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