 who was a professor since two years ago, three years ago in OASP in Okinawa, which is for those who you don't know, it's a wonderful place in Japan. He can tell you about it. It's a tropical island and he will talk today about thermodynamics of better convection, which was a very famous work of him from a few years ago. So I leave the stage to Simone. Thanks to the organizers for the invitation. So today I will tell you a bit about our work on error correction in biology and I'll try to give a bit of an overview of the things we have been doing a few years ago and then in the second part of my talk I'll tell you about some more recent work. So just to introduce the subject, there are several fundamental processes in biology that fundamentally deal with the idea of copying information. So of course everything related with the central dogma, replication of DNA, transcription of genes and finally translation of RNA into proteins. These three processes can be seen from a physical information point of view as processes in which there is some information encoded in a polymer and some biological enzymes need to replicate this information into another polymer. So one aspect I will focus on in this talk is the accuracy of this mechanism. So in particular the typical values of the accuracy in these three processes is what you see in the slide. So transcription and translation have an accuracy of about 10 to the minus four. So one error every 10 to the four monomers whereas the DNA replication is a much more accurate process. So there will be an error on average every one billion monomers. So of course these numbers are not absolute values so they can vary a bit according to the conditions and they are not exactly the same in different organisms. You can think of them as somehow they can be one order of magnitude more or less but still these numbers are very very small. And of course as usually in physics when we think about the small number the question we should ask is small compared to what and to just give you an idea if you think about the possibly the simplest model of replication information which is the Michaelis mental model which you have an enzyme that can bind to either right and wrong monomers to form a bound state and this bound state is finally transformed into a product. If you do the math you'll find out that the error rate is always larger than a limit which is given by the Boltzmann factor. So the difference in e to the minus beta times the difference in free energy between a right and a wrong incorporated monomers. So there are two considerations here to be made one is that you reach this limit when the operation is performed infinitely slow which is clearly not the case in biology. And the second important consideration is that it's pretty easy to put numbers on this expression so we know that 80 bt is about 2.5 kJ per mole delta g in the case of DNA replication can be measured in a relatively easy way and it's in the range of 1 to 16 kJ per mole depending on the pair of monomers that is considered. And so you will get that the minimum error is something not smaller than 10 to the minus 2 which is clearly incompatible with 10 to the minus 9 which is the observed value. So the solution to this paradox is the idea of proofreading. So this is an image from another picture from the stock market where information on a tape which contains financial data is controlled by several people because clearly this is something that you need to read correctly. And you can think that this is pretty similar to what is done by biological systems so if you look at the details of reactions for example that lead to the incorporation of codons in translation these are not simple reactions but there are complex reactions that occur in many consecutive steps and at different stages of these reactions there are checkpoints so stages where if a wrong monomer is attempted to be incorporated this wrong monomer can be ejected and the reaction can be stopped again. So again if you think of this from a physical perspective it is clear that these reactions have to occur out of equilibrium because if you operate close to thermodynamic equilibrium no matter how complex the reaction is in the end you will end up with a population that is weighted by the Boltzmann factor and so you will end up with the same results as before even if the network is more complex. So the idea I want to introduce here is that to achieve error correction you need some combination of a complex incorporation network and driving out of equilibrium so you need to spend energy. It's always a bit awkward to give talks on Zoom so please interrupt me at any time if something isn't clear or if there are questions I'll be happy if the talk is informal. So one of the first concrete models of proofreading was proposed by Hopfield in the 70s in a very influential paper and he proposed a possible mechanism for error correction and this is a relatively simple generalization of the intelligent model in which regardless of whether a right or a wrong monomer is incorporated the reaction has an extra step so this is an irreversible step in which the bound state is brought to a high energy state and this reaction is insensitive of the monomer so here in this figure I the black arrows are rates that are the same for right and wrong monomers and the blue and light blue arrows are specific reactions so if you think of this scheme in terms of an energy landscape this is the figure in the bottom so you have a difference in free energy between the right and the wrong monomer and this difference is kept the same after transformation into a high energy state because the reaction is the rate is equal for right and wrong monomers. So the fact that there is this irreversible reaction essentially permits to discriminate twice so you can have preferential unbinding of the wrong monomer after the first step and another preferential unbinding of the wrong monomer after the second step. So this already brings the error from e to the minus beta delta g to e to the minus beta delta g squared so if the minimum error was 10 to the minus 2 I'm adding this mechanism to get 10 to the minus 4. So this is an idea that has a lot of influence in biology it