This is the Convergent Science Network podcast. Leading researchers in the domain
of neuroscience, brain theory and technology are interviewed by Paul Vershoor and Tony Prescott.
This is Paul Vershoor with the Convergent Science Network podcast together with
my colleague Tony Prescott here
at the 2018 Barcelona Cognition Brain Technology Nausea Summer School.
And we're here with Stuart Wilson. Welcome, Stuart. Thank you.
And Stuart, you spoke this morning about self-organizing models of brain and behavior.
So why do you think self-organization is such a useful concept to think about brain and behavior?
So I think that self-organization is one half of how the natural system works.
So I think that forms
that are generated by natural systems and that evolve and become the things
that surround us in the natural world do so as a combination of the intrinsic
properties of self-organising systems and the forces of natural selection.
And I think that we need to think about both of those things and how they interact
to fully understand patterns
that we see around us in the natural world so how
would we define self-organization for practical purposes
um so there are
lots of definitions of self-organization from different fields
uh from physics thermodynamics people talk
about phase transitions and uh from the
world of sort of complex systems um people
talk about um sort of
edge of chaos dynamics I define self-organization
as where you
have a system of individually simple components interacting in individually
simple ways such that collectively they generate a pattern that is less simple
than those individual interactions.
Okay. And so you started your talk referring to this paper by Jonas and Corling
about what a neuroscientist could understand the microprocessor. Yes.
I always took it a bit more like, okay, that's funny, but we've been talking about that for decades.
So why do you find that useful? It's okay, Tony.
You're poisoning me with your coffee. Hey, you're up to me.
So why did you feel NEMA was a good start? I don't agree with everything in
that paper, but I think that it represents a really interesting kind of thought experiment.
I think it's important for modelers in particular to think about the level at
which we're modeling the systems that we're interested in.
So for me,
the right level of modeling for asking the kinds of questions that I'm interested
in is to actually try and construct the simplest kind of model that can account
for the complexities of the thing in the natural world that you're trying to explain.
And I think that sometimes by pursuing models which are as complicated in their
formulation as the system that you're trying to explain.
I think that you can lose some level of understanding in constructing those kinds of models.
I think we need a mixture of both, but the thing that I'd like to try and guide
my thinking is to create models which are as simple as possible to explain complicated things.
But the other message could be you say, okay, we want to do hypothesis testing.
If you don't have a hypothesis, you're lost.
Yeah. Right? Yeah, exactly. that which is for something that's
not necessarily that new as an insight that's right um
but and the other thing that's interesting is of course that you step into the
self-organization uh boat if you want yep which of course uh when i was your
age there was a big emerging thing right that yeah when artificial life comes
off in the late 80s early 90s was a big hope ultimately people like Stuart Kaufman,
being very vocal about that.
And also in your work, at least in your talk, you confess to sort of have taken
a lot of ideas from Kaufman.
So do you really see a continuity of ideas from 80s till now,
or do you think there were some transitions?
I think there have been fashions in the way that people have thought about these ideas,
is and a lot of that has been determined by computing power
that's been available uh things have fallen in
and out of fashion with neural networks and um
and an artificial life at different times and so on um i think that what i've
tried to do so i was i was quite young when when you were reading those when
you're reading those books um and and the first time i've read them them, they really stuck.
So Stuart Kauffman's description of how the natural world works.
Self-organizes and then selection operates on that that has
stuck with me as a kind of way of thinking
about the world right the way through you know my
my education and and now to the to the point where i'm able to to do some research
on that stuff um and so i think i think i've been i've been not influenced by
uh fashion so much as you know i've just been i've been fascinated by James
Gleick's description of chaos,
Stuart Kaepernick's description of self-organization, and it's just stayed with me.
Well, for me at the time, it was more like a primogy, right,
the origins, and a multiframe, applying it to the brain, right, dynamical system.
And then, but you're on a real, I'm to respect to behavior, right?
This is to that's more and more for me.
Yeah, I'm not quite as old as Paul, but at least a week.
You might not say it. But I do also remember being enthusiastic about these approaches.
But I think looking back, we can say that they haven't had the impact in neuroscience
that we expected them to.
And I did a review chapter for the Living Machines book about this.
And really, the number of papers that take this approach and use it in a serious
way to try and understand brain evolution and development is really rather small.
And the people that have been pioneering in that area have, you know,
did some work and then moved away. You know, I think they find it very challenging.
So, you know, what is the scope now for, I mean, why is it challenging and what
is the scope for taking on the enterprise again and doing it now?
I think that's a very hard question. Well, there must be a reason why you think
it's worth picking that up.
So I think that what is really difficult
about this stuff is that the work that was done originally was so concrete and
so well done that I think you have to have a level of confidence with mathematics
and with physics in order to make progress in those fields.
But I think that for somebody who has biological questions in their mind,
who wants to ask about fitting these
pattern-generating systems to real data
you know examples of real structures that we
see in the natural world i think that the often the
people who are interested in those or who have the competencies in
those uh two things and are not necessarily
speaking the same language um and so uh you know i'm not a mathematician by
training i'm not a physicist by training my background was in sort of psychology
and then computer science um and and and it it is difficult to be in the middle
where you where you want your models to be constrained by biological facts.
