 Okay, so we've heard in the first two days about sort of the brain at a sort of macroscopic to sort of macro circuit level and yesterday Uppi began to talk about sort of intracellular biochemical signaling mechanisms. What we want to do today is to begin to sort of link this in with sort of what we might call neural computation. So the sorts of computations that neural circuits might carry out and so we want to start to think about how we might bridge this gap between sort of different cell types, molecules and what it is which brains actually do which is in some way sort of processing and computing with information. So in a very general sense we might imagine that a neural circuit sort of has some sort of representation of information. Neurons fire action potentials and then action potentials propagate. I don't think this is going to work very well. Yeah, can you can you get the next click? They propagate down axons, they release neurotransmitter and then if you click again and again and then a downstream neuron might fire an action potential and then that would propagate again to the next stage in a circuit. So we want to start to think more about this process of sort of information propagating through circuits. So just a question for you guys. If we're going to start to make these sort of links between information processing and some of the things that we've already heard about how are we going to do that? What sorts of strategies can we adopt to do that? So to make a link between sort of information processing in some sense that this tissue this organ is doing and these physical properties of brains and brain cells that we've already discussed over the previous two days. Okay, it's early I guess. Sure, so that's the type of experiment we might do is to change properties and see what happens. What about computationally in terms of models? So we've heard a lot about data and a little bit from IP about sort of detailed subcellular models. But what types of models might we want to use to make this thing? I mean I know some of you are doing this kind of work so you already have ideas. I'm just trying to encourage you to sort of share them a little bit. Study morphologies. Okay, so how would you do that? You could describe morphologies and make lots of beautiful pictures. Okay, so yeah, the direction I'm trying to go in is to what we need to have sort of or at least my viewpoint would be we need to have computational models that in some way represent the physical properties of neurons and their connections and then we need to be able to study how these sort of physically derived models might carry out computations and this can be a very powerful way to bridge the gap between the molecular and the physical properties of neurons and the types of computations that we do when we're thinking, when we look at things and that we don't really understand yet. Okay, so I'm just sort of trying to make a case for sort of detailed or somewhat detailed physical models of neural circuits. So this will be the focus of my talk and then Ant's talk in the second half of the morning is sort of physical principles that determine how neurons might compute and strategies that we might take to build models based on these physical sorts of principles. Okay, so if we take a neural circuit and think in a sort of cartoon way about what are the properties of a circuit that will determine the computation that it carries out. There are three, I think different types of property that are very distinct and that collectively will determine what computation a circuit carries out. So first of all we have the circuit's wiring. So it showed a couple of examples of different types of circuit with different types of wiring yesterday that were very sort of abstract. We know that if we look at the wiring of different brain areas, there are very different principles that sort of configure which neurons talk to which other neurons and this is likely to be a key determinant of what a circuit does. But alone it's not sufficient. So another key thing is the synapses. So synapses can be eccentric, inhibitory, they can have different kinetics and this also can be very important for computation. And the third property is how neurons integrate their synaptic responses. And this is what we're going to primarily focus on today is what you might call integrative properties of neurons. So one way of thinking about a neuron is as some sort of device that's listening to signals and then it's making a decision about whether or not to produce an action potential. And this you could argue is the fundamental sort of function that a neuron carries out to listen to synaptic input that it receives and then to make a decision about whether it generates its own action potential output. So if we were to do an experiment where we perhaps record from a neuron. And so this is a recording. I'll talk more about this, but this is a recording of the voltage difference between the inside and the outside of the neuron. And if we were to then activate synaptic inputs, that's imagine we activate first of all one input. Here you can see it changes the voltage of the neuron. Then perhaps we activate two, we see a bigger change. If we activate three inputs, this triggers this very large response, which is an action potential, which then would propagate along the axon and possibly drive firing in a downstream neuron. So in a very simple way, what this sort of experiment is showing is that this neuron is making a decision about whether or not to produce an output. If the drive is too weak, if it's below a particular threshold, then the neuron doesn't produce any output. So the downstream cell has no information at all about what signals the neuron received. But once that input crosses a particular threshold, this triggers an action potential. And then the downstream neuron knows that something happened in the upstream neuron. So this is a very simple sort of idea of a potentially