Computational models of stem cell decisions
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Marr, Carsten
Molecular regulation of cell fate decisions underlies health and disease. In my talk, I will present mathematical and statistical models that describe molecular interactions, differentiation decisions, and single cell gene expression. We use these models to infer molecular and cellular properties from biological and biomedical data. For example, in lineage trees of differentiating blood stem cells, we often observe correlated state changes between related cells. Using these correlations and a stochastic model of the differentiation process, we find differentiation events to happen much earlier than previously anticipated. To predict differentiation prospectively, we use a deep neural network trained on image patches from brightfield microscopy and cellular movement. Surprisingly, we can detect lineage choice in blood stem cells up to three generations before conventional molecular lineage markers are observable. Finally, I will present a method for fitting stochastic models to lineage trees. Using a Bayesian inference method, we compare possible models of autoregulation, an important gene regulatory motif in stem cells.>
 Hi, everybody. It's great to be here. Thanks for the invitation. I already enjoyed the mixed crowd of people here during lunch, when we talked about brain research and also the magnetic field of the sun, et cetera. So I really enjoy this mix of topics and people. It's great to be here. So right, I'm from Munich. So this is where I work. It's the Helmholtz Center. Munich is a research center for environmental health. When I give a talk somewhere, I sometimes start by saying, this is to the very north of Munich. So it takes me quite a while to go there. And then I sometimes say, as long as going to the place where I am, this is certainly not true here today, because it took me really quite a while to come here. So from Munich, coming here, it's a travel. Still, you should come to Munich, of course, because it's worthwhile to go there and have a look. So this is the Helmholtz Center. It consists of roughly 30 different research entities. It's quite diverse, from groundwater ecology to stem cell research to computation biology, what we do. We have roughly 2,000 employees, 700 scientists, most of them PhDs. The topic over there is the individual being dominated by its genes, its lifestyle, and the environment. So that's a topic or that's a theme people can agree on, I guess, over there. And we are part of the larger Helmholtz Association with 21 centers all across Germany. I guess you might know that. So great to be here. Great to have a look what the Leibniz Association is doing. I'm really keen on discussing more with you guys. So that's where I'm from. In the Institute of Computational Biology, we are roughly 50 employees at the moment, kind of growing. We have 10 different research groups. And my research group is concerned with the dynamics of single cells. And that's what I'm going to tell you. By the way, we just started. We will start now later this year something which is called HIKU, the Helmholtz Association unit for the Helmholtz Artificial Intelligence Coordination Unit, where we try to spread out AI methods to the whole Helmholtz community. And we started also the science school, a grad school for data science in order to recruit more people doing that kind of research. OK, now my talk starts. What we do, as all of you do, is abstraction, basically. We abstract complex systems to things we can measure and understand. And of course, that's what we call a model. Now in biology, and I just continue with what the two speakers before me introduced, there are a couple of different models in biology. For example, there might be this kind of network model which we already saw. This is a gene network. Every dot is gene. And they are connected. Sorry, it's a disease network. Every dot is a disease. And two diseases are connected. If a gene is associated with these diseases, so this kind of model is obviously qualitative. There's no dynamics. It's static. And it's large-scale because it covers all the diseases we know. We can have other models like that. And actually, if you talk to biologists, they call this a model. Just drawing two proteins, interacting, that's a model for biologists. And you see two proteins here, a pure one and a gather one. And the model is, basically, what you condense here is all the experiments you did before. It's the last figure in a paper. And you also say, OK, these two proteins, they can bind to each other at two particular protein sites. And then they can do something. Actually, they can inhibit the transcription of another gene. All right, so this model is also qualitative, obviously. It's also static. But it's small-scale. It just considers two transcription factors. OK, just as a very short detail, I guess you know that. But when I talk about transcription factors, and the speakers before me also did write, you know they are genes. They are transcribed to messages. And those are translated to proteins. That's how genes are made of DNA. Message is made of mRNA, right? And the proteins are made of amino acids, I guess you know that, right? Some of these proteins called transcription factors can now bind to the genome and regulate the transcription of other genes. OK, let's go over that. So as a final model example here, now this is something what we computationologists would call a model, I guess, right? So we have a rather complex system with 10 players, maybe. Here you see, so the gray line is the outer rim of a cell. And you see a receptor. And things can bind to this receptor. And the receptor can signal downstream into the cell. And then things happen there. And genes are activated or deactivated. And this kind of idea we cast into models, for example, an ordinary differential equation, where you see the change of the concentration of a receptor on the cell membrane, for example, has a couple of elements that determine that, right? And then you can fit even this kind of ODE to measurements. And that's coming close to what we call a computational model. You can also predict things. And then this kind of model is quantitative, right? You can write down numbers. It's dynamic. And it's a mesoscale because you can cover up to 10 players with that. All right, so that's some overview over these different models. If you talk to biologists, they also call other things models, as I told you, right? Little drawings. But they also call species models, right? So for example, E. coli is a model species for biologists. It's a very simple bacterium. It has no nucleus, right? So you can do all kinds of genetic manipulations with it. And it's a model because it's much simpler than more complex mammalian cells, right? Same with yeast. Now, this has a nucleus, but still you can genetically modify as much as you want. And you can do experiments with it. So it's a model system for maybe more complicated animals like the fish, the new rarer, zebrafish, also a model organism. It's great because it's translucent. You can watch it grow in the embryonic development. And then, of course, the mouse is at our place in Munich. And I mean, for drug research as well, this is the most widely used model organism, right? Because it's a mammal. But you can do any kind of experiments with it. OK, so that's what I'm going to talk about. It's just that's basically the frame, right? Where our models, our body model sit in. So I'm going to talk about biological models now in a more computational sense. And I'm going to talk about single cells. So this number is amazing, right? We have 30 trillion human cells. Every one of us is consisting of this number of cells as we sit here. And not just this number is amazing, but it's also interesting to see that most of these cells, we consist of our blood cells, actually. And I mean, this 35 trillion are mostly red blood cells. These are the little, tiny guys without a nucleus running through our blood, right? They transport oxygen. And most of our cells are these guys. And then that's an amazing number. But even more amazing, I think, is that every day, each of us produces 500 billion of these cells, right? So we are not a static system, but we are kind of a dynamic equilibrium, right? We're reproducing ourselves every second. Now, how is that done? Well, the process is called hematopoiesis. It's the production of blood. And after hundreds of years of research, that's basically the dogma people believe in for hematopoiesis. So the idea is you have a hematopoietic stem cell. And these guys, we roughly estimate that we have between 200,000 and 1 million in our bodies. They sit in our bone marrow, and they don't do much. But they sometimes divide. And then they give rise to a more differentiated cell, for example, a short-term hematopoietic stem cell. And then going down here towards the functional cells, the do-really-things, the potential of these cells decreases, right? So if you are a megakaryocyte, erosive-cyte progenitor, you won't be able to become a better cell. But you are very close to becoming a red blood cell, which is actually doing stuff in the body. So you lose potency, and you go towards a functional cell, going from the stem cell level over the progenitor cell level to the functional cell level. All right, let's zoom in a bit. That's one thing we looked into a bit and let's zoom in a bit even more. So you have here a common myeloid progenitor, myeloid, because these guys sit still in our bone marrow. And this cell type is believed to produce two different progenitor levels, which are more mature, right? Either megakaryocyte erosive-cyte progenitor on the left and grondulocyte monocyte progenitor on the right. OK, so what do we know about this system? Well, if you kick out this one transcription factor I mentioned earlier, right? Pew one in mice, of course, because there you can do the experiments, right? If you kick out Pew one in the genome of the mice, you won't get any GMPs. If you kick out Gata one, you won't get any MEPs. So from these experiments, people concluded that these two transcription factors, Pew one, Gata one, are probably very important for this differentiation decision. And then if you think about how such a CMP cell able to make this decision, either to become a MEP or to become a GMP, then these two transcription factors are probably important. And now, that's again what I showed you earlier, right? From some other experiments, people figured out that Pew one and Gata one can bind to each other and then inhibit the expression of the other respective genes. So that idea, together with the functional importance of these two proteins, basically converged on the idea that Pew one and Gata one are for the toggle switch. And that's what I'm showing up there and over there. So Gata one is inhibiting Pew