also has shown that you don't need to discriminate in the non-equilibrium step so you can have some separation between the non-equilibrium mechanism that corrects error and discriminates in part of the reaction but of course it's not the only possibility so the error correction mechanism can be much more complicated and indeed nowadays we know much more about this reaction so in particular in the case of translation there is a lot of research in trying to really dissect each step of the reaction and see and try to measure what the rates are and just to give you an idea I show you a figure from a review from about 10 years ago in which they try to summarize the state of the art of the different steps in protein translation so these are these two lines are essentially the different steps that occur from the initial incorporation until the final stage in which the incorporation is confirmed and what I want to focus your attention on is also here the arrows of different colors so the red arrows represent reactions that occur faster so the higher rate for wrong monomers and the green arrows are reactions that occur faster for right monomers so here you have after an initial step that is insensitive to the kind of monomer step that discriminates backward so tends to remove wrong monomers faster than right monomers then you have the irreversible step which is where a gtp is well started to be is activated actually and this step has a forward rate which is faster for right monomers this is then followed by hydrolysis and finally there is a step in which the wrong monomer can be rejected at a higher rate and the right monomer is incorporated at a higher rate so you can see that there is a non-trivial combination of different steps and some of them there is forward discrimination and some other there is backward discrimination and of course you can ask why nature evolved this reaction in this way rather than any other possibility and you can also start think about this question a bit more in general not necessarily related to translation so the way I like to somehow think about this problem in an abstract way is to think that if you can imagine that there is a template that for simplicity has two different kind of monomers and there is a machine that is trying to reproduce this template so create another one that has the same exact order of monomers but of course again at final temperature this machine can make errors so clearly good properties for this machine would be to have a higher accuracy meaning a low error rate low dissipation because of course you don't want to spend too much energy this is costly for the selling principle and you want to perform this operation at high velocity because both duplicating DNA and producing proteins at high velocity would improve the cell fitness and so the question is how do you design a network that has all this property and if is there a physical limit to how I can how much I can optimize this so this is somehow the long I feel this is the long-term question of this field I won't say that much about the general optimality but I will tell you some ideas about simple network that can suggest something about how things should work so this is a really this was my introduction now I'll go to the outline of the results I will present so I will start discussing about the simplest case in which this reaction occurs in single steps so there are no multi-step reactions but we'll see that also in this case there are some trivial results that are worth discussing then I'll discuss some more general reaction some multi-step reactions in which proofreading is included and I will also try to analyze these systems in the spirit of stochastic thermodynamics so by computing the entropy production rate and use it to derive bounds on between velocity accuracy and dissipation of these systems and finally I will talk about some more recent results that we derived last year really about generalizing all of these to the fluctuating case okay so the first work is really inspired by a paper by Charles Bennett that came shortly after Hopfield paper and was interested in looking at really the energetics of proofreading and error correction so the Bennett model you can think of it as the steady state version of a copy model so instead of having considering incorporation of a single monomer and then the reaction finishes you you are thinking about copying an infinitely long polynomial as I was introducing before so if you think about my example if incorporation and misincorporation because you want everything to be thermodynamically reversible of monomers of course in single step then the whole state space or transition network of the system is an infinity so you have if you see this figure I don't have my pointer but so the transition network that's showing on the left in the beginning you have a state in which the copy is empty and the first monomer you can incorporate might be a right or a wrong match with the template and after that you can incorporate another right and another wrong and so on and so forth so you have these infinite three possibilities corresponding to any possible sequence in the copy and so this is Bennett's model and at this point we have to make a statement about the choice of these rates so there are four rates incorporation and misincorporation of right monomers incorporation and misincorporation of wrong monomers and again in the spirit of stochastic thermodynamics it's useful to think of these rates in terms of an energy landscape so you can see the energy landscape on the right of the slide so zero represents a state before any incorporation because the network is the same everywhere so all the states are the same and w and right are the states after incorporating a wrong or a right monomer from this reference state and you can see that I can describe this energy landscape in terms of three parameters so this gamma represent the difference in incorporation energy between a wrong and a right monomer delta represents the difference in activation barriers between these two monomers and epsilon you can think of it as a driving so if epsilon is large then the reaction is strongly out of equilibrium and forward rate are large compared to