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Strachey Lecture: Medicine and Physiology in the Age of Dynamics · Strachey Lectures

• 0:12
  I want to talk about some high level conceptual things before we get into mathematical modelling.
• 0:23
  I took this from Ian Stewart's book.
• 0:26
  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
• 0:42
  to think about science are often given to us by mathematics and to limit the science that we can do and understand.
• 0:51
  In the 15th century, the prevailing view was that God would use only perfect geometric figures to effect natural motion.
• 1:04
  And so all natural motion had to be resolved in terms of straight lines and circles or segments of circles.
• 1:13
  So if that's your cognitive stance, if that's your desired religious belief,
• 1:20
  then the trajectory of the Cannonball is a straight line, followed by a circular segment followed by a straight line downward.
• 1:32
  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.
• 1:44
  But that's the limitation of the concept. Now I want to fast forward to the 20th century,
• 1:53
  and I want to talk about another dominant master concept that I'm going to try to suggest is imposed upon the data,
• 2:02
  whether the date of it or not, that is the notion of equilibrium.
• 2:08
  Now where do we see the concept of equilibrium in every single science?
• 2:15
  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.
• 2:26
  We take a physics class and we learn about thermodynamic equilibrium,
• 2:30
  where the hotter object warms the cooler object until they come to an equilibrium temperature at which T one equals two.
• 2:40
  You take the.
• 2:46
  You take an ecology class and you learn about the carrying capacity of the environment and
• 2:54
  the concept of ecological equilibrium and the slow population grows to the carrying capacity.
• 3:01
  If it were above the carrying capacity, it would shrink to the carrying capacity and we have the concept of ecological equilibrium.
• 3:10
  We go take an economics class.
• 3:14
  And again, we see the same thing we learnt to make the sign of the cross where supply meets demand is the equilibrium price,
• 3:22
  and we're told that a free market quickly reaches that equilibrium price.
• 3:28
  And in physiology, we also are dominated by an equilibrium paradigm.
• 3:35
  If I can use that word and that equilibrium paradigm is called homeostasis,
• 3:41
  and it says that physiological quantities are maintained constant levels by feedback loops.
• 3:51
  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.
• 4:02
  And these are maintained by negative feedback loops to restore normal body temperature.
• 4:09
  So in addition to the fact of equilibrium, I already alluded to the mechanism of equilibrium.
• 4:17
  The mechanism of equilibrium is negative feedback deviation is restored and we have equilibrium.
• 4:25
  Probably a very popular example of this in physiology is the feedback loops that control hormone secretion by the target organs of the gonads,
• 4:38
  the adrenal cortex, the thyroid. All are involved in negative feedback loops, sometimes multiple negative feedback loops.
• 4:48
  I will stylise it here as a single negative feedback loop, although for research purposes, we would want to get a little more complicated.
• 4:57
  The hypothalamus excites the pituitary that pituitary excites to gonad, and the gonadal secretion suppresses the hypothalamus.
• 5:05
  So there is your negative feedback loop.
• 5:08
  We make a simple three variable differential equation hypothalamus pituitary gonadal this one over one plus g squared.
• 5:19
  That's a descending sigmoid, which is the negative feedback, and we simulate this model.
• 5:27
  And indeed, the quantities go to equilibrium as advertised.
• 5:34
  It's interesting we see the tracing of the three quantities here.
• 5:39
  HP and G. Going to equilibrium is kind of interesting to plot that trajectory as a trajectory in three dimensional h p g space.
• 5:52
  And when we do, we see what is called a stable equilibrium point, also known as a point of trapdoor,
• 6:02
  where no matter where you start the system, it's except zero zero zero.
• 6:08
  Any initial condition anywhere is going to go to stable equilibrium point.
• 6:14
  And that means if we perturb off the stable equilibrium point, the system goes back to the stable equilibrium point.
• 6:22
  And so that is the picture of the homeostatic mechanism.
• 6:29
  Let's talk quickly about gene regulation, because, as you know, genes are the dominant subject in physiology today p53, the guardian angel gene,
• 6:43
  the guardian watchman gene gene,
• 6:47
  the big anti-cancer gene is in a negative feedback loop because it induces a protein called Indium two, which in turn inhibits p53.
• 7:01
  So there is a negative feedback loop in p53 has one extremely important protein in morphogenesis in the laying out of the body plan.
• 7:13
  Some biogenesis has one produces, has one RNA, which produces, has one protein, which represses the expression of the gene.
• 7:24
  So there's another negative feedback loop.
• 7:29
  And then, of course, to come back to temperature, temperature is maintained at 37 degrees by a negative feedback loop.
• 7:38
  Mm-Hmm. So that's a beautiful picture. We have all of these quantities being maintained at steady state levels by negative feedback loops.
• 7:48
  And it's just it just makes you happy to see this. It's so, so beautiful.
• 7:53
  The only problem is it is completely false from beginning to end.