one. Pew one is inhibiting Gata one. Then they might self-activate each other. And this has been termed a toggle switch, right? And you can think of it as they inhibit each other. So if one gets a bit of an advantage, it inhibits the other one and shuts it down. And then you go towards the one lineage. Or the other one has a bit of an advantage. And then it shuts down the other one and you go to the other lineage, right? And this toggle switch, you can nicely model. So you can write down an ODE where you say the change of the one protein, X1, is determined by a self-activation term. And then you have a mutual inhibition term, right? So you have the other guy down here. The larger that is, the less increase of X1 you get. And you also have a decay term because these proteins are degraded over time. And if you do that in a perfectly symmetric matter for the two proteins and you simulate it or you look at the solution of this ODE system, you find that if you tune the parameters in the system appropriately, you see that you have three stable states of the system, one in the middle where both pure one and gutter one are expressed, and then two other states where either the one or the other is expressed. And that's nice because it fits basically to our biological intuition, right? Or the idea we have of the system. You can start with a state in the middle where both states can be reached, but then you tune one of the parameters and you either go to that or to the other direction. So this model is a nice way to abstract or to describe what we think, how these progenitors differentiate and become more functional in such a differentiation decision. All right. Now in 2000, oh, I didn't put it there. Probably 10 years ago, Atom Rath and Coburcus showed that mRNA is actually transcribed in bursts. That means that the DNA which codes for the gene, this is closed most of the time, but then sometimes it opens and then many polymerases run over this gene stretch and produce many RNAs at one time. So we get a lot of mRNAs which sort of burst, and then the gene shuts down again and it's closed. And to describe that, actually, an ODE is not really appropriate, right? For that, you rather need a stochastic description of the system. And so we came up in the master's thesis at that point and tried to just cast this toggle switch into a stochastic formulation, and then you have to write down the equations for the stochastic system. Since it's too complicated to solve it, the only thing you can do is simulating it and that we did. And if you do that, you can also simulate a typical cell trajectory, and then you find that if you start in the middle in an undecided state, you see how such a simulation gives you the one or the other state. And actually, the tractor structure is a bit more complicated as compared to the ODE case. But you get the same thing, right? Starting from one undecided state, you either go to the one or the other direction. All right. Well, we did also another model where we considered more players, but then we have 11 players and we can't model that statistically. So we used a Boolean framework here. And it's not just us, many people, in particular, physicists, like this idea of the toggle switch as a model for differentiation decisions. And many people simulated that because it's such a nice system, right? There's a biological relevance to it, and you can still simulate and understand what's happening. But over the years, when more and more of these models appeared, it became clearer that while we can model it, right, we haven't actually proven that this motion of P1 and G1 is really decisive for this differentiation decision in blood cells. So actually, this question, you troubled our collaborator at that time, Tim Schroeder. Now he's at ETH, and he has a nice system to actually look into the system. And that's using time-lapse microscopy, so taking microscope images every couple of minutes. And then he also had a mouse, again, a model system, right? A mouse where at the P1 locals in the genome, you had a yellow fluorescent protein, and at the G1 locals, you had a red fluorescent protein knocked into the genome. So whenever this gene is transcribed, there's a tag to this protein, which now lights up in yellow or red. So you can watch the protein transcription over time, right? So what Tim then did is breeding mice with these constructs here, sorting out the hematopoietic stem cells from the mice, putting them onto the microscope, and doing time-lapse movies. Because the idea was, well, let's watch these cells differentiate, and then we're going to figure out if P1 and G1 are really doing it. OK, so that's the data, the bright field images, how they look like. We take images at every five minutes, and you see now how the cells run around. These are the stem cells. And at some point, they grow and differentiate. And we not just have these bright field images. As I told you, we also have information about the yellow fluorescent protein. So this is tagged to P1. So whenever we see yellow shining up, this is a marker for P1 being expressed. And then we also have Gata1 as a marker. So we know how much Gata1 is in there. It's a bit hard to see, I guess. But we also have CD1632. This is another marker. And whenever we see this coming up in a cell, we know that this cell has adopted the GM lineage. You can't turn it back from there, right? And then we also see this larger cell, probably a megakaryocyte. And you see that here in that cell, P1 is negative, but Gata1 is positive, and CD1632 is also negative. So that's basically the data set we have. Bright field images every 10 minutes, then every half an hour we do these fluorescent images. And now in order to answer that question, if P1 and Gata1 are really decisive, our idea was to quantify protein levels in single cells. So we want to know in one particular cell how much P1, how much Gata1 is in there. And we want to watch that over time. So we need to track the cells. We have to follow single cells over time. Now to come up with solutions for that, you have to do what is now called bio-image informatics. You have this data set, which is a movie, just a stack of images. And to distill numbers out of that, you have to apply a couple of tools. And if they are not around the right tools, you have to develop them. And actually, we thought that it might be easy to get the numbers out of that, but it turned out that that's actually a difficult part of it. And it took us a couple of years and a couple of PhD students to come up with solutions for that. I'll cut that part short, I guess. If you're interested in it, just let's talk afterwards. So we came up with a solution for segmenting the single cells in the movie, so identifying the single cells in there. Then Tim wrote an efficient software tool that allows it to track the cells in the movie. And that's actually not done by the computer, but automatically. So a student then follows the single cells over time. And nowadays, there's better solution for that. Single-segmented vacation. So whenever you want to track the cells, we again do a segmentation of the cell, which gives you this mask here. And then we just sum up all the intensities in that mask. We also wrote a tool that allows you to efficiently go into the data set and figure out where the segmentation fails and adapt it. And then finally, in all these movies, we have a problem because in all the images, we have more photons being generated in the middle of the image for one photon you put in as compared to the edges of the image. So it's an uneven illumination. And to correct for the shading effect, we came up with a tool that estimates the background of these images using the assumption that the background should be the same in all these images. And if we do that, we can make the images flat and compare cells all over the image. Putting all that together, we were at the end able to track the single cell, as you see. And then once the cell divides, you track the sister of that cell, and then again the sisters. And then at some point, CD1632 is coming up in the fluorescent channel of these images. And the guy who's tracking that annotates that and says, OK, now the red cell from this time point on, we know that this is a GM. All right. So what we got after applying all these tools to our data is these kind of trees. Now, time on the x-axis, and you see that there's a model cell dividing sisters, sisters, and so on and so on. At some point, you might lose the cell because it's running out of the image. Some cells might just die. And then at some point, you're not able to track any further because it's so dense and you can't figure out, from one time put to the next, which cell is which. OK, having that, we also have the information about how much pure one and gather one is in the cells. For example, now I've got only one cell here. In that cell, gather one is rising, pure one is rising. Then at some point, the cell divides, and you get half the amount of pure one and gather one in the sister cell. And then this is rising again, and so on and so on. And we did that for roughly 80 trees and different experiments. And we had these trees. And then, again, we wanted to answer this question, right? Is pure one and gather one decisive for the niche choice? And if you look at that trees, even many of them, and for a long time, you realize that just looking at the trees doesn't help you to answer this question, because you don't really know where to look at, right? The data structure is complicated, because you have these trees in there. You have a lot of noise in it, in the measurements, but maybe also in the process of trees transcription, as I told you, right? And then you also have the cell cycle, right? That always the proteins half at each time, the cells divide in the sisters. So just by looking at the trees, it's really not able to answer this question, I guess. So our idea was to, from these trees, figure out where the decision for a particular differentiation step occurs. And then once we know where it happens, we can look into that time point and compare it with the mutual inhibition model and figure out if that model is actually true. OK, so the second part of this talk is called retrospective inference of the choice, because from the trees, we want to figure out where the decisions happens. Now, how can we be that done? Let me use a little analogy. So this is time. This is my group in July 2015. That guy over there, over next to me is Michi Schlasser, the guy who implemented that stuff I'm going to show you. Michi went for a postdoc to Seattle. And now, if I would see him in Seattle, so in the part of stem cell decisions, you could say he's making a state change, right, from the ICB where he worked before to the ISB, where he works now in Seattle. So if you would see him at ICB in 2017, you would not be able to figure out when he made the decision