 of living of living matter from single cells to single organisms to collections of organisms over the past couple of decades there have been spectacular advances in quantitative experimental techniques that have led to the realization that theory and modeling plays a critical role in biology just as they do in the traditional disciplines like physics. So by tying together experiments with theory, quantitative biology sort of tries to uncover a deeper understanding of the mechanisms that influence the phenomena of life itself and we hope that the colloquiums in the series will convey this broad sense of what fascinates physicists about living systems and the principles that govern them. I would now like to invite co-organizer Professor Antonio Cialani from ICTP Trieste to please say a few words, Antonio. Thank you. Thank you, Mithun. Thank you all for participating in the first event in this series of colloquia. I just want to express on behalf of ICTP that we are very, very happy that this series of events is actually taking place and we are eagerly looking forward to further initiatives that can strengthen the ties between ICTP and IIT, Mumbai. So with that, I will give you back the floor and looking forward to hear from Edgar. Thanks, Antonio. So the first speaker of the series is Edgar Rolden from ICTP. Edgar did his PhD from the Trumpetense University of Madrid. He was then a postdoctoral fellow at the Materials Sciences Institute in Madrid and subsequently at the Institute of Atomic Sciences in Barcelona. In 2014, he moved to the Max Planck Institute for the Physics of Complex Systems in Dresden. First as a gas scientist and then in 2016 became project leader there. So since 2018, Edgar has been at ICTP Italy. His research interests lie broadly in the application of this field of stochastic thermodynamics to understanding biological systems. He's been awarded various prizes, notably among the early career prize with the statistical and non-linear physics division of the European Physical Society in 2017. So today Edgar will speak on the stochastic thermodynamics of active fluctuations in the year of the bullfrog. So before I turn it over to Edgar, just a couple of procedural issues. So all participants are muted by default. So Edgar, if you are fine with this, we can take questions in the middle of the colloquium as well. So if any of you have a question, please either use the raise hand feature on Zoom or you can use the chat box to type out your question. If you have raised hand, then one of the hosts will unmute you so that you can ask the question yourself or if you have typed it into the chat box and you just read it out so that Edgar can address the question. And then at the end of the colloquium, we can of course have a more open discussion within the constraints of whatever time it is. So Edgar, please take it away. Thank you. Thank you, Mithun. I'm really pleased to be here. This is an excellent opportunity and joint initiative between us and IIT Bombay. It's really exciting to be the first speaker. I want to say hi also to all the crowd, 63 participants at the moment. I see many people from India, so I hope this talk is interesting for you. So I'll share screen and you tell me if you see everything as it should. Okay, please let me know if you see my slides and also my mouse. You see? I can see the mouse. Okay, perfect. So thanks again for the invitation and for you to be there. Today, as Mithun introduced, I'll discuss on applications of the field of stochastic thermodynamics, which is an emerging field in statistical mechanics, to understand the active fluctuations in the ear of the bullfrog. So this might sound to you a bit too distant films, but I'll try to convince you that they are not so distant from each other and that we can apply universal principles on thermodynamics to the fluctuations in the ear of this type of bullfrog that was introduced to you in a few minutes. So this is a bit of an introduction on living matter and how life works. So we know that there are many physical or biophysical phenomena that are out of equilibrium. So you will see, for example, the top right microscope image of a cell division or a molecular motor and bottom right. This was the video of a flickering of a red blood cell and this one was of a clavidomonas swimming in a fluid. All these biological processes have some common grounds in terms of physics and mostly they all have to fulfill some thermodynamic roots. In particular, these are all non-equilibrium processes which are characterized by, okay, nowadays people call these active fluctuations, but we can just as physicists call these non-equilibrium because they dissipate heat to the environment in their motion. So they consume energy that comes from mainly hydrolysis of ITP and they produce entropy. They create disorder in the environment and they dissipate heat during the motion. So there are some universal principles that in principle should apply also to living matter. So over the last years, as Mithun was introducing before, there has been unprecedented advances, experimental advances for humans to interact with living matter and to get to know, let's say, the molecular fluctuations of a red blood cell or DNA herping or an oocyte. And this has raised, so the fact that we can now do very precise experiments has raised the question of what can we do with the data from these experiments in terms of understanding, for instance, the thermodynamics of these fluctuations. So these are some questions that different communities like biophysicists or statistical people in statistical mechanics or even biologists are now trying to answer. For instance, if we can distinguish active and passive fluctuations, so you look at that, you put a probe on a biological system, this probe fluctuates and you would like to know whether this probe is performing active or passive fluctuations. I will talk a lot about this concept that this is really a hot topic right now in statistical mechanics. Also, if we can infer from the type of fluctuations that we see, how much heat is being dissipated by a living system or if we can quantify the arrow of time. So if we can say how much irreversible is a biological process and for them theoretical insights that we can think about. So these are many open questions and I'll try to discuss some of them by focusing on this animal, which is the bullfrog brannocatesbiana. So this is a very scholar's American bullfrog. And I'll discuss fluctuations that take place in the inner ear on these cells that have some protrusions I will give more details later, which I'll call the ear head bundles, that displays in a fluid because in the inner ear we have a fluid called the endoline. So when the sound is transduced these fibers are moved left to right and this dissipates heat. So we're trying to understand or to guess or to infer how much heat is dissipated during the hearing process of the bullfrog by looking at experimental data extracted from this process. This is somehow one of the key goals of my talk and of my research over the last years and I'll try to give you some insight about this. But before, as I don't know which is your background, it's the first of this series of colloquium. So I will introduce a little bit of the anatomy of the ear of the bullfrog. So first of all, what is the ear and what is hearing? So this is a sketch here of a, okay, this is a human ear, it's not a bullfrog, do not have ears like this, they have sacrums, but somehow the working principle is similar than in the bullfrog. So the ear is like a microphone. So in the microphone you talk to the microphone and so you give a sound which is a pressure wave that enters the ear and in the microphone as you know, the sound is transformed into an electrical signal that goes to the computer for instance, but we have already this