 OK, thank you. Right, so I'd like to continue discussing the segmentation clock. And I wanted to also just have a tiny prelude today by saying how amazing it is how many people from all over the world are here. So I think I heard that people from 44 different countries are here. Is that right? 34. 34. That's amazing. So I just want to reach out to fellow Australians out there. Is there anyone? OK. OK, not so unusual. Good, OK. Segmentation clock. Today, so yesterday we talked about the idea of having a genetic oscillator in a single cell. In fact, the idea that those oscillators might be autonomous, and we deliberately ignored questions about what would happen if those oscillators could talk to each other, or what would happen if they were organized into larger structures. And today, I want to talk about this what I would call tier two, which is the idea that the cells can talk to local neighbors and share information about their phase. So I'm going to give you a quick reintroduction to the general phenomenology. We're going to talk about synchronization. I'm going to talk about the role of an intercellular signaling system called delta-notch signaling in synchronization. Then I'm going to talk about what happens if there are delays between the oscillators when they try and share timing information. And then that will bring us to some period mutants. And just to give you a look ahead, this idea is that control of the period of the system can be exerted at the level above a single cell in the collective. So that idea will appear today for the first time, and then finish with some open questions. So now just to remind you about the general topic, which is the segmentation of the vertebrate body, is an adult zebrafish? And is there anyone who didn't see the talk last night? OK, fine. So we can just highlight the key points here then, which are that the body segments of vertebrate arise during embryogenesis. And they do so in the mesoderm by budding from, they're called somites initially. These segments have formed several hundred cells. And they bud off rhythmically and sequentially from the tissue in the posterior, which we term the pre-semitic mesoderm or the tail bud. And so we're interested in this, this rhythmicity and the spatial scale that's constructed along the axis. So we're still focusing on rhythmicity today, the timing. So when we focus on that timing, we noticed that the period with which the segments form is very reliable in the trunk of the animal. This is one embryo. And here's a population of 15, which I mentioned yesterday. And this is the mean and the standard deviation of the segment formation time through the trunk. So this is kind of important. This precision is important tonight. Remember, yesterday we noted how imprecise the individual oscillators were, how noisy they were. I'm going to come back to this. OK, and then we also talked about the idea of the general idea of using some sort of clock to measure out space in an embryo. And the idea there was this general sort of collection of models really called the segmentation clock and the general mechanism consisting of a clock, some population of phase-coordinated cells, which are illustrated here by these little squares. The idea of phase being the angle on the hand of a clock as it describes each revolution. And then a wave front, which was the idea that the oscillators can be read out or arrested or read out at some point. And their timing information can be coupled to the movement of the wave front to yield a periodic pattern, which you can see here. So I mentioned that this model we call the infinite snake because the cells are being added continuously here. The wave front's moving at the same velocity to the end of the tissue. And nothing else is changing. I mean, the system is oscillating, but there's no other time-dependent change in the system. And that's important for everything I say today that we're talking about some sort of steady state situation. Tomorrow I want to go to what happens when the system comes out of steady state. But for today, things are at steady state. And so this tells us that the segment length is given by the velocity of the wave front and the period of the clock, which made these predictions about the segment length along the axis and the number of segments that an animal would form using this kind of mechanism. So hopefully this is all familiar to you. Now in a real vertebrate, such as the zebrafish, the segmentation clock looks something like this. We're tracking this with two trans genes. And again, this green trans gene is going to feature a lot tonight. And these waves of gene transcription that are sweeping through the pre-semitic mesoderm, the waves is tomorrow. But just to note that in order to get a wave, you have to have some sort of coherence, at least at the local level, otherwise that would give you salt and pepper patterns, sort of Christmas tree blinking on and off. The fact that you can see waves means that the cells have to be locally coordinated, and that's the topic. And then just to say that the coherence of these waves is notable. And you see that the waves, when they arrive in the anterior, they're sweeping from the posterior to the anterior. And when they arrive in the anterior, their arrival marks the timing and position of each of the newly formed segment boundaries. We zoom in. And now looking at a, with single cell resolution at the nuclei in the tissue, remembering that the transgene we're looking at is a fusion between a YFP and one of the endogenous transcription factors in this clock. And so what we see is the protein entering the nucleus becoming fluorescent. So essentially, each nucleus becomes fluorescent. And then the protein is destroyed in the nucleus. So the nucleus becomes dark again. And from here, I think I hope you can see that the waves of signals, gene expressions, sweeping across the tissue. And again, noticing that there's some, I think you can see here that there's some cell-to-cell amplitude difference, but that locally the cells appear to be all switching on at the same time and all switching off at the same time when we examine locally. So then we had a sort of slightly humorous model of the segmentation clock using this signal display, asking questions about why an individual pixel would turn on and off, asking questions about why neighboring pixels would be correlated, and finally, which is tonight. And then the final question is, what gives rise to the global pattern and what might it do? So that's tomorrow. So good. So let's focus our attention now at this level of local synchronization between two cells. And we can motivate that then returning again to say, we've got this coherent activity in the tissue. But the individual cells we looked at yesterday were highly noisy. Their periods varied from each other. And their periods even fluctuated within a cell trace. And so what do you do if you want to coordinate a bunch of noisy oscillators? There's a very old concept called synchronization. And that's one of the major topics tonight. So synchronization sets an old idea because it was first described, I suppose, in what we'd recognize as its current form by Christian Hogan's, who was hanging out in the 1600s. And he was an instrument maker of some repute. He made clocks. And he made lenses and microscopes. And so he's famous here because of his clocks. And what he noticed at the time, he was trying to build a precise pendulum clock. And some people credit him with the invention of the pendulum clock. And it's actually very difficult to build a mechanical clock that's precise because parts wear and it's difficult to make all the parts fit each other properly. And actually, as temperature changes, the parts of the clock expand at different rates. And so it's really difficult to make a temperature compensated mechanical clock. And at the time, Hogan's and lots of others were trying to build a very precise clock to be able to measure longitude, to be able to sail around the world. You can sail north and south on the globe by looking quite simply, wherever you are, just by looking at the angle that the sun gives above the horizon when it's rich as its peak. And that'll give you exactly your degrees up from the equator. It's more difficult to know how far east or west you've gone. And the trick that they were trying to use here was to know the time in your home port. And then with this reference clock every day, measure the angle of the sun in the sky at the reference time of noon. And the difference would give you your degrees around the world. Now, if your clock's not very accurate, then you can be hundreds of kilometers away from where you think you are in the ocean. And if your clock's steadily gaining or steadily losing time, the further you sail, the worse it gets. And