to go there. Could have been two years ago, four years ago. We don't know. But if Michi would divide at the cells in our movies do, and you would have a decision before the division of him, then you would expect that he shows up in Seattle at correlated time points. There might be a bit back and forth in the middle, but he would show up at the same time points if the decision happens after the division, but then you have uncorrelated time points of him popping up in Seattle. So the idea is to use the tree structure to figure out where the decision for a particular event happens. And of course, in our case, the idea comes from looking at the trees, because if you look at this marker, CT 1632, which is the marker for the one particular limit, you see that it is coming up in a kind of correlated fashion. It's not all over the place. It's not somewhere there and somewhere there. So it's mostly happening here in the force and fist generation. And that's a pattern we see in all the trees. So the idea is to model this differentiation process. And we basically have two steps in here. The one is we call it a point process, right? We just say at one time point, the set just decides to differentiate. And then this probability to differentiate might be constant or we allow it to be a function of time in a function. And then once the decision has been made, we say we start a stochastic gene expression process. And then at some point, we hit the limit, the marker, where the marker can be detected in the movies. And that's basically the expression of the marker as we see the experiments. So let's visualize it here with a tree. So this cell here decides to differentiate. And then this process starts, a stochastic gene expression process. And at some point, you hit the detection limit. And then you say, OK, here this marker turns on the 1632 marker and then the other cell a bit later. And this happens in the system as well. And again, it takes a while. So you have a differentiation process and you have a delay process. And these two things are parameterized with a number of parameters in our model. Now, we have this model and we have parameters in there. Let's call it theta and eta. And we want to figure out what these parameters are. So let's first test if we can figure them out in a simulated test case. So what we do is we simulate trees, which look exactly or which look a lot like the data we have. And if you simulate it, we know, of course, when the differentiation happens and how long the delay is and when the marker comes up. And then we forget about this delay and just see the marker as we do in the experiments. And now we wonder, from a number of these simulated trees, can we infer back these parameters of the model? And we tried that. And for that, we need the likelihood, so the likelihood of observing a particular set of trees given these two parameters. And the way we set it up, it's a sum over, well, first, if you have this observed tree, there are many different possibilities how this can come apart. You can have an early decision and a long delay, or you can have a late decision with a short delay. And the length of these things are determined by the parameters of the model. And then each of these hidden trees, we now decompose into a couple of subtrees, which we can easily model. And we use a graphical model representation for these subtrees to figure out what's the most likely parameter for a given length of delay, for example, and correlation of two sisters. Now we put that all in in our likelihood function and fit data with it. And first, we simulated this to make sure that the algorithm works. We find that from simulated data, we can infer back the right parameters. And then we apply to the real data. And actually, that's the data we used here. So you see this is all the trees that make this GM lineage, so the one part of the two lynches. And you see that the data is quite homogeneous. And that comes just from the fact that the biologists who tracked it, they sometimes tracked the whole tree because they didn't know what's happening there. Sometimes they only tracked one single cell. But the nice thing is that we can put that all into our likelihood estimation. Because also that here will give you some information about how long the processes are. So we put that in. Let's zoom in here. Let's couple of those trees we observed. And then we figure out for each of the trees what are the most likely parameters. And then from that, what is the most likely time point of differentiation. And this I show you now here. So the step from black to gray, that's the time point where we believe the decision has been made. And what you realize is that our algorithm comes up with relatively long delays. So from the time point of differentiation to the Markov onset, it takes five to six generations in all these trees. Now what we can do now is look in what's happening there in our real data. So we go a long time. And now we pick one of these branches. And now we look at the pure one dynamics. So the one of these two-trips effectors, we check what's going on in there. And that's how, again, such a time course looks. So you see that pure one intensity rises is half rises is half, and so on and so on. At some point the marker comes up. And this point over there, this is our predicted differentiation. This is when our algorithm believes that the differentiation has been made from the correlation structure in the trees. Right. We divide the intensity by the area to get a bit of a smooth curve here. And then we fit each of four, for each single cell, we fit these concentrations with a straight line, which is roughly an estimate for the production of pure one in that single cell. And then we can plot this slope of the linear fit, which is production of pure one, basically. And we can plot it for the cell where we believe that the decision has been made. This is generation zero, we call it. And we compare that to one duration before and one duration after. And we also compare it to the generation where CD 1632 is definitely there. And what you can see is that pure one production does not change at this time point where we think that the decision has been made. And actually, if you look at the model, you would expect that when this toggle switch tilts and pure one is winning over a garter one, then at that time point, pure one shoots off. So from looking at it, we thought, well, that's not what you would expect from the model. But of course, it's not enough to reject the model. However, we thought what we can do now to really reject the model is just taking this toggle switch model, implementing it, simulating it, exactly the same number of trees we had in the experiment, and then checking what we get from it. So we simulate trees here with the parameters we inferred. And then from all these trees, we look again at these time points where we think that the friction happens. Actually, in that model, we don't know where the decision happens because in this toggle switch thing, it's a delicate balance between the two factors. At some point, it tilts. But where exactly the decision happens in their tilting process, you don't know. So we also infer for those trees where we believe the decision happens. And then we look again how pure one is developing there. And for these simulations, you see that at the time point where our algorithm thinks the decision happens, there you see indeed a significant increase of pure one production from a level which is around zero to a higher state. So in the model where the balance tilts, pure one is highly produced, in the data we don't see that. And this leads us to the conclusion that the pure one dynamic we see in this thing that says is inconsistent with the mutual ambition of Lynch choice. So now you could say, well, this is quite some effort for rejecting a model. But as you know, that's all we can do. Or that's the best we can do. We can reject models and say, no, this does not fit to the data we have. And basically, that's what we did here. OK. Now, the third part of this story is now questions to that, actually. Interrupt me whenever I make myself clear. So this was the reconstruction of the decision time point. Now that we know that the decision happens before the marker comes up, the question is, can we predict the fate of a cell before this marker is actually visible? Because we know that decision should happen four, five, six generations before. Maybe we can predict what's happening. And the idea is, well, what do we have? We have the morphology of the cells, and we have the speed of the cells, because we watched them in these bright field three minute intervals. So again, we have to identify the cells in these bright field channel. And then let's apply some machine learning again, as the speaker before me did, because that might help us to predict what the cell will come. I guess our problem is a bit easier than your clinical problem with treatments and fine results. So I hope there are no glitches in there. Stinger certification. So that project was done by Felix and Flo. And I showed you before that, I guess, the Stinger certification in bright field. We adapted to that, and it works so we can identify these single cells over time. And then once we have that, we can cut them out. And we get these little patches of single cells. And since we have many of these cells, and we have a high time resolution, we have roughly 2 million of these patches, and now you can think that 2 million, that's a high number. Let's train a machine learning model with it. That should work. So supervised machine learning, before I come to that. So you see, now, you can order them along the track points, right? So you can follow the single cells in bright field. And you see that they are a little bit smallish at the beginning, and that they grow a bit. And you see, if you look at the cell size, that the cell grow, divide, grow, divide, grow, divide. And again, again, at some point, now, they turn on the CD62. And you see that this mark comes up. So at that time point here, we know that this cell is a GM, and we call these cells annotated. And all the cells before, we know that they will turn on the mark at some point, but they haven't yet, so we call them latent. OK, supervised machine learning. Well, we use a convolutional neural network to that. And since this hasn't been introduced before, maybe I do that briefly. So I mean, we all agree, I guess, that they are mathematical or mechanistic models and statistic models, statistical models. So the CNNs are surely on that side, right? So a very short introduction to supervised machine learning. I hope I don't bore you. Supervised machine learning, at least for the images, right? Work in that way that you have different classes. You have a training set, and you have a test set. And you take an image, you extract features from that image, and you use