 And thank you to all of you for coming and thank you to the INCF for the honor of inviting me and as I gather the first of the NCF seminar series So that's where I work Unfortunately, you can't see it from this place anymore because there's a new building right there Which is a very nice building and I'm not now my office is there So I'm actually this title is a little misleading because I'm not going to give you the answer I'm only going to tell you where we are on What promises to be very interesting road to understand how one can get there? And let me just let me start out then by explaining where where the eventual goal is and where we are right now So the idea is this supposing I Wanted to construct a Sort of self-sufficient model of a dendrite So you can imagine my snipping off the dendrite from the rest of the cell So this is ugly cartoon is that of a cell and I'm snipping it off and I'm putting it in a some kind of artificial growth medium so This is not just a question of what you need to Put into it in terms of keeping it alive But it is primarily a question of what you need to put into the dendrite What what are the processes that you need to understand in the dendrite? that That will allow it to take up molecules and inputs and maintain its current form and function and They're very very many functions and many intricacies of the form So the question isn't simply what you need to pump in really the question is How do the things that you put in there? How do the molecules and signals that go into the dendrite work together to give all the functions of the dendrite and further More create a system which sustains itself over a lifetime and performs the very very many computations that a dendrite must do So what do you need for this? So you need of course the synaptic input and the various growth factors that impinge on it That's what I've drawn this watering can to represent you need to understand the Principles the chemistry electricity mechanical and other principles that keep it going you need to know what parts are in there Molecules channels and so on and you need to of course Provide the nutrients so to speak the proteins and other components which make up the dendrite In terms of modeling such a thing what do you need to know? You need to know of course data lots of data on the inputs on the components that make it up on the interactions on what's happening there in the soma and nucleus and of course you need to Instantiate you need to represent all of the principles the biophysical and chemical principles in terms of simulation tools They have to represent the laws of physics So this sort of sets out sort of a very long term to me a Very interesting grand challenge to build up to where we understand enough about what's going on in the dendrite That you can simply supply the molecules at one end and then the rest should happen through the rules that have been built into the system Okay, so that's where we want to go and let me tell you how we're Proceeding along that way and a very long and interesting road still ahead So what I'll do is I'll discuss the building blocks in terms of the component models that we're building up and some of the tools then I'll very briefly go over Some of the operations that this structure this virtual dendrite must carry out in order to Perform its tasks first of course the standard operations of computations that it does internally which are what the dendrite is out Therefore it's it's signal processing roles its roles in memory. I Will skip over some very entertaining stuff to do with homeostasis for lack of time And I'll spend a bit of time discussing self-assembly which I think is of course crucial to this whole thing And then I I'll try and integrate all of this and give you a sketch of how I think how I imagine We might be able to work towards a really I would say complete but a Interesting starting point for a model for a virtual dendrite which has all the nice attributes that I mentioned Okay, so let's start with models and of course models can be of different kinds their word models their mathematical models And then there are the detailed models where you like to put in a lot of the biological attributes that you know are in the system and Of course, this is where we would like to go But let me just give you some glimpses of how we build up to that level So now word models are of course the staple of biology. Here's a very famous word model by Don Donald Hebb To do with plasticity and all of you know this so I'm not going to read it out again That's the short version of this. So here is a model which Makes some very interesting and testable predictions, but does not put it in mathematical form so it is a qualitative model and In biology most models are actually this kind for example theory of evolution was posed in this form That is sort of the baseline model for all of biology But of course we like to go a little bit more precise. So then they're mathematical models So here is one form of a model for a neuron, which is nice in being Something that can be analytically worked upon. So here's a simple summation Device which takes weighted inputs it transforms the the sum value through an output And then that can go to further stages of a network And this is a mathematical way of representing what a what a network does and you can have various learning rules I think these are from we're from Gerstner Which tell you how the weights that you saw in the previous case how these should be adjusted according to previous activity of the network So this is a mathematical level what a biologist biologist likes is something like this I'm not saying this is the full model by any means. This is a small glimpse of a model but biologists like things like this with lots of colorful boxes and interesting letters of the alphabet connected by arrows and Of course these are extremely deceptive because there's a lot more going on once you once you Step into the realm of talking about biological detail, you know, there's there's sort of no end to it But anyway, this is the sort of thing that is at least the starting point for detailed models Now even if you have a detailed model you still have many levels at which you could describe Describe what's going on so you could start out. Let's start at the level of molecules You might want to discuss Stochastic forms in Brownian motion you might want to discuss what's happening at the level of individual molecules as they go About their business and bump into each other