 with this third week and second half of the spring college. So we have a new set of speakers and lecturers. So it's my pleasure to introduce Professor Kaneko. Professor Kaneko spent his career at the University of Tokyo and recently moved to the Nisbold Institute in Copenhagen and is going to lecture about universal biology for the next two weeks. So thank you very much and welcome. Okay, so maybe I should. Yeah, okay. So good morning. Yeah, and so I talk about this universal biology. Maybe almost nobody has heard what is universal biology. Yeah, so but I talk maybe if that kind of field is possible or not within these two weeks, I try to show that, okay, maybe there is some kind of universal law in the sense of physics even for biological systems. So that's my plan. And so, okay, so the basic plan is that so for the first two lectures, I give some kind of introductory parts and some example that there is some kind of universal statistical laws in biology. So that's, okay, the plan for the first two talks. And then, and I think there is a tutorial on by Tuan Pham on Tuesday and Thursday. Probably. Yeah, I guess, yeah. So that's, so in this study, I use some kind of dynamical systems approach and stochastic process approach that is related to statistical physics you've heard already last two weeks. And so maybe some kind of a computer program example, he'll show some kind of tutorial on Tuesday and Thursday. And then so I talk about some kind of examples of such universal biology approach to replication of cells and adaptation or evolution or development. And this order of this evolution or development maybe swapped, it depends on the other seminars. Yeah, and so there are related seminars and the Friday, so actually due to the time difference between Japan and here, so I give the course in the afternoon and instead, so in the morning, Professor Wakamoto at the University of Tokyo gives a very nice presentation on the experiment on the single cell bacteria, how they adapt to new environment and to antibiotics. So that's a very fantastic experimental results. So he'll show that. And then on the next week, so there is a seminar by retorts from Barcelona. And so he'll talk about some kind of evolution-related problem from statistical physics. And so that's a theoretical approach. And then there is another seminar and this is from Japan online and that's Chikara Furusawa, who is both in the University of Tokyo and Riken. And actually he has been a long-term collaborator of mine and he used to be my student, but he is now doing a very fantastic experiment on evolution of bacteria to many different antibiotics and how they are related. And so actually this is related to the theory I present next week. And this is related to maybe you have heard fluctuation, dispassion theorem last week. And so that is kind of application or extension of this idea to evolution. So that I'll talk about next week. Okay, so brief introduction of myself is that so I've been a professor at the University of Tokyo for a long time but then I have to retire with the age rule. And so from last year I moved to Niels Bohr Institute so I'm closer to your place. But actually I do not like a dark cold weather there so in winter time I returned to Japan and so I just came back from Japan. So still a little bit jet lagged. Okay, so the research history of myself, so maybe that's not so important, but anyway I started working on non-linear non-equilibrium statistical physics problem so based on stochastic process. And then I worked on chaos and chaos, especially chaos with many degrees of freedom, pattern, formation and so in that system I worked on for instance coupled map problem and in the coupled map problem there are many many chaotic elements. Simple chaotic dynamics, very simple dynamical systems and then coupled with each other and then it gives some kind of collective dynamics. And so it's some kind of microscopic chaos versus macroscopic chaos and then how this kind of interrelationship introduce some kind of interesting collective dynamics. So that I worked on this and in some sense that is a base of my approach to biology because in biology as I talk today or next day is that there are many many elements so many many molecules and consist of a cell. So there is microscopic and macroscopic relationship and then how this relationship introduce some kind of important biological phenomena. So that's what I called complex systems biology or universal biology. And so as for complex system biology I wrote this book and this is somewhat related to what I talk today but this is a little bit kind of old one. So in Japanese I wrote another book that is this one is universal biology in Japanese. So I hope to give the contents of this through this talk. Okay, so the universal biology so actually this is not the invention of myself this was invented actually surprisingly. More than 50 years ago by this Japanese science fiction writer Sakeo Komatsu who wrote a very interesting science fiction. And so in his one of his novels there is a professor working on universal biology and so that's a very great professor and so that's my kind of hero when I was a high school student and so but it took so long I started to work on universal biology but finally we could start. So the idea is that basically life system has some kind of universal class in nature and so we can have some kind of common phenomenological theory of general laws therein and so in that sense maybe we can understand life system not necessarily restricted to those that happen to be evolved on this earth so maybe in future we may find some life system in some other planet or some other places in the universe so in Canada or some other place and or some people are now making trying to make a kind of protocell so from the laboratory and this is being done for maybe 50 years or something like that and it's progressed and so I had some collaborator working in this experiment and when we did some collaboration maybe 30 years ago or 20 years ago that looked quite difficult but now they're coming close to make a kind of so artificial reproducing cell in the laboratory then when we want to make that okay we can discuss if some general law is applied to such system and the present system also so that's kind of ambition or a dream for long term ambition for the universal biology and okay so actually according to his Novel so universal biology is science