 Let me show the screen. Yes, thank you. So, good afternoon everybody. And I would like to present today, very recent work that was done in collaboration with a theoretical and experimental group in the University of Padua. And I would like to start, yes, with the why we decided to investigate this problem. And we started with basically the observation that adaptation is an ubiquitous phenomenon as we all know in biological systems. They sense different cues in a dynamic and noisy environment and then modulating their behavior and response, exhibiting adaptation in a lot of different ways. These operations are usually mediated by chemical signaling networks that are internal to these biological systems and span a wide range of scales, both in space and time. So there are different examples that I can give you of this adaptation mechanism. One is bioluminescence, where biochemistry is coupled to viscoelasticity to control light emission of usually dinoflagellates, or even chemotactic responses, where the modulation of flagellar motors happens according to the local nutrient concentrations. And if you actually go at a very different scale, both in space and time, we can also see neural responses as a sort of adaptation mediated by some complex chemical signaling networks, where we have a collective response and also the building of a retrievable memory. Of course, let me actually start now with a question for you. And if I show you these two examples of adaptation, there are many of them, just two examples. One is for bioluminescence. It's actually lighter intensity with time upon mechanical stimulation of a perocystid lunula, which is one dinoflagellate. The other one is the neural activity upon repeated visual stimulation in zebrafish larva. So these two patterns have striking similarities. Indeed, you see a reduction in the signal up to a certain steady response upon repeated stimulation. Since these two systems are very different, they also span very different spatial and temporal scales, it is actually reasonable to think that biological details of these dynamics are not so important to understand this adaptation behavior, at least why it happens with this advantage and with this functional role of this adaptation. Indeed, this is not a completely new research line in the sense that the topology of chemical signaling networks have been studied. And indeed, theoretically, two main architecture have been found that are crucial for adaptation as stationarity in biological systems. However, this kind of structure rely on the deterministic description of the dynamics. And there are also studies that show how this structure are actually important even beyond the steady state regime. At an experimental level also, the architecture of several chemical signaling networks have been explored. This case is the one of our two monochromous factor network, and this is a very simplified version of a chemotactic network. And they are experimentally studied, so we know the reaction happening in these kind of processes. And as you can see, there are specific architecture for these kind of networks. So the two questions I'd like to answer is, the first one is, if we actually have chemical reactions and we take into account the fact that these are chemical networks, how this information will expand the range of possible architecture that are crucial for adaptation? And what is the molecular implementation at the chemical level of all these mechanisms we can see described in this kind of architecture at the deterministic level? One of them may be the negative feedback. The other one may be the role of these three nodes and so on. So all these kind of minimal mechanisms, how can they be implemented at the chemical level? I would like to present indeed actually the minimal ingredient that had been highlighted in the literature that are crucial for adaptation. And the first one, of course, it's the presence of a negative feedback. Both in the two monochromous factor network and in chemotaxis, we see that there is a negative feedback and it is very important to derive adaptation in this network, but also in all the architecture that had been proposed, there is always a negative feedback reaction, which is crucial for adaptation. This is not the only ingredient. Indeed, another very important ingredient is the information storage. This is never explicitly taken into account, but actually somehow it is connected in several works to a certain memory or a system or a certain time delayed effect. And in general, we know from Maxwell-Demon lecture let's say that information storage is actually important both for thermodynamic consistency and to take into account properly of the dissipation of the system. Indeed, without the information storage, we also have no thermodynamic consistency and we cannot take into account properly of dissipation of this kind of information processing network or if one of these chemical signal networks. Indeed, also in different chemical systems like molecular transporters, and this is one example, it is very important to have one node, in particular this is the two nodes, whose activity and whose role is the same as the information storage in a Maxwell-Demon. And naturally, emerge also a third ingredient, which is the fact that the system has to be out of equilibrium. So some energy is required to process information and to acquire this kind of information to adapt eventually. So now, let me start with the proposal. And actually, this is the model we proposed that encapsulates these three ingredients, so non-equilibrium conditions, negative feedback, and information storage. Of course, we need to have a receptor. The receptor has the role of sensing the environment and somehow is activated by this environment. The activation of this receptor will activate, in turn, the production of a readout population. And the role of this population is to encode the message and the signal from the environment and eventually to receive it adaptation upon repeated stimulation. And there is also a third