the disordered state. So this process going directly from the disordered state to the native state is very slow because of a large free energy barrier that actually doesn't occurs on a biological level on the time scale. So essentially, folding can occur in this direct passway, but this fraction is very small. And then most of them are trapped in the disordered state and trapped in such a long time that you don't see the transition from here to here. So then the problem is, this is a kinetic expression for the entire folding as long as the KS is kind of not too small then you can actually discover the native states, the kinetic rate to the native state can be described by this kind of a kinetic rate. However, when the KS is very, very small then on a biological level on the time scale only you can actually see the, only fraction of the population is being folded into the native states, okay? So we have the problem with this hydrophobic patches. So in the cellular condition, when this kind of disordered state is like a dominant, then you need to worry about the aggregation of this disordered, among the disordered proteins. So that caused a lot of problems for the cellular function. So cells that are equipped with this kind of protein chaparone, one of the best studies of protein chaparone is grow here. And it looks like some sort of like a cylinder, better like a structure. It actually have a cavity interior of the structure. And then we actually involve this misfolded, it recognize the misfolded structure, hydrophobic patches of the misfolded structure and then it endures it inside the cavity and then spit it out. So, and you need to, I wanna emphasize that this machine actually consume a lot of energy from the ATP and they actually undergoes large conformational change. This large conformational change is coupled with this, coupled to be the protein and that exert a lot of mechanical force to the proteins. So this trapped misfolded protein trapped inside this cavity or maybe it doesn't need to be trapped inside the cavity but whenever this misfolded states or protein in terms of the chaparone, it can feed into the some first, exerted by the chaparone in action and then it unfolded. So what happens in terms of, so when this cycle can be actually, when this cycle is repeated, then a lot of misfolded protein is unfolded into the states, okay? So what happens in terms of the landscape, this is the landscape and the chaparone actually capture the misfolded protein and then unfolded into the HLA, reset the structure into the folding states. So in a sense it actually performs some sort of error correction, okay? So when this process is repeated, iteratively repeated, then what happens is that it actually anneals the system into the native states, native population. So when protein, the chaparone, recognize the misfolded protein and unfolds and unfolds and unfolds and after an iteration, this is a population of unfolded states and then population of native states actually even like this equation, okay? As time goes on, then this is the population of native states actually in the cell environment, population of native states increase like exponentially and the time scale of this exponential increase dictated by this tau zero, which is a cycle of one cycle of chaparone in action divided by the fraction of this partition coefficient of the spontaneous folding, okay? So typically this gloria, this tau zero, the one cycle is about two seconds and for protein like a viscose, this five can be as small as 1%. So the total amount of time needed for folding the entire population into the native states is about the 200 seconds. This is the estimate you can actually make. So shifting our gear to the RNA folding, the story is about the same, but slightly different. I mean, so the story is the same in a sense that the RNA is defined by the four different sequence, G, U, C, A, G, C, A, U and then it actually first collapsed into some secondary structure and then under some proper condition like a magnification ion, it actually is assembled into the three dimensional structure. In this particular RNA is actually, I'm showing the group on internal ribosine, it actually displayed the catalytic activity on the self-possessing catalytic activity. However, this folding, even though we're folding effectively, so folding is very low, is the five only 0.088, so only 8% of the population can fold the native states or spontaneous read, actually read some help from the RNA-SHA pool. Okay? So it's also equipped with this kind of another machinery, this RNA-SHA pool, is the name is actually site 19, it's just one of the best studies of RNA-SHA pool, it was discovered in the early 2000 and it actually showed helicase activity, it online the surface exposes the helices. So whenever some helices is exposed to the surface, they actually, it actually online, it recognize this kind of helice surface exposes the helices, and online this helices into the single-stranded RNA. Okay? This is what happens. So site 19 can recognize, but because of the exposes helices, it's also in the native states. So not only this is native state, but also these foreign states have this kind of exposes helices. So what these people found in their studies that when you add the site 19, it actually unfolded the native states, native RNA as well as misforded RNA. So, and also they found that regardless of the initial population, native and misforded RNA, which is a steady state of value, which is not equal to one. So in the case of Gruyere, if you actually add the protein chaperone, I mean you add the chaperone, entire population of the protein get to the native states after a long time. But in this case, if you wait for a long time, it actually some value, which is not actually zero. And then another point