 I've done with the patch clamp technique. I'm a theoretician and I just make models. Indeed, I'd like to start with this picture, which shows a patch clamp recording from a cerebellar pockinji cell. So you see this glass pipette here, which is filled with a yellow dye, and the glass pipette makes a seal with the membrane of the cell. We're actually the membrane and the glass like each other. And then what you do is put some negative pressure inside, so you suck. And you rupture the membrane here, and that whole cytoplasm is suddenly connected to the patch pipette, and any dye inside can diffuse into the cell and visualizes the cell. And so what you can see here is the beautiful structure of synthetic tree of a cerebellar pockinji cell. Here's the cell body. This is one main dendrite that comes off it and branches very often. Every few microns or so, there's a branch point, and there's these very, very fine branches where all the synapses are located on it. And I'd like to talk to you about the consequences of this very fine cable like structure, tree structure, for the electrical properties of the neurons and for what the neurons can do. We've learned this morning from Matt Nolan that all of these neurons are endowed with lots of different channels in their membranes, but we also have to consider the physical relationships imposed by this cable structure on the interaction of the different channels. So that's what we're going to do, and we're going to use models for that mostly. But first, we'll also look at reconstructions of other cells. So here we have another cell that's like the first one, it's a pockinji cell, this time from a human drawn by Ramone Kachal. It's like the rat cell that we've seen before, flat. So it's one flat, very dense network of highly branching dendrites. Here's the cell body, this is the axon where the signal goes to the next neurons. This here in contrast is a pyramidal cell. This is in the neocortex. It's about a millimeter long. It has a cell body here. It has so-called basal dendrites around here, which are coming off the cell body. And then there's the apical dendrite that goes up to the apex of the brain. It's the apical tuft. So this receives inputs from axons that come from other areas in the cortex, horizontal axons here. And there's also branches here that we'll speak about. They're the apical oblique branches. So we have very, very different branching patterns in different cell types in the brain, in different species. For example, that's a pockinji cell from a fish. Very different from the branching pattern here. And so we'll talk about what the consequences are of these different geometrical structures for the electrical function of those neurons. Of course, there's also the wiring problem of the brain. So it's clear that many of these different geometries are intended to establish different configurations of connectivity in the brain. So for example, this dense dendritic arb of a pockinji cell allows the pockinji cell to potentially read out any axon that intersects it. And there's many axons called parallel fibers that intersect this one pockinji cell. And so it's able, if it wants to, to read out any of those inputs. And this cell is more selective. It will mostly read out inputs arriving here or up here. In between it won't read out so much. So the morphology has clearly the function to allow particular connectivity. But then this particular morphology also has direct consequences for the intrinsic properties of the neurons. So to study and describe intrinsic electrical properties of neurons, you need to consider the properties of this cable-like structure. And we need to consider a little bit the physics of the situation. And so the variables whose relationship we want to describe are the membrane potentials. As we've heard this morning, there's a difference in electrical potential between the inside and the outside. Inside normally is negative. And so we want to know here's the cell membrane. How does the membrane potential, this potential difference, depend on the position? So if you go along this membrane, how does it depend on position X and also on time? Because it evolves with time. And then there are two types of currents that can flow here. There's the axial current, which means current flowing along the axis of a cable. And what you see here is this kind of imagined cross-section. And what it will do is kind of we imagine we'll count all the ions that cross this cross-sectional area at a given point X along the cable and at time t. And that's something we have to relate to the voltage. And then there's also the membrane itself and its resistance. There will be channels in this membrane and even in the absence of channels. It's not a perfect isolator. So we'll always have some current flowing across the membrane. And this is the membrane current, again, depending on the position along the cable and on time. So these are the variables. But there's also parameters. There's physical properties of this arrangement, which will determine the relationship here. And so among them, who can list some of the parameters that will determine the relationship here? So what's, for example, about the property of the intracellular medium? What kind of properties of that are important? So the intracellular medium, as we've learned, contains lots of ions, so mostly potassium ions, but also some other ions. And these ions are mobile, right? So having mobile charge carriers means that this intracellular medium is? Exactly. It's conductive. Exactly. So we have the conductivity or resistivity, which is just the reciprocal of it, of the intracellular medium. So basically we want to know if you have a millimeter-long piece of cable with a certain cross-section, what will be the resistance in ohms? And we get that by multiplying this R i with the length and divide by the cross-section. So resistivity. Then we have properties of the membrane. So the membrane, as we just heard, passes current, which means that it also has some conductivity, right? And also its capacity. So we have a high capacity of the membrane. And this is capacity per surface area, kind of specific capacitance. And we have this resistance. This is time surface area. So imagine you have the reciprocal of that. It would be conductance per surface area. It's maybe more intuitive. So with these three parameters, and that's what we have to kind of determine somehow experimentally or fit or assume if you want to predict how particular currents yield different voltage distributions across space and time. And this was first kind