1 00:00:12,770 --> 00:00:23,180 I want to talk about some high level conceptual things before we get into mathematical modelling. 2 00:00:23,180 --> 00:00:26,840 I took this from Ian Stewart's book. 3 00:00:26,840 --> 00:00:42,320 It's a 15th century woodcut and what it says is it gives you an illustration of the fact that the concepts that we use 4 00:00:42,320 --> 00:00:51,560 to think about science are often given to us by mathematics and to limit the science that we can do and understand. 5 00:00:51,560 --> 00:01:04,910 In the 15th century, the prevailing view was that God would use only perfect geometric figures to effect natural motion. 6 00:01:04,910 --> 00:01:13,370 And so all natural motion had to be resolved in terms of straight lines and circles or segments of circles. 7 00:01:13,370 --> 00:01:20,690 So if that's your cognitive stance, if that's your desired religious belief, 8 00:01:20,690 --> 00:01:32,960 then the trajectory of the Cannonball is a straight line, followed by a circular segment followed by a straight line downward. 9 00:01:32,960 --> 00:01:44,540 That's the best you can do with these concepts. And of course, you're going to get a lousy physics out of this, though physics at all. 10 00:01:44,540 --> 00:01:53,420 But that's the limitation of the concept. Now I want to fast forward to the 20th century, 11 00:01:53,420 --> 00:02:02,420 and I want to talk about another dominant master concept that I'm going to try to suggest is imposed upon the data, 12 00:02:02,420 --> 00:02:08,390 whether the date of it or not, that is the notion of equilibrium. 13 00:02:08,390 --> 00:02:15,620 Now where do we see the concept of equilibrium in every single science? 14 00:02:15,620 --> 00:02:26,360 You open page one of the chemistry book and they talk about chemical, a number of chemicals in a box and they quickly go to chemical equilibrium. 15 00:02:26,360 --> 00:02:30,620 We take a physics class and we learn about thermodynamic equilibrium, 16 00:02:30,620 --> 00:02:40,730 where the hotter object warms the cooler object until they come to an equilibrium temperature at which T one equals two. 17 00:02:40,730 --> 00:02:46,720 You take the. 18 00:02:46,720 --> 00:02:54,220 You take an ecology class and you learn about the carrying capacity of the environment and 19 00:02:54,220 --> 00:03:01,480 the concept of ecological equilibrium and the slow population grows to the carrying capacity. 20 00:03:01,480 --> 00:03:10,960 If it were above the carrying capacity, it would shrink to the carrying capacity and we have the concept of ecological equilibrium. 21 00:03:10,960 --> 00:03:14,110 We go take an economics class. 22 00:03:14,110 --> 00:03:22,870 And again, we see the same thing we learnt to make the sign of the cross where supply meets demand is the equilibrium price, 23 00:03:22,870 --> 00:03:28,270 and we're told that a free market quickly reaches that equilibrium price. 24 00:03:28,270 --> 00:03:35,710 And in physiology, we also are dominated by an equilibrium paradigm. 25 00:03:35,710 --> 00:03:41,860 If I can use that word and that equilibrium paradigm is called homeostasis, 26 00:03:41,860 --> 00:03:51,130 and it says that physiological quantities are maintained constant levels by feedback loops. 27 00:03:51,130 --> 00:04:02,380 And in this case, just pull this off the net normal as everyone knows or think they know, a normal body temperature was thirty seven degrees. 28 00:04:02,380 --> 00:04:09,850 And these are maintained by negative feedback loops to restore normal body temperature. 29 00:04:09,850 --> 00:04:17,740 So in addition to the fact of equilibrium, I already alluded to the mechanism of equilibrium. 30 00:04:17,740 --> 00:04:25,540 The mechanism of equilibrium is negative feedback deviation is restored and we have equilibrium. 31 00:04:25,540 --> 00:04:38,830 Probably a very popular example of this in physiology is the feedback loops that control hormone secretion by the target organs of the gonads, 32 00:04:38,830 --> 00:04:48,670 the adrenal cortex, the thyroid. All are involved in negative feedback loops, sometimes multiple negative feedback loops. 33 00:04:48,670 --> 00:04:57,670 I will stylise it here as a single negative feedback loop, although for research purposes, we would want to get a little more complicated. 34 00:04:57,670 --> 00:05:05,560 The hypothalamus excites the pituitary that pituitary excites to gonad, and the gonadal secretion suppresses the hypothalamus. 35 00:05:05,560 --> 00:05:08,680 So there is your negative feedback loop. 36 00:05:08,680 --> 00:05:19,180 We make a simple three variable differential equation hypothalamus pituitary gonadal this one over one plus g squared. 37 00:05:19,180 --> 00:05:27,760 That's a descending sigmoid, which is the negative feedback, and we simulate this model. 38 00:05:27,760 --> 00:05:34,720 And indeed, the quantities go to equilibrium as advertised. 39 00:05:34,720 --> 00:05:39,070 It's interesting we see the tracing of the three quantities here. 40 00:05:39,070 --> 00:05:52,570 HP and G. Going to equilibrium is kind of interesting to plot that trajectory as a trajectory in three dimensional h p g space. 41 00:05:52,570 --> 00:06:02,680 And when we do, we see what is called a stable equilibrium point, also known as a point of trapdoor, 42 00:06:02,680 --> 00:06:08,680 where no matter where you start the system, it's except zero zero zero. 43 00:06:08,680 --> 00:06:14,320 Any initial condition anywhere is going to go to stable equilibrium point. 44 00:06:14,320 --> 00:06:22,240 And that means if we perturb off the stable equilibrium point, the system goes back to the stable equilibrium point. 45 00:06:22,240 --> 00:06:29,810 And so that is the picture of the homeostatic mechanism. 46 00:06:29,810 --> 00:06:43,970 Let's talk quickly about gene regulation, because, as you know, genes are the dominant subject in physiology today p53, the guardian angel gene, 47 00:06:43,970 --> 00:06:47,030 the guardian watchman gene gene, 48 00:06:47,030 --> 00:07:01,490 the big anti-cancer gene is in a negative feedback loop because it induces a protein called Indium two, which in turn inhibits p53. 49 00:07:01,490 --> 00:07:13,160 So there is a negative feedback loop in p53 has one extremely important protein in morphogenesis in the laying out of the body plan. 50 00:07:13,160 --> 00:07:24,740 Some biogenesis has one produces, has one RNA, which produces, has one protein, which represses the expression of the gene. 51 00:07:24,740 --> 00:07:29,510 So there's another negative feedback loop. 52 00:07:29,510 --> 00:07:38,000 And then, of course, to come back to temperature, temperature is maintained at 37 degrees by a negative feedback loop. 53 00:07:38,000 --> 00:07:48,980 Mm-Hmm. So that's a beautiful picture. We have all of these quantities being maintained at steady state levels by negative feedback loops. 54 00:07:48,980 --> 00:07:53,930 And it's just it just makes you happy to see this. It's so, so beautiful. 55 00:07:53,930 --> 00:08:00,440 The only problem is it is completely false from beginning to end. 56 00:08:00,440 --> 00:08:13,280 And every word that I have said to you in the last 10 minutes is a lie, but normal body temperature is 37 degrees. 57 00:08:13,280 --> 00:08:21,860 That's the one physiology fact that everybody thinks they know here is the reality. 58 00:08:21,860 --> 00:08:27,800 Normal body temperature oscillates. These are student volunteers. 