population, which is actually the one implementing these information storage. Everything here is chemical. So we always look at the system in terms of chemical population and nothing else. But the role of this population here is to basically store some information and apply the negative feedback on the receptor, inhibiting further activation when some information is already present in the network. Before going on, I would like to point out that this kind of structure, which is actually now a chemical structure, and it shares some similarities with the architecture that had been found to be crucial for adaptation. But most importantly, it shares some similarities with the real biological signaling networks. If you look at chemotactic network, TNF signaling, and the factory sensing, they all have one negative feedback part, a chemical population that implements the storage, or a chemical population that implements the readout, and also, of course, a receptor, all of them. And if we actually try to scale up our system, also, in neural response, at least in the visual circuit for sensory adaptation in Zebra-Fisch-Lagove, we can also can somehow cross-grain the network to reconstruct the same architecture at the level of a neural response. So this observation hints at the fact that these three ingredients are actually the crucial ingredient to build a minimal chemical architecture to have adaptation in a chemical network. I would like to detail now how this network has been constructed. And the first part is the receptor dynamics. So of course, this follows a chemical network with two different pathways. These are just cross-grain version of more complicated pathways responsible for sensing the environment and applying negative feedback. And here, the role of the environment is just to apply an energetic driving that brings the receptor from its passive state to an active state. And since the system is fully thermodynamic, we can quantify also how much a system is out of equilibrium and what is the energy dissipated by unit temperature in the system, and of course, is proportional to the energy of activation given by the environment. The activation of the receptor, it's important to note here that an effective distribution can be maintained, even if it's an equilibrium-like distribution, can be maintained only at the cost. Because as long as we have a certain environment, we have an energetic driving and system will keep cycling along this cycle in these two pathways. So the activation of the receptor when the signal arrives will stimulate the production of this readout population, which follows a chemical burden that process. And indeed, we have an activation potential. This activation potential is reduced when the receptor is active. It's basically a reduction in the energetic barrier to produce a readout molecule. It's important to note that, comparatively with biological observations, the dynamics of this readout population is the fastest one in this network. For simplicity, we assume an unlimited population of molecules here. And this chemical burden that process is coupled also to the storage population. So we also have that these readout molecules catalyze the production of a storage molecule. And the storage molecule are responsible for the buildup of the information and the creation of a finite-time memory and, eventually, the application of a negative feedback. Again, this is a chemical burden that process catalyzed by the presence of the readout population. And it's not so possible to show that without this population that implements the information storage has to be slow, or at least its dynamic has to be coupled with the external field. Otherwise, we will see no adaptation. And if we assume that we have a slow dynamics because it's necessary, we also see that it's necessary to have another degree of freedom, which is usually not observed, that implement this kind of information storage. So we cannot have that readout population will apply directly the feedback to the receptor. This will lead to no adaptation at all. And this can be actually analytically proven. So in the end, we have an emergent timescale separation. And with this timescale separation, we can write down the master equation dominating the governing the evolution of the system, including the evolution of receptor, the population storage, and also the evolution of the external environment. And we can fully solve analytically this kind of complete master equation with this timescale separation approach. But before going on with the result, I would like to present the important variables that we look at to quantify adaptation. The first one, of course, is the reduction of the entropy, which is due to the fact that the readout population is encoding some information about the signal. And as usually in information thermodynamics, it's quantified by the mutual information. We can do the same for the storage and applying a well-known inequality in information theory, we can also quantify the effect of the feedback. So how much the presence of S will favor the encoding of information in the entire system? So how much effective is the fact of having a storage population that perform this negative feedback? Let me go to the result now. And indeed, as you can imagine, this is when you have a repeated stimulation, in this case periodic, but it's not actually a requirement. We see an adaptation in the readout population. In particular, we see that actually after a first steady state response, which is very high, then this response will decrease in time up to a certain steady state level. And of course we see an increase in the storage population in turn, because the system is collecting more and more information about the systems. What is crucial here is that usually only the readout population is observed in experiments. The unexpected part of this result is actually that this kind of adaptation is accompanied by an increase in the mutual information that the readout population is collecting about the signal. And indeed, we see