 All right then, let's get started. This is the third lecture about the segmentation clock. And what I'd like to do, oh, wait a minute. This is mostly magic, true, you know. This is, so what you might remember from the last two days was that we discussed breaking down the segmentation clock into three tiers. We discussed, first of all, the idea that individual cells could be oscillators, genetic oscillators, discuss the idea of having autonomous oscillators, talked about their potential control. Yesterday we talked about what happens when two of these, two or more of these oscillators talk together and how their timing could be changed and regulated. And we talked about synchronization, changing the period through coupling. And today I want to go up a length scale again across now to essentially hundreds of micrometers to the tissue scale in embryogenesis and tackle the question about the most obvious phenomenon there, which is the waves. And so I'll quickly remind us all of, no, it's failed. I didn't say the right words. Was this working for you, Stefan? You didn't use it at all. No, but I mean to laser pointer. I think they're triple A's. So yes, reminder of segmentation. We talk about the underlying principle for the generation of the tissue level waves, which is the slowing of individual oscillators as they drift through the tissue. We'll talk about the control of that, both via local coupling through delta notch signaling, which we met yesterday, and also through gradients of signaling activity. And I think you've heard a lot about gradients. And I'm not going to talk a lot about them. I'll mention them. And then I want to talk about the consequences of having waves in the tissue, the existence of a Doppler effect. Thank you very much. And then trying to alter the waves to see what difference it might make if we could change the wave pattern. Then I'll discuss open questions. OK, so it's important particularly today to go back and have a look at the tissue where segments are forming. And here I'm zooming straight to the confocal section where we see the nuclei in the tissue. And we can see them moving. And we can see segments being ejected on each at the anterior end of the precemitic mesoderm, the tailbud here. And remembering that cells are being lost from the tissue on this end, at the same time as they're being added to the tissue at that end. And so the tissue is quite long. It can have up to 100 cells along it. That number will change during development. And so we think of, because cells are being continually removed from one end and added from the other, we think of the tissue as a reference frame in which there's a drift of the cellular material. So that's an important way to think about the tissue. So it's not like the animal starts out with one set of cells, and then those cells are acted upon. The cells that are in the tissue continually change. So it's a different set of cells that are in the cell at different developmental stages. Of course, we think they all run the same kind of program as they go through it, but it's different cells. And then this rhythmic behavior that is the core clock idea, again the clock and wave front model, where we have a population of phase synchronized cells. And here is the model where they're all synchronized with the same phase, and they oscillate together. And so the hypothesis that there's a genetic oscillator in these cells, which is ticking with a well-defined frequency, a clock. That's the hypothesis. And the hypothesis is that this genetic clock is the timescale that's setting the period with which the segments formed. And yesterday, we talked about the idea that synchronizing those cells might change the timescale from that of the individual cells to the collective. But still, then, one could talk about this whole tissue as being a clock and having a well-defined period that delivers a signal here that's converted then into a permanent periodic record. Again, segment length is the velocity by the period of the clock. So the period of the clock is doing anatomical work. And these are the kinds of expectations we have that the segment length and the total number of segments will depend on the period of this clock. So up to now, we've been thinking about this in steady state. And so this is our sort of collective clock here with a tissue-level periodic pattern. The real clock looks a bit different, as you've seen over the last couple of nights. And this is the zebrafish, once again, looking at the HER1YFP transgene, where we see waves of green signal marking gene expression sweeping from the posterior through the tissue up to the anterior. And each time one of these waves arrives in the anterior, it's coincident with the formation of a new segment. So the arrival of these waves is, by inspection, equal to the formation of each new segment. You can see that in that movie. So the waves is what we want to think about today. So now we need to think about, ah, yeah, no, that's a common magical mistake. Those are not the waves you're looking for. So there's a few changes in the reference frame there. So what happens is the wave comes in, and then the tissue, the cells express for a little while, and then they decay. What's happening at the same time is the axis is extending. So those cells that are decaying away are being pushed, which is why it's really important when we want to try and analyze it, is to fix one point in the reference frame. And so we're going to look at chymograph today that will eliminate shifts in the imaging plane. But it's a good observation because it's true in the imaging plane that happened. Sorry to say again. I'm not sure that it has anything to do with the tissue elongating. No, I'm not sure I said anything about that. The axis elongates, and within those cells we see these sweeping waves. And it's not clear to me that there's any evidence to suggest that the ongoing oscillations are required for the axis to extend. Is that what you're asking? No, I don't know any evidence for that. So for example, the various mutants that we talked about before, we crippled the single cell or the tissue level coherence of these oscillations, still extended their axis at the normal rate. So in some sense, you might say that the oscillator might be required for shortening the tissue because each time a wave comes up, it demarcates not the axis now, but the oscillating tissue because each time a wave comes up and then arrives at the anterior end, it appears to demarcate the next set of cells that will be ejected from the tissue. So I would agree that the wave might be involved in shortening the tissue, but not in controlling the axis. I think those are two different to do. They're both going at the same time, but I don't think the clock has anything to do with driving the axis. OK, and then so this was our model, just to sort of make crystal clear the difference between the different levels, single units being the individual pixels, the local correlation. So the single pixels were the Hess-Hur transcription translation feedback loop, the local correlation between the neighboring pixels was the Delta Notch signaling system that was bringing these oscillators into synchrony and global organization where we look at the words that are moving across the screen. So that's the topic tonight. This is the sort of the global level, the waves, the wave phenomena. So how do you get these waves occurring? Tissue level wave patterns, that's what we want to talk about tonight. So the first thing I want to talk about is what do the individual cells have to do as they're slowly drifting through the tissue in order to get a wave pattern? So it's a question about what the cellular behavior is. And so this is a story of single cell slowing. And let me explain to you what I mean. So this is the pattern that we had in that first model where we had the first simulation, where we had all of the oscillators phase synchronized and all beating in perfect rhythm together. And so then as the wave front moves and as new oscillators are added at this end, that's