so lots of people being killed. The governments of Europe at the time don't think, I don't think they really cared about that. We look at everything else that was going on in Europe at the time, but what they did care about was the enormous loss of trade goods. And so there was a major initiative to build better clocks. So in fact, the reason why I'm telling you that long story is because that's the reason that these two clocks are hanging from a beam. Because if you take a pendulum clock on a boat and the boat's rocking, then the pendulum's swinging, but the gravitational direction's changing on the clock the whole time. So if you can swing the clock from a beam to first approximation, the clock stays pointing at the center of the earth while the boat rocks. OK, so Huygens built these two clocks in his lab and they were isolated in the sense that they were on different benches. And he knew that they didn't tick with the same frequency and he knew, he quite accurately described what they did. When he hung them on this beam to prepare them for sea, he found that they synchronized. And what happened was the pendulum moved into anti-phase synchronization like this. And he also found that they now ticked with a common rhythm and that was much more precise than it was before. So this was extremely exciting to him. He wrote it up in a letter to his father and he called it the sympathy of two clocks. Now that was scientific publication in the 1600s. You just write to your dad. But his dad saw what was coming and he rejected it. Needed major revisions, clearly. So actually the major revisions that were necessary took quite a few centuries to come because it was only, I think, was only a couple of years ago. I mean, you can see demonstrations of this phenomenon on the metronome sitting on the coat cans. I don't know if you've seen this. Look this up on YouTube. It's really dramatic. But actually building a scale pendulum clock like Hogan's built has only been done two years ago by a group of engineers. So okay, so that did take some time to verify. Okay, that's the joke. And so now let's go back to the science. And so you could sort of illustrate this in some way by saying that coupling between oscillators will set a collective period. It will synchronize them to the same period. It will move them into some finite phase arrangement. It could be anti-phase or it could be in phase, but the phase between the two oscillators is not gonna keep growing. And so you could take a population of oscillators with different frequencies and once they couple, they'll all line up and actually they perform an averaging and the period they'll pick is actually the average of the distribution. So there's some very, very important theoretical results on this by Kuramoto, for example. And so this sort of phenomenon is seen in chemical systems, in physical systems, in engineering, biological systems, the synchronization of the fireflies that you saw before is a good example. So in this case, you take two fireflies, you isolate them from each other and you see that they tick with different frequencies. You put them together and now they'll synchronize and they'll average their frequencies and tick together. Okay, so that's the general phenomenon. And currently we believe that there is active synchronization, so what I should say, what's really important here is that synchronization in the sense that I'm going to use has a relatively strict definition, which is that the two clocks ought to be autonomous and they can share signals, they can mutually signal. Well what I'm not talking about is a very strong forcing influence from an external source that drives a slave clock. It's really, we need two oscillators that are gonna talk to each other with a weak influence. And I guess in that pendulum clock, the weak influence was the vibration running up across the mount and back in and pushing the escapement to go a bit early. So that's the sense of synchronization that I'm gonna use. This is a sort of mutual entrainment, if you like, of two clocks. So. What's the strength of carbon versus how long do you think it's gonna stay? I mean, does it, when I've seen all these individual, you put them on the clock and it is striking, but it takes few bits, depending on how hard of a place they are, but it takes few bits. But you would think, really, in biology, they don't, then I wanna synchronize them very quickly. So I thought I was just wondering, how does carbon work up? Do you think you can start a million out of things? Do you think one or two times actually? This depends on all sorts of factors. I guess you can, depending on the model, you choose for the coupling, you can work it out, I suppose. Here I don't really know. I have to say I don't actually know the answer in this case. What I'll show you in a second is how long it takes the system to desynchronize, and it seems like it takes the system about the same amount of time to re-synchronize, but that's in the bulk. And so we don't really know the oscillator-to-oscillator coupling strength, which would be expressed in a rate. It's the rate at which two clocks can pull themselves towards each other. But I would say that in this system, it looks like the coupling strength is actually quite weak, and it's probably an order of magnitude smaller than the other timescales in the system. That give you some estimate, but seems to be okay for the fish. That's enough. Actually, I mean, from theoretical results, and this is not my main thing, but the, like Kuramoto, for example, showed that infinitesimally small coupling strength will eventually bring oscillators into synchronization. So it does depend on how long you've got to wait. In that case, it also depends on your starting condition. If you start synchronized, maybe all you need a little tap to keep you synchronized. If you start with random phase, you maybe need a push to get you all into gear. The fish starts in phase. So okay, so this is what we think is happening in the zebrafish. Imagine each of these black circles is one of the noisy autonomous oscillators that we talked about yesterday. So the delta-notch signaling system is a set of proteins that can send a signal from one cell to another. There's a delta on the surface. It needs to be transcribed and translated. It's inserted into the membrane, and then it can bind to a receptor called notch, which is in green here, and binding on that receptor pulls it and triggers a set of proteolytic cleavages which releases its cytoplasmic domain to go to the nucleus. And now the cytoplasmic domain kind of acts like a transcription factor, actually, and goes down and it can influence the activity of target genes and change their transcription. So I'm just gonna give you the cartoon view. There's a whole industry of scientists out there studying all of the different aspects of this signaling. And so one other thing to say is that, well, I'm gonna talk about, I'll use this drug today called DAPT, which can block the cleavage. And it's a very effective way of stopping delta-notch signaling. It will diffuse into all sorts of creatures. So, yeah. Sorry to say again. Selae will, I didn't understand the question. Sorry, may I, can you say that again? Ah, no, they're both, so they're both oscillating. Neither of them are inactive. You're asking whether they're active in inactive states. Okay, so, yeah. So, in the model, in this description, both cells are continuously oscillating. And if you have a look at this pattern here, this is now the tissue level pattern of the expression of this gene, the delta, the signal. So can I animate this? And you'll see what we think, you'll see what the pattern of the activation of this gene is in the tissue. So you remember we saw those waves sweeping through the tissue before, which is indication of the oscillators. So, each time this cell goes through one cycle, it puts delta on its surface and then pulls it off again. So, so there's a pulse of delta on the surface of the cell and then it goes away again. We think that the cells continuously have notch and they have more notch than they need. So we're not short of notch but we're limiting for delta and each cell puts delta on its surface and pulls it back again. Did that answer your question? Okay, yep. The survival of the patient at the point you've come before being a patient of nature, but how is that? The dissipative of the other, of the other. I can't answer that, I actually don't know. Yeah, I mean the whole, is this in a, this is in a, something like harmonic oscillators? Yeah. Okay. Yeah, that's a good question. I have no idea. I mean, all of these cells are massively dissipative. They could be leaking, yeah, okay. So these, right. So these things are massively dissipative and I don't know how, I have no idea how they would be