 So the reason I show this is that it's sort of how it's sort of amazing how effortlessly we read this, right? We cannot avoid reading this, right? And this and I mean this is something we can sort of capture within much less than a second And maybe already when you see that you maybe have like images like this Coming to mind like images of Holland. I actually saw one of these on the way too. I thought they were just like Disney parks But they're not they're actually just down there but anyway, so So so this so so this of course, this is really fascinating about we sort of automatically do do do this Oh, no do this and read and also make these associations So what is new? I mean this of course is something that people have been wondering about for For hundreds of years. So what is special now really is that we now have a way to look into the brain? when when we When we perceive and when we think and when we associate So and this is So even though my topic is modeling the brain I really like to highlight this is what is really special about these times I think in terms of neuroscience at least one of the things that is special is that we have now this this new way to image brain activity at the systems level Maybe should turn off the light. Is it light? Okay? No, okay. I won't do that. So then you can both measure like the the brain structure But also you can also measure brain activity like non-invasively so without putting needles into to people's heads So you can either measure like the things like the MEG EEG Which will measure the electrical activity of the brain? Positron emission tomography pet which measured measures the food consumption or fMRI which will go to learn more about tomorrow which measure the blood blood dynamics and just to to Sort of like to highlight sort of the importance of this thing Oh, this brain and this brain imaging thing is is I like to refer to this book here every 50 years or so There are like the leading physicists of the day Supposedly I don't know really how they are recruited, but they meet in Princeton. I was not invited So and and then they come out to this this book But they identify what is the big questions of that after today and this the last one was in 96 And then this book came out afterwards and it's sort of interesting to look at the the contents because it's Well first down there. It's like five chapters about really small stuff like Higgs boson and like particle accelerations stuff And there are three about the big stuff like universes or universe and these things and then there are three about complexity Actually, we have a neurobiologist mentioned there as part of complexity Which of course is cool and then there one thing on this entanglement is weird quantum stuff But what surprised me maybe was this but this six chapter the ongoing revolution in medical imaging So this was even by physicists deemed to be so important that it gave like a separate chapter in this in this book So with this kind of I mean with imaging this whole new sort of like a new set of tools That is now was intensively used in like in in clinical neuroscience and like in basic neuroscience and psychologists You should use it and so on and so I'm just going to show an example of this kind of the kind of study you can do and This is our brain Like a reconstruction our brain was our brain is is wrinkled But it's not so you have this now It's colored with a green part like facing out and then the red parts covered in like cracks But logically it's not a difference between the cortex which is covered inside the cracks and the thing on the surface so logically you can just sort of Expanded like this. So this is sort of from the logical point of view what the brain look like doesn't anyone know why? Why we were like this and not like this Has anyone given birth? I heard I just sort of I just have a daughter and that wasn't I mean for me. It was okay, but my This was hard enough with this thing. So of course this thing would be really really really tough Right, but it's the key thing is really to have as much cortical area as possible Within like it within a skull so that you can give birth to it. So this is an example of a friend of mine on this Dale who did this measurement of a it was a Mejid was measuring the magnetic field of people who were just like you shown words. He was shown Holland so this was and Then so I'm going to start this movie now and it's you can see the brain here And this is the back part of the brain So when it's turned on when you show this word the first place you have activity is Actually in the back of the brain because that's a camera part of the brain and then you can actually quite I mean immediately after you can see this activity spreading forward I'm going to run it in a loop Because it's running quite fast, but it counts up to 800 milliseconds and then it returns again Okay, now it's going up to 800 and it starts again And then you can actually see that it starts starts there But what we immediately what we see really is so what this color shows is really where on the brain is this What part of the brain is active in processing this this word in this case? It was actually unknown word. So this was a word that people Have not had nothing seen before not like hold and it turns out that just after a few hundred milliseconds You can see a difference in these signals depending on whether it's an unknown word or a known word So this is now used to to explore like the possible application in lie detectors because if you sort of That if you sort of have you seen this person before like this this this Mafia boss and then no and then you can actually see in the brain whether this is a familiar face or or not So this is actually one application of this Anyway, so this is a whole new new forest of I mean lots of activities along those lines But of course, we would like to go in and see where does these signals come from and Then we have to look look into the brain and we have all this this Sort of take a blow-up a piece of this brain. You can have this you have this gray layer at the At the surface here and you have this and this is where all the neurons are the little gray in humans It's like two three four millimeters thick and And and then because these these images are taken by by this is actually monkey monkey brain And then they add one kind of ink which only fills this The cell centers of the new these neurons if you take another kind of ink You actually fill all of the neurons, but only a very small fraction If if it feel everyone it would be completely black But what this shows is that this each of these dots actually are are just I mean are Corresponds to this very branch branch out structure. So here we are taking some of these these these neurons and And superimpose them on this slide just to show what it really looks like So this is like one of these dots which has been replaced by this yellow green thing with the red the yellow red thing The red thing is the dendrites where the neurons gets input from other cells and the yellow thing is where it projects to to other cells So this is really what we are. We are like hundred billion neurons like this Sending signals to each other. So it's just amazing that it works right just by by looking at it But I think at least the key player here is the nerve cell the neuron. That's like the fundamental in some sense of fundamental I mean all life is cellar based and I think they're like the neuron the neuron is like the fundamental Thinking unit or maybe like you would say glia cells also like this like this Like that now there's like this revival of the glia cells and all talk start with a glia community start Oh, they've always said that glia cells were just like this boring janitors and not doing anything But now it's all like anyway, so it's both neurons and glia but glia don't fire action potentials Which are sort of that thing that communicates information so So this is a neuron and then It has all this dedicated Dedicated branches and they are like one axon projecting signals to other neurons And then they have all this input then rides and actually each of these neurons are like a machine with all kinds of Like machinery both like you're also inside the cell and they also have things on the outside which make it work Properly and and what is the key thing that makes a neuron a neuron? Well, the key thing is it has this electrically it's sort of this electrically Excitable cell meaning that has this permanent Voltage difference between the inside on an outside of about one-tenth of a volt like the same kind of volt We have in the plug here. Here's 220. It's like one one-tenth And they are set up by these particular ion channels which are proteins embedded in the membrane which Which then Then sort of makes these little tunnels like in this case There's a tunnel it makes this tunnel which only let through the green ions and not the purple ions and the green ions are in this case the potassium ions