But in order to do new things or to have new insights, you need to understand
the maths and the physics. And I think that's why.
That's why some of the kind of enthusiasm maybe that comes from the potential
application of these ideas might have kind of gone in and out of fashion.
I give you my thought after writing that chapter is that it's difficult to get
the right level of description when you do this kind of work because these initial
models by Kauffman and others were very abstract.
And it goes back to Turing as well, obviously.
Lindenmeier and people like that. So you've got this fantastic early work which
is extremely abstract but shows the power of these general principles.
And then people try to apply it to understanding a particular biological system like the brain.
Then you encounter all this rich wealth of data, and you don't know which bits
are going to help you go from beyond these general principles.
And the problem is that if you don't take enough from the data,
then your model is under constraint, so why are people going to take it seriously?
If you do take too much from the data, then your model is overcomplicated and
it won't do what you want to do.
So this is a fine line that you have to walk. So what's your strategy?
I think that's absolutely right. So the strategy in the project that I'm working
on, which is a sort of collaboration between myself as a computationalist and
Leah Grubitzer and Kelly Huffman in the States, who are biologists.
We're sort of asking the question about cortical evolution and development on two levels.
One is to try and recreate in simulation the kinds of patterns that are out
there in the natural world, and to calibrate that to data from experiments that those kinds are.
Conducting so that we can end up with a model that describes basically what
we think has happened in the biological world.
And then separately, what I'm really interested in, and we all are,
is then asking a question that you've thought about as well,
Tony, which is what is the the design space in which evolution and development have been interacting.
So on the one hand, we kind of want to ask, how can we account for those patterns
that you see that are out there in the biology, but also what possible pattern
forming, what are the constraints on pattern formation.
What is the design space that evolution and development have been working on?
And I think more of the abstract level of description, goes into that second
pursuit, mapping out the design space of evolution and development,
but then calibration to specific experimental results.
How does this gene affect this patterning?
That's the half of what we're doing, which is much more grounded in what a biologist can measure.
To also add a little bit to Tony's historical summary.
If you go back to the early artificial life, genetic algorithms,
neural networks, whatever developments, it was very metaphorical.
And it created very simple models, like cellular automata.
People are really obsessed with cellular automata, the other genetic algorithms,
that did things that if you just close your eyes a little bit,
and you sort of squint at them,
they might look a little bit that things might look like in some biology book
if you also squint your eyes.
And that gave this illusion of control, right?
And now, 20 years later plus, it hasn't really panned out, right?
So if you really take issue of criteria for a theory to be able to explain when
you can control, their progress has been much less, right?
But now in your work, you try to improve that by really taking very specific
constraints that you want to look at.
Also, you're talking, so you take specific brains and you want to model how
the maps in the cortices of these different brains could develop.
But then maybe it's important to now leave this bit of metaphorical biology
behind and go to real science.
So then the question becomes, what then makes a good model? So because you can
also already say you get the variability across species, across mammals.
But if I take two exemplars of the same species and I look at the borders of
these maps, it can be rather different.
So it's not even standardized across these individuals.
So then the question also first becomes, what's really our benchmark here?
What are we shooting for?
So what's the benchmark that allows a model to be good enough? Yeah, right.
I don't think I have an opinion rather than an answer to that,
but I agree with the perspective that you're taking when you phrase that question.
It reminds me of the Rosenbluth and Weiner, the best model of a cat is another
cat, preferably the same cat.
And that's really, again, a sort of a thought experiment.
The point of that is that if you try and recreate all of the detail of the thing
that you're interested in, then you end up with a model which is as complicated
as the thing that you were trying to understand.
And no progress has necessarily been made in the construction of that model.
You haven't learned anything.
So for me, the thing I'm interested in is creating the model which is as simple
as it possibly can be in order to account for the impact. But that's the wrong
side of the equation, right?
So what I was asking for, what's your empirical benchmark against which you
will now compare your model to say the model is good enough?
What's this empirical benchmark?
So it will be a model that can recreate the variability in cortical boundaries,
shape and size, that you can see across all of the species that have been catalogued
to date by the accrual survey and the colleagues.
And once we can do that, and I'm pretty confident that we can do that with fine-tuning of parameters,
because I think that the model that I described earlier today is general enough
that that should be possible.
What I will then try to do is to remove all of the components of that model
that are not required in order to account for the variability and at the point where.
Removing that bit destroys the ability of the model to account for the data.
That's where I would have gone too far.
And so my benchmark will be something that can recreate all of the patterning that we have measured.
And then I will refine that model to remove as many of the implicit assumptions in it as possible.
So you're saying I fit the model and then I protect against overfitting by minimizing the model.
That's right. But you also know if I have enough monkeys sitting behind enough
computers whittling the parameters of any model, you can get your fit.
So would it be relevant to also look at, for instance, the temporal dynamics
of development that you also have to match?
Let's say there will be a certain period of time that an organism needs to develop
a map. Would that be a relevant constraint to insert?
