 Window they have Well, and you see in the title I'm not Very good by submarine and stuff So I will try to to go as fast as possible And I believe the best dynamic is that I Will try to make that but you interrupt me every time that I just go too fast or This is spoken something that somebody didn't understand The general layout of the talk is is this one We are doing inference over metabolic networks. I believe explicitly Nobody have taught about constraint based modeling like the the canonical kind of Of the of the model that I'm being developed the last two decades or so with The larger of our ability of the nervous the second is just a description of of the environmental condition We are interesting in that is the Newton limitation Condition we will define what we mean by that because all these concepts are more or less Very flexible then we will trying to May concrete these these restrictions that we are first encounter Microscopic level experimental level by defining Microscopic kind of of definition of what we mean in the terms of Constraint based analysis by Newton limitation that is using the shalom primes concept that is very easy actually then we will Formally made the questions we are attempting to answer which a spoiler spoiler alert The research is beginning. So we have few good news But we are have an important water ball and neck that I believe Everybody can help me at the end Then we will see where the issues are and trying to implement in these with some example then we we will Talk about some solutions we are thinking about and then the Exploration results is very abstract. Sorry. I will I will Concrete now. Okay. You know it's a metabolic network. I don't know if those are the letters they meant with With the short version of that It is just a list of the reactions that we model that are supposed to be involved in the metabolic process hopefully The metabolism had a finger a fingerprint in the genome because Any meaningful reaction have a catalyst associated with that with it. That is a protein So we have the sequence in the genome so we can more or less Automatize the derivation of new Networks I believe it is very different from somebody. I don't know starting the reactions inside a volcano Where there is no? Genetics there they need to go there and to measure the reaction to in order to talk at this level and we see a paper very recent sorry for my Citation style those are my Sotero This is a part some team just release this paper with a bunch of a large number of reaction from the Microbiots in the gods which may give a sense of the scale of their ability today of this kind of Models and so they are supposed to be pretty complete in the sense that they will try to reproduce the full set of Ensign that are registered in the Okay, they mathematically can be formalized just writing the stoichiometric that describes the reactions Where the columns are the reaction and the rows are the metabolized at the end for modeling purposes Not all the reactions that you include in the stoichiometric are in somatic reactions You do for instance the same biomass Modeling is involved. There is not an encematic per se or also a lot of transformation in this kind of system our State vector variable vector will be all the fluxes are In ball in the in the in the metabolites at a moment And then we can we can write down a first Constraint, this is like them just a much multiplication between the second matrix and and the and the vector of variables That is just saying that any change in the concentration of a metabolite I for instance It is due to The combination of the reaction that are producing this metal lie and the and the reaction that I consume this metal It's very simple. It is very similar what we saw in ecology in the tutorial yesterday that defined because all their construction are linear and Unbounded space so it is useful or indispensable to Bound the the the reactions set in these two limits L and U I'm just saying that we expect the fluxes to be between these ranges Finally what this does is to to to produce a space solution in enemy, I don't know in any realistic Example the space is degenerated, which means we have more variables than constraints So the best we can do it is to to restrict life to be in sign somewhere inside this space I am a biologist for formation from it. That was actually a Surprise that we can at least bound life so formally and at the end Mathematically speaking it is a convex point or which really helps to do a lot of the analysis we can do in this space, okay? There we see one of the classical example. This is also a person paper We see a project a projection of this sample in solution a space into three dimensions It is highly dimensional space, but for most cases There it is for a belief is for a collie and we see to exchange reaction in the Horizontal axis So the carbon source and oxygen and then we see in the in the in the sea taxes I don't know the biomass and we can we can see that they are trying to to draw This is this wall that is defined the space and then we see these dots are our experimental data And we see that biomass maximization actually works on time because you see that They are in the edge of that for the top and the end these models are extremely useful and usually are very good to starting point for modeling metabolism because they have Consistent interface where you can put new data into Into both of those type of contraint you can put for instance Usually the model are already shipped with some thermodynamic data for instance like we more or less know that a given reaction is Irreversible in a given direction and that you can simulate it, but I'm not You can simulate an irreversible just for for illustration Reversible reaction by setting one of these two bounds to zero and the other to be an infinite value that In numerical terms is just a very large number and this way we can