Colloque 2024-2025 : Information Processing in Biological Systems
Conférence du 16 mai 2025 : Precision in a rush: temporal aspects of decision making
Intervenante : Aleksandra Walczak, ENS Paris, France
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Chaire Dynamiques du vivant
Professeur : Thomas Lecuit
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https://www.college-de-france.fr/chaire/thomas-lecuit-dynamiques-du-vivant-chaire-statutaire
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[Music] [Music] And our next speaker is Alexandra Vchak from the econom superior the pari and um Alexandra is going to talk to us about taking or being precise while being in a rush. Is that so? Yes. Thank you. Yeah. So, I mean, basically, I know we’re all starting to be tired and saturated. So, if you need some, you know, the one thing that I want you to retain is I’m going to add time to the problem. And basically, everybody, everything everybody has talked about, I’m just going to add time and worry about time and not having enough of it. And this came out with a long-term collaboration with uh with Natalie here. And then we were joined by Jonathan and Masimo. thinking about it. Uh and uh you can’t see my point. Yeah, here we are. And then Cherry and Tekk and then it led back again to an experimental collaboration uh with uh Mirna and uh Matthew, but I’m not going to tell you that story in that order. Uh I’m going to start off with the fact that cells live in noisy environments. They have to avoid danger. They have to deal with temperature, food sources and other stresses and they build noisy representations of these environments. So given that they are these noisy input signals and cells have these representations, how can they read these noisy signals in a way that they still make reliable decisions? That’s the question that I’m going to talk about. and do cells have enough information about the signal and how do they make these representations to have enough information to make these reliable decisions. So I’m going to start with a simple system which is a signaling pathway which is the map K pathway and its specific subcomponent the K pathway and depending on whether you like development or whether you like the immune system or you like stress response you’ve seen this beast and you probably hate it and your stomach churns because it’s complicated but at the end of the day all that matters is that usually it functions as an onoff switch. That’s what you’re told. There’s some signal, no signal, it responds, it doesn’t. And the question we’re going to ask is how many distinct readout levels can it actually distinguish? Can it go beyond the switch? So, back to what Thomas was saying, typically when you look at signaling cascades, you think about a one time point measurement and you’re just asking whether it can distinguish different outcomes. And in terms of Shannon information, this is one bit. So, but can you actually uh dist can this pathway actually distinguish more doses? Uh can it have different dispos the responses due to different doses? So, here’s an example with four which gives you two bits. And the question that we’re going to be answer is where is the information? Where does it encode this information? And so it turns out if you go beyond the typical view of just this one time show this measurement at one specific time uh time point and you look at traces the you can get more information in a trace than you get in a snapshot. So this is an experiment again in URGK from some time ago that if you look at a specific time time uh moment time time point you get less than one bit of information but if you look at the whole temporal vector it can go up and you get a little bit less than two and this was now later uh again studied in URG in a slightly different context actually a very interesting context context that puts the cell in a context and says, “Well, we’re not just in this artificial setting with one uh cell, but there’s actually the environment.” But if you just look without the environment, you still get a, you know, a little bit more than uh than sorry, a little bit less than one bit of information for the same signaling cascade. And again, we know this is a cascade that’s involved in many different things. But all of these previous approaches have a lot of experimental limitations. They have a limited number of resolved inputs, small samples. Uh they don’t cover the full dynamic range. But that’s not the issue I want to raise. The issue I want to raise is that there’s also self hogenity. All of these previous measurements were done at the population level. And so and we know different cells can behave differently even different identical cells can behave differently. So in terms of this uh what we’re looking here they can have different slightly different input output relations or those response cases. So what Mna did is she decided to study this problem at the single cell level. And so the input to this cascade is FGF. Again depending where you come from you know and you love FGF. Uh and what Midna did is she replaced it by uh optogf. So basically she used uh optogenetics to have a very precise control of the concentration of FGF that goes on. Okay, which means she can vary it precisely and she can turn it on and she can turn it off. And so that’s what Midna did. And then she measured the output uh of this map kynise cascade which is proportional to earth level and she looked at the basically she looked at the nuclei and she saw how much uh of this reporter that is proportional to is expressed. So what she did is she stimulated these cells with seven doses of different amplitude. So basically increasing the light levels so which is proportional to increasing the FGF concentration