 Please people listen to me Okay, so we can start this third day So the first speaker is Andrea de Martino Thank you. Thank you very much Can you hear me? Yes good So thanks. Thanks for having me well So I'm going to so that this is not the title I gave Okay, but this is not the worst I'm gonna do during this talk. So So I'm going to talk about one one paper, okay one article So I'm not going to mix other stuff or previous work in what I did in what I will be talking about So I'm not sure I will be able to finish my 50 minutes. I'll probably finish earlier but I think it's it's a Work that potentially Could be interesting for people working on on metabolism. It's a different view on on some problems that arise in metabolism, especially About stuff that you can do now with data that you couldn't do a while ago So basically as a Let's say executive summary for this talk. This is one slide Okay, so if you're not interested you can basically go to sleep after this slide but What I'm going to try to do is the following so I'm will tell you a story about a Collaboration we had with some really really good experimentalists That are capable of mapping the pH in Cell cultures at high Spatial and temporal resolution. Okay, and I tell you how they do this And then we use this pH data to learn or to infer The proton fluxes the net proton fluxes so the proton exchange fluxes of single cells inside that culture Okay We then use these Inferred fluxes to reconstruct the entire pH landscape. So not only At the points where the pH was measured by these guys, but in the over the entire sample Okay, and then we used all this data to construct a Network that represents the exchange of protons between cells in the culture. Okay so this is basically Something where we start from experimental data and we do some statistical inference and we learn about what single cell Inside the cultures are doing Okay, we don't learn the entire metabolism of the cell although we could okay at this point We could but what we do here. We only learn how much what is the net? Flux of protons coming in or out of the cell each single cell So basically I will tell you how we go from from the first step to the last step. I will draw some Really simple light and open conclusions Basically about what we see from what we learned from this It's basically a story about how these exchange networks are formed what they look like and how they evolve in time Okay, and then something that it's more interesting for me personally. It's what we learned from this piece of work That can be useful for Building models for models for building models of metabolic activity of cell populations, okay Of course the models we have in mind are not Necessarily mechanistic let me put it this way So we are trying to understand what are the key physical constraints that we have to consider when we want to model the metabolic activity of a cell population Okay, so of course life is what it is, okay So I'm not going to talk about bacteria. This is there's no bacteria here. I'm aware of the title of the conference Okay, as an organizer. I'm aware, but but This this is not about bacteria. Okay, the cells that that are we work with are not bacteria There's not much I can say about it so What You recognize what I mean, don't you recognize it? I mean come on as soon as I saw the image I could tell this is pancreatic cancer. I Mean, I'm sure many of you have come to the same conclusion Okay, so So what do we do this? Well first of all because we can okay because basically we met these we have actually we have been interacting with these experimentalists for some time and We never had an idea of what to do with them. That was good enough to actually start working until we Until they showed us these pH data Okay, and because we have been doing this kind of inference on metabolism for some time. It was kind of a really easy Thing to do so we can do it and that's one of the main reasons why we did it and then there's a few other reasons that I Consider sort of let's say an appendix to that. So first of all This is a so if you use statistical inference you have a way That is non-destructive to learn something about what single cells are doing in a population. Okay Because these people are just following the culture with basically microscopy, okay, and we are Eating up their data and we are looking at what single cells are doing and the culture is still there and it's going on for days and days and days and we can Do this online? Let's say So this is this is nice especially because of course I Mean personally We as let's say the theoretical part of our collaboration some basically me and Daniela de Martino Mainly we are really really interested in heterogeneity in metabolism So learning about this directly in from experiments is a really really good thing for us Then also this was like a Way by which we could learn something about What theory needs in order to be useful for this kind of systems, okay? Because this is something that we are really Being banging our heads against the wall for some time What are the really important constraints that we have to consider and this was a really? let's say Expectedly good starting point for reasoning about theory Then let me say that The method we have developed is is absolutely trivial, okay? It can be applied to many things what we can't do is use this kind of data for bacteria And you will see now in a minute why okay, but you can use different types of data, and I think next week Shawn McLean is gonna be here is from From Caltech and Tokyo Tech, and he's I think he'll be talking about some work. We're