• 8:00
  And every word that I have said to you in the last 10 minutes is a lie, but normal body temperature is 37 degrees.
• 8:13
  That's the one physiology fact that everybody thinks they know here is the reality.
• 8:21
  Normal body temperature oscillates. These are student volunteers.
• 8:27
  Over four days you see day and night in white and grey.
• 8:32
  And what you see is No. One, there is an oscillation in the air that has one degree Celsius peak to trough.
• 8:41
  That's a serious oscillation. It seems to be very stable day to day.
• 8:48
  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.
• 8:58
  This is a regular, reproducible physiological phenomenon.
• 9:06
  And yet everybody here is warning. Not everybody here, but in the general public is walking around with a complete misunderstanding of this.
• 9:16
  Nobody seems to have noticed, and I do have to say something.
• 9:21
  This is a theme that I'm going to start touching on, and the data are published in a reputable journal.
• 9:30
  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.
• 9:46
  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.
• 9:59
  Let's talk about hormone regulation. There is the negative feedback loops, they maintain steady state levels in hormones,
• 10:11
  except they don't because hormones are not maintained at steady state levels by anything.
• 10:20
  Here's a typical luteinizing hormone and Mr Dye all over 24 hours and a healthy female.
• 10:28
  And look at what you see. Number one, there's a big day night isolation during the daytime, these smaller oscillations at night.
• 10:40
  They get very large, very well formed and a lower frequency.
• 10:45
  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.
• 10:58
  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.
• 11:09
  These are profound oscillations, and in fact, all of the physiological variables of the body oscillate like crazy serum potassium.
• 11:20
  Look at that over four days catecholamines are all undergoing profound oscillations.
• 11:32
  Let's talk about the p53 negative feedback loop that maintain stability in p53,
• 11:43
  the group at Harvard Systems Biology had the revolutionary idea that they wouldn't just consult their personal philosophy of equilibrium.
• 11:55
  They wouldn't actually do an experiment and look to see how p53 changed over the course of time.
• 12:04
  And what they found was clear oscillations in p53 and in team and corresponding oscillations in its inhibitor in the too.
• 12:16
  So here's p53 in green and Mdm2 in red.
• 12:21
  That's twenty nine hours there. And so you see two hours of p53, two to three hours of Mdm2.
• 12:29
  This is an oscillatory system. Let's talk about his one, so has one.
• 12:38
  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
• 12:53
  oscillation in the expression of has one with a corresponding to our oscillation a little bit out of phase with it,
• 13:03
  as should be in. It has one on wall and has one protein, which inhibits the transcription of has one.
• 13:15
  We haven't talked yet about NF kappaB,
• 13:18
  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.
• 13:31
  And they found high expression, low expression, high expression over six hours.
• 13:41
  Finally, let me ask you a question. You biologists.
• 13:46
  What happens when sperm meets egg? The moment of the genesis of life, the answer is intracellular calcium oscillations.
• 14:00
  That is the first act of morphogenesis in the fertilised embryo that post fertilisation.
• 14:09
  We begin to get regular oscillations in intracellular calcium,
• 14:13
  which serve as a kind of a time beta for the subsequent the clock to time the subsequent more full genetic processes.
• 14:27
  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.
• 14:39
  A Russian chemist named Bamboozle had a laboratory model of the Krebs cycle the reduction of Malartic acid by bromide.
• 14:51
  But it's a model of the Krebs cycle, and he gets up this reaction in his lab and this is what he observed.
• 15:02
  He observed oscillations in all the reaction, intermediates and products.
• 15:10
  And that's an awfully good. I mean, that looks like a mathematical model, but that that is his chemistry experiment.
• 15:19
  And so he was very excited right up. The paper sent it to a big Russian chemical journal.
• 15:25
  Big Russian Chemical Journal sends it right back to him and says, Do not insult us with this.
• 15:33
  So he gets a friend of his who speaks English and they rewrite the paper in English, and they send it to nature.
• 15:41
  Nature bounces it right back to them, and the editor includes the note from the reviewer and the note from the reviewer said,
• 15:53
  We really must develop a form letter to send to these crackpots who think they have invented perpetual motion machines.
• 16:06
  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.
• 16:15
  I mentioned oscillatory chemical reactions. Oh, oscillatory chemical was very interesting.
• 16:20
  I've always wondered about that. How do you make one? And I said, Well, the recipes are in the papers.
• 16:25
  Let's go look up a paper reader. He says, I like them. I thought that. I thought, I got that.
• 16:29
  Let's let's go to my lab. He starts grabbing things off a shelf, including concentrated sulphuric acid.
• 16:36
  So don't try that at home. But he grabs a bunch of things off a shelf.
• 16:40
  He mixes them up. He gets an oscillatory chemical reaction.
• 16:45
  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.
• 16:55
  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.
• 17:02
  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.
• 17:12
  And there was really no point doing the experiment. It's like,
• 17:17
  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.
• 17:27
  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.