Or let's say the DNA specification
of unblanked parameters must also so it cannot be more than a certain number
of of basis right yeah so yeah the article strains from Gothenburg in because
if you only stick to one level of description it might still be undetermined yeah yeah I think yes,
I think that um.
It goes back to one of your suggested components of your model is prediction.
That's not the only thing that models are for. They help you reveal simple things
as complex and complex things as simple. No, it's explaining predict control. Okay.
So prediction, I think, is the benchmark, right?
So can I calibrate the models, formulating them as simply as possible,
to data that exists from experiments that have been done?
And can I then run a broken model, generate a prediction about the consequence
that you'll see in the shaken size of a cortical area,
and will that be borne out by the biology when we recreate that simulated experiment in the lab?
And I think that's when I'll know that the modeling's in a good place, I think. Okay.
So now we have sort of a day where I want to go, right?
So we have mammals, we have neocortex, we have the development of neocortex,
different maps of neocortex.
Where of course there's a layer of Cougar chest, and it's just a nice idea.
But how this is sort of modular and this kind of co-evolved with the periphery.
And now in some sense you're saying well these cortical maps emerge because
you have different gradients essentially that guide the.
Organization of global circuits or how let's say thalamic projections will iterate
the cortical map and how cortical neurons will connect to each other right yeah so,
I could not trivialize this okay well big deal because the students are saying
well I will need as many gradients as I have sub maps and then I'm done.
Yes, but that's a departure from what I was trying to explain in the talk earlier.
So in the talk, what I was suggesting is that if the patterns of gene expression
across the cortex are themselves generated by a self-organizing process,
like a reaction-diffusion system, which is what I was thinking of earlier,
then only some patterns will be possible given a cortical boundary shape and
a given choice of diffusion constant.
So there were kind of two free parameters in the model that I presented earlier,
at that level of description at least.
The boundary shape range over which chemicals are signaling to one another.
And what Alan Turing's original analysis, which I'm kind of inheriting into
thinking about the system that I'm working with, what that shows is that only
certain patterns are possible.
And so I'm no more able to sort of handpick.
There's not an infinite space of possible starting conditions for the model that I run.
There are pretty good proofs out there about what modes these systems will like
to be in, what are the low energy states for a self-organising system.
And my bet is that that is what Natural Selection has been working with.
It has been finding those low-energy states and cobbling them together in ways
that enable an animal to better adapt to its environment.
And I think at that level of description, you know, it's not a free-for-all
in terms of parameter change. Right.
So I really appreciate that in your inner model, because there's also the transition.
I mean, previous models that you described very much rely on that prior of predefined
gradients, and then in some sense you can get away with a lot, right?
And also so you can get something that looks like quite easily.
But indeed, I think you changed that game quite a bit by removing that prior
now and making it part of the self-organizing process.
But now, what do we really know about the temporal dynamics or the spatial dynamics
of these gradients in the developing brain?
How rapidly are they expressed? How rapidly do they infuse? How stable are they?
Yeah, I think I'm going to get myself into trouble trying to answer that question
because the truth is that my this is where my knowledge yeah um one thing that
i find that i find really interesting in the context of,
put that, is inheriting from a paper by Giacomo Antonio and Jeff Goodhill in
Post-Computational Biology,
2010 I think, where they summarised a bunch of biological facts that were already
out there in a nice model.
And what they describe is a kind of minimal network of five genes,
so FGF8, EMX2, PAX6, QTF1, SP8, all wonderful names.
And what they observe is that at embryonic day 8 in a mouse,
only FGF8 is expressed in only the anterior pole of the developing cortical tissue. issue.
We don't know how FGAF8 comes to be expressed there, but when it is,
you then have a kind of cascade of interactions that flip these other genes on and off,
such that they end up forming a patterning of gradients, which could potentially
be used as a coordinate system for guiding thermocortical innovation.
That happens over the range of maybe 10, 15 days or so, I think,
in the development of the mouse cortex.
So I think what happens is you've got some kind of signal that's extrinsic to
that network of those five genes that triggers an event which leads to a self-organising
process from which these complementary gene expression gradients fall.
And yeah, that's over the course of a few days.
The other sort thing that i'm interested
in uh from the context of your question is um
kaufman's original uh description of
how these uh how these gradients unfold in
the uh the embryonic development of the
drosophila uh egg um and what he imagined is that that as the tissue grows the
relationship between between the boundary shape and the range over which cells
are communicating by diffusion or chemical signalling,
that flips the self-organisation into between a set of predefined modes.
So when the tissue is small relative to the diffusion size, the mode will be a kind of low mode.
You'll get a gradient from front to back, and that gives you the distinction
between the animal's head and its tail.
And then as the tissue, as the egg grows, that same process now likes to be in a mode where,
to have more modes imprinted on the tissue, and that gives you then a separation of the, sort of.
Lateralization of the body and then as the thing continues
to grow the relationship between chemical diffusion
and tissue size uh keeps
uh flipping from into successive
modes and from there you get the kind of more fine-grained structure of the
uh of the animal being specified um and so i think there is a there is a place
for thinking about the time course of these developmental mental events unfolding,
which is neatly captured by that kind of reaction-diffusion formalism,
which I haven't really touched on in my work yet, which has mostly been about
considering how spatial patterns form.