converted into a permanent periodic pattern. And there you saw a cell drifting through the reference frame of the tissue, but actually being at rest in the slide reference frame, the low reference frame. Now, if we go inside what's happening in that model, what we instruct the oscillators to do is to tick with a position-dependent frequency. So in the posterior, they tick with the highest frequency. They maintain that frequency. They're all synchronized. And then when they get to the anterior end, we arrest the oscillators. We read out their phase just before we arrest them, and then we switch them off. So that gives this pattern on, off. Now, if we want to get a traveling wave, what we need is a difference between the phase of neighboring oscillators along the tissue. And a very simple way to do that is to change the frequency across the tissue. So now, we can instruct this model. The only difference will be to instruct the cells to slow their oscillations as a function of their position in the PSM. It's what I would call a frequency profile of the oscillators across the tissue. And the consequence of doing that, and only that, and so maybe it could, is now seen here. And this is what you get. That's the only change. We asked the oscillators to slow gradually. And you can think of this as if I have a row of oscillators going this way, if the oscillator in front of me is going slower, then its clock is gaining on mine. And so the difference between our times grows continuously. Even though I slow, it's slowing ahead of me. And so this creates a continuously growing phase difference between us. And that's what's required to get a stripe, a phase difference. So you can imagine going once around the cycle, twice around the cycle, three times. And that would be a six-pi phase offset across that whole tissue. OK, so another way to think about this is just sort of a crude analogy is if you're driving in a car and you're coming up to a stop sign, you could drive at a constant frequency towards the stop sign and then jam on your brakes. And you would come to a rest right at the stop sign, hopefully. You may want to go a little easier on the brake pads. And so you might choose to brake more slowly. And so this could be your angular frequency of your wheels, if you like. You slow gradually, come to rest, and you stop at the same point. So you've got the same starting point and the same stopping point. You just chose to slow gradually, right? And then in that case, in this simulation, if we measure the oscillations of that cell, then this is what that cell looked like. It oscillated rapidly as it was in the posterior. And then over time, it slowed and then stopped its oscillation. So this is the expectation from the theory. This is important. This rate of slowing is important because, actually, this changes the wave pattern. If we choose different frequency profiles, he was the sudden stop. He was the gradual stop that I just mentioned. But we're free to choose any frequency profile. And then what we'll produce is different patterns. And because we can quite accurately record the patterns in the animal by looking at these patterns of the oscillating genes, we can very accurately fit this pattern to a particular implied frequency profile. Actually, a phase profile. But then we can infer the frequency profile that would underlie that if there were no extra things going on. So you don't need any coupling to do this. Up to now, there's no coupling involved whatsoever. There's no noise in the oscillators. And all we're doing is slowing them. And we can get that pattern. If we were to add coupling to this, we could potentially change that wave pattern. And we're going to talk about that in a minute. But at the moment, I'm just talking about the behavior of individual cells. They have to slow down. OK, in the model. OK, good. So do they slow down? And so to ask that question, we're going to go back to these time lapse movies that we discussed yesterday when we were trying to work out whether the cells were synchronized with each other. And so now we don't have to worry about having cells that are column or cohorts. Remember, the synchronization question required that we track cells in a row so that they have the same position in the tissue. It doesn't matter. We pick up cells as they come through. And what we're interested in is whether each successive cycle grows or shortens or fluctuates or what do they do? Are they getting slower or not? And so this is one typical cell here. We just measure interpeak distances or intertroph distances. And then plot for a given animal the cells that we see and compare the length of one cycle versus the following cycle. And if the cycles are growing, we'll see all those data points land in this triangle. So here's one example, one animal, where we saw the cells more or less always slow down. This is January the 5th. I don't know if you can see that from the back, but that's my birthday. So on my birthday, everyone's in the lab doing experiments. And there's a good chance if you do an experiment on my birthday, then I will talk about it in a talk. So that's how it works. It's actually the only time I actually see everyone in the laboratory now and come to think about it. OK, so now we can do this for now four independent experiments and plot all the cells that we follow in the tissue. And you can see that not all of the, so this is quite noisy. But as you can see by the distribution of the ratios, but on average, in these four different experiments, cells slowed by about 20% each time they went through a cycle. So this slowing across the tissue is quite robust. And in fact, you can take that average slowing and you can go back and look at the pattern you'd expect and it matches very well to what you see in the fish. So I think we can say that these wave patterns, the basic mechanism then is that the cells are slowing as they are in transit through the tissue. So how is this slowing going on and how they slowed and stopped? So the question of the wave now becomes, in some sense, how the oscillators slowed and stopped. So I've just, now that question, it could be through the coupling. Because everything I talked about now, everything I talked about said I said the cells can do that without coupling, but we just discussed yesterday how the cells can adjust each other's frequencies by exchanging delta notch signals. So we should consider that possibility. And one other illustration of that kind of situation is in this amazing experiment from Jeff Hastie's lab, where they've engineered quorum sensing bacteria to swap a signal that at some quorum of density triggers an oscillator. So we know by construction that these cells in an isolated state won't oscillate. So they're not very much like the cells that we saw from the zebrafish. But this is what happens when they grow together. And that is the reporter gene, so the siphirase, which the bacteria are expressing once they reach a certain density and can communicate with each other. So here's traveling waves that are generated by coupling. It's not delta notch coupling, but it's local communication between the cells. And in fact, there's more than one model where the oscillator coupling itself plays a fundamentally important role in the slowing of oscillations. But remember, in the model, we just imposed a frequency gradient. We didn't say where that frequency gradient should come from. Now, good. So let's go back to delta notch coupling and test that idea. So remember, delta notch coupling was a short range intercellular signaling system involving delta. We're now looking at the delta transcripts in the tissue. So remember that the cells cyclically express delta on the surface. And then ligands to notch. And then the notch cytoplasmic domain can act as a transcription factor and cause the s-her genes, which form this negative feedback loop, to be transcribed earlier. That's the model. And we talked about that a lot yesterday. So now we're going to go back to the experiments that we yesterday used to compare, to look at the synchronization