59 00:08:27,800 --> 00:08:32,510 Over four days you see day and night in white and grey. 60 00:08:32,510 --> 00:08:41,240 And what you see is No. One, there is an oscillation in the air that has one degree Celsius peak to trough. 61 00:08:41,240 --> 00:08:48,260 That's a serious oscillation. It seems to be very stable day to day. 62 00:08:48,260 --> 00:08:58,190 It has a constant waveform notice how it rises and saturates and stays high, then plunges late in the evening and stays low all night. 63 00:08:58,190 --> 00:09:06,320 This is a regular, reproducible physiological phenomenon. 64 00:09:06,320 --> 00:09:16,550 And yet everybody here is warning. Not everybody here, but in the general public is walking around with a complete misunderstanding of this. 65 00:09:16,550 --> 00:09:21,620 Nobody seems to have noticed, and I do have to say something. 66 00:09:21,620 --> 00:09:30,260 This is a theme that I'm going to start touching on, and the data are published in a reputable journal. 67 00:09:30,260 --> 00:09:46,100 It's been 50 years, and yet this data is probably new to even most of the people in this audience, let alone the general physiology public. 68 00:09:46,100 --> 00:09:59,350 So that's kind of worth remarking that I have to stand up here and deliver you the news that was delivered in science 50 years ago. 69 00:09:59,350 --> 00:10:11,440 Let's talk about hormone regulation. There is the negative feedback loops, they maintain steady state levels in hormones, 70 00:10:11,440 --> 00:10:20,350 except they don't because hormones are not maintained at steady state levels by anything. 71 00:10:20,350 --> 00:10:28,600 Here's a typical luteinizing hormone and Mr Dye all over 24 hours and a healthy female. 72 00:10:28,600 --> 00:10:40,300 And look at what you see. Number one, there's a big day night isolation during the daytime, these smaller oscillations at night. 73 00:10:40,300 --> 00:10:45,280 They get very large, very well formed and a lower frequency. 74 00:10:45,280 --> 00:10:58,180 So we have oscillations here at a number of time scales the 24, the 12 and then these three three hour oscillations here s2.0. 75 00:10:58,180 --> 00:11:09,190 All, on the other hand, has a large two hour oscillations during the daytime and then is fairly constant with some noise at Night-Time. 76 00:11:09,190 --> 00:11:20,980 These are profound oscillations, and in fact, all of the physiological variables of the body oscillate like crazy serum potassium. 77 00:11:20,980 --> 00:11:32,070 Look at that over four days catecholamines are all undergoing profound oscillations. 78 00:11:32,070 --> 00:11:43,620 Let's talk about the p53 negative feedback loop that maintain stability in p53, 79 00:11:43,620 --> 00:11:55,770 the group at Harvard Systems Biology had the revolutionary idea that they wouldn't just consult their personal philosophy of equilibrium. 80 00:11:55,770 --> 00:12:04,980 They wouldn't actually do an experiment and look to see how p53 changed over the course of time. 81 00:12:04,980 --> 00:12:16,470 And what they found was clear oscillations in p53 and in team and corresponding oscillations in its inhibitor in the too. 82 00:12:16,470 --> 00:12:21,000 So here's p53 in green and Mdm2 in red. 83 00:12:21,000 --> 00:12:29,010 That's twenty nine hours there. And so you see two hours of p53, two to three hours of Mdm2. 84 00:12:29,010 --> 00:12:38,650 This is an oscillatory system. Let's talk about his one, so has one. 85 00:12:38,650 --> 00:12:53,980 Represses its own transcription, but the result is not constancy here is has one expression over 12 hours and you see very clearly a two hour 86 00:12:53,980 --> 00:13:03,130 oscillation in the expression of has one with a corresponding to our oscillation a little bit out of phase with it, 87 00:13:03,130 --> 00:13:15,610 as should be in. It has one on wall and has one protein, which inhibits the transcription of has one. 88 00:13:15,610 --> 00:13:18,880 We haven't talked yet about NF kappaB, 89 00:13:18,880 --> 00:13:31,390 which is sort of everybody's favourite protein group at Caltech looked at and they've captured the expression in a number of different cell lines. 90 00:13:31,390 --> 00:13:41,020 And they found high expression, low expression, high expression over six hours. 91 00:13:41,020 --> 00:13:46,840 Finally, let me ask you a question. You biologists. 92 00:13:46,840 --> 00:14:00,820 What happens when sperm meets egg? The moment of the genesis of life, the answer is intracellular calcium oscillations. 93 00:14:00,820 --> 00:14:09,580 That is the first act of morphogenesis in the fertilised embryo that post fertilisation. 94 00:14:09,580 --> 00:14:13,960 We begin to get regular oscillations in intracellular calcium, 95 00:14:13,960 --> 00:14:27,690 which serve as a kind of a time beta for the subsequent the clock to time the subsequent more full genetic processes. 96 00:14:27,690 --> 00:14:39,990 Let me go back to chemical equilibrium for a second, because it's a very powerful concept, and we all learnt it in the early 1950s. 97 00:14:39,990 --> 00:14:51,270 A Russian chemist named Bamboozle had a laboratory model of the Krebs cycle the reduction of Malartic acid by bromide. 98 00:14:51,270 --> 00:15:02,670 But it's a model of the Krebs cycle, and he gets up this reaction in his lab and this is what he observed. 99 00:15:02,670 --> 00:15:10,380 He observed oscillations in all the reaction, intermediates and products. 100 00:15:10,380 --> 00:15:19,320 And that's an awfully good. I mean, that looks like a mathematical model, but that that is his chemistry experiment. 101 00:15:19,320 --> 00:15:25,470 And so he was very excited right up. The paper sent it to a big Russian chemical journal. 102 00:15:25,470 --> 00:15:33,270 Big Russian Chemical Journal sends it right back to him and says, Do not insult us with this. 103 00:15:33,270 --> 00:15:41,730 So he gets a friend of his who speaks English and they rewrite the paper in English, and they send it to nature. 104 00:15:41,730 --> 00:15:53,550 Nature bounces it right back to them, and the editor includes the note from the reviewer and the note from the reviewer said, 105 00:15:53,550 --> 00:16:06,240 We really must develop a form letter to send to these crackpots who think they have invented perpetual motion machines. 106 00:16:06,240 --> 00:16:15,810 Now what's interesting about that is I was having lunch about five years ago with a friend of mine who's a chemistry professor, and we were talking. 107 00:16:15,810 --> 00:16:20,040 I mentioned oscillatory chemical reactions. Oh, oscillatory chemical was very interesting. 108 00:16:20,040 --> 00:16:25,680 I've always wondered about that. How do you make one? And I said, Well, the recipes are in the papers. 109 00:16:25,680 --> 00:16:29,580 Let's go look up a paper reader. He says, I like them. I thought that. I thought, I got that. 110 00:16:29,580 --> 00:16:36,630 Let's let's go to my lab. He starts grabbing things off a shelf, including concentrated sulphuric acid. 111 00:16:36,630 --> 00:16:40,980 So don't try that at home. But he grabs a bunch of things off a shelf. 112 00:16:40,980 --> 00:16:45,270 He mixes them up. He gets an oscillatory chemical reaction. 113 00:16:45,270 --> 00:16:55,740 So now I want to come back to that point that every year the reviewers of Bell office paper could have done the same thing. 114 00:16:55,740 --> 00:17:02,430 They could have grabbed it. But this guy's crazy grabbed a bunch of reagents off the shelf and they would have seen this right. 115 00:17:02,430 --> 00:17:12,540 But they didn't do it and they didn't do it because they didn't need to do it because they already know that this is impossible. 