But now you know the abandoned brain, is it like more or less five radians or
is it more? What's the set?
In descriptions I've seen from people who are more biologically informed than I am, there is...
So, Ermin Traut's claim, whose work I piggybacked off today.
Was that a minimal circuitry would involve three genes, which is FGF8, EMX2, and PAK6.
Other descriptions have defined a minimal gene interaction network,
which encompasses five.
When I talked to Leah Kruvitzer about this, she's not impressed by the claim
that only five genes are involved.
I think there are at least...
And of course, the genes that regulate F and efferent expression are also sort of players as well.
And are these genes, again, controlled by master genes?
Is it really a regulated expression pattern, or they work independently?
I don't know. my claim.
Because I would predict in your case you would need some sort of controlled expression,
of your gradients right if they wouldn't go off
independently to very different kinds of map organization so there have been
experiments done and the way that you arrive at a kind of description of there
being three main genes that are involved old EMX packs and FGF8,
the way you arrive at that is to do knockout experiments.
And if you knock out packs 6, there's not much of an impact on FGF8.
There is a bit, but you'll still get patterning. If you knock out EMX2,
you'll get no interaction between doing PAX6 and FGF8, but you'll still get
patterning. It'll be a little bit disturbed.
If you knock out the transcription factor FGF8, the morphogen FGF8,
you'll get no patterning or very disturbed patterning.
And so I think the picture of exactly how these genes interact with one another
to affect patterning on the cortex is,
you know, that's a question that developmental neurobiologists have been working on and they're...
They have been creating a picture of this gene interaction network,
which I'm taking from the textbooks and representing in my equations at some level.
But what I'm trying to do a little bit beyond that is to ask about the space
of all possible gene interaction networks.
Works you know which you know okay in
in in uh the examples of animals
with cortical patterning that we have on planet earth at the moment
uh the you know the network looks like this
but but does it have to look like this does it matter that it's specifically
those genes that are talking to each other or is it just that you know you need
to have um uh you need to have a minimal animal network that comprises X genes
of which there are N interactions between them?
What are the general principles of constructing pattern-forming,
pattern-constraining gene interaction networks?
I think that's a separate question from what happens in the mouse brain on planet Earth in 2018.
So that was extremely long-winded. I like the approach, but to be devil's advocate,
I think that taking the constraint of cortical area and the shape of the cortical
area in the adult animal,
there are obvious problems in that.
That one is you know it assumes aerialization is a late process that you know
that shape happens first yeah it also assumes that um aerialization is certainly
complete in in junior in young animals sort of maybe uh.
Maybe they're already born, but, you know, a few weeks old at most.
And they still have a lot of growing to do, including growing brain.
So, I mean, are those assumptions borne out? So that's a really important observation.
But I'd say it's an observation of the model that I presented at the stage of
development, which I'm at, right?
Yes. I do not believe that… So my assumption,
the assumption that's represented in the model I presented is that only the
boundary shape and the diffusion constants specify the process by which.
Arialization occurs.
And I showed examples of, okay, if you have different boundary shapes,
as you see in different species, then how do they constrain these processes
and generate generate different patterns.
I personally agree with you that the model is not complete as I presented it
today in the sense that the boundary itself changes over time.
It expands both in size and it changes in shape,
presumably under the influence of genetic processes
which are not in my model and and and
i haven't yet posed that question of
the system that i've i've developed so um so
i don't think that the adult boundary shape on its own is
enough but i also what we're basically working on now is is a is a is a way
of thinking about the how the shape morphs from some initial probably quite
regular shape into the um the adult shape and we want to build that into the
process of development.
And this is where the collaborators in UC Davis and UC Riverside come in because
they are currently measuring the...
Boundary shapes and the efferent expression and gene expression patterns across
those shapes at different points in development and in different species.
So we don't have data, or I don't have knowledge of data, on the changing boundary
shapes during embryonic development,
but we're collecting that as part of the project and as that data comes in,
that can then be used as an additional set of constraints in the model.
Okay. Could you imagine a version of the model where a boundary shape is an
emergent property of the model?
Once it's appropriately defined, you take it out altogether as a constraint.
I mean, obviously, the constraints is the size of the skull,
but I mean, all of these things are changing in time.
It's interesting if you look at the the literature uh
on uh for example experiments with
mutant mice in their ability to flip
one gene and see some cascade of
interactions with the developmental process that you know that compensate for
the effect of flipping that gene so that rather than creating an animal that
dies you know there are the the developmental process adjusts to incorporate
that actually flipping. Yeah, I can imagine that.
I can't imagine to the level at which I would type code into a computer and recreate that process.
We haven't done that yet, but it's something that we want to do.
So just to give you a kind of.
Idea. So a lot of the work we've done as well as the mathematics and trying
to understand the biology through the modelling is the software development,
which has been done by Seb James in Sheffield.
We have this kind of method for simulating these self-organising processes on
a hexagonal lattice with an arbitrary boundary shape.
So what we do is we take a drawing that's been made by a biologist in vector graphics.
And we take that boundary shape, we cut out of a hexagonal lattice a simulation
domain, and then we run the evolution of the equations on that domain.