very powerful way of producing computations in the brain. So I'm not going to say very much about neural codes. I think more will come up tomorrow and later in the week. But if we imagine that this action potential that propagates down the axon is the primary sort of code that neurons use to talk to each other, there are two very generic and sort of distinct ways in which this action potential can be used to represent information. So we can imagine firing rate codes where the frequency or the number of action potentials in a particular period of time can represent signals or information. Or we can imagine, and there's evidence for both of these sort of possibilities, a spiked timing code where it's not the frequency of action potential firing that represents information, but it's actually the time of action potential firing. And this is usually relative to some kind of a reference signal. So there's a lot of sort of oscillatory signals that one can record from neural circuits. And one idea is that these oscillations could be reference signals for timing codes. So here we imagine that maybe an action potential fired near the trough of this oscillation signifies A, whereas an action potential that fires near the peak signifies B, and one that fires very late and the cycle might signify C. So these are two different sort of types of code, but both that rely upon firing of action potentials. Okay, so how then do we think about, so generating action potentials is going to be important for neural computations. And we want some way of kind of making mathematical sort of models or representations of this process of generating action potentials. And we'd like to be able to sort of link this to the things we've heard about the sort of Allen brain out this data set, this enormous molecular complexity that brains have, but at the same time we'd like it to be as tractable as possible because there's a danger that things could just become incredibly complex and you could make models that were just difficult to really understand. So a very simple model which could capture many of these sort of elements that I've described is it's just what's called an integrating fire or sometimes of the peak model. And so the idea here is that a neuron is sort of represented as a capacitor and a resistor in series and synaptic input charges the capacitor and if the voltage difference between the sort of one side and the other side of the capacitor reaches some threshold, this would trigger a sort of firing of an action potential and then the membrane potential would reset. So this is one of the simplest sort of ways that one might sort of in a sort of mathematical sense represent what a neuron is doing now. This is potentially very cool. Are there any sorts of, from what you've already heard about any sorts of problems that you might or limitations that you might think this sort of very simple scheme might have for some problems. Some. Yes. Yeah. So that's very good. So possibly, so some neurons sort of don't just fire in sort of random ways but they have very sort of stereotypical patterns of action potential firing and this model certainly wouldn't produce that type of activity and that could be very important. Yeah, that's a big limitation. In terms of if we want to sort of map neuronal activity onto some of the sort of molecular diversity that Sasha and Angie have sort of referred to is this, how helpful would this be? Is this a sufficiently detailed or rich sort of way of representing a neuron? Okay, I'm sort of pushing towards that it isn't. So it's very simple. And if we think at a sort of molecular level this is now a sort of an evolutionary tree just of ion channels which we're going to talk more about and there are several hundred ion channels which produce things like action potentials and other electrical properties of neurons and it's clear at least to me that this very simple scheme although it's powerful for addressing some problems can't really kind of, it's very hard to integrate this sort of richness into this sort of scheme. So we need a sort of a more detailed way of sort of representing neuronal models. Okay, so what I'm going to do with the time is a couple of things. So first of all just to take a step back. So we want to build models that incorporate the electrical properties of these ion channels and we want to first of all just take a step back and actually to the basic physics of how ions work in solution and how ions move in solution. And just I think for many of you this will be already familiar but I think it's worth sort of revisiting is just the basic physical principles that determine how ions move because this is really the brain works and electrical signals work because of the movement of ions across membranes. So I think this is worth sort of revisiting. What we'll then move to is models of the opening and closing of ion channels and in particular class of models that were developed originally by Hodgkin and Huxley and used to explain at an ionic level how action potentials are generated. And then I'll talk very briefly about how these models can be used to think about things like synaptic integration and synaptic computation in more complex brain circuits. Then after the break aunt will talk about in more detail I think about how in neurons which have quite complex morphologies how we can kind of integrate this information and look at the effects of a neuron's morphology on computations that neurons might carry out. So that's okay. So we wanna think about how an ion might move in a solution and the key sort of thing to keep in mind is that ions move randomly and each ion's movement is independent of any other ions movement. And when we think about an ion and its important properties for neuronal signaling there are two types of what we might call force that act on an ion and determine where it will move. And these forces are important if we have ions in solution separated by some membrane, okay? So