leaking the other modes but I think leakage would be the least of our worries. It'd be leaking going on all over the place, but it's good. So, okay, so what we, what we have are the cells exchanging information and if you look at the, if you look at the stripe thing here, what you have is cells that appear to be mutually signaling each other. So cells are saying, okay, I'm at this phase in my oscillation, I put delta on my surface and the neighboring cell receives a signal and adjusts the gene expression cycle that it has in its own cell. So that's the model that we have at the moment and I want to show you some of the evidence for this model now. This of course is in cartoon form. So the first thing to say is when we add the APT or when we mutate any of the delta notched genes, we see a similar phenotype. The fish begins by making what look like normal segments. They seem to be well formed and after some time there is a failure to segment properly and the segmental borders become very disorganized and even though this compound or the mutant was acting at the beginning. So we have independent reason to think that delta notched signaling is being blocked from the very beginning but it takes some time to see this defect. When we look at the organizational pattern of the gene expression in the tissue when the first segment is being made, what I hope you can see here is that we have organized waves in these are two different examples of animals that are making their first segments. So it seems like the system is well synchronized even from the beginning even in the presence of delta notched even in the presence of this inhibitor. So the system doesn't need delta notched signaling in order to start in a synchronized state. So that's a fact but what happens is over time is the system becomes more and more desynchronized. So by the time the fish is making 12 segments which is about here, you can see that the pattern has gone from these well synchronized stripes into a kind of a salt and peppery pattern of gene expression that's scattered along the tissue and by comparison, this is what that tissue would look like at the same stage when we don't add the notch blocker. So no delta notched signaling, normal delta notched signaling. So what's going on here? Well, it could be that these oscillators are continuing to cycle and they've been desynchronized but it could be lots of other outcomes. One thing one can do, a very simple experiment is to cause the animal to desynchronize and then wash out the DAPT. So this has advantage in a mutant, it's very difficult to bring the mutant gene back but with this drug we can wash it out and this is what happens. The animal undergoes this sort of decay. It makes defective segment boundaries then we wash out and then there's a recovery phase. So it was washed out here and it takes some time until we get good segments again and when we look at the tissue organization at this point you can see that the embryos have got their stripe pattern back. So this is consistent with the idea that there's a longer term process, a desynchronization process then at some point that wave has become so disorganized it can no longer be used to build a boundary. We wash out, now the oscillators might start to synchronize with each other and they gradually gain coherence and then at some point they're now coherent enough to rebuild a stripe. So this is consistent with this but what we need to do is we need to actually look at the oscillators and that's what I want to talk to you next, yeah. So okay so let me try and say that again. We added DAPT in these experiments before actually a long time before the first segment was formed. Actually right back at the stages that Carl Phillip was talking about. So before the mesodome was even formed and I'm not showing this here but when we do that the initial cycles of these oscillating genes are indistinguishable from animals where they do have delta notch signaling. So the, and the reason is I didn't want to go into this embryology but the reason is that the genes are initially triggered. Their very first expression comes from an outside system. Comes from nodal signaling or TGF beta signaling which I think has been, will be or has been discussed in terms of early embryonic formation. So that first level of coherence that starting point of coherence at T0 if you like is an external signal. So I wouldn't call that synchronization because it didn't arise by mutual interaction of the oscillators. And then from that sort of, from that uniform phase state if you like now the system runs and the idea is that the oscillators they now, we now see their noisiness and they now desynchronize over time. So the simultaneous start is given by an external signal and now we just watch the rundown of the synchrony. Is that, is that cool? Okay. Yeah. It's about 10 cycles from when I add it to when I see the first defect the fastest I can get that to go is 10 cycles when I use some 50 micromolar dpt. If I come down the concentration it'll take longer and longer to show me the first defect. Yes, there are levels of blockade we can put on the animal we don't see any defects at all. So there's, so we, I mean from this study we calculated that the coupling strength was probably three or four times higher than the noise which is surprisingly over coupled but that's the number we got, yeah. Very broadly. I didn't show you the distribution of frequencies yesterday when I talked about the single cells. Right. I can show you that. It's a unimodal peak. I don't understand if it's too broad or not broad enough but it's a good question, yeah. It's a good question. Okay. It does. In fact, it interrupts delta notch signaling throughout the animal. So neurons don't form properly. The kidneys don't form properly. The gut doesn't form properly. So in specific the sort of differentiation of neighbouring pairs into alternate fates fails across the embryo. The embryo is surprisingly resilient to not getting those numbers right and in fact it will survive when we do this. So DAPT, I don't know. We didn't grow these guys up. The delta notch mutants are homozygous viable and fertile. So without going into too much detail I think one has to be careful there. I think the development of the embryo is amazingly robust but we're not, these guys don't have to try very hard to survive because we feed them as much as they can eat and we don't chase them to eat them. So small differences in brain function are going to be lethal out in the environment but in our aquaria they're fine, so yeah. So let's do the experiment now to see whether this idea about the desynchronisation about whether delta notch, so really the question is delta notch required for this synchronisation is delta notch required for the oscillations at all or is it just required for synchronisation? Now you kind of know the answer because I told you yesterday that the cells can oscillate in vitro in the presence of serum and lots of FGF they can oscillate by themselves but let's see what happens here. So this is how we do this kind of experiment. We use this kind of recording of the individual cells oscillating in the tissue and then we pick up a set of cells in the posterior that are just entering the presemitic mesoderm that come out of the tailbud, entering the presemitic mesoderm and the reason we do that is technical, it's not very interesting except to say that cells in the posterior are moving around so much it's really difficult to track them at the moment at least when we did these experiments it was difficult to track them whereas the cells settle down as they come through the tissue and now they're quite easy to catch that they sit in a line orthogonal to the direction of the waves because we want to compare the phases in a group of cells at the same position in the tissue as they move through the cell and so we're going to track them from the entry in the tissue to when they exit the tissue into a soma and this is the kind of plots we get these are these nine cells here and they seem to be oscillating together so you can see a variation in amplitude but they're quite well temporarily coordinated and there's a way to measure that with an order parameter that we're going to use so what about what happens when we add DAPT to the animal and now I'm going to show you an animal that has grown in the presence of DAPT and this is now already we've waited for quite some time about ten cycles after we added in the DAPT and it's quite difficult to see any waves sweeping through that tissue I don't know if you can see any waves sweeping through the tissue but there seems to be a lot going on and so if we track those cells here's the control animal and if we track the cells in the DAPT animal you can see that the cells the green cell is still oscillating still has