uh and uh she let the cells break in between the bosses and then she repeated this 20 times. So this experiment took a couple of days. Okay, this is painful. And then she got the output which I said is this reporter of K. This is what the curves look like but because these are the same cells stimulated in the same environment she could basically get reproducible uh distribution. So we’re back to what Thomas was talking about and then we used uh machine learning to uh machine learning based algorithms to estimate the mutual information from that. But the important thing is we’re able to get the input and output distribution here. So we can perform this and then it’s sort of technical details. Okay. So what do we get? Uh so this is the mutual information in bits between the dose so the light dose or if you want to think about it as fgf and the output uh as a function of time and we see that there’s a peak around the six and 8 minute time points which sets a time scale for the response and the green line here is uh the information from individual single cells and the blue line is from the population of cells or pulled cells and we immediately see that individual cells have nearly double the double the amount of the information that pulled cells. So single cells are able to discrim to tell you what the input concentration is way better than a population of cells. That’s what this result is telling you. And then we can group the data and look at time intervals. So we can look at uh what happens at one time and at two minutes and then what happens between two and four minutes, two and six minutes and so on and so on. So we’re basically taking intervals of the traces and seeing uh where the information is and again population level in blue, single cell in green. And by comparing these high time points which are still below one bit to the individual cell data when you take intervals you’re able to see that there is more information in trajectories than in single time points. Basically even the most informative single time point doesn’t come close to the information you’re getting from a trace. So by integrating over time you will look taking into account more time points cells actually have more information. This is true for single cells and pool cells and but the distinction that you always have more information in single cells remains with the caveat that single cells are very heterogeneous. So you have some cells that really perform very close to the theoretical bound of being able we have seven input doses. So that was gives us 2.8 bits and some do worse. Okay. So there’s huge cellto cell variability. So the information there is much more information in a trace. If we ask where is the information the information is in a trace than the information that is in a single time mission. Of course, there’s still information as single type of measurements. So, we can now turn the question around and say, well, okay, so now I’m measuring the output. Can I build a decoder? Basically, can I figure out by measuring the output what the input was? And I can build a universal decoder meaning I take the outputs from all the cells and then I try to uh ask each cell I give you this machine this decoder tell me what the output was. And if we do that then we see that basically the universal decoder works better for some cells than for others. Again future hogenity but generally doesn’t do very well. So cells uh it doesn’t allow us to figure out what the input dose was. However, if we built an individual decoder for each cell, basically we we train each machine for each cell separately, then it’s perfect for all cells. So we have perfect decoding at the single cell level. So really information processing here happens at the single cell level. And so then we also asked well are cells that are closer to each other do they are they more similar is there any information like that is there any correlation like that and so we again we remember we saw this this distribution and we don’t see this is colored by information and we don’t see really a correlation between where the cells are and how much information they have and uh pushing that further we asked well the daughter cells uh have sort of are more similar in their uh information processing capacities than randomized cells and that’s not the case. So basically we’re getting to the point where cells in this setup we see that cell single cells are able to process information uh better. basically they they have their own ways of of making a readout. This huge heterogeneity it’s something intrinsic to the cells. It’s not linked to uh sort of some baseline noise in in output levels uh and uh but it’s not linked it’s not linked to some sort of lineage structure or spatial structure. So what we saw here is that cells have more information in a single trace. And so how is the fact that you cells have a representation of a trace because they express mRNA? The mRNA they express is some sort of rep representation. How does it allow them to make reliable decisions? So this brings me back to the fly and as I said the sort of starting point for all of this uh and uh the fact that when bitcoin the bitcoin gradient controls the expression of hunchback and this results in this precise uh boundary where cells at the boundary are able to result in a different decisions which means to read out hunchback or not read out hunchback uh based on a 10% difference in the Bcoid concentration. So the input concentration differs by 10% which translates into 70 molecules and this just results down the road to different cell tips and this is done in a noisy environment because it has to find the binding site diffuse to it. uh it’s it’s not a simple problem and sort of 50 years ago now Berg and Pcel put