So why the the purple are the Sodium ions and that's if you think of it It's not that easy to make a tunnel that lets through like only through the green guys are not the purple guys I mean it's because they're very very similar just atoms with the one plus, right? But anyway, so these these proteins know how to do it But it's like the combination of these proteins and ion channels that makes a neuron a neuron So this all these activities have activity at all the way from the nanometer level up to the meter level going on in the neural neural system So this all this this is sort of like this multi-scale multi-scale feature of the brain But it's not only multi-scale in space It's also multi-scale in time because they have molecular processes Larging the lasting like a normal second or so up to like the the lifetime of the Of the organism So there's all this I would say now There's all these initiatives now trying to to to make models of the brain Combining I mean bridging all these all these levels. You may have Heard of some of them one is this human brain project in EU, which was started last year Which involves a lot of money and also a lot of researchers where the idea is really to use these models or this kind of like a set of models To to integrate all this this information and also make simulations for For to make us help us learn about how the brain works Then you also have the brain project in in us Which maybe have a little bit different focus, but also is about bridging scales And then also this is I think very interesting project at the allen allen institute for brain science in seattle Where they now want to actually do this reverse engineering of the mouse mouse cortex So what I hope to do what I plan to do today is sort of talk a little bit about sort of how you can sort of How one can approach or trying to bridge these These these levels and the good thing I think the good thing is that we we have this here. We have these different levels all the way from From molecules the synapses and market circuits all the way up the systems And we sort of know We know the basic laws of physics the laws of physics was Essentially at at least within the brain. I think was essentially determined in the 20th century So that's sort of like I think that's going to be like the legacy of the 20th century in terms of science Well, there's many legacies gene is one thing But in terms of like one of the legacies will be that this is the The century where we we figured out on like the basic laws of nature We figure out how the atoms and ions and everything moves In the solar system, I think and and also in the brain. So we know how to describe We know how to describe that the basic building blocks of the brain And essentially at the molecular level, it's used essentially this one of these Newton laws f equals ma But you also need some help from quantum quantum mechanics, but this is this Molecular molecular dynamics field, which is sort of like a very active field which does this kind of Our computation. I think the last year's Nobel Prize in chemistry was given to the people who developed major contributions to that and then Because up at the higher level you are at this when you have like this all these molecules making New molecules and and reacting and so on then you have these rate acuations And then we have these special acuations up at the at the neuron level Which is a combination of something called a cable acuation And maybe the diffusion of creation one acuation for the membrane potential across the Across the cell membrane and one for the diffusion of of ions the key like like calcium For example, it was like the me a key a key signaling molecule And I think that I would say like one ultimate goal I think would be to if you can make a model Construct it at least from the neuron on upwards Which then could predict these what comes out of these new brain imaging techniques So this is just like a mock-up simulation of sort of more like illustration of a dream. I guess made by Ingo Boyack where he actually took this neural network Model like when I actually put it on on on nodes corresponding to Like structural nodes of the brain and then they put in some kind of dynamics But but what this shows is sort of the the kind of predictions that you can get this is like all model generated So this is the same model that both predicts Like the eg that you would measure electrical potential to measure at the surface of the brain And also if you do something called the voltage sensitive die imaging where you can measure the average Membrane potentials in the neurons at the top of the brain Then it would look something like this and this slow thing here is is what you would measure with the functional functional MRI So I think this is sort of like one it's sort of like this one of the so one of the holy grails of This one modeling the brain is sort of how to go from this Microscopic scale up to this macroscopic scale, which you can then Measure not on so because this is something you can do with humans. I mean this this doesn't this is like non-invasive So we want to go all the way from molecules to To up to this and the cns or the the whole system But I will focus on unlike starting with neurons, which I think is like the The most central part the key the key element and so we have this Mental activity is due to as I mentioned a hundred billion nerve cells. Maybe a factor thousand or ten thousand more connections And interestingly we I showed you the piece of the of the human cortex And if you took a little section of my human cortex and and looked just looked at it and compared to a little section from the rat Cortex it wouldn't look much different So the key thing that we have is that we have much more cortex. That's what it seems at least So that is also good from a research point of view We can actually learn a lot about our cortex from looking at the mouse cortex or the rat rat cortex So and what do these neurons do? Well, I think the if you put in a sharp electrode In the center of a neuron you can measure this potential difference about one tenth of a million one tenth of a volt and then occasionally Like it's a little bit a little bit of a noisy behavior And then occasionally you get these sharp pulses which last about one millisecond One thousandths of a second and they are these action potentials and they are the only ones which are projected to other cells So that is sort of what the how the brain communicates they send these action potentials to each other And they essentially all look the same. So it's not information in the shape of the action potential just in the timing so All information is essentially is in the coded in the arrival times of these action potentials So, uh, I used to do semiconductor physics in the in the in the old days before I came to my senses And I switched to neuroscience which is much more much more fun Now for me, it was a little bit accidental. But anyway, what uh, what I didn't know was that Neuroscience because you think the brain is so complicated. You can how can it model this thing? But the the key thing is that then well neuroscience is actually what I think maybe that that The subfield of top of biology where these computational methods have been most used And at least among them and and I think the reason is that there is We we have a good mathematical description for how one single neuron process information So we have a good precise description of that and and and after all neurons are our information processing units So and that has been essentially available for well almost 50 years In almost 50 years and that has given us a very good starting point for for using this this like this this using the program which they have been Which they have like had in physics with this combination of experiments and modeling which has been running for at least 100 years And so that's what I'm going to go through that I think the key the key thing is really to that you have an idea to tell you a little bit about How do you model this thing the processing in neurons? And the first thing to know about the neuron is it that it says this of course all cells are Enclosed by membranes, but these membranes from electrical point of view are very insulating So they don't if they can actually sustain enormously enormous amount or a very very high electric fields without short circuiting The and the good thing about that is then if you put in a little tunnel in it like with an ion channel Then you can sort of you can regulate it very well that they current Because it's insulating to begin with so that was sort of what evolution found out that you could put in these different ion channels which Do all kinds of things you can sort of selectively let through sodium Or or potassium or also chloride channels and have all the channels and they have all the all the channels or Who who does other things like these ion pumps? for example setting up the right the right concentration