of applied to neurons in 1959 by a guy called Will Rawl who helped experimentalists interpret their data. So experimentalists at that time, for the first time, were able to record intracellularly from motor neurons in the spinal cord. So they stuck these glass tubes into the cell and they injected currents and measured voltages. And they had some difficulty understanding what was happening. And it was Will Rawl who understood that, well, we have to consider when we inject current here that this current will actually not just go across the local membrane here in the cell body. It will also go along all the axes. It will form this axial current and then only exit through the membrane of the dendrites. And that this is a more complex problem than people thought previously. So this was the first kind of early indication that to describe the electrical properties of neurons, we do need to take into account their structure and then the properties of the membrane and cytoplasm. So what does the solution look like in simple cases? Just to give you an intuition what does this thing behave like. And the simplest cases, we have one electrode that, or one synapse, imagine that injects current at a certain point x and it does so constantly. So it's a steady state solution. We don't change the membrane potential this time. So the capacitor that would be charged or discharged doesn't change charging state. All that matters is the axial resistance and the membrane resistance. And the equation produces a solution that looks very simple. That the voltage just decays with space with a single exponential as a function of distance from the side where the current enters. There's a single exponential going to both sides and the space constant. So kind of, you know, the factor with which you have to multiply the space coordinate to get the argument of the exponential. That is dependent on things like the thickness of the cable and axial resistivity and so on. So thin cables cause steeper attenuation of the voltage as you can see here. So if we move the electrode from this thick part into the thin part, then we see that in the thin part, because the axial resistance is higher, the cross section is smaller, if the steeper attenuation which then becomes a flatter attenuation again as we enter the thick part. So branch points, they have some kind of special significance for the way the membrane potential spreads and the ratio between diameters is important as well. Next, we can go to more complex structures like real neurons with many, many branch points. And so building trees have certain properties that are common to most of them, such as the domain dendrites that come off the cell body tend to be quite thick. And then the higher order dendrites tend to be thin and also quite long. And this means that if we inject current here at this point i, the voltage attenuation across this very short but thin piece of dendrite is very, very large because the axial resistance is very large. And all the current that has to enter the cell has to go by this path if the current injection happens here. So lots of attenuation here and then it becomes flatter and flatter as we reach the thicker dendrites. In contrast, if you put the electrode into the soma, you are in kind of a central location in the cell and you reach the thick dendrites immediately and so your attenuation of voltage is much less. So dendrites are intrinsically asymmetric due to this diameter and branching ratio that you always kind of split up into two. And we can see this directly. So this is trying to model pockinji cells. So we, you'll see in a second, we've measured voltage responses to current injections and made a model to determine these values, memory resistance, memory capacitance and intercellular resistivity. And we have the morphology. So we can run simulations, numerical simulations of this. And we find that indeed if we inject current here, the voltage kind of spreads nearly entire cell. So the control of voltage from the point of view of the soma is very good. If we try to inject current at each of those points here and try to see how well we can control the soma voltage, that's much poorer if we, you can see here we drop a little bit if we put things out in the dendrites. So what was color coded here is the voltage control from the point that was color coded. If my electrode is here in this very thin one, it will be very poor in controlling the soma. And the asymmetry is also there for the older cell. This is kind of 14-day old. This is 21-day old. But already you can see in the control from the soma that the control has gotten worse. So thick, so large interdictories are harder to control than small interdictories. And this is the transient solution. So this is the steady state again with the single exponential. If we have a short pulse of current, then during the pulse we have this situation that looks like this with this kinky edge. But as soon as the current stops, it's a round edge and it becomes like a Gaussian basically. It's like a diffusion equation. So this equation that we have here for voltage as a function of space has the same properties as a diffusion equation for the concentration of some stuff as a function of space and time as well. And the solution of that is a Gaussian function which becomes wider and smaller in amplitude as time increases. That's kind of a dissipation of a little drop of ink in some glass of water. And we can use this, this time-dependent properties sometimes at least to infer things about the configuration of the neuron. For example, we can see that as we move a synapse from the cell body out to define this thing as terminal dendrites, then the shape of the synaptic potential, so the shape of the response in voltage that the soma sees when the synapse is active changes. So it takes much longer to rise and also stays up longer if the synapse has been here and we measure here compared to when we measure where the synapse is. So then reading out experimentally these waveforms, we can kind of extrapolate back where the synapse must have been, at least under some conditions. And we can use this for some information processing, so or the brain can use this. And this is the first very, very direct intuitive demonstrations from 1964 using the first numerical simulation of dendrites. That dendrites can do something somewhat unexpected with their inputs. So imagine you have this dendrite here. Here's the cell body where the one is. And you have two synapses that are active at a given time. And you can kind of switch which of the synapses are