 I've been to Caltech graduate students over the last decade and a half. Gary Holt, Carl Gold, and Eric Schoenberg, and by post-doctoral fellow Kostas Amistad. Can you hear me better? All right. The funding is by Paul Allen, and more recently, and then NSF, HFSP, National Institute of Neurological Disease, and Stroke, and the SWAT Foundation. Every time you stick an electrode inside the brain, you measure an electrical signal. The high-frequency portion of that, typically we associate with unit activity, either single unit or multi-unit activity, that's a classical exacellular recording, and then the low-frequency component, typically below 500 or 300 hertz, we call the local field potential, which is actually point out really in abused elongage, because people also talk about fields, and of course, that's nothing to do with the actual electrical field, which is the derivative of the local potential. So it should really be called local potential, but everybody now calls it field. Let's skip that. So there are really two distinct problems. There's a forward problem and an inverse problem. The forward problem Gautier alluded to, which is how do the various transmembrane currents across all sorts of cellular membranes, so neuronal membranes, including axonal, dendritic, and synaptic membrane, as well as, of course, glia, astrocytes, et cetera, because they also contribute. How do they contribute to the exacellular potential? So in a sense, how do the micro variables, if you think about the individual neurons as the micro variables, they're roughly 100,000 neurons per cubic millimeter, so how do these micro variables contribute to the micro variables that you can measure outside most of an electrode, and ultimately outside the skull with big surface electrodes? Then there's the inverse problem, which I find utterly fascinating, which people never consider, so-called adaptive coupling. But you can ask the question, to what extent does the exacellular field influence properties of the individual neurons? So in other words, can the micro variables influence the micro variables? To give you an analogy, in the heart, you can go to a cardiologist, and the cardiologist can use the sound generated by the heart for diagnostic purposes, right? Same thing, the way the electrophysiologist uses the action potential for diagnostic purposes to understand what goes on in the brain. Now, nobody believes, though, in the case of the heart, that the sound the heart makes actually has any causal effect. It seems to be purely epiphenomenal, useful for cardiology, but without any function for the body proper. The question is posed in terms of the electrical field, to what extent does the electrical field influence back neurons? That's so-called adaptive coupling, and if I have time today, I'll talk a little bit about it. There is some fascinating evidence for the relevance of the adaptive coupling. In other words, that the potentials that you measure exocellularly actually can feed back onto the individual neurons. This is actually the original reason I went into this, because of the, there's some interesting possible connection there to consciousness. But let's talk about the forward problem. So essentially, it's really, from a physical point of view, it's very similar. It's very simple. Under the assumption, there's some very good evidence from the logotitas and from rank, some classical paper study that across the frequency domain that we consider, roughly between 0.1 hertz and 10,000 hertz, you can essentially consider the exocellular cytoplasm as purely ohmic. In other words, there are no filtering effects per se in the exocellular field. And then essentially, because everything is linear, then essentially everything reducing, you essentially compute the exocellular potential at any given location. It's just the sum of all the trans membrane currents. So you're sitting, the tip of your electrode is here in your brain and you have a whole bunch of neuronal processes. And each time you ask, what's the transmembrane current? You know, at this particular dendrite or axon and synapse, right? That's your, that's the current eye here. And then you scale it with one over the distance. So the further the current sources away, you know, the, and the less it contributes. And then, of course, this is a sine variable. It can be inward-outward current. And then essentially, as I said, it's all linear. So then you just sum everything. So conceptually, it's really, it's really very simple. Now here, this is what I alluded. This is actually the field. So for a faptic purposes, what really matters is the field. In other words, you know, let's see, typically in the brain, you get fields on the order of 10 millivolts per millimeter or something like that. But people often refer to this as a field, which is really, really very bad language. But I mean, it's stuck now. We're stuck with that. Well, okay, I guess I have to hold it in front of my, all right, I'll try to do this. So one of the, the first thing we're interested in was to try to understand what's the exact quantitative relationship between the inter and the extracellar-recorded action potential. So Michael Brecht in the previous talk, for example, gave you some beautiful intercellar data in the hippocampus and entorhinal cortex. So you can ask the question, in this case, was asked by Giri Bizaki. What's actually the relationship between the intercellar potential and the extracellar potential? Now the vast number of, there are