• 17:45
  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.
• 17:54
  Nobody did them because of this psychiatric clinging to the concept of equilibrium and damn the data.
• 18:08
  So this is really a kind of a scientific psychosis of denial, of pretty straightforward reality.
• 18:20
  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.
• 18:33
  Next question What are the mechanisms of isolation? So what are the mechanisms of everything in physiology is a funny question.
• 18:44
  Mechanisms of oscillation. Because in physiology, there is already a view of what is a mechanism, mechanisms and physiology, according to this view,
• 18:57
  or that tiny little proteins and the genes and the components of the genes and some components of the genes.
• 19:06
  That's the smallest physical and chemical elements of a process that is the mechanism of the process.
• 19:15
  And so we see see things like the mechanism of the cardiac long kutty syndrome or the mutations here in the cardiac sodium channel,
• 19:27
  and there are indeed mutations in the cardiac sodium channel.
• 19:33
  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?
• 19:47
  How do how does that gene defect surface in the whole heart arrhythmia and in the EKG pattern that we see?
• 19:58
  And the answer is we don't know.
• 20:01
  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.
• 20:15
  So I reject this idea, that mechanism and physiology are the tiniest little elements because they're not really telling us anything.
• 20:27
  Hmm. Let's talk about what the mechanism, for example, of oscillation is.
• 20:36
  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.
• 20:49
  So negative auto regulation of has one transcription is what is responsible in their view for these oscillations,
• 20:59
  we keep in mind that we already said that negative feedback explains homeostasis. Now we're hearing that negative feedback explains oscillations.
• 21:09
  So I'm going to address that in a minute. But in their paper, they lay out this model.
• 21:16
  We simulated this model and indeed we saw two hour oscillations, the p53 Mdm2 system, as described by the Harvard Group.
• 21:30
  They put forward a straightforward three variable differential equation model,
• 21:35
  and we simulated we indeed get the oscillations that they claim would be produced.
• 21:45
  Let's let's talk about Cap,
• 21:49
  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
• 22:03
  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.
• 22:18
  So that is another negative feedback loop. And when you simulate their negative feedback loop, you get oscillations.
• 22:25
  And indeed, when you knock out the genes for some of the suppressor proteins, you lose the oscillation.
• 22:38
  Although when you knock out other genes that are less involved in the filtering mechanism, the oscillation continues.
• 22:48
  So here's another point to hold, on the other hand, which is negative feedback can create oscillation.
• 22:57
  And it's probably the paradigm case of this is the predator prey equations which surfaced in 19-teens 100 years ago.
• 23:10
  Imagine a population of sharks and tuna, and the tuna population increases the shark population by feeding it,
• 23:20
  and the shark population decreases the tuna population by eating it.
• 23:26
  And the result of a simple model produces oscillations in the shark populations and the tuna populations.
• 23:34
  Now we did a little experiment with this model.
• 23:40
  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.
• 23:52
  So we do the experiment of simply removing sharks.
• 23:59
  So we instituted a shark removal programme right there. And the population of sharks declined.
• 24:06
  And then the population of tuna rebalance to a higher level, as hoped for.
• 24:14
  But when that happens, the shark population also recovers to a higher level than before.
• 24:23
  So the net effect of removing sharks is to increase the number of sharks afterwards.
• 24:32
  Moral of story complex systems defeat naive interventions.
• 24:39
  You just can't go in there and say, I want more tuna and fewer sharks.
• 24:45
  And so I'm just going to lower the shark population. And there you go, because the system will not stay there.
• 24:56
  From that point of view, it becomes difficult to understand statements like this, which I pulled out of a paper.
• 25:09
  We're going to unleash p53 by blocking Mdm2.
• 25:17
  And we heard this from a speaker a couple of weeks ago.
• 25:21
  This is I pulled this out of a paper. Everybody's trying to unleash p53 by blocking Mdm2.
• 25:30
  And that is exactly know, increasing the tuna population by blocking the sharks.
• 25:37
  And you will get a higher peak, but you'll also get a higher peak of MDMA, too.
• 25:43
  You will change the frequency. You will do all kinds of stuff.
• 25:48
  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.
• 25:59
  Think that's pub sink pub stool thinking that is really not worthy of this kind of phenomenon.
• 26:11
  So does negative, let's go back to our question, does negative feedback promote homeostasis or just negative feedback promote oscillation?
• 26:19
  We've heard both views. There's an answer, and the answer is perhaps by vacationed there.
• 26:28
  So here's an example. Let's take the classic negative feedback of the thermostat and the heater.
• 26:36
  The thermostat turns on the heater, the heater puts out heat, which turns off the thermostat.
• 26:42
  That's your negative feedback we make.
• 26:46
  A simple model of this tea is the temperature of the thermostat stages, the heater state.
• 26:53
  We make a differential equation. And in this differential equations, the thermostat is going to respond to the heater.
• 27:02
  Notice one over one plus h to the end. That's down going sigmoid.