116 00:17:12,540 --> 00:17:17,250 And there was really no point doing the experiment. It's like, 117 00:17:17,250 --> 00:17:27,810 you know that pigs don't fly and you're not going to do an experiment to verify that pigs don't fly because you know damn well what they don't. 118 00:17:27,810 --> 00:17:45,270 And there's an interesting psychiatry there, which is denial behaviour, a kind of a mass psychosis that says, I don't want to see the data. 119 00:17:45,270 --> 00:17:54,180 I don't want to do the experiments. And we believe in experiments. You know, we have to do you have to do the experiment to verify the theory. 120 00:17:54,180 --> 00:18:08,520 Nobody did them because of this psychiatric clinging to the concept of equilibrium and damn the data. 121 00:18:08,520 --> 00:18:20,460 So this is really a kind of a scientific psychosis of denial, of pretty straightforward reality. 122 00:18:20,460 --> 00:18:33,750 So let's hold that there because having established that so I take it that I have established the fact of association in spite of all of this denial. 123 00:18:33,750 --> 00:18:44,200 Next question What are the mechanisms of isolation? So what are the mechanisms of everything in physiology is a funny question. 124 00:18:44,200 --> 00:18:57,370 Mechanisms of oscillation. Because in physiology, there is already a view of what is a mechanism, mechanisms and physiology, according to this view, 125 00:18:57,370 --> 00:19:06,730 or that tiny little proteins and the genes and the components of the genes and some components of the genes. 126 00:19:06,730 --> 00:19:15,520 That's the smallest physical and chemical elements of a process that is the mechanism of the process. 127 00:19:15,520 --> 00:19:27,310 And so we see see things like the mechanism of the cardiac long kutty syndrome or the mutations here in the cardiac sodium channel, 128 00:19:27,310 --> 00:19:33,070 and there are indeed mutations in the cardiac sodium channel. 129 00:19:33,070 --> 00:19:47,070 But. What do they tell us about what is happening in the heart when you have the arrhythmias that are associated with that gene defect? 130 00:19:47,070 --> 00:19:58,110 How do how does that gene defect surface in the whole heart arrhythmia and in the EKG pattern that we see? 131 00:19:58,110 --> 00:20:01,740 And the answer is we don't know. 132 00:20:01,740 --> 00:20:15,870 But we still believe that the mechanism is there in the gene, but we can't really take you from the gene defect to the actual phenomenon itself. 133 00:20:15,870 --> 00:20:27,930 So I reject this idea, that mechanism and physiology are the tiniest little elements because they're not really telling us anything. 134 00:20:27,930 --> 00:20:36,300 Hmm. Let's talk about what the mechanism, for example, of oscillation is. 135 00:20:36,300 --> 00:20:49,440 Well, that has one paper already put their finger on a key dimension oscillatory expression if it has one regulated by a negative feedback loop. 136 00:20:49,440 --> 00:20:59,970 So negative auto regulation of has one transcription is what is responsible in their view for these oscillations, 137 00:20:59,970 --> 00:21:09,780 we keep in mind that we already said that negative feedback explains homeostasis. Now we're hearing that negative feedback explains oscillations. 138 00:21:09,780 --> 00:21:16,080 So I'm going to address that in a minute. But in their paper, they lay out this model. 139 00:21:16,080 --> 00:21:30,420 We simulated this model and indeed we saw two hour oscillations, the p53 Mdm2 system, as described by the Harvard Group. 140 00:21:30,420 --> 00:21:35,460 They put forward a straightforward three variable differential equation model, 141 00:21:35,460 --> 00:21:45,420 and we simulated we indeed get the oscillations that they claim would be produced. 142 00:21:45,420 --> 00:21:49,050 Let's let's talk about Cap, 143 00:21:49,050 --> 00:22:03,780 a big enough cap a b is also involved in the negative feedback loop NF Kappa B here is sequestered or locked down by these proteins and 144 00:22:03,780 --> 00:22:18,690 input breaks the lock and freeze NF Kappa B and if Kappa B translates to the nucleus where it creates more of the proteins that block it. 145 00:22:18,690 --> 00:22:25,890 So that is another negative feedback loop. And when you simulate their negative feedback loop, you get oscillations. 146 00:22:25,890 --> 00:22:38,820 And indeed, when you knock out the genes for some of the suppressor proteins, you lose the oscillation. 147 00:22:38,820 --> 00:22:48,960 Although when you knock out other genes that are less involved in the filtering mechanism, the oscillation continues. 148 00:22:48,960 --> 00:22:57,870 So here's another point to hold, on the other hand, which is negative feedback can create oscillation. 149 00:22:57,870 --> 00:23:10,530 And it's probably the paradigm case of this is the predator prey equations which surfaced in 19-teens 100 years ago. 150 00:23:10,530 --> 00:23:20,370 Imagine a population of sharks and tuna, and the tuna population increases the shark population by feeding it, 151 00:23:20,370 --> 00:23:26,190 and the shark population decreases the tuna population by eating it. 152 00:23:26,190 --> 00:23:34,530 And the result of a simple model produces oscillations in the shark populations and the tuna populations. 153 00:23:34,530 --> 00:23:40,260 Now we did a little experiment with this model. 154 00:23:40,260 --> 00:23:52,740 We asked ourselves, Suppose we have the view that we want more tuna and we don't like sharks and we want to free the tuna. 155 00:23:52,740 --> 00:23:59,370 So we do the experiment of simply removing sharks. 156 00:23:59,370 --> 00:24:06,840 So we instituted a shark removal programme right there. And the population of sharks declined. 157 00:24:06,840 --> 00:24:14,550 And then the population of tuna rebalance to a higher level, as hoped for. 158 00:24:14,550 --> 00:24:23,400 But when that happens, the shark population also recovers to a higher level than before. 159 00:24:23,400 --> 00:24:32,640 So the net effect of removing sharks is to increase the number of sharks afterwards. 160 00:24:32,640 --> 00:24:39,720 Moral of story complex systems defeat naive interventions. 161 00:24:39,720 --> 00:24:45,000 You just can't go in there and say, I want more tuna and fewer sharks. 162 00:24:45,000 --> 00:24:56,850 And so I'm just going to lower the shark population. And there you go, because the system will not stay there. 163 00:24:56,850 --> 00:25:09,270 From that point of view, it becomes difficult to understand statements like this, which I pulled out of a paper. 164 00:25:09,270 --> 00:25:17,310 We're going to unleash p53 by blocking Mdm2. 165 00:25:17,310 --> 00:25:21,810 And we heard this from a speaker a couple of weeks ago. 166 00:25:21,810 --> 00:25:30,540 This is I pulled this out of a paper. Everybody's trying to unleash p53 by blocking Mdm2. 167 00:25:30,540 --> 00:25:37,980 And that is exactly know, increasing the tuna population by blocking the sharks. 168 00:25:37,980 --> 00:25:43,950 And you will get a higher peak, but you'll also get a higher peak of MDMA, too. 169 00:25:43,950 --> 00:25:48,120 You will change the frequency. You will do all kinds of stuff. 170 00:25:48,120 --> 00:25:59,970 You don't. You can't simply look at this as I'm going to take away the inhibitor and unleash the activator that's bar stool. 171 00:25:59,970 --> 00:26:11,060 Think that's pub sink pub stool thinking that is really not worthy of this kind of phenomenon. 