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Even though virtually for the last talk of the day, Professor Kaneko now at Niels Bohr Institute in Copenhagen. And his talk will be about the theory for development, self-differentiation, and reprogramming. So please, Kuni, thank you. Okay. Thank you. So I'll try to speak louder. Yeah. And so today I talk about this dynamical systems theory for self-differentiation and reprogramming. And I'm now in Niels Bohr Institute at Universal Biology Group. And I just explain a little bit on universal biology just in a minute. And so usually life system consists of many, many components. For example, in a cell, there are many, many, many molecules that interact with each other. But as a cell total, it becomes a kind of stable structure. So the guiding principle here is macromicroconsistence. So molecule cell, so molecule producing cell. That cell gives some kind of constraint to each molecular reaction. So microscopic, very diverse components and high-dimensional. And macroscopic, so there is some kind of unit to sustain and reproduce as a whole. So probably in some cases there can be a whole-dimensional description. So that's the approach to universal biology I'm taking. And by that, so for example, molecule cell and with this consistency between molecule and cell reproduction, so we can have some kind of general law or some kind of general properties. And so cell to multi-cellar. And in the case of evolution, so genetic change is very slow. And phenotype dynamics or development is much faster within a generation. But still there is some kind of consistency with so different time scales. And actually I'm mostly working on this kind of evolution these days, but today, so I talk about this level, cell to multi-cellar organism. And for that, so important phenomena there is cell differentiation. So initially there is some cell type, so stem cell. So it's called pluripotent cell. So that can produce diverse types of cells through the developmental course. So initially this cell type. And then after some time, there are several cell types appeared. So they have the same genes, but still they have a different cell types. And actually in 1957, the famous biologist Waddington wrote a book, The Strategy of Genes, and he introduced them, very famous picture, Epigenetic Landscape Picture. So that's a kind of general this body, shallow body, and then branching to several small, higher bodies. And also he proposed to discuss this in terms of dynamical system. And also he tried to understand how this complex system is controlled by genes. So, but at that time, it was difficult to make a theory advance. And after that, so maybe there are many studies on dynamical systems. And in this picture, each body, so attracted is expression, gene expression or protein concentration is attracted to a certain level, and that is called, so this attractor in terms of dynamical systems. And so there are several studies for this, so many attractor systems. But another important thing in Waddington's picture is that this body changes in type, so the landscape changes in type. And actually Waddington coined the term Homo-Resis rather than Homo-Stasis. And this is robustness in past or developmental process itself or landscape itself. So, but what this landscape really means? So these days, many biologists draw this diagram, but actually what that means is not fully understood. And probably X axis, this axis is some kind of collective expression variable of many genes, protein concentrations, maybe low dimensional distribution for that. And this height, maybe it's a kind of changeability. If it goes down, it cannot change so much. It's a more robust or less plastic. So, or you can say that this is if you have some kind of probability for this X, then log 1 over Px, maybe that, so this potential. But the question is why this axis? And this means that there is dynamics, past dynamics in X, but there is slow change of this dynamic system. So there are two possibilities, I think. So this slow change is due to the developmental process and due to this number of cells in this development. And actually we worked on this kind of picture. So initially single cell and as a cell number increases, these cells interact and this cell interaction changes the dynamics in cells. And by that, we have seen that initially fully potent state and then some attractor state appears. So that's discussed here. But something strange happens. Yeah, okay. But another possibility and that is discussed these days is that there is a process called epigenetic change and that's the change in chromatin structure or how this gene expression is feasible. And that changes slowly. This is another possibility. And so we try to discuss this point. So basically with this epigenetic modification there are some histone modification, maturation, and etc. And that changes feasibility that the gene is expressed. So openness, chromatin, or something. And so maybe by post-claiming this process we assume that there is no variable representing the feasibility of expression itself. And this changes with this. So that's another possibility. And we try to focus on this. And by focusing on that the basic question we want to address is that, okay, of course there is landscape, so robustness of each valley to perturbation. So that first requires it. And then, so multi-level robustness. That means when you have a development this number of cells in each valley is robust to perturbation or initial condition or something. And then homeoresis how this branching process is stable. And also there is some kind of hierarchical branching process. So initial stem cell and there are two levels and three levels and higher levels. So that is necessary to understand development. Okay. So we consider a simple model. So as for gene expression dynamics there are many studies using some kind of gene regulation network. So that's basically simplified some kind of activation energy efficient. So something like some threshold dynamics of these hyperbolic tangents and Jij gives that network structure. If it's positive, so this expression of this gene activates this other gene. Okay, the red one. And if it's negative, if this gene is expressed and this protein is produced this suppresses the expression of this. So this model or kind of variant of this model have been extensively studied. And in this case theta i is the threshold for this expression. So actually minus threshold theta i. So with this