to explore universal patterns and possible variations of living organisms in this cosmos and it started to expand at the end of last century and actually this science fiction is so he wrote 50 years ago but this is the topic it's already 21st century so that means 20th century and since then characterization of life term in terms of topological geometry and maybe that corresponds to dynamical systems has developed and now grand theory comparable to relativity is anticipated so and now is now I think so we need to do some kind of thing to realize his novel so that's our plan and actually so inspired by his novel so in University of Tokyo so we set up universal biology institute and there is also universal biology group at Illinois I'm not sure that's maybe that's mostly organized by Nigel Goldenfeld but he moved to California so I'm not sure how it is going on but anyway so there is some approach for that okay so the grand challenge of this universal biology is that in this cell so there are many many components so you have so at least when we discuss about life maybe we can think of cell and cell there are many many so many molecules and actually not only the number of molecules is large so that is common in statistical physics but there are many many too many species so molecule species so for example in even for bacteria so about maybe 5,000 different protein species and similar messenger RNA or some other RNA species and there are many other metabolites and so there are so many chemical species and so people try to make a so reduce this number but still they are not so successful so mostly the important thing is this kind of very diverse diverse molecule species or diverse maybe components so that is maybe most universal property in the life system so still this can be somehow stable and sometimes reproduce so that's amazing in some sense because so many species here and then when this cell grows and divides into two it's not completely the same of course this contents but roughly same so that's quite amazing for in the sense of physics it's so many different species and maybe some of them are not so many so as a number it's not so many but still they can keep some kind of stability so the challenge for us is can we understand it such kind of complex diverse system so that looks too challenging but consider thermodynamics so in thermodynamics we know there are many huge number of molecules here in this room for instance but we have some theory and actually very strong universal theory we have so in that case so we can set up such theory by restricting to equilibrium states or transition between them and so microscopically there are huge number of molecules but by restricting that macroscopically we can have a theory so governed by just a few degrees of freedom that's thermodynamics so in that sense so stability of the equilibrium system is quite important so let us first recall the thermodynamics maybe you have already known quite well but maybe maybe we have such success in the history of physics so when we try to make a kind of universal biology maybe we have to learn such success so we recall how it was successful and so first as I said so we restrict to equilibrium state and maybe transition among them the important thing is that if we just consider any condition of these molecules and with any different conditions it's almost impossible to describe this system just few degrees of freedom so for example here this is very hot here it's not so hot you may need a huge number of temperatures for instance but assuming that equilibrium we can just have few degrees of freedom or maybe temperature pressure or something like that and the important thing is that this equilibrium system is stable so this is stability and stability and irreversibility is maybe the two sides of coins because if the system equilibrium system is stable so if you part up this from this somewhere it comes back here so part up here it comes back here so always there is a direction towards it so that is some kind of irreversibility so assuming that kind of stability of equilibrium system we need some kind of irreversibility so maybe that's how we so from that we introduce so if you have irreversibility then it's going here, going here and then we can make some kind of ordering and then by this ordering we can introduce entropy and actually there is some kind of such axiomatic theory for thermodynamics by Leib and Engafso also so anyway stability and irreversibility is one of the important issues and then of course in thermodynamics we have thermo so that is corresponding to energy and energy but energy and free energy is different so the energy itself is conserved but free energy that can be used is somehow different from that and we have this kind of relationship and so that's the basis of this thermodynamics and related to that so we have some kind of equation of states in so forth that's ideal gas or something and another important point related to also stability and irreversibility is that some kind of fluctuation-response relationship and Le Chatelier principle Le Chatelier principle is that when you perturb the system so then the system tries to react to reduce the applied change and actually so it's again the statement by stability and we will see that something similar will exist in biology because biological system is also stable so and fluctuation-response maybe you already had is that this kind of fluctuation in a biological system or in the thermodynamic system is related to when you apply this external response and external field and response and so these are kind of basic issues in thermodynamics and also in establishing thermodynamics the use of ideal model such as Carnot cycle or ideal gas is quite important and actually of course we know that thermodynamics is not restricted to ideal gas but to establish that by using that is quite useful so these are lessons from thermodynamics when we try to make a kind of universal biology so in the universal biology so inspired by this success by thermodynamics is that okay maybe we consider kind of restriction to kind of steady state or stable state or steady growth state so of course bacteria when you put bacteria into a very bad condition this internal state will change dynamically so during this dynamics occur many interesting but complex phenomena occur but first of all we just forget about that and consider focus on that