we wanna deal with this just in a very abstract way first of all and then we'll put it into the context of a real neural cell. So the first force arises and it's not a real force. It's a force that comes about just from the concentration differences between two ions on either side of a membrane. So if we imagine here that you have a high concentration of some ion on this side and a low concentration here and this is a question that I really want somebody to answer which direction is that if you have a few pores in the membrane which direction are the ions gonna move in? Yeah, they're gonna move from high to low, okay? So we can think of a driving force down this concentration gradient with ions moving from high concentration to low concentration. And this comes about simply because of the random movement of ions in solution, okay? And we can describe that with this equation. Second force is the electrical force. If we imagine now we have again two ions in solution this time their concentrations are identical but we impose an electric field across the membrane. So let's say this is a positively charged ion and this side of the membrane is at a positive voltage relative to this side. What direction will the ions move in then? If sorry, if the ion has a positive charge and this side of the membrane is also positive relative to that. Yeah, from which side to which side? Yeah, so the ions move from left to right. So the positively charged ion will move in the electric field to the negative side of the membrane, okay? This is simple physical principle. So again, this is described by a simple equation. So there's two types of driving force. And if we think now at the simple sort of cellular components of a neuron or most of the cell types we have the cell's membrane which is a lipid bilayer and ions can't cross lipid bilayers. So the lipid bilayer essentially is an insulator. So ions are unable to cross from one side of the bilayer to the other. But there are two types of protein in the bilayer that can enable ions to move. So the first is a pump. This is the sort of cartoon representation I use for a pump. And the second is an ion channel, okay? Now the pumps are important but often I've looked what the pumps do is move ions either into or out of the cell and set up concentration differences between the concentration of an ion inside and outside of a cell. So in a typical neuron, potassium inside a cell might be in the region of 130 to 150 millimela whereas potassium outside the neuron is much lower. And this concentration difference is established by pumps which use energy to transport the ions either appropriately into or out of the cell, okay? The ion channels on the other hand, they don't use energy directly. They don't actively move ions across the membrane like the pumps do but instead they provide pathways through which ions can diffuse according to these driving forces. So the electrical and the chemical driving forces. And what's really crucial to understand your own signalling is how these driving forces affect the movement of the ions. Okay, so the first key sort of parameter that we'll use in modeling is the membrane potential which we're going to define as the units will be volts or millivolts and as the difference in the electrical potential between the inside and the outside of the cell. So many cells will have, and all neurons will have a membrane potential which is negative. So the inside of the cell will be electrically negative compared with the outside of the cell. And what we want to do is first we'll understand how a membrane potential is established. So we'll imagine a cell which has, here it has a lipid bilayer and a high concentration of potassium inside and a low concentration of potassium outside. And this is just a thought experiment, okay? I want you to imagine that initially there are no ion channels at all in this cell membrane. So what might be, would there be a membrane potential necessarily between the inside and the outside of the cell if there are no ion channels present? If. As long as each anion is balanced by a cut ion there should be no potential difference between the inside and outside of the cell. So we could start with a membrane potential of zero, okay? So we can imagine there's no membrane potential difference across this non-conducting bilayer. And what we want to do is just open one ion channel and imagine what happens to the membrane potential when this ion channel opens. So I'm gonna draw this on the board and ask you to sort of help. Okay, so we're gonna have this is membrane potential which will start at zero and this is time. And at this point in time here we're gonna open this ion channel. So initially there's no electrical driving force because the membrane potential is zero but there is a concentration gradient. So there's a high potassium inside the cell and a low concentration of potassium outside the cell. So what's gonna happen when this single ion channel opens? Yep, so the ions are gonna go out because of the concentration difference. And so what will happen to the membrane potential is a potassium ion so they're positively charged what will happen to the membrane potential will hyperpolarize. Yeah, so it will move in a negative directional hyperpolarize. So what will happen then to the electrical driving force? If it hyperpolarizes then you have a potential difference between the inside and the outside of the cell so the inside becomes negative. Yeah, so okay, you know the answer already. So the electrical driving force increases because the inside of the cell becomes negative. So that's gonna, if you like, try and attract the electrical driving force to then be acting in this direction whereas the chemical driving force is acting in that direction. And as the membrane potential increases the electric driving force will increase until you reach some equilibrium and then you'll have a steady state of the value of the membrane