and perhaps react You could decide okay. No, I'm not interested in that I'm more interested in what's happening at a bulk level and so some kind of chemical equations of the more Differential equation kind would be applicable where you treat the molecular Molecular concentration as a continuum rather than as individual molecules and then you go up through diffusion Ernst equation cable equation various Hodgkin-Uxley forms and so on so Actually, I like this set of equations. It's a compact set which does an awful lot It describes a great deal of what happens for the purposes of modeling neuroscience and Anyway, so we're somewhere in there is our level of detail that we would like to choose and it's actually an art to pick an appropriate level of detail which gives you Enough information about what's going on but doesn't make it unbearably difficult to do the calculations Here's another form of Looking at the level of details For example, you might want to represent through mass action kinetics You might say that this is my favorite level of detail You might want to discuss how receptors and ligands bind and give rise to transduction So here's the point version of that so the ligand binds the receptor gives a complex that binds the G protein gives a Turnary complex you get your GDP GDP exchange and then off you get your molecules to do further things downstream now, of course, this is Very very oversimplified even though, you know, we're already starting to put a fair number of equations into this This is the level at which most people do modeling these days if you're discussing chemical systems You have separate compartments for different key parts of the of the system the exocellular region the membrane and Intercellar region and then you put the reactions appropriately So this is a fairly common way to do things to do this kind of modeling so However, you could also go Way over to the other extreme and now look at each individual molecule as it bounces around in space and then occasionally bumps into Something it wants to react with and you could model all of that in excruciating detail Which is wonderful except it takes a long time And of course, you need the parameters in far more detail if you're going to do this kind of calculation so these are levels of description even within the framework of Chemical kinetics if you've decided that is what you want to describe So what do we want to put in the model? Yeah, so supposing you picked some level of description what we need to put in we need to put in a parts list We need to know what we're going to model and you need the numbers for those things So here's a as I said a very partial parts list This is in fact the parts list for my first study, which is the one that Jeanette referred to which I foolishly and overambitiously decided I wanted to model Memory and What happened was that I would model some small part of it and then Ravi anger would say, you know it would be nice if you also put in this additional pathway and so this happened for many many months and Well sooner or later ended up with this this mess so this is one version of the parts list and if you now look into each of these Deceptively simple blobs you'll discover that actually inside each one of them. There's something like that a lot of reactions and more of them as you go along to look at more and more details and When you put it on your computer screen to represent the Calculations it looks like that and this again is now very dated. It's much worse now You know even even Now 13 14 years ago, there were more than a hundred known Essential players in synaptic plasticity and this is from a very nice review by Josh Shane's Sains and Lichtman from a 99 So unfortunately things have gotten considerably worse At last count there were over 1400 Components identified. This is Seth Grant's work in the post-synaptic density alone and So now what do you do? You know you have these these alarming the Large numbers of interactions to deal with Anyway, we'll discuss how we how we manage is managed to deal with this But these are just the parts So now every part every molecule in there has multiple phosphorylation states And if it's a complicated molecule like camkinase 2 it may have millions of potential Permutations and combinations of phosphorylation states. So that's not much fun Each state will have multiple reactions Each state also you need to now specify Concentrations and if you're doing it in 3d you need to specify where it is and then you need to give parameters for the actual reactions so I'm just trying to tell you this is Not a trivial process and it relies on the work of hundreds of thousands of Scientists doing experiments as well as lots of people doing modeling work to be able to construct stuff like this How do you set up the parameters again? Here's a you know the ultra brief version of that You identify the key pathways So here's a set of key pathways that is involved in control of protein synthesis at the dendrite You take any one of these pathways and you break it down into those little reactions that you saw And so there could be 5 10 even many many more reactions You fit the data which sounds easy, but it's actually one of the nastiest as all of you know And now you have to do this for all the pathways Now even if you have this pathway beautifully parameterized that's still not enough because now you have to make it talk to its Neighbor pathway and you now need to do this for all of them One by one and get the whole thing to work properly and then you validate it by comparing the data So this is a ultra brief Overview of the process which takes a long time to do So for example, here's some curves that my student pragati jen has built up In a study on as I said on protein synthesis. This camkin is three not camkin is two camkin is two is much worse Okay, so you parameterize it and now You you've got to the point of being able to Say that you have a way of doing all of this for some Few sets of pathways and so at this point, you know, we've been doing this Incrementally over the years and many people have been doing this over the years So there's some dozens of reasonably well parameterized pathways We think these are the most important ones. Of course, that's why we do these first This is a case of you know, the drunk who looks under the lamp post to find his keys Uh, not because he dropped them there, but because that's where the light is Yeah, so unfortunately, that's the situation we are in we look at pathways which are