• 27:10
  And we also have a time delay town heater and each tower simply h tower seconds ago.
• 27:21
  The time delay value of h because that's what the thermostat sees.
• 27:28
  It doesn't see what the heater is putting out right now.
• 27:32
  It sees what the heater was putting out 20 seconds ago, 30 seconds ago,
• 27:37
  depending upon the circulation of air in the roof and the distance from the heater to the thermostat.
• 27:44
  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.
• 28:00
  Low end gentle feedback. High and steep feedback.
• 28:06
  And now we apply the hot bifurcation theorem to this model.
• 28:13
  And this is what emerges that we can look at the two parameters and we can make that two parameter diagram.
• 28:26
  And the theorem says that there's a hyperbola there.
• 28:30
  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.
• 28:42
  And if the product of them is below that, then you're into equilibrium.
• 28:48
  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,
• 29:01
  whereas if the feedback is steep and the time delays are significant, you are going to get oscillation.
• 29:13
  So let's talk about, for example, slope of the negative feedback.
• 29:18
  We talked about the hypothalamic pituitary gonadal system and you saw that model and you see that two there.
• 29:26
  That two is a gently sloping sigmoid one over one plus x squared is a gently sloping sigmoid.
• 29:35
  And when we do this model, we indeed get equilibrium.
• 29:39
  What happens when we increase the steepness of that, the harshness of the feedback or the sensitivity of the hypothalamus?
• 29:49
  And the answer is the system goes into oscillation.
• 29:53
  So just that same model with N equals 10 instead of two gives us stable oscillations in all three quantities.
• 30:04
  And now if we do that technique of plotting the three variables as a trajectory in h p g space.
• 30:16
  We get that. And what that is telling us here is HPD space, this is a trajectory in three dimensions.
• 30:25
  If we start at very high values, we spiral in to a red loop.
• 30:33
  If we start inside very low values, we spiral out to the red loop.
• 30:39
  All initial, all non-zero initial conditions in this system go to the red loop.
• 30:49
  This is a new object. This is called a limit cycle, a trap door.
• 30:56
  And what it represents is a stable oscillation because wherever you are, you're going to go to the red loop.
• 31:09
  That's the dynamics of the system.
• 31:11
  Notice that all of the oscillatory systems we learnt about in physics, the harmonic oscillator, the pendulum, the spring don't have this property.
• 31:23
  If you pull the spring out to a larger initial condition, it yo-yos back and forth to the larger initial condition forever.
• 31:33
  But if this is body temperature and you have a fever one day,
• 31:39
  you would love to be able to go back to your normal body temperature oscillation and not stay in a large amplitude oscillation forever,
• 31:48
  which is what the models of physics predict.
• 31:52
  So this limit cycle a tractor is a very important new concept, and this is the mathematical model for physiological oscillations.
• 32:07
  Very pretty work by Julian Waite, Julian Lewis and Mark also stressed the importance of time delays in negative feedback
• 32:19
  loops that transcriptional delays provide sufficient time delay to get the time delay,
• 32:27
  plus negative feedback mechanism going that they can therefore account for oscillations.
• 32:36
  The Nobel prise two years ago was given to all rise, benefiting young.
• 32:44
  And if you ask most people, they'll say, Oh yes, they're the ones who discovered the genes period and timeless,
• 32:51
  and those are the genes that govern the circadian rhythm. That's a mistake.
• 32:57
  The period period and timeless the genes that are involved, the circadian rhythm been known for 20 years.
• 33:03
  Not to that. What they did, which was truly interesting, was to deduce the mechanism of the oscillation that is the circadian rhythm.
• 33:16
  And that's not something that you do by staring at the gene or its subcomponents.
• 33:23
  You have to understand this is all there drawings, in their words,
• 33:28
  that period and timeless produce products that come back and inhibit their own transcription.
• 33:37
  In both cases, there's the inhibition, and then they make the point that there was auto regulatory feedback loops.
• 33:46
  That is, negative feedback and oscillations are achieved by delaying various steps in the network, for example.
• 33:57
  Period was retarded in the cytoplasm by phosphorylation.
• 34:04
  So this is a mechanism of oscillation. You could make the mistake of saying, Well, I'm a physiologist.
• 34:14
  I certainly recognise the word phosphorylation, but we have a lot of phosphorylation going on in a lot of our systems.
• 34:21
  And so the mechanism of the oscillation here is phosphorylation.
• 34:26
  But that's really a mistake because phosphorylation in 99 other systems does not produce oscillation.
• 34:37
  The important mechanism here is time delays in the negative feedback loop and any thing,
• 34:46
  any molecular changes whatsoever that are going to produce oscillation are going to produce it by either increasing the slope of
• 34:55
  the negative feedback or increasing the time delay or wannabe mechanisms must go through one of those two mechanistic factors.
• 35:12
  Talk about train delays, let's talk about economic equilibrium.