So we have a set of software tools that allow us to simulate self-organizing
processes on any boundary shape that you could imagine,
in filling in the details of what that boundary
shape should be to run a particular simulated experiment or
to you know somehow we need to define what
those boundaries are um and at the moment we're doing it by drawings but i'd
certainly be interested in perhaps talking to you a little bit more about uh
to get your thoughts on how um on how the biology shapes the boundary at the
moment we're saying that a biologist gives us a drawing of a boundary and that's
our constraints on the model i think you're right the biology also plays around
with boundary shape in a way that that i don't have a set of formal i don't
have a formal model of that process so the um.
You showed us these pictures of different mammals that you are looking to fit
the brain to and you There's a huge diversity of different animals,
and particularly if we're looking at the sensory motor areas of the brain,
very much the morphology of the animal, its lifestyle.
Largely predicts the size of some of these areas. If you get a blind mole rat, huge tactile area.
Or a squirrel, highly visual animal.
So those are other constraints on your model. So how rich do you want to go
in terms of incorporating those kinds of constraints?
What can you do to take the model towards being more realistic in terms of reflecting
what's happening in terms of the evolving lifestyle of the animal?
So I'll answer that on two fronts, if I can.
So one is that there is nothing about the model which, as I've described it today,
that excludes the possibility of thinking about stimulus-driven processes.
So, for example, I showed patterns of orientation maps forming within the boundaries
that I showed, And that model was based on a model by Fred Wolff.
It's self-organizing, but it is self-organizing under the influence of sensory input.
So that model was on each time step you have the self-organizing dynamics are
adjusting the receptive fields towards the direction of the current input pattern.
And you make a choice as a modeler about how you think where those input patterns
come from. Do you take them from natural image statistics, for example,
is one thing that you can do.
And if you bias the input statistics to the model, you'll get a different organization,
at the other end, which represents those biases in the input statistics.
So there's nothing about the modeling at the moment which closes the description
of how the functional organization emerges from the outside world.
The other kind of aspect of that is some of my other work,
which is where we're trying to imagine where the behavioral constraints on the
sensory inputs that come into the brain,
how does the behavior of the animal constrain the nature of its developmental
experiences which are then driving these self-organizing processes in the brain?
And for that, my approach has
been to think about collective behaviour in animal groups, specifically,
as you're aware of, work on rodent huddling, which I've described as a self-organising
process where the individual animals are competing for nice warm locations in
the centre of the huddle.
But in doing so are crashing into each other and having contingencies between their visual input,
their somatosensory input, the noises they hear from inside the huddle being
determined by, in that case, one environmental parameter, which is the temperature of the environment.
And I think it's kind of interesting to...
To think about the organization of the brain and self-organization of the brain during development,
as being something which is coupled to the body morphology, which determines
the interaction that the body has with its environment,
which includes the physical environment, and in the case of huddling,
also the kind of social context in which the animal's developing.
But then you reason to move it also more to sort of epigenetic view
on this right yeah of course we have to specify what then
these feedback mechanisms might be yeah to your
to your map formation yeah so I think so the
reason why I want to go as far as connecting things to the the sort of huddling
work is because in that context it is very easy very clear to define what natural
selection should be caring about and I think maybe that's at the crux of some
of these some of some of this this discussion is,
you know, if we're going to, we haven't yet said why evolution should try and
make one pattern versus another.
What is it that's good about some patterns in the brain versus others?
And that's a question I've been sort of struggling with personally for a long
time is, you know, if you want to get an evolutionary algorithm to constrain.
The initial conditions of your self-organising processes, what's the fitness function?
And I think in the context of the huddling, the fitness function is actually reasonably clear.
The animal that exploits self-organising interactions from contact with the
slitomates such that it uses less energy,
such that it minimises metabolic costs in doing so, It should be one that is
more favoured by natural selection.
So that's, I think, ultimately everything needs to be… Yeah,
well that's circular almost.
That is circular, right? Because in the end that would mean that we don't huddle
whenever we stand on top of each other or something, because all the huddlers,
the guys who go to the centre win.
So no one stands on the periphery. But there are two, so yeah,
that's really interesting, but there are two ways that you can win.
So you can either win and be at the center because you generate lots of heat
and you're trying to cluster around you,
which is individually expensive to you, but is beneficial to the group.
Or you can win because you can exploit the heat that's generated by those that are at the center.
So what you have in the huddle is this kind of balance of cooperation and competition,
which I think selection should care about, because there is a good balance.
There is, there is, um, Peter Van Doren Yeah, but I find that through problematics
because the problem we've tried to solve, I think, in the end is where are the
boundary conditions, where do the boundaries come from in your model? Yeah.
Peter Van Doren Because that's now the assumption. You don't assume the whole
gradient, but you do assume boundaries.
And I don't really see how your huddling analogy helps us to solve that problem.
Yeah, I don't think it's far too far away from what we were talking about.
But also in your lecture, the huddling came up.
Yeah. And also then I didn't really see the link. And of course,
you can say, well, there are self-organizing processes, and they might be driven
by simple rules and leading to complex results.
But still now, we discussed this
earlier, right? So the old models made assumptions about whole gradients.