well Studied not necessarily because they are the only essential ones But because those are the only ones where enough is known to do the modeling So this is a start So this is where we're starting and this is sort of the the initial steps in Working towards this virtual dendrite Okay, so that was the models So now let me tell you a little bit about the tools that we use And as you can see from this cartoon And this picture Our favorite tool is the moose And moose is the name of our simulator Which is not really a simulator per se It's actually an environment in which you can do simulations using whichever numerical methods happen to suit your problem So this is Aditya Gilra Who's one of the people in it And that's a stuffed moose alas But a very pretty one anyway Okay, so I should stress that moose is just one of the many tools in the ecosystem of modeling Tools and databases that is essential for this kind of an effort So moose talks to various databases. It talks to various standards It talks through mpi and music to other simulators potentially It talks to python and perhaps other languages depending on your requirements and really a lot of this Infrastructure this ecosystem is made possible by the efforts of the iron cf And which is one of the key goals of the iron cf to make all of this possible So um, so moose, what does it do one kind of thing it does is standard compartmental calculations Differential equations that describe the electrical properties of a neuron standard cable equation Channel formalisms and all of that my kinds has written about this years and years ago Moose also does the chemical calculations And it does these not just individual point or compartmental wise. It also does it in terms of reaction diffusion calculations Um, and you can anyway you just shrink together the compartments. You do spatial discretization and you get back to work Um, there's a meeting starting tomorrow where we actually discuss a lot of these technical technicalities in a lot more detail I'll just skim over this So what moose is able to do is to model across a very wide range of scales starting from single molecules using A plug-in through to smolden which is a simulator developed by steve andrews and denis spray single particle Monte Carlo calculations all the way through The kinds of chemical calculations i've been describing Going up to cellular biophysics and even to fairly large networks of tens of thousands of neurons So these are all things that we are interested in and are doing using moose Okay, so that's sort of a very brief overview of the tools that uh are applied and as I stress moose is only one of the many Many tools in this large ecosystem. Um, and there are other tools which can do similar things and uh better things So now let me change gears and discuss some of the things that I feel that our virtual dendrite should be able to do And uh, this is of course a very very small subset of what it clearly does and what other people have studied But let me just go and begin on this So one of the key computations that Uh, the dendrite does then the synapses do Is pattern selectivity And i'm going to use the example of memory for this of learning and memory And these are all curves that have to do with both with pattern selectivity and learning and memory So let me start with this. This is the classic bcm curve. Yeah been stocked cooper munro And uh, the idea is that at low levels of activity, you could call it low frequency of input The synapse Does not change in other words it faithfully transmits whatever it gets and it doesn't change as a result of this information At higher levels it actually depresses in other words the Synaptic weight gets smaller and at higher still it goes up the synaptic weight increases So this is performing an interesting computation. It is deciding What are the input patterns? What kinds of properties should be there in the input signal to convince it that Now is the time to change and how it should change This is a Okay, here's another one. So this is one Extreme here's another extreme that's sort of averaged over time And this is over extremely precise times of the order milliseconds And this is of course the stdp learning rules spike time independent plasticity rule And yet here, do you have a very interesting computational operation where depending on the pattern of input The cell decides the synapse decides whether it is going to be weakened or strengthened And here are other examples of patterns. This is an ltp Pattern given by giving a strong burst of input and here's an ltd pattern long-term depression given by giving a weak Stimulus for a long time So these are all forms of pattern selectivity So many people have looked at this and I here's just a very very brief list of it At calcium dynamics and signaling Many people have looked at cam kinase 2 and kelm modeling Jeanette and others have looked at protein kinase a dynamics and how that does pattern selection And we've looked at map kinase signal and so on and so on. So many people have looked at this Here's one study. We did where we looked at Where we started out doing some simulations which predicted That if you give two pulses of in this case calcium stimulus and monitor map kinase activity in our model Then there would be a peak at around 10 minutes interval between the pulses So this predicted that there was some kind of pattern tuning in this network And we went and did the experiments. This is work done by my student, Suryama Jay So he he found that yes indeed if you measure the synaptic plasticity There's a peak at around the same interval at around 10 minutes And then he actually went so far as to measure the chemical activity and that too has a peak at the 10 minute time period So this was a nice matching up of experiments and and models And you can go further I played around this some more and I asked what happens if you now introduce stochasticity It turns out that a weakly tuned Response if you apply a threshold to this system, which happens through signal which can happen through Switching in the signaling pathway that can give you much sharper tuning in Something like a stochastic resonance like effect coming out of the chemical kinetics So this is just you know This is just to illustrate some of the kinds of computations that we need to start to build into the This virtual dendrite that i'm building up to let me talk now about memory Which is I think one of the obviously one of the key operations that you need to think about So I am