this together and then Thomas uh and Bill put this together again specifically for the fly and it sort of depends on the parameters but you get the estimate that you need of the order of 40 minutes to do this with the precision that you explain in experiments but the early cell cycles have about five minutes so not with Natalie, we looked at this in in detail and she basically built concurrently with Thomas and MS2MCP report which allows you to track mRNA and you see that uh this is a chimograph so this is time and this is position and even in the very early cell cycle cell cycle 11 uh you get this precise boundary forming within 3 minutes of the start of the readout. So you get reproducible and well-defined uh decisions at the mRNA level uh or meaning high and low hunchback readout in 3 minutes. So this led us to take a step back and sort of think about the problem differently. So what the Berg and Pcel scheme does is basically you give yourself a fixed amount of time and you measure binding and unbinding events and you ask given you basically treat your gene as a as as a measuring device as a receptor and you ask based on that based on how I’m collecting my data do I think I’m in a high concentration regime or low concentration regime right everybody agrees with that I have this binary decision and I’m trying to make it in fixed amount of time. So instead we said what if I don’t have a fixed amount of time but I just I’m measuring and as a function of time I’m comparing the likelihood that I’m in a high concentration regime or low concentration regime. So as a function of time I update the likelihood between these two scenarios and at some point I reach a confidence level that I’m happy with and then I say I make a decision. Okay, so this is my log likelihood my two scenarios. I compare this and this basically leads to a random walk in decision space which is given driven by a deterministic bias h and some noise and I stop it when I reach uh prescribed error. So this is a mean first passage problem uh which can be solved and in fact everything is basically that time to a decision is then inversely proportional to this bias which for those who care is proportional to the fisher information rate. So okay so fish information is another measure of information which basically tells us how the parameter we’re changing in this case the log of bitcoin concentration is informative about the difference between the two scenarios. So very similar to what Adam was talking about. Okay. So the bottom line time is inversely proportional to the bias. The stronger the bias the faster the decision. So the blue one has a stronger bias. the decision distribution is moved to shorter times than the red one which has uh shorter bias. So stronger bias, better discrimination of concentration, faster decisions and so then we can optimize the parameters for fly system with six binding rates. Uh and we can ask how fast can you make the decision specifically can you make it in under three minutes. We have different rules for what constitute activation. how many binding sites you need to to have bound for the gene to turn on. So, but basically for most of these cases, we see that we’re able to make a decision reliably in under three minutes without any problems. We also w asked if we can make it with a sharp boundary. This makes a decision harder, but it is still possible. So basically there’s plenty of time to make this decision if we if we change the way we make a decision going from fixed time to variable time. But remember what h we still have the representation of the signal which is basically the trace of the mRNA. And so that that’s the question we had is well can we implement this in a real system? Can we get the so the log likelihoods have contributions to the uh off time and the on time that have certain forms that we need to fulfill. So basically our molecular system will have to have inertia and uh so there’s some has to be some time delay. This is quite easy to implement in gene regulation and it needs to forget. So mRNA needs to be degraded which in this biological system maybe is a little bit harder to reproduce but basically there are schemes for making this happen. So at this point uh we sort of went back to thinking about the trace because it seems that this representation of a trace is something the cell has but it doesn’t mean this is what the cell has to use to make a decision to make a readout. So so far in in what I just described we assume that it does use the full trace but it could be something different. So here we turned and this is work with TADK who’s here. Uh we considered a slightly more complicated system where we have the transcription factor binding site but we also explicitly look at mRNA binding. So we now for one binding site we have a four state system and we compared the decision based on the full trace to a decision based on a reduced readout of the trace which will be accumulated mRNA. Okay. So if I think of the trace as being my representation in the cell then I say well maybe I will be making a decision to express or not express on some further statistic of this trace. So how does that change how we make the decision on basically what parts of information we use? And I think we this is an idea that we heard this morning uh too. Uh okay. So now we’re looking at this fish information which is proportional to bias uh as a function of the concentration we’re trying to measure. So these are high concentrations and low concentrations. in red. This is the how uh how fast we can make the decision uh based on the full transcriptional trace compared to in black the cumulative mRNA. The higher it goes, the stronger the bias, the faster the decisions. And so we see that in higher concentrations, of