• 35:20
  We can make a very simple model where the change in price is equal to the total money available on demand,
• 35:31
  minus the total amount of money available for supply when demand is greater than supply.
• 35:39
  Prime is positive and the price goes up when supply is greater than demand.
• 35:46
  This term is negative and prime is negative and the price goes down.
• 35:50
  And we make a simple model of this as a pattern of exponential and negative exponential.
• 36:00
  And we simulate that model and lord,
• 36:03
  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.
• 36:15
  Except Mike Mackey, who's at McGill, should have three Nobel prises in economics because Mike discovered an unbelievable fact,
• 36:33
  which is it takes time to grow corn.
• 36:41
  It takes time to make an automobile. So the adjustment of supply to price is not instantaneous.
• 36:53
  There are time delays in that process. So this is genius.
• 37:02
  It takes time to grow cool, folks. We make that change in the standard equilibrium model.
• 37:14
  We have supply is now reacting not to price, but price to our time units of gold.
• 37:22
  And we run that model when we get big time oscillations in supply and demand and price.
• 37:33
  Now, I just I have to say something about this, I'm sorry, I'm going to be very unpopular.
• 37:39
  What the heck is going on here? A hundred years?
• 37:43
  Well, 80 years of economics students have been taught equilibrium supply and demand.
• 37:51
  And only Mike Mackey from McGill discovered that it takes time to grow cool.
• 38:02
  This did not occur to the Nobel prise winners of the Chicago School of Economics.
• 38:10
  What's up with that? What do you want to say about that?
• 38:15
  What is their mental state that this is a revelatory discovery?
• 38:25
  So what I want to say is the hot bifurcation theorem gives us the mechanism of our solution.
• 38:32
  It's the product of sensitivity and time delay and anything.
• 38:36
  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.
• 38:50
  This is the true mechanism. We go on.
• 38:58
  I hope I've argued that oscillation is a widespread phenomenon.
• 39:05
  What why do we have this oscillation? What is the teleological function of all of this?
• 39:13
  So there was an absolutely stunningly beautiful paper which got very nicely published in Science,
• 39:20
  in which I never see referred to because it's unpleasant and they're looking at yeast metabolism.
• 39:34
  And here's oxygen pressure. And as you see it oscillates in yeast,
• 39:41
  and then these people or rather their graduate students and postdocs looked at six thousand two hundred nine open reading frames over time.
• 39:58
  And this isn't over a plot of six thousand two hundred and nine time traces,
• 40:04
  and you'd expect to see total junk, but you see definite form here in this over plot.
• 40:14
  And you also see that things are coordinated with O2 pressure in the metabolic isolation that these are all happening at this phase.
• 40:27
  So then they looked at the six thousand two hundred nine genes and they were actually able to segregate them into three groups.
• 40:38
  So this is an overclocked of all of those genes on the top line.
• 40:46
  This is an overclock of all of these genes. This is an overclock of all of these genes.
• 40:52
  Notice the consistency in the waveforms, which is really remarkable.
• 40:58
  And then they're able to say with these three groups, which they give names to the oxidative group,
• 41:05
  the reductive building group and the reductive charging group.
• 41:11
  These succeed each other in regular succession.
• 41:16
  The Red Group two Green Group, the Blue Group and the Red Group,
• 41:20
  the Green Blue Group and the Blue Group all occupy preferred places in the respiratory cycle.
• 41:30
  So they coined the term temporal compartmentalisation.
• 41:37
  What do you do with incompatible processes? Some processes require IPH other processes of which some processes are oxidative, others are reductive.
• 41:48
  How do you reconcile that? Well, there are two things. One is spatial segregation, but the other is temporal segregation.
• 41:59
  You take care of different aspects of your business at different times and the incompatible conditions.
• 42:05
  You merely cycle through them.
• 42:09
  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.
• 42:23
  And this is what I'm suggesting should replace this homeostasis.
• 42:30
  It's saying that out in the peripheral liver lungs, you have all of these peripheral oscillators and core body temperature,
• 42:42
  which of course speaks to all the organs of the body that is the one ring to rule them all.
• 42:51
  And it synchronises and governs those peripheral oscillations,
• 42:57
  which are then in train to the day night cycle by the super charismatic nucleus and the oscillations of the super charismatic nucleus.
• 43:06
  But the day night cycle and the suprachiasmatic nucleus are not the causes of the oscillation.
• 43:13
  They are merely synchronised to that by these peripheral oscillators is governed by core body temperature.
• 43:23
  Again, functions of isolation.
• 43:27
  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,
• 43:37
  different cell components, things are seen at the up things as opposed to the downfalls high.
• 43:47
  Hence, one means notch is off and you get a mesodermal fate for these stem cells.
• 43:57
  Whereas low has one means that it's inhibitory.
• 44:02
  The thing that inhibits the notch signal is on and you get a different you get the neuro, the thermal three.
• 44:09
  So the cycling produces different components of sodium, which.