type of microphones in our bodies because the ear is doing this. The sound enters the auditory canal, it's a pressure wave that hits the ear drum. This makes that these bones that are connected, the ear drum to the inner ear also move and vibrate. And this ultimately generates a traveling fluid wave here in the cochlea that stimulates some cells that then generate electrical signals. So in the end, this is a very, very complicated process, but the key point in the sound transaction happens here in the cochlea which if we look at the cochlea, it has this type of spiral shape in which it's arranged into cells that have this structure and that are sensitive to different stimuli. So this is very particular because it looks like a piano. If you have played piano, you know that there are the tones of high frequency on one side and low frequency on the other. In the cochlea, we have a structure like this already built in and this happens in our ears. So when you put the sound that is a very high frequency, you will only stimulate these cells and when you hear a sound that is sensitive to low frequency stimuli, you stimulate this part of the cochlea. This is really fascinating and okay, this is an image of a piece of tissue of the cochlea and you see that this arranging in this type of structure that look like, I mean, modernist buildings, very strange and they have fascinated the attention of many physicists and we are still understanding their non-equilibrium properties. So I'll focus in one of these. So this is the epithelium of the bullfrog saclus. So this is extracted after sacrificing a bullfrog. You extract the tissue and you can do a electron microscope and see these structures. So you can take this structure out and you discover that this is part of a cell which is called the ear-head cell. You can see this image here. These cells have a very big, big cell body. Here is the nucleus and in the membrane they have these particular structures called the head bundle, which is a series of filaments that are arranging this way, which have a size of around seven microns. So in this talk I'll focus on how these head bundles behave and how the inflections are responsible for sound transduction and I'll mainly try to discuss which are the thermodynamic properties of the oscillations of these head bundles. So from now when I say head bundle I will be talking about one of these. As I said, they can have different sizes. This is a bit of an average and some of them are sensitive to low frequency stimuli and others to high frequency stimuli. So there is really in the tissue of the ear of the bullfrog you can get many of these sensitive to different frequencies. So how sound transduction happens? So in the end the traveling wave in the cochlea bends all these structures. It makes that all these are called stereocilia, these long filaments. They are bent and this creates that some other filaments that are called tip links, which connect each of these stereocilia are stretched and when they stretch they generate the opening of an ion channel. So here this is a microscope image of the ion channels that are present in the structure. So when the ion channel opens they allow the passage of calcium and potassium ions, which then are the responsible of the electrical current that goes to the auditory nerve. So this is a... Ekka there is one question. I'll just read it out from Anidvan. So he's asking how is this conical structure that you showed that is connected to the spiral that you showed? Ah yes yes, very good question. So if you have this spiral structure and okay this has a basilar membrane. So if you take a piece of this tissue and so if you I don't know how to say but maybe I can do an image. So if you take a small region here and you chop it then you see this one. This is a magnification of a small region here. So this is like a very very thin film in which there are all these cells arranged in this vertical arrangement. Thanks. Yeah thanks. Okay, okay, all right. Okay, so I was discussing that this is the way their cells transduce sound into an electrical signal and of course this is an active process because the ion channels are connected also to molecular motors that are responsible of adaptation. So adaptation is the phenomenon in which when you hear a very very strong noise your ear is able to adapt to very strong stimuli and this is done thanks to the action of these motors that are moving also the channels and therefore they are responsible of changing the length dynamically of these techniques. So here they say typical consumption, this is an active process and still we are trying to understand how much energy is dissipated in this phenomenon but this is just to tell you a bit of the biology of this process. Okay, as a physicist there are many fascinating features for this that have been discovered for the ear health bumbles. One is amplification, so they are able, so this is an experiment where they put one of these head bundles in a plate and they move the base of the plate and this is the motion of the base and they see that the tip of the cell moves with higher amplitude so they can amplify sound or stimuli. Another important feature is frequency selectivity, so different animals we are sensitive to stimuli of in a range of frequencies, so for example lizards can hear sounds that we cannot. Nonlinear response is another important. Edgar, excuse me, there is another question. Yes. So Dibbendo has asked how do the hair bundles in different regions sensitive to different frequencies differ? Okay, this is what I'm trying to explain now, so you can see this is experimental, it's not a model and they could experimental techniques measure the sensitivity of, okay, this is the entire ear to different frequencies. It is still an open question how this works, so what we can do is to extract the cells, see how they look and then try to guess why, so how can you make something say sensitive to one frequency and not sensitive to another, this is a big question, still it's an open question in the field, so we know what happens, we know because you can take out from the frog cells from different parts of the tissue and see that they oscillate at different frequencies, okay, so this is just let's say an empirical observation as for now and still we're trying to understand why in some parts the ear is sensitive to high frequencies and why in other parts to low frequencies, okay. Thank you. All right, so another important phenomenon is that they have nonlinear response, so when you listen to the sound of a needle falling close to you, you're, this is a given amplitude in decibels, whereas when you go on the streets and there's construction works, you will hear a sound that has 10 to the four times the amplitude of the fall of a needle, but your ear doesn't respond in a linear way, so if your ear would respond 10 to the four times stronger to the sound of a construction work, you will probably die, so you need a system that is able to respond to different amplitudes in a nonlinear way and this is actually have been shown in many experiments and finally the one that I will talk most is something called spontaneous oscillations, it means that the ear doesn't need sound to oscillate, so if you look at these her bundles and you put them in a quiet environment, they still vibrate and develop this type of spontaneous motion, so if you put yourself in a quiet room with a very, very precise microphone, you will hear sound coming from your ear and this is due to the fact that there are molecular motors that are consuming energy and they generate this type of active motion, so this is a very fascinating phenomenon I believe and we are trying to understand how this works and how is this possible from a physical point of view. So one more thing Edgar if I may, so there is another question that