course, decisions are easier. Noise is smaller. Low concentrations decisions are harder. So, uh the the the are harder. So slower. So uh but if we look into the so we can basically make faster decisions by exploiting the whole transcriptional trace. Uh but if we look at h which circuits are optimal for you exploiting this information for making this readout they’re very different in the two cases. So this is the optimal circuit uh for when you basically have the whole trace at your disposal. This is the optimal circuit when you only have the reduced statistics of the accumulated mRNA. And so when you have the whole trace to in both cases the name of the game is basically to return to the off state. So where you’re not bound and you don’t have the polymerase bound because you want to be unbound to be able to sense concentration to bound bind the transcription factor. You want to you want the transcription factor not to be bound to basically be able to function as a receptor otherwise you know you’re stuck right you can’t sense anything. So in both cases you want to return to this off state as fun as fast as possible because that’s the only place you can um you you can make a measurement but and so basically in the transcriptional trace you go through the network as fast as possible and I should add another thing that the which is actually very important and I forgot to mention that we do all of this optimization assuming constraints on rates. So we assume binding is diffusion limited uh but we also assume other rates have maximum values otherwise you could go through the roof. So and this does change the result significantly. So you basically max out the rates. However if you look if you’re read what you’re trying to read out is accumulated mRNA well the mRNA trace has by default information about the on state. it’s encoded there. You can’t get rid of it. So what you try to do is you try to basically reduce the variance as much as possible and use it as best as possible. And that gives you this back rate because then by going back and forward here you’re actually able to use that you you you modulate your on periods uh depending on the concentration of the light and you get information from that. So you’re forced to use them. So that that’s the difference. Uh and this translates into different activation functions. So if you use the full transcriptional trace, you actually you don’t you’re not cooperative at all. You have uh your your sharpness or steepness remains small. The hill coefficient is less than one. But if you’re reading out accumulated mRNA, you generate effective cooperativity through using this four state system, but steeper. What this tells you, so you’re way steeper with the accumulated mRNA, which doesn’t mean you’re more precise because you’re more precise with the full transcriptional trace. So in this fly field there’s also this idea that you want to be steep and precise and it’s the same thing and it’s not all right. So let me then bring this back to the fly and as this is very much work in progress um and what we’re trying to sort of figure out exactly what’s going on. But these are measurements from Ben well these are this is data from Thomas’s lab with the analysis of uh Benzola where they for different gap genes they looked at the uh time spent in the on well it’s actually on off states and the the effective time spent in a cycle and uh the interesting thing here was that this effective time spent in a cycle was constant. And so we looked at our two models and um because of this concentration depends in the on state, it’s the cumulative RNA model which is here denoted in this dashed line that reproduces this data and gives us this effectively constant readout where this transcriptional trace uh we always gives us a fixed on time. it doesn’t give us these dependencies we see in data and so it actually doesn’t give us an effective constant rate. So long of the short, it’s the cumulative mRNA that has similar signatures for the duros time span in the cycle to what seems to be going on in gap genes. And uh so so maybe a point to make here just because the information is there and you could be making a faster more precise decision that doesn’t mean that that has to be what the biological system does. We’re not saying it’s actually using cumulative mRNA but it’s at least more uh consistent but the information in principle is there and it could be used by other processes. And that’s why I think it’s important to distinguish between in this representation and what is then read out. But if we go with this cumulative mRNA readout and we put in six binding sites and um assume we want this uh cumulative decoding with a hill coefficient of at least five, we still we see that we can still make it with concentrations of where the Bcoid system functions in under three minutes. So um okay. So to sort of summarize what I tried to show you is that there is much more information in trajectories than snapshots. So maybe it’s sometimes useful to think about uh trajectories. Uh then we have internal representations of input the MRNA trace being a trajectory version of that. that we can then have different projections or readout which give us both different information and different optimal molecular encoding. And what does that mean? Different molecular encoding, it means different architectures. It means different promoters. It means different uh structure. And so single cell decoders are generally more accurate than universal decoders at least in the setting that we show. And this can give us um uh putting this all together we can get real time decisions uh that are uh that are fast and real-time decisions can actually be much faster than uh fixed time decisions. Okay. Thank you. [Applause] [Music]