doing with his group Along similar lines with bacteria. No, not a coli with photosynthetic bacteria. So it's kind of different beasts, but It's kind of related. Okay, and The input data are different, but the basic idea is not that different. Okay, and also there's something Let's say more biologically if I may I'm not a biologist, but So that's kind of an issue That people like to discuss about in certain assemblies about how Mixed populations of cancer cells and let's say aberrant and non-aberrant cells interact when they're put together when they coexist Okay, and in particular there's been There's an idea let's say that there's a kind of Division of labor between these two cell types with cancer cells Donating lactate to fibroblasts to mutual benefit. Okay now I have to say So this lactate shuttle business is sort of a touchy subject for me Now I don't want to get too personal because it's embarrassing But I mean I've been giving a talk about this lactate shuttle in a totally different context in brain energy metabolism because there's a similar problem over there and I gave a rather similar talk in terms of conclusions. Okay there that was ten years ago And I learned that people in that community have really really really strong feelings about This lactate shuttle business much stronger than me and much longer than I could imagine So I hope nobody here has really strong feelings about about these things So what I'm referring to to be clear is is the following so rather accepted picture is Basically represented here Where people expect that cells that whose metabolism is predominantly glycolytic so that they convert pyruvate to lactate as the last step of Glycolysis, okay They fill up with lactate and they have the problem of expelling this lactate from the cytosol And they do this to these family of transporters, which are called MCT and They co-transport this lactate out of the cell with a proton so The reason I'm linking proton trafficking to lactate trafficking is that basically they go together Okay, so when you talk about acidification in in cancer you usually talk about lactate being expelled, okay And then what happens is that once the lactate is outside? It's treated as a perfectly good carbon source by non aberrant cells Who are oxidative? Okay They suck up the lactate perhaps they don't find enough glucose perhaps their glucose import is way down Regulated compared to the glucose import rates of aberrant cells for whatever reasons They suck up this lactate and this is good for cancer cells because the environment sort of stays clean Okay, doesn't acidify too much So this kind of cartoon that you see here is basically my model of of the complicated things Why is It's that's the way the transporter works, but there will be could there be other ways that Protons get in and out. Yes Myriads of ways, but so you're assuming that this is the dominant way. This is the dominant way Yes, you can normally check that this is actually the dominant way in cancer But there's Thousands of ways Okay, so the scenario is usually that there are these kind of two sort of metabolic phenotypes One is a donor the other is an acceptor and they sort of establish this crosstalk for mutual benefit through this Shuttling of lactate So this is this kind of work is also a way to sort of check how good this idea is how general this idea is The problem is of course is that we only have one one sample We have one experiment with one type of cancer cells So it's kind of you can imagine all the limitations of this but at least in this case we can check that Okay, let me give you an idea of how the really good people do this So first of all, I should say that these experiments were not done in Torino. They were done in Leche She's a really charming city in the southeast of Italy, okay It's actually a town more than a city but it's also the the place where the National nanotechnology facilities located so these people are really really good at making small stuff really small stuff Okay, so among the many small things that they do there's also these sensors these kind of Balls tiny balls they're around one micron in linear size Which are silica particles that they can coat with Many different types of things and among the things they can call them with is fluorescent dyes that are sensitive to pH Okay, so these particular these specific particles were coated with two types of dyes One that is sensitive to pH and another one that is not sensitive to pH and the goal their goal was to be able to make Russian metric measures of pH through these sensors, okay And then because you want these sensors to be still you don't want them to move around in your culture They also fabricated these fibers. So these kind of lines that you see here. These are nanofibers Which they fabricate by electrospinning Which basically means they Sucked them out of a of a big solution Where they have both the material for the fibers and the sensors Okay, why don't you want the sensors to move around because I want to know the pH at one at the exact location Where for for the inference reasons, right? It's more convenient to have the pH at fixed locations rather than at variable locations okay, but You would still have a signal even if they're diffusing, right? Yeah, you're right But then there will be timescales involved. I guess. I mean, it's simpler if everything is still so they basically build this matrix of fibers and Sorry, so these fibers in the end they contain these sensors at random positions So you can imagine a long elongated nanofiber with these beads attached and they construct matrices of these fibers