that an increase of the mutual information or if you want a reduction in the entropy of the readout population as the adaptation goes on. And this is also, at some time, this is also accompanied by a reduction in the dissipation which is to produce all the internal molecules that we are studying. So the system across that dissipates some energy to produce both the readout population and the storage population that indeed actually are responsible to create a certain memory. But the energy required for this production reduces in time as the adaptation goes on. Indeed, we can actually conclude that there is a twofold advantage that emerged from this very simple chemical network, very simple architecture of adaptation. The first one is to increase the information of the system and the second one is to reduce the internal dissipation to create all the molecules that actually we are actually considering. Of course, all this effect is constrained by the fact that we are building a certain finite time memory, a chemical memory in the systems. And indeed, these two signals are too far away in time. We will see less and less adaptation and indeed at some point no adaptation at all. And this is also compatible with several observations in this kind of chemical systems. In case of bioluminescence, in the end, after 24 hours, the system will recover in total its ability to respond to certain stress. And in the end, if these signals are too far away in time, you will see no adaptation at all in response. This is just one example of several of them. Of course, it would be nice to understand what is the optimal phase space in the regional parameters when the system operates. And to investigate this part, we started with a constant field. So in the case of a constant field, we only see a steady state adaptation and not really an information dynamics in the system. But it's actually useful because in this context of a static signal, we can maximize the adaptation performance, which is encoded in both in the storage in the feedback performance and also in the neutral information while minimizing the dissipation of the receptor to have this kind of adaptation. So if we find the disparate or like surface that can be identified in the, in particular in the region of beta and sigma that quantified beta is, of course, the usual inverse temperature and sigma is the activation potential of the storage population. We're gonna ask ourselves what happens when we actually now have a periodic field. So now this surface is just a static optimal behavior of the system. And it might be not informative at all about what happens during the dynamics. What actually we observe is that adaptation itself is optimized around this gray area, which is indeed the static Pareto-like surface. So we have that the system actually exhibit an optimal adaptation around the static optimal curve. There are also regions in which we see no adaptation at all, but it's very crucially, these regions are characterized also by a detrimental effect of the feedback on the receptor or an increase in the dissipation of the chemical processes. So this means that actually the two features that we highlighted, the reduction in internal dissipation and also the efficacy of the negative feedback are actually crucial to have adaptation. Indeed, when one of the two is missing, we see also no adaptation at all in our system. We can finally also conclude that in this studying this optimal, the optimal performance of the system in the space of beta and sigma, we can see that in the low noise condition when the thermal noise is actually low, we need the higher dissipation to overcome the energetic barrier. Of course, the thermal noise is not enough to come in spontaneously, but with the higher dissipation, we also get a higher information gain, so a higher adaptation performance, while in close equilibrium conditions where thermal noise is actually strong enough to let the system to overcome all the energetic barriers by itself. A very low dissipation is sufficient to have adaptation, but the information gain is actually smaller because it's somehow hindered by thermal noise. So this means that higher dissipation is important, especially in low noise conditions. I would just like to conclude by scaling up this model and just the final part. Basically, as I mentioned before, our chemical structure and our minimal ingredient can be also identified for neural response to visual stimuli of the fish larvae. Indeed, we can actually scale up our model building a neural theory to generate a raster plot for neural activation without implementing any neural dynamics. Here everything is just chemical with the minimal ingredients I exposed before. And we can actually reconstruct in a pretty good agreement the adaptation features of this neural system. In the end, this is actually hinting at the fact that this minimal architecture is enough at least to capture the adaptation dynamics. And of course, biological details are necessary to capture also how this adaptation is achieved in time and how the dynamic response happens. For this biological knowledge is important but to understand and capture adaptation in particular to have an idea of its functional role we only need apparently just three minimal ingredients and our proposal is just one of the minimal architecture to condense and encapsulate these three ingredients. Of course, it's not the unique one but it's one we proposed in especially because it shares the similarities with real chemical networks. These are just the conclusions of basically from chemical modeling where we were able to extract the entire dynamical information processing features so how they evolve in time during a certain modulation of an external signal. This chemicalization also allows to quantify noise and also to consistently quantify dissipation and to define the reduction of entropy in a self-consistent way. The rotation comes with a two-fold advantage which is actually a new result that hints at the functional role of this adaptation and the final