172 00:26:11,060 --> 00:26:19,130 So does negative, let's go back to our question, does negative feedback promote homeostasis or just negative feedback promote oscillation? 173 00:26:19,130 --> 00:26:28,760 We've heard both views. There's an answer, and the answer is perhaps by vacationed there. 174 00:26:28,760 --> 00:26:36,620 So here's an example. Let's take the classic negative feedback of the thermostat and the heater. 175 00:26:36,620 --> 00:26:42,540 The thermostat turns on the heater, the heater puts out heat, which turns off the thermostat. 176 00:26:42,540 --> 00:26:46,220 That's your negative feedback we make. 177 00:26:46,220 --> 00:26:53,000 A simple model of this tea is the temperature of the thermostat stages, the heater state. 178 00:26:53,000 --> 00:27:02,840 We make a differential equation. And in this differential equations, the thermostat is going to respond to the heater. 179 00:27:02,840 --> 00:27:10,220 Notice one over one plus h to the end. That's down going sigmoid. 180 00:27:10,220 --> 00:27:21,470 And we also have a time delay town heater and each tower simply h tower seconds ago. 181 00:27:21,470 --> 00:27:28,040 The time delay value of h because that's what the thermostat sees. 182 00:27:28,040 --> 00:27:32,210 It doesn't see what the heater is putting out right now. 183 00:27:32,210 --> 00:27:37,610 It sees what the heater was putting out 20 seconds ago, 30 seconds ago, 184 00:27:37,610 --> 00:27:44,960 depending upon the circulation of air in the roof and the distance from the heater to the thermostat. 185 00:27:44,960 --> 00:28:00,830 So now we have this model that has two parameters the time, the way now and this exponent and which governs the steepness of the negative feedback. 186 00:28:00,830 --> 00:28:06,980 Low end gentle feedback. High and steep feedback. 187 00:28:06,980 --> 00:28:13,100 And now we apply the hot bifurcation theorem to this model. 188 00:28:13,100 --> 00:28:26,420 And this is what emerges that we can look at the two parameters and we can make that two parameter diagram. 189 00:28:26,420 --> 00:28:30,410 And the theorem says that there's a hyperbola there. 190 00:28:30,410 --> 00:28:42,170 And if the product of the slope of the negative feedback and the time delay is greater than a certain constant, then you're in oscillation. 191 00:28:42,170 --> 00:28:48,920 And if the product of them is below that, then you're into equilibrium. 192 00:28:48,920 --> 00:29:01,790 So there is an exact answer to our question. Negative feedback loops promote homeostasis when the slope is mild and the time delays are small, 193 00:29:01,790 --> 00:29:13,040 whereas if the feedback is steep and the time delays are significant, you are going to get oscillation. 194 00:29:13,040 --> 00:29:18,320 So let's talk about, for example, slope of the negative feedback. 195 00:29:18,320 --> 00:29:26,000 We talked about the hypothalamic pituitary gonadal system and you saw that model and you see that two there. 196 00:29:26,000 --> 00:29:35,270 That two is a gently sloping sigmoid one over one plus x squared is a gently sloping sigmoid. 197 00:29:35,270 --> 00:29:39,950 And when we do this model, we indeed get equilibrium. 198 00:29:39,950 --> 00:29:49,490 What happens when we increase the steepness of that, the harshness of the feedback or the sensitivity of the hypothalamus? 199 00:29:49,490 --> 00:29:53,870 And the answer is the system goes into oscillation. 200 00:29:53,870 --> 00:30:04,040 So just that same model with N equals 10 instead of two gives us stable oscillations in all three quantities. 201 00:30:04,040 --> 00:30:16,480 And now if we do that technique of plotting the three variables as a trajectory in h p g space. 202 00:30:16,480 --> 00:30:25,930 We get that. And what that is telling us here is HPD space, this is a trajectory in three dimensions. 203 00:30:25,930 --> 00:30:33,790 If we start at very high values, we spiral in to a red loop. 204 00:30:33,790 --> 00:30:39,940 If we start inside very low values, we spiral out to the red loop. 205 00:30:39,940 --> 00:30:49,120 All initial, all non-zero initial conditions in this system go to the red loop. 206 00:30:49,120 --> 00:30:56,440 This is a new object. This is called a limit cycle, a trap door. 207 00:30:56,440 --> 00:31:09,040 And what it represents is a stable oscillation because wherever you are, you're going to go to the red loop. 208 00:31:09,040 --> 00:31:11,950 That's the dynamics of the system. 209 00:31:11,950 --> 00:31:23,200 Notice that all of the oscillatory systems we learnt about in physics, the harmonic oscillator, the pendulum, the spring don't have this property. 210 00:31:23,200 --> 00:31:33,940 If you pull the spring out to a larger initial condition, it yo-yos back and forth to the larger initial condition forever. 211 00:31:33,940 --> 00:31:39,400 But if this is body temperature and you have a fever one day, 212 00:31:39,400 --> 00:31:48,790 you would love to be able to go back to your normal body temperature oscillation and not stay in a large amplitude oscillation forever, 213 00:31:48,790 --> 00:31:52,450 which is what the models of physics predict. 214 00:31:52,450 --> 00:32:07,030 So this limit cycle a tractor is a very important new concept, and this is the mathematical model for physiological oscillations. 215 00:32:07,030 --> 00:32:19,630 Very pretty work by Julian Waite, Julian Lewis and Mark also stressed the importance of time delays in negative feedback 216 00:32:19,630 --> 00:32:27,700 loops that transcriptional delays provide sufficient time delay to get the time delay, 217 00:32:27,700 --> 00:32:36,390 plus negative feedback mechanism going that they can therefore account for oscillations. 218 00:32:36,390 --> 00:32:44,850 The Nobel prise two years ago was given to all rise, benefiting young. 219 00:32:44,850 --> 00:32:51,540 And if you ask most people, they'll say, Oh yes, they're the ones who discovered the genes period and timeless, 220 00:32:51,540 --> 00:32:57,360 and those are the genes that govern the circadian rhythm. That's a mistake. 221 00:32:57,360 --> 00:33:03,900 The period period and timeless the genes that are involved, the circadian rhythm been known for 20 years. 222 00:33:03,900 --> 00:33:16,710 Not to that. What they did, which was truly interesting, was to deduce the mechanism of the oscillation that is the circadian rhythm. 223 00:33:16,710 --> 00:33:23,850 And that's not something that you do by staring at the gene or its subcomponents. 224 00:33:23,850 --> 00:33:28,800 You have to understand this is all there drawings, in their words, 225 00:33:28,800 --> 00:33:37,470 that period and timeless produce products that come back and inhibit their own transcription. 226 00:33:37,470 --> 00:33:46,770 In both cases, there's the inhibition, and then they make the point that there was auto regulatory feedback loops. 227 00:33:46,770 --> 00:33:57,900 That is, negative feedback and oscillations are achieved by delaying various steps in the network, for example. 228 00:33:57,900 --> 00:34:04,500 Period was retarded in the cytoplasm by phosphorylation. 229 00:34:04,500 --> 00:34:14,280 So this is a mechanism of oscillation. You could make the mistake of saying, Well, I'm a physiologist. 230 00:34:14,280 --> 00:34:21,030 I certainly recognise the word phosphorylation, but we have a lot of phosphorylation going on in a lot of our systems. 231 00:34:21,030 --> 00:34:26,910 And so the mechanism of the oscillation here is phosphorylation. 232 00:34:26,910 --> 00:34:37,050 But that's really a mistake because phosphorylation in 99 other systems does not produce oscillation. 