in favor for for whatever reasons of the idea of Synaptic memory being bistable And this has got a lot of pros and cons to it and I won't go into that debate But let's just consider what it would take to make a chemical system Which could store information as a bistable switch So consider a feedback system involving two molecules a and b Where a activates b and b reciprocally activates a so it goes around the loop And if you were to block the Transmission of information from a to b and just looked at b as a at a activation as a function of b You would get some kind of curve like that standard chemistry And vice versa you would get some kind of curve like that if you looked at how b depends on a So the key thing for this analysis is to plot these two curves on the same axis Which you can do by sort of taking this and flipping it over the 45 degree line And Then those of you who are familiar with this kind of operation realize that the intersection points here tell you a great deal So for example, if there's a single intersection point right down there This intersection point is that point where each of the Values will sustain the precisely matching value of the other molecule And so this is a stable point So for example, if you were to start over here with b It would produce that level of a that level of a now reading off the red curve would produce that level of b And so on and so forth until it ended up there it would converge to that point and vice versa if you have a Curve that if you have the curves intersecting only up there Then that is the only stable point and it becomes interesting when you have multiple intersection points like this So that that turns out to be stable that turns out to be stable and that is like a threshold So if you start just above that point, you'll always converge there if you start below that you'll always converge there So why is this interesting for memory? Well, one reason out of many is that of course it's got two stable states But I emphasize the word stable Which means that if there's a perturbation If for example, there's some molecular turnover new molecules are synthesized old ones are degraded That is just like a small shift away from the stable point and the system by virtue of its kinetics and dynamics will end up At the original stable point. So this is a mechanism for memory storage, which is robust against Molecular turnover and other disruptions, which is what you would like for a memory So this seemed like you know fairly exotic idea and one thing we I did with Narendra Ramakrishna in a few years ago Was to ask Are such chemical circuits all this unlikely? And so we just sort of systematically went through An alphabet of possible reaction systems and built up arbitrary, you know systematically built up reaction systems of ever-increasing size up to six reactions And we discovered that 10 percent of everything we tried was by stable In other words, so this was a big surprise to me I had thought that by stables were extraordinarily rare and Unlikely things to happen. I don't you know Almost miraculous that evolution stumbled upon it But it turns out that actually they are very common in chemical space if you just arbitrarily connect up reactions And it turns out furthermore. This is meant to represent a tree or relatedness of these different by stables So here's the simplest one we found And a lot of things are quote unquote descended from it. In other words, they are elaborations of the simple by stable These are ones which are not elaborations of that But are their own new routes and they have again a whole bunch of descendants So the key thing is that there are lots of by stables and they're Interconnected with each other in various interesting ways. So it is actually quite easy in principle to make chemical systems that store information So here are some of them So for example camkinus 2 has long been proposed as a molecule that stores information at the synapse Interestingly, john lisman who's proposed this for all these years is now stepping back and saying actually perhaps It is not the memory molecule But it is clearly involved in setting up the memories and we'll revisit that right towards the end of the of the talk Here's another form of by stability, which um, I've been very interested in over the years This looks at a feedback loop involving protein kinase c map kinase cascade and phospholipase a2 And this can be triggered either through calcium or through a stimulus like a pdgf platelet derived growth factor any other growth factor And if you remember the analysis we had of the intersecting dose response curves This is the same kind of analysis for these pathways and there are indeed Three intersection points and two stable points and you can analyze what happens in time and so on So this is something which i'm particularly fond of not just because it was my first foray into the field But also because subsequently Um We and others were able to show that this actually works So uh pralad ram in in rubby einger's lab worked with worked with me to do this analysis And the key thing in trying to analyze a pathway like this Is to say What happens to the response? If you don't if you leave the actual direct pathway alone in other words, your direct stimulus is left unchanged But you block part of the feedback Right if you are able then to abrogate if you are able then to eliminate the storage of information Then this system might be an interesting way That might be a signature so to speak of the ability of the system to store information And so you can block phospholipase a2 or you can block protein kinase which are not as I've said in the direct pathway And that's what you see so the solid black lines are the simulation curves So that's what happens if you block it. That's what happens if you don't and the Colored line in green is the experimental data three data points For what happens if you leave the pathway alone and that's what happens if you block it And this is blocking it with the other thing and this is gels and things to analyze it with So the key prediction of this is that even if you block Things which are not in the direct line you will greatly truncate You will reduce the duration of the response, which is something that was confirmed experimentally And even more recently George augustine and he did an aka in in his lab at duke We're able to do a similar kind of analysis through the In this case looking at purkinje neurons and ltd, which they had predicted which actually kuroda et