with the Sensors and they seed cells on top of these matrices. Okay, so this is a an artistic rendition of this thing Which was remarkably done but one by one of our co-authors. I have no idea how she did it But it's really impressive even if one of my daughters said that's ice cream. It's not ice It's cancer, okay So but basically this gives a good idea of what of what I'm talking about. Okay, so then they use Confocal microscopy confocalizer microscopy to get the readout the fluorescence readout Okay, and they get the images like that where they have Ways to distinguish different cell types. Okay, so in that case That's a mixed culture of pancreatic cancer cells and I think these are the magenta ones and of Cancer associated fiber blast Which are the purple ones Okay, but you can see in this image these lines sort of green lines That crisscross the image in random directions. These are the fibers So the green dots are the sensors Okay In this case, they are green because they were looking at that specific channel But there's two so they can also measure another channel. They do the ratio of intensity They have a calibration curve and they know the pH That's how it works basically and they know the pH essentially at the points at the green points Across the culture at the green points. So what we do with these images is first of all we segment them to extract the position of the Sensors and of the cells Okay, so we literally have XY positions of both sensors and cells And then we also have the information about the cell type So whether a cell in that position is a cancer or a fiber blast Okay So when I'm talking about data here when they say the data So in this case, you probably see the fibers a little bit better. So this is a fiber. This is a fiber. This is a fiber and so on So the data are these kind of Matrices so one concerns the the sensors and I think it's the top one So the one in the top left is data for sensors so there's basically indicators of the position of the sensor and Each line is a different sensor. We have the position of the sensor. We have the timestamp Okay, at which the measurement was taken the measurement was taken and then we have the value of the pH And then we have the error on that while in the bottom There's the cell data Okay, for which we have the position of the cell we have Again the timestamp and we have an indication of the cell type whether it's a cancer cell or a fiber blast Yeah, yes, so we they have these They prepare these populations. Okay, so and they divide during yours. Okay, that's There so Overall, we are looking at a System, let's say a snapshot that describes about 500 nanometers square. I mean 500 nanometers by 500 nanometers a Culture that big Over six hours and we take measurements roughly every nine minutes and by we I mean them they Usually so in these images we have around 500 sensors scattered across the square and the number of cells is Usually around 160 some cells move a little bit so they sometimes they go out of the square sometimes they come back from to the square Okay, so the number of cells is not fixed But fluctuations are very small and the usual number is 160. Sorry just last second to answer him So now in we are there following these cells over time for eight days and They usually start dividing after one day so they are viable and they divide etc. But What we do we do in the lag phase so we do in the very beginning right after seeding We follow the cells for six hours. So everything I'm going to say is for the adaptation phase Okay Yes, I just just to have an idea how big are these cells compared compared to the sensors I have no idea so the sensor is around one micron Which is also why we can't use this for bacteria. Okay, and the The cells are about 10 to 20 microns Thanks, I mean big Yeah, so so what do we do with this data? Okay So this is like, okay, let me go through this Okay, step by step then Don't worry about Destroying this because I'm going to torpedo it myself in a while. So maybe just let me just go through every step and Okay, so first of all we have to make assumptions in order to make inference because otherwise there's no inference So the first assumption that we make is that Proton concentrations stabilize the equilibrate much faster Much before the over timescales that are much shorter than experimental timescales. So much long before nine minutes. Let's say Okay, so this means that effectively we can assume that proton concentrations Satisfied the Laplace equations. So I should have told I should have said that There's also a small z direction. So these are not really 2d systems There's also a tiny tiny z direction there. So that's one assumption we make Okay Then We say, okay What are these concentrations? How do they what do they look like if I have to write a formula for those? Well, we'll just take the multiple expansion and cut every term after the first Okay, so they look the solutions look like one over air essentially one over The distance from the point at which you're interested in knowing the concentration and by linearity, of course Every cell in the system contributes to the concentration of protons at a certain point By just truss omation essentially So that's how you get here the concentration of protons at position are in the system It's just the sum of the contributions of the individual cells Okay plus There's a boundary term that basically looks exactly like the other term except that it represents The protons that are coming in and out of the boundary of the system So instead of having a sum over cells you have a sum over bits of the boundary Okay, I