that feature for the classification. For example, you have this image of this flower here. You extract the petals, and then you calculate petal widths and heights, for example, and look at different flowers. You see that they differ in these features. So if you look at petal width of these different classes of flowers, you see that you can use that feature to discriminate these different classes, right? Classification performance, however, is then highly dependent on the feature extraction. So you have to be able to extract the features in the image, and you have to know which features to extract in order to make this classification work. Now, like seven years ago, the idea of convolutional neural networks has disrupted the field of computer vision, actually by the idea of making this feature extraction obsolete. Or making obsolete, but integrating it into your learning process, right? So these convolutional networks, they are based on the idea that the network itself learns the optimal features that you need in order to classify your problem. So it's not longer you who segments the objects, calculate features, but it's the network itself. And how is that done? So these convolutional neural networks have a couple of these layers, convolution layers, pooling layers, and so on. And the convolution layers basically are simple, right? You just take an image, and you just multiply part of that image with a filter. And here's my filter, 101, 010, 101. And with that filter, you move over the image, and you just multiply everything with the image content. And for example, you get a 4, right? And then you do it again, and you just move over the image with the filter. And you get a new image that is convolved with the filter you used, right? And of course, there are many filters. You can have an identity filter or an attitude filter, sharpening, or that is in our iPhones, I guess, right? You can use that and run over it. And you also have these nonlinear rectifying units here, which help you basically to learn. And then you have this pooling step where you say I now look at the image from a more cross-credent perspective. So in that part of the image, I only take the maximum, and also in the other parts. So I shrink my image size down. And if you now put all that together, you can say that the first part of these CNNs is the feature extraction. So in here, the network learns which filters it has to use in order to extract features from the image. And then the second part of the image is cluster classification, right? So you figure out what the feature is, and then at the end, you classify. Right, so we use exactly that structure for our problem, where we have patches, and we have the annotation if that patch will become either the one class or the other, right? GMP or MEP. And then we put that in. And then again, you have this feature extraction part here with the convolution max pooling layers. Here, the optimal features are learned that you need to extract features that allow you to classify your patches accordingly. So you take a training data set, and for each of these patches, then you get a patch lineage score, which tells you how much the network believe that this patch belongs to the one or the other class. Now, we also add displacement. That's just how much did the cell move in the time between the last image and the image I do now, so the speed of the cell basically. And all these patch features now we use. And since we have tracking and we have images every five minutes, you see that we have a lot of these patches for one cell, and we can just average over the lineage patches to get a cell cycle average lineage score. And while the patches are very noisy, you see this patch score for one cell that's relatively robust. So this allows us to put one score to a cell. So in that case here, this cell here gets a score of 0.7. And that means that our network believes that this cell is a GM cell and not a Maggie cell. All right, this average thing is one approach. The other approach is you can try to put that into a recurrent neural network and use the temporal information. We tried that as well, but it didn't give us much of an advance. Now, let's see what we get from it. This is all our data. These are all the experiments. These are the same trees I showed you before in the one color, but now also the other color. So not just the one branch, but also the other in there. And we use two experiments for training, and we test it on a third experiment. Actually, these experiments are quite diverse. I mean, they haven't taken different years from different PhD students in the lab. So there are variations in the lightning and how the cells are treated. And in order to do that, we make sure that we don't overtrain our model here. We do it in a round-drawer fashion. So we do it three times, and we get these true positive, false positive ratios. We calculate the area on the curve as a measure for the goodness of a prediction. And now we put in the end. So we train on the annotated cells, those that have the marker already, and then we test on the annotated cells in the third experiment. And you see that we get AOCs for these annotated cells above 0.8 mostly, and that's quite OK. But the more interesting thing is that if we now take a cell that hasn't turned on the marker yet, these latent cells, and we do the classification, we find that up to three generations before the marker comes up, we get similar AOCs. So we are able to predict the cell fate up to three generations before this marker is visible. And since these blood cells divide every 12 hours roughly, we can go 36 hours before the conventional markers come up to predict what the cells will be. Now, what can we do with it? Well, one idea would be to not do an experiment where you put the cells in culture and watch them differentiate, track them, and then come with the trees, but to stop the experiment in between when they haven't turned the marker on yet. And then do maybe a single cell RNA sec experiment where you profile the expression of each of these single cells, and then use our prediction to separate the cells into two classes, and then figure out which factors actually are differentially regulated at this early time point in the experiment. And that might tell you, if not pure, want to go to the Gada one, which other factors, which other factors are involved in this differentiation process. So Fabian Thais, who was initially invited here at the meeting, actually my boss, he would give a talk about single cell RNA sec because that's what he's doing all the time. You can imagine that if you do an experiment where you measure the mRNA expression in a bulk population of cells, million of cells, you get 20,000 data points, basically, which is expression for each of the genes we have. If you do it now in 10,000 single cells, you get a matrix of 10,000 by 20,000. And these matrices are faced with at the moment to make sense of it. It's a high dimensional problem. It's about a couple of gigabytes in the raw data. And Fabian and other people are developing methods to be able to make sense of this large data set, clustering the cells, finding trajectories in development processes, and basically what's he doing. Right. So the last part is clinical application of what I just showed you. And the idea here came when working together with clinicians in Munich who actually get blood samples of patients suffering from acute myelodochemia and diagnosing leukemia is still based on this morphological assessment of people who are trained to do so. So if you don't feel well, you've dropped a drop on blood and then this is smeared out on a glass slide. And cytologists look on that glass slide on the microscope and count cells in there. So if we're able to recognize single cells, it might be a nice application for algorithm to do that in a clinical setting. So these are the blood smears that are assessed by cytologists. And we took 100 of those blood smears from AML patients and then from individuals which do not suffer from AML. And we digitized these samples in a scanner, basically. And these guys are the red blood cells here. And we are more interested in the leukocytes. So the cytologists go through these leukocytes, count them and classify them into roughly 18 different cell types. And that's exactly what we did. So to get a draining set, we asked the cytologists, please mark 100 of these cells in each patient and classify them into eight different classes. And then the idea was to, again, train a CNN with it and see how it would perform there. So after scanning the stuff and after the cytologists doing the annotation, which is not that easy because they're busy with clinical routine, of course, we ended up with 18 thousand of these things leukocytes. And then we wondered, sorry, this is a scheme of these 18 different classes. So these 18 different classes, we asked the cytologists to put the cells in. You can put them in this kind of hierarchy. So here are the mature cells, the immature cells. Some of the immature cells are allowed to show up in your blood, but these blasts here, they shouldn't show up in your blood. If you recognize blast cells in your blood, then that's a clear sign of acute maloed leukemia. And now the task was to identify these blasts from the other cells. So that's what we asked our classifier to do. And if we train the classifier with these cells and then figure out how we can do it, you see that our sensitivity and specificity is pretty high, 99.2 area under the curve. It's just a number. It doesn't tell you much in order to get a better feeling of what that means, we asked a second cytologist to just do exactly the same what our computer did. So we showed the cytologists the same images of a test set that the computer got and do against classification into 18 different classes. And you see that the human cytologists performed roughly as good as our approach, which is, I guess, a good indication that this can be used in further applications in the clinics. One last thing you should do when applying these CNNs, you should check whether you learn real information or just crap. And one of the ways to do that is using salency maps, which tell you which of the pixels you have in the image are actually important for the final classification. And we did that here. And you see that for the monocytes, the computer considers those pixels inside the cell where the nucleus is as important, similar to what the cytologists think is important there. Same for the classes. OK, I showed you that image computing can distil numbers out of these images. I showed you that pure-born dynamics is inconsistent with the toggle-search model. And morphodynamics of single cells is predictive of Lynch's choice. Well, I skipped that. I want to thank the people involved, basically, who did the work, collaborators, my group at the moment, funding by the end. Thank you very much for your attention. Thank you very much for this presentation. So that's time for one minute full.