backward rates it turns out that since this network has no loop you can always solve this model so there is a general equation for the error rate which is this equation in the box so the and you can think of it as a sort of self consistent equation so the fraction of errors which is eta is proportional to the net incorporation rate of error which is the forward rate of wrong monomers minus the backward rate of wrong monomers multiply by the error rate so this is a sort of self consistent equation and you can say the same for a right monomer and by taking the ratio you get the equation which is from from which you can compute the error rate exactly but instead of looking at the general expression I think it's more illuminating to look at limiting cases so there are two limiting cases that are interesting one is the equilibrium limit so in which epsilon is driving is very small and in this case we are ready new from what we discussed before that the error rate must be given by the the Boltzmann factor so e to the minus gamma in this case which is the free energy difference between wrong and right monomer and in all of this I'm taking I'm working in dimensionless units some details if I want here sorry Simone there is a question in the chat so it's the following oh yeah I can't see the chat sorry yeah okay okay you cannot see it okay sorry sorry I can repeat the question I thought please go ahead I just wanted to ask basically the delta g is also depend on the concentrations so do you assume that the right and wrong monomers are the same concentration you can do either I mean you can think of it as equal concentration or you can think that there is a chemical potential and that enters these rates so if yeah normally we think for simplicity or concentration but essentially if you have a case with an equal concentration then you can somehow effectively incorporate into this delta g so these are really yeah free energy and gives free energy so yeah thanks does that answer your question yeah thank you so the other limit I was mentioning is the limit of a fully irreversible process so very large epsilon and in this case only the forward rates matter and we know that the forward rates are dictated by the energy barrier so in this case you can easily compute that the error is e to the minus delta so the difference in activation barrier between right and wrong and of course by increasing epsilon I interpolate between these two limits but the interesting aspect of this model is that of course e to the minus delta can be either larger or smaller than e to the minus gamma so depending on the choice of these two parameters you can have a case in which by increasing the driving and pushing the reaction out of equilibrium of course the velocity was increased as you can see in these plots but the error can increase or decrease depending on whether delta is larger or smaller than gamma does that make sense so you have an error rate which is dictated by the barriers and also that is dictated by the energy difference and if the error the say kinetic error is smaller than the equilibrium error then you will get a higher accuracy by driving the reaction faster and if the equilibrium error is smaller than the kinetic error then you will get a better accuracy by slowing down the reaction so to summarize this result you can think of it in parameter space and from the solution of the model you can look at it in another way so imagine that I fix the error and I look at the values so the parameters will be compatible with this value of this fixed value of the error and what you will find is that is this region is given by this inequality that is in the box and it's also represented in this face plot that you can see so you can see that there are two color this joint regions which are the regions that are compatible with a given value of the error rate so the white regions are regions where that given error is impossible there is no value of the driving that will give you that error and so if you are in the green region and if you want to reduce the error you need to increase the driving and this will imply a higher dissipation but also a higher velocity so there is always a trade-off whereas in the energetic region if you want to reduce the error you need to slow down the reaction which means you will pay less price in terms of entropy but also slow down the reaction so this this will be two opposite trade-offs and to see whether biology will choose one over the other we looked at the rates of incorporation of monomers from two DNA polymerase one which is polygamma which is used in a lot of eukaryotes and higher organisms and one from the pht7 and we found that the rates these two polymerases if you remove profiling have a pretty similar error rate but they will correspond to two different regions in this plot so this is somehow a proof of principle that biology probably uses both these strategies for different organisms um so of course we are very happy with this yeah do you have a an intuition or a story of why they are in the respective region no and honestly i would have expected the opposite because i would have said that phages wouldn't care about the error and they would only care about reproducing faster so this is a bit surprising to me yeah of course once you see the result you can always find the justification but i like to be honest and say that you know if i if you ask me before i saw the the numbers i would have expected the opposite so i i don't want to overinterpret this and i guess maybe one can make a hypothesis but i i don't have it that clear really um right so of course um after we saw this result we try to think about um a bit more in general um how can more complex reactions combine these two modes so the this more forward the kinetic discrimination and backward energetic discrimination so we started thinking about more general model and the idea is to generalize it by thinking that still you have these three of possibilities corresponding to any possible sequence in the copy but now each incorporation is not a single step but can in general occur by an arbitrary network of reactions and what we have in mind is that this network is the same for right and wrong monomers