this characteristic rise of amplitude but they're now no longer well coordinated we've marked the peak in the top here and here we've marked the peak again so they appear to be scattered their phases appear to be scattered one can quantitate that in a bit more detail by keeping a running average of the phase along between the cells and across the time this is important to do a running average across the time and we can calculate then an order parameter the order parameter is quite simply done it's done by saying going back to this idea of the phase of the clock sweeping around a hand and you say at a given point in the tissue you superimpose all the clocks and you add all their hands together and you divide by the number of clocks you looked at and if they're perfectly synchronized your hand will be one if they're perfectly unsynchronized that will go to zero so that's basically a measure of the phase coherence of all the different oscillators now what we see here is probably no surprise that the oscillators weren't perfectly synchronized but we have a non-zero value of the order parameter for DAPT and I'm going to ask you to believe me that that is a consequence of sampling a small number of oscillators we've simulated sampling increasing number of oscillators and what the explanation I just gave you is true in the limit of enough oscillators to really cover the circle so that's a long discussion I think there was one like that this morning as well we're pretty close actually when we got this data we couldn't but there's a number of one is continually trying and continually swapping hints and stuff it's taken years and lives have just you know and grey hair um yes good so okay so so in fact I'm going to make the claim that from this data set which is nearly 80,000 pairwise comparisons between cells this is actually the expect from these small sample sizes that's actually the expected order parameter for completely uncorrelated oscillators so we think there's no other coupling between these cells at least for this phase synchronization for these short time scale oscillations that would be the claim now I'm going to follow up on something that you asked me yesterday what's the difference between the precision of the individual cells and the tissue and if we yeah sorry that's a super question I mean I think we have to accept that delta notch molecules are involved somehow but you know when they were first discovered they were published to be a cell adhesion system because if you express delta and notch on two different cell types and you mix them together in dish they clump together beautifully these were very strongly over expressed but still in fact you can't ligand another cell without pulling on it in some way so I so I can make arguments about expressing the cytoplasmic domain inside a cell and seeing a change in gene expression in the recipient oscillator circuit without any pulling on the surface but I would be brave man indeed to say that mechanical coupling couldn't have anything to do with it so maybe there are a number of different ways that information is given between cells I like to try and think about that yes I agree I agree so what if we instead of driving delta of the promoter that responds to the hergene oscillator we took the delta out but we put in like a coherent which would form homotypic binding to the neighbor it's a good experiment okay I don't know the answer I like the experiment though I've tried a few cohorts of students to convince them to do that experiment but no one's taken up the bait yet so precision so this is one of the things that synchronization can do for you it can take a population of oscillators with imprecise cycles and synchronize them and make them precise and so what we can do is we can drive a phase from the intensity trace and then we can look at the autocorrelation function how that decays and that will give us a time constant from the autocorrelation we define a quality factor just being this time constant divided by the period and in some ways it's just how many cycles ahead can you trust if you're going to catch a bus can I do it four hours ahead am I going to be there in the right place one hour I better not try and catch a bus in four hours if my quality factor is one so let me just compare these numbers I think you were asking yesterday about the difference so if we pick the very most precise cells set what we call the persistent cells from the zebrafish and we plot quality factors we get this distribution here these blue guys are the best of the individual cells now we look at the embryos just measuring now the collective signal from the tail butt of the embryos and we get this distribution here so this is the shift in the medians and it's quite significant so this is a measure and I think it underestimates what I'm talking about about saying it's one thing that they can do so this has all been the zebrafish and data from other vertebrates has been a bit scarce but there is now some and there's some papers just in the last year and I'm just going to mention them because I think they provide a view from another vertebrate and this is a new system of cell culture from the Alex Alela's lab what it's able to do is to dissect off a tail butt from a mouse and actually it's the very mouse that you saw in Safano's talk before not that actual mouse presumably but that mouse line and you get the cells out and you mix them from six different animals mix all these cells together plate them in a little bubble and then they spread out like this the cells are imaged to detect the transcription of a cyclic gene what it is doesn't really matter but you could think of it as the equivalent of a whole one because it will keep track of the cells going around this cycle and I tried to put the movie in here but I couldn't get it to work so what I have got here is a chimograph and if you can see these ridges down this way those are the pulses there is a gene expression activity in the culture over time so they're relatively coherent and that's from a group of cells that initially had their phases and frequencies randomly scrambled so quite quickly they will synchronize and give an almost tissue level pulsing expression so go and have a look at the movie you'll see these pulses happen they also organize into these you can have a look at the average culture expression and then when they add DAPT they see the culture average drop away in time time along here and this is the collective amplitude that they're getting from measuring a bunch of cells oscillating at the same time now there's two explanations for a reduced amplitude like that one is the cells have stopped oscillating and the other one is that they're now no longer oscillating in synchrony and so you're getting a low amplitude that's making Christmas trees and then they provide the data set consisting of two cells to have a look and I've showed you them here and the cell in green I think you can see three peaks here that's the one that was grown in DAPT these are cells that are imaged from within one of these cultures so I think it's more difficult to image cells in this culture than it is in the zebrafish so I think this is the evidence we have and I think this is entirely consistent with Delta Notch signaling performing a similar role in the mouse as it does in the zebrafish so I think the jury's still out about how that's going to work in detail which one? don't shoot the messenger I have no idea it's not quite clear how they made this plot so I can't I can't give you any more details I'm sorry I thought you were I thought you were okay so let me and what I want to do is so what's the consequence? if the cells become desynchronized I already showed you pictures where those embryonic boundaries were defective there's a consequence to the adult animal and that is that without the arrival of each of these coherent waves it looks like that the animal can't build its skeleton properly and so here's a wild type fish here's a mutant that's taken out from the gene that we were just looking at and you can see that it's neural arches and it's hemilarchs and it's ribs and it's backbones are sort of tangled and twisted same happened to mouse which has lost the same gene here's the backbone of the mouse you can see down here compared to a normal mouse and this is a human a baby that's been born also carries a Delta like 3 mutant mutation and it has and it's backbone is also malformed so it's called congenital scoliosis I'm using this just to illustrate that the synchronization of oscillators has a consequence to the adult anatomy okay so that's what I wanted to say about synchronization as a first pass the next thing that's important to discuss is coupling with delays and so the premise here is that if two cells are sending each other messages