literally thousands of published, of studies being published where people record extracellar action potential. It might shock you to realize, of course, there's no common definition of what it meant by an action potential. In fact, at some point at Caltech, there was seven different labs doing extracellar recording in varieties of animals. Everybody was using a different algorithm to go from the electrical field to action action potential. And people are more likely to use each other toothbrush than to use each other algorithm for what is actually a spike. And it's quite shocking if you think about how important extracellar recordings are to systems in your science, and we do not have a well-accepted understanding of what constitutes an action potential. So one of the very, very, very few studies, in fact, right now I only know of two in these tissues, who came out of the Buzaki lab, was Henze, where they recorded, they did microelectrodes inside a neon in the hippocampus while they used silicon probes outside to probe at the same time simultaneously the extracellar potential. So in other words, you have ground truth, you know, the exact transmemory potential at the soma are close by, while you're recording simultaneously from the outside. So now you can compare. They also injected into these cells biocidal and reconstructed them. So then in principle, it's a beautiful database that we can use based on earlier work we did with HOLD, where for the first time we did a very detailed modeling of the extracellar potential surrounding a neon as it spikes. So essentially we do the same than doing optimization techniques to try to fit. So here you have a single CA1 pyramidal cell. Here you have the actual recorded data. You can see here inside, as it's recorded inside from the glass microelectrode, you can see here. This is time-scaled at one millisecond, 20 millivolt. This is recorded simultaneously outside using the silicon probe. Of course, here the potential is vastly, you know, it's roughly three hours of magnitude smaller. This is 20 millivolt and this is 20 microvolt outside. And then you do, you carefully adjust since we have the known morphology, we can adjust the electrical using a very steepest grade in descent technique to adjust the memory conductances. So finally, you can get these very, very nice matches. You have the known morphology, you can match the inter and the extracellar potential, which is actually a very strong constraint. And then you can see here how the potential falls off and you can study, for example, extracellar shapes. You can have a whole lot of fun doing that. So the canonical extracellar spike that most of you are familiar with has three different components. Now, those components, they are there all the time, but sometimes they superimpose because it depends on the exact morphology, on the exact timing of the individual currents and on where they are located with respect to the axon, the axon hillock, the soma and the active dendrites if they are active dendrites. There are three phases. So here the first one, which you often don't see is a very rapid capacitive phase that's really dominated by the capacitive current. It's positive and very often you don't see it because it gets overwhelmed by the sodium current. So the dominant component here is a sodium current. It's negative due to the influx of sodium current during action potential. And then you can have a third phase that's typically much longer, can be one or two milliseconds that can have multiple phases that you can even see in the exocellar potential that's dominated by the various potassium and calcium-dependent potassium currents during the repolarization. Now, as I said, all three currents are there all the time. It's just you might not see them because they overlap. And so for example, the capacitive ones you don't see or if you do filtering, you might also remove it. So what you can do, Carl Gold did this for his PhD, you can look at for all these different cells where Buzaki had both the inter-the exocellar potential as well as the morphology, you can reconstruct, you can sort of see the listening diameter. So assuming here that your signal to noise, you require 40 microvolt in the animal in order to detect the action potential, then sort of you can detect this cell within this volume. If you're outside of here, you couldn't listen to the neuron anymore because you could not pick it up reliable with your exocellar electrode. So this clearly depends on the ambient noise, it depends on the tissue and its input impedance, depends on your instrument noise, of course, but most importantly, it depends on the distance to the spike initiation, those and on the geometry of the soma. Overall, it turns out the geometry, if you just listen, care about exocellar potential, the detailed geometry of the dendritic three doesn't matter at all because everything is totally dominated by the current at the soma or by the currents at the axon initial hillock. So in fact, you can swap in a model, you can swap geometries and it doesn't really matter. It's all dominated by the very large spiking currents which are essentially proportional to the membrane area, so to the size of your soma and your axon initial hillock. You can in this model, you can then do what's very difficult to do experimentally, you can go outside here, so here you measure within 50 micrometer, you can look at the peak voltage potential of the exocellar electrode, of course this depends critically on the