kind of steady state so after you put this bacteria into a bad condition it takes some time then it becomes stable and it starts to grow and divide and starts to grow and divide they produce basically similar bacteria so we focus on such kind of steady state so that means and actually biological system has quite robustness and that is also we I will discuss this kind of robustness in these lectures basically even if you perturb a little bit it can come back to this original state so that's similar to thermodynamics but of course this is not a equilibrium thermodynamic equilibrium but still it's robustness and then so we can have stability and irreversibility in a similar way as thermodynamics has established so actually that kind of picture is also discussed in famous biologists and actually in this lecture I sometimes discuss about this Waddington's landscape oh waddington somehow the spelling is different Waddington energy aspect and Waddington's landscape so in Waddington's landscape so he discussed cell differentiation so in this multi-cell organism so we have initial cell type and then after cell differentiation development cell differentiates into many different types and so he introduced this kind of landscape so initial cell type and then different cell types but each cell type is sits in the bottom of the valley so that means even if you part of it it comes back so it's a kind of representation of robustness or stability so maybe you can see that this structure of this landscape is somewhat quite related to free energy landscape so in thermodynamic system you have free energy and this is equilibrium so of course this is not free energy his landscape is not free energy but there is some kind of similar concept here so we try to understand that and so maybe for free energy so actually I said that free energy and energy is different but here also in a cell they take for the growth they take nutrients and growth so if there is some kind of conservation all the nutrients imported here can be used for the next generation and nothing is lost but actually that is not true even for the cells in some condition these cells cannot grow still they need some kind of nutrients and consume that so there is some kind of minimal energy to sustain itself so that is some kind of growth so the rate growth rate is nutrient flow minus loss so that is a little bit similar to free energy energy relationship and so okay equation of states so maybe I'll skip that but I'll talk later and as for the Châtelier principle so this is consequence of stability and so evoked first change is compensated by internal response and that is similar to adaptation biological adaptation and evolution we will see and so fluctuation response relationship is that okay I'll talk maybe later yeah this next week yeah okay and also in this universal biology maybe we still lack the so very good ideal model so similar to ideal gas so we want to consider kind of ideal cell model so of course in the real sense it's very very complex and complicated but somehow minimal minimally simplified ideal cell model so I try to introduce some kind of cell model simplified maybe one of the candidates for ideal cell model but maybe that is not the final ideal cell model so maybe you can think of your better ideal cell model so that's yeah after hearing this talk maybe you can consider okay this will be better ideal cell model and that is yeah so our plan okay so that's our hope but of course there is some difficulty and because one of the things that I said that there are many many kinds of molecules many different types of molecules and in the statistical physics mostly they are concerned that's few number of molecular species and instead number is large so statistical physics number this is large so that is thermodynamic limit but here this is how many different types exist that is much more so this is large so this is a kind of new challenge to us and also in statistical physics so microscopic phenomena fluctuation of each molecular dynamics and macroscopic dynamics the time scales are quite well separated and so that's how we can we do not need to discuss so much on each molecules motion when we discuss thermodynamics and so in the biology case if that kind of separation can be applied or not so that's also a challenge but still we can see some kind of consistency between microscopic and macroscopic level and also maybe another difficulty may exist in somehow maybe inherently cellular processes are dynamic so oscillation and that kind of thing exists but maybe that is not so big problem as we see okay so basically what I want to discuss this kind of this problem yeah I already said that and maybe I show that few examples that how biological system is complex and this is a kind of famous picture of this metabolic network of bacteria and actually here at each point here you cannot see but this is some kind of molecule each shows that how this molecular and molecular reaction goes on to make some other so biochemists are so intelligent so they explore each of these and actually this is just only one eighth of the total bacteria and maybe this may not be enough maybe there is some other more exists here but anyway such complex such complicated so that's maybe you can see but still it's amazing that even though this kind of complexity but it's bacteria is bacteria so after division it can have basically same so same of these so in that sense it's a very strong robustness so that's one point and another point is that when we discuss of microscopic level and reaction actually we use a simple reaction dynamics but sometimes this may not be enough is that within this cell every molecules are very much crowded in a condition so like a rush hour in Japanese train so in that sense so it's a strongly interacting system so maybe if you are in quantum physics or condensed matter they are interesting strongly interacting system but this is a very very strongly interacting system each molecule so interact with all nearby molecules always and so such kind of strongly interacting diverse components and still robust so that's maybe you can see the impression of biological system so my standpoint for universal biology is as I already said a little bit is that even though you have very very diverse components and but this has some kind of microscopic macroscopic consistency and so focusing on this microscopic and macroscopic consistency