don't write this specifically because it's really not important from what I'm going to say in the following So the really important thing here is that this quantity UI so D here is just the diffusion coefficient of the protons Which in case somebody is interested is around seven thousand in water. It's around seven thousand micron square per second And the really important quality is this UI which represents the net exchange flux of protons of cell I so this tells you how many protons are coming in or out of the cell then We say okay, we have the pH at M fixed locations that I Indicate by the index mu Okay, so we can write the concentration of protons at position mu in this way Where AI mu is simply These So it's a it's a matrix that contains the inverse of the distances. I'm just using a shortcut not to repeat myself So this is the expression that we use for the concentration and notice that I introduced the timestamp T Okay, so from now on I'm assuming that the time we're working with a fixed at a fixed frame So that fixed timestamp, okay, then we say right We want to find the values of you. That's what we want to learn Okay So can we do I will build a cost function the simplest cost function you can imagine is basically This one you say that the pH You want to minimize basically the difference between the pH at the position of the probe mu and The estimate that you get of the pH from the solution of the Laplace equation Which is basically a way to say that you are assuming that the difference between See the concentration at position mu and this sum here are Basically Gaussian random variables Okay, so this sort of Gives you the logarithm of the conditional distribution of C given you And what we want to find is the use that maximize this and there's the key constraint here is that the reconstructed Concentrations at every probe so these things cannot be negative because negative concentrations are Mysterious, okay, and then Yes That would mean that cells only excrete protons and don't take them up. No, no you has a sign So if they if you is positive So you can be positive you can be positive or negative. It's a net. Thanks. Sorry. It's a net. It's a net flux So if it's positive they excrete if it's negative they import, okay, and how yeah Well here So we use the boundary term here so Basically, I gave an index zero to the boundary term and I just include the contribution of the boundary to the value of the Concentration at a certain point and from then on the boundaries appears Okay, there's some assumptions And then this is one of the concentration or one of the use you fix but it has a it's very very complicated position We ignore that we consider the flux along the boundary to be uniform So it's only we have to infer only a single flux for the boundary. Okay, then the way we Define an exchange. So a passage of protons from cell i to cell j Is by taking these quantities ui and uj that we have inferred and calculating this This thing here, this is a where D is the distance between cells i and j. So this is a diffusive System so we have we know that the exchange has to be the probability that a particle goes from i to j is inversely proportional To the distance. So we have a prior for this Sorry, this looks like symmetric in i and j the flux shouldn't be asymmetric There's a so there's a proportionality constant in front which ensures It's done in such a way that the sum over all cells that import Protons from cell i has to equal the outgoing flux of cell i So I didn't write okay. This is all wrong. Okay, I Mean wrong is a strong word But I mean you have to look through every step to understand really what what this means So first of all when we use the Laplace equation, okay We are neglecting the possibility that there is transport that these protons are moving in a certain direction Okay, which means we are neglecting terms in the Equation for the time evolution of the concentration that looked like the divergence of c times a velocity field Okay Can we do that? Yes, I mean we have Made some back of the envelope. Let's say calculation to show that the ratio between the Transport term and the diffusive term is actually Really really really small so Also, there is no indication that there is any so there's many ways in which you can check Experimentally that there is no preferential direction in for example in the in the movement of cells and you can argue that kind of movement of protons can't be too different let's say from an eventual movement of cells so We believe that the transport there's no transport going on here, okay But in principle, there's an extra term here that we are neglecting even at steady state Then of course because we keep only the first term We are limiting ourselves in the fact that the second term in the multiple expansion would allow us to distinguish import fluxes from out port fluxes Okay, so if you remember from electrostatics right when you calculate the electrostatic potential generated by a complicated charge distribution because if the charge distribution is easy then life is peachy, but Life gets really not peachy fast when the charge distribution is complex Then you need to take care of the other terms in the multiple expansion and the simplest term is the dipolar term Okay, which Accounts for the way charges distributed and how it's oriented and so on and so forth So in particular that term here would allow us to work not with the net flux But with two separate fluxes for each cell one Export flux and one input Okay, the problem is that the number of parameters to infer Increases and then you need more data to be able to