part of this talk highlighted also how this minimal ingredient might be valid across multiple biological scales. So if you want to learn more about this work there is also a preprint and this is the QR code associated with the reasoning appeal on the archive. And thanks for your attention. Okay, thank you. Thank you for this nice talk. I think there are some questions in chat. Yes, Thomas asks. Thomas, yes. Okay, may I read it? Well, I can ask. So the point is so you've presented the adaptive circuit having information and I assume you mean information with some time very signal in the outside world, right? As like a virtue of an adaptive circuit. But my experience of adaptive circuit is that the point is to respond to a perturbation such that you return the internal degrees of freedom to a fixed level that is independent of the circuit and independent to the input. And that's the story that you kind of have with chemotaxis models or feedback controllers. And now obviously often they create information in an ancillary degree of freedom as part of that. But is it immediately obvious that having more information in the response is like a good thing? Okay, so I mean, I would say there are two. I mean, I can answer saying yes. I mean, basically also all the works that have been done in literature basically refer to this sort of steady state adaptation where you return to a certain level of activity after the signal. And indeed this is, I would say this is also compatible to what we presented. Maybe not with this particular architecture. And of course there are some other architecture that one can consider that might have different different kind of behaviors, of course. And but are we going to find info? I don't know if it's actually connected to the fact that the system is acquiring more or not information about the environment. But the way we want to find information is just looking at the chemical population. And basically if you see these kind of patterns it seems that there are some other of them. It seems that basically the population keeps adapting and keeps reducing its, I mean, the amounts of population that is activated over time. Well, these data we can't, like from these graphs we can't tell what the information is with what, right? But in your model, in your model, you have information between what, here are your degrees of freedom. What's the information between you and H? So we can't, I can't tell what H is from this picture. So what's H and you? I'm not sorry. Yes, H is just the terminal field. So it's these, basically this is called the periodic stimulation. And you is the instantaneous readout. Yeah. Okay. So, all right. So information between the instantaneous readout and the environment. Okay. All right. So it might not be the usual way that people look at the information in this sense, but in this case, it's information in the sense how much this response is correlated with the time evolution of the signal, which is basically what you're quantifying. You are comparing the joint distribution with respect to the two marginalized ones in the end. So I might argue why, why I should adapt, why it should be important that I adapt in the systems. And I mean, one thing is, is that the system is actually responding in a more correlated way with respect to the signal. If you want, it is just a very complex measure of correlation, more, more complete than correlation, but it's just in the end of complete measure of correlation between the population and the center field. But why, so this is showing that over time, the information increases, right? Yeah. But it's, this graph is not showing itself that having the, having the negative feedback is helping you have more of that information. What, what's the control? Okay. You have no negative feedback. This is not showing the effect of the feedback. Actually, I didn't say it, but delta I is actually the effect of the feedback. And so indeed it is how much the knowledge of S in favors the collection information of the readout with respect to the field. So the more you know S, the more you can actually obtain information about this, about, about the feed. I also, and also if I cut the storage part, if I completely eliminate the storage and I completely eliminate the feedback, of course I have no doubt patient at all. But if I also implement the feedback directly through the receptor, I also have no adaptation at all. And you, I mean, the system is completely solvable. So you can, you can prove it analytically. There is, there's no adaptation at all. If we eliminate basically, sorry. Let's maybe get into this a bit more, because it's the discussion after this, right? So there's another question. So. Yes. I think it's Peter Ryan. I have a question, but I was waiting for the chair to point in my direction. Well, my question is actually very similar. But maybe I can start with a state with a question. So do you think that adaptation in general enhances information transmission? Okay, this is actually a question to which I don't know. I don't know how to answer. In a sense that in this kind of context, at least for the kind of observation that we wanted to, to somehow understand, I would say that this, the adaptation of response in time, increase the information that is shared or if you want the correlation between the readout population and the field. It might be not always the case. And in particular, I don't know what happens if we change the chemical structure of each building block, or if we change the architecture, keeping the same building blocks, we change the architecture or how the feedback is implemented. Because I would, because what I would say, right? So I think it depends strongly on the dynamics, the statistics of the input signal. And then it depends strongly on what you want to measure. Right? So if the input signal is, let's say an Einstein-Ulembach process, a Markovian signal, then you can show that the optimal network is one that just copies the input signal instantaneously into the output signal. Right? That maximizes sort