maybe we can have some kind of universal properties or universal laws so that's our plan and yeah so and actually this approach can be applied to many different levels in biology and actually in biology there is always some kind of hierarchy and that is also an important point and why such kind of hierarchy exists or should exist that may be a topic in universal biology and I'm not sure I may not have time to discuss on that so much but anyway usually there is molecules and molecules replicate and with the proteins so it replicates with the aid of DNA and DNA replicates so there's mutually helping and interacting to replicate each other and then they form a cell and then cell reproduce so molecular replicates and cell reproduces and then maybe there is some kind of consistency between this cell reproduction and molecular replication and then as a higher level so multi-cell organism like us has many many different cell types so again many different cell types many different kinds but there is some kind of stability so we have this part of this has a kind of some skin cell or muscle cells or these different cell types exist in a certain fraction and in a certain pattern so that has some kind of multi-cell stability and then at a higher level so there is a ecosystem so like is working on but yeah so that's also a problem of this kind of approach but for this I cannot go on to the ecosystem so much yeah ok so maybe I can say ok this already I said this and so this I already said ok and ok another issue is that this kind of microscopic macroscopic maybe you think of mostly spatial scale so molecule and cell and cell multi-cell organism so that is concerns on the spatial scale but in biology also many different time scales exist and so in within each so consider cell within each generation to produce this there are several reactions going on this reaction is very very fast time scale and then according to that molecules replicate or if you put this cell into a different condition this some kind of adaptation change to change this concentration of these molecules so that's a very fast response and then maybe adaptation to new condition so that takes some time and then as a higher level scale longer time scale there is memory when you put cells into some condition this external so experience to external conditions are memorized to cells sometimes a few generations or so even after division this state is memorized so there is some kind of memory and then for longer time scale there is evolution that occurs much longer time scale because genetic change here to govern the evolution is occurs in a very low rate so that takes more time so for the evolution so again in this case how these different time scale phenomena interfere each other and make a kind of consistent structure so that's a question in this universal biology and actually in the evolution we discuss that consistency with this faster time scale and evolution time scale somehow surprisingly related so that's maybe the topic of next week and this is also the good experimental result by Chikara Furusawa okay so okay I'm not sure maybe so from now I just want to say so I'm not sure how many know about dynamical systems they already know most of them know okay then I can skip that dynamical systems so basically just a few words and actually Tuan will give a kind of somebody already talked about dynamical systems or not in this but but maybe yeah maybe they know already okay so basically dynamical systems approach is that if you have many for instance many components and then the concentration of each molecule so maybe I explain in terms of this kind of problem in dynamical systems the equation of chemical species and chemical species 1, 2, 3, or 4 and if you have thousand chemical species so this is thousand dimensional dynamical systems so the state is the point in a thousand dimensional state space and then dynamical system is that this moves around according to the rule of this equation and then so we can discuss how this goes to some kind of so maybe attractor and final state and this can be yeah discussed in dynamical systems okay maybe then I can skip attractor and so this is a fixed point attractor and limit cycle attractor so as time goes on it reaches to this kind of states and then so maybe we can discuss how this kind of attractor is obtained so maybe so an example here is that okay maybe I'll skip this here today and maybe Tuan will give kind of this example but you also give kind of dynamical systems I don't think we would make the phone dynamical system tutorial but we will briefly mention to try example yeah so okay so maybe I for this moment I skip this and I may come back again okay then okay so then I go to the questions okay so yeah if you have questions so I may go to a little bit next but this is so so general so maybe you have any questions maybe so maybe maybe so so far this is so kind of imagination not something in the fantasy or something like that so I show at least one example that maybe this kind of approach may really possible okay so so this kind of consistency approach so okay so as I said that okay this if you have 5000 so for instance 5000 protein species you have 5000 dimensional system and then can we have some kind of general law from there so I discuss one simple example okay even though you have many many components here so basically if you have 5000 components or something like that so you have okay this kind of this 5000 dimensional but basically this cell grows and divides so within this process each molecule number so there are 5000 species so for instance so this changes with some rule of this reaction so there are some reaction dynamics so this change depending on all others probably and then so this is there is nothing here but then according to this growth maybe at least this grow and divide so basically within this process all molecules number have to be roughly doubled so actually they grow in the same rate so for example if you consider this kind of so this function of all this and in any dynamical systems this can be different by each molecule but if you have a kind of stable growth system that means this should be equal to all molecule components because if you have for instance mu1 is larger than others then as cell grows then this fraction of chemical one increases and then the fraction of chemical one increases and then maybe it cannot be sustained in