have this thermodynamic data introducing in the system The second kind of information is it's a less We'll say less objective in some sense that we can put into the model. It is Establishing or defining an operation over this space. This is the case of FPA with the maximization of the entropy this objective function such of the biomass these Objective function you can see it as a parametric pulse actually that is one of the disaventures of these kinds of methods that Sometimes it's very hard to to establish which is a good objective function. I don't know the time Okay, so this is the branch of how to model metabolism. I don't know if somebody have any question about what say Okay, so pause does branch have a Parallel one that will start now is another threat that is the the kind of experimental condition We are interesting. Okay. I will put an example in a chemostat is not necessarily restricted to chemostat, but I like more We are talking about nutrient limitation what what I mean by that sometimes Experimentalist just tell you I make this culture and have all this amazing data and as a food node sometime it is Not really central sometimes you say, okay It is nutrient limited and I know I happen to know that the glue causes the limited What more or less formally that means it is that they can kind of establish a connection between Moving a parameter that is defining or controlling the input of this nutrient with some parameter That is linked with the grow or Something that you're measuring the culture and the case of the chemostat the grow rate itself the culture is fixed We are talking about the study state. So they are illustrating some kind of nutrient Limitation by those two graphs where you have time in the Horizontal axis and then you see in the left are the concentrations of two or the of the component of the feed median Let's say I believe I named that glue cause and And ammonia it's like the carbon source and nitrogen source and we can see that The first one we can perturb it and we don't we don't get a response in the in the biomass But then when we do the nitrogen source, we see we see our response That's that's what means for instance in this case to be nitrogen limited More or less is that High-level and you can define it probably in other ways But it's equivalent in the sense that it's just establishing a Relation you can you can see a picture that is like less local said he the perturbation is around the value Here you see the more a belief common one that is just you do a range of concentration This is actually experimental data from E. Coli starting iron limitation Of course, I don't need some micronutrients. So you have very small Concentrations and you see that is that have the two typical regimes one in which we plateau And so that just means that at those high concentrations Something else is the limiting, you know, the biomass a star and And responding to to change in this In this substrate, but here in the in the starting region. We can actually pretty much Sometimes Fitted with the line we see that that the biomass is highly sensitive to that. Okay What is the the problem with that? Okay? We will try to now Formalize a concept of neutral limitation in the context of the metabolic model that we were talking of the beginning Okay, because this is very high level and the other we can see it as as the Microscopic the description of the culture. This is just an how an observable is behaving, you know, it's a ball kind of constraint. Okay We do using a very straightforward Concept that is a shallow price I believe price come because from from economy because I believe they use it there first Which is actually very in tone with the school and the shallow price just The ratio between the two magnitudes you are you are Trying to measure the relationship in this case we will be focusing is this very specific Shadow price formulation. We are saying that in the top that we are Okay, it's better to start from from the bottom in the bottom. We're just saying okay We will fluctuate the exchange rate of the upper bound of the exchange rate of one of the nutrients This is important. You will always refer the lower case use we all refer to an exchange reaction He we have a network that as an example. We have two nutrients that are Potentially being taken by the cell. Okay, what we'll say here is that we will of this reaction to touch The the the upper bound and we can do a fluctuation and then we can measure our response on the maximum Biomast Rate that we can achieve given that So we are assuming a lot of stuff there for instance we are assuming that our jet diffusion is already the the maximization of biomass which is Make less general our work here, but we are trying to do everything with a goal. I which I was we saw sometimes Maximization works so and we can try to figure it out You know how this this this network that is the microcopic picture It's coherent with the microscopic picture that we did before and for that I want to pass with you this this network is For me it's quite simple in the sense that genomes scale are big and we can see for instance that All what is important is the definition of a biomass and of course the the network itself There's the way in which we can produce the components of the biomass from the intakes for instance we see that both Metabolize that are being taken are explicitly Components of the biomass first this is Sometimes tricky. This is not an algebraic Gebrics This is not Algebra equation actually is that the chemical representation of Reaction is It's a Boolean equation what we are saying is there is a Boolean and you know say we we need n1 and n2 and e So do we cannot have zero in the first one and still have a biomass? I don't know why they pick the same symbol is confused So and that is important because what we're saying is that we can connect the upper bound of this reaction with the bounds of