of the cells. And yesterday, we discussed that we had managed to desynchronize the cells by blocking delta notch signaling with DAPT. I'm just reminding you that we're discussing that. And this is now by looking at cells in these columns. We've got this desynchronization. So it's important that we think we've properly desynchronized, because it means we also think we've properly blocked delta notch signaling. So coupling should be off in these animals. But now, we can look at all of these traces and ask whether they're still slowing or not. And the answer is very clear. Here's all the animals that we've added DAPT to. And here are the data that I just showed you. So we can't tell the difference from looking at individual cells slowing the oscillations across the tissue, whether they're coupling through delta notch signaling. So I think this is really, it's sort of a negative result. But I think it's very important because coupling can do a bunch of things to oscillators. But in this case, what this experiment tells us is that notch is absolutely required to maintain this pattern. Without notch, that pattern breaks down. You remember these salt and pepper Christmas tree blinking patterns that we saw. And remember also that the animals couldn't make a good skeleton under those conditions. But so it appears to be required to maintain the pattern at the local level, keeping cells synchronized. But it's not required to generate the basic behavior, which is the slowing of the cells. So that's an important distinction, yeah. Yeah, yes it does. That's quite typical. Actually, in this particular example, it's even more extreme. This animal looks even more extreme than in the wild type. Yes, that's right. So this, yeah, that's a typical plot of cells increasing in amplitude. They don't always do it. But again, they mostly do. Just as most of the cycles get longer, most of the time they rise in amplitude as they do so. Yes, OK, so right. So other candidate processes. What else is there that might be acting in the tissue that could cause this slowing independently from the local delta-notch coupling? And the current thought in the field is that signaling gradients, which spans tissue, might be providing that information. And James earlier today talked about FGF and WINT and retinoic acid gradients that were present in the tail butt of the mouse. And he was interested in their roles of directing the differentiation between neural cells, posterior neural cells, and paraxyl mesoderm. I'm going to talk about exactly the same gradients, but I don't care about their role in making cells. I'm just care about their role and what they do in the most important tissue back there, which is the paraxyl mesoderm. And so here's an example. So this is certainly our signaling gradients there. Here's an example. Here's the transcription of FGF. So here's the paraxyl mesoderm of a mouse embryo in a lateral view. And this experiment is done looking at the mRNA. If you let this reaction run for a short time, you see some expression in the posterior. If you let the same animal accumulate signal for a longer time, then it looks like this. And this is one way of showing that there's a distribution of mRNA along the tissue. That's important for technical reasons because in these kind of colorometric assays in the tissue, they're difficult to quantitate. So this is a qualitative illustration of a spatial gradient of the mRNA along the tissue. And this is a fluorescence image of an antibody directed against FGF protein. And here you can see what looks like a gradient along the tissue. So this is from the mouse. Gradients of signal transduction components like DP-IRC, which are downstream, so reading out the activated state of the FGF signaling have also been recorded in all these species. And actually, if you want to see one, you should have a look at Wei Ting's poster. Wei Ting, put your hand up just out here because she's got some images of this from the zebrafish and they're really nice. So here's the idea then. RNA is being made mostly in the posterior. But as the animal's growing out and cells are leaving the tail butt and drifting through the tissue, their mRNA will be carried with them and it could degrade slowly over time. So you might get an mRNA gradient just by being inherited by the cells coming out of the tail butt. And then you have some sort of protein gradient and that could be by direct diffusion or it could also be created from release from the cells as they drift. These two ways, two sort of different mechanisms that could contribute to the observed signaling gradient across the tissue. OK, so this general scheme is also true for Wint and the other gradient that was mentioned before was retinoic acid, which is being synthesized from the formifomites and would form a countervailing gradient. So let me illustrate that now in the pre-semitic mesoderm in a cartoon version. Anterior retinoic acid and in the posterior FGF and Wint. And what I'm going to tell you now is kind of a, this is the hypothesis I think that's present in the field at the moment, is that as a cell moves along these gradients, it's in some sense integrating the sources of information and it can work out its position, its positional information in the tissue by in some manner integrating these different systems. So what it might do as a result of that, and as a result, arrest its oscillations at a particular point. And I think there's actually good information in the literature to suggest that FGF and Wint and retinoic acid can change the position in the tissue, fluctuations, perturbations in those signal systems, can change the position in the tissue. Now something else that's going on of course is what we were talking about before, the sustained oscillations and then the slowing of the oscillations. There's no good evidence at the moment that any of these signaling systems affect this slowing. So I can't really say anything but they could and I think it would be an attractive hypothesis. Could imagine that the cell would read off the amount of FGF and Wint and use that to somehow change one of the parameters in that, as her model we were talking about, so as to slow its oscillation in proportion perhaps or some function of the amount of signaling molecule it got. But also using these signals to know when it should become determined and express a marker of segmental determination, so for example, MESP. And actually there was a movie missing. No, there wasn't. You remember the movie with the green stripes moving up the tissue? And I forgot to mention the bands of red gene expression that were appearing sequentially down the tissue. Do you recall that? Shall I show it again? OK, you've seen it lots of times by now. So that's the two transgenes. We've got her one and MESP. So I would say we don't really know what's going on. And the reason we don't really know what's going on here is because of two different time scales that might be present in the tissue. One is the cells could be acting like a radio receiver. So there are some gradients where that really seems to be the case. The cell will be sitting in a field and it will be over some shorter time scale. It was a good example of integrating over short windows that Stefano just talked about. Be receiving, OK, how much signal am I getting? How much signal am I getting? Now I'm crossing some threshold. Or the last three minutes I saw this much signal and so bang, now I make my decision. Could also be that the cell, as I pointed out before, because the cell can just carry in the flow some of the signals with it, it might be that it got that signal by inheritance. And it may not be listening to the moment to moment changes in the signaling gradient supplied by a diffusive process. Maybe that's not relevant, or maybe it's a mix of the two. And it's just been extremely difficult up to now to distinguish those two possibilities in the tissue because the cell flow is so fast in the system. So I'm going to leave that there. I might come back to that. So I just want to leave these ideas as