Then you made the next step and said, no, no, gradients are part of the self-organizing
process and they can get away.
I can agree to them as long as I still define their boundaries, right?
So now we'd say, well, you know, you got from the panel to the fire because
you still explained now where the boundaries come from. Yeah.
Huddling or no huddling. Yeah, yeah, yeah. Yeah, let's ignore huddling. so
so okay where
so so how are we going to solve this uh i think
i have to accept that that is that's where we've got to in in in what i've been
considering so if correctly your the boundary is the is the final the stable
point of the map right that's what the boundary defines finds?
Sorry, there are two levels of boundary. There's the overall boundary,
which is the edge of the cortex, if you like, and then within that we have the
boundaries of the different domains.
Right, exactly. So, at.
So my sort of claim in the talk today was that what we have in this model is
a description where there are a bunch of constants that go into the parameters of the model,
and diffusion constants mostly in coupling strengths between genes that are
interacting in the network and so on.
And that in addition to that choice of parameter values, all kind of scalar
numbers, which I think could be,
sort of specified by the genetic code, if you like, in addition to that,
there is the shape of the cortex which imposes a boundary condition on all of
those self-organising processes.
And that is as far as I've got. I agree with Tony that there's a step further
if we really want to pin everything down to the level at which natural selection
operates on this, which is tinkering with the DNA,
then we need to think about how the DNA is defining that boundary, hand-cut boundary,
which changes in shape and size over the developmental period.
So that's, there's another level of kind of, if you like, reducing the system
onto a genetic code, which I haven't done yet.
And for which I don't have clear
ideas right now today in this room about exactly how I would do that.
Are you considering a recapitulation hypothesis because if you look at this
hierarchy of mammalian brains, you would argue, well, from a developmental perspective,
the more advanced brains go to a stage that they look somewhat like the symbol brain.
But that would mean that at that stage, they have the boundary conditions of
that simple brain, right?
So you could, from that heuristic here, then predict that as long as you make
sure that your developmental trajectory follows roughly the shape of the whole
series of mammalian brains,
if I want, then I just need the parameter settings of this intermediate stage.
So the core process at that developmental stage is the same.
All brains have that shape all of us have that volume I see where you're going
with that I think so my answer to that is no,
I'm not thinking about recapitulation so I'm not thinking about recapitulation
at this point because I think that what discriminates in the model as it's described at the moment.
What discriminates between you know this species X and species Y is not the
species Y that emerged later in evolution had to have gone through the boundary
conditions of species X in order to get there during its development.
I mean, that might be true. That's an open question.
But at the moment, the thinking is that species X and species Y have different
parameters for the same set of self-organising processes, but they're parameterised
slightly differently, constrained by different boundary conditions,
which I acknowledge I don't have an explanation for genetically how the difference there is specified.
But we're talking about different initial conditions on the same developmental mechanism,
not having a developmental scaffold which is reflecting the evolutionary branching.
Yeah, I mean, I think we're talking about factors which aren't included in the
model, which is a bit mean considering the model's only existed for a few months.
And you're starting from this point.
But just continuing to speculate about that, one of the big differences in mammals is brain size.
And obviously some of the factors in the cannabinoids you're talking about are
going to be, size is going to be an important variable. So it's not simply going
to scale with a bigger brain.
But you could take species which are otherwise similar.
I mean, for example, you've got the Brazilian short-tailed opossum.
You've got the Virginia opossum. One's bigger.
I'm not sure if the brain's a lot bigger, but I think it's a bit bigger.
And then you've got all sorts of other animals where you can get big and small versions.
So, I mean, that might be another useful parameter to look at.
How brain size scaling impacts on all of this.
So that is a really important component of this, and that is one of the kind
of questions that we want to ask in the bigger picture of this project that we started.
My understanding inherited from talking with Leah is that the differences between
some pairs of mammals, models,
some relationships between brain size and brain area size scale linearly,
and some do not. Some scale non-linearly.
And I think, as we discussed a little bit earlier today, I think currently in
the formulation of the modelling,
there is no parameter that I can
point to in the model which should in some situations
give you the linear scaling of brain area size
with brain volume size versus a non-linear scaling
i haven't done the experiments with the model to to
test that's true but i also in constructing the model i don't have the model
as it stands doesn't have um a natural kind of parameter that's that can be
tweaked in order to make on the one hand it's scaled in every on the other hand
non-linear and so i think but But, you know, this is where we need to go to the biology.
This is where we need to go to the data and ask the question,
you know, where might those differences come from?
What is different about the relationship between the genes of two species for
which the scaling is linear and two species for which the relationship is nonlinear?
You know, what are those differences and can we kind of recreate some of those differences?
That would be an example of what we talked about earlier where we said,
you know, We're looking for the minimal model that can account for all of these things.
And I think that at the moment, the model that I presented is,
probably at present cannot account for those differences, and so it needs to be refined.
But I think that's part of the usefulness of modelling here, is that we can take these,
reasonably informal descriptions about how the biology works,
and we can translate those those informal assumptions into a sort of mathematically
well-defined representation of those assumptions.