is that if you add more chaperone, native states, population actually decrease. This is what they found, which is kind of weird, but I'll get to this later. I'll try to explain, discuss this observation later. So, in terms of this kind of log in the landscape, what other chaperone does is the following. It actually recognize misforded states and then reset the system into non-forded states, intermediate states. And not only that, it actually also recognize the native states and then reset the native states to the initial condition, but different extents. So it recognize misforded states better, but the kappa is actually, so therefore kappa is smaller than one, is the number is between zero and one. So the iterative value in the kinds of, I write down the equation has to be modified to some other form. This is the equation which I derived from the earlier, but other than chaperone, you have to write down, you have to need to include the effect of kappa in the equation. We need some modification. So we need to generalize this iterative value mechanism by other than chaperone into this way. So let's assume there is some sequence of RNA. It actually fold into the native and misforded states. Chaperone recognize this misforded RNA and then reset the system into non-forded states and then give another chance to fold. Then this population is divided into the folding state and the misforded state again. This is what defines the lawyer, right? But not only that, the chaperone actually recognize the native states as well and then unfold. It actually recognize the expositiveness and then unfold it. So that even the native states are given another chance to unfold. So a fraction of kappa of them are misforded and the one minus kappa of them are left folded. So this is the population of being, not being affected by the chaperone and this population will be given another chance to fold and unfold. So therefore, at the second stage of this iteration, what happens is the population, this is the first stage of the spontaneous folding. This misforded the population and second stage, second iteration, this is the population of misforded states, right? M2. And this top population is actually folded states. So if you repeat this process many, many times, then you can write down this kind of recursion relation and then you can actually solve the equation. So this one coming from this pathway and this one coming from this pathway and then you have to add these two. So you can think about some sort of this kind of logic. Then finally you can get a native population after any iteration of this kind of process, right? So the native is can be obtained by solving this recursion relation and this is an expression, okay? So which is a function of kappa and an iteration and the partition factor phi, okay? So if you plot this partition, that native yield as a function of iteration time or time, then this is the curve which apparently parameterized with respect to kappa. When kappa equals zero, the case is exactly the same as the gray year. So every population, all the population reaches the native states when kappa equals zero. However, when kappa increase, the steady state population is not one but some number which is more than one, okay? So and the steady state population is you can actually obtain by putting this n equal to infinity. So this is the expression, okay? And kappa equals zero, this is the expression for, it's the same expression as gray year. And when kappa equals one, which means that the native states and this for these states is recorded as equally by the Arlene Chaperon, then there's nothing happens, right? I mean, because the Chaperon acting on the native states as well as the, this for these states equally likely. So therefore there's no effect by the Chaperon. So the native yields just remain as phi. So nothing happens when kappa equals one, okay? So, but what is the meaning of this kappa? To get a better idea, we can actually map this entire landscape picture into three state model. Like if you see it, there's a, I mean, air going down and air going up and there was some transition from this for the state native states, potential transition between these two states. Therefore you can actually map this one into the three state kinetic model, reversible kinetic model like this. And this is just a very prototypical example in the non-equivalent statistical dynamics. So you can solve everything. So this magenta arrow is due to the Chaperon action, which increase with the, so because of it burning ATP, the rate of this Chaperon action, it can be increased. So it actually function of ATP. So if you add more and more ATP then this rate increase in a Michaelian type, hyperbolically increase like this, okay? And this three state kinetic model can be solved analytically and you can actually get the expression for the current flowing in this cycle. So this is an expression for current. So in balance of the kinetic rate, actually produce some sort of a non-vanishing current like this. If we kill the other, there's no current in this cycle. I mean, all the I and M and N species will be accumulated via the Boltzmann rate. However, if there's any imbalance, I mean, K, I, M, M, N, and K, N, I and something like that. So I mean, for all the rate and reverse rate, if there's any imbalance, then there will be current. So that's the signature of a non-equilibrium. And also you can actually get the steady state population of the native states or misworded states and even I states. So these are the expression, okay? So, so two, I mean, so these are the, so the expression for this native rate as steady states, as I mentioned, can be obtained by putting this N equal infinity, this the steady state expression for the native states. And you can now compare this expression