do that reliably Okay, so this is the main reason why we we stop here Also We know that this is not correct, okay, this is a sort of mean field approximation to the true exchange fluxes and we know that people in the network community they have Actually found the correct solution to reconstructing these exchange fluxes When you have data for the net import and output flux of each node in a network Of course, it's much more complicated than this. This is very easy So the only justification that we have is that it gives a very very good approximation I don't know whether Luis Carlos is here and he has He will be able to show you that if you do things exactly You get something that has a really really good correlation with the predictions that you get from you But we are aware that this is incorrect. Okay, this is just a very crude approximation. Yes So How how can one count for buffering pH buffering does that just linearly scale the The numbers you mean from the fibers No, just the fact that the protons are in some in some some medium That is just not just water but may contain things that that may may buffer pH I don't know. I mean we had to check that Fibers and sensors do not contribute to pH buffering. Okay, because we have to ensure that. Yeah, and that we did then I mean pH does what it does Yeah, just a converting proton numbers to to pH What? Yeah? Good think about buffering Okay, so So if you accept this picture this kind of inference scheme for the single time frame This means that basically every time frame every snapshot we get we do that Then in order not to repeat the same thing 40 times Okay, we basically solve everything together Try to infer the fluxes of all snapshots at the same time So what we actually do is we minimize this cost function The one that I just described as a single time frame plus some Terms that regularize the fluxes that we want to infer Okay, so basically there are three terms in here each one is weighted by different constant alpha beta in gamma so the first term is just a sort of so in the in let's say in the idea that This chi essentially is a proxy for the conditional probability of the concentrations given the fluxes This term here just represents a prior for the fluxes Okay, so we are saying that a prior distribution for the use is Gaussian with zero And we fix this value alpha in such a way that Well, okay the second term is Let's say and forces are a quest that we want to be satisfied That the fluxes don't change too much between two snapshots Okay, if consecutive times fluxes have to remain sufficiently close to each other and the third term is a Requirement that the average flux from the cells Okay, should match the bulk Proton flux that we can Read out from the culture as a function of time. Okay, we see how The overall pH of the culture is changing in time So we can have build a model for the overall flux of protons in the culture And we want the mean flux of cells to match this quantity. Yes Are the times points time points equally separated in time? Otherwise, I would expect some coefficient. Okay nearly Okay, so we do this this is done by Monte Carlo period Sorry, whatever I done wrong so So we learn these fluxes for all the snapshots that we have and for each cell in every snapshot Okay, and this is the quality of the reconstruction that we get. This is a sort of Representative probe so what you see is the pH measures as a certain probe at a specific location over time and The blue is the measurement the experimental value and the orange is our reconstruction. So it's not perfect. Okay, but it's not bad either Yes, so regarding this test I don't know if it's a test because it's testing how strong is gamma, right? So did you do it or maybe I didn't understand because you are measuring pH You mean this test here? Yeah, the first plot But the first plot is we take the we didn't understand we take the pH measures as a fixed location Okay, and then we reconstruct it from the inferred fluxes. Okay, not the bulk. No, no, no Okay, anyway about the bulk One thing that we so I'm not going to show you how we did it I'm very happy to explain this. Let's say a technicality So we are able to infer we have to let's say make a model for this overall bulk acidification flux and What we get is what you see here in the the red flux that you see here as a function of time Okay, and what is important in this plot is the order of magnitude of the fluxes, which is really really tiny and this is by the way also consistent with Lactate measurements that were made in the culture totally independently of our calculation. So anyway, the important thing is that this bulk flux is Roughly of the order of 10 to minus 2 millimore per gram per hour. Okay. Now, let me show you the results So this is these are three snapshots at three different times. Okay, each each Circle is a cell and The cells are colored according to the value of the flux. So reddish flux means out Outport of let's say Export of lactate. Okay, and bluish flux means they are importing. Sorry protons. Okay, they're importing protons and Background color gives you the map of the reconstructed pH across the cell culture now These are three different times So you see there's a lot of activity going on there We don't distinguish in these plots between cancer cells and non cancer cells and there's a reason for that show you in a second but as you see the pH landscape is extremely heterogeneous Okay, there are areas of a certain type that could exist with areas of a very different type and Cells can change their behavior Between different time steps. Okay, some cells may be importing