this one That is what we want to do here. Why because for for instance imagine that the bounds of n2 is infinite Okay, we the cell can take whatever they want and let's say that also the bounds of n2 n1 is infinite The cell can take whatever work who can predict the values upper bound of ceta Yes, it's it's infinite. Why why because you can produce an infinite amount of all the components You see the third one is just e which more or less resemble energy and you have connection from both these two Metabolize and you can Produce all the old what you want. So this is an unbounded Kind of a space which is not obviously realistic, but it was a good test Then we will we can recover this behavior if we just set one of the two to infinite and one to to to be finite For instance, we say that that n1 have an upper bound and n2 is infinite What we can say about the about the upper bound ceta Exactly, it will depends on how proportional linear in this case because everything is linear To this bonus and n1 and it is what we've seen here. Okay, we are changing the concentration in the chemostat Which I didn't include it, but you can relate with the upper bounds of the fluxes very very easily you are you are in charge of Putting food into the chemostat. So the cell cannot eat more than what you are given to them at least there is some kind of black market of Not of Newton that you are not Taking into account. So you can always from concentration. That's why I like chemostat You can work at the upper bounds of the network and and this way we saw we see that the channel price of this infinite Newton would be zero because It doesn't matter if if if end it is finite And I have an infinite amount of n2 when I maximize the the biomass I will Hit first the limit of n1 and from there on if I Still like a perturbed the value of the upper bound of n2 that is very high relative to n1 I won't see a Response the biomass because actually the effective from training is n1 this Okay This is what what we mean by we can formalize the nutrient limitation Concept in the macroscopic lever is just that the nutrient limited nutrients It is the one to have a non-zero shallow price and that is that is more important. Okay This more or less is the question we want to to answer is a little bit abstract because I believe We need to start from from here. We haven't found any any any other development that is furthering it in this path We are just okay We are doing an inference question what I mean by that all these constraints that are here that the typical constraint and define this solution in space You can say that the solution is paid represent your current state of knowledge About the metabolism, you know, the metabolism is inside that that volume that that is all that you know, okay Now the experimentalist come and tell you no yes, but I in addition know that glucose is the limiting nutrient how I can Now Update my space. So it is coherent with this new data. Okay. It's a bias and kind of perspective And I don't know how to do it directly Because this is not a linear constraint and so on maybe it is obvious for somebody more mathematically involved sorry but but so I will need to make a very Your long journey to try to at least say something about this question mark there Okay, but it is important to have clear what we want to do We want the same way we can form formally introduce for instance what I told at the beginning day The the knowledge about the thermodynamic directions of the reactions that is by tuning this open and over bound We are moving our our solution in space by knowledge that we have Okay, we want to do the same but with this new knowledge that is this that we happen to know the neutral imitation Conditions any question Okay, this is an example This is echo lie What they're doing is They're like a very straightforward kind of Experiment they are just changing the ratio between a carbon source and a nitrogen source And as we discussed this is the equivalent of what we did we that in my in some Area we can envision the nitrogen to be infinite with respect to the carbon and the other side We can say that the the other way around I don't I don't remember what I said And we see that everything move accordingly and I will describe that and that you can map it also to the Microscopic interpretation the shallow price, okay here and in Rub it in here. We have this radio between carbon and nitrogen source and we have in this size we have a small radio this means that Compared with this corner here carbon is less relevant in the culture And if we found all these dots we see that for instance this one is the nitrogen and It is not a surprise. Oh, this is a sorry a chemostat all these points are a steady state So what they are describing is at the concentration of these nutrients in the in the culture, okay? At the steady state, so we see that that the the the cells in this regime here in the steady state They are ignoring some amount of nitrogen. Okay, we still have nitrogen in the culture I mean that we are feeding the Cells faster than Than what they can eat and why they cannot eat more nitrogen all because If we follow now the squares, I believe this the carbon source we see that that it is in this area Very close to zero which which is a very good Indicator that that that is the actually the constraint that you hit in the culture, okay? We like kind of double check that if we start to move in this Ratio if we increase the carbon relative to the nitrogen we start to consume on nitrogen Why because remember this is a boolean equation I cannot consume more carbon if I don't have nitrogen to put it together into whatever and producing that is that is the deal So I need more carbon for use more nitrogen At the same time of course all this is being used to make biomass that it is the the solid the squares Okay, and we see that we keep moving in this direction till we hit This