233 00:34:37,050 --> 00:34:46,530 The important mechanism here is time delays in the negative feedback loop and any thing, 234 00:34:46,530 --> 00:34:55,800 any molecular changes whatsoever that are going to produce oscillation are going to produce it by either increasing the slope of 235 00:34:55,800 --> 00:35:12,940 the negative feedback or increasing the time delay or wannabe mechanisms must go through one of those two mechanistic factors. 236 00:35:12,940 --> 00:35:20,500 Talk about train delays, let's talk about economic equilibrium. 237 00:35:20,500 --> 00:35:31,780 We can make a very simple model where the change in price is equal to the total money available on demand, 238 00:35:31,780 --> 00:35:39,960 minus the total amount of money available for supply when demand is greater than supply. 239 00:35:39,960 --> 00:35:46,420 Prime is positive and the price goes up when supply is greater than demand. 240 00:35:46,420 --> 00:35:50,980 This term is negative and prime is negative and the price goes down. 241 00:35:50,980 --> 00:36:00,370 And we make a simple model of this as a pattern of exponential and negative exponential. 242 00:36:00,370 --> 00:36:03,910 And we simulate that model and lord, 243 00:36:03,910 --> 00:36:15,520 if it doesn't go right to equilibrium with supply equal to demand and the price is stable and everything we learnt in economics is true. 244 00:36:15,520 --> 00:36:33,820 Except Mike Mackey, who's at McGill, should have three Nobel prises in economics because Mike discovered an unbelievable fact, 245 00:36:33,820 --> 00:36:41,020 which is it takes time to grow corn. 246 00:36:41,020 --> 00:36:53,800 It takes time to make an automobile. So the adjustment of supply to price is not instantaneous. 247 00:36:53,800 --> 00:37:02,020 There are time delays in that process. So this is genius. 248 00:37:02,020 --> 00:37:14,020 It takes time to grow cool, folks. We make that change in the standard equilibrium model. 249 00:37:14,020 --> 00:37:22,030 We have supply is now reacting not to price, but price to our time units of gold. 250 00:37:22,030 --> 00:37:33,560 And we run that model when we get big time oscillations in supply and demand and price. 251 00:37:33,560 --> 00:37:39,620 Now, I just I have to say something about this, I'm sorry, I'm going to be very unpopular. 252 00:37:39,620 --> 00:37:43,910 What the heck is going on here? A hundred years? 253 00:37:43,910 --> 00:37:51,410 Well, 80 years of economics students have been taught equilibrium supply and demand. 254 00:37:51,410 --> 00:38:02,540 And only Mike Mackey from McGill discovered that it takes time to grow cool. 255 00:38:02,540 --> 00:38:10,780 This did not occur to the Nobel prise winners of the Chicago School of Economics. 256 00:38:10,780 --> 00:38:15,250 What's up with that? What do you want to say about that? 257 00:38:15,250 --> 00:38:25,200 What is their mental state that this is a revelatory discovery? 258 00:38:25,200 --> 00:38:32,070 So what I want to say is the hot bifurcation theorem gives us the mechanism of our solution. 259 00:38:32,070 --> 00:38:36,840 It's the product of sensitivity and time delay and anything. 260 00:38:36,840 --> 00:38:50,250 I will say this one more time. Any one because that wants to promote or abolish oscillation must act through one of these two factors. 261 00:38:50,250 --> 00:38:58,790 This is the true mechanism. We go on. 262 00:38:58,790 --> 00:39:05,780 I hope I've argued that oscillation is a widespread phenomenon. 263 00:39:05,780 --> 00:39:13,730 What why do we have this oscillation? What is the teleological function of all of this? 264 00:39:13,730 --> 00:39:20,720 So there was an absolutely stunningly beautiful paper which got very nicely published in Science, 265 00:39:20,720 --> 00:39:34,940 in which I never see referred to because it's unpleasant and they're looking at yeast metabolism. 266 00:39:34,940 --> 00:39:41,960 And here's oxygen pressure. And as you see it oscillates in yeast, 267 00:39:41,960 --> 00:39:58,100 and then these people or rather their graduate students and postdocs looked at six thousand two hundred nine open reading frames over time. 268 00:39:58,100 --> 00:40:04,400 And this isn't over a plot of six thousand two hundred and nine time traces, 269 00:40:04,400 --> 00:40:14,810 and you'd expect to see total junk, but you see definite form here in this over plot. 270 00:40:14,810 --> 00:40:27,440 And you also see that things are coordinated with O2 pressure in the metabolic isolation that these are all happening at this phase. 271 00:40:27,440 --> 00:40:38,960 So then they looked at the six thousand two hundred nine genes and they were actually able to segregate them into three groups. 272 00:40:38,960 --> 00:40:46,610 So this is an overclocked of all of those genes on the top line. 273 00:40:46,610 --> 00:40:52,820 This is an overclock of all of these genes. This is an overclock of all of these genes. 274 00:40:52,820 --> 00:40:58,910 Notice the consistency in the waveforms, which is really remarkable. 275 00:40:58,910 --> 00:41:05,960 And then they're able to say with these three groups, which they give names to the oxidative group, 276 00:41:05,960 --> 00:41:11,990 the reductive building group and the reductive charging group. 277 00:41:11,990 --> 00:41:16,910 These succeed each other in regular succession. 278 00:41:16,910 --> 00:41:20,390 The Red Group two Green Group, the Blue Group and the Red Group, 279 00:41:20,390 --> 00:41:30,410 the Green Blue Group and the Blue Group all occupy preferred places in the respiratory cycle. 280 00:41:30,410 --> 00:41:37,800 So they coined the term temporal compartmentalisation. 281 00:41:37,800 --> 00:41:48,240 What do you do with incompatible processes? Some processes require IPH other processes of which some processes are oxidative, others are reductive. 282 00:41:48,240 --> 00:41:59,040 How do you reconcile that? Well, there are two things. One is spatial segregation, but the other is temporal segregation. 283 00:41:59,040 --> 00:42:05,370 You take care of different aspects of your business at different times and the incompatible conditions. 284 00:42:05,370 --> 00:42:09,240 You merely cycle through them. 285 00:42:09,240 --> 00:42:23,040 So the picture that emerges and this was drawn very clearly by the news and views article about this paper is a very pretty picture of physiology. 286 00:42:23,040 --> 00:42:30,510 And this is what I'm suggesting should replace this homeostasis. 287 00:42:30,510 --> 00:42:42,180 It's saying that out in the peripheral liver lungs, you have all of these peripheral oscillators and core body temperature, 288 00:42:42,180 --> 00:42:51,690 which of course speaks to all the organs of the body that is the one ring to rule them all. 289 00:42:51,690 --> 00:42:57,840 And it synchronises and governs those peripheral oscillations, 290 00:42:57,840 --> 00:43:06,480 which are then in train to the day night cycle by the super charismatic nucleus and the oscillations of the super charismatic nucleus. 291 00:43:06,480 --> 00:43:13,230 But the day night cycle and the suprachiasmatic nucleus are not the causes of the oscillation. 292 00:43:13,230 --> 00:43:23,660 They are merely synchronised to that by these peripheral oscillators is governed by core body temperature. 293 00:43:23,660 --> 00:43:27,390 Again, functions of isolation. 