change it's more easy to express or harder to be expressed. So usually this is assumed to be constant. But considering this epigenetic modification we assume that theta i is also a variant and it can change slowly. And furthermore it is known that if one gene is expressed sometimes it's more easily to be expressed so the threshold decreases. So we assume that there is some kind of positive feedback process between theta so x to theta. So something like this equation very simple equation. So that means if expressed easier to be expressed if replaced harder to be expressed. Okay, and this v is the rate of epigenetic or speed of this theta change. Then we consider simply a fixed point analysis. So first. So this is zero and this is zero. So that means a x equals theta and then if you put this and if a is large so feedback is strong then all xi plus minus one close to plus minus one. So plus one is expressed minus one is no expressed. Fixed point address. But the question here initially this efficient modification is set to zero in the stem cell. And then through this feedback process theta changes then what attractors are accessible. So that's the question. And if v is very large so this is very fast and so any a this a x theta is reached then all two to the end states are reachable. So x equals each xi is plus or minus one. So every possible bit patterns are reachable. But actually what we are concerned here is that efficient process is slow. So we need to consider v small limit. So the question is that what happens there? Okay, initially assume that this theta equals zero state dynamics as just a few fixed point attractors. And then with this fixed point attractors so this process is with this positive feedback this is stabilized. So basically if you have two fixed points and then each theta for this to stabilize this with this process. So you can produce so many of few attractors. But in this case so if you start from initial condition here then initial condition here then it can just go here it can just go here. So for each spacing of attraction only one type of fixed point attractors is generated and then so the number of ratio of each fixed point is not stable depending on initial conditions and no robustness in time course, no hierarchical splitting in time. So we cannot support but in terms of then we consider the case that initially this dynamical system with theta zero is a limit cycle and in this case first limit cycle attractors are converged and then cover the space space and then some fixed points attractors are generated and stable. And we'll show that this case the requisite of Waddington's landscape is satisfied. So first we consider the minimal case just two genes and so there are cases that in this plus and minus and in this case so nucleicline and space space is X1 and X2 is something like that for theta equals zero. And so it shows this kind of limit cycle here and we have nucleicline to nucleicline and there is some kind of limit cycle attractor here but this is for fixed theta and if x changes here then theta changes and if x goes here theta changes and with this actually we found that finally two fixed points attractors here and here are generated and actually slight change of initial condition can produce this and this so independent of initial conditions we can have this with mostly half and half in this case so this can be understood in dynamical systems as follows so theta goes to one side so in this equation basically gives the nucleicline so with the theta change so nucleicline goes to one side so with this so theta changes this nucleicline goes up and goes up or in this case so this nucleicline goes to the left and goes this up and it goes here so depending on initial state nucleicline motion changes and finally it produces this fixed point this fixed point or this fixed point so that's how these two stable states are generated and actually this is just a simple limit cycle case but if you have some kind of a little bit more complex limit cycle case then so initially okay this limit cycle and limit cycle is separated to double limit cycles and then it's fixed so in this case so three fixed points are generated so basically from this global limit cycle so separation to two sublimit cycle occurs first and then three so we have hierarchical splitting so and okay and then in this case so with this hierarchical attractor generation from limit cycle so this satisfies homoeresis and this given time span is splitting occurs and also even for depending on so changing initial condition so if you take some initial condition initial distribution of cells and then finally these in this case so four, five, six, seven attractors in this PCA plot so actually in this case any cost engines and we plot the PCA of this Xi to extend and then so basically you have these eight attractors eight cell types and then this is tense so that means these all have higher cell population and these three are less so this is independent of in-shell cell distribution disappears but in the case of fixed point as I mentioned such kind of robustness in the distribution does not appear so basically the distribution is independent of in-shell condition we have taking initial different in-shell condition but this distribution is same so orange and blue are same okay so from that by taking the PCA of gene expression dynamics of X and distribution of PX and taking log PX we can draw the Waddington landscape something like this and so in this case again so we can have a stable Waddington landscape starting from oscillatory behavior so that's a theoretical consequence okay now another problem here that is the reprogram so this is a kind of very deep question in statistical physics also because usually these cell types are fixed and initially this pretty potent cell can produce many other cell types but this can produce only this type and this can produce only this type so there is irreversible direction of development so changeability of pretty potency is large and here it's zero it's fixed so in the normal development process it's always irreversible but these days so by Takashi and Yamanaka they found that induced pretty potent stem cells so they found a way to reverse the reversible process and actually it's not so difficult they over express few genes so XI is changed for a while and then somehow return to the original state there are basic questions here so how? so actually in his case they over express just four genes so without operation