al had predicted Use a similar kind of feedback loop and they showed that yes indeed if you block The phospholipase a2 pathway you are able to eliminate the long-term depression So that's that was very very gratifying that someone else was able to show this in a neuronal context Okay, so There's a lot of interesting stuff to discuss on the homeostasis front and i'm going to skip over it entirely Because I thought we i'm i would like to talk a bit about the self assembly part instead But this is where we do a lot of calculations which involve both electrical and and chemical Simultaneously So let me talk out now about self assembly And this is Sort of coming to the crux of what I think is key for making a virtual dendrite How do you build a system where if you feed it molecules it will assemble more it will Sustain itself it will preserve the unique subdivisions of the compartments of the spines and the dendrite and so on And sustain these for long periods of time So let me scale this problem down a great deal. Yeah, supposing you have two coupled compartments How can these set up different molecular identities? How can it be that compartment a Is going to have one set of molecules and compartment b has another set of molecules Yeah, so for example, how could a piece of dent how could just a piece of dendrite Decide suddenly that it wanted to become a spine Yeah, so the general analysis I'll discuss with you actually does quite a bit more it works It can handle different forms of coupling to transport or snares or synthesis or turnover or even simply diffusion And I actually came across this effect through a very large simulation I was doing which gave me and a result which I did not understand at all Which is I had been modeling the Responses of camkiness to in one of these big Multiscale models with electricity and all of that And it did something very peculiar which took me a long while to figure out I mean so the simulation was running and it was you know You know, this is one of those situations where in principle, you know everything that's going on I had built the simulation. I had all the parameters at my fingertips I knew I and I thought I knew what I put into this and I knew what I expected it to do What it actually did was this I would give it a pulse of stimulus Which did the right thing for map kinase fine. It turned it on It seemed to do the right thing for the bulk number of camkiness to in the in the bulk of the Of the adendritic spine But if I looked at the post synaptic density it oscillated And this just did not make sense. I mean Leaving aside the the fact that this is Experimentally extremely implausible. I just could not figure out how I got oscillations out of the system And it was actually several years later and fiddling around with a lot of analysis that I'm going to tell you about that. I finally realized what what the reason was And this is the analysis framework So if you consider a system where you have two compartments a and b And these compartments are coupled through some kind of Trafficking process which could be as simple as diffusion or it could be some very very directed snare mediated or other process And if you permit these compartments to have pretty much any reactions in them With the only stipulation being that there's a some species of molecule m Which is converted to m star And then that is transfer transferred to the other compartment and m is also transferred to the other compartments, right? So you have in principle a possibility of a trafficking cycle With various reactions going on along the way And so here are the assumptions the traffic rates depend only on the levels of m and m star Yeah, and whatever trafficking processes take it Take it through these through the compartments the signaling events that take place are faster than the trafficking events and finally Something that everyone should agree with that there should be flux balance at steady state In other words the total amount of m going in is equal to the total amount coming out At steady state which is almost by definition going to be the case so you put this together and It turns out that then one critical curve accounts for a lot of what you see in the literature and that is the value of m As a function of the total concentration of m in all forms In this compartment. So let me just rephrase that So let's say m total is the total amount of molecule m in all possible chemical forms Present in compartment a that's m total and m is just the amount of m in this particular state So now if you go through the literature and analyze how this Function looks it turns out that there are only three forms Well to a very good approximation. There are only three forms One is something that looks a little bit like a breaking wave And this is an unusual form this happens only when this reaction s1 is a bi-stable reaction when it's a bi-stable system So this breaking wave system is one possible Dependence of m and on m taut another one is a negative slope one where it goes up For a while and then as m taut as the total amount of m increases beyond a point it starts to decline This is actually quite common. This happens. For example, if there's Double phosphorylation this happens if there's various kinds of feedback There are many ways in which you can get this kind of a curve and that's what the literature analysis showed A good fraction. I think 30 or 40 percent of all cases I looked at had this kind of dependence and the rest of them were a simple monotonic increase So that means that the more of m you put in the more of this molecule you put in there The more is present in that form Okay, so now the analysis which I will Just tell you about and not go over the mathematical gory details is that if you now Include the flux balance requirement Saying that the amount going in must balance the amount going out at steady state Then you end up with a null climb which is another constraining curve And this is a typical null climb the heavy black line And if this null climb intersects the Curve that you got for m versus m taught Which it does here and here and here that is a fixed point of the system And it turns out that that is stable that is stable and that is an unstable fixed point And you can calculate these for very many possible combinations of trafficking and curves Okay, so This equation hides a lot But it's very very simple to derive from the flux balance requirements for the system And as I said, these are the three possible Shapes that I found by