294 00:43:27,390 --> 00:43:37,580 Is a very pretty paper going back to the has one oscillations, which we saw that says that here's the has one protein oscillations, 295 00:43:37,580 --> 00:43:47,900 different cell components, things are seen at the up things as opposed to the downfalls high. 296 00:43:47,900 --> 00:43:57,350 Hence, one means notch is off and you get a mesodermal fate for these stem cells. 297 00:43:57,350 --> 00:44:02,520 Whereas low has one means that it's inhibitory. 298 00:44:02,520 --> 00:44:09,770 The thing that inhibits the notch signal is on and you get a different you get the neuro, the thermal three. 299 00:44:09,770 --> 00:44:18,500 So the cycling produces different components of sodium, which. 300 00:44:18,500 --> 00:44:28,910 I want to talk now an example, not of good oscillations, but of bad oscillations. 301 00:44:28,910 --> 00:44:36,590 And how do we use the half bifurcation criteria in this case not to create oscillations, 302 00:44:36,590 --> 00:44:42,710 but to abolish them when they're unwanted, when they're pathological? 303 00:44:42,710 --> 00:44:53,510 So here is a simulation of ventricular fibrillation. 304 00:44:53,510 --> 00:44:59,750 The approach correctly said the leading cause of sudden cardiac death here is a normal beat. 305 00:44:59,750 --> 00:45:07,000 Follow the bouncing ball. We get another normal beat. And now something bad is about to happen. 306 00:45:07,000 --> 00:45:20,060 An ectopic beat right there, and that ectopic beat is now going to produce a stable of unfortunately stable, 307 00:45:20,060 --> 00:45:26,360 chaotic state of electrical conduction, which is what ventricular fibrillation is. 308 00:45:26,360 --> 00:45:37,550 This is where they yell clear on the medical shows and they apply the paddle, which is, of course, a massive intervention. 309 00:45:37,550 --> 00:45:43,700 This is VCF. So what's going on in the tissue in IVF? 310 00:45:43,700 --> 00:46:01,310 It was funny. For 100 years it was describing Victorian literary terminology, frenzied and incoherent construction of a bag of worms. 311 00:46:01,310 --> 00:46:14,930 I want to say this. This is the leading cardiac killer, and that's the best we can do is described it as a frenzied and uncoordinated contraction. 312 00:46:14,930 --> 00:46:20,660 So it wasn't until the 80s and the 90s and the advent of computerised mapping systems. 313 00:46:20,660 --> 00:46:29,390 This is a 30 by 30 computerised electric system that scientists were able to say what the heck is going on there, 314 00:46:29,390 --> 00:46:36,680 which is multiple waves of electrical excitation colliding with each other and 315 00:46:36,680 --> 00:46:44,900 extinguishing and then new waves daughter whales being formed by a process of wave break. 316 00:46:44,900 --> 00:46:53,270 So that's what the mapping systems can tell me. So then the next question is what causes break-up? 317 00:46:53,270 --> 00:47:05,450 Cardiologists were 100 percent clear that what causes break-up is external heterogeneity is shown here by the black trauma. 318 00:47:05,450 --> 00:47:16,910 And there are plenty of them. You have necrotic regions, fibrotic regions, the skin regions, lots and lots of heterogeneity. 319 00:47:16,910 --> 00:47:24,470 And the idea was when I was starting out, a cardiologist said to me, Son, it's just like a wave at the beach. 320 00:47:24,470 --> 00:47:29,120 It hits the rock and it divides into two. 321 00:47:29,120 --> 00:47:44,840 So this is a form of explanation that says explain things like break-up by appeal to externalities you bump into a rock dynamic. 322 00:47:44,840 --> 00:47:56,600 Cysts in the 90s realised that there was another mechanism for break-up, and I'm going to show it to you. 323 00:47:56,600 --> 00:48:05,000 Here is a 600 by 600 grid of cardiac cells, a very simple 2D model of cardiac tissue. 324 00:48:05,000 --> 00:48:19,520 We're going to send a wave from left to right. The heart is going to recover, and now we're going to put that ectopic beat in there. 325 00:48:19,520 --> 00:48:26,690 And there you see the genesis of a spiral wave and you see the death spiral wave is inherently 326 00:48:26,690 --> 00:48:38,990 unstable and is breaking up of its own dynamics in mathematically homogeneous tissue. 327 00:48:38,990 --> 00:48:44,300 So don't talk to me about external breakthroughs. 328 00:48:44,300 --> 00:48:56,870 The breaker here is internal psychiatrist like to talk about internal locus of causality and external locus of causality. 329 00:48:56,870 --> 00:49:03,950 And if you have an external locus of causality, that's unhealthy and unfortunately, 330 00:49:03,950 --> 00:49:11,600 the external locus of causality view seems to dominate in a lot of the sciences. 331 00:49:11,600 --> 00:49:20,840 Asked why break-up? You look for externalities? But here's a dynamical explanation of. 332 00:49:20,840 --> 00:49:27,290 Here's a cardiac action potential produced by a stimulus during the diastolic interval, 333 00:49:27,290 --> 00:49:32,720 the ions are all being pumped back out of the cell and into the cell, 334 00:49:32,720 --> 00:49:42,560 and you wait a nice long diastolic interval and you give a second stimulus and you get an action potential identical to the first. 335 00:49:42,560 --> 00:49:56,630 But if you begin to encroach on the diastolic uniform you're going to get because the process of restoring the arms hasn't completed, 336 00:49:56,630 --> 00:50:00,200 you're going to get a stunted action potential to action. 337 00:50:00,200 --> 00:50:13,520 Potential duration is shorter than the way. If you encroach further on diastolic interval, the blue action potential is even shorter than the rest. 338 00:50:13,520 --> 00:50:26,300 And if you encroach majorly on the diastolic interval, the green action potential is so stunted that it does not have the force to propagate. 339 00:50:26,300 --> 00:50:35,270 And that is going to be an engine of wave break right there, that very, very short week action potential. 340 00:50:35,270 --> 00:50:46,820 So we make a curve of the diastolic interval on the x axis and the following action potential duration on the y axis. 341 00:50:46,820 --> 00:50:51,170 And that is called the action potential duration restitution curve. 342 00:50:51,170 --> 00:51:05,390 And the hypothesis is that a steeply sloped restitution curve is going to produce violent oscillations in action potential duration. 343 00:51:05,390 --> 00:51:16,310 Because suppose now we force the heart from the pacemaker at a nice long cycle if we get this periodic training with action potentials. 344 00:51:16,310 --> 00:51:26,660 But now, if we start to pace fast, the long action potential gives us no diastolic interval before we ask for the second one. 345 00:51:26,660 --> 00:51:35,120 And that's going to mean a standard second one, which is going to give us a long thanks to all chemical, which is going to give us a long third one. 346 00:51:35,120 --> 00:51:47,210 So we have a feed, a negative feedback, long action potential produces next one short, short action potential produces next one long. 347 00:51:47,210 --> 00:51:59,450 There is a negative feedback loop with a time delay and those oscillations in action for short duration when they become violent, large amplitude. 348 00:51:59,450 --> 00:52:06,990 The very short ones are going to be too short to propagate and there is your engine of weight break. 349 00:52:06,990 --> 00:52:22,220 And in fact, in general, steeply sloped relations or input output, steeply sloped inputs relations are modifiers of differences. 350 00:52:22,220 --> 00:52:31,130 You put a difference Delta X into a steeply sloped relation, and Delta Y is bigger than Delta X. 351 00:52:31,130 --> 00:52:35,300 In other words, the small difference got magnified. 