Then we can play around with them and we can find out what we don't know and
what can't be found. Well, we can also do experiments that haven't happened in biology.
So we can play with impossible cortical sizes or we can also just experiment
with inventing parameters,
if you like, and seeing what influence that has and then saying,
well, this parameter might exist in the biology because it would be useful to have a gene that did X.
So one of the other things, obviously, that changes with mammals is the number of cortical areas.
You go from about 15 to 200 in people.
And size is going to be a factor there, but not just size.
I think dolphins have big brains, but they don't have as many cortical areas
for the brain size as you would expect if you looked at humans.
So what are these factors that.
Impact on arealization in that
sense of the number of quarter full areas yeah i i
think um i mean i have i'm running
a simulation in my head as we as we speak but the the kind of natural way to
approach that from modeling perspective i think is to look at the the relationship
between the um diffusion constants representing how how local are local interactions
versus the size of the domain.
So essentially, if you shrink your diffusion constants down such that cells
are communicating very locally, then they will naturally form smaller boundaries.
And if you form smaller boundaries on a big domain, you will have more cortical areas by definition.
So that is actually the number of cortical areas that you're going to have is
actually a very natural question to ask with this level of modeling because small diffusion,
big boundary, you'll get lots of individual areas.
So it's exciting because you potentially have a model where you tweak a parameter
and turn out another paper.
Well, even more so, the next thing we're going to do is think about evolutionary
algorithms that can tweak those parameters and evolve a series of papers.
But think about it like this, right? So what you brought into these models of
coordinate development are the reaction diffusion models from mandatory.
Yeah. Well, when you're speculating on very comparable lines,
right, about pattern formation by natural systems.
But that's a long time ago. It doesn't mean he was wrong.
No, no, that's exactly what I wanted to get to. So how much progress have we
really made? If you would tell the story to Alan Turing, maybe we could revive him.
Yeah. Would he be surprised? Would he be shocked?
No, no, I don't think so at all. And I think what has changed.
I mean, what I'm doing
at the moment is stitching together what I think are brilliant
ideas that have been for which the foundations have
been laid by very smart people um
uh with with incredible work
and that includes ermine by derman trout as well actually whose
ideas i've been directly stitching together um the i think that the that there's
nothing that there isn't anything new here i think probably if you if you pinned
if you had a very if you had this level of conversation with many developmental neurobiologists,
I think they probably tell you that this is how the thing works.
All I'm trying to do is kind of formalise that so that we can ask you questions of that knowledge.
I think what has changed though is computing power.
So I can run the kind of simulation that I showed today in a few minutes.
And Alan Turing would would have had to, on the Enigma code-breaking machine,
would have had to have waited quite a long time.
The Manchester Mark II. Yeah.
And I think the hard work is in doing the analysis, really.
But there's now a new era of hardware to do,
which is when you start connecting these kind of quite computationally intensive
simulations to an evolutionary context, because what evolution has been doing,
has been trying out, has been experimenting with these systems en masse for generations.
Generations and so you know it might take me only
a couple of minutes to simulate on my computer now but if i
want to run a sim an evolutionary algorithm
which considers uh you know
generations each uh comprise thousands of
generations comprising thousands of populations of
these these these things to find uh you
know what are the what are the most likely candidates for evolution to come
up with um that's the kind of thing that is you know that it's hard work even
on on sort of in the current context of computational power is that a little
bit of the curse set off of the new millennial generation of scientists.
By not that young but i mean the future we're looking
at there's some sort of complacency right because we
have this enormous compute power you can just do dumb things
which you can look at millions of permutations of dumb things and
something will happen well i'm ensuring 80 years ago
or 70 years ago had to
think very carefully about the problem he had
to get it right because he couldn't afford it wasn't even a
possibility to look at millions of permutations of
a dumb thing yeah right so so in that sense don't you
feel there's a bit of a risk here that an even increasing computer power
we sort of sacrifice intellectual power i
i completely agree with you I like to think that I'm part of a special generation
that has seen the evolution of computers over my lifetime from when I was interested
in computers to now where I'm able to develop ideas using computers.
Computers um i you know i've been at a really good time where i've seen crap computers.
Start off as being crap and you have to talk to them on a very basic level um
to to then becoming these things that you can wave your hands at um and that can you know,
think on orders of magnitudes uh greater than than we can um and so uh so yeah
i think there And don't forget the excellent mentor that you've had.
Of course. I forgot to mention that to you.
So one bit, can I...
You know advice um code in c++ or code in c because it's hard work but it forces
you to turn the mathematics of the system that you're studying into if statements and for loops and
you know you then you understand every component of what you're simulating um
you know python is wonderful for visualization and these other these other things
that allow you to talk to your computer in more and more abstract ways are great,
but I think you know, sometimes when you're stitching together.
Computational components that have been run by the people,
you're removing yourself away from the underlying assumptions of the mathematics of the system.
People take apps and they go in together and they don't really know what happens
inside. They don't have these patches that they link together.
That's where we're at now. Yeah, and this is indeed a problem.
People will be running black boxes. Yeah. I've tried not to.
I've been grinding away with C++, and it's done me well. Very good.