of epigenetic modification so only just control of these few genes, few variables of many many dynamical systems many x genes so variables produce to come back to the original state and Tadama this original state is not so stable because this can differentiate so somehow so they can go to some kind of unstable or maybe sudden state in dynamical systems so so these are basic questions we need to address and actually the previous process of this oscillation in G expression and slow epigenetic process can solve this and so basically the same model so what we did is applied some input for a while so just for few genes so previous this and so put some input for some time and then see what happens taking the differentiated state so this final fixed point state and put this value for a while and then what happens so this is an example so this is an example in the case of n equals 10 so initially before reprogramming so we have some kind of state and finally it goes to some fixed point states so this is a differentiated state and then taking this differentiated state and in this case we over express just three genes among 10 genes for a while and then it starts to come back to this oscillation and then so we already stopped this over expression then it comes back to the original state and then the differentiation occurs later so we could just add few over expression this can solve so in the state space of a space picture so initially this kind of pluripotent red state and then in the normal development it goes to this or this or this or this so in this case so five fixed point states are generally and what we did is that take for example this fixed point and over this profile and this changes the state for a while to here and then cut off this over expression and somehow it comes back to this original pluripotent state and then again differentiation start so it worked but it's a little bit strange how unstable state is reached so we consider a simplest example so there is some kind of limit cycle generation case in the gene expression that is called and that is negative so expression so control and so this is just a standard and that shows this limit cycle oscillation of this each x and then of course we put this here and then what we did is that so we start from this initial oscillation and put this data dynamics and then so it goes to either of these fixed points so initial oscillation to either of these fixed points so in this case so theta so one two is positive three is negative and then we did this kind of so reprogramming process so put some kind of input to x1 or x2 or something and then it comes back to this oscillation and then this over expression is as long as cut then it comes back to this oscillatory state and differentiation occurs so it works and then so we can see how these dynamics changes so in this case so just three variables in x three variables in theta and if we look at theta dynamics so this theta dynamics goes something like that so initially theta is so that is somewhere here so this is a kind of subtle form so through the dynamics of x there is some kind of so this theta is a subtle so it's attractive to several directions but unstable towards another direction and that is the direction that this kind of landscape changes occurs so this this direction of this theta changes something like that so in that sense this is subtle so it can be attractive but it goes out but usually we know it goes so it puts this back to near to the subtle it's not so easy we need to put the state exactly to this stable manifold so the question is that just putting some input to x for a while can we come back to this state and actually in this case so if we eliminate this first variable and consider theta and depends theta is subtle and so this is stable direction in this case and unstable direction and this is something like that and then in this case so we show that with this of this first oscillation this so instability along this unstable manifold is suppressed due to this so up and down, up and down this oscillation so instability is somehow so averaged out and usually so this instability goes through this and this d theta u along this direction should be something like that but it's according to this it's suppressed and so with this we can see that with this slow epigenetic process and first oscillation dynamics shows generic mechanism for dynamic systems to stay or approach to the near this subtle point so by that we can so have this kind of reprogram and so this is quite general and actually we checked a more realistic model so there are some so several nano and some names of these genes and this seems to be corresponding to some kind of themselves and so by doing that we have shown that this kind of process again occurs so starting from this oscillatory dynamics and differentiation and reprogram and maybe the last goal is the previous study of cell-cell interaction and this epigenetic process so we combined this and actually we did this some time ago and actually this is a paper by this and so in this case so with this realistic 4G model class cell-cell interaction and again this differentiation occurs and then so by putting some process this so cell-cell interaction is fixed and then epigenetically fixed and then so by overexpress it can come back to the original state so we can explain this okay so today I talked about this homeoretic epigenetic landscape and so we show that from starting from oscillatory limit cycle state with this epigenetic process there is some kind of hierarchical attractor generation and that is robust and in this case reprogramming is generic just by control fusing and this occurs through first oscillatory expression dynamics and slow efficient change and this mark is mostly done by this previous student Yuki Matsushita and also Tetsuhiro Masaki Takayama okay so I could not talk other topics in universal biology but I give lectures in ICTP next March so if you are interested please come to this school and also some students are called okay thank you very much thank you very much for the very interesting talk now we are looking for questions from the audience anyone wants to ask a question okay it seems that we don't have any questions from the audience if this is the case let's thank Kuni again see you in ICTP next spring bye bye okay with this we close our afternoon session and now there is poster time so those of you who have posters please stand by your posters and be prepared thank you bye bye