differences between the inside and outside of the Of the neuron membrane in order to get this like in membrane potential of about one tenth tenth of a volt And we know how to model this and because we can model this As sort of a like current going through a biological membrane can be modeled as sort of like Like currents going through the tunnel with like normal ohmic Resistance and it has this additional and then it has this additional capacitive current Due to the fact that it is biological membrane has these capacitive properties So if they look very much like the electrical circuit that maybe some of you had in like in in one of us if you started physics But the big difference is that in in electronics it's electrons That that moves But in the brain it's ions and ions are much bigger. I mean electrons are small pieces of atoms very very light ions are just essentially just atoms who have Who charged so they are very sluggish and and I mean much harder to move and that's why that the time scales the time scales in in in neuroscience or in like in in Like for signal processing in the neuron is much much slower than in the Than in electronics But anyway, we know how to model it for example, if we then have assumed this cellular Cell where you inject an electric current this could sort of mimic sort of like a current that you get from a synaptic input Then we can So the the the relationship between the the voltage and injected current Follows this very simple equation, which is actually Kirchhoff's current law saying that current or charge cannot vanish So it's actually like a current conservation law And from that we can actually predict for example, if you have a cell which is then turn where we have this Where the current is turned on at time t equals zero And then turn off at t equals capital T Then you can actually compute and get these exact expressions for the how the membrane potentials gets over what's like essentially like it's called depolarized and how it releases back to the resting potential and so on So the first simulators that people used in computation neuroscience were just taken from these people who make investigate electrical circuits by the people who design these Electronic circuits like p-spice and so on But this is a rather boring neuron because if you had then like input currents from other neurons shown shown here Well, if you get to like a Synaptic input current like an extra current from another neuron you get sort of like deep depolarization and then it goes back and Not much happening But luckily there's the neuron does more because it turns out that if you get enough of these Currents in at the same time so that this membrane potential Gets depolarized it goes from like minus 60 mole volt to maybe tell like in this case a minus 40 millivolts then the the A so-called action potential is spontaneously generated And then if you sort of start living essentially the membrane starts living on a life on its own And fires this gets this very actually Polarized state and then before it comes back and that's what this this spike is so And I think the starting point in many sense of computation neuroscience was that was when we Or not when we we as the field when the field found out how to model such action potentials And that's this work that maybe some of you have heard about How many of you have heard about Hodgkin Huxley? So that's good. So that's So I can I'll go through it. Anyway, but so what they did was sort of they they focused on Well, they found this essentially this mathematical model that describes how action potential propagates down the axon of a particular particular animal And this animal was a particular squid And what was special about this squid was that it had a very thick axon. So instead of like one micrometer thick One thousand millimeter. It was like one millimeter thick So that meant that you could sort of do all kinds of manipulations with it And and change the solution inside and of course outside and so all kinds of things in order to identify Identify the system so based on and that was really the key key thing that they had all these ways to manipulate The system and I think that's it's something to learn about that when you if you want to Because it turned out that even though This is that they found this model for this one millimeter thick axon the same thing could be used for like Ordinary axons one micrometer thick axon. So it's essentially the same formalism the same insight That we got or the insight we got from this system could be generalized to other neurons So it's all about finding right model system. And I think it's the same when you look back at quantum mechanics Actually, everybody worked on the simplest atom the hydrogen atom and that was done in 1926 And that was really really really hard to find that Schrodinger equation But that was done if they had like helium and the other Atoms in the periodic systems within like at least in principle within a couple of years So I think that's it's something to learn about finding the system which is sort of Most vulnerable or most least complicated to understand Okay, in order to to understand their experiments they had to assume these different conductances that in addition to the To these passive conductances they also had these active potassium and sodium conductances So these are sort of like very Well, finely tuned filters which only lets one of these types of iron through So they set up this essentially for the model they set up in addition to the capacitive current and the passive current had had this sodium and potassium currents and they had formally the same Shape as this oh me currents as like this sort of conductance, which is one of the resistances multiplied by the by essentially the voltage voltage drive But there's a lot of things hidden in these. These are not numbers anymore. These are actually function of voltage and and time and in order to To to to study that or they model these these So that was So anyway, so they did they they thought of this the gates of this The the gating of or these conductances as governed by these different gating variables m h and n Which could sort of a sort of like well Well guards to sort of a central well control the the current flow to going through this These items yes I would like to make a comment on the On the difference between irons and electrons on this because this is I mean you mentioned that the irons are much slower than electrons And that's why everything is a little bit sluggish But on the other hand that actually has been a very smart move of nature to use irons because There's only one type of electrons, but there are many kinds of irons and that allows Biology to use colored currents in a way So you have colored wires, which Otherwise are very difficult to make we have to use insulation to do this But by using irons you get all this for free. That's true. No, no, that's true Colored because I have two types of current Colored because you see they have all these suffixes potassium sodium calcium Yeah, whereas if you just have electrons, that would just be electrons. There are no sodium electrons. There are no calcium electrons So but functionally that So the role that plays you In an electrical circuit that would corresponds to different wires, which you have to insulate against each other Ah, okay. Yeah, that's right. So here you get this for free So you have like two slow guys compared to one really really fast one So anyway, but it's true. So but it's true that it also has to do with the time scale of the process Because having a much faster method of processing would be harmful. I think they're having that problem with the spinnaker the simulation using the Yeah, I mean that's sort of like that. This is like what's called alternative history writing or whatever that's like Just if anyone's interested if you're ever in Plymouth England, you can visit the Hodgkin-Huxley lab It's now a museum and you can see on the ceiling covered by Plexiglas or perspex Depending which side of the Atlantic you're on Where all their failed experiments are because they if they Made a giant axon prep that didn't work Forgotten which one I think Hodgkin would just throw it up and it would stick on the ceiling So all these things are stuck on the ceiling there. Oh really? Fantastic The instruments are really crude Okay Okay, anyway, these back to these gating particles. They were then all essentially described by this this like first order dynamics And we have all this voltage dependent coefficients And but at the end of the day They had to fit this this coefficients here Alpha this this Well determining in the dynamics of these gating variables and that was just fitted to experiments And that ties a little bit back to Jonathan's I mean because he talked about descriptive models models how to describe Essentially data and at that time this they at that time They didn't even know what an iron channel was or whether they existed So they had