potential, okay? And we call that the equilibrium potential if we have only ion channels that are permeable to one ion in the membrane then we would call that the equilibrium potential for that particular ion. And if we know the concentration of the ion inside and outside the cell then from this equation called the Nernst equation we wouldn't predict what the equilibrium potential for that ion would be, okay? So simply knowing the concentration of an ion inside and outside a cell enables us to predict what its equilibrium potential is, okay? The other important thing here is if we really did do this experiment we wouldn't need to move very many ions from the inside to the outside of the cell to produce this membrane potential equilibrium. So the amount of charge that moves is very small and really doesn't affect in most physiological situations the concentration of the ions inside and outside of the cell. So the charge movement is very small to produce physiological changes in membrane potential. So in a real, things are more complex because we have different types of ion channel which are permeable to different types of ion and because the concentrations of each ion are different in the inside and outside of the cell so whereas potassium has a high concentration inside a cell and a low concentration outside the cell giving it a negative equilibrium potential sodium ions have a high concentration outside the cell and a low concentration inside the cell giving them a positive equilibrium potential. Chloride ions differ at different stages of development in their concentration but typically their equilibrium potential is in the range of minus 60 to minus to your minus 90 millivolts, okay? So these are the main ion types which are involved in electrical signaling in most neurons, okay? And here's another equation, a famous equation which if we have now a neuron with more than one type of ion channel then they're all going to potentially influence the membrane potential of the cell. So if we have a situation with only one ion channel then the cell's actual membrane potential will be the same as the equilibrium potential for that ion channel. But if we have a situation where several different types of ion channel are open then they're all going to try and drive the membrane potential towards their own equilibrium potential. And so the actual membrane potential will be determined by the relative influence of each type of ion and that's described by this equation. Essentially, the important thing is that as the amount of conductance or that the permeability to a particular ion increases relative to that of other ions then the membrane potential moves closer to that ion's equilibrium potential. So in a typical neuron, in resting conditions there's a very low permeability to sodium ions but a very high permeability to potassium ions. And so the resting potential tends to be quite close to the potassium equilibrium potential but not usually exactly at the potassium equilibrium potential because other ion channels or ion types do also cross the membrane, okay? So a typical neuronal resting membrane potential might be minus 80 or minus 70 millivolts whereas the potassium equilibrium potential is typically minus 95 millivolts or so, okay? So we can sort of take this cartoon model and we can represent it as an electric circuit where you have a voltage on the outside of the cell and two parallel arms to the circuit. Here we have a capacitance which is equivalent to the non-conducting cell membrane. And here we have a resistor in series with a battery. The resistor we can think of as being equivalent to the ion channels. So a low resistance would be equivalent to having lots of ion channels in the membrane so current can easily flow. And the battery represents the driving force which comes from the equilibrium potential for that particular ion or the difference between the equilibrium potential and the cell's actual membrane potential. So if the membrane potential is a long way away from the equilibrium potential for an ion there will be a large electrical driving force. Okay, so we then have a simple sort of equation which can describe current flow. First of all through either arm of the cell first of all through either arm of the circuit so the current through the channels is the product of the conductance of the resistor times by the difference between the membrane potential and the resting potential. And the capacitive arm of the circuit is described by this equation so the capacitance times by the rate of change of the voltage. Okay, so that is a sort of pretty uninteresting circuit so all you can do with this circuit is kind of charge the capacitor up and down but there's not very much signalling that one can do with this circuit and it's not sufficient to explain the action potential. So to explain the action potential we need to start thinking about the ionic mechanisms that will move the membrane potential very quickly and the sort of classic sort of series of papers that gave us the first sort of accurate explanation of how the action potential works were published some 60 years ago by Hodgkin and Huxley and there's a number of key sort of observations but one is that the action potential isn't all or nothing electrical event so this is a recording of the membrane potential of a squid axon and where this arrow is a brief pulse of current or charge is being applied to the membrane and what you see here is responses to responses where the size of this current pulse has been increased so this is the smallest response and you see that the membrane potential charges and then slowly discharges and this is somewhat like the behave you would expect from the circuit that we've just seen but as the size of the current pulse has increased what you see first of all the duration of this sort of discharge first of all increases and then at this point here in action potential is triggered so this very large regenerative electrical