and they're doing it by synthesizing proteins then that takes some time now if a cell sends a signal with a protein message and the period is 24 hours let's say like the circadian clock then if it takes one cell half an hour to make that protein then it's effectively an instantaneous transfer of the signal but if the frequency of the oscillator is on the order of the synthesis time then we're in an interesting situation where it takes almost as long to get a message across as it does to go around the cycle and that has consequences so this is a situation we talked about before some sort of instantaneous coupling you think about fireflies fireflies are blinking every few seconds but the speed of light and the speed of neural reception is much much quicker than the period with which they'll blink and so you can describe that very well using instantaneous coupling what happens if there's a significant delay in the coupling is that the population can still synchronize this is theoretical results now first pointed out by Jung and Strogatz but the population can still synchronize but they can pick a period that's completely different to the average of the population this is quite surprising and we're going to I'm going to dig into that a little more and show you what we think about that so okay you can write down this situation of delayed coupling in the following way and this is work that we did to try and think about the oscillators in the zebrafish segmentation clock and now I'm swapping model completely this is not a model that describes genes and proteins it's a phase oscillator model so here's how it works we're inspired by these two cells talking to each other we say that each cell has an autonomous frequency and so as that changes with time that gives us the phase the phase of our oscillators and the cells can talk to each other and they do so they do so by looking at the ith oscillator will look at it a neighbor at some time in the past and that's the delay in getting the signal it always looks as neighbors in what they were doing in the past and it compares it to its own phase and then it takes the difference so this approximation the coupling function by sine works well for weak coupling if it's very strong coupling then that fails and you have to pick some other coupling functions so this is coupling the delay enters here the cell looks at all its neighbors and then the coupling strength is some sort of pre-factor that tells you how much that coupling strength works you could imagine that the delay is the time it takes one cell to make it signalling molecules traffic them, put them on the surface and signalling and you can also imagine that the strength might be for example the number of interaction events between Delfer and Notch it's not what we're representing but that's what it's standing for that's the kind of coarse-graining we're trying to do with this model that's it although I think Kuramoto coupled frequencies but still we're coupling yeah yeah, yeah, yeah so this is Hommage to Kuramoto that's where you start so okay so now here all the autonomous frequencies are going to be the same and so if now of course what you notice are these wave patterns and I don't want to go into the wave patterns except to say we might have to deal with them is there a consequence to having the wave patterns there so we can extend the model by making the autonomous frequencies have some dependence on spatial position so imagine you have a 1D chain of oscillators and they will have some sort of frequency profile that we impose from the outside it's not explaining why there's a frequency profile it's just imposing it and here's the consequence and now in some sense I'm just replaying that first simulation I showed you with the difference being that there's a frequency profile there's a bit of noise in here as well okay so that's what I did I introduced the frequency profile and the moving boundaries to those previous equations okay so what can you do with this let's just play with it first and we pick a given autonomous period for the oscillator I'm going to pick 28 minutes for no good reason particularly because it's close to what the fish oscillates at around about 28-28 degrees and so now if you do that simulation with no delay your system oscillates with a period that's identical to the frequency of the oscillators in the posterior so there's that's exactly the same now let's increase the delay so now it takes about a quarter of the period to get the signal across 7 minutes out of 28 and you can see the whole system has slowed down it's made longer segments the pattern has changed this is a simulation result and now let's just keep increasing the delay now to three quarters of the period and look what's happened the collective period has gone to 23 minutes so it's now beating faster than the autonomous oscillators in the posterior this is now at a coupling delay of 21 minutes so adding coupling delays into a system of oscillators like this doesn't just slow them down it depends on what does it depend on it depends so you can solve that system for the collective frequency and if you do that and I can't derive that for you I'd have to cheat from our paper but this is the result and I'd ask you to follow it up if you like it says something incredibly simple the collective frequency with which the system oscillates in steady state is given by the frequency of the autonomous oscillators at the posterior end remember they're slowing where they're ticking faster than the posterior modulated by this coupling term coupling strength and a coupling delay times by the collective frequency so it's a and you can do some pretty simple expectations here if we could switch off coupling then this whole term would disappear and the collective frequency would equal the autonomous frequency so one way to get a look at this is now to say if this sort of statement is true oh sorry and then I should say the reason why we're changing the collective frequency with increasing delays is because of the sine so we're getting effects one way and then the other way as the sine function moves with with its input here so I'll show you that in more detail but this is what's giving this periodic effect on the output period so we expect if this is true, if something like this is true we'd expect an altered period, altered segment length and altered cellular oscillation patterns so we can check in the collection of mutants that we have and we can see that in a mind bomb which is responsible for trafficking delta and in which coupling strength is reduced we can see longer segments and we can see slower we can see that the segments form more slowly now remember we just talked about desynchronization so for these animals we have to look in the 10 or so segments that form before the system desynchronized and that's what we see we see that those segments are larger and they form more slowly we can measure that here so my length has increased I just hinted at that in that previous slide it's true for all of the delta notch mutants and for the use of DAPT when we analyze the gene expression pattern we can see by measuring the wavelength along the tissue we can see longer wavelengths in an animal with decreased coupling and we can and that seems to be coming from a change in the frequency sorry, in the change in the collective period and not in the frequency decay length so that's what you would expect if the collective population had slowed down and now we can do that the next experiment is we can see what happens as we tune the coupling strength we're doing that with DAPT by using different concentrations of DAPT to block different amounts of notch and this is kind of similar to what you were saying but now, instead of waiting to see how long it takes for the system to desynchronize we're going to measure the period with which it beats until it desynchronizes and you can see that as you add more DAPT the period slows and then comes to some sort of asymptote and if we're blocking notch signaling completely here this term disappears and now we've found the frequency of our autonomous oscillator okay, so what is the difference? the difference is about is about 20% so let's turn this the other way around and if a notch signaling synchronizes these cells they speed up by 20% so that's the effect of synchronizing is that the whole system goes faster by about 20% so now we can get some idea let's go back and compare this to the isolated cells because they don't appear to be getting any delta notch coupling and we see that to first pass we see what we expect that is that they slow down so that's the prediction of what I just told you but actually and here's the distribution of the periods and those periods don't change through the culture experiments so the cells aren't speeding