active in a certain sequence. So you can start with the proximal synapses. So at time A you have those two active, at time B those two, then those two, then those two. What happens at the cell body is this response. So it raises very fast because you have this response from the very proximal synapses. And then it kind of stays up because as the response would decay, all the other responses kind of come on and keep up the level for a long, long time. In contrast, if you first activate the most distal synapses, then at first nothing happens at all because it takes a long time for this distal response to arrive at the soma. But then as you activate more and more proximal ones, they tend to sum up at roughly the same time. So the response takes a while to take off, but then it takes off to a higher amplitude than this one. And it also is shorter. So if you imagine that the threshold for an extra potential in this neuron is somewhere here, then this sequence of inputs, even though it's the same number of inputs in total, will not lead to an extra potential, but this sequence will. And if you imagine also that the synapses are somehow, you know, spatially mapped onto the tree, like in a retinotopic fashion, that this thing really is left in the field of view and this thing is right in the field of view, then the single dendrite could discriminate directions. So that's the first demonstration that dendrites could be relevant for the information processing of a neuron. We'll examine that in some more detail. And then it's also discovered that dendrites are not just passive. So what we had so far is just omic resistances in capacitors. We also have ion channels in them. We have sodium channels, potassium channels in them. And it turns out that they can support extra potentials, a bit like an axon. But in a weak way, so the amplitude is decremental. It goes down in amplitude and is also a bit wider. This was shown by patching the cell twice. You have a pipet here and a pipet here. And it's the same cell. You fill it with two different dyes. And you can record simultaneously from the soma and the dendrites. And you can see the soma is always first. Soma always makes action until first. It actually comes from the axon. Then invades the soma and then the dendrites. And so we look at how this depends on the mythology of the cell. And ultimately what we are after in the lab is to understand how really should we describe the information processing algorithm that the single neuron is using. In the big network model of the brain, what should be the algorithm kind of the replacement for this big question mark that we use for each neuron? And it's likely the answer will be different for different types of neurons, of course. So we'd like to know how we should multiply, add, or whatever, integrate with time the inputs to produce the spike output. And we see this kind of as a complementary question to this question, which is, what are the functional effective compartments in a neuron? So at what spatial scale should I consider things kind of fine-grained enough in my description to be a accurate description of what's happening? Should I really treat every spine as an individual electrical compartment? You don't know, perhaps. Could I see a whole spine cluster as such a branch or whole subtree? So we'll address that, and we have kind of descriptions for different levels here. And there'll be four parts for little stories that I'd like to tell you. The first is to come back to the cable equation properties and to look at different morphologies and how voltage spreads in them, if, for example, we activate synapses. Then we'll come to the extra-tentials in dendrites and how their propagation depends on morphology. Then in one cell type, we will study the interaction between two kinds of extra-tentials, sodium extra-tentials that come from the axon and back-propagate dendrites and calcium extra-tentials which are generated locally in the dendrites. And we'll see how they interact and how morphology modifies the interaction. And finally, we'll talk about how very local sodium spikes are made and what are good sites for initiation of local sodium spikes in dendrites. So, we go back to Bukinjusau. And first, we have to determine those values of resistivity of the cytoplasm, R-I, resistance of the membrane, R-M, and capacitance of the membrane. And the way we do it is we inject brief pulses of current, let's say here at the soma. We have the 0.5 millisecond, one nanoamp current pulse, and we get a big voltage response right here at the soma, which is mostly characterized by actual artifacts of the amplifier and the pipette, because the pipette has some resistance, too. And injecting current across this resistance means that the voltage here, seen by the amplifier, is actually very large as long as the current is flowing. The amplifier tries to compensate for that, so you have this kind of undershoot here, this overshoot. So, we shouldn't really use that for fitting, and indeed we use only that part after two milliseconds for fitting. You see, the color traces are the data, the black traces are the model fit, and we fit only from this point here. But we also have the second electrode. The second electrode is just recording the voltage, not passing any current, zero current. So, the voltage drop across the electrode is also very, very small. So, we can trust this voltage recording here, the blue one, and we can actually use it in its entirety for fitting. So, we have two locations and simultaneously any model that we make of the real neuron. So, we reconstruct the cell and place different regions in it and assign values for C, M, R, M and R, I. And of course, at first, the response will be very far off the measured response, but we can adjust the three parameters and we can fit it. And then simultaneously, we should be able to also predict what happens if we inject current here. So, again, at the pipet injecting current, we can trust the voltage, the blue one. We can only trust it starting from here. But now the red one isn't injecting anything. So, we can trust that the whole time and fit it. And so, in this way, we can establish member and parameters and then we can use them to make predictions. What does this cell do with its synopsis? So, here is lots of simulations for synopsis, one at a time that move around into the tree. Let's say the synopsis here at this point and we measure the voltage at the synopsis, that's the green trace, and at the soma, that's the red trace here. So, you see that the green trace is a bit higher than the red