are the hair bundle frequency sensitivities related to the sizes, the sizes of the bundles? It's not clear, it's not clear, I'm not 100% sure, so I think it's not clear yet because you can have also different hair bundles with okay, so here I show you for instance one case which have maybe 50 of these stereocilia, but there are others which have 30, so there's not a one-to-one relation between number of stereocilia or height and frequency, as far as I know, but I invite you to take a look to recent biology papers, maybe this is better known right now, it's an open it's an open area. Thanks, and are the spontaneous oscillations is there like some characteristic frequency that depends on the motor? Yes, this is clear, so if you see here in the frog you will see that there are some characteristic frequencies in the in the fluctuations and this is what I'm going to show you in three of our slides, so you will see, so this time sheet is here, it's not like a particle in a double well with exponential waiting times, it's not like that, and this is a key insight from the hair bundle, you'll see, so it's an oscillation with a given frequency plus noise, you'll see. Thank you, thank you. Okay, I will talk about this in a few minutes, but yes, so physicists have tried to come out with models that describe this type of spontaneous oscillations, and at the beginning of the hair bundle studies there were many proposals about the fact that the ear may be near a critical point, yet there was this very influential paper that found that it was, you see, a critique of the critical cochlea, so it was saying a hop-fi forkation is better than none, so here they propose dynamical systems near a hop-fi forkation as a paradigmatic model for these oscillations, you can find some information about this in a great book by Strogatz on dynamical systems and think for example of a complex number, and here I'm plotting a complex number, I think the complex plane, which its radius and angle follow these equations, which are defensive equations that are non-linear, and you can have for when changing this parameter mu, you can change your dynamics in a way of hop-fi forkation, which means that you go from a situation where there is one stable point to a situation where this stable point becomes unstable, it opens up and then you have a stable orbit in which you perform oscillations, so okay this is no connection, I'm not talking about any biological parameter here, but this is just a physical system that can have these spontaneous oscillations, so this hop-fi forkation can be of different types, I won't discuss much now, but I invite you to take a look to the book of Strogatz, but the main point is that this idea is and it's very useful to discuss the possibility of having a model that has one stable solution in which you have one stable point here from where you may escape because of fluctuations, or oscillatory solutions in which you have the system oscillating continues. Of course this was only the beginnings in which there were these models which have no noise, so one cannot have this type of oscillations with noise with these models, one has to add thermal noise for instance, but yet with this type of modeling one can get many of the key features of the hermandal like very sharp power spectra, non-linear response etc, so it was a very important development in the field of hermandal modeling, yet however it has been 40 years of modeling, so 40s, 2010s and 20s people have been developing different models starting from dynamical systems close to hop-fi forkation, in the 2000s there were developments of models which are two-dimensional or three-dimensional longer than non-isothermal models, it is non-isothermal because we think of one variable is the top of the cell, another variable is where are the motors, and the motors are active so the fluctuations are not in a thermal bath, they are in an effective temperature somehow, then the next decade there were many multi-dimensional longer models with non-linear forces, so this is important that non-linearities are key to reproduce most of the experimental data, and in the last decade okay there are many developments, for example this is a very nice idea of a hidden vulnerable oscillator, or we just propose another model which is linear but which has no Markovian noise and we can solve, I will talk about this at the end of the talk, so this is one of the most important models in this, one of these I think this was in the 2010s or so, which is described by three non-linear couple stochastic differential equations, as I said this is the position of the top of the bundle and this is the position of the motors, this one is the concentration of calcium in the cell, I won't enter into details here but just to tell you that this model has been fitted to experiments, you see here this is for the question of methane, the power spectrum density of the spontaneous oscillation has a peak, so they have a characteristic frequency and this model can fit the experiment very well, moreover for different parameter choices you can build this type of phase diagram in which you can have bi-stable oscillations, mono-stable, and also this oscillatory regime I was talking about and an important question is where is the experimental data in this diagram, so the experimental data from this paper is shown to be right in this point, so close to a hop-fly vacation, so here we go from mono-stable to oscillatory through a hop-fly vacation, so it has been really the, say the bread and butter of the community to establish that the air of the bullfrog is close to a hop-fly vacation, so this is something that's well accepted in the community because of these experimental advances, okay so these models they are not only like nice to fit data but they are also good to do predictions and this is a very fascinating work where they coupled a real hair bundle to a computer, so they had a computer that was performing the simulations of this model here, so the computer is integrating langevin equations and responding to the motion of the cell, the real motion, the experimental motion of the cell and what they observe is that okay first they can have synchronization between the these cyberclones or virtual cells and the real cell and also that the response of the cell in this case is the same as if you have it in a real tissue, so this is a very very strong way of validating a model and it's really a crazy experiment if you think about, but then later on it was shown that cell headband is not only oscillates spontaneously but when they are close to each other you can put probes on top of them and see that they after some time they can synchronize, so you put them in a in a medium where they are connected back through their base, they okay there is a race they can synchronize among each other, I think there is a question yeah I'll just unmute please, hi, hello, I had a question if you can go back to the PST diagram of the previous page, so which parameters does that correspond to and just a quick question what are s and f max again I think I missed it, yeah yeah sure very good question so this model has around 20 parameters, so I invite you to go to the paper and see the parameters because there are these are mechanical parameters for example the the stiffness of the this is the stereocilia pivot stiffness, so it's the stiffness of the stereocilia to move in the basilar membrane this is the stiffness of the tip links so there are many mechanical parameters which you can extract from the fit they are available here and these two parameters are somehow the ones that they cannot be measured in any other way so there are different ways to estimate friction, stiffnesses, diffusion coefficient, etc but these two they are like three parameters across the the fix so one is the maximum this is called f