response and as the amplitude is increased further the latency before this action potential is triggered becomes shorter and shorter and shorter okay so this kind of this shows us that all or nothing nature of the action potential and it also shows us that you have to reach some kind of a threshold in the input to in this case to an axon but also to a neuron before you trigger an action potential so what we want to know is how to explain this and how to make models that would sort of account for this and the major experimental method that Hodgkin and Huxley applied and that's still used today for investigating electrical signaling is the voltage clamp circuit so that in the traces you've just seen the neurons membrane potential is allowed to move freely in a physiological way with the voltage clamp the membrane potential across the cell the potential across the cells membrane is clamped and you can then record the current that passes through the membrane as you artificially change the voltage difference between the inside and outside of the membrane and this is one of Hodgkin and Huxley's first voltage clamp experiments so here what they do at time zero they make a step change in the voltage across the membrane of their preparation was a squid axon and they either apply a voltage change that would be depolarizing so that would move the membrane potential above what would be the threshold for action potential firing and that's shown here now Hodgkin and Huxley plotted their current anyone who's used to looking at modern electrophysiology traces Hodgkin and Huxley plotted their currents kind of upside down to how we do today but what they essentially saw is a fast current which would be an inward currents this is positive charge moving into the cell followed by a slower current which would be an outward currents this is positive charge leaving the cell and this is in response to a depolarizing current step if they applied a step of the same amplitude but in a hyperpolarizing direction they essentially saw nothing so the membrane potential of the cell has this very voltage dependent property so this fast followed by this slow current is conducted in response to a depolarizing step but there's virtually no current flow in response to a hyperpolarizing current step so there is some voltage dependent flow of current across the cells membrane and one of the things they did is to try and dissect the ionic basis for these voltage dependent currents and there weren't many pharmacological tools around at the time so they were restricted to things like replacing the sodium ions in seawater with choline which is larger and so any conduction through using sodium ions should no longer be present and what they find when they did this is that this fast inward current in choline seawater is abolished or is reversed so it now moves in the opposite direction but you still see this slow outward movement of positive charge which is unaffected by manipulating the sodium ions in the in the bathing solution for the for the axon and this is a very reversible effect this is something that you can wash on and wash off the choline seawater and the effect reverses so what they concluded from this and a number of other experiments is that this fast component of the current response to the change in membrane potential is mediated by sodium ions or by some conductance of sodium ions across the membrane whereas this slower component doesn't involve sodium ions at all so that they could separate out currents through carried by different ions and this led them to what's much closer to a modern picture of the sort of circuit diagram for a neuron where again we have the cells capacitance and we have these parallel arms of the circuit but now we have a separate arm for each ion so we have a driving force a battery for sodium separate one for potassium and a separate one for chloride and then a separate resistor or conductor representing the permeability of the membrane to each of these ions so the next challenge is to try to understand how so we know that these permeabilities must depend upon membrane voltage so if in their experiment if they move the membrane voltage in one direction no current flows at all if they move it in the other direction they see both a sodium and a potassium current and these currents have different kinetics so the next challenge was to come up with a mathematical description of these independent currents and the way they did that is to study current responses to many different changes in voltage so you can see here the there's a threshold for activation of this inward sodium and potassium current and then the amplitude of the current changes as they change the test voltage and what they're able to do then is to plot what we now would call a current voltage relationship for the fast inward current and for the slower outward current and so you can see they're very different so this is the current through the sodium channels this is the potassium current and they could also by separating the currents with this choline manipulation they could then look at the kinetics so this is now a fit of an exponential function to the potassium current and they could come up with descriptions of the um of the kinetics of these currents so here this is the potassium current this is looking for an equation that would fit this activation or deactivation of the current and and their model what they do is they represent the potassium current as the maximum value of the potassium current times by this gating variable which they call n and this is a variable which describes the activation of the current as a function of of membrane voltage so um the rate of change of n with time is described by this equation where these rate constants are shown here and all they have to do essentially is to derive these rate constants as a function of voltage and this would give them a description of the gating of the current they could do the