• 44:18
  I want to talk now an example, not of good oscillations, but of bad oscillations.
• 44:28
  And how do we use the half bifurcation criteria in this case not to create oscillations,
• 44:36
  but to abolish them when they're unwanted, when they're pathological?
• 44:42
  So here is a simulation of ventricular fibrillation.
• 44:53
  The approach correctly said the leading cause of sudden cardiac death here is a normal beat.
• 44:59
  Follow the bouncing ball. We get another normal beat. And now something bad is about to happen.
• 45:07
  An ectopic beat right there, and that ectopic beat is now going to produce a stable of unfortunately stable,
• 45:20
  chaotic state of electrical conduction, which is what ventricular fibrillation is.
• 45:26
  This is where they yell clear on the medical shows and they apply the paddle, which is, of course, a massive intervention.
• 45:37
  This is VCF. So what's going on in the tissue in IVF?
• 45:43
  It was funny. For 100 years it was describing Victorian literary terminology, frenzied and incoherent construction of a bag of worms.
• 46:01
  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.
• 46:14
  So it wasn't until the 80s and the 90s and the advent of computerised mapping systems.
• 46:20
  This is a 30 by 30 computerised electric system that scientists were able to say what the heck is going on there,
• 46:29
  which is multiple waves of electrical excitation colliding with each other and
• 46:36
  extinguishing and then new waves daughter whales being formed by a process of wave break.
• 46:44
  So that's what the mapping systems can tell me. So then the next question is what causes break-up?
• 46:53
  Cardiologists were 100 percent clear that what causes break-up is external heterogeneity is shown here by the black trauma.
• 47:05
  And there are plenty of them. You have necrotic regions, fibrotic regions, the skin regions, lots and lots of heterogeneity.
• 47:16
  And the idea was when I was starting out, a cardiologist said to me, Son, it's just like a wave at the beach.
• 47:24
  It hits the rock and it divides into two.
• 47:29
  So this is a form of explanation that says explain things like break-up by appeal to externalities you bump into a rock dynamic.
• 47:44
  Cysts in the 90s realised that there was another mechanism for break-up, and I'm going to show it to you.
• 47:56
  Here is a 600 by 600 grid of cardiac cells, a very simple 2D model of cardiac tissue.
• 48:05
  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.
• 48:19
  And there you see the genesis of a spiral wave and you see the death spiral wave is inherently
• 48:26
  unstable and is breaking up of its own dynamics in mathematically homogeneous tissue.
• 48:38
  So don't talk to me about external breakthroughs.
• 48:44
  The breaker here is internal psychiatrist like to talk about internal locus of causality and external locus of causality.
• 48:56
  And if you have an external locus of causality, that's unhealthy and unfortunately,
• 49:03
  the external locus of causality view seems to dominate in a lot of the sciences.
• 49:11
  Asked why break-up? You look for externalities? But here's a dynamical explanation of.
• 49:20
  Here's a cardiac action potential produced by a stimulus during the diastolic interval,
• 49:27
  the ions are all being pumped back out of the cell and into the cell,
• 49:32
  and you wait a nice long diastolic interval and you give a second stimulus and you get an action potential identical to the first.
• 49:42
  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,
• 49:56
  you're going to get a stunted action potential to action.
• 50:00
  Potential duration is shorter than the way. If you encroach further on diastolic interval, the blue action potential is even shorter than the rest.
• 50:13
  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.
• 50:26
  And that is going to be an engine of wave break right there, that very, very short week action potential.
• 50:35
  So we make a curve of the diastolic interval on the x axis and the following action potential duration on the y axis.
• 50:46
  And that is called the action potential duration restitution curve.
• 50:51
  And the hypothesis is that a steeply sloped restitution curve is going to produce violent oscillations in action potential duration.
• 51:05
  Because suppose now we force the heart from the pacemaker at a nice long cycle if we get this periodic training with action potentials.
• 51:16
  But now, if we start to pace fast, the long action potential gives us no diastolic interval before we ask for the second one.
• 51:26
  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.
• 51:35
  So we have a feed, a negative feedback, long action potential produces next one short, short action potential produces next one long.
• 51:47
  There is a negative feedback loop with a time delay and those oscillations in action for short duration when they become violent, large amplitude.
• 51:59
  The very short ones are going to be too short to propagate and there is your engine of weight break.
• 52:06
  And in fact, in general, steeply sloped relations or input output, steeply sloped inputs relations are modifiers of differences.
• 52:22
  You put a difference Delta X into a steeply sloped relation, and Delta Y is bigger than Delta X.
• 52:31
  In other words, the small difference got magnified.
• 52:35
  If you have a shallow sloped relation slope blasted one, then the same difference gets translated on the next beat to a smaller difference.
• 52:46
  These relationships heal differences. These relationships magnified differences.
• 52:53
  So we thought, Well, that's interesting. Let's try this in a cube of tissue model.