max is the maximum force done by the motors so we assume that the motors are fluctuating and they exert forces they appear here on the on the bundle and this is okay this is like a sigmoidal shape and it has a maximum value which is called f max so this is the maximum force exerted by a motor of the updation motors and this s is a parameter that is called the calcium feedback strength which tells you how strong is the feedback of the calcium concentration on the motors so somehow this is a parameter that relates c to xa and this is a parameter that relates xa to x in a brief very briefly okay for details i invite you to to take a look at this reference as it replies thanks thanks i think you can continue okay all right so okay this is another fascinating phenomenon that we assert and as from now i will focus among all these features on the spontaneous oscillations i'll try to understand what can one do with the experimental traces experimentally one can put a fiber close to the headband as we show here and move the deflection of a fiber as a function of time which has this type of shape this is a typical time series of 20 nanometer amplitude and frequency of typically for example here before i was showing frequency of eight hertz in the bullfrog we can extract and resolve oscillations of eight hertz in this case so um of course experimental life is quite hard so i think most of you are theories so i will skip this so i tell you there is a fiber that we can look on top of it but this is taken from the pictures of my colleague and it's a very complicated device so so when you see one of the time series please take into account that this took a lot of a lot of work and time ratios and i start with my questions for for you so what can th smith do about bad tracheons and you may ask what these stages means this is a bit of a joke but i take it from this paper by christian mice which says th smith is the statistical mechanism in the street so someone like you maybe a statistical mechanism and would like to know if you get data from a biological experiment what can you do for your street knowledge and statistical mechanics so the first thing we may wonder is you take an experimental time series and you would like to know if it's equilibrium or non-equilibrium this work answered this question by revealing that these fluctuations are active so please take into account this is 2000 so now there is a lot of work on active matter but and this active matter has really a long story so just keep keep an eye on this paper and what they do is they compare the spontaneous fluctuations of the bundle to the response so they look also at the bundle when this probe is it's exerting a sinusoidal force so we will get two time series the spontaneous and the first time series and one can analyze them and try to see with these two time series one can say that this is equilibrium or non-equilibrium so to answer this question we can use common knowledge in statistical mechanics namely the green cubo sorry cubo fluctuation dissipation theorem so as you know you can take a collate for example in a thermal bath have a time series and compute the autocorrelation function of the time series which is defined like this and from it obtain the Fourier transform which is called the power spectrum mainly and on the other side you can do a second experiment where you drive this colloid so there is a trap and you move the colloid sinusoidally and look at the average motion of this colloid as a function of time and build from this the linear response function so you assume that the force is small so you put a small force sinusoidal force and you can extract this quantity which is the response function which is typically complex it has a real and imaginary part so cubo found that if the bath is in equilibrium these two quantities are related through this equation which is called the fluctuation dissipation theorem this part is the fluctuation in the sense that you just look at the spontaneous fluctuations and this is the dissipative part of the response and you see that here the relation is through the temperature of the bath so you must have an equilibrium thermal bath and driving these fluctuations so let's let's do what statistical mechanism can do is to test if this theorem works so you get a time series you build the stationary density is is bimodal and you can compute the autocorrelation function which has this type of oscillations and from it the power spectrum so what I show you before is just the Fourier transform of this of this function on the other hand you can force the the head bundle with a sinusoidal force of different frequencies and see that the response function of to this force has a very particular behavior because it has a peak the real part has a peak and the imaginary part changes sign in a given frequency and this is exactly at the frequency of the spontaneous lasers eight hertz so now you take this one and the power spectrum you compare them and you show that if you do these two experiments on a passive cell so force more them the fluctuation dissipation theorem holds for any frequency so you do the experiment at different frequencies and you get the fluctuation dissipation is fulfilled on the other hand when you do this to an active cell you see fluctuation dissipation is broken and this is a signature of the fact that these fluctuations are non-equilibrium it's a very very strong proof however you may you may want to to go deeply in this question so it's not only a binary question are you in equilibrium or not but of course we guess it must be ultra-vegilibrium because it's an active process but you'd like to know how far from equilibrium like to quantify the entropy production for example in the motion of herbana and for this we we published a paper last year but it took us a lot of time so I started this as a PhD student so it's nine years of research it's a long time so I'll try to give you a fresh update on this so first of all there is this fact that currents are a footprint of irreversibility so if you think of a simple model like a Markov process with three states if you are in equilibrium you will have no current so no net current between any two states and this will imply that the entropy production which is usually formulated as the sum of suitable forces times currents is zero in an equilibrium process let's say when when you have a Markov chain with all the rates fulfilling detailed balance however when you have non-equilibrium stationary states it means that you are biasing the rate for example here you go more clockwise and counterclockwise you have currents between all the states and this is a signature of heat dissipation so or or entropy production which typically takes this for so in the last year's in the field of stochastic thermodynamics it was there was a big development on how to compute the entropy production of a of an entropy present rate of a process for instance a land-driven dynamics in two dimensions in terms of stochastic trajectories produced by this process and here I cite a result that is valid for for all a non-equilibrium process in the stationary state in which we do the following first we look at the trajectory I think a trajectory in a phase space for example here is two variables so you have this sequence of states and you look also at the time reverse trajectory and of course if this is an equilibrium process you will see more time the blue and the red sorry if it's equilibrium you will see the same time the same number of times blue and red but if it's non-equilibrium there will be drifts so you will see more times this trajectory than this one it turns out and we can show in in stochastic thermodynamics that computing the uh cool back level divergence which is say the this is a measure of how different is the probability to see a trajectory