no no choice but to have this descriptive or the statistical model Of the how these things depended on On on voltage and of course that was also the key that really also established this thing of an iron channel That's a way to think about think about the neurons so um anyway, so they They They used one set of experiments to fit all the parameters in the models And then they sort of tested it on a separate experiment essentially just letting this extra potential move And and then tested that in the experiment it moved around well like 20 21.2 meters per second and a theory it was 18 point 0.8 So this is among the I like the the the best of the quantitative agreements in Well, certainly in neuroscience and also in computational biology Full time. So I think this really was like the This was some sense the starting point of computational neuroscience even though it took a long time before I it sort of became a Like at least many people working in the field But I go a little bit back on this as I mentioned this Now we know that these iron channels are Uh Not I mean they they are really just these iron they well. They're really proteins Uh embedded in the membrane because this is like new new insight, but it also shows this this idea of a that the Model hierarchy. We don't want to have a model for the brain where you just put in all Ions and atoms and lipids what have you into this big simulator and just sort of do like Newtonian mechanics on on everything it wouldn't work one thing but also It would be very difficult to understand what understand the model it wouldn't sort of given a much insight So I think there's sort of this that you need these models to sort of uh, well What what models really I think at least if you look at this where the successes have been so far It's really been as acting as sort of bridges between Different levels of understanding that you have sort of you you develop these sort of different concepts at different levels like molecules iron channels neurons and so on and then And then these models ties these different concepts together So I think this is well illustrated by for example, this key concept of the hodgkin-huxey model the iron channel where these This is sort of a mechanistic Model because it's based on this circuit description of the neuron and then when you go look look into the elements of the Of this this currents you end up with this like descriptive Model of the Of the the the voltage dynamics So I think this is an example of a multi-scale what's a like model hierarchy Where for example, if you have like a mechanistic model for proteins and cell Membranes, this is not what hodgkin-huxey had but in principle then from that you should be able to derive the statistical model for the iron channel the kinetics that Actually hodgkin-huxey fitted to their experiments And that can be used as input into a mechanistic model for action potentials in neuron like hodgkin-huxey did And then again because then we get this statistical model for action potentials in neurons that's essentially what uh Essentially just a firing rate or whatever spiking spike trains and that is essentially what Jonathan talked about Which then can be used into like models for I mean network models Okay, so So now based on essentially this since the work of hodgkin-huxey The their approach has been generalized to to essentially cover all parts of signal processing in the neuron not just Not just the axon. So we now have we're in this very fortunate situation to have this Essentially mathematical descriptions available for all processes dealing with signal processing in the in the brain And one thing is I mean you have like these dendrites that they'll get signals in and they have this If you have enough current coming into the soma during a time window Then the signal propagates down the axon and Then they get down to the nerve terminal connecting to other cells and then you have this diffusion Across the sign apps and so on. So then it's a different process It's like diffusion. It's not electrical, but nevertheless it's well understood. I would say like mathematically And the scheme we use then this is what's called compartmental forward modeling scheme You take this taken neuron divided up into small compartments each compartment is so small that That the membrane potential can be assumed constant within the compartment And then for each of these compartments for example compartment. I you keep track of all the currents going into or leaving this compartment we essentially say that this They can't they can't vanish. You're just like a keeping track of all the currents and saying that it has to to sum to zero And this is the kichov's current law So then if one specifies all parameters For all current segments for all current terms in all segments the mathematical solution is in principle Straight forward. So there are like these free mathematical simulators which are Are available Sure Slides back. Yeah So the the the body does the body have any structure? Not in this not in this. Well, I mean that's Typically the does it ever If it has typically the question of whether it has to be so the question is really do that Can it be a single compartment? Yeah And and the question there is not really so much related to shape as it is to whether It's electrically compact meaning that the potential Differences within the soma is very very small and typically it's very small because the soma is quite big Right. Okay. But does anybody worry about that or Does anybody who model model the does these multi-compartmental models worry about the structure within the body? Within the soma within the soma. Well, I mean it's also been tested I mean you can just if you want in a multi-compartmental models, you can just divide the soma up into whatever So I guess in things like the state of the art now in terms of modeling I mean like the blue brain or things like that do people worry about that there or Yeah, I mean this is I don't think this is there's there are other issues I'm coming to which is more or worse on but at least this is something you can systematically explore How small how many compartments you need to make or divide the neurons up into in order to not have this problem So this is something we can we control Yeah, I can comment on this so the You always have to ask is there what is the precision of the description of any element that you actually get Before you reach the typical measurement variability Yeah, and and so for many cases this type of modeling is good enough And you don't really have to worry about the exact shape of the dendrite as long as you have this equivalence tree, correct Things change, of course If you put multiple neurons next to each other then because then the the shape Determines which neuron can connect to which other neuron because there are many ways in which you could bend and elongate any of the branches And another thing that we that Gauter maybe mentions, but we also have to keep in mind that the Hodgkin-Huxley model as such and also the cable equations are also Gross simplifications. So the Hodgkin-Huxley model by itself is just a phenomenological model. It doesn't explain Why the iron channels actually do what they are doing and then if you want to really go a level Lower then you're you're reaching an entire different set of tools where you actually model the lipid layers As they are and then you also will learn that the iron channels are actually not Sitting at a fixed location, but they're kind of diffusing around And that nothing is stable anymore and things become amazingly dynamic It depends at which precision you look at the dynamics of the neuron for certain processes For example, if you if you want to understand what's happening in the vicinity of the synapse During information transmission and also during plasticity these things become highly relevant because suddenly then the activity determines Which type of new iron channels get expressed? And and then go into the membrane and and everything one thing I would like to mention there and Also, you have a talk afterwards No, but I know that's fine. But but the point is that we don't really know what goes What what we know how to model things we just don't really know What all the elements are going we don't know where our iron channels are But we so it's like a different I used to do semiconductor physics and the modeling there and there we knew all the parameters to like four or five digits and And and that was not but then it was still hard calculations But when we knew what went into the model here, we don't really don't really do that Can you elaborate about nonspecific iron channels? So for example any Sales excitative cells, maybe brain cell or any other smooth muscle or heart cell So we have no idea about that nonspecific ions. So how to model those nonspecific channels? Yeah, I think I'm this is sort of like there's a whole two of of channels There's some of these nonspecific cat cat ion