352 00:52:35,300 --> 00:52:46,520 If you have a shallow sloped relation slope blasted one, then the same difference gets translated on the next beat to a smaller difference. 353 00:52:46,520 --> 00:52:53,540 These relationships heal differences. These relationships magnified differences. 354 00:52:53,540 --> 00:53:00,170 So we thought, Well, that's interesting. Let's try this in a cube of tissue model. 355 00:53:00,170 --> 00:53:08,870 We tried a couple of drugs that as we type in different ideas for drugs, 356 00:53:08,870 --> 00:53:20,570 and what you see here is two steeply sloped feedback relations, one with a long action potential and the other with a shorter one. 357 00:53:20,570 --> 00:53:29,820 But it doesn't matter. You get break up and vef in either A, B or C. 358 00:53:29,820 --> 00:53:35,960 Now, if you flatten that relationship, reduce the slope. 359 00:53:35,960 --> 00:53:45,890 Now the spiral wave remains intact and pharmacologists like to talk and we talk about and try a rhythmic pharmacology. 360 00:53:45,890 --> 00:53:50,780 And one of the big categories is Class three potassium channel blockers. 361 00:53:50,780 --> 00:53:59,150 So this is a class three action here in B, and this is A. Class three action here in C, 362 00:53:59,150 --> 00:54:10,580 but you see that it don't matter what it what really matters is the slope that class three or not class three. 363 00:54:10,580 --> 00:54:16,760 But did you flatten the slope or did you not? That's the deciding factor. 364 00:54:16,760 --> 00:54:24,620 So we figured, let's try this in a whole hard model. So here's v f and a whole heart model. 365 00:54:24,620 --> 00:54:31,160 You see, the spiral wave immediately broke up into the multi wave fibrillation. 366 00:54:31,160 --> 00:54:37,880 We put in a novel drug that lowered the slope. 367 00:54:37,880 --> 00:54:42,410 And the spiralling does not break up. 368 00:54:42,410 --> 00:54:52,250 So we started showing these and cardiologists said, well, the Sun, the heart is much more complicated than your mathematical models. 369 00:54:52,250 --> 00:55:00,020 There are all of these external ischaemia fibrosis necrosis, what have you. 370 00:55:00,020 --> 00:55:15,380 So we one of our group, T.J. Woo, is now chief of cardiology at National Taiwan, decided to do an experiment in around the heart. 371 00:55:15,380 --> 00:55:27,170 So here is an isolated Langsdorf Rabbit heart imaged with a voltage sensitive dye so you can see the voltage on the whole surface of the heart. 372 00:55:27,170 --> 00:55:38,640 And here is fibrillation in a radically. Red is depolarisation, you see, the waves are coming from the left. 373 00:55:38,640 --> 00:55:47,310 Now they're not. Now they're going around and around, then that's going to stop and they're going to start coming in from the top right. 374 00:55:47,310 --> 00:56:03,690 For a while, this is fibrillation. When we administer heat, T.J. and his advisor and consult consultation with us found this drug. 375 00:56:03,690 --> 00:56:13,050 G600, which is a fast acting calcium channel blocker is a heavy calcium channel blocker. 376 00:56:13,050 --> 00:56:24,840 You wouldn't want to use this clinically, but this heavy calcium channel blocker in a dose dependent manner reduces the slope of that curve. 377 00:56:24,840 --> 00:56:32,820 So we gave a nice head. Heavy dose of it lowered the slope of that curve, 378 00:56:32,820 --> 00:56:42,810 and the induced spiralling wave remains intact in spite of necrosis, fibrosis, anatomical heterogeneity. 379 00:56:42,810 --> 00:56:53,550 All of those externalities that were supposed to be the causality of break-up didn't have that effect. 380 00:56:53,550 --> 00:57:05,910 So this is a further argument for understanding mechanisms, and I want to close, Roger mentioned the most sacred name of them all. 381 00:57:05,910 --> 00:57:12,330 And I'm going to get to that. I want to talk just for a few minutes about spatial pattern formation. 382 00:57:12,330 --> 00:57:19,650 And these are, of course, not temporal oscillations. These are spatial oscillations. 383 00:57:19,650 --> 00:57:26,340 And we want to ask the same question where this spatial oscillations come from. 384 00:57:26,340 --> 00:57:41,820 For example, here's segmentation in Drosophila Presegmentation embryo is pretty homogeneous, except for the nucleus there and post segmentation. 385 00:57:41,820 --> 00:57:53,280 Look at this pattern very regular notice that the curvature increases of the segments as the curvature of the embryo increases towards the ends. 386 00:57:53,280 --> 00:58:07,890 How do we explain the emergence of a pattern that the person who answered that question is Alan Turing and Turing does not get enough credit for this? 387 00:58:07,890 --> 00:58:14,340 I think people think, Oh, he just looked at science and he liked to explain animal print patterns. 388 00:58:14,340 --> 00:58:18,810 And isn't that cute? And where does the tiger get its spots? 389 00:58:18,810 --> 00:58:30,630 I think that's a huge disservice to Turing because his real contribution is fundamental in and what he really thinks. 390 00:58:30,630 --> 00:58:38,340 This is the famous paper chemical basis of morphogenesis. 391 00:58:38,340 --> 00:58:52,020 A system of chemical substances called Morpho James and he is coining this term in this paper is the first use of the concept of morphology. 392 00:58:52,020 --> 00:58:58,950 Reacting and diffusing is adequate to keep from being phenomenal morphogenesis. 393 00:58:58,950 --> 00:59:06,000 Now look at what he says here. Such a system, although it may originally be quite homogeneous, 394 00:59:06,000 --> 00:59:15,270 may develop a pattern or structure due to an instability of the homogeneous equilibrium. 395 00:59:15,270 --> 00:59:24,680 In other words, the equilibrium is unstable and the system will go into spatial oscillations. 396 00:59:24,680 --> 00:59:34,070 What is his model? It requires two things it requires short range activation. 397 00:59:34,070 --> 00:59:40,550 Positive feedback and long range negative feedback. 398 00:59:40,550 --> 00:59:46,400 So the short range positive feedback builds up the pattern. 399 00:59:46,400 --> 00:59:50,600 But if there were no inhibitor, that would simply then take over the whole space. 400 00:59:50,600 --> 00:59:55,490 You have one huge spot or one huge stroke. 401 00:59:55,490 --> 01:00:10,070 The role of the long range inhibition is to sculpt that pattern, produce voids in between the maximum, and that's where pattern is going to come from. 402 01:00:10,070 --> 01:00:16,400 We make a model of this with two chemicals an activator, an inhibitor. 403 01:00:16,400 --> 01:00:21,830 The activator activates the inhibitor. The inhibitor inhibits the activator. 404 01:00:21,830 --> 01:00:31,520 They both diffuse, but the key is the inhibitor diffuses faster than the activator. 405 01:00:31,520 --> 01:00:40,790 Touring himself used the story of the think of these as little fires and think of these as the little firefighters. 406 01:00:40,790 --> 01:00:45,710 Now, if the fire progression of the diffusion of the flame, 407 01:00:45,710 --> 01:00:55,040 the fusion of the fire is faster than the firefighters can run, then you're going to get one big fight. 408 01:00:55,040 --> 01:01:08,030 But if the firefighters can run faster than the fire, then they can aggregate into little firefighting units and create a fire free zone. 409 01:01:08,030 --> 01:01:16,340 And you're now going to begin to get spotting expression of fire and firefighters. 