with respect to the probability to see the time reversal trajectory if we compute this quantity this is related to the entropy production and in fact it's a lower bound always to the entropy production so whatever course gaming you do if you build trajectories and you do probabilities of trajectories and time reversals this quantity will give you a lower bound to the real entropy production which is a physical quantity so on this left hand side we have a quantity that it will depend on the on the specific model so some models are isothermals and this is just the heat for the temperature other models are have two thermal buds and this takes a different expression so this is the physics whereas this on the right is just a statistical quantity so it's just computing probabilities of trajectories and reversals so of course um your estimates to the entropy reaction will depend strongly on how many variables to see so here we can see with two variables we can see currents and compute the reversibility with two variables which is close to the entropy reaction in some examples whereas if you don't see the two variables for example you see only x1 you have like something oscillating but you cannot see currents so it's very complicated with one variable to see entropy production so these bounds that we establish are not always informative so if you reduce a lot the amount of information you will you will get very very weak bounds to the entropy production and this is the the case of the head bundles in the head bundle in experiment we only get one variable so it is really challenging if we want to estimate entropy production from something that doesn't have a current so you go the same time the same number of times left and right you are oscillating so we try to do this to estimate the reflection from one variable with in 182 recordings of these are 180 to workflows each recording has 30 seconds it's record excuse me there is a question so the question but either see it's like what happens if the dynamics in under damped if the dynamic dynamics is under damped where velocity is also slow variable will your formalism for entropy production and bonds hold yes so here i'm assuming over damp all the variables are over damp but you can extend this to under damp the only thing that you you have to be very careful is that in under damp they are not only x's they are also v's so when you time reversal trajectory you have to change the sign of the velocities so you can do it in under damp you can do it in under damp but instead of having only x's you will have also x it will be x1 and v1 x2 and v2 etc and here there will be minus v's so one can do it also with with velocities okay yet experimentally it's very difficult to measure the real velocity but but one can extend this i can give you reference if you're interested about this thank you yeah all right so this is our challenge and we'd like from this time series to estimate the underlying entropy production so i repeat we need to compute the probability for trajectories in the probability of their time reversals and there has been many developments we for example using the krasberg trokacian algorithm which i call the coolant tasks because they they basically try to compute so they discretize the time series and they try to compute probabilities of very long sequences and you see you have to do t go into infinity so that's quite complicated so we under uh introduce a trick which was the following we take the time series and the time reversals and we apply to them a whitening filter so what we are doing is mapping so we pass this by a machine gives you a new time series and now we pass the reversal time series for to the same machine and give you another time series i'm skipping details but this is called in actually machine learning there is a lot it's called whitening transformations in which you you do a one-to-one transformation between the original trajectories and the new trajectories such that the new trajectories are iid so the original time series have correlations and this one are iid and yet using the same transformation you can see that the distribution of this iid process are different when there are irreversibilities in the original time series so this map is very efficient because you map the original so the original autocorrelation functions like this and the autocorrelation function of the whitening time series is zero so you can do this very very easily with a computer and the main advantage is that this simplifies a lot the calculation of entry production so when you are in the iid process you don't need to compute anymore the probabilities of the entire sequence but the one-time probability density it's a major simplification so you just do the transformation you have two new time series and you compute the histograms that's it you don't need anymore to look at trajectory probabilities i'm skipping many details but this is the trick i'm just trying to give you a first smell of how this works and for more details i encourage you to look at the paper or i can also explain you later more so if we apply this technique of whitening and we compute irreversibility by this difference of histograms we can apply this to experiment time series and to also let's say a negative control which is a particle jumping in a double well when a particle jumps in a double well if you assume this is equilibrium you will have also these jumps yet you know it's equilibrium so when we apply this measure as a function of the number of data that we use you see that this case gives you zero irreversibility within the error whereas the experimental cases they give you positive irreversibility so we can distinguish between these ones which are hard to say they are irreversible from a purely equilibrium case so this seems to work moreover we can apply this technique to different conditions for example these are cells that are active so they are consuming a tp and you see that this irreversibility is larger than when we take the cells and we drag them so we put a drag that doesn't allow the channels to open and close so they are somehow passive and they have less irreversibility and this irreversibility of the passive is comparable to the one of the experimental noise so we can classify different cells in between active and passive very efficiently yet something I didn't say is that how this sigma one so this this irreversibility in the white n time series compares to entropy production this is an open question and what we try to do is to use models because we don't know the second variable in reality typically we have two oscillators we don't know the second variable the position of the motors but we can use simulations of of the model like I showed here to compare the irreversibility in x1 to the full entropy production in this phase space and the main result is that in this f max s diagram in the oscillatory regime we detect in the in the oscillatory regime we detect irreversibility this is the place where there is entropy production but yet the order of magnitude is very low so we say 10 10 to the one here whereas entropy production is 10 to the fourth so we are still far with sigma one to detect entropy production compared to the case when we have two variables where we see these things very well we almost collapse the real entropy production so this is a bit a bit of a pity from this approach so we try to get one step further and the step for that is if you are able to infer the second variable so of course this you could do by imposing this model you see machine learning and getting the time series x2 this would be a very beautiful approach but we we try to do an approach that doesn't require machine learning that is simplifying this model and have a second variable that is easier to to infer and this is what we we did in this last