the same but here I assume that this kind of steady growth cell so after division they have basically same composition so if this is larger then after division then one molecule fraction is increased so it's not steady so to have kind of stable growth this all mu i should be equal so that's a very strong constraint so because mu i is a generally a function of all other molecule components if you have many different molecules here some type of molecules then some reaction going on more and then mu1 or mu2 changes so this gives so mu1 mu chemical species is you have mu1 minus 1 condition so even though you have m or 5000 dimensional dynamical systems this restriction gives mu1 minus 1 so if you try to change this cell sustaining this kind of steady growth then there is so this is constrained into one dimensional manifold because even though m dimension but m minus 1 condition so this is just one so that means if you try to so change this cell in a slightly different condition and keep that so kind of steady condition then it should follow along one dimensional line so here if you do not change no stress here or no environmental condition it just stays there but what we did is that we apply a little bit stress and then after so when we apply a stress maybe internal state will change and during that we cannot discuss because we are restricting kind of steady growth state like we are discussing in equilibrium state so during that change we are not sure but after this change maybe we assume that this cell comes to a kind of stable growth state again and then in that case again this relationship should be satisfied so then maybe this one dimensional constraint and then slightly change external condition and then along this and along this so by that we have can consider this one dimensional constraint and then from that we show that there is some kind of general relationship and that can be confirmed experimentally so that's this so plan for 20 minutes or something like that okay so so in some sense maybe this is somewhat analogy to thermodynamics so when we put this equilibrium system in a different condition then maybe if you put this kind of this is very hot this is lower temperature then each position's temperature may change but after equilibrium it goes to sing temperature and then we discuss this equilibrium state so when we discuss this cell and put this cell into a different condition maybe then responding to this external condition maybe chemical one is more needed here and this abundance is increased then during that mu one increases and mu two decreases or something like that but after all it comes back to the state that this growth rate is same as long as this cell keeps kind of steady growth after in this condition I have a question so this picture seems to suggest that the only thing that matters to understand the system is the growth rate or mu but suppose that you have E. coli growing with the same growth rate in two different conditions then the composition will be different so here I assume that okay this will not bifurcate so it's always kind of there is single stable state so that's kind of restriction also yeah so there is some kind of yeah so in that sense we are not putting this very very strong stress so if we put a very very strong stress maybe we may hear some example by professor Akamoto that this cell may become a kind of different states but here we are assuming that okay the stress is not so strong to switch to a completely different state I have a sort of I mean even if the stress is not strong suppose that I apply two different type of stress right I don't know I change the temperature or I give antibiotics yeah so actually if you apply a different type of stress okay maybe for one type of stress this goes along this and for a different type of stress it goes a different line so it's yeah yeah okay so we try to write a simple equation for this okay so now instead of the number we consider the concentration of each chemical component so you have xi xi so basically you have yeah now you have chemical species here and each concentration of this is xi so i chemical component so just for instance just consider protein you have 5000 proteins and this concentration xi and then this concentration is so concentration is basically if you have volume of this cell and then each component here but the point here is that volume increases as the cell grows and volume grows and when it becomes twice it's basically yeah split into two so V increases and so as I said this increases so with this but also volume increases and if this all increases with the same rate then this volume also increases with this so basically cell volume growth rate is mu here so with this growth each molecule concentration is diluted if the cell becomes twice the volume becomes twice then the concentration becomes half if it's not increased so basically there is a term so by this volume growth it's diluted so this is dilution so if nothing occurs this is just this term but here there is some reaction and produce each chemical component and that gives any other so maybe it depends on any other molecule concentration in general so you have some equation here and this so this is the equation here and then we are considering the steady growth state steady growth state means that this is so after all this is basically constant so that means this cell so for this yeah and so that's the condition here and I can use the concentration itself but in many cases it's more convenient to use log concentration instead of concentration itself so in that case this is just a change of variable and then assume that this can be written so this is just a change from small f to large f it's just a change of variable and so that means this original equation changes to because dividing x so this is just what I just used this logarithmic x derivative so this question yeah I assume that everything is not 0 correct yes yeah so you are using deterministic equations so whereas what is happening there is large distochastic because there are reactions that is not discussed here and actually this may lead to some kind of problem of fluctuation and actually I may go into the fluctuation problem later just to forget about the is there a rational by which you can neglect fluctuation it's just an approximation for the moment it's just an approximation yeah and actually so maybe some molecules concentration