and this expression in a certain condition. So this entire full expression can be actually compared with this expression if you think about, in our previous scenario, I said that this not, this, I assume that this rate is very small, okay? And then, so what happens is the following, okay? So I mean, if you actually put this expression into this steady state expression, native yield is expressed by this three kinetic rate and the kappa, right? And however, in this expression, if you actually assume this rate is very small, then what you get is the following expression, okay? So you can compare this kappa and this, this kappa can be expressed by this two rate, the ratio of this two rate. This two rate is nothing but a ratio between these two arrow from unfolding rate from native state, unfolding rate of the, before the state by the chaperone, okay? The ratio between the two, okay? So in the absence of a chaperone, KMI and the KMI is actually zero. In this case, you can actually erase these two arrow, the reverse arrow, and then what happens is that, you know, this RNA or protein actually get into these two states, L and L. And then, as long as you can wait for a long time, then these two species will be equilibrated. So this is just a hypothetical situation. So if you wait for a long time, then, in the absence of chaperone, they'll actually get to the equilibrium distribution, okay? You just get rid of this MMI and KNI, and then you just erase all the time associated with this rate constant, then you actually obtain this expression. So steady state expression for native states is nothing but equilibrium distribution. It's equilibrium probability for the native states, which is to take about stability difference between the misforded and native states, right? So, in fact, this is the conventional view. I mean, what is the aim of a molecular chaperone? In conventional view, people consider that the biochemists typically consider the molecular chaperone consume ATP-free energy to establish native areas about the potential distribution. This was the conventional view, but the IR view is a little bit different. Molecular chaperone actually consume a lot less and less of ATP-free energy to establish a non-equivalent steady state distribution dictated by this kind of rate, a magnetic rate constant, okay? So therefore, this equilibrium distribution and the steady state distribution should be different, but the confusion was that for the case of Gloria, which has to be studied for the last 30 years, this is a bit hard to actually dissolve this distribution, this distribution, because for the case of Gloria, kappa equals zero. So, when kappa equals zero, as you can see, this steady state distribution for the native state is just a steady state, even the native state is just one, right? And for the case of many proteins, the stability difference between native and misforded states is very large. So, equilibrium distribution is also close to one. So, there's no way to actually distinguish whether this mechanism is due to the equilibrium or non-equilibrium, but at least for the RNA case, this is kind of obvious. I mean, as I showed you, RNA, native state is not, the probability is not wise, it's just a non-zero value, right? So, apparently, we actually try to compute how many ATP has to be consumed to actually, to fold misforded states to the native states for this kind of ribo-land case. We analyzed the experiment data and then we found that about 100 of the ATP has to be consumed for the collection of the misforded states in the native states. Okay? And, okay, as I pointed out, unlike protein chaperone, RNA chaperone actually, if you add more and more RNA chaperone because kappa equal non-zero, it actually reduced the native population into non-zero value, actually, non-reality value. So, if you add in more and more chaperone, the native yield actually decreases. That's kind of puzzling because then, why on earth you are using the RNA chaperone to fold the RNA, actually unfold the RNA and then put it into the misforded states? But, if you think about this as a kind of molecular machine, you have to think about the yield per unit time. So, if you multiply this native steady state yield by the time scale of this entire process, actually, both processes increase as a function of chaperone concentration. Okay? So, molecular chaperone, basically maximizes the native yield on a biological time scale by driving the substrate out of equilibrium. So, that's the mechanism, okay? So, all this, even though I just multiply this lambda from some number we obtained from the analysis, this lambda can be actually obtained by, I mean, analytically from the three states of the magnetic model. So, you just multiply this lambda and then this entire expression for the small phi and the large phi. And, I mean, as you see, if you increase the chaperone action, lambda PSS increase whatever kappa is. I mean, it always increased this yield per unit time. To summarize, so, I talked about the logarithm, it's folding on the logarithm landscape. In that kind of logarithm landscape, protein or RNA has to fold via kinetic partitioning mechanism and then chaperone basically helps the folding of protein or RNA by iterative annealing mechanism, which is essentially non-equilibrium. And then iterative annealing mechanism, the previous iterative annealing mechanism has to be generalized by considering the unfolding of a native RNA, native states. And so the final conclusion is that the chaperone, which expands a lot of the ATP, drives the population of protein or RNA out of the equilibrium and making the native population more accessible on a biological time scale. Okay, so I think time is, I think I have a little more slide, but the time is up. So, this many of the work was done this