for a while and then they start exporting and then they go back to import This is during the lag phase. It's a transient. So previously they were not Doing exporting and then they're switching them This is nine minutes after seeding But when you see them, I Guess they're already in some conditions where they're already doing something Are they changing what they're doing because you see them is it a shift like a transient or is it Well, maybe I'm not the ideal person to answer but I Can't really see you see well, but do the values for the left and right charts stay the same because it seems also the size of the Circles is largest On the side the size of the circles doesn't change the left So the right color scale stays the same the left Doesn't but roughly they all go from five point eight to nine Roughly, so the last one goes from five point seven to eight point nine something like this But they're roughly the same so the the value of seven is always the transition between the pinkish and the bluish So this is very far from a homogeneous pH situation like very very far and also these cells are This the fluxes of these single cells are very Very large because I mean if you look at the there are some cells in here that export protons at a rate of ten Millimoles per gram per hour Okay, so at a rate that is much much higher than the bulk Rate of acidification, which means Which suggests let's say that when you observe acidification in a culture that is sort of the spillover From a very intense exchange network. So this is a The network is very well balanced, but except for this small spillover, which is what you observe in culture. Yes What's a is this one clonal? I'm using sorry. I'm used to bacteria. So maybe clonal is not the word, but it's the same Population of cells at the beginning or the cancer cells There are two types of cells in these cultures. So these they are for mixed population of pancreatic cancer cells and of pancreatic Cups so cancer associated fibroblasts and the proportion here is 70 30 so 70 cups and 30 cancer And you say these fluxes or the sign of the fluxes are not related to the types Yes Yes, so I'll show you in a second. So if I think there is not here if he was if he was here This was bacteria. He would ask what is the pre-culture because there seems to be like a lot of heterogeneity. Yeah, yeah There is is this Expected I mean, this is like because not well No, it's totally unexpected totally unexpected with we didn't text especially the heterogeneity does not Disappear over time. I'll show you in a second Okay, then I don't know exactly how much the pre-culture affects these data, okay But we have new data now that we can actually do the same thing and these new data actually include the Exponential phase so we kind of Okay, so and this is the networks that we extract in the way. I told you before At the exact three time points now. I have to say I failed in producing a video where I can show you the network Behavior in time. I don't know why it doesn't work, but so I could only put these three snapshots. Let's say Now I have to say the I mean, you know when you place arrows in a graph these arrows Represent a value that has exceeded a certain threshold Okay, so In the sense that if the exchange flux is below the threshold, you don't see the arrow So things may depend on the threshold in our case the threshold is set in a reasonable way So it has to be basically above noise, right? And if we change this threshold Let's say considerably the quality features of these networks do not change but of course I mean the Some graph properties like the size of the largest component, etc. They depend on the on the threshold you use So I'm not going to discuss the graph analysis the network analysis of these networks here. Also, it should be kept in mind that these networks are really weighted network because each link comes with a flux So some links are much stronger than others So I'm representing here everything as if this is just topological links and they're all the same So we are Now using this data to do a much more detailed, let's say graph theory analysis, and this is not my main point here. Yes So the pH goes between varies between 5.7 and 9 let's say roughly in 6 and 9 Okay in in all in all snapshots that we have Of course, you see there is a very strong local structure. There are islands, etc. So Measuring the size of these islands and correlation length, etc. This is also something that We are trying I mean we are done Okay, but so yes, so can you identify cells as emitters or absorbers and ask whether this Quality is persistent in time No, they don't persist in time. They should be switch And can you characterize the switching? It's very variable. It's a very good question. We have we're now so Some cells persist for longer than other cells. We don't see a characteristic time, but keep in mind This is only a hundred and sixty cells Okay, and the other thing is that there is no well I'll show you in a while But basically there is no difference between cancer cells and no cancer cells. They behave in the same way Okay, the interesting thing here is this that When you yes There's a huge And so like Are the fluxes expected to only spread like within this field of view or will you expect? With the rest of the culture so this is taken into account in those fluxes staying to account in the inference. Yes, I mean We believe it is So the interesting thing here is this that if you look at this network again This is the lag face so it starts in some way and then you observe the formation of really really Large hubs Okay, something like that