are very minor and so this very few number then the fluctuation is much larger so that is an important question but here I just forget about fluctuation yeah and also another important assumption here is that okay this x is not 0 so sometimes molecule number may go to 0 but maybe most important chemicals we are concerned on this so important chemicals then probably we can assume that they are not 0 of course this is a assumption yeah sir I have a question how are we incorporating these stresses into the equations okay now okay it's okay now we import the stress condition here and so if you apply so this is the condition here and then there is some kind of external condition and external condition change of course by changing external condition this reaction process changing so if you put some stress some reaction is not going on if you put some heat then some reaction goes on much more and some are not so much and then this changes so this is a function external function of environment of stress and so if you write here there is some kind of environment so then also there accordingly the growth rate changes so this is also concerned and x is also finally it goes to change of this environment so the if you assume that okay environmental stress is represented by a scalar variable e then you can write down this equation this equation put e and then the steady condition is this something like this yes so why we are considering only linear dependence up to mu in the mu like can't we take higher order dependence this mu here yeah yeah but this is just dilution so if you increase the volume rate so every yeah component so if v increases just so v increases then accordingly the concentration decreases so it's a yeah x is yeah n divided by v so the increase of v so and in the derivative form yeah so if you increase this real then accordingly so then and if this is just so slow so derivative change so it's just so if you make this a larger and if nothing occurs then it's so the concentration is diluted and then so with the derivative yeah you can write down maybe you can check easily by this calculation yeah okay so so we have this equation so this is yeah kind of condition that I said for this kind of one dimensional constraint because this means that mu is a growth rate of the cell volume so so finally it goes to this steady state this should be satisfied here f1 f2 fm so it's a different reaction process is going on so it's a different function and different form but this mu this is independent of i so this should be equal to this equal so you have m minus 1 condition so that's one dimensional constraint so that's what I said okay from this I make another okay another kind of simple or it's some kind of traditionally physics approach is that linearization so starting from the original state you put some kind of environmental stress and assuming that this change external change by stress or external degree of stress is not so large then we can linearize the change everything and so that leads to okay from this equation and change e to delta e so after you make a change from e to e plus delta e and then this is also e plus delta e then linearize everything but delta e is not so large so then we can use okay so this is just a very simple jacobi matrix here so for each component and then plus maybe environmental stress change itself this function for myself and so slightly change so that's kind of this and then delta mu change accordingly and the point here is that this is computed at without the stress condition so this is computed without the stress condition because we linearize everything around here so put some kind of stress delta e is not so large and then linearize everything so of course originally maybe like that but linearize everything so then so I write down this equation here so here I use jacobi matrix j a i j here and so this is some kind of susceptibility so this depends on environmental type so heat and different type of yeah stress may change this so okay so you agree this equation of course this is linearize linearize I'm not sure if it's really good to linearize or not so that's also approximation and then so using that okay then basically if you use the inverse matrix of this jacobi matrix L then you can solve this so basically you have j delta x so and assuming L is then we can write down this kind of equation that delta x is and then okay delta mu again this linear regime so this should be proportional to some yeah environmental stress here so basically you have alpha and then delta e and so you get this equation here so this is just a linear algebra simple calculation so assuming that I assume linearization so this is just yeah then okay from this we can write down this equation here so this is just a linear algebra calculation then if you apply two strengths two types of strengths so what we want to do now is that you apply heat stress for a little bit and a little bit much more and then you can have a state different and then we compute here and delta x i and much more e plus or something like that then you can write down two equations here if you apply two strengths of this yeah equation and put e and e prime so that means delta x j we have these two equations this is just simply we write this e to e prime and divide these two so and these terms are cancelled here gamma i depends on the stress type because gamma i was so if you have a totally different strength type this may be different so this depends on stress type but for the same stress type and as long as this change is not so large we can have the same gamma i so this is measured at the state at e equals zero no stress state so basically this can be cancelled out so we get this equation so this is an interesting equation because this delta x j e delta x j e prime so this can be measured by so putting this cell into a different condition each component and the concentration changes and then we can measure each and growth rate can be measured by measuring this bacterial growth and the important thing is that mu is just the growth rate of a cell so it's independent of each molecule so the left side sign which includes j each molecule component but if you divide these two this value is independent of each molecule so that's theoretical consequence of course here we assume that kind of steady growth and everything molecule is not zero and linearization so this is a simplification so we can