exocellar row on the conductance which is different in hippocampus than it is in cortex. So this is data for hippocampus where after 50 micrometer, 40, 50 micrometer at least in the living animal, you're not gonna be able to pick up cells anymore. So in other words, your listening radius is 40 to 50 micrometer. Now what we're doing, this is a work that we're doing together with Perrin, Rodrigo Perrin, and Giri Bezacchi and Henry Markham which is where Kostas Anastas uses the Caltech postdoc I mentioned where they do simultaneously inter-in-exocellar recording using modern and neural nexus. So these are 32 channel probes and then they use the system that Rodrigo Perrin in the Markham lab has set up which is a 12-patch system where you can patch with 12 different electrodes simultaneously under visual control in the near infrared. So here you have these four, these silicon poles. Here you're recording from four cells. These are layer five rat cells. So patching simultaneously. So here you can see the electric activity from four cells, spiking activity in response to an injected current into these cells. Well, here you're listening from the various electrodes. So here you can see this here, this activity is from this electrode here. This is a scale bar. So in this case, although this may be only 30 micrometer long, you can see those are the action potentials. And then so you can see, so these are different sides from two different neurons, cell one and cell three, this one and this one. You can then compare, so here you have ground truth from the intercellar patch clamp recording. You've got ground truth. These are the individual action potential. And here you can match them up against the exocellar recorded ones. And then what you can see, this is all preliminary data, not published yet. So here what they did, so here you can see the, so these are the action potentials of four sides. And here you can see only, you're only here you show only the one that fire at low frequency between zero and two hertz. And here you show the one that fire between eight and 10 hertz. And you can see they're not the same. Of course classical theory says they should be exactly the same because here the spiking is so low it's 100 milliseconds at any residual effect should have decayed, but in fact they do differ. Here you plot for the four different cells you plot at the various frequency whether the cell fires very slow, i.e. between zero or two hertz or whether it fires fast between eight and 10 hertz. You can see the systematic changes to the shape of the action potential. So in principle, the idea here is that you do this very careful study into comparison between inter and extra. Of course it depends on your silicon probe and the nature of the silicon, the exact nature of the silicon probe. And then match them up against the various algorithms. Right there are a few dozen algorithms around for spike detection because that way you can really ascertain sort of ground truth, what's the exact relationship and what are these different algorithms measuring. So as I mentioned before, the contributors to the local field potential are really every piece of excitable tissue in the body, scaled with the inverse distance. So primarily it's post-synaptic activity. So in general the local field and particularly the EEG thought to be dominated by a post-synaptic activity. However, there's also a presynaptic component that people know very little about. In other words, the current generated at the presynaptic terminal will also contribute the fast action potential. In general people think they don't contribute too much just because action potential of course are very thin. And so they have to be highly, highly synchronized in order to contribute significantly. And so it's thought that in general the local field is pretty much independent of spikes. It turns out to be not right. The calcium potential currents are somewhat slower. Spike hyperpolization and downstates, gap junction and glia contribution. We know almost nothing about the last three contributors. Just nothing, shockingly. It's shocking because that's the basic variable most of us use to understand the brain. So one thing we do know about the brain about local field potential, there's one of these power loss decay in the temple time cost. This is from our data from humans. We work with Isaac Fried since many years to record from patients doing epileptic that are where people have implanted depth electrode for possible epileptical surgery. So you can see in the front lobe, temple lobe, pride lobe and occipital lobe you can see these very nice power loss. So here you can see the local field going from 0.1 hertz or so to 400 hertz here it's plotted in a logarithmic. You can see very beautiful slopes here. In this case it's two, it doesn't have to be two, it can change, that exact slope can change, can depend on all sorts of cognitive tasks, different animals, different location it can change. But the important thing is it tends to be one over F. So in other words, the higher the frequency the lower the power contribution. Now it is, so once again this tends to emphasize if you look at here where action potential of course we think action potential you know here 500 or 1000 hertz so you would assume that action potential don't contribute anything. Look at here the logarithmic scales here in terms of power. But that's in fact not quite two and in some condition there's now some nice evidence both for V1 as well as for