trace. Of course, locally, the voltage is higher. It attenuates as it spreads to the soma. And if you put the synapse here at this arrow, you have this situation. At the soma, it's still very much the same. It's much lower here, but not much. And at the dendrite, it's much, much higher. And then we go on and repeat the simulation all over the tree and we plot in color the results. So, for example, this here is the rise time of the somatic response. So, the 20 to 80 percent rise time of this, we see this is slower here. That's why this is purple and this is kind of green. So, the rise time increases as we go out. But the peak amplitude from baseline to peak doesn't change much, at least as soon as we leave the soma. So, as long as we're in the dendrite, this changes by only a factor of two or so. It's very, very constant. So, the different synapses, even, you know, the rise time is quite different. As far as the amplitude goes, they have about the same amount of say about what happens at the soma. They're democratic. They don't really put these at a disadvantage. And the local amplitude, which is the amplitude of the green trace, that increases very strongly. But as long as we are in the thick main dendrite, the local amplitude is small. This is in contrast to say, pyramidal cells. It's the same type of simulation in a different morphology now, with very similar membrane parameters. What you can see is, for example, that the range here of the amplitudes at the soma vary by more than a factor of 10 than previously they varied by a factor of two only. So, this is much less democratic. The synapse out here on the basal branch is at a big disadvantage compared to one close to the soma. A synapse up here in the apical tuft has basically no influence at what happens at the soma. The way these synapses can gain influence, we'll see later is via calcium spikes that are made here. So, different morphologies have very different kind of results for how neurons treat their inputs. This one treats different inputs very differently. This one somehow tries to treat all their inputs the same. The way it does it is to have very short and very thick dendrites with small axial resistance. If you imagine that the intercellular resistivity would be zero. You have lots of ions, it's very conductive. Then you can really describe the neuron as one point. Then you have this ideal, simple integrated fire neuron, for example. As long as we try to cheat that by short and thick dendrites we are kind of close to that. We can't make the intercellular resistivity zero as impossible. We have finite concentrations of ions and we have always finite resistivity. Okay, any questions regarding this part? Yes. Does the capacitance for the membrane area do it for the last part? It's a good question. So the capacitance per membrane area is one of the more constant things in this business. The membrane resistance, you can see, can vary about tenfold or more. Also the intercellular resistivity can vary. This is roughly constant. But what's not constant is things like the density of spines. So in the Purkinje cell, for example, you have lots of spines in these thin branches here. But you have very few spines in the thick branches. So that, in effect, forces you to model that differently. You have a different scale factor for membrane area in spines and therefore also a different scale factor for membrane capacitance and membrane resistance. So in this cell it does depend on where you are effectively via the spine density. Any more questions? Okay. So let's go to extra-tentials. This is the experimental finding. It's kind of a representation fit of many, many different data from different publications showing that the amplitude of the extra-tential as it goes out in the dendrite is decremental in most cells but to a different degree and sometimes not decremental at all. For example, in the neocortical pyramidal cells, which I showed you, it is somewhat decremental. So at 400 microns, we are down to about 60% of the somatic amplitude. And it's similar in pyramidal cells in contrast, in pockinogy cells it breaks down very quickly and kind of dies out and is effectively very, very small as we go out in dendrites. And in dopamine cells in spesangian nigra, the cells that die when you have Parkinson's disease and in mitral cells of the olfactory bulb, it turns out the amplitude is nearly fully maintained, it's like in an axon. So different dendrites and different parts of the cells have different amplitudes as a function of distance for this. And we'd like to know what's the influence of the morphology of these cells. Of course, there's also influence of different channels. Each of these cells have different channel densities. And so we'll vary both and we'll see what the influence respectively is. First, we'll go for morphology and use a fixed set of channel densities and properties. And that's something that's an experiment we can only do with the simulation because most of these cells do have different channels and densities and we can't do anything about that. But in a simulation, we can artificially give those morphologies that we've reconstructed different channel densities or the same channel densities. So in this case, we gave all of these cells the same channels and densities as a pyramidal cell is thought to have. And in the pyramidal cell, we get this decremental amplitude and then in the end if we go up here it breaks down completely, similar to the experiment. But the same channels in the substantia nigranuron basically have amplitudes that do go down but then kind of go back up towards the end and every dendrite is invaded by the action potential. It doesn't break down like here. In contrast, at a very, very short scale the action potential fails to invade the trig tree and so clearly there must be a difference in the morphology causing it because the channels are the same. The same recipe for placing the channels. So how robust is that? Is that because we pick just one particular channel density set and only then it works? Well, we can vary that of course and see how robust it is. So this is a plot looking at the action potential amplitude at 200 microns from the soma, the fixed distance to be fair to all the neurons. It has to be short because pocini cells are short. We can't go further out. And here is the standard density of sodium channels that we had before and it leads to some variability in AP amplitude. So in pocini cells it's very low as we expect and in nigra cells it's very high. In between so for example C1 primal cells it kind of clearly