which persists over time, but then the network starts to decay So links start to die and you end up with a system formed Where the exchange is mostly dipolar? So there's basically couples of cells that form and they exchange protons one with the other. Okay And they are very stable once these couples are formed which is heartwarming really except that these are cancer cells So, you know, but I mean, this is a very robust pattern that we see once These cells adapt and they start approaching the growth phase These dipolar moments become stable. Okay, this step stabilize so this is a Way to quantify this dipolar moment. So I'm showing I'm showing you these two Cells in the top right corner of the picture and what you see below is the infer fluxes for these two cells over time And you see that really sort of okay positive and negative Okay, and this is the other thing I was telling you about so we don't observe any appreciable difference between the behavior of stromal cells and cancer cells They seem to behave in the same way. If you look at the movements of married cells Do they move together or do they divorce we didn't look they don't move a lot these cells? They don't move a lot I have to say but That's a good point. Sorry. I have a question. But if there are these couples shouldn't expect the Right plot to be sort of by model If there are these couple some that have a typically Okay, so now comes the Let's say the lessons learned. Let me put it this way. Yes. Yes, they're cells to be exporter So so is it wrong or what is your interpretation? This is what we see. I don't Also keep in mind that we don't see cells keep a Donor or acceptor phenotype forever cells switch So basically they behave according to what they find They don't seem to have Yes, I'm just wondering in the in the inference method that you use you you also regularize the That what the quantities that you try to infer infer right so that they vary over time rather relatively smoothly But I suppose also spatially So how do how then if you have these dipoles that co-vary? You kind of expect that from the inference. So how how sensitive is that or am I seeing this wrongly? I mean you say because of the regularization you expect the formation of dipoles Well, at least that the neighbor neighbor interactions are go varying more than okay So we we try to see whether there is a correlation between the phenotype and the local density Okay, we don't see that but keep in mind that we only have this So I we can't rule out the possibility that that is actually happening if I understand correctly question the question is Whether this is stable respect to changing the parameter gamma Which is the parameter that orbit? I don't remember the parameter that determines the time scale the strength because then you can be stuck The let's say the hardest parameter to fix is is actually beta which says how smooth things are across time and for that we basically chose To let's say Chose beta in such a way that changes in fluxes reflect changes in the pH measure that probes So typically the pH measure that probes changes by 10 10% even less than 10% between two time points. So we want the changes of the same order for the fluxes But yeah, I mean yeah, I mean one should check all these things. Yeah, okay, so So first of all these are let's say Ideas that are Work in progress some of them are actually not so working progress. We are actually Should be writing a paper right mule. What is mule should be doing? but Okay, so the first thing is not This system is very heterogeneous and of course if you start by assuming that cells are heterogeneous You're gonna get something very heterogeneous But if you if we don't see that different says be a very differently Then heterogeneity should be a consequence and not an assumption somehow. So this is our This is the first thing that we want to stress so the second thing is actually really trivial and And we knew but we forgot Somehow we had already discussed this years ago, but then we forgot we had discussed this so When you have stuff that diffuses okay diffusion essentially couples Sells together in a population in a way that you can write down mathematically right because you imagine that you have a certain source of a Compound that is at a fixed concentration, right then the concentration of that compound that position are is just given by This formula, okay, this is classical diffusion Okay, so this means that The uptake rate at the cell If we assume that the cell sizes are is bounded by this value here Or by the R times Availability of this compound Now of course when you have many of these absorbers There is still so that basically the concentration of position R is affected by all of them Linearly again, because we're dealing with a plus equation in the end this kind of Thing translates into a global constraint over the use of all the population Okay Now when you consider that type of constraint into a constraint base model that can make a really big difference And you have one such constraint per everything that is diffusing in your culture So you have one for oxygen you have one for glucose and you have one for lactate as well Okay, the one for lactate is special because C infinity is zero for lactate. There's no source outside source of lactate, right? so for lactate the constraint has a zero here, but it's still there and And This changes this can have a quite dramatic impact on on for example the flux polydope to use the terminology that was introduced by Jose yesterday So the other thing is that because these cells continuously switch between Being importers and