high gamma in CA1. You can actually get, so this is a detailed model we've been doing with Giri Buzaki where you can actually show that here is a model that has 10,000 pyramidal cells with active currents in the hippocampus and you can see that the high gamma or the ripple set you can see, the sharp wave ripple set you can see in the animals that typically has frequency between 100 and 200, 150, 200 hertz, high gamma sometimes also called epsilon. That's really a significant power, at least half of the power can be contributed by action potential. So in other words, if you look at high frequency some of the high frequency gamma oscillation what you're really seeing are action potential, at least a significant fraction of that signal will actually be action potential. So it makes sense for example to use that as a proxy if you're using proximal clinic, if you're using large scale ECOG like mapping you can use that as a proxy for post-synaptic spiking activity not just presynaptic activity. What's the spatial reach of the local field potential? The best data really comes here from a paper that by Linnet Al in Neuron headed by Gautis Group. I think you're gonna talk about this afternoon at five. So here they used both an analytical or semi-analytical approach and then backed it up by detailed computer simulation. So the idea is once again you have a ring so they did something very similar to what we did in hippocampus. So you have this cylindrical morphology you assume all your neurons are located in this disk. This disk has a radius big R and so if you're just looking at a sliver sort of an annulus here each time you increase the diameter of this annulus you're gonna increase the number of neurons. In this case linearly, here you can see that the number of neurons here in the disk scale across linearly as for each segment that you ask that you add. So once again here you have the contribution from the individual neurons and then you just add them with that scaling factor one over R as I showed you in the first equation in order to get the population or what we call the local field potential. Now you can make simple assumption you can for example assume that the neuron at far distances like a closed field geometry like a small spiny stellar cell behaves like a magnetic monopole so then the spatial part of it should decay as one over R. We expect that from a monopole. If it's a dipole like you have a pyramidal cell where you have which you can model sort of which you can better approximate by dipole then you expect one over R square decay. So now of course as you go to larger and larger distances you're gonna get more and more neurons involved so more and more neurons are gonna contribute to the electric field as this function shows. On the other hand as you go farther, farther away the contribution from each individual neuron will scale either one over R or one over R square or with some fractal power. So first of all it's not a given and I looked at points that out and I think it's important to point this out that this process necessarily converges. In fact so you can see what he studies he looks under two different assumption which turns out to be critical. He asks what is the spatial reach of the local field potential under two conditions. One is when neurons are not correlated, when they're not correlated in the extreme case when they're not correlated at all they add SS square root of the number you know the variances add. If they're all correlated so it's the other limit where they're all perfectly correlated then of course their contribution adds is linearly. And so here he looks at as you increase the population radius what is the compound amplitude under two conditions either when it's a dipole or when it's a monopole. And under a number of conditions the system does not necessarily convert. So it turns out the amount of synaptic correlation is really essential. This is if they're not correlated the neurons all right then you get this very flat function if they're highly correlated then you get this increasing function. So he looks at here this is a summary diagram. So here you have this model where you assume you have a couple of thousand I think up to 10,000 layer five cells as a function of distance. And you can see here the normalized contribution to the local field potential. So if you have, so let's first look at either input into the apical dendrite or input only into the basal dendrite under different conditions of correlation when the neurons are not correlated at all then you get this very rapid convergence. In other words in this case after 200 or 250 micrometer you don't get any additional power anymore. In other words if the neurons are not correlated and you have this sort of synaptic input of this then the spatial reach of the local field is 250 micrometer which is in agreement with some experimental data. On the other hand if neurons are highly correlated then the reach is much larger then the reach can be up to a millimeter which again is in agreement with some other experimental data. So what this paper very nicely unifies is it tries to reconcile different experimental observation that depending on the degree of synaptic synchrony among the neurons the spatial reach is either very small, a couple of hundred micrometer or can be large a millimeter or so. That's not true under all conditions. If you get input both into basal and apical dendrite at the same time you get a small reach. Now we're extending, we are continuing