same thing for sodium currents now they have two different gating particles or two different gating uh... numbers they have an activation and an inactivation particle we will skip through this because we don't have very much time um then meant that they had a model with this this electric circuit where each of these conductance values for sodium and potassium were dependent upon membrane potential and they had a set of equations that describe how the sodium conductance and the potassium conductance depends upon membrane potential and that was based upon their voltage clamp experiments so if their voltage clamp descriptions of these conductances that they could isolate if they were accurate then they would expect that using this equation and their descriptions of the voltage dependence of these conductances they would be able to explain the action potential this was the first sort of real simulation of an action potential uh... using experimentally derived voltage clamp data and this is their experimental data which we've already seen so here you see the action potential being triggered by a very brief current pulse and when they took their kinetic descriptions of sodium and potassium conductances that they'd figured out from their voltage clamp experiments and then plugged them back into this equation describing current flow across the membrane they found very pleasantly and this is really quite remarkable it's still a better fit than most models that we make today uh... of action potentials being initiated by these brief current steps so this really was very strong evidence that they'd sort of uh... they could account for action potential firing through voltage dependent changes and the permeability of these conductances what it also gives us and it's been tremendously influential as a framework for doing this not just for simple preparations like the squid axon but essentially the methods we use today for simulating action potential firing and computation in neurons are essentially the same as those that uh... hodgkin and hoaxley uh... developed so in their model what happens is that the brief current pulse depolarizes the membrane potential this leads to activation of the sodium current whose kinetics and voltage dependence they described the sodium current which is the fast current so it activates first is inward so positive charge flows into the cell and this gives you the fast up-shoot uh... action potential the potassium current which you remember activates more slowly but also on depolarization begins to kick in slightly later as the sodium current begins to inactivate and the potassium current causes positive charge to leave the cell so the membrane potential moves back in a hyper-polarizing direction and resets back towards the resting potential okay so that's a sort of sixty-year-ago picture of how one produces an action potential we now know a great deal more I want to highlight just a couple of sort of important properties of the ion channels that we now know immediate action potentials and other important electrical properties so first of all hodgkin, hoaxley and their experiments were recording very large ionic currents so currents that were several nanoamps in size and at the time the physical sort of basis for these currents was completely unknown so they speculated a little bit but nobody knew that ion channels existed hodgkin and hoaxley simply described these uh... as conductances or changes in permeability what was discovered by uh... when narenbert sapman using a technique called the patch clamp is if they recorded now instead of from a whole squid axon this is a recording from a a muscle fiber using what's called a patch pipette which enables one to record a very small region of membrane what they discovered is these very tiny events which turn out to be the opening and closing of just a small number of ion channels so these are electrical currents flowing across the membrane but what you see is that these currents are not sort of continuous in the way that the macroscopic currents that hodgkin and hoaxley recorded are, but instead they're step-like changes so you can see here i think probably two there's a sort of a closed level which is here and two different open levels so the underlying sort of physical basis for these currents are ion channels which essentially can either be an open or closed states so when hodgkin and hoaxley described their changes in permeability or changes in conductance as a function of voltage what they're actually describing is the changes in the probability that single ion channels could be in open or closed states as a function of voltage so if we study this at a at a sort of more detailed or higher resolution we see that these single ion channels open and close probabilistically so this might be clearer this is a simulation and this is a simulation of a sodium current so it's a response kind of like the hodgkin-hoaxley experiment from a a negative membrane potential to a more depolarized potential and in this simulation there are fifty ion channels in the patch of membrane and in red is the average response of all of the ion channels across many trials but because each individual ion channel gates in a probabilistic way if we have a small number of ion channels in the patch what this means is that from trial to trial the actual current can fluctuate really quite a lot although the average probability is very predictable for any single ion channel whether it's in an open or closed state at any particular point in time is essentially a stochastic sort of decision so this is a essentially channel gating is is a change in probability of a very stochastic process and this we'll see this afternoon can lead to sort of very noisy fluctuations in neuronal activity when we start looking at a sub-cellular level where only small numbers of ion channels might contribute to to a process so the other important discovery which I've already mentioned is that