exploring the literature The outcome of this in a nutshell is the following that if you add Signaling to trafficking in a manner I described you can end up with Compartments which take up different molecular identities So the same system can have different stable states with different Sets of molecules in each compartment It can end up with switching of states as a process of organelle maturation That is as you add one molecule at some point they'll be flipping over of states And the compartment will take on a new identity You can end up with sustained receptor insertion Which is something that happens actually in synaptic plasticity And this is the case that started me off on this wild goose chase This is the case of oscillation you can end up with systems where the molecule concentrations actually go up and down And you know, I'll be very happy to sit with you and work through the math for all of this So here's an example of what you get for diffusively coupled compartments So there's the simple case where if you have very boring reactions for This reaction system s you will just end up with one stable state With many kinds of cases you will end up with a by stable system in other words your molecules can Either preferentially be phosphorylated here if it's a phosphorylation thing Or there and that state will sort of self organize and become distinct You can have try stable systems quite a few of them And then there's this really ugly case, which is actually quite contrived. It's in a very narrow parameter range You can get a four-way stable system a chord stable system So that I think is implausible, but it's interesting To see that this can happen mathematically speaking Okay Another thing that you get from something like this is is symmetry breaking and this is starting to inch towards What might be an interesting possibility for the virtual dendrite? Which is that as you Add molecules into the system, which I'm doing in a very very slow time course in this in these calculations As you add molecules to the system It will suddenly reach a point where The system can now exist in one of two states And so let's say the parent dendrite will Decide to pick one set of one state one set of molecules there And then another subset of the system will pick the opposite state. It's a it's a it's one or the other And that's what's happening here. This is stochastic calculation I've slowly been adding molecules and you'll see that initially this was the one building up The the marker molecule and then at this point Stochastically things flipped around and then this one took over and now there's no chance of it ever flipping back Yeah, it's the as you as you continue to add new molecules to the system This is going to remain the one marked with the marker molecule. So this is an example. This is this is very preliminary Data, I'm afraid. But anyway, this is an example of how this kind of Trafficking and internal reactions can cause subsets of a system to adopt different Molecular configurations, which is of course a prerequisite for forming different kinds of compartments They were identical to start with okay, that's that's the key thing so they were completely identical So they could have been anywhere along say a patch of dendrite and you just Flow in more molecules and at some point the system Stochastically picks one or the other So this I'm I'm asserting is one possible basis this kind of trafficking thing, which is of course Like all such mathematical analyses. It's grossly oversimplified This could be the basis for something that we are well familiar with in the case of dendrites Which is that you start out with some configuration of the dendrite and following activity uh, you Produce new protrusions a new dendrite expires and that I think is a key step in the self assembly that I would like to be able to understand So I've actually recently been modeling One variant of this which is the process of insertion of amper receptor Through stargazin. So this is a a mechanism that has now got quite a lot of experimental evidence where the molecule stargazin anchors an amper receptor And this is The stargazin that is Is attached to psd95 a a key post synaptic density protein Depending on its level of phosphorylation. So this is an extremely simple thing right at face value. All you have is Stargazin and the receptor and then It gets stuck to it more tightly if there's more phosphorylation More sites phosphorylated on the stargazin So it turns out that if you run through this analysis and you can see it's actually a very very simple reaction system All you have is the three phosphorylation states zero phosphorylation one phosphorylation two You have the camkin is two in the calcium urine And you have the the supply of the receptors which is in the unphosphorylated state over there And this very very simple system If you run through this analysis Has this beautiful negative slope property that you saw earlier There's the null client going down And it turns out that you can give this lttp or lttp like stimuli stimuli. This is a stochastic calculation And it can flip on and it will stay there and it can flip off and it will stay there Okay, so this is a a system which by virtue of the self assembly process is also capable of storing information And there's another way which we had analyzed again This was a a result which I got before I before I understood the mathematical principles underneath it Um, whereby another form of trafficking of ampereceptor can also cause State switches to the on state or the off state where the on state is defined by having a lot of receptors in the synapse Which will keep it there Okay, so at this point Um, I will Start to pull these threads together and give you a glimpse of How I think one can work towards analyzing and building up a virtual dendrite So this is this is what I think ought to be there First of all, you need to have a bunch of processes that describe what happened at the spine and synapse And I've color coded this to indicate where I am where my group is and of course many other people have been working on this So there are good models for some things which I have not done myself But uh, so blue means very little Modeling has been done. I think in fact for transmission very little modeling has been done because it's been hitherto a very inaccessible system Green means it's thoroughly studied. There's lots of models out there And yellow Means that it's somewhere in between that there's it's an interesting point for