models this is a work together with Sean Hill, Michael Reimer and a student in the Markham lab. We're doing very large scale using blue brain simulator where we have 12,000 neurons. So here a couple of, I can remember, 5,000 layer four cells and 6,000 layer five cells. These are all uniquely characterized. They have a whole bunch of active conductances and 1200 inhibitory cells. These models are rat, some of the sensory cortex, interconnected in appropriate way. Then you can get these very complicated electrical fields where you have, and I'm not gonna talk about it, we're now dissecting them where you get these very, so the trouble is if you do this very large scale simulation, A, they take a long time to run. So typically it's one hour on a 4,000 process of blue G and P. It's one hour using 4,000 processors to simulate one second. Of course you have a very, very large number of parameters. And so it's not an easy method to dissect out what are the various contributors to the active field. So I'm gonna leave that. Let's see, what's the time here? All right, let me just, I thought I'll just throw in a fun series of slides how we can exploit the local field in people to enable them to control their own neurons in the hippocampus using to explore this electrical field. So this is work, as I mentioned, I've been doing since many years now, 15 years with Isaac Fried. So these are depth electrodes, so these are microelectrodes. That's a spiking. These are microelectrodes where you have these large clinical leaves. These are used to record in intracranial EEG to help monitor, to help the epileptologist to locate the seizure. Focus at the same time, they added micro-wise here. These are conventional micro-wise isolated until the tip. And you can record individual action potential. So typically you have a patient like this who's on the ward for a week or two weeks, and you can record from their brain. So typically the 70% of the seizures tend to be in medial temporal lobe structure, so that's where most of the electrodes are. So already a couple of years ago, we discovered together with Gabriel Kreiman, who's here in the audience, we discovered these neurons here, you can see. So this is all awake human, this is three seconds, one second before between these two vertical tick marks for one second we show these individual images, either text or pictures of famous or familiar people. We show famous or familiar people because typically unlike a V1 cell, these cells don't respond to things that are meaningless, that are meaningless, like random bars or random dots or things like that. Typically these cells will only respond to things that the patient actually recognizes. After all this makes sense, we are talking about a very high level part of the brain here. So here what Gabriel first found was Bill Clinton, but this is another actress, Holly Berry. You can see here these different pictures, you can see typically after 300 to 350 milliseconds, very late these cells will respond with a burst of action potential, quite stereotypical, almost always between three and 400 milliseconds. So here you can see response to various pictures, Holly, here you can see a woman in a leather dress. Now it's not a random woman in a leather dress, that actually turns out to be her professional attire, she's an actress and she played the woman, the movie Catwoman, that the patient himself had seen. And here's actually the name. So the cell respond in this very high level invariant way. Here is a cell that responds to the late dictator Saddam Hussein. So these cells, they go across different modalities. So here you have pictures, here you have text, Saddam Hussein, here you have a computer voicing, Saddam Hussein. They don't respond to other names, other people, other similar people who look very similar. Now you can use that and Moran Server, grad student in the lab, use that to actually read off the electrical potential in real time and to feed it back to the patient. So the patient can himself, him or herself, learn to control within a single trial or within two or three trials to control their own neurons deep in the Middle Temple Lobe, which is sort of cool. So here I'll show you a movie. So here are four different images of four different people. This is George Brolin, not very well-known American actor who was the favorite actor of this particular patient. This is the famous picture of Marilyn Monroe. This is Michael Jackson. And this is Venus Williams, the tennis star. So you can see here we are recording from four different microwaves in these four different areas. And you can see each of the microwaves responds quite strongly and selectively to one image, but not to the other images, right? You can see, I mean, we have a lot of data here, 20,000 spikes. So essentially the idea is now what we do, we feed back, let's see, in this case the movie I'll show you, we feed back this electrical signal and this electrical signal. We do the following. We feed back the activity of all four wires and we take an image on the monitor. The image consists out of a morph of this image and this image, and depending on the firing rate, so there's a decoder, so it's a four-dimensional space corresponding to the four neurons and the firing rate. And we essentially now a decoder that controls the expression of an air of a morphed image on a computer screen, and you'll see it in the movie, that's this image superimposed on this. The closer you are in this four-dimensional space to the response