check experimentally if this is valid or not and actually there is an experiment so in this experiment so now in biology there are many many recent technological advances and so they can get many important quantities they are quantitatively so in this experiment what they did is that they measure so in this bacteria there are maybe 4,000 proteins and corresponding to each protein there are messenger RNA so they measured messenger RNA so different types, different chemical species of messenger RNA so you have maybe 4,000 messenger RNA so that corresponds to XI so they can measure this XI concentration by some kind of technological advances so what they did is that they measure the protein into some condition and they wait for some time that the cell can recover the steady growth and then they measure this concentration so in this case they measure not the single cell but average over many cells so in that sense of stochasticity is removed from all the cells so this is XI and then they measure this XI in a different environmental stress and then what this theory says ok instead of using XI maybe you use log X XI and then XI we measure and then XI we put some stress stress so for instance in this experiment so they put some increase the temperature a little bit and then a little bit and increase the temperature more so this degree of this temperature increase here and then they measure this and then what the theory says that we consider delta XI delta XI is just delta E minus XI original so we can measure this from this experiment and then the theory says that ok let's plot delta XI delta XI E and delta XE prime and plot this then it's independent of each component I so then what we need to check is that E1 delta XI E2 and we have for instance 4,000 messenger RNA species and then maybe for one messenger RNA this value, for another messenger RNA this value, for another messenger RNA this value, this value so the theory says that this log, this fraction is independent of each messenger RNA so it should follow this line and so let's check that experimentally and so this is the result so this is an example that you put this is some temperature increase and this is a much larger temperature increase and so each point corresponds to a different messenger RNA ok, looks like ok of course there are some kind of fluctuation but maybe this experimentally technical problem also exists and maybe there are some inherent fluctuation exists but still ok and they did this kind of osmotic pressure and there are a few messenger RNAs that are a little bit deviated but consider that there are 4,000 points here so most of these points follow the same line and this is starvation so decrease the nutrients and then ok, so this kind of simple theory seems to work at least to some degree so and also this slope so from this theory this slope should be, the theory says that and actually this is the line we put here so expected from this and actually these can be measured separately because this cell grows so one can count the number of cells and then how this number of cells so the number of cells increases basically if the cell grows and it's divided so the number increases accordingly so basically the number of cells with this great mu and this, so they experimentally they can measure how this cell number increases the growth rate so that that can be measured separately so it's a kind of, so the same experiment but in a different measurement condition measurement too but anyway they measure mu and from this we can measure how this growth rate decreases and actually this is this example of this growth rate this growth rate is originally here so maybe roughly in this case in a good condition bacteria divides by roughly by 20 minutes so 1 over 20 minutes is the growth rate and then in kind of this heat condition then this decreases and if you put more heat this decreases and if you put more heat this decreases and we actually measured comparing these three different conditions little stress, medium stress and high stress and plot all these conditions and measure this kind of thing so for instant for this osmotic pressure so three levels of osmotic pressure here and heat three levels of heat and three levels of starvation so you can see somehow osmotic pressure there are more deviations, we do not know why but there are little deviations some deviated chemicals but anyway it's not so large compared with the total 4000 just maybe 10 species or something and heat as you can see mostly along this line and starvation mostly along this line and this is the estimate so this slope from this growth rate so the theory is so simple but it works rather well in this experiment and there are ok maybe I need it's almost time so I finish soon ok there are ok maybe one may think ok this is maybe not may not be so much surprising because ok the bacteria anyway in a steady growth condition we try to make this so carefully and maybe one questionable thing is that we used linearization so linearization usually we know that ok small perturbation then we can make linearize everything but in the reaction process within this cell maybe highly non-linear many many reaction processes going on many many molecules commit with each other so this function generally should be rather non-linear and so linearization if it works or not we are not so sure and also interestingly in this experiment you can see this growth rate decreases in this condition and actually this is some strong stress condition according to that delta mu is delta mu mu after environmental stress is that almost 0.2 or 0.0 original so initially 20 so the bacteria can grow per 20 minutes but in some condition it grows only after maybe 2 hours or something like that so in that sense very strong stress and actually the experiment do not impose further stress actually they impose further stress but then the steady growth condition cannot be reached so well so they try to make many quite large stress as long as the steady growth condition is satisfied linearization seems to work rather well so you can consider some kind of yeah spring and then hook slow is valid before as long as it can be the spring shape form and if you try to make this spring is broken so the cell is something like that so as long as it can steadily grow it's almost linearization works so it's a linearization works so so that's one mystery so so far the theory cannot say anything why