but it might have different rates so the rates are parametrized as usual in stochastic thermodynamics so you can see the formula you probably it's very familiar so um this is essentially what people call generalized detail balance or microscopic detail balance so each state inside this network has an energy um and there is an a time scale associated with each transition of course the energy of each internal state might be different depending on whether the monomer is a right or a wrong one and each of this network can be driven by a chemical driving which is this parameter new so of course this is completely general but there are not so many general things um that we can say about this general model there are a few things so first of all it is possible to do a similar game for some simple example so one case is kinetic proof reading which is somehow the polymerization version of op-field model in which there is an intermediate state and a second state from which you can discard the incorporated monomer and what we found is that if you try to minimize the error with respect to the all the possible driving then there are two regions in this case so one is in a region in which we call the kinetic lock in which essentially the error of the coping reaction is determined by the first barrier so the kinetic activation barrier of the first reaction and this is further corrected by the proof reading reaction and the second is something which is resembling to what is called the induced fit in the enzymatic literature so in this case the reaction the first step is low so the reaction can use in an energetic way the first reaction it can use the barrier of the second reaction and this is again corrected by the proof reading mechanism so we did also simulation and we showed that indeed you had these two different regions in which the behavior depends in different ways from the different parameters of the reaction but of course this direct solution is something you can do in this case but you can't really do the minimization for very large systems so the other thing you can do is to try to derive more general constraints based on physical principles so one thing that you can do is to write the second law stochastic thermodynamics so write the explicit expression for the dissipation and you know that on average this might be greater or equal than zero and for this general model you can do this exactly and what you will find is that the entropy production per step which is the entropy average entropy production rate divided the velocity of the reaction this is this can be expressed in terms of three different terms so one is the average work performed every time a monomer is incorporated a second term is an equilibrium free energy difference so the equilibrium free energy of each incorporated monomer and then there is a third term which is related to information which is given by the cul-back library distance between the binary distribution of the error and the equilibrium error so this is eta log eta time divided eta equilibrium plus one minus eta and so on so this is an interesting expression for a couple of reasons so one is that it tells you that if you want to achieve a given value of the error which is lower than the equilibrium error there is this dictates a finite dissipation rate so the amount of dissipation you need is greater it's not only greater than zero but it's greater than a finite constant that you can write down because and this is due to the fact that the cul-back library distance is positive and the second thing is the interpretation of this in terms of information thermodynamics and the idea is that if you generate a polymer that has a more order structure than a random polymer this is something you can extract work from so there is a free energy in the incorporation of the monomer which is the classical equilibrium free energy but there is also a free energy content due to the fact that the this entire copy polymer is not a random string and this is something essentially you can feed to a Maxwell demon and extract work out of it and of course since you can extract work from this order sequence you need to perform work to create this sequence so this is a way you can look at this result however I have to say that in practical terms this is not really a very useful bound because the if you start looking at realistic reactions in which you have proofreading typically the dissipation is way larger than the cul-back library distance between the error and the equilibrium error so this is not really a good bound for complex reactions but using the similar approaches you can for example look at the dissipation of only the proofreading reaction because also if you have subnetworks this must satisfy some inequalities and for example you can write another inequality in which the states that the the error is must be greater than the equilibrium error times a factor which includes the free energy difference and the work spent in the proofreading reaction and this is actually a much better bound so you can see that if you start this is for a for a model which is similar to the op-fil model and if you start including increasing the proofreading work you find that this bound is very is a very good prediction of the actual minimum error of this reaction in a broad range of parameters values of the parameters so yeah there are other aspects of this that are interesting and and so once it's something that we wanted to really understand is the issue of velocity error trade-offs and here it's also you're interested in codon bias you told me I like to cite this paper that I find quite interesting so it seems like in in a complex reaction like in protein translation you tend to have a negative trade-off between velocity and accuracy so this is similar to the energetic discrimination that I described before and and this kind of trade-off has been extensively tested experimentally so this is a relatively recent paper from erenberg group in which they really saw this trade-off in vitro for different codons so of course the different codons have different rates so the the slope of this trade-off is different but this seems to be general okay so now I'll tell you a bit about some