hypotheses. Because I still don't think there's any really good evidence that I would hang my hat on about how that works. I think there's lots of interesting experiments being done, for example, by waiting. But I think we still don't really know how that works. OK, is that fair, Waking? Yeah, OK. OK, so regardless of how these are controlled in detail, we do have waves. And they are due to slowing oscillators. And so now I want to ask, what is the effect of having waves in the tissue? And so the waves in the tissue, are they just a nice epiphenomenon? Or don't they matter at all? And do you remember when we were analyzing the effect of coupling and we were asking, what's the collective frequency that the oscillators would tick when they're coupled with delay? The frequency profile that was in that model did not appear in the solution. So that is to say that at steady state, it actually doesn't matter whether the cells slam on their brakes, or whether they slow gradually. You can't tell. The collective period of the tissue doesn't depend on the internal dynamics of flowing. So that's a theoretical result. And it holds at steady state, and I tend to believe it. And so I think for a while, we had sort of discounted the role of waves. And let me kind of put this in a different way. If the system's at steady state, then that wave pattern repeats perfectly with the formation of every new segment. You can't really tell it was the fifth segment or the sixth segment, the pattern repeats, and then you get another segment, pattern repeats. And as a consequence of that, and this is sort of to restate that in another way, we can think about three periods. One is this pacemaker input period, which is the time of the genetic oscillations in the tailbone. And you could think of that as sort of you have a bath, and you're at one end, and you're putting some frequency into the water waves, and then they're moving across the bath. So let's not have any reflective conditions at the other end. And the waves are arriving at the other end of the bath. The frequency ought to be the same here and at the other end when they arrive. So of course, the pattern across the tissue can repeat perfectly, and that pattern will have a repeat time, which should be identical to the input period. Again, think about this simplified situation of the bath. And then the submitted genesis output period is the time that it takes to make each successive somite, and that should be exactly the same, because it's just the arrival of each wave. So this equivalence of all these periods across the tissue is what we'd expected. The pattern repeats, a wave departs from the posterior with the same frequency that it arrives in the anterior with the same frequency that a somite forms. And so this genetic pacemaker has the same period as the submitted genesis. And that's another way of stating the core idea of the clock and wavefront hypothesis. A clock and wavefront hypothesis says there's a genetic oscillator, and that's supplying the time, and it's that time that's important, whether it's collective or individual cells, that's important for forming the somite. So is that true? And so what we thought we would do would test that idea by measuring time at different parts of the pre-semitic mesoderm. And this is the result we got. So the experiment, we took a whole one transgenic line, we measured the frequency of oscillations in the posterior, and the frequency of oscillations in the anterior, just where the wave arrives. And not the form somite, but just as that wave arrives. And here's the signal in the anterior, and here's the signal in the posterior, now over the formation of about 20 segments in the animal. And here's the signal in the posterior. And so if we detrend those signals, I think it's a little bit clearer what's going on. Here's the first peak. By the time the signal in the anterior has done 10 peaks, the signal in the posterior has only done nine. And out to, here you can see that the signal in the anterior has done 18, and in the posterior you've only done 16. These signals have constant frequency. They're not, one of them isn't slowing down or speeding up through time. Both of those signals are ticking with constant frequency, but they're ticking with different frequencies. So this is kind of, this was surprising to us at the time because it violated what we expected to see about a clock having a well-defined period across its spatial extent. So the incoming waves in the anterior have the same period as you formed somites, so that's what we expected from looking. And the surprise then is that the period of the genetic cycles in the posterior are reliably slower than what's happening in the anterior. Yep, so this point back here is in some sense fixed because its reference point is the posterior end of the tissue, but this point in the anterior keeps sliding with the formation of each new segment. Now if the tissue had the same length in the infinite snake then their distance would be constant, right? But it's not, and I'll show you that in a sec. So this was confusing, and actually for a year we tried to make the result go away because the pattern repeats, right? But eventually we had to admit that it was a fact and we saw it in several different transgenic lines and we tagged two different genes from within the clock and all of them gave the same result. So at some point you start thinking that this is true and what I'm saying is that submittogenesis is faster than the pacemaker region of the clock. So this is uncomfortable because what happened to the clock? You might imagine you could make some sort of structure slower than your timekeeper, there might be delays and stuff, but now I'm saying that you're making segments faster than your oscillators are oscillating. Where's that extra time coming from? Okay, so this can be resolved relatively simply actually and so I'm gonna tell you what one can do there. So before we compared the period at the anterior and the posterior, now we want to capture the wave pattern along the tissue by plotting this distance and straightening it out and I'm gonna anchor this point to the left, the anterior part of the tissue is over here and then through the total elapsed submittogenesis we plot all the time points down here and so I think there are two things that are really important to see off this chimograph. The first is that you can see the waves and these are these ridges of light that are the signal that are moving across the diagram and you can see that they curve downwards on the diagram and that curving downwards is the movement through the tissue in the chimograph. The other thing that's kind of obvious but it becomes really obvious when you look at the chimograph is that the tissue shortens its length dramatically and in fact over this interval it shortens by about 60%. So now imagine that you are some sort of Maxwell segmenting demon and you're standing on this end of the tissue and you're looking to the tailbud and you're using the incoming wave to do something like the arrival of the M on the Moorgate sign but as through development now you are moving towards the source of these waves and so this sounds a lot. An observer moving into a wave train sounds a lot like a Doppler effect and so the Doppler effect is caused when an observer moves towards the source of waves. For example, this cyclist moving towards the violinist which I'm sure has occurred to you many times. It's kind of typical isn't it? Riding along and there's a violinist and so actually this is a Doppler effect works in two ways of course. The sound, the frequency is higher as you move towards the source and it drops away as you move away from the source. So the relative motion of the observer is important. This is the version I'm going to talk about with a fixed source because we've anchored the tailbud and because the medium is at rest then and but if you were a clever violinist practicing on the side of the road and you saw a cyclist coming you could adjust your pitch so that it canceled out their movement and you mentioned