of the instantaneous information. Is this thing true also in the presence of our storage? But then the push-pull network would suffice, right? So a push-pull network is basically a simple copying device and that works. However, the readout that you have is that. It's effectively a push-pull readout, right? So we can ask Daniel. It's a birth death catalyze. Yeah, exactly, right? So I would think so, but maybe Daniel can correct us, but your readout is essentially a push-pull network, right? I mean, it basically remembers the pass signal, no? The readout here is, here the dynamics. Basically, the readout here is just a built-in death process. So I don't know actually if this is what you meant. I think it is. It's pushed off by the thing being active, when it's inactive. Kind of. I mean, the crucial point here is that the readout population is actually fast. So in the sense that it reaches steady state immediately when the signal arrives. Did you put that in a priori or did it come out of an optimization? No, this was put a priori. But actually we checked that it was not a crucial assumption. And it was put, I mean, in the sense that actually the system works more or less the same way if we relax a little bit this assumption and perform a Gillespie simulation without this assumption. It actually was, of course, important to solve the system analytically, but Gillespie would agree not with an infinite adaptation. And of course, we also put this assumption because in several systems actually we know the time scales of this dynamics and the time scale of the readout usually faster with respect to the one of the storage. So there was some how inspired some observation, but we put this a priori and we checked that it was actually compatible with a relaxation of this assumption. Of course, we cannot relax totally this assumption in sense that if the readout is adapting at the same time as the storage population, we have an entire network. I don't know exactly now what it is, the readout, what it is in the storage and what actually is what we are observing in this case. Maybe it goes more in the direction of what you're saying. Actually, I agree. It depends on what you are observing and what is the adaptation in your kind of system. Then maybe this might have different consequences if the information is always maximized during adaptation. I strongly believe, for example, in the case of bioluminescence, when the storage is actually somehow connected to the readout because it's only implemented by a certain finite capacity of the molecular network. At some point you have no molecules to have light emission. In this particular case, I don't know if this information between readout and field is actually maximized over adaptation. Probably some other quantity that is somehow maximized or optimized during adaptation, for which adaptation is actually important and not necessarily what I mentioned. I would say adaptation, as Tom pointed out, is often discussed or studied in the context of the systems that have to reset to a particular value. But of course, systems that adapt, they also have this inherent capacity to predict derivatives and so if you have a signal with some inertia and if the system wants to predict the derivative, as for example in the E.C.O.R.I. Kepo-Texas system, I think, wants to do, right? We argue that it basically needs to predict the derivative. It just wants to know is the concentration rising or is the concentration falling, right? And this is really a derivative taking question. And then an adaptive system can be useful, right? Because you basically compare the current signal with the signal further back into the past, right? And so in that context, the adaptive systems can show up. But it really depends on what the system wants to measure, what it wants to predict, and what the statistics of the signal itself are, right? And so I think in general, in many cases, push-pull network suffice and only in specific cases, you need a more specific system like an adaptive system, yeah. And also, let me also mention that in this kind of case, we didn't consider motion of this sensing unit. So everything is somehow fixed in space because we had in mind, essentially, the experiment that I showed about the Zebra-Fischlachwa, basically. And so everything was fixed in space, so there was no motion there. But actually, the next step would be to add, and it's actually working on this, to add also the spatial degrees of freedom. This might change a lot of the picture, actually. Also because at some point you have a dynamic that somehow is driven by the changes in the information or the changes of the nutrient concentration. I don't know if these two are exactly related. It's not so trivial to understand. It's actually a change in information and increase or decrease is immediately related to a change in the local nutrient concentration. And if this kind of structure is enough, it's suffice to describe what you're serving chemotaxis because it's a network in which you also have a spatial degree of freedom. It's something that is not included in these models. So I'm not so, let's say, confident in extending these two chemotaxis formally, at least in the sense of the observation of chemotaxis responses. Can I, if we go to your system, and so if you assume that you had a very slowly varying environment, so that the environment varied slower than the negative feedback, the base signal, obviously the receptor signal would fluctuate. The, would you think that having the negative feedback would increase the information between, so this graph doesn't help us very much because you've got very rapidly varying signal. Yeah, so we also, this was basically to show the, I mean, to have a nice picture. We also, I mean, basically, this is what happens when you have a lot of posts within one signal and another. So in the end, in this kind of building the model, the memory somehow, or if you want the effect of the storage, it's as a finite time because it's a chemical memory. So of course, if you have a longer poses