depends on the amplitude conductance density of sodium channels. So for some cells we can regulate the amplitude of the action potential by changing sodium channel density a bit. For some cells it's impossible. We would have to really really increase it by a lot to force action potentials to invade it. In pocini cells they are kind of prohibitive for some reason. If you play with the potassium channel density it's a similar picture. So at the standard sodium channel density of course pocini cells regardless of whatever potassium channels we have won't support action potentials and dopamine neurons always will and potassium channel density does decrease the amplitude somewhat. So in C1 primal cells where we know that we have highly modulatable potassium channels, 8 type potassium channels that if we depolarize get inactivated and so the availability decreases then we can see how this leads to regulation of action potential amplitude in C1 cells that's been described experimentally. And this is a plot where we kind of vary sodium and potassium channel density simultaneously and we keep the sum constant and we just vary the ratio and you see again that it's easy to modulate propagation of action potentials in C1 primal cells it's hard to modulate it in pocini cells it's also hard but at the other end it's always there for dopamine neurons. So that leads us to a single variable that we would like to use to describe how easy or how hard a morphology is making it for action potentials to invade them. And we choose the sodium channel density here that leads to full back propagation. So the density for pocini cells must be very high and in different pocini cells it is very high to get up here. But in different cell types we need different amounts of the sodium channel density and in dopamine neurons not surprisingly the least amount to force back propagation. So here's our single number that is an index of how amenable a morphology is for allowing action potentials to backpropagate into it. And then we're going to correlate this with features of the morphology. So first we're going to also simplify the morphology. Morphology has many parameters right, every branch has its diameter and length and so on. So there's a lot of numbers. We like to simplify this. So first we collapse all the branches into one unbranched cable but with varying diameter. And we make sure that at each kind of distance from the origin we have the same input impedance as the real neuron has. So I have to make these things thicker if there's many branches simultaneously. And then we get different shapes of this unbranched cable if we start from different cell types. The substantia nigra neuron gets this kind of uniform monotonically decreasing diameter. The pyramidal cell is similar but does a little hump here with increases again. And the bokehine cell is very, very different. Not only is it very short, it also has this usually increasing diameter at first. So it starts with the soma here then a single dendrite that's very thin and then the diameter explodes basically. And we will see what the consequences of this are for electrical function in a second. But first we'll do some more simple minded analysis of morphology. For example we can count the number of branch points in the tree. And we see that this sodium channel density that allows full back propagation scales, increases with the number of branch points. So something happens at branch points. That's what we can conclude from that. We can also look at the surface area as we go out from the soma. So it turns out in bokehine cells the area increases very steeply. Just as the diameter increases. It's related. Diameter and surface area. And so surface area probably has to do something with this difference in bokehine cells. So we can, for example, correlate the slope here of this curve. So it's a very steep increase in surface area and it's not steep at all for dopamine and pyramidal cells. So if this slope against the sodium channel density special increases with that slope. So what's happening? Well, ultimately what we found is that if you compute the impedance that the existential is facing where it's going towards and the impedance where it's coming from. So the source region and the destination region if there's a mismatch between those two that's a bad thing for the existential. Basically, if it comes from a small impedance, therefore small source region and it has to depolarize and put charge into a low impedance and therefore big sink region that's what's happening here at the bokehine cell that comes from a small and goes to a big region and so for a sustained distance there's this high mismatch of the impedance and that means the exponential is working very hard. So few sodium channels have to depolarize a big membrane area and that just doesn't work. If you don't maximize it, you don't activate more sodium channels to come. They have an even harder time to depolarize what's lying ahead and so on, next potential just dies out. So this is the best correlation we could get with the sodium channel density threshold. So the only way to rescue it is to have so many sodium channels available that they just force it to happen and you need a higher density if you increase this impedance mismatch. And you can also look at this from the point of view of the dendrite. So we can make extra potentials in dendrite. We can inject current and make a little spike and we can do this here, here and here. And then we can study how far this propagates and turns out that's also different for different cells. So it propagates hundreds of microns towards the soma in the substantia nigranuron. It propagates less but also still hundreds of microns in the pyramidal cell and it's very, very local in the Pekingya cell. So that was just one location each. We can repeat this in many locations and then plot how far we get. So the best location to start from is this branch point. If we're here, we get 400 microns towards the soma. The best location in the pyramidal cell is also somewhere here near the main bifurcation and there is no best location. They are all bad in the Pekingya cell but there's many, many of them. So many independent little zones of spiking. And we can also predict from the impedance mismatch from the point of view of the dredig location for making the spike how easy it is to force the spike to go to the soma so how far we have to increase certain channel density and it also matches the correlation is also best with the impedance mismatch from the point of view of the dredig site. So we have this