how confused you would be as a cyclist in those conditions. Okay, so maybe it's easiest to think about this geometrically. It's how we can sort of talk about it in a simple form. Time runs down here. This is plotted out a lot like the Presemitic Mesoderm for good reason and as each wave is emitted from the posterior it travels across the tissue. Its wavelength is the distance between two waves in this direction and the period is in this direction and you can very quickly get a gauge for the magnitude of a Doppler effect just by counting the arrival of waves and comparing them to waves leaving the other end of the tissue. So here nine waves leave during this time but the moving observer sees 11 arrive and that's the elevation in frequency. More events per same unit of time frequently goes up. That's the pitch rising. Okay, so now the question is does this situation happen in the zebrafish? The number of waves decrease over time and is the wavelength constant like you would expect in an optics or acoustic scenario? So to do that properly we wanted to convert the intensity time plots into the intensity space time plots into the variable of a clock which is its phase and so using a wavelet transformation we can convert each of these time traces down here into the phase and then we can re-plot that in terms of the clock variable, the phase and you can see we get the same information back 14 waves leaving the posterior and 16 being received at the anterior. So we've got this 10%, this very reliable 10% offset. The segments are falling 10% faster in the anterior than the signals being released is coming from the posterior. Yeah, it is true. It is true. So I don't know if you, by inspection from the movies I might have said a couple of times that as the waves come from the posterior they change their wavelength and appear to slow down. So that very qualitatively but that's what you're seeing in that plot and there's a way to analyze that and I'll show you in just a sec because it turns out to be very important. So good eyes. So okay, so that's one embryo. We can now combine, this is very reliable, this is now the median phase map from 18 different embryos and I'm gonna play this, so this is data, this is not a simulation, it's a median phase data from 18 embryos and now play this. And so what we're looking at then is the view in the tissue as an observer goes through time and I think what you can see is that this anterior end of the tissue is moving into the waves and it's experiencing a Doppler effect. So the number of stripes, if you like, that you can see back here is decreasing continuously in time. So that pattern is not scaling. The phase offset is being eaten up as the tissue shortens. So another way to do that is to count the number of waves across the tissue through time and you can see that it's continuously decreasing. A word of caution, of course, if I was to make, if I was to try and do this study over a short time interval, let's say I looked over these three cycles, I'd probably conclude that the system was in steady state. But when you increase your time window to look at a longer thing and you see that in fact the system is not at steady state. So, okay, the pattern doesn't repeat. So there's no scaling of this pattern. And now we can ask the question whether that effect, the Doppler is sufficient to account for the 10% difference that we saw. And it turns out that it's not. So this diagram is constructed for a reason because it's approximately the angle that the tissue makes. And given, if it was strictly a Doppler, like you were saying, the wave didn't change, then we actually would have expected a much stronger Doppler effect, something that perhaps we would have spotted a lot earlier. But we quantitatively don't get it. We would have got it expected about a 25% effect from the Doppler change in the period. But we only see a 10 and we actually really trust that number. So we need to know what are we missing? And perhaps it's in our other expectation from a Doppler about the wavelength being constant and you're absolutely right, the wavelength is not constant in the system. And so you can see that in one way by picking out a particular point in the phase and then looking how long you need to go to get to the next position around the clock. And you can see at this point in the tissue that shrinking continuously during time. So it doesn't shrink uniformly across the tissue, but it does shrink across the tissue all through development. And so what does that mean? And so again, intuitively, you can see that by making another wave diagram. And this time I'm gonna take the observer out. So we can see what the effect of having a shortening wavelength is. So here's our waves. And now the wavelength is shortening. This is drawn in by hand, but it's approximately the same as what goes on in the fish. And you can see just by counting the number of cycles, nine in the posterior, and now you only get seven in the anterior. So a shortening wavelength in the tissue actually has the opposite effect to a Doppler. It's actually decreasing the frequency from the observer at rest. Okay, now of course, just like the Doppler, this you can flip this around. If you redraw these waves so that that wavelength is growing, then even an observer at rest will see an elevated frequency. But that's not what the fish does. That's what the fish does, it slows. And so it turns out that you can, so we're actually looking for a name for this and we searched all of the usual scholarly sources like Google and we couldn't find anyone like Doppler who had reported something like this happening in a naturally occurring system. And so I propose that we call it the oats effect. This didn't get through the lab meeting for obvious reasons. So we're calling it the dynamic wavelength effect. And its definition is a time and space dependent change of refraction in a wave carrying medium. We've chosen that very carefully. It can occur in dynamic waves, so energy transfer in waves like light or acoustics, even though that isn't the way the waves move through this tissue because they're kinematic waves. Okay, it actually turns out that plasma physicists use this effect and we found this out more recently because the density of the plasma changes so fast that it's on the right frequency to see a color change if you shine a laser in when you ignite a plasma. So the reason why no one had spotted, I think the reason why no one had spotted this effect before was that in order to see this effect, you actually need the time scale of the change in the wavelength to be around about the same as the time scale in the period. So that is to say, as soon as you, okay, let me go one step further and then I'll come back to compare the time scales again. So the rhythm of segmentation then is really in some sense and you can do the maths and show that you can linearly decompose this. There's a Doppler effect and a dynamic wavelength effect and their combination gives you quantitatively what the observer sees at this end of the tissue. So another way of thinking about this is to ask the Hof and the analogy I would use is to say, imagine you're standing at the beach and, sorry, imagine you're out in the water and the Hof is at the beach and you are out in the water and you're measuring every time you go over a wave and the Hof standing on the beach is measuring every time a wave rolls over his suntan feet. And so despite the fact that you're out here in the wave field and he's at the edge, you're gonna record the same period. Now imagine, so that's the system at steady state. Now imagine you start to sink and you call for help and the Hof grabs his large orange thing and he goes into the waves and he swims powerfully through the waves and then he, but he's a good scientist so he is keeping recording every time he swims over a wave peak. And so are you, even though you're drowning because you're very dedicated to? And now you compare the two frequencies. Now what's interesting here is that, of course, he's gonna hit the waves faster because he's swimming