410 01:01:16,340 --> 01:01:25,010 We put this into a partial differential equation of the reaction diffusion type. 411 01:01:25,010 --> 01:01:38,420 And there is a touring bifurcation, which is really the hop bifurcation in space, just like the provocation we saw before it was in time. 412 01:01:38,420 --> 01:01:46,940 Now, the touring bifurcation is sometimes called the half tour of the bifurcation because the turning by friction is in space. 413 01:01:46,940 --> 01:01:58,610 And it says that for low diffusion rates, the Hamid noticed that the axis here is space, not time for low diffusion rates. 414 01:01:58,610 --> 01:02:07,280 The homogeneous equilibrium is stable, but for rapid diffusion of the inhibiteur. 415 01:02:07,280 --> 01:02:18,910 The homogeneous equilibrium is unstable and produces a sinusoidal spatial pattern. 416 01:02:18,910 --> 01:02:29,260 Is an example of the simulation of a reaction diffusion equation in an oval shaped domain. 417 01:02:29,260 --> 01:02:37,900 Notice how many of the features of segmentation are captured by this incredibly simple model. 418 01:02:37,900 --> 01:02:39,160 For example, 419 01:02:39,160 --> 01:02:53,740 the fact that the boundaries of the segments are everywhere perpendicular to the outer surface is captured without further effort emerges, 420 01:02:53,740 --> 01:03:00,190 which is the right word there emerges directly from the reaction diffusion model. 421 01:03:00,190 --> 01:03:11,500 So this kind of explanation is very, very powerful, and I've gotten into a lot of unpleasant discussions with people over this, 422 01:03:11,500 --> 01:03:19,300 and they say, Well, this is the one crack with one Nobel prise winner said to me, it's the biggest piece of crap I ever heard. 423 01:03:19,300 --> 01:03:24,430 And I said, Thank you, sir. Thank you for sharing why. 424 01:03:24,430 --> 01:03:28,390 And he says, Well, everyone knows that segmentation is carried out by home mailbox teams, 425 01:03:28,390 --> 01:03:35,350 which are basically expressed in this endless gradient of that and gives me a whole molecular biology 426 01:03:35,350 --> 01:03:45,520 piece of hand hand-waving and doesn't really answer the question Where does the panel come from? 427 01:03:45,520 --> 01:03:59,530 Can I give you one more example, then I'll let you go. There was an incredibly beautiful paper ten years ago in nature. 428 01:03:59,530 --> 01:04:09,880 They looked at the branching programme of the long, long, obviously developed embryo logically by. 429 01:04:09,880 --> 01:04:22,600 And these people, or these people and their graduate students detailed three different types of breaching in the long side, 430 01:04:22,600 --> 01:04:34,060 branching blue orthogonal rotation of the branching plain and bread and plain, or briefly splitting in green. 431 01:04:34,060 --> 01:04:41,230 I won't have a chance to do the blue or the red, but I do want to address myself to the green, to the tip splitting. 432 01:04:41,230 --> 01:04:45,670 Here's a tip splitting here, by the way, is orthogonal rotation of the branch you played. 433 01:04:45,670 --> 01:04:57,730 The first bifurcation in the anatomical sense is in the lateral medial point, and then the next one is in the anterior postural plate. 434 01:04:57,730 --> 01:05:05,890 So they have this beautiful documentation of these forms of branching in the lung. 435 01:05:05,890 --> 01:05:10,240 But what is the mechanism in here? 436 01:05:10,240 --> 01:05:26,260 One is profoundly disappointing. All they can say is each mode of ranching has a genetically encoded subroutine, 437 01:05:26,260 --> 01:05:38,850 and it will be particularly important to identify the genes that underlie the periodicity generator, the fight for Tinder and the rotator. 438 01:05:38,850 --> 01:05:52,770 There was a news & views about this paper in which the author chose the extremely unfortunate metaphor of the master and the slaves, 439 01:05:52,770 --> 01:05:59,890 which is unfortunate not just for its social communication, but its bad biology. 440 01:05:59,890 --> 01:06:05,100 Not just saying it's offensive socially, it's bad biology. 441 01:06:05,100 --> 01:06:10,800 And what are they saying here? They're saying, How does bifurcation happen? 442 01:06:10,800 --> 01:06:14,940 There's a bifurcated gene. What causes orthogonal rotation? 443 01:06:14,940 --> 01:06:20,730 There's a role for the location gene. What determines the length of the segments? 444 01:06:20,730 --> 01:06:25,680 There's a periodicity gene. This is hand-waving. 445 01:06:25,680 --> 01:06:31,620 How is this different from saying why this bifurcation happened? 446 01:06:31,620 --> 01:06:40,530 It pleases God to have bifurcation. How does orthogonal rotation Bob Wills orthogonal rotation? 447 01:06:40,530 --> 01:06:52,140 This is nothing more than that. It's the brainless postulation of a gene for every possible condition. 448 01:06:52,140 --> 01:07:01,600 Or if you're wearing a blue sweater, there must be a gene for wearing blue sweaters. 449 01:07:01,600 --> 01:07:07,960 This is very unsatisfactory. This is bad science. 450 01:07:07,960 --> 01:07:15,880 It's beautiful description. And when they go for the mechanisms, all they can say is genes make everything happen. 451 01:07:15,880 --> 01:07:21,070 So there must be a gene making each of these things happen. Period. 452 01:07:21,070 --> 01:07:28,450 That's all that's going on. So we thought, well, maybe we can do better. 453 01:07:28,450 --> 01:07:37,180 We went to an old model 40 years old by Lionheart, which postulates an activator chemical, 454 01:07:37,180 --> 01:07:43,240 an inhibitor, chemical, a substrate chemical and a marker for cell commitment. 455 01:07:43,240 --> 01:07:52,420 We simulated this model and tip splitting and also the other two, which I don't have time to tell you about. 456 01:07:52,420 --> 01:08:02,830 But these are all three modes emerge from that differential equation model with no genes at all. 457 01:08:02,830 --> 01:08:07,330 In particular, what causes tip splitting here? 458 01:08:07,330 --> 01:08:15,340 The activator rises. The activator gives rise to the inhibitor after a certain time delay. 459 01:08:15,340 --> 01:08:25,780 The inhibitor then rises and provides the inhibition that splits the peak of the activator having split the peak of the activator. 460 01:08:25,780 --> 01:08:34,030 The peaks now amplify, and you just produced tip splitting. 461 01:08:34,030 --> 01:08:44,710 So in that way, we were actually able to do replicate all of the phenomena and give it a very different 462 01:08:44,710 --> 01:08:52,520 kind of explanation for these branching modes than simply postulating the gene. 463 01:08:52,520 --> 01:09:03,050 So my final sly quotes, two of our best mathematical biologists here in town. 464 01:09:03,050 --> 01:09:13,580 Dennis and fill mine and look at what they both use the Humpty Dumpty metaphor, which I think is. 465 01:09:13,580 --> 01:09:23,780 Dennis says if you look at that molecular biology as breaking Humpty Dumpty into many pieces, we need to start and I totally agree with this. 466 01:09:23,780 --> 01:09:27,050 We have been breaking Humpty Dumpty into lots of pieces. 467 01:09:27,050 --> 01:09:35,600 I'm tired of seeing the little pieces, and I would like to see somebody start to put them together. 468 01:09:35,600 --> 01:09:43,830 And as Phil correctly points out, the tool that will put those pieces together is mathematical model. 469 01:09:43,830 --> 01:09:49,013 Thank you.