channels, which both I think both has like then sodium and potassium so but so but these I mean it's In principle, this can be can be Be modeling the same Modeling the same way, but you need like separate experiments actually to find good models for each of these These these ion channels So Galta I had one last or one other question, which is do you do anything special about the axon hillock and the generator Sure, I mean this is because Presumably where the spike is initiated Is important to what happens. Absolutely. So there are I mean, but I mean you have neural models where Some of the neural models have the spike starting in axon hillock Yeah, so it's nothing. It's just ion channels where you put the high density of ion channels So it's sort of like the the biophysical modeling scheme. It's more about where you put ion channels Which is like, you know, of course an open-ended thing But the cool thing I think is that we know we can we can try out all kinds of things We know how to model it with just all what are the consequences of Having these sort of a high density in the axon hillock instead of the soma or Dividing the soma into two and whatever. I mean you can do all kinds of things So it's like an open-ended program. That's why it's I think it's really You have a solid starting point. You can get off the ground as Jonathan would I guess would would say it So there's just an illustration of the kind of of modeling You can do this is just five neurons or something that is put around like an electron I think that's the four things are just showing that this this this was a simulation we did To to test or essentially there is some measurement methods How are the spikes that you pick up an electrode related to to firing activity? But the point is that this is just pure We have like we're like masters of our little model universe and can try out different things and And investigate so we so we have a solid starting point. I would say for For these kind of model explorations and also moving on into to networks I Also like to I don't know this is The cable equation was essentially was derived 150 years ago Because then I think I think now we would say that the coolest project of the day is figuring out how the brain works And I think from that list from the european point of view, maybe the coolest project 150 years ago Was to get a cable across The atlantic so that we could set the signals in morse and not tie these boats going for weeks, right? And then of course a problem. How do you one thing with many issues? How do you get a long cable? I why and how would you put it into the sea and so this is like this boat that I like to put out there and the cable thing but also how How do you make the cable so that the signal actually makes it across the atlantic? So that's when you had to do make the cable accuration. So we Sort of like interesting that the same accuration that was used to describe this cable Also is now this used to describe describe neurons because which is at the heart of of like this multi compartmental model Just I want to show an example of This is like a project we did we tried to build this multi compartmental model For a particular inter neuron in the early racial system. It's an lgn or thalamus So it had all these very branchy structures and it's complicated behavior And and then we had this this like a very standard kind of computational science project We had some experiments They were you had like collaborators putting a sharp electrode into the center the soma injecting current and getting out these spikes There's like two inter neurons and then we looked Essentially looked at them the kind of the set of I think it was like 10 11 Conductions or something which are known to be present in these neurons and then We fitted the models and so we got models Which could explain that take a kind of data And then we declared victory and published essentially and And this is all like the typical thing to do but this sort of Everybody can see the elephant in the room there So where's the I think there's a big elephant in the room in computation neuroscience Which has to do with this how we deal with these parameters Because it's really clear that that I mean we find these models which are able to account for the data and then we some sense Think of it that these are sort of unique parameters which are typical for these neurons But really it isn't I mean it's you can actually see that these neurons they these ion channels are continuously sort of updated and and changed and transcribed So I think this is one of the big I think one of the questions that some of you asked before this course was sort of what are the big things big challenges in Computation neuroscience where can you be in like five years or something something that can be Improved in like a reasonably short time frame And I think this is a key thing because I think there's some recent actually some papers from this year From eve martish group if some of you know her where they've seen how he can actually some of these Conductions which everybody else is just fitting actually could stem from From like homostasis or plasticity rules That essentially these are regulated by the calcine concentrations in in the dna Or or in the nucleus which essentially regulates this transcription of the different ion channels So I think we're going going to move away from this parameter fitting to go get more into these Plasticity rules that the parameters are set by Or plasticity or homostasis rules, and I think that's that's a very exciting topic of study okay, so um Now, okay, it's maybe we should take a Like a little break now because it's been an hour or like 50 minutes Maybe if you have some questions at this stage Yeah, that's I have a question or like if you have any comments on burst firing or like firing patterns in in neurons from models or this model So some of these neurons turn out to be I mean are such that they when they fire a spike it just they don't only fire a single spike But they actually get a like send like a burst of Of spikes and it's these are also lots of neuron models Which actually accounts for this bursting and it also turns out to whether you burst or not depends on essentially like your immediate history if whether you sort of like Receive more inhibition and excitation in the in the in the in the past So this is quite there's certain conductances combination of conductances which gives this bursting activity instead of like individual spikes In these models when you then fit your model to the data, how do you validate? the the results Yeah, I think these are sort of what we Yeah, what what we I mean what we typically do is that we sort of we look for We look for for Parameters or that actually some can sort of get I mean you have like this Just like there's different ways to do it I mean it's like this least square fitting that you essentially just look at the what is the how do you? I mean you need a cost function or an error function and it could either be That you look at the difference between the voltage in your model and your experiment Or it could also could be that you look more for Features meaning that when you're the distance between different spikes to be a certain So there's like different kind of cost functions You you you check it for the data that you just use to deduce the parameters you don't then cross check it with you That's also that's also done right. So you have like this different kinds of that There was one question back there Yeah, what do you think what is the role of the neuron in case of Keeping the data not only the transmissing data and keeping the data What do you think what is the role of So how that's more like the question of memory. Yeah, yeah, so the the The idea is that I would say like the traditional idea of memory Is that there has to do with the synaptic connection strengths meaning that if you have synaptic connection between two neurons And then then I mean Like if you get an incoming spike that will give a certain response at the at the receiving neuron And this way Determining its connection can be Actually updated and or it can be can be changed according to So that's this spike timing Spike timing dependent plasticity For example, so there are like essentially synapses is like one one key thing. There's also All the ways to remember right that's I mean you can you can you can make changes in the neuron at a longer time scale That you essentially make another set of ion channels or to change the ion channel distribution There's also now some some recent Recent work which points to or suggests that actually these extra cellular matrix molecules That that they can actually sort of play a role in sort of like really long-term memories that in some sense Incapsulating the synapses something called perinural nets, which I just learned about this year actually so for me. It's actually quite quite new, but it's a so there are several candidates so in this point the soma