into them and so his frequency is gonna go up. But the amount that his frequency goes up also depends on where he is in the wave field. So on the local wavelengths that he encounters. So this is an analogy to what we think is happening but it's not so far. Actually to get the full analogy, you would need the tide to be going out at the same time. That would give you the shortening of the, that would give you a changing of the wave profile over time. Okay, so what do we think about this? So this, I think we can say that the time scale of genetic oscillations is not sufficient to describe the period of segmentation and the key ingredients then are the period of the genetic oscillation. So don't get me wrong, that's critical, that's core. It turns out though that the genetic oscillators are organized into these waves and as soon as you have a wave, that wave can have a consequence in the tissue if it's not at steady state and that's the key because the tissue shortens and you get a Doppler effect and the wave pattern also alters gradually. We know much less about that and both of these things contribute to the output frequency that you see at the anterior end of the tissue. We only see these effects. So let's say if you have any wave effect and a shortening domain, you must get a Doppler effect unless you're pattern scaling. You must get a Doppler effect. But if your frequency is on a different time scale to your shortening, then you'll never see it. It'll be so tiny, it really doesn't matter. And I think what we've got here is in some sense a fortunate ratio of time scales such that at this rate of shortening and that period it really does matter. It will change the number of segments in an animal, 10% makes a difference to the animal. Okay, so I think that's quite spectacular. And I think you say, oh well, it's all just wave effects and stuff, it doesn't really matter. And maybe another way to think about it is that this enables the fish to form segments faster than any oscillator is ticking. That's the consequence of these waves in the system. Okay, now, so we've got waves. And we know that they change during development and we can estimate their contribution to the observed frequency. But maybe the waves don't have anything to do with this actually forming the segments. And so can we alter the wave? So that's the question that one wants to do as a scientist. If you've got waves, can we tune them differently? And we can, and now I'm going to tell you about experiments where we, and these are just, this is brand new. So, and I think this suggests that we can tune the waves and that the effect that you, then you see another kind, you see it's another example of a wave effect in the tissue. Okay, so what Bokai did in the lab was he engineered an animal with an elevated level of Delta D expression. And we're going back to Delta Notch signaling. He was hoping to examine coupling and so he created an animal where he took the Delta D gene locus and he inserted a YFP at its C-terminus and then he created transgenic animals with this piece of DNA. And when he did that, he created two stable lines. Actually he created quite a few, but he kept two for analysis and he named them both after cities that start with D, Dover and Damascus. And when we looked at their expression, we saw that the patterns of Delta D expression from the trans gene, as far as we could tell, matched the endogenous patterns very well. And I think this is important. If we overexpress Delta, we block synchronization and we don't learn very much about it. We knock it out, you saw what happened, the system desynchronized and this was an attempt to supply more coupling into the system by expressing Delta in the right place under its own regulatory controls. So we can estimate the copy number, seven copies for Dover and probably close to, that's 150, it should be about 100 copies for Damascus. Okay, and the protein expression correlates well with the transgenic number. So we've got antibodies to these proteins and we can see that as we increase the copy number of the trans gene, we see a corresponding increase in the protein that's produced. So the trans gene's working. And to ask the question whether we had delivered elevated Delta Notch signaling, we first checked in the central nervous system and it's not something that we've discussed at all, but Delta Notch signaling is active in the central nervous system and elevated and makes a difference when individual neurons are competing to, sorry, individual neuroblasts are competing to become neurons by a process called lateral inhibition. What I want to point out here is three different markers of neurons and so you can see these neurons down the spinal cord. There's sensory neurons on each side and motor neurons down the middle and then there's a trigeminal ganglia is right here. And so this is a wild type fish and when we remove one of the copies of Delta D, we see is probably not so obvious here, we see an increase, it's more obvious here, an increase in the number of neurons and we take both copies of Delta D out, we make even more neurons in these different domains. So as you lose Delta, the key thing to see here is that as you lose Delta Notch signaling, you get more neurons. Now when we look at the transgenic lines, we see as we increase the copy number and hence the amount of protein, we get fewer and fewer and fewer neurons in those domains and we can quantitate that. The primary motor neurons decrease their number with the amount of Delta and that's true also for the Rohanbeer neurons and the trigeminal ganglia. So okay, what's the point here is that as we've tuned the amount of Delta in the system, we've smoothly decreased the number of neurons and that's telling us that these different transgenes are active in Notch signaling. That's the point of this control experiment. If you study segmentation, it's a control experiment. If you study your genesis, it's the main experiment. Okay, so now let's come back to segmentation. What happens? So the transgene is capable of completely rescuing the aft eight phenotype. So here's a wild type animal forming good body segments. It makes 17 segments at the anus and 34 segments on average in the end of its tail. The aft eight mutant, no Delta D, desynchronizes and that's what we discussed yesterday. So the anterior segments are a bit longer and then it shows this defect in somitogenesis. So you probably recognize that from yesterday. Now the Dover transgene, which has seven copies, completely rescues the pattern formation, the synchronization and the number of segments in the axis. So we think that by tagging it with YFP by making the transgene, we didn't change the activity. But what we saw was that in the Damascus, which now has a high overexpression, we see a couple of things. We occasionally see defects. Can you see there's a gap in that segment? So it's not rescuing perfectly, but it's doing something else as well. There are now 18 segments in the trunk and 37 in the whole axis. So this animal has made more segments in its axis and that's what we might expect if we'd sped the clock up. So here's the data. It forms about seven and a half percent more segments that corresponds to about three more segments, Damascus. The other transgene's don't but Damascus does both in its trunk and tail. It's important that it does in the trunk and the tail. It's not that the extra segments are just being added to the end of the tail. They're being smoothly formed all along the axis but there's more of them and they're shorter. And here's the key measurement from the time lapse movies is that, so we compare here, here's the wild type. Here's a aft eight, heterozygote and the dover, the dovers. There's no significant change between their period but the Damascus is making its segments faster and it's actually making them about 6.5 percent faster than the wild type. So this is in really good agreement with the change in the size and the number of the segments. Again, it looks a lot like the segmentation clock, the predictions of the segmentation clock by