between signals. But I'm not really talking about, I'm not really talking about pulse signals. I'm saying, imagine you had like a flat signal which could then change to another value and then change to another value. So you've effectively, what I'm saying is you've effectively got a system that is responding to effectively constant signals which do vary on some very slow time scale. But so slow that all of the dynamics of the downstream network reaches a steady state. So do you think that the negative feedback thing that you've got will increase the information between H and the signal, ignoring any information that you have in S. So obviously if you put S in, you've put extra molecules in. You've been yourself the capacity to have extra. That's okay. Just looking at H, would the negative information in negative feedback increase your information? I'm pretty confident that you would say no it won't. It will make information less. There are two points. I would like to mention on this question. So the first one is that if the storage is also relaxed to steady state because the signal is too slow. So the answer is no. The second point is that everything is steady state. So you have no really a negative feedback that dynamically works in this way. You're just one steady state for the entire network. The gain goes to zero, right? I mean your gain just goes to zero. I mean if you adapt on time scales that are shorter than the time scale on which the signal changes then on that time scale the response magnitude goes to zero and then the mutual information also goes to zero. So I think this only works if the peak of your frequency dependent gain of your network, if that matches the frequency of the input signal. Yes. This works when the storage molecules have a dynamics which is in terms of time scales coupled to the one on the signal. Otherwise everything reaches basically a steady state where you have a dynamic adaptation in this sense I showed here. That's the point. So it's crucial that the dynamic of the storage has to act more or less on the same time scale of the external signal. That's for sure. Another thing which is actually I would like to mention in answering this question is that this i, u and h is already the mutual information shared by u and h with no information about s at all. In the sense that s is in the system, of course, the storage is in the system but here we are just comparing the joint distribution of u and h with respect to their marginalized distribution. So we are not really looking at the effect of s. I mean the effect of s is there but it enters in an integrated way in this kind of observable. Of course we can study even u and s with h or some other quantities. Nothing changes so much but the nice thing is that even integrating out the effect of s still we see some increasing in u which was actually quite unexpected for us. This is a point. These graphs in some sense I'm not saying they do show this but if you just had a transient dynamics of u with respect to h and no s they would also show an increase in the information over time. I suspect. So the key comparison is not to say that the information increases over time. The key comparison to prove the adaptation is doing something in this regard is to show that if I cut the s circuit out so is that what the bottom delta i is? What's delta i? This is this quantity here and probably it's delta i f actually is this part here. Of course we cannot cut the storage. I mean that something probably that is missing in this picture here is that every point here is a steady state. So every point here is actually a steady state. Because you assume it's a very fast response. So that's why I'm using this kind of quantity here because we cannot mean every point here is a steady state. So it's not just a transient. The ED made this information in the storage. Maybe this was not clear at the beginning and sorry about it. It's not just a transient of h because h is reaching a steady state. Yeah, yeah. It is the integrated effect of the transient of s. Yeah, exactly. And that is apparently increasing the mutual information due to some frequency dependent effects. Yeah. Yeah. There are any other questions in the chat because I looked at the chat but it was there are some adding questions in chat. Thank you anyway. You're welcome. Actually I appreciate all these questions and so they were very interesting. Actually it also gave me the opportunity to discuss several points where maybe not so clear or in general maybe not complete in the model like the spatial part or those kind of things. I appreciate it. Okay. I can briefly answer to the question in the chat if the guy is online. And basically the answer to the first question is that this is every point here is a steady state. So it's not like just a convergence. So it's a system which is steady state and we estimate the information every time basically what I said. And the other question was the information between some variables and the system and the written signal. This is yes in the sense that you have a mutual information if you just have a static signal and you let the system relax your steady state you have a mutual information of course because at some point the signal reaches a steady state and this steady state is somehow correlated with the central signal. Of course we have some mutual information but the point here is that since the part of the mutual information is changing in time is a consequence of the fact that you is reaching a different steady state in time as a consequence of this time integrated effect of the storage population. So the answer is yes we always have a mutual information but the increase of mutual information is usually not there if you reach a steady state if you don't have another node that implements some kind of transit effect of course. You just get a value that's all. You have no gain in the mutual information it's just one value. Thank you. We are already in the discussion time so we have still sometimes are there any questions to the speakers?