has a important role, I think to keep connection history, let's say Yeah, but these synapses are are all over the place not only at So the synapses are all over the neuron So I said like the the soma is more like the Like the cpu in a sense that it That's where if you had to get enough currents in electrical current in from all the branches In within a certain time window then you generate an action potential. So I think that's That's at least one. That's obviously I think that the soma does so it's not clear that the soma has a particular role At least not in a synaptic part of it Uh the threshold for a particular ion channel It is always constant or it changes, you know What can repeat the question for a particular ion channel? Yeah, the threshold to trigger the spike For example sodium or calcium like this. Is it constant or it varies according to Some yeah, I don't know this is I think typically it's assumed to to be constant Uh, but I think there are also like some of these there's things happening inside the cell like that This phosphorylation things that you can sort of attach things from the from the insights I can actually change Change things also. I'm not quite sure if it's If it's I don't have a full overview of it, but I think typically in these models you You think of them as as constant and if you Consider the all or non-principle This spike peak is always constant or it also varies. Well, that that is typically it's I mean The peak the spike itself may vary a little bit depending on how far how long and go the previous spike fired So in bursts, for example, the the second spike is It's often smaller than the first spike and so But but typically if it's been a long time, then it's it's the same in long times It's the previous spike then it's the same I have a question about Back propagation into the dendrites. I've heard that when the action potential is fired or or not fired you have A back propagation of the voltage differences back into the dendrites I wonder is that something that comes out of your models or is it stopped So that you don't get this or no, no So this we have that they have also models of this kind. There's this one model which came out from It was actually from this blue brain group. It's like the first author is hey It's plus competition biology 2011 which we use a lot because it has all these These elements of back propagating spikes and and like many of the the fancy things So you have models of this type Which also include this this new like the more fancy processing up in the apical dendrites of a5 cells and this NLDA spikes and all these All kinds of things so it's not like It's like an open anything. It's not a phenomenon Which has been I would say on a neural neural level, which is not sort of not capturable by a version of this Oh all these models are generic models are region specific models because we have neurons from various regions of brains because If we deal with any cognitive disease What will be the response of the neurons or the communication? Is there any variation between The communication from region to region So there's yeah, there's there's also lots of variation within the same Cortical area, so I mean for one thing you have different neurons Like even within like a different Well in neurons with different parameters, but which maybe has the same function And then you have like for example, this is like this bursting neurons typically like what's called layer 5b But if you go up to like just like in the top of layer 5 layer 5a another like a little bit higher up in cortex you get very different types of of of neurons and When it comes to pathologies, it's it's really It's really not not not clear even though I must maybe I should mention that now Is that this the result of this question about GWAS studies? GWAS studies are this, you know the the human genome Was discovered or so they mapped out 10 years ago. So people have been trying to to link Of course the the the genes Statistically, I mean looking at groups of like for example, I have collaborated with people who get schizophrenia So now there was this paper that just came out in nature, which had like consortious from I mean rolling hundreds of researchers all over the world had been able to collect and like DNA samples and and like gene analysis from 40,000 people with schizophrenia And then 40,000 controls. So then they had enough data to statistically find out what are different Statistically between the genes of a schizophrenic person compared to control and many of these when you look at and they found about 100 100 genes In that in that study and many of them coded for things Are codes for proteins which are used for example for calcium channels and so on so it could be that like that that is that certainly I mean there are there are hits They probably like to like some sense disease genes genes related to disease which operates on the neuronal Neuronal level because the interest is if we Of course all these models electrical models just matter of resistors and capacitors and charging and discharging if we could model region specific models and that could incorporate the pathology And the communication of communication between different neurons and other things And it will be easy for us to develop new systems that can take care of different diseases and because most of the Memory related brain diseases are unique. I mean Common the symptoms remains common and it's difficult to differentiate the different neuro degenerative diseases So is there any scope for building region specific models? Compressing of the neurons and its responses. Sure. I mean, it's sort of like the principle one knows How to sort of reconstruct neurons and how to I mean, it's certainly the technology is already there for for doing For doing this I would say Okay, I think I'll move on now to to Simplify neural models because now I talked about this multi-compartmental Models which are sort of like biophysical detailed, but there is also Different variations the other types of neural models which are simpler because it turns out that Again, it has the question what kind of kind of questions you're asking and also in sometimes Sometimes it you can actually get away with Essentially reducing the dendrite to a point That doesn't mean that the neuron itself is a point. It just means that the the that the dendrites are so thick That the potential is the same all over the neuron so that you can Yeah, so that you can sort of Get away with that approximation So there is this whole all the class of neurons which has been or All the type of neurons or class of neurons is integrating fire models Which typically has been more less like the single compartment is point neurons which has been investigated a lot because they are Much they're simpler so that they can you can do larger networks simulations with them But also that you can understand them from a more From a more I mean you can analyze them with more traditional tools and learn more about them So it's a it's a very simple kind of a kind of model that It's actually just gets all kind of synaptic inputs has this very quite sort of simple Like passive model dynamics, but then when it reaches the threshold it fires a spike and then and is then Reset so that's one type of and then you just count or measures or the or just read out the read out the spikes there's also variation of this model which has instead of like in And the integrate the fire models are typically there's the one ordinary differential equation But there's also variations of this we have two where you can get all kinds of Spiking and bursting and all kinds of different different spiking dynamics And then We have the the firing rate models Which can be like even more coarse grained level where instead of modeling individual action potentials We model the probability for firing Action potentials so you have this multi-level descriptions of of neurons where you Where you can then either have like this biophysical detail model simplified spiking neurons of this it can direct the fire type Or firing rate models and one yeah Okay, sorry. So again going back two slides maybe one more So in in the case of let's say asikovic's model if you so that is for for a single neuron at the At the axon i-lock So then if you want to if you want to model the The transmission of the signal How do you get how do you get that one? Because then you don't have an integrated model. You just have that one that at the axon i-lock You just yeah, so this is like then you have one so you see that this generates Then red spike so it is like it's an integrated fire type model So these spikes are then sort of collected and sent to other maybe the neurons in the network But directly to another neuron with no Modulation over the dendrites. Well, typically you put in you can put in some time delay Okay, yeah, but that's but that is sort of the key thing about that's it Yeah, that's it because it turns out that at least that's