more recent work so something that we try to do which I think it's quite interesting is to think since these complex reactions are always yes can you go back and so what are the different colors in this figure different codons so we have you have polymers we always like repeat the the same codons and and you look at the trade-off per codon uh-huh okay so this is I find it interesting information yeah thanks yeah so we have been thinking about different approaches to this problem so one is what if instead of having reactions with discrete step we think about a continuous reaction so normally this is actually pretty common in chemistry especially when it is possible to study reactions with some kind of molecular dynamics so one has an idea of the continuous energy landscape of the reaction and so our idea is that we can think of incorporation of right and wrong monomer as some kind of one-dimensional reaction coordinate that evolves along a free energy landscape which in this case is continuous and of course the delicate point is that one needs to so one would have a large event dynamics on each branch but then the delicate point is how to treat the branching point so then you need to figure out what are the boundary conditions associated with these long-joined equations but this is something that you can do and you can use this framework to ask other questions for example you can have a situation in which there is a kinetic discrimination but not only you have a difference in height of the activation barrier but the width of the activation barrier is different and you can find out that it is possible for example to discriminate by having broader barriers instead of narrower barriers so this extends a bit our understanding of how these forms of discriminations work so sorry I have a question so in this small event it's like you have a particle in the blue free energy in the B and suddenly you switch to the red free energy or yeah to the C when you reach when you reach the boundary you you take one branch or the other with certain probabilities okay okay so you need to figure out what are the probabilities according to so it's like a first passage problem no so you you wait until you cross the barrier in one and then you appear either in the blue or in the red correct correct very nice very nice yes okay okay so the last thing I want to tell you is this issue so um something that this is something actually we have been discussed for a while with ui2 that also worked with us on this project and the issue is that pretty much everything we have seen on this topic is not really stochastic in the sense that essentially what we have been doing and other people have been doing is solving um you can think of them as master equations but you can also think of them as topometric equations so in some sense there's not nothing um intrinsically related to the fact that we are dealing with the something of course that's low in low numbers and we have been thinking for a while is there something interesting some problems that can be related to the fact that we are thinking about really a microscopic problem and we ended up also with one of my postdocs like the qq to think about the following problem so imagine that you have again the same situation as before so you have an enzyme that needs to replicate a given polymer and you perform this process a given number of times finite number of times but this time I'm not thinking about the infinity limit I'm thinking about a finite time so I give to this enzyme a fixed time and then the enzyme is stopped the reaction is stopped and I repeat this process or I do it in parallel if you want and so I will end up with the different copy polymers that will have different lengths and different number of errors and now what I'm asking is um are the error fractions and the length of the copied polymers correlated so in this case the error fraction is an empirical error fraction it's not the theoretical again before everything was we were solving the steady state equation we were getting the average error fraction for an infinite uh polymer but here you have a finite time and you're looking at the empirical error fraction and empirical length and you want to know whether these are correlated or not um there is a an alternative problem there is also I think interesting which is the fixed length case and this is actually very um relevant for biology because you can think that you have to copy one gene so the gene has a finite length it's not in fit and also in this case you can think that if you repeat this process many many times uh every time it will the time it will take to replicate the gene is a stochastic quantity and the number of errors on the gene is also stochastic quantity and again you can ask are these two things correlated or not and of course if I'm telling you about this obviously the answer is yes they are in general correlated quantities uh so again I'm not I'm not telling you exactly what is the model here because now we will discuss this problem in general uh but if you have a specific model for how uh monomers are incorporated and error are incorporated you can find that um if you repeat this process many many times in the first scenario at fixed time you can observe indeed um significant correlations between the length of the copy and its error fraction and also in the fixed length scenario you can find significant correlation between error fraction and time so something that I like of this thing compared to the usual um idea of trade-offs is that this is really something intrinsic of the process so in the experiments where you look at say trade-offs between velocity and error you observe the trade-off by varying something in the experiment so in the case of the experiments I showed you before what's valid is the concentration of magnesium ions that essentially speed up or slow down the reactions whereas here essentially you're not uh touching any external parameter this is something you're really looking at the steady state fluctuations of this process um to understand what's going on so the first thing that we could show is that um the fixed time and fixed length scenario are related with each other and in fact you can think of