why linearization works so well and okay another point okay another point okay maybe I that's we solve this next week is that another point we are concerning here surprising point okay surprising point is that okay we can consider a different type of stress so heat versus osmotic pressure or starvation versus heat or something like that and the theory cannot say anything because when we derive that equation we assume that gamma i is identical for different type of stress different strength of stresses because it's when we divide into this for different stress condition so we need to cancel out but for a different stress condition one condition go in here and another condition may go to a different direction then we cannot these two terms cannot cancel then we cannot derive that linear relationship and actually of course in the experiment still we have experimental data we can just plot this and then the result is something like that okay this is much worse compared with this comparison between the same strength but still considering that there are 4,000 points so many different so in this case of starvation versus osmotic pressure heat versus starvation this roughly follows the linear relationship of course this deviation is larger but still there is some kind of common trend so that's another mystery so linearization why it so works then across different environmental conditions still somewhat okay these cannot be answered with this simple theory and what is missing here is that bacteria is not just a kind of steady growth system it's a result of evolution and then considering evolution we may derive this kind of thing on the topic of maybe next week okay so maybe okay it's about 30 minutes so okay so yeah thank you Questions? Thanks I was wondering can deviation from the low in gene expressions can consider that signals that the specific gene is important for the correct and steady reproducibility of the organism because maybe the tighter like the more important is the gene the tighter has to follow that expression you cannot be wrong that much with respect to the total yeah so probably these so mutually linear relationship region is that so they keep the state in a good condition and as long as it keeps in this kind of stable state so this kind of mutual relationship should satisfy should be satisfied and then but still some molecules specifically respond to some kind of specific external condition and that may not be so cancelled out by others so such kind of specific molecules exist probably and so actually similar thing is so okay this kind of yeah probably in a different so environmental condition maybe some are deviated here so maybe this is specific to osmotic pressure or something like that but others there are 4,000 points here so others are mutually consistent with each other to have a kind of stable state so that's a very high dimensional but it's restricted to this kind of and actually recently yeah Yuichi Wakamoto measured some kind of many many new techniques and many changes and he found this kind of behavior and we are calling this homeostatic core so many molecules so they are mutually consistent so among 4,000 maybe 3800 molecules are homeostatic core and maybe some others are kind of specific yeah but that's quite important question yeah other questions when you say that setting all mules to be the same corresponding to the system being in steady growth could you expand that a bit more like why is it like why is setting mules the same is the steady growth okay so in the experiment so one can see that if mu is changing so this cellar state after division may change yeah so if maybe one can check that okay this kind of concentration of this Xi does not change so much after making divisions so if you put this cell into bad condition initially this change and then after so repeating this cell division process and then maybe after one day or something yeah that comes to kind of steady condition so only after that we know that and how long it takes we are not sure at this theory yeah after a long time and how long it is is a kind of difficult question so in this experiment they did this condition okay up to this kind of stress and if you put much stronger heat then the cell state changes and maybe if you wait much longer time it may go to a steady state but then the question is that if you wait many many time then cells may evolve so that the problem of time scales initially I said that this different time scales exist and here I consider the time scale that's only within the adaptation so during which cells do not evolve so they do not change the mutation if that occurs then maybe we revise this theory totally so far this is not included but here I assume within this time scale for adaptation this is yeah so experimentally it's quite difficult to choose such kind of condition so actually I'm not doing any experiment but this group Yomo's group they did a very yeah nice yeah techniques yeah I have one question so the equation you showed delta mu equals to that Jacobian time something that equation so can it be related to other kind other equations in some statistical system like I want to physically understand that equation is that equation derivable in some other processes so you mean this equation of this kind of yeah so you mean to get some from statistical physics or something yes okay so for instance it's not so easy to get from for instance in equilibrium statistical so yeah I think it's not so this is purely dynamical systems type approach and of course this reaction rate is determined by from some kind of term dynamics so from that so maybe you can use some kind of statistical physics and but this law is in a kind of different level from a usual yeah term dynamics statistical equilibrium state and for instance this reaction rate and this reaction process is not necessarily given by thermal equilibrium equilibrium yeah so but the point is that independent of the details of this reaction rate or something we can derive this kind of thing so it's a kind of different universality from the usual different universality of the statistical physics or for thermodynamic equilibrium okay there are no other questions we can take the break thank you yeah it is I don't know if I will have time because I also have lectures oh okay yeah the paper with the signatures so you are giving a lecture no no no I'm lecturing in the university in the university