region here that for this particular paper is very interesting because they have the solution of why do you have a degenerate Range that it is the third or fourth. I don't know Marker here that is a storage, you know cells are very small and and they reach a point here where they cannot keep growing Because now the nitrogen is also depleted, but they have a lot of carbon yet outside on the same I would not ignore that carbon. I would just start to pocket In the storage kind of compound that there is this phb. I don't I don't Really know the name of the compound, but what we see is after we end off of that We reached the mirrored part of that now carbon is In abundance and now this the cells cannot even store more is full the bank is full and now we start to to know that okay so That can be seen here Doing that word that we already did so we do fast that that Changing which one is infinite to respect to another we can work out that the shadow price will actually signal Which which one will be the limiting given the conditions? Okay? We don't we don't need experimental data other than defining which are the composition not in terms of quantitative composition in the sense of how much The the culture is is is Composed by by glucose or not, but that it has glucose and nitrogen for instance the only data we need To to to reproduce this in the sense that we know that when we will be in this condition the limiting will be nitrogen and so and we Be that here is what what is shown there is a little convoluted. I will try to explain. Okay, as I was saying you can take The metabolic network this full set of reaction plus the definition of the biomass and so on and you can start to ask the question if you're open bound of Glucose is a given number. Let's say here and your lower bound or your open bounds. I'm sorry Sorry if you open bound of glucose is this number here for instance and your open bound of nitrogen is this one I can ask you the shadow price of boats there All without experimented there in the sense that this is built in in the in the topology of the network and the biomass composition And in this case blue means that the never is saying. Oh, no here the shadow price. It is Non-zero only in the in the carbon. Okay And zero in the case of nitrogen and and the black region is the opposite Okay, so the background is built only with the with the networks and I'm using two networks this is like a Simplified version of the main Meta only path of equal eye And this is a genomes scale model although old I could actually date this picture. I should do it We see that we are looking only the background right now forget minutes at the points We see that they change like this line is Different slope and so on and that's because it is important for building that this Tegeometric and also the biomass the biomass composition. Okay, so now how would this kind of Yes, very good. Okay. I think that's very cool Is it clear that you can only be limited by one or the other? No, that is that is what I meant When okay, you need to contextualize this model at least telling that you have a single source of carbon in this case And the city goes a single source of nitrogen this data the kind of binary data which nutrients are outside You are putting from the from the experiments Okay, so the answer is no but in this case we are We are on purpose targeting this kind of cultures with this only to two nutrients So in this model, it's true that you can be either or we will see that that is actually why this is Might be useful. Yes, exactly The I don't really understand the the graph like every point. Is that a steady state of I haven't reached the points yet? I was I was explaining the background only the points are okay. Well, I want to while I'm trying to spread with these figures eyes that what the experimentalist said about the Grow condition is in the sense of of mutual limitation match with our definition of grow Limitation in them in the microscopic kind of of the definition, which is which is the challenge price Well, we have in the background is just a map of the challenge price of glucose and an ammonia belief Which is only depends on the network. Okay, and then I am placing dots in the top of that that are The red one are dots of experimental Data that the experimentalist actually say no, we know that the carbon for instance It is the limiting factor and we see that all the road where the red one are Maybe not very clearly in the area when they should be but at least they are higher than the rest The blue one are the mirrored image that experimentally are telling us that yes this culture It is in nitrogen limitation condition and what I do the coordinate as actually the the the flux values of the coach Okay, what I what I mean is I should maybe do that If you only give me the fluxes I can predict more or less What was the condition that the experimental Experimentally would tell me because you you you see that all the carbon the carbon defined in the upper Power compared with the nitrogen ones and more or less. This is the same Distribution of the two phases the exact boundary depend on the biomass composition with using the one that come by the fall in the spare and in the genomic scale network, so It is not so price that is not very tuned to the data in this case And I'm showing all the points and showing the the iron limitation points to know that they Have no reason to be anywhere in particular This is little stars here are if I ask the Network, okay, which is the perfect ratio of nitrogen and carbon. So any anything is left in the medium It reached it fall in this boundary Which means both we have an on-zero challenge price Okay Which more or less give a son interpretation to this one is on any question to now I see What time I need to end? Five minutes in five minutes. Yes Was a disaster already, okay. Well as the question he asked When we have more than than a