sort of like the standard way to That the action put that then So you trust that it'll be uh transmitted Faithfully over the dendrites Over the axon yeah across the axon with a time delay In this model you consider that each incoming spike has the same weight Yeah, well, I mean that this that is sort of a little bit independent No, it's not the same. This is just about the neuron dynamics So it's not about sort of the the synapse is driving it so you can have this is just how about the neuron Process the inputs maybe maybe to help go to here So I will I will cover a little bit of this in the in the following talk So you can you can actually see how you would produce these types of figures and how to Be patient Okay, so But one thing which we need to do I don't know some of you have studied physics And then you know that a gas of molecules Can be described at two levels of detail at these two levels of detail You can either describe it at the level of molecules and they move around with certain velocities And so if and and there are certain positions. So if you had like Uh, if you had like the list over like all the velocities and positions of all these billions and billions of billions of gas molecules You could actually in some sense understand the gas but that's not How you typically describe a gas typically describe it in terms of Thermodynamics in terms like things like pressure and voltage and not voltage pressure and volume And and temperature and so on so these are boltzmann show how this different of level that actually it's not a contradiction here you can start Start with this and use the tools of statistical physics And and then you end up with these thermodynamics And this is of course at the end of the day what you would like also to have for these different neural models that you cannot just I mean at least in principle. You cannot just have any kind of model at the Coral level of detail. They must be They must be related Well, there's a lot of work going Trying to link these levels level two and level three And we yeah, so that's so that's But it's still work to be done Also connected Yeah, but well, but that's sort of harder because but also a problem here that is very few sort of like Of the shelf multi-compartmental models you can take and which are sort of like to be Where it makes where it's just sort of like general purpose models So it's a little bit unclear what is sort of the ground truth to start with So I think they are for the for the management models. There are two things to to separate the one is you have the dendritic tree Which is cable equation and it's typically passive and for that you can actually show That it is mathematically equivalent to a certain type of single compartment model because it's purely passive. It's a linear system The second aspect is a spike generation Which is governed by the Hodgkin-Huxley equations in the one case and by a simple threshold in the other case Now what you can do is as a very old paper by Wolfram Gersner You can do a Volterra series expansion similar to what we've seen um earlier today and there you can actually see that the first kernel would represent the integrand fire Representation and the higher terms Which of course depend on the Specific morphology and equations that you use in your level one model But these kernels would then capture all the differences and all the extensions Apart from the I think the limitation there is that that I mean these dendrites are not really passive So in when it's so if you now they get more and more I would say models we have more active dendritic conductances and then this thing breaks down and But it's sort of like I would say it's and it's not really clear what this model should look like to begin with And also you need to do something else in order to reduce it to level Level two, but I think I'll I'll go on to neural networks And I would say it's not too much is known about neural networks If I should say one thing, you know quite a bit a lot of things about single neurons Much less about neural networks. I think one thing we have learned is that Because it was a long time a puzzle that Why are if you look at sort of measurements of spikes? In the brain, they're very irregular Well, typically in the old models they got various like very regular firing patterns But it turned out so that I think this is like a really cool idea that came like 10 15 years ago That there's actually this this variability comes from a very special kind of balance between excitatory and inhibitory Input so that's all like a more generic Question, I would say which has been answered Otherwise, I mean people are now built starting to build sort of like models for Pacific I mean specific structures. We have done some work on the on the visual system And I'll just where you what I think I'll Where we can sort of do make models essentially of This is actually a model made by Hill and Tonone Which later was implemented by my colleague Hans-Eckhardt Pressit in Nest Where essentially take Build models by having like two dimensional sheets Covered by this integrated firing neurons in this case and each of these sheets, which then covers the visual field I mean, there's like different types of neurons It's our retina and then lgn cells and the visual cortical cells and so on and then you can do this kind of Essentially simulations where you drive in this case you drive this sinusoidal stimuli on the retina This is like a piece of the visual field And then we drive these these neurons and you can see that When when these these things are on you can see these stripes here and so on So at least we know how to I mean we know how to make models and we also now have tools which Marco will talk about which can make it possible to simulate quite Large networks. I think the problem now is that we don't really know how to hook them up We don't really know what parameters to Specify the networks, but at least we have the tools for for systematic exploration So now I'm going to switch gear a little bit and going back to this thing of Like imaging And this point that there is many many measures of neural activity In the brain And just to illustrate this point that they don't really measure the same thing And that has to be taken into account when thinking about it This is sort of like a picture of them of mankind or earth This is actually from from outer space say that you wear this alien civilization I wanted to figuring out things learning things about About the humans you just one thing you could do is just measure the electrical activity So this is actually pictures taken from the space This is a space station or from outer space And from this you could sort of it seems like everybody is living in in europe And on the eastern part of us and maybe a little bit in japan and so on but if you somehow We're able to measure the like metabolic and like the food consumption Then you'll see that actually that most people Live there, so it just illustrates that if you want to make to These are meshing to two different aspects of of human activity So we have to know when we make models. What do we really measure? and If you allow i'm not well if you now for example not focus on the whole Well on mankind, but to focus on the piece of cortex. This is now a set of There's a set of different ways to to measure neural activity. You could even go in electrically with very sharp electrodes and measure like either the membrane potential directly or if the electrode is just immediately outside You can measure the spikes or you can with this kind of electrode where you have it's not so sharp It has many contact points. You can measure that well You can measure more like the like spikes from many neurons or something called the local field potential Which is actually more like the the population response of how how a population around the electrode Because the process is synaptic inputs and in addition you have all this Light techniques where you send in light And you put in different kinds of markers and so on and then you for example calcium Markers so that you get and then you pick up or you measure the light that comes out of it and interpret that So there's all kinds of of different Techniques for doing that and the typical way to I would say analysis analysis this data has sort of to To measure them separately maybe and then try to look for correlation that it's very very confusing. So What i'm at least advocating is that we should try to we should keep in mind that That actually these different measurements they they it's it's known But as many of these measurements, it's known How how what you measure is related to neural activity for example If you have a neuron here who's active If you put a a a sharp electrode here, you will the spike you measure Will be essentially a weighted sum or the transmembr recurrence in the soma region And we know the link between activity and what you would measure there While the LFP or the contribution to