So you've taken Turing's reaction to fusion systems, and you've applied it to
this new data set that Leia's collecting, and you're also taking Stuart Kaufman's
Boolean nets, and you're trying to plug them in as well.
So two of these foundational approaches, if you like, in A-life.
And, you know, Boolean nets are interesting because they are extremely abstract
compared to the sort of cellular machinery which builds animals.
But, you know, Kauffman and others have argued that it's an appropriate level of abstraction.
But you are kind of leaping across different levels of abstraction in building
these models, picking things which you think might work and are mathematically elegant and so on.
What's the sort of bigger picture here in terms of a theory of what makes a good theory?
You know, sort of, you want to make a minimal theory?
Is the building network the next step in having a minimal theory?
Or was it that it was an elegant abstraction that you can plug in and you can see how to plug it in?
I mean, there's a certain amount to which you're, you know, driven by the history
of your field to use these tools, but maybe you should have,
we should develop a new set of tools.
Yeah, I think.
I see your point um i think that
the the overarching idea i mean i'm not kind of ready to declare my theory of
everything but the but the um but that's why we're here but i think but i think
that it that that it might touch base with something called the baldwin effect effect,
which is the idea that things that emerge during the interaction between an
organism and its environment,
and that can include other agents,
adaptations to your environment that happen during a lifetime can create a sort
of scaffold that the genes then climb upon.
So the genes end up specifying initial conditions for interactions with your
environment that allow you to get to that within your lifetime of the next generation,
to get to that good adaptation more quickly than the previous generation.
And that kind of hints of Lamarckism, but it's which is where the phenotypic.
Uh information is communicated back to the
genome breaking the viceman barrier and so on um
but it's a kind of loophole um for for for
that if you like which is the organisms that that
that are that are born with initial conditions that are closer to uh to to fully
specifying the the the the phenotypic form are going to be favored um uh by
natural selection um and and not but But isn't this captured in the current
discussion on epigenetics,
basically, and so on?
Yeah, yeah, yeah. But in effect, to me, it's a very sort of caricature of these processes.
Yeah, very much so. But if there's going to be a type of theory which is going
to connect those different levels of modelling which Tony was asking about,
the kind of abstract Boolean network description of gene network evolution and
reaction diffusion controlled developmental processes for pattern formation in the brain,
I think you're correct to point out that I've so far been thinking of the sort of polar ends,
one more about the details of individual brains.
One about asking about the sort
of design space in which evolution and development has been occurring.
And I think the point at which those two things come together will be in the
context of cortical map formation, because that's always interested me.
But I think I will be happy at
the point where I can run a simulation where evolution of development of specific
cortical plans is accelerated by the constraints that are imposed,
that are inherent from self-organisation.
And I think that that will end up looking like a
demonstration of the Baldwin effect where self-organisation will
generate useful patterns in the brain and the genes on evolutionary timescales
will catch up and will become more efficient at guiding the process of self-organisation.
That to me will be a Baldwin effect and that's where I think the two levels
of modelling might come together.
But thanks for asking an extremely difficult question. So Stuart,
listen, so you're doing all the right things, right? So you made it to BCMET.
I mean, it's really an early pinnacle in your career. Thank you very much.
It's just fantastic. You do great work. You really work with the biologists.
You get the data, the model data.
So you're making all the right moves. Thank you.
So if we would like now to take this as a paradigm to understand mind,
brain and behavior, what is Stuart's law that we should follow?
Read kaufman everyone should go back to kaufman and turing and and should think,
should should try to see the value in the models which are defined at the most
abstract levels and to and to not dismiss them as being abstract and therefore
of no consequence to understanding real things that are out there in nature.
I think Stewart's law should be to work hard to think about the details of this
natural world that we live in in the context of those abstract models,
because I think some of those original thinkers and people before Kauffman and
Turing, I think they had it right.
And I think it's fine
for the rest of us in their wake to be working to
catch up and filling in some of the some of the
the the gaps between the data and and
those elegant theories no programming in python
no no no actually somebody
you don't know about your your ex-mentor or your mentor uh
don't have a secret project what's this
he's the monitor of all predictions yeah
okay so basically everybody we talked
to in in our podcast um you'll
have to make a prediction and tony will go check it and think of it as it
is a british project so we can
only deal right now with labs that are within a 10 mile radius of tony's office
um so four years from now tony will go and come to your lab yeah which will
then still be sheffield i'm short yeah and he will come and check when the prediction
you make today will be falsified and verified.
So what's the most central prediction in your research program that you want
to see tested in that time frame and that you can communicate to Tony in terms
of it was false or it was true?
That is a great question. Can I have a moment?
The central prediction, so the level of the modeling, how would I know that
my model was wrong? Okay.
The prediction that I have about the course,
the potential of this work is that we will be able to account at the resolution
of the functional organization of the entire cortex,
we will be able to account for all of the variation that we see between the
species for which the data has been collected,
via different parameterizations of essentially the same model that I presented today.
And that I won't have to add any new equations.
I might have to tinker a couple of them, but I won't have to add any new equations
to the modeling in order to account for that variation to the level of detail
at which it's currently described. All right.
Stuart Wilson, thank you very much for this conversation. Thank you.
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