there are not just one sodium channel and one potassium channel and one chloride channel in the brain but in fact there are hundreds of different types of channel and they can be classified in molecular related families so some of the more important ones are a voltage dependent potassium channels which would be somewhat like the Hodgkin-Huxley channel potassium channels voltage dependent sodium channels which are a smaller family which would be like the Hodgkin-Huxley sodium channels and various other types of potassium channel which can set the resting membrane potential but then there are whole groups of other channels which don't contribute to the action potential but play other important roles in your own signaling and we'll talk about one of these the HCN channels very briefly in just a minute okay so the sort of final sort of thing that is how do we start to associate these sort of channel properties with with what neural circuits do in behaving animals so I want to show you sort of two pieces of evidence this is now moving to sort of modern work um that ion channels might not just play roles in producing action potentials and setting the resting membrane potential but they might also shape the response to synaptic inputs before action potentials are initiated so if you remember what the membrane potential of most neurons has to do is to depolarize and eventually trigger an action potential but there's a range of membrane potentials across which neurons respond to synaptic input but they don't necessarily produce an action potential and this produces an opportunity for some types of ion channel which can be modulated to sort of dynamically control synaptic responses and influence whether or not action potentials are actually generated and it's been a it's not always been obvious that this would be important and I want to show you sort of two pieces of evidence that it might be important um from a functional and from a behavioral perspective so the first piece of evidence comes from looking at the organization of a circuit so this is um some data from a lab in norway um from edvard and may maybrit moses lab and this is recordings in a behaving animal from a neuron in this brain region here called the enterinocortex and this is a recording from a neuron here and the black this is a this is an arena and the black lines of the path that an animal follows as it explores the arena and the red dots of where this neuron fires action potentials okay so what you can see is that this neuron is representing the animal's location in the arena and it's doing this with this really quite strikingly organized firing fields that you see this sort of triag triangular sort of organization of the sort of location at which the neuron fires action potentials this in itself is interesting what's really very interesting is this is a recording from another neuron in the same brain area but now you see it's a little bit further away from that red line so it's at a slightly more ventral location and it's also representing the animal's location and it also has these firing fields that are organized as triangles but now you see that the spacing between the firing fields is a little bit further apart okay so this at the sort of circuit level we think is probably one type of neuron so when Sasha spoke about neuron types last night this is probably one type of neuron both neurons are found in layer 2 and this one type of neuron is representing the same kind of information it's representing spatial information but it's doing it slightly differently there's a sort of topography of how these neurons are organized so there are high resolution cells up here and then what the Mosul lab found is as they recorded from neurons at progressively more ventral locations this resolution sort of drops you see lower resolution cells so this is interesting for many many different reasons but one sort of potentially interesting opportunity that comes from this observation is to establish whether there are cellular properties that might map onto this topography of what the neurons are doing in a behaving animal and one of those cellular properties of course is how a neuron responds to its synaptic inputs and so one might test this with experiments that are sort of not dissimilar from the methods that Hodgkin and Hexley use but using sort of more modern sort of tools so this is now a slice of brain that's been removed from the entorhinal cortex but kept alive and now with a technique called the patch clamp one can record voltage or current from these cells this is probably the same type of cell in layer 2 of the entorhinal cortex and then study how the cells respond to synaptic inputs and one thing we might expect is that if ion channels are shaping responses to synaptic input in a way that's behaviorally important then we might expect these neurons to respond slightly differently to synaptic input than these neurons would do and this is something that actually turns out to be true so if you take neurons that are found up here so these would be neurons with the closely spaced firing fields then they respond here to a train of synaptic input really without much summation so if they receive a burst of synaptic currents they really don't sum the responses very much whereas a neuron which is the same neuron type but found at this more ventral location so representing space at a lower resolution here the same train of synaptic input produces very strong summation of the synaptic potentials and this difference in how the neurons respond to synaptic inputs is explained by a difference in the density most likely of two different types of ion channel in the membrane of the neurons so these are in this family tree you saw before this will be a HCN channel and a K2P channel this doesn't really matter for our purposes but the important point is that it seems that neurons can tune very precisely how they respond to synaptic input by changing the density of the