paper introducing this no markovian model okay i'm a bit tight in time but i'll try to give you a brief idea so this is an effective model in which we say that we have a particle in one potential and the potential is switched to another potential you go from blue to red and these are two harmonic potentials that have different centers so you are switching the harmonic potentials at random times okay so the particle is trying to follow these switches and you see here the dash line is the c process which is jumping into states and the blue is x process which is trying to adapt to these jumps the main point is that these switches happen with a time distribution that is arbitrary we set it arbitrary so it therefore breaks the balance between the jumps so it is a non-equivalent process the nice thing of the approach that we introduced in this preprint is that we select so we put the two distributions the top and in the bottom state of the of the c process here of the center we set it as arbitrary so there are two waiting time distributions that are arbitrary so if you put them exponential you will have a markovian process whose power spectrum looks like this like a Lorentzian whereas if you put them a non-exponential like they have a peak you will have a non-markovian process very important and the spectrum has a peak so this looks more like what we see in the bullfrogs moreover we can solve okay there are two big classes of models when the exponential exponential and when they are not exponential when they are exponential we can solve the problem analytically and see for example that the distribution of the of the tip of the bundle can be unimodal or bimodal so we find that there is this type of phase diagram which depends on two parameters so this r is the average time between the jumps so when you switch very very fast you cannot be bimodal so you need to switch slow but yet the c0 cannot be the c0 has to be large enough so you can resolve the two peaks so this we can derive analytically and it resolves somehow all this part of the of the diagram so we can take and we can describe with this model monostable unimodal and by stable this part yet is not taken into account in that model so it is a model valid for all this region of the headband so why i'm saying that we don't use exponential distributions is motivated by experiments so we took experimental data and tried to fit the weighting time distributions and to try to fit it to any function we found a very good agreement between the experimental data and a gamma distribution like the one i show here which is a power times an exponential this motivated us to introduce this model but and it also allowed us to do predictions from the data so here i introduce you to alfred which is a one of our brookfrogs from jim hasped lab and here you see the experimental time series and the stationary distribution and what we do is we compute the autocorrelation function and we fit it to the to the analytical value so for this case even though the size are non-exponential so the dynamics of x is no marcovian we can still even though it's no marcovian find analytically the expression for the autocorrelation function so somehow we take alfred it's here we look at the time series we build autocorrelation function and we fit it to a to our n formulas and from here we extract the parameters so somehow it's a it's an advantage in respect to previous models which were not analytically solvable so we can now do predictions of the herman this alfred is a power spectrum but we have also manfred and which you see the agreement between experiment and and the theoretical fits are perfect and this is lotard also it's very well fitted by by this minimal model and then okay this is the last thing i will tell you is that not only we can fit the data to a model but we can do predictions for thermodynamics because now this is a very simple model in which you introduce energy whenever there is a jump so when the particle jumps up you are you are accepting work on the system whereas when the particle jumps down you are extracting work so we are computing the and somehow the energy changes of the of the system whenever this switches happen okay this is the theory but what we can compute is how this changes in time on average so if there is a power dissipation in the ear we get this nice expression which depends on the parameters and also on on the laplacent forms of the waiting times distributions which we say is gamma so it's a very simple formula evaluated at this is our like characteristic frequency this is the stiffness of the trap divided by the friction so this is a very nice formula this generic for any waiting time distribution and now what we do is we take the data of alfred mounted and lotard we extract the parameters we plug in here in the power and we get an estimate of the power dissipated in this relation which is much bigger than what we are getting with the reversivity measure the reversivity measure was like 0.01 here you get around 100 kvt per cycle sorry in the reversivity measure we were getting one kvt per cycle now we get 10 kvt per cycle so it means that for every oscillation cycle you have to burn an energy of 100 kvt so it is not a fluctuation if it's a fluctuation equilibrium it will be one kvt so this is really a clear signature of activity and dissipation in the system and this coincides if the same order of magnitude as the full entry production that i reported before with the more complicated model so this is a simplification and it's a very robust tool that you can fit to many things and indeed with this i will give the last technical slide which is there is a lot of interest in the last few years 2019 on revealing reversibility in waiting times it's not only us but there is this very beautiful paper by martin vizker parrondo horowitz major communications which also pinpoints that if you if you have asymmetric waiting times you can detect reversibility there is also this clinical paper major physics where they they look at a cell crawling in this two chamber compartment and look at the waiting times in each state and it's also like non-exponential like the one we use so one could use our technique to estimate the dissipation in this model there is also this very crazy application of irreversibility so entry production estimate from waiting times in cows so you can look at the cow how long it stays sleeping and awake and they estimated in this paper entry version from cows and and finally okay we will also have a contribution on more theoretical coming next week in archive about also waiting times which i hope that you can read soon so with this i will conclude i have three main conclusions so the first is that stochastic dynamics has been applied through decades to very uh let's say a reduced set of experiments like colloids molecular motors you know hate this electrons but now i think the best is coming because still there are few applications on real biological process and this is one of them like we are highlighting this and this is only one of the many possible directions second is okay for bullfrogs we estimate dissipation of around 810 ATP per cycle so i said around 100 kVT per cycle and this is around 10 ATP so maybe we are starting to to infer the number of ATP molecules necessary to to drive the system and this is an important result because the molecular motors is an hypothesis in the end they know there's myosin but nobody has seen the molecular motors in the microscope moving because these experiments they do cryoem so they kill the cell to see the structure and then okay the truth is yet out there i mean there are still many things to do like look at the power and efficiency of sound of dachshund so we are we are using spontaneous oscillations we are not looking at the transduction yet the phonetic aspects it's