exporters of lactate It's hard to start by assuming that they prefer one or the two one of the two carbon sources, right? They I mean they seem to import what they find okay and what this means is that Basically what lactate availability in the medium So let's say this environmental source of lactate really shifts the bounds of what cells can import in a time-dependent way so this is the net effect of The one should try to incorporate in a theory and also the other thing is that if you want to check predictions made with this Theory against experiment the simplest parameter that you can change is the cell density Okay, because obviously things have to depend on how closely packed cells are because this is a diffusive system. So Basically you want this the mean cell density. So let's let's keep things easy Okay to play a role in these kinds of theories Okay, so the picture that we have in mind is more or less this So imagine that Again, this is purely speculative. Okay, at least until Moulet does his job, it's pretty but But okay, so imagine you want to write Theoretical model to describe the metabolism of a population of cells and you can see there are spectrum that Goes between two extreme behaviors. So on one hand you have cells on one extreme you have cells that let's say they don't want to Peel the environment with waste, okay, they want to minimize Lactate export, okay, they want to keep the environment clean Okay, so these cells are going to be predominantly oxidative right and pH panorama that you will observe is relatively trivial. So you will have very homogeneous pH and The import or export flux of protons is going to be zero On the other hand on the other extreme you have cells that are very greedy and they want to For example maximize growth, right Except so they they're interested in basically importing as much glucose as possible and they don't care about how much they pollute Okay, but they have an internal degree of freedom they have an internal cap that says if you import too much glucose at some point I will divert it to lactate and you start polluting Okay, and this is eventually going to lead to the other extreme where the environment is Acidified completely acidified and southern now imagine having a parameter that allows you to interpolate between these two situations okay Like a temperature for example, and at some point you will go through a situation where the Fluxes of individual cells are going to be heterogeneous and where you will have a very heterogeneous pH landscape where you will have islands of Very different pH and you will be able to for example make predictions about How large these islands are going to be and the key parameter is likely going to be the the density of cells at least that's Something that we hope but basically the point is that the observed situation seems to be sort of in between these two Extremes one in which they don't want to pollute and the other is one in which they don't care about how much they pollute and They sort of try to optimize things in in in between these two extremes and the result is What we seem to observe in this data, so this is the kind of theory We are interested, so I'm not going to repeat because I'm out of time Happy to the great questions. I just have to thank my co-authors so Valentina and Krishnadev are the postdocs who work with us and Daniela and Loreta del Mercato. Loreta del Mercato is the Experimentalist to actually let the group that made all measurements and Daniela de Martino has been I've collaborated with him for several years on metabolism and inference and these kinds of problems and I also want to thank Roberto Mulet and the others and Luis Carlos is also here and also is also here. We are working with them on let's say Developments of what we learn from this paper, so I'm done. Thank you very much So I think we have time for a couple of quick questions So maybe I just missed it but in patient and calf heterogeneity is a big Like big buzzword currently and they have very different functions. Can you comment anything about? What is happening in like in your more cell cultures set up with the calves? Are they rather Homogeneous in their functions or do you can you comment anything about this from a meta? So you know, so our culture is a I mean It's not a physiological Okay, so what we observe is that calves behave exactly like cancer cells, so they switch their phenotype back and forth Yeah, so we don't it's they're very heterogeneous Or you don't know if there's any subpopulation, I just don't know how it is in No, we don't you don't know if there's any subpopulations. Okay, and do you know how the local concentration of lactate compared to the Concentration of glucose that the cells are fed with I mean Am I understanding right that the cells are basically bathed in a solution that contains certain starting concentration of glucose? Yes, and that's what they have and then they sort of like some of them start consuming it and so like Can you do you have an idea of like how those local concentration can compare or? Because it feels like cells that are eating a lot of lactate will deeply delectate around them and will be more likely to then start We were looking also for these density dependent things like in areas of the culture where cells are more dense Of course, you expect this kind of things to happen, but we don't see them in this specific example So we can as far as I understand these cells are basically flush with glucose There's a lot of glucose in this culture. So this is what And the bulk flux of lactate is really really really tiny Okay, let's thank Andrea again