them as two different ensembles um essentially this is something you can show in different ways one one possibility is to use large deviation theory but um the bottom line is that the most natural way of characterizing this correlation is by a correlation coefficient so looking at the covariance between error and time divided the standard deviation of error times standard deviation of time and similar for the length error um correlations and if the model is the same what you will find is that um these two correlation coefficients are the same with the with the difference sign and to prove that these are simulations of two different kind of incorporation networks that you see in the plot with random rates and for each value of the rates we plotted the correlation coefficient in the two different cases and you can see that they fall perfectly on the on the straight line so essentially these are really two equivalent ensembles and there is no need to study them both so for from now on i'll just talk about the first case about the fixed time case because it's simpler to treat analytically um so to understand what's going on here we decided to work with a slightly simpler model and the simplification here is that we assume that the last incorporation network is the incorporation reaction is fully reversible so this makes everything simpler because uh i cannot go back so once a model is incorporated it's incorporated forever and in this case i don't even think about the entire network i can think of it as a binary process in which um errors are incorporated with an a priori probability at a zero and the right monomers are incorporated with an a priori probability one minus a to zero and the important thing is that these two processes might take different time so there is a probability distribution of the time you will take to incorporate a wrong monomer and another probability distribution uh which is the time to incorporate the right monomer and these two are arbitrary so if i if i use this model then i can easily um write down the probability of having incorporated a given number of right and wrong monomer at a given time so this is a sort of path probability and um it's maybe lengthy question but it should be quite reasonable so you have in the beginning of a binomial factor which takes into account the different ways in which i can arrange this right and wrong monomers and then the integral term takes into account that the sum of incorporation times so you have r variables tau i distributed from the distribution of right monomers and the number of variables from the distribution of times to incorporate the wrong monomers in connection to the number of wrong monomers and the sum overall these variables must be equal to the total time that i'm fixing so by playing with expressions and taking the limit in which the time is large but it's not infinite what you can find is that the correlation coefficient can be approximated by this expression so it's essentially proportional to the difference in the average incorporation condition incorporation time between right and wrong monomers times the square root of their rate divided the the variance of the incorporation the distribution and corporation time of right monomers and the way you can think about this result is essentially if the time it takes to incorporate right monomers is longer than the time it takes to incorporate wrong monomers then of course you would expect that so this essentially will generate a correlation because in the in a finite time there will be a different probability of incorporating a number of right and wrong monomers so effectively this integral is correlating the fraction of errors and and the length of the copy so what else did i want to say here so another thing that i want to stress is that these are conditional probability in fact the interesting aspect of this model and this is something that convinced us for a while that there was no effect whatsoever is that if you take these distributions to be exponential then the correlation coefficient is zero because essentially you don't have really a difference in the in the expected correlation time in the condition correlation in the condition time between right and wrong monomers so you can observe an effect only these distributions are not exponential essentially due to the fact that exponential distribution is memoryless so let me show you a few examples so again one example is the Hopfield model and in this case where the this correlation coefficient is positive and by playing with the parameters of the model and using this theory we could find found a bound on the intensity of this correlation so for small errors this correlation scale like the square root of the error rate the the magnitude of the correlation coefficient we also looked at a model of protein translation which is similar to the 3d model but there is a step which incorporates forward discrimination as we discussed before and we found in this case an approximated expression for the correlation coefficient and interestingly in this case the sign is the opposite so this is a case in which there is a negative correlation between the error and the length of the generated polymer so again this is an approximated expression but it seems to work pretty well with simulations and also if we compute the value the expected value of this coefficient from measured parameters from the measured rates in in different strains of E. coli as you can see the figure so this is a nice I find it a nice result because essentially just the sign of this coefficient tells you something on whether there are forward discrimination reactions or not in in your network and this is just it doesn't need to does not require any tuning of external parameters so I'll reach my conclusion so in the first part of my talk I'll tell you I'll tell you a bit about simple reaction in which incorporation of monomers occur in a single step and I showed you that in this case one can distinguish between kinetic discrimination and energetic discrimination the idea of this strategy survives if one studies more complex schemes but things become suddenly quickly more complicated and it's it's not so easy to extract general rules