changing the timing, change the anatomy of the animal. We wanted to check that the effect of Damascus was due to elevated delta notch signaling on the segments because it could have been that that transgene had hit some other gene and we're looking at some completely unrelated effect but we can remove the effect on the period that we see in Damascus by blocking notch signaling. So that acceleration, if you like, is notch sensitive. We block that with DAPT. So otherwise it's a normal axis. It spends the same amount of time going from its first segment to its last segment, so this is the duration that it's been segmenting. It extends its axis at the same rate and its PSM shortens at the same rate. So that would be important if we're thinking about a shortening tissue because now we have to consider that the system is not at steady state. And so that means that these two relationships seem to be holding. Okay, so what's going on here? We've got more delta notch signaling. We've produced faster segments. We've produced more segments. We haven't otherwise altered the body. One possibility that came to our mind was that we might have changed the wave pattern because we've been thinking a lot about waves. And so we talked yesterday about the ability of delta notch signaling to change the collective frequency of a population of oscillators and that's certainly true. But it's been well studied for quite a long time that by changing coupling strength and delay, you can also change the wave pattern. And in a way, this is going back to this... This is the reason why we were interested in testing whether delta notch signaling was required for the cell slowing. So it's not required for the cell slowing. That doesn't mean that if you put more delta notch into the system, you might change the wavelength. So sort of theoretically, it's certainly possible to alter the wave patterns by cranking up the coupling by changing the coupling strength and the delay. So the measurement that we talked about before was following the individual cells and watching their slowing in a delta notch loss of function. And in that, following the individual cells, we couldn't tell the difference between the wild types and the delta notch loss of function. Couldn't tell the difference between those cells that were coupling to each other and those cells that weren't coupling to each other. So to the precision of our measurements. Now, what does that mean? That means that if we go from the level of coupling that's in the animal and we go down, we don't significantly change the wave pattern. What I'm wondering now is whether if we dramatically increase the coupling, whether we can see the wave pattern change. Now, if delta notch signaling is active in that tissue, I would say it's impossible to cut the coupling without some change in the wave pattern. But it might be very small. And in our experiments, we couldn't pick a change in the rate of slowing. And so I'm not using that experiment to say that delta notch can't affect the wave pattern. I'm using that experiment to say that delta notch is not required to slow the cells down. There must be something else that's slowing them down. But if you take, so that means to say that we have to take the idea of an intrinsic frequency profile very seriously. And now, given that intrinsic frequency profile, let's put coupling on top of it. And that can act to modulate the phase profile that comes out of the tissue built from the frequency profile across the tissue plus the local interactions, if that makes sense. Okay, right. And now what I think potentially by putting in a 50-fold elevation in delta D into the system, what we've done is we've tweaked, we've tweaked the coupling strength to the point, possibly where we maybe could change the phase pattern. We might change the wave pattern across the tissue. So this is what Bocai measured. And I'll show you what he saw. So this is the experiments he did. What you really want to see, full disclosure, what you really want to see is us going back to the time-lapse microscope and looking at the fluorescent signals, construct a chymograph and measure all that out. The problem is that when we made the transgene, we tagged it with exactly the same fluorophore that is our marker for the Hess-Hur oscillations. So we actually can't measure the internal oscillations in the system at the moment because of this cluster of fluorophores. What we can do is go back and look at the endogenous gene expression and look at the stripe pattern that we see down the axis. We can get some idea of the intensity profile of these stripes and then we can collect that information for many animals that are carefully staged and compare them together. So here is his wild-type animals. You can see four, three, three, two, two waves that are visible and we can measure the wavelength, estimate the wavelength by going peak to peak. It's not perfect but it's a reliable measure of the pattern. Now in a Damascus, we see two things. We see an increase in the number of stripes that are visible along the tissue. So we go from an average of three during these stages to an average of four and in these later stages we go from an average of two waves to an average of three. So another way of saying that is we put an extra two pi of phase offset across the tissue by overexpressing these deltas. And we can, with some reliability, we can, I should say with a good reliability, we can measure the anterior wavelength. Now why do I care? So the phase pattern has changed across the entire tissue but I care about the anterior wavelength because if I'm Maxwell's segmenter, that's the wavelength that I'm hitting as the tissue shortening. If I'm making a decision on the incoming wave, I don't make a decision on the wave back there. I make a decision of the wavelength that I see as I pass it. So we measured that wavelength and we saw that it was systematically shorter in the Damascus. So those are the green measurement bars across here. And it's about 20% shorter. So what does that mean? If we now go back to the ideas of the Doppler, the Doppler effect and the dynamic wavelength effect, and we just ask what period would we predict with the Doppler effect that was the same as a wild type? With this shorter anterior wavelength, we predict a 5% shorter, 5.5% shorter period and what we measure is a 6.5% shorter period. So actually we can account for nearly all of the period change by this change in the anterior wavelength. So we don't have access to the frequency in the posterior. We know that the wavelength across the tissue has changed, but in the end, the signal that's arriving in the anterior is a shorter wavelength and that's what the segment is seeing in the anterior. So our model for Damascus would be that the shorter wavelength in the anterior means that with the same movement of the observer, we're seeing the segments form more quickly in the anterior due to a different Doppler contribution in the system. Okay, so that's the best evidence we've got that by changing the wave pattern, we simultaneously change the frequency of segmentation and we can almost quantitatively account for the change in the observed segmentation frequency by the change in the wavelength in the pattern in the anterior of the tissue. I'm not completely happy with this because I think to really understand the full changes that that transgene has made to the tissue, we need to be able to see the waves in real time across the whole tissue. But I leave that data with you now as being consistent with the idea that by changing the wavelength of the pattern, we can alter the output frequency of the segmentation clock. Good, okay, I think we're gonna finish early tonight. And let me then make some conclusions for the main points that I wanted to make in the lecture tonight. The first is that cells slow down before they stop across the tissue and that's the basis for the traveling waves of gene expression, that's the cellular basis. In some way, gradients of signals appear to be involved at least in setting the position where the new