• 53:00
  We tried a couple of drugs that as we type in different ideas for drugs,
• 53:08
  and what you see here is two steeply sloped feedback relations, one with a long action potential and the other with a shorter one.
• 53:20
  But it doesn't matter. You get break up and vef in either A, B or C.
• 53:29
  Now, if you flatten that relationship, reduce the slope.
• 53:35
  Now the spiral wave remains intact and pharmacologists like to talk and we talk about and try a rhythmic pharmacology.
• 53:45
  And one of the big categories is Class three potassium channel blockers.
• 53:50
  So this is a class three action here in B, and this is A. Class three action here in C,
• 53:59
  but you see that it don't matter what it what really matters is the slope that class three or not class three.
• 54:10
  But did you flatten the slope or did you not? That's the deciding factor.
• 54:16
  So we figured, let's try this in a whole hard model. So here's v f and a whole heart model.
• 54:24
  You see, the spiral wave immediately broke up into the multi wave fibrillation.
• 54:31
  We put in a novel drug that lowered the slope.
• 54:37
  And the spiralling does not break up.
• 54:42
  So we started showing these and cardiologists said, well, the Sun, the heart is much more complicated than your mathematical models.
• 54:52
  There are all of these external ischaemia fibrosis necrosis, what have you.
• 55:00
  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.
• 55:15
  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.
• 55:27
  And here is fibrillation in a radically. Red is depolarisation, you see, the waves are coming from the left.
• 55:38
  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.
• 55:47
  For a while, this is fibrillation. When we administer heat, T.J. and his advisor and consult consultation with us found this drug.
• 56:03
  G600, which is a fast acting calcium channel blocker is a heavy calcium channel blocker.
• 56:13
  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.
• 56:24
  So we gave a nice head. Heavy dose of it lowered the slope of that curve,
• 56:32
  and the induced spiralling wave remains intact in spite of necrosis, fibrosis, anatomical heterogeneity.
• 56:42
  All of those externalities that were supposed to be the causality of break-up didn't have that effect.
• 56:53
  So this is a further argument for understanding mechanisms, and I want to close, Roger mentioned the most sacred name of them all.
• 57:05
  And I'm going to get to that. I want to talk just for a few minutes about spatial pattern formation.
• 57:12
  And these are, of course, not temporal oscillations. These are spatial oscillations.
• 57:19
  And we want to ask the same question where this spatial oscillations come from.
• 57:26
  For example, here's segmentation in Drosophila Presegmentation embryo is pretty homogeneous, except for the nucleus there and post segmentation.
• 57:41
  Look at this pattern very regular notice that the curvature increases of the segments as the curvature of the embryo increases towards the ends.
• 57:53
  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?
• 58:07
  I think people think, Oh, he just looked at science and he liked to explain animal print patterns.
• 58:14
  And isn't that cute? And where does the tiger get its spots?
• 58:18
  I think that's a huge disservice to Turing because his real contribution is fundamental in and what he really thinks.
• 58:30
  This is the famous paper chemical basis of morphogenesis.
• 58:38
  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.
• 58:52
  Reacting and diffusing is adequate to keep from being phenomenal morphogenesis.
• 58:58
  Now look at what he says here. Such a system, although it may originally be quite homogeneous,
• 59:06
  may develop a pattern or structure due to an instability of the homogeneous equilibrium.
• 59:15
  In other words, the equilibrium is unstable and the system will go into spatial oscillations.
• 59:24
  What is his model? It requires two things it requires short range activation.
• 59:34
  Positive feedback and long range negative feedback.
• 59:40
  So the short range positive feedback builds up the pattern.
• 59:46
  But if there were no inhibitor, that would simply then take over the whole space.
• 59:50
  You have one huge spot or one huge stroke.
• 59:55
  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.
• 1:00:10
  We make a model of this with two chemicals an activator, an inhibitor.
• 1:00:16
  The activator activates the inhibitor. The inhibitor inhibits the activator.
• 1:00:21
  They both diffuse, but the key is the inhibitor diffuses faster than the activator.
• 1:00:31
  Touring himself used the story of the think of these as little fires and think of these as the little firefighters.
• 1:00:40
  Now, if the fire progression of the diffusion of the flame,
• 1:00:45
  the fusion of the fire is faster than the firefighters can run, then you're going to get one big fight.
• 1:00:55
  But if the firefighters can run faster than the fire, then they can aggregate into little firefighting units and create a fire free zone.
• 1:01:08
  And you're now going to begin to get spotting expression of fire and firefighters.
• 1:01:16
  We put this into a partial differential equation of the reaction diffusion type.
• 1:01:25
  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.
• 1:01:38
  Now, the touring bifurcation is sometimes called the half tour of the bifurcation because the turning by friction is in space.
• 1:01:46
  And it says that for low diffusion rates, the Hamid noticed that the axis here is space, not time for low diffusion rates.
• 1:01:58
  The homogeneous equilibrium is stable, but for rapid diffusion of the inhibiteur.