another direction in so-called thermodynamics yes from optimal control etc so there's much things to do as you see there are many open questions yet this is a system that is known since 40 years okay i would like to finish with acknowledgement to all my collaborators in this in these adventures on the bullfrog and also my job is to be right now the people who are working with me directly and also the curious section in which i'm working since four years and it gives a good environment i want to highlight two people here in this list roman and genaro roman has been postdoc here two years and has done most of his work on the last part and also genaro did the pitch team here in cisa now just moved to mpi gottingen for a postdoc and the last work is mainly thanks to him uh i would like to thank you for your attention this is the place we work and this is the website from our institute and i leave you with this beautiful batrachian for the end of my talk thank you thank you it got uh that was it that was a really uh nice talk uh so i think uh we can take questions we have some time so um okay so i see please if anyone has questions please raise hands and we'll get on youtube when you can ask the question so i think ishant has a question so ishant please hello hi uh thank you for the informative talk professor role i just have uh two questions i would like to ask first one is in the end you mentioned uh this uh the switching of harmonic potentials when you simulated so uh i want to ask maybe i misunderstood so is something similar happening in the hair bundles inside the bullfrog is there is the equilibrium of the hair bundles shifting from one to the other is that why the model is predicting so well yeah i need uh so if i show you the time series okay there's a big collection of time series so i don't think i can give you all of them but if you look at the time series you see that it looks like that there are two stable points in which you are um jumping between each other but there is a relaxation so this doesn't happen instantaneously okay so so if you zoom in this this time series you will see a relaxation towards an equilibrium more or less but it depends a lot on on the time series so some of the time series look like this and you can describe this model but others look like sharks so they are extremely reversible they do and i don't know if i can draw here but sometimes these look like this okay so there's a big fenomenology and we can we can fit a subset of all the states mainly the ones that look by stable like the ones i show here okay thank you for this answer i have just one small question another question which is when you mention the spontaneous sound that one hears in a quiet room the are you talking about tinnitus the that that sound that when you are in an you hear an explosion or something that no no so i can tell you a very fascinating case okay of course and what i'm showing the last data is just a single set so this is a sound that you will not hear unless you have an incredible amplifier but i can tell you okay but i i knew in germany of a patient who who had some strange mutation in the ear and it was a family and this family at night they were realizing that the daughter was somehow producing sound and they didn't know what was going on so it seems like some humans they produce sound from the ears it's like a spontaneous production of sound that can be measured with a microphone so it's a it's really at the level physiological level so we are continuously producing sound even though you put yourself in a quiet room we'll be still producing sound because the motors are alive they're consuming ATP and moving this structure so it's uh i don't know if this answers your question but this is what i meant somehow okay okay thank you so much for your answers you're welcome you can go ahead with the question yeah so i had a couple of questions actually so one of the questions was uh in the in the theoretical models that you are building uh how do you account for attenuation of sound so in biological systems um the sound stops therefore you stop hearing it but the stereocilia have a period of recalcitrance because it is a mechanical perturbation it requires some time to reset back to state zero so in the in the theory aspects how is this accounted for uh this is not yet accounted because um this model is for a single cell it's not for the for an let's say a collection of cells so you would like to see like the traveling wave and the cochlea passing through a collection of cells this is not accounted by our model because we are at the level of a single cell but uh there are very interesting recent modeling from i think the both of the club is doing this in ucla in which the the model a collection of cells coupled to each other in which uh uh the stimuli is passing and it has a spatial structure as well as space time so one would need to extend the model to many many degrees of freedom but in principle one should be able to do it so in in theory if you multiplexed cells because stereocilia the the cilia are arranged in a particular pattern and that pattern is okay okay so sorry there's another paper you can take a look which is i will write in the in the chat take a look okay i'm trying to send i think it's a paper by baungardner i forgot the year okay it's in nature not nature very nature this is a very good model of which is a mechanical model that's an engineer type of the stereocilia with all the elements and so on these type of studies were very popular okay also and and they give an idea of this but it's out let's say i'm not an engineer i look at very tiny things which is a single cell and i'm i'm doing a very effective model in which i i'm ignoring really the atomic resolution but if you look at this paper you will see uh something some work in this direction okay my other question i got the chat i looked that up um my other question was um in at a single cell level as well um when cilia are lost when a collection of cilia are lost would your model be able to tell what are the um let's say the breaking points of that cell which when heat the cell stops responding can you repeat the question so the the model is based on the movement of one cell cilia yes okay one important point and this is also the question of arnav pal is um what you look is at the motion of of the tip of of these cells you see this is in the this is the outer membrane of the cell and this protrusion so you look at the motion of the tip of the herbal is a single cell yes okay but your question is my question is my question is so generally there is a there is the the sound wave is encountered by the the front bundle or the back bundle and it matters like where the sound hits so in your model is it possible to to reverse the the the starting point of this wave to see how the wave propagation would be perturbed would the wave propagation be perturbed at all and it's so strong you will need you will need a model with many of these excess yeah and then you have to introduce another variable and also external forces that that have the the properties that you look so so from the model that i just showed you before typically uh these models okay they look like this okay this is for one one cell so you will have to extend the model for many cells and then there's an external force that is coming to the cell so you need to add these forces and and tune it in a in the way you would you would like to look moreover this excess will okay will be different in different positions so the model will become very complicated but it's it's it's it's a good direction i think so this is the equation on the basis of which i was asking you the question because you have fixed the position right you have you fixed the position where your wave begins yeah maybe biologically also that is true that that's the