relationship between morphology and backpropagation of the exponential where we have it across different cell types. We know different cell types do have different channel types as well. So this was kind of problematic because we use the same channels in different cell types. Now let's focus on just one cell type where we know that across individual cells the channel types are much more similar and look for effects of morphology on their different properties. And we do this in pyramidal cells. Pyramidal cells have this funny interesting behavior if they are old enough so if they are several weeks old in rats and mice. You can record from them so Matthew Larkham who did his experiments recorded from them at multiple locations along the soma and the dendrite he has just two shown and he finds the usual behavior if you inject current here you give the current pulse at the soma and it backpropagates. So far that's exactly what we know. We can also inject current here and if we inject enough that's several nanoamps here then we trigger this big long calcium spike. You can see it's a calcium spike by this inflection here so it's not just an EPSP like this. This would be something that is too small to trigger the calcium spike and you have just an EPSP. Here the slope increases again signifying that you have recruited more and more voltage-gated calcium channels that drive up to marine potential to this level and then it lasts very long that tells you it's a calcium spike not a sodium spike also you can do calcium imaging and so on and pharmacology. So this is a sodium spike, this is a calcium spike. Now interestingly they interact in a nonlinear way so the threshold for making this guy alone was very high several nanoamps so the dashed line is the same level here it drops to about a third if before we try to initiate it we trigger an extra potential that backpropagates so we can lower the threshold for making this calcium spike by preceding it with an extra potential and we can do this in different cells and we find that that's different in individual cells so this cell here didn't reduce the threshold very much so the amount of current you needed is nearly the same as with the dashed line whereas here it dropped by about 70% and also the shape looks different whereas the somatic AP is very stereotyped this thing is not so there's differences between cells yes So while we're talking about nonlinear interactions between IPSPs and backpropagating action potentials in a normal situation you also have like multiple somatic inputs arriving simultaneously so to what extent do these individual synaptic inputs tell you something about what's going on when you receive a purple bar because those interactions will also be nonlinear right, you'll have one IPSP spreading and it'll shunt possibly if it activates the channel there's lots of nonlinear interactions so the amount of current that we use here this is multiple nanoamps is not made by a single synapse but it's kind of the equivalent of activating many synapses up here so you can get this with synaptic stimulation you stimulate axons here and you get this same kind of thing and also you can observe this in vivo so under normal bombardment even now under behavior people observe these calcium spikes and they also know that there are sodium spikes and we know about interaction so we know that this happens during the ongoing barrage of inputs but Asteris is right so this is kind of a simplified you know, mechanistic way of triggering it and analyzing it and in reality it's more complicated in reality these current inputs aren't made with pipettes and with rectangular pulses all of this is made by synaptic inputs around here if there's enough of them it triggers a sodium extra potential and then there's inputs here that come from other cortical areas with axons coming horizontally from different regions and if there's enough of them they might trigger a calcium spike that's how it really works so we have morphological differences between the cells and we have this functional differences so let's ask how much can morphology contribute to this difference and to do that we have to have a model that behaves properly so we have to have a recipe for placing sodium, potassium, calcium and other channels that makes back propagating APs calcium spikes and this combined event where you have first a back propagating AP followed by a calcium spike and this model does it and it does it robustly so that if we place this recipe for placing the channels, our model our recipe into different reconstructed pyramidal cells we get different degrees of this threshold reduction for the calcium spike we call that coupling so one cell initially had this 70% reduction of the threshold that would go about here and so in different cells they have different amounts of threshold reduction and that mirrors very closely and experimentally found distribution of this threshold reduction because if you do experiments on these cells you also find that this threshold reduction varies so what in a morphology which is now again the only variable here we have the same recipe the same channels only the reconstructions are different what is it? so we went systematically about this and we analyzed the different morphologies that are classically inspired plots of the number of branches as a function of distance called a shawl plot and we modified this to have two variables so we looked at distance from the soma and simultaneously the distance from the most distal end so for example these guys they are branches in this apical oblique then right here so they are close to the soma right they are close to here and close to the most distal end so they are branch points here and then there's branch points up here for example they are far away from the soma and close to the end and these are these guys and so on so we have plots like this and we then asked well do we have enough of this information and the way to test that was to accumulate these data for two subsets of our pyramidal cells we grouped them into whether in the simulations they were showing a strong threshold reduction for calcium spikes or a weak one so we have two classes functionally defined for each class we compile these branch you know point statistics and you know then write diameters and stuff for more than shown here and then we roll the dice and we draw numbers from these experimentally determined distributions that kind of matches these synthetic morphology properties so we synthesize neurons here and again we place the same recipe for channels into them and we