• 1:02:07
  The homogeneous equilibrium is unstable and produces a sinusoidal spatial pattern.
• 1:02:18
  Is an example of the simulation of a reaction diffusion equation in an oval shaped domain.
• 1:02:29
  Notice how many of the features of segmentation are captured by this incredibly simple model.
• 1:02:37
  For example,
• 1:02:39
  the fact that the boundaries of the segments are everywhere perpendicular to the outer surface is captured without further effort emerges,
• 1:02:53
  which is the right word there emerges directly from the reaction diffusion model.
• 1:03:00
  So this kind of explanation is very, very powerful, and I've gotten into a lot of unpleasant discussions with people over this,
• 1:03:11
  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.
• 1:03:19
  And I said, Thank you, sir. Thank you for sharing why.
• 1:03:24
  And he says, Well, everyone knows that segmentation is carried out by home mailbox teams,
• 1:03:28
  which are basically expressed in this endless gradient of that and gives me a whole molecular biology
• 1:03:35
  piece of hand hand-waving and doesn't really answer the question Where does the panel come from?
• 1:03:45
  Can I give you one more example, then I'll let you go. There was an incredibly beautiful paper ten years ago in nature.
• 1:03:59
  They looked at the branching programme of the long, long, obviously developed embryo logically by.
• 1:04:09
  And these people, or these people and their graduate students detailed three different types of breaching in the long side,
• 1:04:22
  branching blue orthogonal rotation of the branching plain and bread and plain, or briefly splitting in green.
• 1:04:34
  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.
• 1:04:41
  Here's a tip splitting here, by the way, is orthogonal rotation of the branch you played.
• 1:04:45
  The first bifurcation in the anatomical sense is in the lateral medial point, and then the next one is in the anterior postural plate.
• 1:04:57
  So they have this beautiful documentation of these forms of branching in the lung.
• 1:05:05
  But what is the mechanism in here?
• 1:05:10
  One is profoundly disappointing. All they can say is each mode of ranching has a genetically encoded subroutine,
• 1:05:26
  and it will be particularly important to identify the genes that underlie the periodicity generator, the fight for Tinder and the rotator.
• 1:05:38
  There was a news & views about this paper in which the author chose the extremely unfortunate metaphor of the master and the slaves,
• 1:05:52
  which is unfortunate not just for its social communication, but its bad biology.
• 1:05:59
  Not just saying it's offensive socially, it's bad biology.
• 1:06:05
  And what are they saying here? They're saying, How does bifurcation happen?
• 1:06:10
  There's a bifurcated gene. What causes orthogonal rotation?
• 1:06:14
  There's a role for the location gene. What determines the length of the segments?
• 1:06:20
  There's a periodicity gene. This is hand-waving.
• 1:06:25
  How is this different from saying why this bifurcation happened?
• 1:06:31
  It pleases God to have bifurcation. How does orthogonal rotation Bob Wills orthogonal rotation?
• 1:06:40
  This is nothing more than that. It's the brainless postulation of a gene for every possible condition.
• 1:06:52
  Or if you're wearing a blue sweater, there must be a gene for wearing blue sweaters.
• 1:07:01
  This is very unsatisfactory. This is bad science.
• 1:07:07
  It's beautiful description. And when they go for the mechanisms, all they can say is genes make everything happen.
• 1:07:15
  So there must be a gene making each of these things happen. Period.
• 1:07:21
  That's all that's going on. So we thought, well, maybe we can do better.
• 1:07:28
  We went to an old model 40 years old by Lionheart, which postulates an activator chemical,
• 1:07:37
  an inhibitor, chemical, a substrate chemical and a marker for cell commitment.
• 1:07:43
  We simulated this model and tip splitting and also the other two, which I don't have time to tell you about.
• 1:07:52
  But these are all three modes emerge from that differential equation model with no genes at all.
• 1:08:02
  In particular, what causes tip splitting here?
• 1:08:07
  The activator rises. The activator gives rise to the inhibitor after a certain time delay.
• 1:08:15
  The inhibitor then rises and provides the inhibition that splits the peak of the activator having split the peak of the activator.
• 1:08:25
  The peaks now amplify, and you just produced tip splitting.
• 1:08:34
  So in that way, we were actually able to do replicate all of the phenomena and give it a very different
• 1:08:44
  kind of explanation for these branching modes than simply postulating the gene.
• 1:08:52
  So my final sly quotes, two of our best mathematical biologists here in town.
• 1:09:03
  Dennis and fill mine and look at what they both use the Humpty Dumpty metaphor, which I think is.
• 1:09:13
  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.
• 1:09:23
  We have been breaking Humpty Dumpty into lots of pieces.
• 1:09:27
  I'm tired of seeing the little pieces, and I would like to see somebody start to put them together.
• 1:09:35
  And as Phil correctly points out, the tool that will put those pieces together is mathematical model.
• 1:09:43
  Thank you.