for arbitrary large networks another approach is to use stochastic thermodynamics and the fact that the second law of thermodynamics always must hold to derive bounds on speed, accuracy and dissipation of these reactions and finally I showed you this recent result that for which the kind of discrimination schemes can be identified by looking at correlations steady state correlations between error and speed and yeah I conclude by thanking my collaborators so this is actually a relatively old picture of my group of toys because due to social distancing we cannot take one this year but the person in circle is Naride that did most of the work that I presented in the second part and I will also acknowledge my collaborators Pablo Sartori that is now group leader in Lisbon who collaborated with me on the first part of this project and you have also worked on this last project and finally my findings and thanks. I send you a virtual clap in the name of everyone so I leave the state for questions. Any questions? Yeah so I'm a bit puzzled by this positive correlation between the error rate and length when you do with the finite time so can you because say you would imagine that when nightly if you have a certain probability I mean especially in this case you were saying that the waiting time for so the average waiting time for doing mistakes is smaller than the average waiting time for doing sorry did you expect it to be positive or negative? No no I find it strange that in the case of the op-film model where there is proofreading there is a positive coordination so can you explain a little bit better why why so? I can try so this is also has been a bit of a puzzle for me like it took me a while to wrap my hand around this result so nightly I was thinking if you have proofreading you discard wrong monomers so this you know you have this process in which you start incorporating then you throw them off then you start incorporating so that takes a lot of time but this argument does not work because when you discard when you somehow yeah discard the reaction you don't necessarily start incorporating a wrong monomer again mm-hmm so so the the proofreading reaction brings you back to back to square one right and from there you don't necessarily start again the wrong reaction so these as a so you have somehow loops in which you start you see what I mean? So the the proofreading reaction is neutral with respect to whether uh uh to is neutral with respect to this correlation? uh I wouldn't say it's neutral because it changes the shape of these distributions uh-huh okay so it affects these times but it's not it's not simply slowing down the wrong incorporation pathway it has a complex effect on both. So essentially in the Hopfring model you have the average weight in time for uh incorporating the wrong monomer is larger than the one to incorporate the right one okay let's see yeah sorry the right is larger than the wrong are the right is larger than the wrong okay yeah isn't this continue to do it? it is because can you go back to the former? uh this one or this one? the previous one uh sorry am I thinking? this one? this one? correct it's correct it's very interesting so can you give an idea? let me let me maybe try to give you an argument which for me it works I don't know if it's good enough for YouTube but so if you're proofreading you have that very likely when you are at the say last step and you have the wrong monomer this is the reaction is restarted which means that the wrong monomers that are incorporated actually spend a very short time in the last step so this is selecting fluctuations in which you really go through the network very quickly so if a wrong monomer spends a lot of time in the last step it will be reset okay would that make sense? I think so I mean that that's the way that's my intuition I don't know I think it's an idea of how you derive these last bounds that you put there it's all large deviation bounds or isn't there any shortcut to this? we use mostly large deviation it's not really large deviation because in the end it's um we are looking at correlations so it's really the first correction around the average value but for example for the equivalence it was more convenient to work with the large deviations because yeah and other questions I think Rami so I'm curious about the protein translation model and I wonder if you can estimate what is Nikolai what is the fraction of energy that is going to specifically to error correction in the process is it 25 percent or more? what do you mean the fraction of energy fraction of which energy? I understand that you have to you have to spend some energy in order to do error correction but is it important in the global picture I mean how much of the energy that you have to invest in order to translate goes specifically to error correction? I'm not sure you can really it's not obvious to me whether you can really ask that question in the sense that of course ribosomes consume a lot of energy and I'm not sure how easy it is to make a statement of which fraction of this energy is error correction because it's the same reaction it's not you see what I mean yeah I mean I understand it's hard to separate it because it's like a it's a whole network basically some of the reactions are there for a translocation and others are for well I understand what you mean ma'am it's not clear what I mean it's pretty clear that there are some constraints on the error and there are some constraints on the velocity like if you have slow ribosomes then you cannot have a high fitness and of course the same network achieves I mean the same reaction achieves high velocity achieve the dissipation which is whatever it is and achieves low error so isn't you can't say okay the same energy budget performs all the reaction that has all these properties so I'm not sure I wish is to say this is the energy budget for error correction this is the error budget to make the ribosome run past yeah it's it's it's more complicated than I thought and it's kind of interesting all questions are you from students we're very silent I don't see any so it's also late in Japan so I would say we close the session and so thanks a lot Simone for the great talk thanks