simulate a threshold reduction and it indeed turns out that we've had some bias so there's some things that have 100% threshold reduction which means there's a calcium spike even without a sodium spike right so no sorry the sodium spike immediately triggers a calcium spike that way without any input and then write so we have some bias but we have this difference conserved that neurons that have a morphology that allows coupling to be effective will generate synthetic neurons that also have effective coupling and the opposite for the poor couplers so we have the information hidden somewhere here what is it and so one thing we found was if we look at the number of branch points coming off the apical here at different distance regions there's this region here that distinguishes good couplers from bad couplers so the good couplers they are the open symbols they have few branches here and the bad ones they have lots of branches here and that's just the correlation having the model allows us to immediately turn this into a causal link because we can modify the model easily we can for example remove branches like this so if we remove randomly some of those branches we increase the coupling if we add them like the orange one we decrease it so clearly there's something about the branches here that influences the coupling very strongly and the explanation is that basically as the sodium exponential propagates along here to reach the area where calcium channels are and where they could be activated and where the nonlinear interaction could take place then having lots of branches here constitutes a bigger capacitive load increasing a bigger impedance mismatch and it will reduce the amplitude of the sodium action potential as it gets along here if it reduces it to a point that it cannot activate the calcium channels anymore then this coupling will decrease and experimentally we actually then surprise we're really surprised that this works because we start well okay it's such a small effect very likely any change in sodium channel density can override that yes you would expect all you have to do is increase more sodium channels here and you change that back to normal but the thing is that in fact somehow it still survives in the experiment so here it is the experimentally measured coupling that was measured long before so experiments were done before the model and we subdivide the oblique branches in the real cells into two kinds those that are within a distance of 150 microns the proximal ones and then we plot the percentage of how many proximal obliques there are and having many proximal obliques implies there's few distal ones right so there's few here and we know that the distal ones are the bad ones so having few distal obliques means there's high coupling so it works surprisingly any questions on that part the fourth part is about very fast very local sodium spikes and then writes and the motivation is again this big kind of question mark what's the algorithm that we should substitute for what a single neuron does in the brain and there's been proposals by Bartlett-Mell about what this algorithm should be or could be for different types of neurons so for pyramidal cells in this case hypercamphal pyramidal cell he's been proposing that we should consider not just the cell body or the axon as a site where this non-linear decision is taken whether to make or not and where the inputs are summed there's a certain coefficient according to the attenuation to the soma and then the decision is taken whether to spike or not that such decisions can also be taken at a more local level ideally in each local branch there could be mechanisms like sodium channels like NMA receptors like calcium channels that also have a threshold or have some strong sigmoidal like non-linearity that they don't linearly sum their inputs but if the inputs exceed a certain threshold then some mechanism kicks in like a sodium spike, calcium spike and NB8 spike that boosts it and then sends the outcome of this decision to the soma which again decides whether to make an action or not or you can have another layer which is what we just described which would be this kind of non-linear multiplicative interaction between the sodium spikes and the calcium spikes there could be even these three layers so local sodium spikes here then there's interaction between calcium and sodium spikes and then the output so we'd like to look at the conditions for initiating spikes in dendrites, so how should we assign these idealized kind of first layer units to different branches in the morphology the Bartlett-Mell, he knows how to do it he's shown that if he assigns them by hand we can get a very good match between what the full cell model does and what this simplified two-layer network model does but can we do this objectively can we have a computer assign what would be one such subunit can we build some bias if you go from one part to another part I mean I understand that when you when you get a program it should probably be both ways but sometimes because of the of the diameter of the dendrite it should be some bias to go in one way absolutely yes yes totally so basically the current will always flow most easily into thick dendrites and will have a harder time flowing into thin dendrites or short dendrites because the terminations they are closed, the current can't go across it so the current is stuck and it can't escape but it can escape along the thick dendrites and we'll see in a second what the consequences are so maybe you can ask the question again if what comes now doesn't address it so this is just to show experimentally what the spikes look like and that they are really there this is injecting current into a dendrite of a pyramidal cell you see in red the dendritic voltage and in blue the somatic voltage what happens if you increase the somatic spike it's the basal dendrite of a layer 5 pyramidal cell it's not this calcium spike it's much shorter it's not as high as the somatic spikes but it's not the calcium spike it's much shorter at the soma you see only this little kink and then if you increase the amplitude even more we have the sodium spike followed by normal extensors that then back propagate so here the soma is first blue and then the dendrite follows here the dendrite does this in isolation and it's dependent on sodium channels so if you model this we kind of proceed in the same style as we proceeded when we looked at the sub threshold EPSP amplitudes we go from one point in the cell to another we increase the input amplitude and then we plot in color how