simple nutrient in the in the culture Everything is like more difficult. Actually, it is hard to solve for instance. This is data from from bacteria Where we have in the same medium? Several nutrients, you know, this is a batch. This is time. This is the initial concentration Of the new team. We see that all these nutrients here are carbon source. Everybody are At the same time and we see very very interesting that for instance the cell can do anything almost like for instance Ignore everybody and just consume glucose, but of course our problem is not necessary to explain this. It is to try To see what we can do with the network that is actually missing all this action Why because again what we can say about this culture at the beginning is just that you can eat all these options and if I Toalize the network this way the network do something very differently. Usually it just eat everything as much as it can okay, so that that is That the conclusion of this party that in the context of what we call complex medium That is this medium that have Redundant nutrients the definition that the shadow price is not enough because in this condition The network would give you that everybody have a shadow price and that is not what experimental data tell you So in the three minutes I have I Will really try to To give an intuition about what I try to do here. I cannot do it analytically I cannot do in that direction. So I will try to do it in the other direction What I do is okay. I will just start to perturb the the culture. I will do I will do a hit-and-run Monte Carlo and then this is the this is the kind of of problem like a prime Multiplication that is easy to evaluate but hard to work backwards No, I can give you two number and you can check if the third one is the The motive of this too, but the other way around it is all about mining big point and That is what I'm using evaluating if I have a single Nutrient with the shadow prices is more or less less as Non-expensive so what I will do is start to hit the network with With modification that can be knockouts or down regulation that depending of your computation of power And what we're doing is kind of traveling for all the action the space of the regulatory network That what I mean by that is the the ultimate like product of the regulation It is tuning the fluxes what I do is just randomly selecting configuration of the fluxes So I am kind of ignoring the rest but not the consequence of the rest So very this is like the Monte Carlo thing that I have all this point I can try to separate which one actually comply with my whatever and Yes, yes, okay, that is possible because This is a very nice approach because the combinatoria of that it is just insane Just trying to do stuff But it is possible because actually Networks are Connected so if you start to do modification to a network at some point you have a configuration that is not Interesting for instant nobody grow for instance So what we can do it is start from the beginning in the sense that the original network We know it grows and we start to preserve it till we hit That network then we can we don't need to check in that path of modification anymore We can start from the beginning and have other trajectory. That is what I'm representing here And that allows us to have the combinatoria effect that it is trying to make the computation of feasible Exploding but we have this boundary constraint that for instance We are demanding the cell to grow which I believe it is commonsensical and and but that one is in bird Is is related in the best way to the perturbation lens to the amount of perturbation we do and that will create a situation and I'm finishing A situation in which we can do this Monte Carlo. This is an example with echo live at the core, which is is small is like 53 degrees degree of freedom which is Big but not that big compared with that you don't scale and we see that more or less We can do the Monte Carlo and see the effect that we were talking about. Okay. This should explode Till infinite, but because we are just selecting the ones is smaller. We have well Now I can measure a lot of properties of all these networks and all these very good Spaces space is very important and a lot of properties of all these spaces a lot of properties of the spaces we can even do Because we are not in the business of network contextualization. We are the business of analysis So we have cool tools to analyze data so we can try to approximate the volume of the polytome and see how information is being pumped into the network and and okay, and That is the current state of the research We more or less have a method that happened to to have some hopes or at least to do this Monte Carlo that that is what we allow us at the end try to explore this space and Maybe inspire us of how analytically or more efficiently to to incorporate this constraint. Okay, but Our problem is is is actually the follow. This is the bottleneck. This is like the perspective It is of course try to see if we can target more realistic networks with you know, it's getting better. We know which I believe we can Then of course we're generating all these ensembles and biologists. So I need to learn how to more or less do a professional analysis of that But the more important thing and I believe is something that maybe you can help me it is this is the Example from from from the talk we saw yesterday That they they have this kind of same situation they they define in a space by sampling all but they have these pretty Points there. There is a perimeter data And the problem we have it is the validation of a stuff and exploration of stuff is very non-efficient if you don't have experimental data and because we need Data that is in complex medium. I don't know why and maybe I am bad searching But it is not like I'm available and see if anybody knows I'm very open to We want dots dots to put So your