modeling There's a lot of stuff going on and we would like to see some more So what do you need at the spine and synapse? You need to have a decent model of transmission Associativity and memory storage. There's loads of models out there There's loads of components that you could start to plug into your virtual dendrite Molecular traffic is getting there, but I think there's a lot more to be done there Pattern selectivity again, you've seen has been studied in great detail Restructuring of the spine. I think is an absolutely critical and interesting and relatively unexplored Topic, I think that's uh, absolutely going to be very interesting to follow up Going on to the dendrite The dendrite Is the site of a huge amount of very interesting balance of of channels You know which sustain its electrical properties, even though the spines are becoming active or inactive Even though the cell is undergoing different kinds of metabolic conditions and so on So this is something which is fascinating Gina to Reggiano and Eve Marder and others have been working on this for a long while And I think there's a huge amount still to be done to unravel the molecular details underneath the these processes Spine formation and growth again. I think this is this is going to be key This is obviously key to the to the to this enterprise The signaling in the synapse in the dendrite, of course a lot still has to be worked out there Protein synthesis and turnover. This is something that we have been modeling and I think we've got a decent model of uh now And then the molecular transport. I think there's A lot to find out exactly about how molecules and which molecules end up in the right place And then there's the support processes what happens at the cell body and nucleus So again transport and housekeeping relatively understudied Transcription control and protein synthesis. These are things which Pragati in my lab is currently doing a model on and actually has a model on we now need to do the we're in the validation stages for this And once that's going then that actually is I think an important step along there Molecular sorting how does the cell decide which molecules go where what decides whether this is the axon and that is the dendrite So I think a lovely set of questions there and then of course there's electrophysiology action potentials and so on Which is very well studied And then of course you need to go to the network you need to find out what What convergence of activity come to this particular cell this particular dendrite that's essential to know from the From that and then likewise partly because of this activity But because of information from other parts of the brain You need to know what the growth factors and other broadcast neurotransmitters that impinge on this dendrite And in order to do this in a reasonable amount of time You need some kind of abstracted learning rules for the whole system because you're not going to model every single spine at the level of detail That we would love to achieve Okay, so That is the sort of grand scheme that I have in mind and which I'm keen to have many people Come along on board with Because it's a huge project. We need to know the network context and inputs We need to know what's going on at the spines and dendrites We need to develop the the simulation tools that embody all the laws And we need to have some idea of course of what's going on at the cell body to make this work and the key thing is to Get a picture of you know How is it that you can just feed molecules to the system in principle feed things to the system and then the molecules take it from there They are going to decide they're going to use their own logic to assemble new spines depending on input To store information to manage the channel densities To make structures and maintain those structures for a lifetime that I think is where we would like to go with all of this So to wrap up then an overview we looked at the building blocks that we've been assembling over the years the models and the tools We look at some of the computations that the dendrite must do some of which are Essential for its role as a computational entity in a cell and some of which are essential for its role as a system which maintains its own identity and Expands and extends that identity in response to stimuli And then I ended up with a sketch of where I think all of this is going and where we'd love to have people provided So what we need we need more data. We need more models We need models where we put all of it together multi-scale models We need tools to make this possible and collaborations with you and with everybody on the in the world To get all of these things together So I'll wrap up there. I'll thank the my collaborators my students cg harsha Arnold who's known strives lab prageti suba niraj and aditya and sources of funding and support and all of you for your attention So When you assemble a dendrite you have Most of the cells in the system probably don't have spines You have them Yes All these that have probably a lot of pesticides. Yes, but wouldn't it be rather simple to start with The others that are non-spining Complication of spines Or that's not a challenge. Oh, no. No, it's a I think I think it's actually harder Okay But yeah, I mean I need to work through that and the nice thing about a spine is that it is a relatively relatively isolated by diffusion-wise compartment I'll just say that you know It's actually very tricky In when you're considering the the different differences in concentrations between Even the spine even the spiny synapse and the other ones and the and the dendrite It's actually very tricky because you now need to if you're doing a composite model you need to account for not only the Presence of concentration gradients you need to maintain those concentration gradients And I think this will become much harder if now you you have a Cylinder and now you have to maintain much steeper concentration gradients over just the post synaptic density So I actually think it would be it's a it's a great challenge, but it's hard I I think that they may be specialized for that, but I don't think that's the only way to do it by any means But yeah So yes, I would like to some day have multiple kinds of virtual dendrites including the non-spiny ones I'm starting, you know, this is again, perhaps a case of looking under the lamp post Yeah, there's a lot of data on the spine. And so maybe that's where we we begin So in the beginning of your lecture you discussed