wave always begins in a particular position okay this is constrained to you take the area of the workflow you you do a section you take one of these guys boom you put it in a plate and you look at the motion this is what we are describing yeah yeah not not an ensemble because doing an experiment with an ensemble it's it's very challenging and and you cannot have this resolution for an ensemble you will have to do a video microscopy and and this is less accurate so yeah yet yet it's a bit science-fixing but one day it will be reality so it's it's good to do for the future actually okay thank you welcome so can i ask uh raja she yeah yeah so this is raja she edgar uh no edgar i have a very general question so what about the physics part of it this is regarding entropy production now how how the way one defines this entry production how unique the definition is because you can have a model one model two model three you can break your time reverse of symmetry by introducing noise or you have two harmonic wells switching between them numerous way you can do for each model you can define some sort of intro production and then i'm just curious what is the status of this intro production business in active matter right now we wrote some papers years back but yeah i'm not much okay you're asking many questions just general generic general question i have yeah typically in stochastic thermodynamics we have a system with states and we say that the rate for for a to b to happen divided by the rate of b to a is is related to the environmental entropy change in this process this is an assumption that we use always in stochastic thermodynamics for instance this would be in an isothermal bath this would be the heat over the temperature so you need you need an assumption that is the transition rates are related to to physics to heat so we have this type of assumptions and then you can't if you have this type of assumption you relate the environmental entropy to probabilities of trajectories given the initial states uh moreover you okay this is a very long story but typically you you describe the entry production as the log race of of the path probabilities and then the point is where does the physics come from so when you specialize this quantity the specific models you start to see the physics so if you have a land given model in an isothermal bath you compute this quantity and you get the work minus the free energy so this is if it's isothermal if it's not isothermal you compute this quantity and it's the system entropy minus the heat fluxes in each of the baths for example in a in a Feynman ratchet so it seems very obscure but when you apply it to specific examples the usual expression for entry production specific to each model appear this in the sum in inactive matter is an open question so you can still compute this quantity is the irreversibility but uh typically you are ignoring non-equilibrium degrees of freedom so this doesn't give you the heat it gives you only a lower bound so one has to be careful inactive matter to call this entry production one has to be careful so it's it's more the degree of irreversibility than that entry production thank you thanks welcome so uh the next question is why or no or no please hi hi it was very very interesting talk very much liked it yeah this I was just curious about this physical I mean I understand in the model you have been beyond like exponential working time to non-exponential working time just I was trying to understand like also in experiment you indeed see a non-exponential working time which you think with the gamma distribution but do you understand that what is happening because you say that essentially there is a switch between two states also in the real experiment right the one which you are showing so do you understand that why actually there is a non-exponential working time in the system itself in the real system well um I don't know how deep is the question or do you understand but this is an empirical observation so we we never see exponential distributions in the bundle never never because this is a system that has so it's an oscillator which has a characteristic frequency exponential waiting times I've never seen in in the 182 cells that I look never so uh one way you can build this is if you think on a model with okay this is something we were thinking for a long time so if you if you think the model of the her bundle let's say it has okay this is a very bad drawing okay you have this model in which uh okay now there are these deep links let's say like this here and like this here and this bundle at some point will move uh to the left so it will this is one equilibrium position and the other one will be all these three coming here no okay so to see it at some point you need to to take actions on this channel so you need to pass from closed channels to open channels and you could do a very minimal model which is each of these channels throws um throws a random number or has a waiting time to be uh open so each of these has a exponential waiting time to pass from open to close and then you you should have to wait until all of the channels are open so you're right so collectively it's it's a collection of exponential waiting times essentially yeah so exactly so if you combine a collection of of exponential waiting times you will get something like this but but this is really my hypothesis so it's nobody has thought about this idea before so it's um it's a nice hypothesis and actually this this k here is related to the number of of exponentials if you want to build it like this and the k the k we get is around is around 10 which is close to the number of of ion channels thanks so it just reminds me of this airline distribution which essentially has this you know like collection of waiting time exponential waiting times and the number of steps essentially gives you this k there so yes yeah exactly so this is our a bit of hypothesis we we are trying to explore it so it's a bit intuitive by now but we're trying to verify this in more experiments but also just almost a similar question so in both the cases actually you see the bimodal distribution right for the stationary case right what do you mean what do you mean by both cases so both in the exponential and non exponential working times right yes yes so how do you actually differentiate between them i mean like in real experiment let's say that i mean okay i understand from the parameter perspective you will probably feed something and get this yes but but just looking at the bimodal distribution it is not possible for us to infer something about the waiting time probably no no no no that that's clear that's clear because the stationary distribution does not depend on the correlation you can have different correlations and obtain the same distribution so you need the way we feed the data is we feed the distribution and the correlation they are two things they are two phases of the same problem but they are independent each other okay so it's different this has information of one time this is information of two times correlation and in the normal case you have to go to beyond in reality but as for now this is what we can feed thank you very much thank you again it was a very nice it was good to see you here same okay so i think there are no further questions and i think we were short of time also very quite a bit so thank again i think from all of us thanks that guy it was really really nice talk thanks to all of the participants as well for attending and for participating through the discussion session the next colloquium in the series will be on the 13th of April so remember again it's the second Wednesday of every month so the next one is on the 13th of April and it will be by professor Rukh Malik from IIT Bombay so hope to see all of you there for that talk as well