original plan which did not completely materialize included extending those results to the Ecosystems right and ecology is thought a lot about this topic of nutrient limitation. In fact, if you consider microbial community, then there will be Different organisms will have different limiting molecular compounds usually so Maybe maybe an answer in my question. You can share some of your thoughts how you plan to extend your approach to Communities of organisms But the community you can just to do a very big Metrics of the community so you can start perturb this is the winter metrics Computational like Performance is a limitation there. We're trying to hit single-cell kind of of Genomic scale levels. I don't know maybe of course that was programmed with with some care about performance But maybe we can start to decrease all these constants so we can use feasible physical performance. Yes Okay, that's great. I will let ask you Have you ever tried to solve this problem using elementary modes? analysis because it seems like these are the span the metabolic network and they have fixed ratios of nutrients that they take up and biomass that they produce so I I Can imagine that they will give well, you can kind of exclude some modes because they will never have this One nutrient with a shadow price And then you can maybe select the right modes and only Take combinations of those as your inferred space Yeah, I haven't done that. I probably doing various sounds very similar to But instead of iterating over the elementary modes. I'm iterating over those perturbations I don't know and I wouldn't be surprised that it's the case if which one is It's more efficient and maybe Doing the iteration through the elementary modes may be faster than doing more naively just doing it randomly. I hope Yes Exhaustive I don't think well, maybe yes. I don't know because I don't know the the exact number of this Boundary condition that we can do to eliminate the explosion of a combination But it is a very long shot to try to do exactly. I don't know. Maybe I'm just not Aware that it is feasible for for metabolic network But I believe it is even harder than just trying to do a Monte Carlo and at least extracts on the statistics Only the statistics from from the distribution But yes So we have time for one last question Okay, yeah, I first wanted to say it's very cool to see like these old papers from like late 90s Thomas Higley and then see this Yeah, it's a different era and then Fused it with the metabolic model. There's another piece of theory that's kind of old And this is metabolic control analysis and they also talk about control on fluxes I'm not I don't know this theory. Maybe people in this room know this better I would definitely be interested to understand it. Have you established any connection with metabolic control analysis? Also a question on when you do the Monte Carlo, so you you perturb your system till you get to a neighbor and so that's your new New part, but if you have many, how do you decide which one the cell will prefer right now? I'm doing a little bit smart thing that is I'm only iterating the free degrees of freedom I can try to do memory stuff and so on to make more efficient the path But I am doing randomly. I'm not choosing where you can go I'm trying to diffuse to all this space With the hope that this boundary is close enough that I will have a fixed points in the distribution with my Computational research was quite fast, but on one of the slides you you went there was like Distribution there was like two stability regions. Okay This is the shadow price for instance of galactose each point is The coordinates of a bunch of these networks that we produce from from the contextualization And we are have the color the third dimension is just how many networks happen to be in this coordinate of for instance I do 50 perturbations and this happened to have this shadow price for the galactose What is saying and there is like sorry This is in a log scale. So we have a bunch of perturbation death More or less reached sufficient amount of stuff And I don't have an explanation one of The perspective is trying to do a better analysis of this data that we already have I'm not very happy with that in the sense that we can only start topological Information from a network that is a simplification. So I wouldn't wait till do this in the real Denomest scale so any insight that we have it is actually validated That is something that I didn't show but that this how close the core cloud Resemble a cloud that you compute in the in the big one and because we are modeling growth We see that the actually this core model is Rich at least in biomass that is this point here more or less a good correlation Which is not surprised because the core Metabolism is called core For something and so yes one very last question really really short um I Did something I genuinely don't know how good is FBA at predicting growth rates in complex media That is the problem you have you need to put so much information that is usually It's as good as the information you put into the into the model. That's the short answer The a typical non for instance no contest what I never it's just wrong It will give you the addition of everybody being taken So in this in this in this case The case on this case it will give you Literally what you will produce with in taking all this carbon because you don't have any internal constraint That is limiting the network In a way that that prevents everybody to enter Sorry, it is bad, but it is not full of FBA is your missing information You don't have this internal constraint. It's yeah, it's like the world will affect that for you Switching you need to incorporate so internal constraint somehow and it's so difficult that it's better to do a Monte Carlo to try to To see if some part in the marriage Okay, so let's this let's thank the speaker again Remember the data