segments form which would be equivalent to the position where the oscillators arrest, but it's still unclear how this works. The segmentation clock doesn't repeat. This is a really important point. So I wanted to spend just a minute on this. So you think of a clock, typically a clock has a well-defined period. So it doesn't matter where I look in the inner workings of the clock. I'm gonna read the same period. The segmentation clock fails that test. During development, it's, because it's changing its length and it's changing its wave pattern, it, sorry, start first. The frequency you read out of the segmentation clock actually depends where you read it. So it doesn't actually have a well-defined period. Of course, from an embryological sense, the period that counts is at the anterior end, because that's the business end, okay? So that's fine, but in a more technical sense, it's not actually a clock. It also changes through development. So it's internally changing as it goes. It doesn't scale, it doesn't neatly shrink down from a big segmentation clock to a mini segmentation clock, its internal dynamics are changing as it goes. So, and then I, we discussed that wave effects can influence the period, and that completes our tiers of effects in the clock. So we discussed how the time scales in the genetic circuit would give rise to sort of a base frequency coming from the autonomous oscillators. Then we saw how coupling could alter that frequency by interactions. If there are delays in the coupling. And now finally, at this third level, this tissue level, I've showed you that wave effects add another modulation to the output frequency. So to understand the period of segmentation, we actually need not only a sort of microscopic or cellular level rhythm, but we need to include collective effects at two additional levels of organization in the tissue. And it's, so it's not possible to describe the segment, period of segmentation just by looking at an individual cell. It's not there. It's not actually in the single cell. It only emerges once all of these effects come up together. And there could be more that we don't know about yet. But I think that to me, just personally, that's extremely exciting to see the richness of dynamics in this piece of tissue in an embryo. Okay. And finally, I think the last point we looked at with the coupling itself can affect the wave pattern. And that has a consequence to the timing and actually the anatomy of the animal that that results. Okay. So don't let me fool you into thinking, well, he understand what's going on. This would be when James would put up his hand and say, but you know, why doesn't this all fit neatly together? And it doesn't yet. And there's lots of things that we don't know. And one of the sort of embarrassing things in a way that I didn't talk about today, but I think it's a really interesting question and this is something that we were discussing of the day is where exactly in the pre-Semitic Mesoderm is the decision being made to make a new boundary? And in what I talked about today, the assumption was that it's being made where the waves stop, that the rest front of the genetic oscillations is where all the heavy lifting is being done in a sense, biologically. And in a biological sense, we would call that a determination front where the cell become determined to their fate. But there is evidence to suggest that the cells might be making starting to make decisions before the oscillators have stopped. And that to my mind is not yet reconciled. Whether that means it's just a small, is it a small modulation? Do we just need to check what the waves are doing back a few micrometers into the tissue or have we really missed something? And so I don't know. I think that's one of the major questions in my mind. How does, I think what we don't understand is how do we get the precision that we see in the system? How do we get consistently the right length of segments? There's a whole bunch of whole set of areas where noise can be entering into this process. Synchronization is a great way to reduce noise. But as soon as we have these tissue level processes, then we sort of have to trade off with other things like the movement of the cells, the movement of this front, all of those can have noise as well. And one way to think about that is to wonder how the left and right hand sides are symmetrical. Because if you're thinking about a process that's being transported up each side, and yet each of the target tissues on the left and right, which anatomically are completely separated in the animal, there's this idea that the left and right hand sides of your body, at least in your skeleton, are completely symmetrical. And I think that's an open question. I'm not, I think we don't know how symmetrical they actually are when they form. And I think that's something that would be really interesting to look at in more detail. The role of cell flow, I think, is important. And I'd be coming back to this over and over again. And it plays an important role in trying to understand this difference or the sort of contribution of maybe diffusive signaling in the tissue versus advective transport of signals in the tissue and their balance. That's actually would be what you would call the Peclet number in the tissue, the ratio of diffusive to advective transport. And I think we don't know, but the cell flow in the reference from the tissue is so fast that we really ought to consider that advective transport might be sufficient. And finally, I suppose I've sort of skirted around this. What is the mechanism of slowing the cells? How do they actually slow down? And I think that is, I think we know almost nothing about that at all. And so I'm deeply curious, for a while it appeared to be sort of a baroque interest. If you don't think the waves make any difference, in steady state they don't, then exactly how they slow is sort of, it's sort of academic or baroque interest, right? But once you realize that the waves set the output period or at least involved in setting the output period, now it matters how you slow the oscillators because that's going to affect your output period. So how does that work? I don't know. And I'm gonna offer you one last little tidbit, which is an experiment where a couple of people in the lab pulled individual cells out of the tailbud and they put them into culture in the absence of any of the gradients. And this is one of the reasons why I think we don't really understand the gradients, this result. And this is, everything else I've tried to tell you has been thinking about what's been published and collectively as a field what I think we know and what I think we don't know. And this is, this next bit is we definitely don't know and it's not published, but have a look at this. Here's a cell that Laurel pulled out of the posterior end of the animal, put it into culture. There's no growth factors. There's no wind, there's no retinoc acid, there's no FGF. And what this cell does is it oscillates, its amplitude grows, it slows down, it stops, and then it differentiates. So this is something I leave, that's the last thing I, the last piece of thing that I want to give to you. I find this deeply interesting. Here's a, so if we believe this, and so I'm showing you a typical cell, but we've seen hundreds of them and this is very, very reliable. And what this means then is that the cells coming out of the posterior of the tissue and entering into the flow, they already have all the information they need to qualitatively run the whole program that gives rise to the stripes, the slowing, the rest, and the differentiation. And so that doesn't leave a diffusive signaling at long range across the tissue with very much left to do in terms of producing the behavior. Perhaps what it does is it coordinates the behavior. Perhaps that's what it's doing. It's not instructing the cells what to do, but it's telling them do it all at the same time. So I leave you with that speculation. And I'm looking forward to teasing this stuff apart in vitro now. Okay, thank you very much.