 Hi, everybody.  It's great to be here.  Thanks for the invitation.  I already enjoyed the mixed crowd of people here during lunch,  when we talked about brain research and also  the magnetic field of the sun, et cetera.  So I really enjoy this mix of topics and people.  It's great to be here.  So right, I'm from Munich.  So this is where I work.  It's the Helmholtz Center.  Munich is a research center for environmental health.  When I give a talk somewhere, I sometimes  start by saying, this is to the very north of Munich.  So it takes me quite a while to go there.  And then I sometimes say, as long as going  to the place where I am, this is certainly not true here today,  because it took me really quite a while to come here.  So from Munich, coming here, it's a travel.  Still, you should come to Munich, of course,  because it's worthwhile to go there and have a look.  So this is the Helmholtz Center.  It consists of roughly 30 different research entities.  It's quite diverse, from groundwater ecology to stem cell  research to computation biology, what we do.  We have roughly 2,000 employees, 700 scientists,  most of them PhDs.  The topic over there is the individual being dominated  by its genes, its lifestyle, and the environment.  So that's a topic or that's a theme people  can agree on, I guess, over there.  And we are part of the larger Helmholtz Association  with 21 centers all across Germany.  I guess you might know that.  So great to be here.  Great to have a look what the Leibniz Association is doing.  I'm really keen on discussing more with you guys.  So that's where I'm from.  In the Institute of Computational Biology,  we are roughly 50 employees at the moment, kind of growing.  We have 10 different research groups.  And my research group is concerned  with the dynamics of single cells.  And that's what I'm going to tell you.  By the way, we just started.  We will start now later this year something  which is called HIKU, the Helmholtz Association unit  for the Helmholtz Artificial Intelligence Coordination  Unit, where we try to spread out AI methods  to the whole Helmholtz community.  And we started also the science school,  a grad school for data science in order  to recruit more people doing that kind of research.  OK, now my talk starts.  What we do, as all of you do, is abstraction, basically.  We abstract complex systems to things  we can measure and understand.  And of course, that's what we call a model.  Now in biology, and I just continue  with what the two speakers before me introduced,  there are a couple of different models in biology.  For example, there might be this kind of network model  which we already saw.  This is a gene network.  Every dot is gene.  And they are connected.  Sorry, it's a disease network.  Every dot is a disease.  And two diseases are connected.  If a gene is associated with these diseases,  so this kind of model is obviously qualitative.  There's no dynamics.  It's static.  And it's large-scale because it covers all the diseases  we know.  We can have other models like that.  And actually, if you talk to biologists,  they call this a model.  Just drawing two proteins, interacting,  that's a model for biologists.  And you see two proteins here, a pure one and a gather one.  And the model is, basically, what you condense here  is all the experiments you did before.  It's the last figure in a paper.  And you also say, OK, these two proteins,  they can bind to each other at two particular protein sites.  And then they can do something.  Actually, they can inhibit the transcription of another gene.  All right, so this model is also qualitative, obviously.  It's also static.  But it's small-scale.  It just considers two transcription factors.  OK, just as a very short detail, I guess you know that.  But when I talk about transcription factors,  and the speakers before me also did write,  you know they are genes.  They are transcribed to messages.  And those are translated to proteins.  That's how genes are made of DNA.  Message is made of mRNA, right?  And the proteins are made of amino acids,  I guess you know that, right?  Some of these proteins called transcription factors  can now bind to the genome and regulate  the transcription of other genes.  OK, let's go over that.  So as a final model example here, now this  is something what we computationologists would  call a model, I guess, right?  So we have a rather complex system with 10 players, maybe.  Here you see, so the gray line is the outer rim of a cell.  And you see a receptor.  And things can bind to this receptor.  And the receptor can signal downstream into the cell.  And then things happen there.  And genes are activated or deactivated.  And this kind of idea we cast into models,  for example, an ordinary differential equation,  where you see the change of the concentration  of a receptor on the cell membrane, for example,  has a couple of elements that determine that, right?  And then you can fit even this kind of ODE to measurements.  And that's coming close to what we call a computational model.  You can also predict things.  And then this kind of model is quantitative, right?  You can write down numbers.  It's dynamic.  And it's a mesoscale because you can cover up  to 10 players with that.  All right, so that's some overview  over these different models.  If you talk to biologists, they also  call other things models, as I told you, right?  Little drawings.  But they also call species models, right?  So for example, E. coli is a model species for biologists.  It's a very simple bacterium.  It has no nucleus, right?  So you can do all kinds of genetic manipulations with it.  And it's a model because it's much simpler than more complex  mammalian cells, right?  Same with yeast.  Now, this has a nucleus, but still you can genetically  modify as much as you want.  And you can do experiments with it.  So it's a model system for maybe more complicated  animals like the fish, the new rarer,  zebrafish, also a model organism.  It's great because it's translucent.  You can watch it grow in the embryonic development.  And then, of course, the mouse is at our place in Munich.  And I mean, for drug research as well,  this is the most widely used model organism, right?  Because it's a mammal.  But you can do any kind of experiments with it.  OK, so that's what I'm going to talk about.  It's just that's basically the frame, right?  Where our models, our body model sit in.  So I'm going to talk about biological models now  in a more computational sense.  And I'm going to talk about single cells.  So this number is amazing, right?  We have 30 trillion human cells.  Every one of us is consisting of this number of cells  as we sit here.  And not just this number is amazing,  but it's also interesting to see that most of these cells,  we consist of our blood cells, actually.  And I mean, this 35 trillion are mostly red blood cells.  These are the little, tiny guys without a nucleus  running through our blood, right?  They transport oxygen.  And most of our cells are these guys.  And then that's an amazing number.  But even more amazing, I think, is that every day, each of us  produces 500 billion of these cells, right?  So we are not a static system, but we  are kind of a dynamic equilibrium, right?  We're reproducing ourselves every second.  Now, how is that done?  Well, the process is called hematopoiesis.  It's the production of blood.  And after hundreds of years of research,  that's basically the dogma people believe in for hematopoiesis.  So the idea is you have a hematopoietic stem cell.  And these guys, we roughly estimate  that we have between 200,000 and 1 million in our bodies.  They sit in our bone marrow, and they don't do much.  But they sometimes divide.  And then they give rise to a more differentiated cell,  for example, a short-term hematopoietic stem cell.  And then going down here towards the functional cells,  the do-really-things, the potential of these cells  decreases, right?  So if you are a megakaryocyte, erosive-cyte progenitor,  you won't be able to become a better cell.  But you are very close to becoming a red blood cell,  which is actually doing stuff in the body.  So you lose potency, and you go towards a functional cell,  going from the stem cell level over the progenitor cell  level to the functional cell level.  All right, let's zoom in a bit.  That's one thing we looked into a bit and let's zoom in a bit  even more.  So you have here a common myeloid progenitor, myeloid,  because these guys sit still in our bone marrow.  And this cell type is believed to produce two different  progenitor levels, which are more mature, right?  Either megakaryocyte erosive-cyte progenitor on the  left and grondulocyte monocyte progenitor on the right.  OK, so what do we know about this system?  Well, if you kick out this one transcription factor I  mentioned earlier, right?  Pew one in mice, of course, because there you can do the  experiments, right?  If you kick out Pew one in the genome of the mice, you  won't get any GMPs.  If you kick out Gata one, you won't get any MEPs.  So from these experiments, people concluded that these  two transcription factors, Pew one, Gata one, are probably  very important for this differentiation decision.  And then if you think about how such a CMP cell able to make  this decision, either to become a MEP or to become a GMP,  then these two transcription factors are  probably important.  And now, that's again what I showed you earlier, right?  From some other experiments, people figured out that Pew  one and Gata one can bind to each other and then inhibit  the expression of the other respective genes.  So that idea, together with the functional importance of  these two proteins, basically converged on the idea that  Pew one and Gata one are for the toggle switch.  And that's what I'm showing up there and over there.  So Gata one is inhibiting Pew one.  Pew one is inhibiting Gata one.  Then they might self-activate each other.  And this has been termed a toggle switch, right?  And you can think of it as they inhibit each other.  So if one gets a bit of an advantage, it inhibits the  other one and shuts it down.  And then you go towards the one lineage.  Or the other one has a bit of an advantage.  And then it shuts down the other one and you go to the  other lineage, right?  And this toggle switch, you can nicely model.  So you can write down an ODE where you say the change of  the one protein, X1, is determined by a self-activation  term.  And then you have a mutual inhibition term, right?  So you have the other guy down here.  The larger that is, the less increase of X1 you get.  And you also have a decay term because these proteins are  degraded over time.  