up or slowing down in the culture experiments but this is very slow and if you take an animal growing at 26 we would expect that we measured the period to be about 20% longer but look at the period we're getting on our single cells in culture this is much slower than we expected and we can't really explain it so we can't explain this value let me go back one step the first control we did was to just ex-plant the tissue and grow that so maybe ex-planting slows things down and it actually does if we film the oscillations in the tail bud we can get a period from those experiments and what we found is that just ex-planting the tissue slows it down about 1.5 times, so 42 and now I think probably this is the right comparison to make is to make a comparison from the ex-plant to the isolated cells and that is still nearly a two-fold slowing so we can't explain that data by only using the effect of coupling on the cells there's got to be something else going on when we pull the cells out of the tissue let's pull the cells out of the tissue or ex-plant, sorry that's this experiment sorry mate, just this experiment to ex-plant something is to chop it out of the embryo and then put it in culture and then film what it does so effectively what we're doing in the single cell experiment is we're chopping a piece of the tissue out and then we're dissociating the cells and then we put the cells in culture so here I'm sort of telling this backwards the first thing we do is we chop the piece out so we better know what that period oscillates at and then we isolate the cells from it so that's the right comparison and period to make if we're just looking at the change in the collective going from being in the tissue to out of the tissue so I can't explain that the previous data I showed you suggested that delta-notch signalling was the only coupling in the tissue because of the complete loss of phase correlation but when it comes to the period of the kind of synchronization that we think is going on we don't get the numbers right thankfully it goes in the right direction but that's still cause I would say now to say we don't understand what's going on it might be a trivial explanation it might just be that when you put things in culture in this case they're lacking some tonic input onto the promoters of the oscillators it might be that the mechanics in the tissue is required to keep the oscillators going at a certain speed but that could be I guess now our job is to try and get these things to tick faster in a reasonable way to work out what it was we lost when we came out of the embryo this is of course all in the name of complete disclosure so that you know what we don't know you know that we have a reasonable description of the behavior in the embryo we have a good ability to make some predictions but some of them are more about the assay system than the coupling but that doesn't match at the moment they do divide and it looks like they divide less frequently than cells in the tissue would so that is consistent with your with that general idea it could be it could well be I can't say yeah right yeah the universal moves and suffer ways that are not immediately accessible on the label so how do I reconcile this well I mean maybe we've changed their metabolic status because we've pulled them out into a new medium that's possible maybe we've changed the mechanics so I don't know I mean one way to change the speed of the assay so when we talk about the period you may have noticed that I'm often giving things in percent change in period one very very effective way to change the period of this clock is to change the temperature the clock beautifully formed segments over a temperature range of at least 10 degrees difference over which its frequency goes up three fold so the whole system can operate over a very wide range of frequencies and in fact when we grow embryos at 20 degrees for example when we grow embryos at 30 degrees I'm not sure this is really answering the question we can't tell afterwards what temperature we grew them at because the distribution of segment lengths and the total number and the total length is identical but we didn't go and check the time stamp on the movies we couldn't actually tell the temperature we were growing at so I mean if you rescale because that's probably the temperature now if you can rescale and protect the problem from the other genetic distribution as shown yesterday we mess some rates compare to other rates and things come out of things that may not match so that's how they can accommodate maybe so so the system is remarkably robust to physiologically relevant changes maybe like changing temperature the I would say the most dramatic single change we've seen is the hessix mutant that I talked about yesterday because that animal swims around and looks perfectly normal it breeds you would think it was a different species if you're a field biologist and you pick that animal out of a pond it has a different number of segments otherwise looks normal as far as we can tell and so you'd say here's a new danio species that's the best example we've got some of something that you would say would be a one-step jump that you could consider evolutionary everything else we've done we've been able to do has pushed the system and it's gone but it's gone very grudgingly and then something else is broken while we're trying to do it yeah this is the facts right that's where we are yeah well that's a really good question I think the one you could try and do a back of envelope there and say what proportion of the cells energy budget does it spend on transcription for example and what proportion of all the genes transcribed are these and so I don't know but I would I would sort of guess that it's a pretty small fraction compared to maintaining the potential difference across the membranes and I don't know does anyone have a good idea for cellular energy budgets and could help us here but you didn't invite anyone who knows about cellular energy budgets I mean okay I'll think about that yes sorry yeah yes there I think that's a really good question to ask and when we did the measurements on the when we blocked with the DAPT and we did the the order parameter we calculated the order parameter on the phases of these cells and we saw that they had exactly the same number as the same order parameter as if we had sampled from a population same number of cells with guaranteed zero correlation that made me think there's no more phase correlation between these cells they're really desynchronized and so that makes me argue that there's no other kind of there's no other kind of there's no other coupling system at work in the zebrafish so but in amniotes for example so there could be mistakes in that argument we could have made the measurements incorrectly in I show you a picture at the end amniotes have they don't just have delta-notch signaling oscillating they also have Wint and FGF signaling that appears to oscillate and those molecules can act at a distance and it might be that in order to understand synchronization in the amniotes we need to take into account some sort of long-range signaling let me take a step back too to say that delta-notch expressing cells can reach out phylopods and they can signal at a distance too I don't know about across the whole tissue but certainly back one back one neighbor we make lots of approximations like it's near neighbor only but there are some systems known where the cells can reach for example sensory organ precursor formation in flies so they can't yes so I think the messages that so I think that when we look at the individual cells they have no input no delta-notch signaling at all that's not being stimulated at all in that pathway when they come together now they can receive delta-notch signaling and two things happen one is they become synchronized and the other is they speed up because of the delays in the coupling so that's what I think is going on I think that's the picture that this evidence paints yeah that's a good question so that's going to be one of my open questions at the end yeah so it's a really good question whether delta-notch signaling is directional in the tissue could it be that there's a delta-notch wave that sweeps down the tissue and triggers this wave I'm going to come to waves tomorrow and I will I promise to try and tackle that try and look at that question but let's try and stay in this local neighborhood for today if that's acceptable because I'd like if it isn't I'm afraid I know I could swap to the other lecture okay so right so so we've got a we've got a quantitative gap between our cell culture experiment and our expectations from in vivo not quite sure is at the end of the theory have we got it all completely wrong or do we need to is there something else we're