Union's home. He was actually, in my room now, he's working, doing some experiments in Harvard. And these are the collaborator and then these are the paper. I mean, just I, some of the contents of the paper and then put it into this slide. Okay, thank you very much. The degradation of proteins. Yes. Should also play into this, right? Because there's a lot of ubiquitinization that... Right. So that they're also going down the ubiquitinase, the, you know, the degradation funnel at the same time. Yeah, yeah, yeah. So I haven't actually, but the duration rate is actually compared to other rates. It's very small. Maybe this, maybe the duration rate is comparable to this transition, but as I described this rate, directed, direct the transition from native to Missfulton state or vice versa is a kind of a, not, it's a kind of a negligible in my story and the degradation is also very small. So, but in case we can write down all the effects. So I haven't actually explained the situation in vivo, but you can actually write down all the equation and then get this kind of expression. So which take into account to the effect of degradation. Yeah. But the story just remained the same. Of all message, I convey it remained the same. Yeah. Professor Hyun, thanks for great talk. So can you tell what would be another benefit having a non-equilibrium system compared to the, the steady state? The left side example was sort of fully steady state but right side example, RNA, chaperon, what is non-equilibrium dynamics? What is the biological? Everything is non-equilibrium here. Yeah, yeah. Here is pseudo, what are the benefit of having this flux in this, yeah, yeah. In direct sense. So benefit, maybe I can, I can talk about the benefit in this way. So what happens is that even though the yield of the relative state is smaller, what, if you have a larger flux, then even though that population is smaller, you can make that accessible to the cellular condition. That's very important. So even if your, let's say your yield is like 100%, but if this yield is, yield getting to 100%, take like one hour, then what's the benefit? Right? If this process is very, very slow process, then the biological system will be dead after 10 minutes. So you have to make the things very accessible to the system even though yield is smaller. That's very important, I think. That's the role of Chaperone, I would say. That's kind of not well appreciated by the experimental community, at least the biochemical community. This point is not appreciated very well, right. So when you are considering the ATP consumption, 100 ATP, I think, then you are also considering the amount of ADP that is produced due to the ATP hydrolysis. Right, right, right. Means ATP versus ATP to ADP ratio is fixed in your system. Right, it's there, yeah. So the thing is, this is kind of a local situation, right? The concentration of ATP and ADP is maintained to be one million more than 70 micromole in the cellular condition. This is taken care by other machineries, like ATP, F0, ATPs, all this kind of stuff. They actually take care of the homeostasis of the cellular environment. So concentration is kind of fixed. There are some, you can consider there are chemical baths. External chemical baths is actually working on this system so that you don't need to worry about the production of ADP, but eating with degraded. Or I mean, putting it back to the ATP by the ATP synthase. Yeah, so entire concentration remain constant. Okay, thank you. Other questions? Or comments? I think there can be a multiple state of misfolded. So my question is that, is it okay to consider all that multiple misfolded states into the one state? Say that again. I cannot hear, can you? Can you say without mask? I think there can be a multiple states. Much what? Multiple misfolded states. Multiple misfolded states, yeah, yeah, yeah, sure, sure. There can be several misfolded. I see. So you explained it as one state. There are multiple misfolded states, but I, okay, so you are referring to this state, right? This is like a many state, but I just said that this is ensemble of M state, which is somehow separated by the time scale from the native states. You can actually have a transition between misfolded states. Maybe I don't know, but I can consider this as ensemble of the misfolded states, which is separated far away from the native state by the large barrier. So this is the situation. Thank you. I have another question. It seems our cells make a lot of mistakes and errors, but Penny, for you, you show us on some theoretical viewpoint. How can you confirm that this calculation is correct in real cells? This calculation is correct for the, I would say for molecular shaperone, but not all the resetting process. I mean error correction process, but general underlying idea is that baseline is that in order to make some error correction, you have to consume ATP, and error correction means you are resetting things into the, and then give another chance for this system to evolve again, right? So this is the idea of resetting. It sounds very pleasurable. All right, all right, but it's not purely theoretical. I never, I didn't show any experimental data, but there are a lot of data which is supporting this, and this whole, like let's say, graph I showed you, I mean, this graph is the data point I didn't actually specify, but these are the, these numbers are all from the experimental feeding. And then after feeding that, after determining many, many parameters, I actually draw this line, actually. So it's not just a thought experiment. I see. I was confused because you showed a clean theoretical. Yeah, yeah, yeah, there are many, I mean, noisy data points, but I just removed everything. Thank you. Another question? Okay, if not, let's send to Professor Heng. Thank you.