And if you do that in a perfectly symmetric  matter for the two proteins and you simulate it or you look  at the solution of this ODE system, you find that if you  tune the parameters in the system appropriately, you see  that you have three stable states of the system, one in  the middle where both pure one and gutter one are expressed,  and then two other states where either the one or the other  is expressed.  And that's nice because it fits basically to our  biological intuition, right?  Or the idea we have of the system.  You can start with a state in the middle where both states  can be reached, but then you tune one of the parameters and  you either go to that or to the other direction.  So this model is a nice way to abstract or to describe what  we think, how these progenitors differentiate and  become more functional in such a  differentiation decision.  All right.  Now in 2000, oh, I didn't put it there.  Probably 10 years ago, Atom Rath and Coburcus showed that  mRNA is actually transcribed in bursts.  That means that the DNA which codes for the gene, this is  closed most of the time, but then sometimes it opens and  then many polymerases run over this gene stretch and produce  many RNAs at one time.  So we get a lot of mRNAs which sort of burst, and then the  gene shuts down again and it's closed.  And to describe that, actually, an ODE is not really  appropriate, right?  For that, you rather need a stochastic description of the  system.  And so we came up in the master's thesis at that point  and tried to just cast this toggle switch into a stochastic  formulation, and then you have to write down the equations  for the stochastic system.  Since it's too complicated to solve it, the only thing you  can do is simulating it and that we did.  And if you do that, you can also simulate a typical cell  trajectory, and then you find that if you start in the  middle in an undecided state, you see how such a  simulation gives you the one or the other state.  And actually, the tractor structure is a bit more  complicated as compared to the ODE case.  But you get the same thing, right?  Starting from one undecided state, you either go to the  one or the other direction.  All right.  Well, we did also another model where we considered more  players, but then we have 11 players and we can't model  that statistically.  So we used a Boolean framework here.  And it's not just us, many people, in particular, physicists,  like this idea of the toggle switch as a model for  differentiation decisions.  And many people simulated that because it's such a nice  system, right?  There's a biological relevance to it, and you can still  simulate and understand what's happening.  But over the years, when more and more of these models  appeared, it became clearer that while we can model it,  right, we haven't actually proven that this motion of  P1 and G1 is really decisive for this differentiation  decision in blood cells.  So actually, this question, you troubled our collaborator  at that time, Tim Schroeder.  Now he's at ETH, and he has a nice system to actually look  into the system.  And that's using time-lapse microscopy, so taking  microscope images every couple of minutes.  And then he also had a mouse, again, a model system, right?  A mouse where at the P1 locals in the genome, you had a  yellow fluorescent protein, and at the G1 locals, you had a  red fluorescent protein knocked into the genome.  So whenever this gene is transcribed, there's a tag to  this protein, which now lights up in yellow or red.  So you can watch the protein transcription over time, right?  So what Tim then did is breeding mice with these  constructs here, sorting out the hematopoietic stem cells  from the mice, putting them onto the microscope, and doing  time-lapse movies.  Because the idea was, well, let's watch these cells  differentiate, and then we're going to figure out if P1 and  G1 are really doing it.  OK, so that's the data, the bright field images, how they  look like.  We take images at every five minutes, and you see now how  the cells run around.  These are the stem cells.  And at some point, they grow and differentiate.  And we not just have these bright field images.  As I told you, we also have information about the yellow  fluorescent protein.  So this is tagged to P1.  So whenever we see yellow shining up, this is a marker  for P1 being expressed.  And then we also have Gata1 as a marker.  So we know how much Gata1 is in there.  It's a bit hard to see, I guess.  But we also have CD1632.  This is another marker.  And whenever we see this coming up in a cell, we know that  this cell has adopted the GM lineage.  You can't turn it back from there, right?  And then we also see this larger cell, probably a  megakaryocyte.  And you see that here in that cell, P1 is negative, but  Gata1 is positive, and CD1632 is also negative.  So that's basically the data set we have.  Bright field images every 10 minutes, then every half an  hour we do these fluorescent images.  And now in order to answer that question, if P1 and Gata1  are really decisive, our idea was to quantify protein  levels in single cells.  So we want to know in one particular cell how much P1, how  much Gata1 is in there.  And we want to watch that over time.  So we need to track the cells.  We have to follow single cells over time.  Now to come up with solutions for that, you have to do what  is now called bio-image informatics.  You have this data set, which is a movie, just a stack of  images.  And to distill numbers out of that, you have to apply a  couple of tools.  And if they are not around the right tools, you have to  develop them.  And actually, we thought that it might be easy to get the  numbers out of that, but it turned out that that's actually  a difficult part of it.  And it took us a couple of years and a couple of PhD  students to come up with solutions for that.  I'll cut that part short, I guess.  If you're interested in it, just let's talk afterwards.  So we came up with a solution for segmenting the single  cells in the movie, so identifying the single  cells in there.  Then Tim wrote an efficient software tool that allows it  to track the cells in the movie.  And that's actually not done by the computer, but  automatically.  So a student then follows the single cells over time.  And nowadays, there's better solution for that.  Single-segmented vacation.  So whenever you want to track the cells, we again do a  segmentation of the cell, which gives you this mask here.  And then we just sum up all the intensities in that mask.  We also wrote a tool that allows you to efficiently go  into the data set and figure out where the segmentation  fails and adapt it.  And then finally, in all these movies, we have a problem  because in all the images, we have more photons being  generated in the middle of the image for one photon you  put in as compared to the edges of the image.  So it's an uneven illumination.  And to correct for the shading effect, we came up with a  tool that estimates the background of these images  using the assumption that the background should be the same  in all these images.  And if we do that, we can make the images flat and compare  cells all over the image.  Putting all that together, we were at the end able to track  the single cell, as you see.  And then once the cell divides, you track the sister of  that cell, and then again the sisters.  And then at some point, CD1632 is coming up in the  fluorescent channel of these images.  And the guy who's tracking that annotates that and says,  OK, now the red cell from this time point on, we know that  this is a GM.  All right.  So what we got after applying all these tools to our data  is these kind of trees.  Now, time on the x-axis, and you see that there's a model  cell dividing sisters, sisters, and so on and so on.  At some point, you might lose the cell because it's running  out of the image.  Some cells might just die.  And then at some point, you're not able to track any  further because it's so dense and you can't figure out,  from one time put to the next, which cell is which.  OK, having that, we also have the information about how much  pure one and gather one is in the cells.  For example, now I've got only one cell here.  In that cell, gather one is rising, pure one is rising.  Then at some point, the cell divides, and you get half the  amount of pure one and gather one in the sister cell.  And then this is rising again, and so on and so on.  And we did that for roughly 80 trees and  different experiments.  And we had these trees.  And then, again, we wanted to answer this question, right?  Is pure one and gather one decisive for the niche choice?  And if you look at that trees, even many of them, and for  a long time, you realize that just looking at the trees  doesn't help you to answer this question, because you don't  really know where to look at, right?  The data structure is complicated, because you  have these trees in there.  You have a lot of noise in it, in the measurements, but maybe  also in the process of trees transcription, as I told you,  right?  And then you also have the cell cycle, right?  That always the proteins half at each time, the cells  divide in the sisters.  So just by looking at the trees, it's really not able to  answer this question, I guess.  So our idea was to, from these trees, figure out where the  decision for a particular differentiation step occurs.  And then once we know where it happens, we can look into that  time point and compare it with the mutual inhibition model  and figure out if that model is actually true.  OK, so the second part of this talk is called  retrospective inference of the choice, because from the  trees, we want to figure out where the decisions happens.  Now, how can we be that done?  Let me use a little analogy.  So this is time.  This is my group in July 2015.  That guy over there, over next to me is Michi Schlasser, the  guy who implemented that stuff I'm going to show you.  Michi went for a postdoc to Seattle.  And now, if I would see him in Seattle, so in the part of  stem cell decisions, you could say he's making a state  change, right, from the ICB where he worked before to the  ISB, where he works now in Seattle.  So if you would see him at ICB in 2017, you would not be  able to figure out when he made the decision to go there.  Could have been two years ago, four years ago.  We don't know.  But if Michi would divide at the cells in our movies do, and  you would have a decision before the division of him, then  you would expect that he shows up in Seattle at  correlated time points.  There might be a bit back and forth in the middle, but he  would show up at the same time points if the decision happens  after the division, but then you have uncorrelated time  points of him popping up in Seattle.  So the idea is to use the tree structure to figure out where  the decision for a particular event happens.  