to George Brolin, the more the patient will only see the picture of George Brolin, the more it's closer to Marilyn Monroe, the more the picture will morph towards Marilyn Monroe. So what you'll see, each movie is a walk through these two-dimensions, so this one-dimensional space, are you gonna see, mainly, you always start at 50% George Brolin, 50% Marilyn Monroe, and then the task, each time the patient is 10 seconds, we ask him, this trial, try to suppress George Brolin, or this time, try to suppress Marilyn Monroe, and the task, the patient has done successfully, if at the end you end up with a pure 100% picture of either George Brolin or Marilyn Monroe. Now, of course, if some other neurons will fire, like the Venus William or the Michael Jackson Neon, then the image will not change at all. All right, so let me show you the movie. So this has to, of course, be done in real time, so we feed this back in 100 millisecond. So it's always, what the patient always sees is the effect of the firing rate over the last 100 milliseconds in their own head. All right, so clearly this cell is turned on by Marilyn Monroe, and the nice thing is that this is, as I said, it's very invariant. You don't have to use this particular picture, you can use text or other things as long as the patient recognizes at the individual. All right, so this is the control, and now we do this, what we call fading. So here, the first thing is, he's supposed to concentrate on Marilyn Monroe, that's the target. All right, so she did this successfully. Now she's supposed to concentrate on Josh Brolin. This is her, it's a failure. It's the only failure. Now this is only the third time in her life that she's being asked to do this, right? So there's no, we don't have to go through a lengthy period of training. People can do this very, very quickly. When we ask what they do, they think of, when we ask them to think of Marilyn Monroe, that's what they think of. I mean, that's what they tell us, they think of. So you can think of these, each has a little movie, the movie's up to 10 seconds long, and the movie essentially is entirely a product of the fine rate of those four neurons. All right, yeah, so the performance is highly, I mean, these bars, so this is the performance, to what extent they can do this task. The yellow bars is 10 to the minus three significant, so it's highly, highly significant. So these are some of the numbers. So we have, for this paper, we had 72 medial temporal lobe units. The best ones are in the hippocampus. We don't know in what sub area of the hippocampus. So the increase of baseline rates from four hertz, in general the fine rate is very low, which is typical for behaving animals in this part of the brain, is four hertz and it goes from four hertz to 12 hertz if they do this successfully. And the fine rate decreases to roughly from four hertz to 1.4 hertz when their preferred stimulus is a distractor. So in other words, in this case, when you recorded from the male monorone, the Josh Brolin, when you're supposed to think of Josh Brolin, the Josh Brolin neuron went from four hertz to 12 hertz, and the other neuron went from the one that responded to male monorone, went from, on average, four hertz down to two hertz. Now in most of the time, this happens at the same time. So in other words, people simultaneously enhance the representation of the target image, Josh Brolin, while suppressing male monorone. So what has to go on there, because I make it sound like that there are two different people here. There's a patient and then there's a brain, but it's like being John Malkovich, right? Because what the patient has to do the following, the patient takes the instruction and puts it, let's say, into a prefrontal cortex, into a neuron there. So for the next 10 seconds, I've got to enhance male monorone. And then the neurons have to reach back, those neurons that encode the instruction, have to reach back and have to enhance the male monorone neurons, and at the same time, suppress the neuron from the competing stimulus. All right, so the, and the last thing I briefly wanted to mention was this inverse problem. How does the field influence neurons? So if you just look at the basic linear cable equation, you see already how it couldn't potentially, so this is the basic cable equation, right? That you all know, second derivative of space here. Now here you have this term, the second spatial derivative of the exicella potential. Now in 99.99% of all modeling, that's assumed to be zero. You either assume the exicella potential is zero as constantly neglected. Now of course in general, there's no reason to neglect it, particularly if you're in the brain, because we know there are fields here, right? So this is the second derivative. So it's the first derivative in the field. So if you have changes in the potential, as we know you have, if you do simultaneously recording with more than one electrode, you don't record the same potential at, it changes of course, as a function of space. So then you would expect this term to be non-zero. And so you get additional currents, all right? So for example, if you simulate them, so this is doing theta, doing a sharp wave in the hippocampus, if you simulate them, you expect them to be very small. So this is one millivolt. Here you, here from Pusaki's lab, they've recorded the potential at many locations. So we can estimate the second derivative, although very noisy, and then you can see, you expect in doing theta, for