the EEG MEG this distant things Actually corresponds to is reflects the weighted sum of transmembr recurrence all over the neuron while The voltage sensitive dye that's another kind of optical measurement technique reflects this membrane potential in the top The key thing if I have a good model for the neuron I can predict all these things at the same time. So one model can predict all these things So I think this is sort of kind of multimodal Modeling it's a separate kind of problem. It's more like the measurement physics Kind of it's sort of if you think about CERN you have the people who think about why you need the Higgs boson And then you have the people who just think about how to measure it the detector people which are like the Most of them actually so this is more on the detector side than on the information processing side. So we need to work out all these mathematical connections Between the neuron dynamics and the different experimental modalities So what you would like, I think if you want to like a long-term perspective for this like multi-level multimodal approach For understanding say a cortical column is that if you like to have Well three at least three models at different levels of detail for the same thing level one level two level three which should then be interconnected and then you need to develop these links between Well these models and the things that you can measure and it turns out that typically if you want to make precise connections between The neural activity and things that you can measure you need to have this biophysically detailed model But maybe in order to get the right spiking dynamics in order to understand the information flow and so on You can get away with this level two or level three so Let's see now. We're starting to get a little bit low on On time. Let's see. I'm just going to see Where we are With a lot of questions, which is quite good Okay, I think I'll Okay, I think I'll just Oops Oh, that's Okay, so I'm just going to briefly talk about this this measurement of electrical potentials in the brain Because what you typically do then if you have a piece of cortex and you put down an electrode in the middle of the brain Then you measure a small Potential difference if you compare it with an electrode far away But it's only a few it's like 10 microvolts or something not millivolts. So it's really really small signals that's why it took a long time to to to actually Like it couldn't really be Systematically used until maybe like at like 80 years ago or something because only then the amplifiers were good enough to take full advantage of it And then the typical data analysis of this has been that you do a Filtering and look at the higher frequency part contains information about this the spikes low frequency part contains information about About the sub like the dendritic inputs the key thing here is really that We know how to model this if you have Say in this case If you have a neuron this orange neuron if all that happens is that it gets a current in here and it leaves there Because that sort of follows from the Multi multi compartmental description if you know that's the only thing happens in this part of the brain Then the potential you measure here will be a weighted sum of two contributions just one From this current and one from this current And it sort of looks like Coulomb's law, but it's it's sort of like mathematically the same But it has a different Like physical interpretation, but nevertheless the key thing here is that this can be generalized to Two multi compartmental models. So if we do this multi compartmental modeling We can we can do this essentially calculate Just keep track of all the transmembrane currents in addition to say the membrane potential and other things you're interested If you keep if you know all the transmembrane currents And where all these compartments are you can just do this simple sum and then calculate the potential So this is just illustrates the potential you would see just from following this forward formula This the population you would see If you had like a one hertz oscillatory input Uh Driving well coming in there. You will get this dipolar antenna of uh of in the in the potential And if you do the same thing hundred times faster, you get a very different pattern and this will reflect this is actually And this kind of yeah, so this this from this alone You wouldn't see that actually the hundred hertz component of the things you measure say with eg Is um The hundred hertz component of what we measure with eg is much damp just to the measurement physics just to like the detector part Detector physics so One thing that this is important for is that it can be used for mind reading Or called brain prosthesis because these neurons they set up that is like dipolar and these antennas sending out extra cellar potentials Or potentials and they can be picked up by these measurement electrodes And then used for For controlling robot arms So this is a quite this is an example from a a monkey That was trained to uh To feed itself. I think it was marshmallows or something so So this is you can see that his arm is actually in that tube So you can't really grab it with his arms But he has this electrode on top of his head So he's taught himself which then has sort of controls his robot arm. So he's able to feed himself by just thinking about it essentially So this is of course important for For them I mean This is now already sort of been been been used in also in humans who are not able to communicate or control their Control their limbs It's actually it's placed in the motor cortex on top Yeah Yeah, no, so this is inside the inside the motor cortex So, uh So this of course also opens up for this other thing about implants. This is more like mind reading But implants meaning that just that they have technology to aid. I mean like input input to the brain That is I think at the moment is like three Three four hundred thousand people with like cochlear implants In the in the world. So this is not something new and And now people are also exploring this thing of using brain stimulation with electrical currents and magnetic fields another way to To instead of just taking day doctor day's best inch nineshine to affect your brain. You can actually just Use these magnetic coils and this is illustrated I just show by this like a little movie clip showing how this this could work We're going to show you how the trans cranial magnetic stimulator works So first thing yoshi is going to put the magnetic coil over top of the area of my motor cortex That's responsible for the muscles of my hand and forearm When she's there she's going to deliver a magnetic pulse And you probably saw my arm twitch there And we can also see this response over here on the oscilloscope Because we've measured it using the e and g electrodes over the muscles of my hand and forearm Now what we're going to do is move that Magnetic coil over the span of my motor cortex from one side all the way over to the next And what you'll see is muscles slowly recruited from my hand up to my elbow shoulder Right leg and after she switches hemispheres We'll see some of the left leg come in and then down the muscles of my left arm. So here we go So right hand A little bit of elbow Some shoulder and leg Still right leg Little response in my left leg there we've switched hemispheres More leg on the left side Left shoulder Left elbow And left hand Thanks for joining us So what what this illustrates Is of course that that with the neurons are electrochemical machines So it can be affected both by chemistry taking drugs but also Also, electrically. So I think I'll I'll just finish off with I think it's a Movie here, which There's there's another this is a little bit. I think it was It's another application of this kind of a electrical Electrical stimulation of that Yeah Sorry about this. I should have been So these are people who are sort of using this technology to To do remote control on cockroaches Oh, that's that's wrong Let's see if that's So easy And kids They're about to raise so this right here is our And it allows us to study and see how micro stimulation works. So this technique is already used for people with deafness And Like this when they walk around and touch things you want to turn the other way So we're essentially telling it that it's touching something by stimulating his antenna with a signal similar to what they use So Okay, so I'll just end with this list of Of books Which I sort of collected about where I think is sort of like we can learn more about competition neuroscience Actually, my favorite is the one where David will show the organizer is It's not only because it's the leader of the training committee But it's actually it's a nice that's what I use in my course now principles of our competition modeling in neuroscience But there are several good books out there for those. So you want to study more Okay, so I think that's a good place to to stop