this Description and then towards the end you have the part list for the virtual dendrites Could you comment on what Right that's that's yeah, that's You know really important question I think that Almost certainly you will need to do Monte Carlo perhaps single particle diffusion level description of stuff happening in the spine It's just a matter of numbers if you take Resting calcium concentration or resting concentration of pretty much any of the molecules the numbers of molecules are in the Low tens or even under 10 for calcium to A few hundred for maybe say receptors or some things that are there in high concentrations So the numbers are small The dimensions are the the geometry is extremely tortuous and You will also want to for example, consider the structural remodeling which I think is best done in a Monte Carlo context So I think this is so that is what I think we'll have to do here You may have to You know restrict yourself to doing that purely on technical grounds You may have to do that only for one or a small number of spines simply because you'd lack the computational Power to do that. So you have to do some kind of abstraction for the rest of the spines in the cell For the dendrite Again, it's it's a matter of constrained by computational power. You're probably going to have to do reaction diffusion Perhaps gillespie method stochastic calculations for some of it But I suspect that will be very expensive for most of it and for the cell Cell is a big volume. I don't think you need to Worry too much about that The spine size But my question is as far as I know what argument is The spine size is critically depends on interaction between cal modeling and reactants But I haven't seen you include the actants in that Yeah, you're absolutely right. So I I sort of fake it. I'm I've been modeling the translocation Of calcium of cal modeling and and camcineness and all of that And I've just been saying, okay Here's a reaction that happens when the conditions are right. I've not put in the mechanisms So, you know, this is these are all Levels of detail, which one would like to put in One needs the parameters one needs Tools which can deal with the actual, you know mechanics and motors of of things moving But at this point, we're just faking it Yeah, sorry. Last question because I'm I'm kind of scared of like modeling this Chemical process One question is I always have a have a problem about how to estimate the parameter by feeding the Data because in real experiment when they do this experiment Actually, they perturb the whole whole network So the parameters that you obtain from the current like an experiment mostly kind of biostream So when you model that and you cover beauty model based on some biostream experiment Data, how how you how you concede it? Yeah No, no, I mean this is this is a problem that all models face So, you know, one just has to go through a process which is systematic to try and Make the best of what you of the data that you have Clearly you like to get data from multiple sources preferably different kinds of experiments which Are relevant to that parameter Another thing that one routinely does is a parameter a sensitivity analysis to ask Does this parameter actually matter? Will it change the outcome if this parameter is Twice as big or 10 times as big or small as as you estimated It turns out that for a very large fraction of the parameters You can change them by a factor of two without anything happening Some of them are more sensitive you can change them by a factor of maybe 50 percent or 20 percent and then bad things will happen But usually those parameters are precisely the ones which are the key regulator regulators of the system so In general though I don't know if evolution has been kind to us, but I think I think it makes sense right your Cells your these systems have to function under a very wide range of metabolic conditions and so one would hope at least one would like to argue that The reaction systems are therefore robust to parameters being off For metabolic reasons, but that's helpful to us as modellers because we know our parameters are bad But hopefully they're still within the range where the cell behaves No, these are all hand-waving arguments and of course the only resolution to it is more data Which is why we need collaborations Oh, okay, no, no, no, I'm just doubling the rate constant How would you define what is doubling the parameter? Well, it's very for rate constants. I just say, you know kf was one and now it's two So temperature something quite special and we know that at least in mammals the temperature range is narrow but The parameters that I'm thinking of our concentration and the rates such as kf and kb for a exchange or conversion reaction and km for an enzyme catalyzed reaction So these are parameters which are typically insensitive in this factor of two range Yeah, temperature is not I mean if you double temperature, well a you would die Um, but Yeah, it's I mean it's this it's a whole it's a whole other thing But it's actually quite remarkable how some species are able to carry out their biochemistry over a temperature range of of you know tens of degrees or more Unlike us And still be able to function properly and that's through some very interesting compensation mechanisms I'm not dealing with that Yeah, I guess everyone is sort of satisfied. I was just curious myself You have you and With some of this reasoning on on These graphs where you see where stable and unstable points are and whether the system can switch And that is These nice curves so I know you have sort of looked at this how Can you comment upon what happens if you take Well, yeah, yeah, so stochasticity tends to mess things up So as you saw in one of my slides, I actually had done This switching calculations. Well, here's an example. Here's here's this kind of analysis and here's the stochastic calculation, so in some cases It works just fine in some cases. It doesn't some so this is again a matter of sensitivity So some reaction systems don't care very much if you're if your molecules are Are fluctuating if your chemistry is fluctuating as it in fact is and some some do The I should say that although I had done this analysis through mathematics initially I then implemented all of these calculations as actual reaction systems To convince myself that the analysis was working And so now once they as reaction systems, I can do stochastic calculations on them and that's something I want to do Okay, thanks again. Thank you