example, these theta waves, you expect to see these theta waves reflected in small fluctuation of the membrane potentials. You can say, ah, you know, they're half a millivolt or so, which is what you would expect. I can routinely neglect them. Now that may be true that you can neglect them when the cell is at rest. Of course, real cells and real animals or people are never at rest, right? The only time the brain's at rest is when you're dead. So to test that, so once again, we work with Henry Markham and Rodrigo Perrin, and he has this fantastic 12-catch setup where he can simultaneously monitor up to 12 locations. So what we did here is to record, again, once again, these are layer five cells where you have, you patch one of them, and then you can have a stimulating electrode outside here, from which you can unipolar or bipolar, you can apply an exicellar field, and then you can record from all these different neurons. So you can measure precisely the potential just outside in the microenvironment, just outside the neuron. And then what you can show, well, first with substratial, you do get the expected, the fact, the coupling, but it's very weak. So if you apply externally a sine wave at very frequency at eight hertz or at 100 hertz, then of course you measure in the intercellar potential, you measure this, so that's measured exicellularly. This is just induced by the external electrode. Then intercellularly, you measure the small potential, and then this is actually the membrane potential, so it's the difference you inverted. You flip it by 180 degrees, and once again, you can see very small potential here, but it's nice, this is exactly what you expect from theory. But now, what happens if now you get your cell actually to spike? So now you inject a spiking current into the cell, and now you ask the same question. What happens now? What's the relationship between spiking, particularly with the timing of spiking of these and the external field? And I think I have to shorten here. Let me just come to this summary diagram. If you look at the coherency, the spike field coherency, as a measure of the relative power of the frequency at which you're applying the external field, what you can see is very large shifts in the timing. So this external field will not induce any spikes in and of itself. You don't expect that because the potential is too small, but it'll significantly affect the timing of action potential. So here you can look at, so these are the exocellar field, sorry, these are exocellar potential. This is the exocellar field. The order of magnitude is five to 10 millivolts per millimeter. And here you can see the change in the spike field coherency. So they can be very, very large at low frequency, at one hertz or at eight hertz. At higher frequency, 30 or 40 hertz frequency, they're not very large. But at theta, they can be very significant. And at low delta, they can be very significant where the external field will shift the timing and therefore will influence the timing of the action potential. All right, so in summary, so we are beginning to understand quantitatively, finally after having used the exocellar potential over the last century to record from Neon, we're finally beginning to understand the first step, the exact quantitative relationship between the exocellar field and the intercellar field. So now we can begin, we have a much better idea of how to manipulate in particular what we are measuring with all of our recording technologies. Thank you very much. Okay, there's also going to be a panel, okay, go ahead. I'll ask you these one question. So the first example, I think, of looking for the effect of extracellular potentials on intracellular potentials was the study that I mentioned at the start of my talk in looking at the interactions between mitral and granule cells using computational methods. And there we did calculate the density of the mitral cells and granule cells and calculated the effect of the field potentials and it was in the order that Christoph has mentioned. However, I think it's very important to realize that without this ancillary data, we're essentially carrying out computation, we're making computational models of cells that are essentially functioning in a vacuum, similar to molecular models that have no context, environmental context. So I think we should encourage modelers to include these field potentials in their computational models of neurons as well as the effects of ions in the extracellular environment that have fluxes, extracellular fluxes that can affect excitability, as well as the effects on glia that Christoph also mentioned. Thanks. In fact, it's ironic. So your study with Will Rall that established that for the mitral and the granule cell and the gap junction there, which is sort of at the beginning of the quantitative exploration of the field, here we are 40 years later and we have very, very little idea of what, for example, all the gap junctions do in cortex. We know they're there, you can see them, of course, but almost no models of cortex incorporate them right now because they make modeling much more difficult, particularly large-scale parallel, modeling much more difficult, which is ironic. It makes modeling more difficult but on the other hand, it provides much more in the way of constraints on matching our models to the neurons. Well, most importantly, they're there, so we have to take them into consideration. Okay, then I think we just move on to the next question. Next speaker.