And of course, in our case, the idea comes from looking at  the trees, because if you look at this marker, CT 1632, which  is the marker for the one particular limit, you see that  it is coming up in a kind of correlated fashion.  It's not all over the place.  It's not somewhere there and somewhere there.  So it's mostly happening here in the force and fist  generation.  And that's a pattern we see in all the trees.  So the idea is to model this differentiation process.  And we basically have two steps in here.  The one is we call it a point process, right?  We just say at one time point, the set just  decides to differentiate.  And then this probability to differentiate might be constant  or we allow it to be a function of time in a function.  And then once the decision has been made, we say we start  a stochastic gene expression process.  And then at some point, we hit the limit, the marker, where  the marker can be detected in the movies.  And that's basically the expression of the marker  as we see the experiments.  So let's visualize it here with a tree.  So this cell here decides to differentiate.  And then this process starts, a stochastic gene  expression process.  And at some point, you hit the detection limit.  And then you say, OK, here this marker turns on the 1632  marker and then the other cell a bit later.  And this happens in the system as well.  And again, it takes a while.  So you have a differentiation process and you have a delay  process.  And these two things are parameterized with a number  of parameters in our model.  Now, we have this model and we have parameters in there.  Let's call it theta and eta.  And we want to figure out what these parameters are.  So let's first test if we can figure them out in a simulated  test case.  So what we do is we simulate trees, which look exactly or  which look a lot like the data we have.  And if you simulate it, we know, of course, when the  differentiation happens and how long the delay is and when  the marker comes up.  And then we forget about this delay and just see the marker  as we do in the experiments.  And now we wonder, from a number of these simulated  trees, can we infer back these parameters of the model?  And we tried that.  And for that, we need the likelihood, so the likelihood  of observing a particular set of trees given these two  parameters.  And the way we set it up, it's a sum over, well, first, if  you have this observed tree, there are many different  possibilities how this can come apart.  You can have an early decision and a long delay, or you can  have a late decision with a short delay.  And the length of these things are determined by the  parameters of the model.  And then each of these hidden trees, we now decompose into  a couple of subtrees, which we can easily model.  And we use a graphical model representation for these  subtrees to figure out what's the most likely parameter for  a given length of delay, for example, and correlation of  two sisters.  Now we put that all in in our likelihood function and fit  data with it.  And first, we simulated this to make sure that the algorithm  works.  We find that from simulated data, we can infer back the  right parameters.  And then we apply to the real data.  And actually, that's the data we used here.  So you see this is all the trees that make this GM  lineage, so the one part of the two lynches.  And you see that the data is quite homogeneous.  And that comes just from the fact that the biologists who  tracked it, they sometimes tracked the whole tree because  they didn't know what's happening there.  Sometimes they only tracked one single cell.  But the nice thing is that we can put that all into our  likelihood estimation.  Because also that here will give you some information  about how long the processes are.  So we put that in.  Let's zoom in here.  Let's couple of those trees we observed.  And then we figure out for each of the trees what are the  most likely parameters.  And then from that, what is the most likely time point of  differentiation.  And this I show you now here.  So the step from black to gray, that's the time point  where we believe the decision has been made.  And what you realize is that our algorithm comes up with  relatively long delays.  So from the time point of differentiation to the  Markov onset, it takes five to six generations in all  these trees.  Now what we can do now is look in what's happening there in  our real data.  So we go a long time.  And now we pick one of these branches.  And now we look at the pure one dynamics.  So the one of these two-trips effectors, we check what's  going on in there.  And that's how, again, such a time course looks.  So you see that pure one intensity rises is half  rises is half, and so on and so on.  At some point the marker comes up.  And this point over there, this is our predicted  differentiation.  This is when our algorithm believes that the  differentiation has been made from the correlation  structure in the trees.  Right.  We divide the intensity by the area to get a bit of a smooth  curve here.  And then we fit each of four, for each single cell, we fit  these concentrations with a straight line, which is roughly  an estimate for the production of pure one in that single  cell.  And then we can plot this slope of the linear fit, which is  production of pure one, basically.  And we can plot it for the cell where we believe that the  decision has been made.  This is generation zero, we call it.  And we compare that to one duration before and one  duration after.  And we also compare it to the generation where CD 1632 is  definitely there.  And what you can see is that pure one production does not  change at this time point where we think that the  decision has been made.  And actually, if you look at the model, you would expect  that when this toggle switch tilts and pure one is winning  over a garter one, then at that time point, pure one  shoots off.  So from looking at it, we thought, well, that's not  what you would expect from the model.  But of course, it's not enough to reject the model.  However, we thought what we can do now to really reject the  model is just taking this toggle switch model,  implementing it, simulating it, exactly the same number of  trees we had in the experiment, and then checking what we  get from it.  So we simulate trees here with the parameters we inferred.  And then from all these trees, we look again at these  time points where we think that the friction happens.  Actually, in that model, we don't know where the decision  happens because in this toggle switch thing, it's a delicate  balance between the two factors.  At some point, it tilts.  But where exactly the decision happens in their tilting  process, you don't know.  So we also infer for those trees where we believe the  decision happens.  And then we look again how pure one is developing there.  And for these simulations, you see that at the time point  where our algorithm thinks the decision happens, there  you see indeed a significant increase of pure one  production from a level which is around zero to a higher  state.  So in the model where the balance tilts, pure one is  highly produced, in the data we don't see that.  And this leads us to the conclusion that the pure one  dynamic we see in this thing that says is inconsistent  with the mutual ambition of Lynch choice.  So now you could say, well, this is quite some effort for  rejecting a model.  But as you know, that's all we can do.  Or that's the best we can do.  We can reject models and say, no, this does not fit to the  data we have.  And basically, that's what we did here.  OK.  Now, the third part of this story is now questions to  that, actually.  Interrupt me whenever I make myself clear.  So this was the reconstruction of the decision time point.  Now that we know that the decision happens before the  marker comes up, the question is, can we predict the fate of  a cell before this marker is actually visible?  Because we know that decision should happen four, five,  six generations before.  Maybe we can predict what's happening.  And the idea is, well, what do we have?  We have the morphology of the cells, and we have the speed  of the cells, because we watched them in these bright  field three minute intervals.  So again, we have to identify the cells in these bright  field channel.  And then let's apply some machine learning again, as the  speaker before me did, because that might help us to  predict what the cell will come.  I guess our problem is a bit easier than your clinical  problem with treatments and fine results.  So I hope there are no glitches in there.  Stinger certification.  So that project was done by Felix and Flo.  And I showed you before that, I guess, the Stinger  certification in bright field.  We adapted to that, and it works so we can identify  these single cells over time.  And then once we have that, we can cut them out.  And we get these little patches of single cells.  And since we have many of these cells, and we have a high  time resolution, we have roughly 2 million of these  patches, and now you can think that 2 million, that's a  high number.  Let's train a machine learning model with it.  That should work.  So supervised machine learning, before I come to that.  So you see, now, you can order them along the track  points, right?  So you can follow the single cells in bright field.  And you see that they are a little bit smallish at the  beginning, and that they grow a bit.  And you see, if you look at the cell size, that the cell  grow, divide, grow, divide, grow, divide.  And again, again, at some point, now, they turn on the CD62.  And you see that this mark comes up.  So at that time point here, we know that this cell is a GM,  and we call these cells annotated.  And all the cells before, we know that they will turn on  the mark at some point, but they haven't yet, so we call  them latent.  OK, supervised machine learning.  Well, we use a convolutional neural network to that.  And since this hasn't been introduced before, maybe I do  that briefly.  So I mean, we all agree, I guess, that they are  mathematical or mechanistic models and statistic models,  statistical models.  So the CNNs are surely on that side, right?  So a very short introduction to supervised machine learning.  I hope I don't bore you.  Supervised machine learning, at least for the images, right?  Work in that way that you have different classes.  You have a training set, and you have a test set.  And you take an image, you extract features from that  image, and you use that feature for the classification.  For example, you have this image of this flower here.  You extract the petals, and then you calculate petal widths  and heights, for example, and look at different flowers.  You see that they differ in these features.  So if you look at petal width of these different  classes of flowers, you see that you can use that feature  to discriminate these different classes, right?  