ion channels in the membrane and they can do this in a way that seems to map very precisely onto the type of information that they're representing during behavior so this is one way in which so these are with an electrical stimulus and to layer one which is where many the axons are found that project to to these neurons and the synaptic currents themselves don't differ at different locations it's simply the integration of the responses that that differs okay so that's one sort of piece of evidence that sort of ion channels are playing quite sort of sophisticated roles in control of synaptic inputs another piece of evidence that sort of Astrid sort of alluded to this approach before another sort of way to address this problem is to focus on particular ion channels and to remove them genetically and then to ask what happens to to behaviors or to circuit computations and because one's made a very specific manipulation of an ion channel this can provide quite strong evidence that they play roles in particular circuit functions so this is an iron child HCM which is very unusual because unlike the Hodgkin Huxley sodium and potassium channels or most other ion channels that you'll encounter it doesn't activate on depolarization but it actually activates when the membrane potential is hyperpolarized so this is a step from a sort of roundabout the threshold for action potential firing in a negative direction and this step actually causes this channel to sort of open and current to flow in an inward direction through this channel so you can if you plot the sort of probability that the channels are open as a function of membrane potential for most ion channels this this plot would be in this direction for this ion channel that goes in the opposite direction okay and this is pretty interesting if you want to start to figure out about functions of synaptic integration as opposed to action potential firing because this is an ion channel which definitely doesn't contribute to the action potential but it's it's it's steepest dependence on membrane potential is that membrane potentials which are close to a neurons typical resting potential so this is suggesting then that it might play very important roles in synaptic integration and if we manipulate this ion channel then we might have a tool where we're very specifically manipulating synaptic integration and we could study effects on behavior and so if this channel is removed it affects interesting behaviors such as hippocampal dependent learning and memory which become enhanced and it also affects synaptic plasticity so UPI introduced this kind of plot of synaptic potential and what actually this channel seems to do is to actually make it harder to induce plasticity and it doesn't do this by interfering with the biochemical signaling pathways that UPI described but it does this by affecting the integration of synaptic responses so it makes it harder for the membrane potential of the neuron to depolarize and that makes it harder to initiate the biochemical cascades that then lead to synaptic plasticity so this is one of the types of functions then that ion channels might have above and beyond simply playing roles in action potential firing okay so I'll sort of wrap up there for the first half of the morning so we sort of began with this sort of hopefully not it's hopefully not one or the other sort of computational versus molecular approaches but more we want to have ways to sort of unify the two and we sort of introduce this framework that comes from the Hodgkin-Huxley models where we can sort of explicitly represent ion channels in these equivalent electrical circuits and then use that to produce models of electrical signaling and of course it's possible to produce it's possible to sort of first of all experimentally determine the the kinetic and the voltage dependent properties of many different types of ion channel and these are just this is one particular neuron type that my lab's interested in and one of the sort of important things to see is that you have here for example two different types of sodium channel and if you plot in black their activation as a function of voltage you see that the these two different types of channel have slightly different dependencies on membrane potential and just these bands are to help you kind of calibrate from these plots to this plot of action potential firing and what you can see is that this sodium channel the persistent sodium channel has steep voltage dependence in this range of membrane potentials which include potentials when action potentials are not yet initiated so what this means is that in principle at least this channel might not be playing a major role in the action potential but instead might be modifying these synaptic responses in ways which could influence whether or not an action potential is triggered and this again you can see something similar for this type of a type potassium channel and this type of hcn ion channel which we saw a few slides ago and to this really a molecular level gives neurons many different ways in which they can control exactly how they respond to synaptic inputs and some of the work that Sasha showed us last night demonstrates that different neurons choose different combinations of these ion channels and one consequence of this is that this can then lead to them computing or modifying or integrating these sub-threshold synaptic responses in very different ways and this we think could be very important for how different types of neuron might carry out different types of computation so I'll leave it there and that's final slide so let's take a break for well let's see if there's any questions first of all no okay right let's take a break for 15 minutes and then we'll come back and we'll move from thinking just about ion channels to actually the distribution of ion channels in dendrites and the impact of a neurons morphology on sorts of computations that neurons might carry out so