missing we need to tweak the cell culture so that's I leave that there now what I wanted to do was plot the solution space for this equation because it's really interesting and what we can plot here is the collective period so not the frequency but the collective period on this axis here's the period this yellow line marks the period with which the autonomous oscillators would tick and of course that's also the collective period when we add DAPT so I've got coupling is zero here and if you've got zero coupling it doesn't matter how long your delay is you're not sending a signal you don't care it's irrelevant that's why that that's why that line is flat and now as you as the delta notch coupling increases in the model increases more specifically this flat line buckles and it starts to rise up and now you see the the sign and this is part of this is the explanation of why you can both speed up and slow down depending on the ratio of the delay to the period so we think that the fish we know that the fish speed up when they couple and we know they slow down when they uncouple so that's to say that they've got to laid down here somewhere under the line and if we we know the amount of time that's different and so we're looking for some stable part of the solution to sit on and so we think that the fish is probably here if that makes sense we don't think it can be longer because the solutions that we get are multi-stable and that's not going to be a good evolutionary strategy to keep a system ticking stable we think the system ought to sit somewhere it's monestable we actually had a measure of the coupling strength from those decay experiments where we measured how long it took for the system to desynchronize I'm not going to go into that but we think it's about this amount and so if your coupling strength is this high 0.07 per minute then this is the this black line is the is the branch that you would be sitting on now this dotted line this dotted line sits at where the delay of the period so exactly halfway through the period the system is not stable so as you increase the delay the system slows down that's what you saw in that first simulation and then the system becomes unstable and then as you increase it further the system becomes stable again but now the system is ticking faster and then as the delay approaches the period again you go back to sitting as if there was no delay in the coupling anymore here can we decrease the delay and hit the instability this is a question are the instabilities that we can find and these instabilities ought to be distinct from desynchronization this instability will have a hallmark of being antiphase so the cells won't be able to settle down in phase and they'll be continually perturbing each other and we tried to do that experiment by over-expressing this enzyme called mind-bomb I showed you the mutant for that a minute ago and it's an enzyme that influences the rate at which delta is trafficked and can become ready to signal so we thought well maybe if we over-express this guy we'll put delta on the surface more quickly and that might have the effect of shifting us towards this instability and now I'm going to show you what happened when we did that experiment and how we interpreted it here's the wild type experiment this is a snapshot of the wave pattern in one arm of the prismatic mesoderm of the wild type and when we simulate that using that theory on a hexagonal lattice this is the kind of pattern we get and we look at the correlation function of the stripes along the axis and so the real data comes in the thick line and the theory is in the grey line so this is a good match and it kind of says that we've got at least some idea of what the parameters are to get the delayed coupling theory to match what the fish embryo are. Now we over-express mind-bomb and we see that the tissue loses the coherent stripe pattern but it doesn't become smoothly salt and peppered like the loss of coupling does I'm not showing you that data you saw some examples before and rather it has these areas of alternating high and low cells and we think that that fits quite well to the delay in the simulation to a delay of about 17 minutes so these oscillators haven't been imaged directly so I would consider this indirect evidence but it suggests that by shortening the delay and moving us in this direction we can find a state of oscillator pattern that is neither synchronized nor desynchronized it's in some sort of antiphase opposition state that's a constant of changing the delays let me finish up the bit on the zebrafish here and I think that the core message here on synchronizing the delays is that if the delays are on the same order as the period you can't neglect them and depending on whether they're shorter or longer than half the cycle time you can either slow down or speed up the system and so if we're thinking about this segmentation period like yesterday I was saying look we need to think about all the time scales in this loop that's how we will get the magic prize when we understand that time scale we will be able to understand it and I think James was saying well how come you're so hopeless at understanding the period and I said well maybe it's because one idea would be that there are other things going on that just aren't described in the single cell and this might be one example so I will argue that the period that the system gives rise to of course has input from these time scales but is modulated by this level it's synchronized but the period itself is also changed so the final period of submittogenesis is an emergent property that comes from the way the cells synchronize so I've got about quarter of an hour left and if people give me some indication of oxygen levels I can I can discuss I think one more experiment that was done in the mouse and that altered delays another attempt to alter delay and see what happened okay I can see some metabolic activity that's good yeah okay so now this is a paper that came out recently and so I guess you can see what I'm doing I'm saying I'm trying to tell you what I think we know but I'm also putting in papers that just came out and that I don't understand yet I haven't really I don't really understand them but I think it's important to look at the data because it's new stuff and we need to sort of incorporate this and think about how it fits in so this is a paper from Riichiro Kagiama's lab and Hiromi Shimojo was the first author and she made a reporter of delta like one in the mouse so she could see the she could see this delta promoter making leciferanes and so when she imaged the precemitic mesoderm of the cell of the mouse embryo she got she got expression in the precemitic mesoderm and when she ran a measurement window along the precemitic mesoderm she got a time-space diagram a timeograph of oscillations like this so time's going this way these pulses are the successive oscillations and the curvature in that in that line there is the wave moving forward so we'll come back to waves more tomorrow and then she says okay well I can she puts another measurement line across that way and now she picks out the period with which those pulses are happening in the tissue so it looks like that's a good way to get a live notch reporter okay so you can look at this as evidence that notch is oscillating in the mouse now the question was can they change the delay in delta signaling to the neighbors and they tried to do that in two ways one was to take away the endogenous so the endogenous delta gene is about eight kilobases long and remember yesterday we were discussing how you might change the production delay in a gene by cutting out introns was one idea so if you put more introns or make the gene longer you should take longer to produce the gene so that's the trick they did here the first version what they called type 1 they deleted the endogenous gene and just expressed the cDNA so that's basically a piece of DNA that has no introns in it it encodes the protein directly and it's much shorter and then the other type of mutant they made was they inserted this cDNA upstream of the endogenous gene and so they made the whole gene longer and went to tissue culture and this time using a blue light inducible promoter which we were discussing briefly yesterday they shone blue light on the cells to trigger the expression of these genes now from a light sensitive promoter not from the endogenous promoter and then they measured the increase of Luciferase fluorescence over time and here is the wild type in green the blue is the type 1 mutant so it's being produced faster it's coming up earlier and the red is the type 2 mutant so it's coming up slower and they estimated that the version without any introns was being made about 6 minutes earlier than the wild type and the version with