Classification performance, however, is then highly  dependent on the feature extraction.  So you have to be able to extract the features in the  image, and you have to know which features to extract in  order to make this classification work.  Now, like seven years ago, the idea of convolutional neural  networks has disrupted the field of computer vision,  actually by the idea of making this feature extraction  obsolete.  Or making obsolete, but integrating it into your  learning process, right?  So these convolutional networks, they are based on the idea  that the network itself learns the optimal features that you  need in order to classify your problem.  So it's not longer you who segments the objects,  calculate features, but it's the network itself.  And how is that done?  So these convolutional neural networks have a couple of  these layers, convolution layers, pooling layers, and so  on.  And the convolution layers basically are simple, right?  You just take an image, and you just multiply part of that  image with a filter.  And here's my filter, 101, 010, 101.  And with that filter, you move over the image, and you just  multiply everything with the image content.  And for example, you get a 4, right?  And then you do it again, and you just move over the image  with the filter.  And you get a new image that is convolved with the filter  you used, right?  And of course, there are many filters.  You can have an identity filter or an attitude filter,  sharpening, or that is in our iPhones, I guess, right?  You can use that and run over it.  And you also have these nonlinear rectifying units  here, which help you basically to learn.  And then you have this pooling step where you say I now look  at the image from a more cross-credent perspective.  So in that part of the image, I only take the maximum, and  also in the other parts.  So I shrink my image size down.  And if you now put all that together, you can say that the  first part of these CNNs is the feature extraction.  So in here, the network learns which filters it has to use  in order to extract features from the image.  And then the second part of the image is  cluster classification, right?  So you figure out what the feature is, and then at the  end, you classify.  Right, so we use exactly that structure for our problem,  where we have patches, and we have the annotation if that  patch will become either the one class or the other, right?  GMP or MEP.  And then we put that in.  And then again, you have this feature extraction part here  with the convolution max pooling layers.  Here, the optimal features are learned that you need to  extract features that allow you to classify your  patches accordingly.  So you take a training data set, and for each of these  patches, then you get a patch lineage score, which tells  you how much the network believe that this patch belongs  to the one or the other class.  Now, we also add displacement.  That's just how much did the cell move in the time between  the last image and the image I do now, so the speed of the  cell basically.  And all these patch features now we use.  And since we have tracking and we have images every five  minutes, you see that we have a lot of these patches for one  cell, and we can just average over the lineage patches to  get a cell cycle average lineage score.  And while the patches are very noisy, you see this patch  score for one cell that's relatively robust.  So this allows us to put one score to a cell.  So in that case here, this cell here gets a score of 0.7.  And that means that our network believes that this cell is a  GM cell and not a Maggie cell.  All right, this average thing is one approach.  The other approach is you can try to put that into a  recurrent neural network and use the temporal information.  We tried that as well, but it didn't give us much of an  advance.  Now, let's see what we get from it.  This is all our data.  These are all the experiments.  These are the same trees I showed you before in the one  color, but now also the other color.  So not just the one branch, but also the other in there.  And we use two experiments for training, and we test it on  a third experiment.  Actually, these experiments are quite diverse.  I mean, they haven't taken different years from different  PhD students in the lab.  So there are variations in the lightning and how the cells  are treated.  And in order to do that, we make sure that we don't  overtrain our model here.  We do it in a round-drawer fashion.  So we do it three times, and we get these true positive,  false positive ratios.  We calculate the area on the curve as a measure for the  goodness of a prediction.  And now we put in the end.  So we train on the annotated cells, those that have the  marker already, and then we test on the annotated cells in  the third experiment.  And you see that we get AOCs for these annotated cells  above 0.8 mostly, and that's quite OK.  But the more interesting thing is that if we now take a cell  that hasn't turned on the marker yet, these latent cells,  and we do the classification, we find that up to three  generations before the marker comes up, we get similar AOCs.  So we are able to predict the cell fate up to three  generations before this marker is visible.  And since these blood cells divide every 12 hours roughly,  we can go 36 hours before the conventional markers come up  to predict what the cells will be.  Now, what can we do with it?  Well, one idea would be to not do an experiment where you  put the cells in culture and watch them differentiate,  track them, and then come with the trees, but to stop the  experiment in between when they haven't turned the marker  on yet.  And then do maybe a single cell RNA sec experiment where you  profile the expression of each of these single cells, and then  use our prediction to separate the cells into two classes,  and then figure out which factors actually are  differentially regulated at this early time point in the  experiment.  And that might tell you, if not pure, want to go to the  Gada one, which other factors, which other factors are  involved in this differentiation process.  So Fabian Thais, who was initially invited here at the  meeting, actually my boss, he would give a talk about single  cell RNA sec because that's what he's doing all the time.  You can imagine that if you do an experiment where you measure  the mRNA expression in a bulk population of cells, million  of cells, you get 20,000 data points, basically, which is  expression for each of the genes we have.  If you do it now in 10,000 single cells, you get a  matrix of 10,000 by 20,000.  And these matrices are faced with at the moment to make sense  of it.  It's a high dimensional problem.  It's about a couple of gigabytes in the raw data.  And Fabian and other people are developing methods to be able  to make sense of this large data set, clustering the cells,  finding trajectories in development processes, and  basically what's he doing.  Right.  So the last part is clinical application of what I just  showed you.  And the idea here came when working together with  clinicians in Munich who actually get blood samples of  patients suffering from acute myelodochemia and diagnosing  leukemia is still based on this morphological assessment of  people who are trained to do so.  So if you don't feel well, you've dropped a drop on blood  and then this is smeared out on a glass slide.  And cytologists look on that glass slide on the microscope  and count cells in there.  So if we're able to recognize single cells, it might be a  nice application for algorithm to do that in a clinical  setting.  So these are the blood smears that are assessed by  cytologists.  And we took 100 of those blood smears from AML patients and  then from individuals which do not suffer from AML.  And we digitized these samples in a scanner, basically.  And these guys are the red blood cells here.  And we are more interested in the leukocytes.  So the cytologists go through these leukocytes, count them  and classify them into roughly 18 different cell types.  And that's exactly what we did.  So to get a draining set, we asked the cytologists, please  mark 100 of these cells in each patient and classify them  into eight different classes.  And then the idea was to, again, train a CNN with it and  see how it would perform there.  So after scanning the stuff and after the cytologists doing  the annotation, which is not that easy because they're  busy with clinical routine, of course, we ended up with 18  thousand of these things leukocytes.  And then we wondered, sorry, this is a scheme of these  18 different classes.  So these 18 different classes, we asked the cytologists to  put the cells in.  You can put them in this kind of hierarchy.  So here are the mature cells, the immature cells.  Some of the immature cells are allowed to show up in your  blood, but these blasts here, they shouldn't show up in your  blood.  If you recognize blast cells in your blood, then that's a  clear sign of acute maloed leukemia.  And now the task was to identify these blasts from  the other cells.  So that's what we asked our classifier to do.  And if we train the classifier with these cells and  then figure out how we can do it, you see that our sensitivity  and specificity is pretty high, 99.2  area under the curve.  It's just a number.  It doesn't tell you much in order to get a better feeling  of what that means, we asked a second cytologist to just do  exactly the same what our computer did.  So we showed the cytologists the same images of a test set  that the computer got and do against classification into  18 different classes.  And you see that the human cytologists performed roughly  as good as our approach, which is, I guess, a good  indication that this can be used in further  applications in the clinics.  One last thing you should do when applying these CNNs, you  should check whether you learn real information or just crap.  And one of the ways to do that is using salency maps, which  tell you which of the pixels you have in the image are  actually important for the final classification.  And we did that here.  And you see that for the monocytes, the computer  considers those pixels inside the cell where the nucleus is  as important, similar to what the cytologists think is  important there.  Same for the classes.  OK, I showed you that image computing can distil numbers  out of these images.  I showed you that pure-born dynamics is inconsistent with  the toggle-search model.  And morphodynamics of single cells is  predictive of Lynch's choice.  Well, I skipped that.  I want to thank the people involved, basically, who did  the work, collaborators, my group at the moment, funding  by the end.  Thank you very much for your attention.  Thank you very much for this presentation.  So that's time for one minute full.
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