much conductance we needed to trigger a spike and red means the numbers are very low and we need to make a spike so it means that if we are here in those thin branches or here in the basals or apical obliques on the tuft we need very little conductance to make a spike if we are in the thick or more central regions of the cell can be that we need huge, huge conductances to get the spike so why is that? well there's a simple explanation for that it mostly reflects the input impedance of these different locations having a thick dendrite means that the input impedance is low current has an easy time escaping so you need a lot of current, a lot of conductance to depolarize to the certain threshold where the spike can start if you are in a thin or terminal dendrite then there's not many regions for current to escape so a small current gets you to the same depolarization to the same threshold for making the spike but it's kind of trivial to factor out these different effects of input impedance let's try to look at something that's better in reflecting how easy or hard it is to make a spike and that's the voltage threshold so now we see that actually those regions that were read have a quite high voltage threshold so we need to depolarize two levels of say minus 20 or maybe sometimes 0 millivolts to get the spike out so the voltage threshold implies that if you look at the activation curve of the sodium channels that you heard about this morning we have to really go all the way up to the activation curve where we could all the channels that's what signifies kind of a difficult location for making a spike and these are those terminal branches for example and they are also some of the central regions the thick branches but here in the middle of one of those sub-trees the voltage threshold is low so we need only a small fraction of all the sodium channels that are available to actually get the spike and that's because in these regions we can easily activate a whole range in space of sodium channels so if we go here we get this entire sub-tree basically and all the sodium channels in it but then from this sub-tree there's not much escape routes for charge to be lost and this is one of the connections where it cannot get out of it's captured and there's just this one thin connection to the main dendrite which is not much of a sink this is a thin dendrite so there's a high axle resistance not much loss and that's why this is kind of a very good location for making a spike similarly in pyramidal cells you can see that kind of the outer third of those basal and oblique branches is the best location for making a spike and indeed it kind of seems to be you know having one at least if it's long enough it's too short it's connected too well to the main dendrite and it's lost but if it's long enough it can be its little spike generation site and then once the spike is made it stays localized to this branch so this plots the surface area invaded by the spike and read again in small numbers and it means that in one of those thin branches the spike is very localized escaped beyond this local branch similarly here, if you make a spike here it stays within one of those branches doesn't invade the soma and so they are really independent subunits they don't trigger spikes neighboring subunits if you want to get a spike in the entire cell you have to go here to the main dendrites and that's what a particular axon called the climbing fiber in fact does in pocini cells so in pocini cells you have two kinds of inputs you have these 100,000 inputs called parallel fibers that kind of are in parallel intersecting this dendrite perpendicularly and they invade mostly these spiny branchlets the thin branchlets and they have one axon that goes along the thick dendrites and so it strategically goes to where it has to go if it wants to force a spike on the entire cell which in fact does calcine spike called complex spike also in praminal cells if you want to get most of the neuron we have to go here to the soma to in effect trigger a backfogging exponential so the morphology does create conditions where individual branches can be their own local subunit that can make its own decision whether to spike or not and then transmit the result of this decision to the soma where it finally will lead or not to an exponential so that confirms basically this model and so to summarize shown you that differences in dendritic morphologies across cells or in individual cells of one type can help to explain what people have experimentally observed for the back propagation of axon potentials that is different for different cell types forward propagation of local spikes and also in praminal cells differences in the interaction between sodium and calcium spikes so we have seen that some praminal cells are very amenable for having a strong interaction and other cells keep them mostly independent also by changing the amount of sodium and potassium channels in a given morphology we could see that in different morphologies there is a different sensitivity to such changes so some cells are very robust they forbid back propagation basically regardless of what the density of sodium channels is like pocuncia cells and see one praminal cells in those very small differences in sodium or potassium channel density mean a big difference in axon potential back propagation and finally we've seen that if we look at the fine grained local spikes it's the morphology that can determine how local they are and how likely it is to make them therefore kind of what a subunit structure would look like in this two layer model and if if this can be used kind of as a parameter to tune the function the network this would be a way to do it so you could grow your neuron to have many apical obliques in the right location then you could forbid nonlinear interactions between sodium and calcium spikes if you don't want them and if in another region of cortex you want this logical and between top down inputs and bottom up inputs then you have to remove them and if that's the case if that's really used which we don't know it's just hypothesis then the morphology of the neurons would be a feature for tuning the function of the neuron not just the bark that makes life harder and makes recording as hard as we interpret I'd like to thank people who I had the pleasure to work with so backfiring so the interaction between calcium and sodium spikes was with Andreas Schaefer and Matthew Larkum in Bert Fackmann's lab and the backfiring edge potentials they were modeled by Philipp Fetter in Michael Hauser's lab thank you