the extra cDNA at the front was being made about 6 minutes slower than the difference now remember that 6 minutes should be now compared to the 2 hours approximately that the mouse cycle takes so these are quite small changes these are sort of on the order of what 5% or something ok so that's experiment and now Hiromi made transgenic animals with both of these with both of these transcription factors now replacing the endogenous delta and this is what happened both of them broke the segmentation clock so here's a wild type trace looking at the pulses in the tissue over time and this I'm only showing here the type 1 mutant the one that's ready too early here maybe these are real oscillations maybe not, it's not clear Hiromi didn't think that that was a reliable periodic measurement and so in this paper they make the argument that there is a very narrow window and this speaks to exactly what we were discussing the narrow window of production delays that the system can tolerate if the delta gets there too early or gets there too late then coupling doesn't work even though they showed that the proteins were being expressed at comparable physiological levels and they also know that that CDNA will rescue so there's nothing wrong with the CDNA itself just changing the delay was enough to stop the coherent oscillations in the clock so it doesn't have a dominant negative whereas the other one did I think it means that if you can signal with the right time scale it doesn't matter if you've got some distribution to your delay it's actually one of the open questions I had was about the distribution of the delays whether you have a hard delay or you have some distribution to your delay that theoretically can affect the communication but what I would say here is that this essentially means you've got your wild type protein let's imagine the wild type protein arrives on time but there's also a little there's some arriving early but then there's some arriving on time and the system appears to be okay there was no analysis of whether the period had changed but it still oscillates in a coherent manner yeah that's I mean that's a good question I need to go back and double check but this is the evidence that they presented and I don't know if like in the previous cases we're talking about you mean where the system starts out okay and then after some time it decays I don't know let me look so if it were I think this is again a good open question which is the coupling really symmetrical so if you have the way we write the coupling down it doesn't matter when in the cycle right you couple but if you really pulse coupling then it might matter if I pulse with delta then I might use up all the notch okay I argued in the zebrafish notch is not limiting but I don't know in the mouse and then maybe it does matter the other thing is that if notch is acting to couple to the oscillating circuit in the neighbouring cell by transcriptional activation then if I signal early I've already started I've already started expression on the on those promoters early now I put more later they're already going I mean I find that yeah but they're still massive yep yep maybe the average hasn't shifted far enough here but it has shifted far enough here yeah I agree that makes sense sorry say that again yeah yes okay let me yes so by coupling I guess I'm I guess we're I have to be careful here because I've been using coupling as synonymous with delta not signaling coupling is really any communication in some sense so I don't know if I'm answering your question so would you like to ask your question again given that I'm trying to clarify coupling I yeah I don't I don't know I mean if it's got a receptor on the surface sort of biochemically if it has a receptor it'll it ought to trigger some biochemical change within the cell so that's interpretable to the cell will depend on I guess the composition of signal transduction molecules inside and potentially also whether the relevant promoters if we're talking about a signal to a gene are active or not and so I think it's a good question for example we don't have a phase response curve for this system we don't know when when in the cycle so just take a cell take a coupling away with the promoter produces a lot of her or his protein that comes back into the nucleus and now let's say is in excess and that promoter is now shut down it's repressed now it may be that if I deliver a not signal at that time point there's nothing that the cytoplasmic domain of the not receptor can do because the the stoichiometry of the molecules around the promoter is dominated by the repressors so there may only be a window within the cycle where a not signal makes sense to the cell is that is that anywhere does that make sense okay I don't know if that's right but okay yes so good okay so so the discussion here is that in the paper it's discussed that there's some very narrow stability window and if you move slightly outside that window the system shuts down and so this again we're back to this sort of discussion about why is it so hard to change the period of a biological oscillator I think that's a really good question I don't have an answer for it so let me just summarize now in the last couple seconds and say what I've tried to discuss with you today is the idea that these neighboring oscillators communicate that in the in the zebrafish and probably also in the mouse delta not signaling is not a not only involved but potentially required maybe it's the only communication synchronization overcomes noise and I would say that's it's in some sense that's its primary function in the animal is to make sure that oscillators are coherent to produce the boundaries but it also has the effect the delays in these coupling appear to tune the period so this you sort of get for free some papers to read here if you're interested and then so there's plenty of open questions and actually these have come up I think nearly all of them have already come up in questions all of our models assume that the cells signal to each other symmetrical and the symmetry is a bit deeper because with a coupling function like I showed you the cells are in communication all the way around the cycle but it's not clear that either of those things are true it could be that one sends a signal and then the other cell replies it could be that if one cell has more delta on its surface it dominates the conversation and there's not much coming back we don't know about how the delays really work we haven't measured them directly we've only estimated them using the models what difference would a distribution in the delay make I think that's an interesting question and what's the coupling strength and this is the question you asked how long would it take so now let's get simple we can do an experiment like this we can take two cells out of the segmentation clock and let them come in to touch each other and you can see these two cells have touched each other and they've formed a kind of a surface where they're in close contact and now play the movie that's going to loop can you see that what's happening is that the two cells are oscillating first the right then the left then the right then the left that we've been talking about all evening in the tissue the cells always synchronize in phase but sometimes when they come together in the dish they also synchronize in phase but sometimes they synchronize out of phase so I think this is going to be super fun to play with these cells and try and work out what the minimum rules are away from the rest of the tissue away from the gradients which we'll talk about tomorrow when they touch each other and maybe we can then by tagging the delta get some idea of how long it takes a cell to send a signal right this is the walkie-talkie model David Springzak's paper when he was in Microsoft yeah I think that's right are these walkie-talkies are they talking to each other continually like Italians or or Indians what's going on there so maybe this is the way to at least ask those questions in a different way I'm still curious about what's happening in amniotes and this is the picture I promised to show you later this is the sort of sketch about how many genes in the FGF pathway and the WINT pathway are thought to be oscillating and in contrast in the zebrafish as far as we know only delta and the Hess-Hur are oscillating so maybe this comes back to something I said at the beginning yesterday maybe one advantage of studying in the zebrafish is not just the imaging but also that for some reason maybe the system is really stripped down and maybe we get a look at some of the core dynamics without all of the large-scale molecular activity that's all I wanted to say about synchronization tomorrow we're going to look at the tissue level WINT pattern thank you very much