 apologize for making you wait. Today we're going to talk about action potentials. On Monday we talked about the microscopic individual single channel basis of action potentials and of electrical signaling in the nervous system. Today we're going to talk about macroscopic events and if the gods are with us I will show you some simulations. The first point to make is that electricity is a language of the brain and so we need to understand electricity. I'm going to show you a movie. This movie is taken from the brain of a rat. There is a sharp electrode inside that cell recording voltage and you may remember that most often these days in isolated preparations we don't use sharp electrodes but we use patch electrodes. But in this case there are definite advantages to using sharp electrodes and in all cases of course when one measures a voltage and electrical potential one measures it between two points so we are looking at the difference between the voltage inside a neuron and the voltage outside the neuron. We're also going to remove the speaker and let's see if we can turn on the volume in the room if we can try that. My apologies is the time course that you might see on an old-fashioned oscilloscope or a modern artificially to sell the fire spikes because we are putting current through the electrode. We are putting current through the electrode as well and so decreasing its membrane potential from roughly that is to a more positive value all of those words mean the same and we are bringing the cell to a position back to firing on its own. These cells have what's called pacemaker activity they fire on their own this one does as well but in addition used to fire more frequently with also taking the signal from the cell and connected it up to an audio channel to a speaker and that's what we are hearing there we go so there are a few interesting aspects of this recording we'll play it again the spikes in this recording the action potentials are between 50 and 100 millivolts in amplitude but in fact in most cases they would overshoot 0 to plus 50 millivolts or so which is the nernst potential for sodium the key though is that the cell is encoding messages and sending it to other cells via synapses and is releasing transmitter now there are some very interesting aspects for instance there appears to be lots of deep structure where a cell actually becomes hyper polarized for a while and then depolarized as it is pacemaking and there are some ion channels that are responsible for that and also when the experimenter begins to add current the cell does not immediately respond with a graded higher frequency most do but this one does not and that's because of some other electrical characteristics of a channel that essentially put it into a no man's land between two extremes of membrane potential and it would take deep simulations of the various channels and their state to understand this but it has been done in what happens so this is an example of electrical signaling in a cell and the audio that you heard is a very common occurrence in a neuroscience lab people are always listening to the audio from an electrode always nodding when a cell responds more quickly or less quickly except that these days it's possible to have multi electrode arrays so you can hear signals from many cells at once have to be careful that the audio signal does not itself distort the experiment but once that's done it's fairly nice let's go to another example now in which a cell also from the thalamus is being exposed not simply never show off your kids your dog or your software this played just well let's look at this recording here we are so now we have a I'll go back to that it wasn't doing very well again we have the sharp electrode inside the cell we have we're recording the difference between the inside and the outside of the cell but here instead of applying current we are applying a neurotransmitter acetyl choline that's H and the cell seems to be responding to acetyl choline but again not in a simple fashion let's see if that happens now the experimenter adds the acetyl choline you can hear the spikes and then it stops now if you look carefully before the acetyl choline was added the action potentials which were being filmed from an old-fashioned oscilloscope whose screen glowed seemed to have a triangular base but during acetyl choline they were much sharper and this is part of the encoding properties of any neuron that spikes can indeed accompanied by sub threshold oscillations now what you don't see in these beginnings quite since that they're actually quite large the triangle part that you see is actually just the base let's try that once more you can just barely see the entire spike there on the screen so again cells respond chemically they respond first of all electrically they also respond chemically because chemistry is also a language of the brain we'll learn in detail that the artificially applied acetyl choline is acting on muscarinic acetyl choline receptor again changing the membrane potential and increasing the action potential frequency any questions about what we just saw and it's important in neuroscience so the question is whether the first initial spikes were induced the answer is no this was the cell pacemaking on its own why did it go flat when they put it in acetyl choline at the beginning this cell like the previous cell has a no man's land of membrane potential where it does not like to fire spikes it actually has two states and this has to do with its complement of ion channels in detail it's called a t-type calcium channel but the encoding properties of this neuron are fairly complex any other question okay so today's lecture does involve electrical circuits and so you should remove to renew your material from this one and you can also look in candel the textbook and appendix appendix a I'm going to plug the microphone back in I think you get better the recording on the video at least I hope so okay you can still hear me fine can you good so hero of the story today is very much the electrically excitable sodium channel and it's been only a couple of years now that we've actually had atomic scale structures of electrically excitable sodium channels although potassium channels have been known for now as crystal structures for about 20 years you'll remember that the electrically excitable sodium channel has four domains homology domains only one subunit but potassium channels have four distinct subunits that come together and look a whole lot like this and the key point for today absolutely is that an open channel looks acts electrically like a conductor now this is not perfect because the concentration of ions on the inside and the outside of the cell sodium ions differs there's more on the outside less on the inside so it's not a perfectly linear resistor you could say that it acts a bit like a diode and rectifies a little bit but on the whole we find it very convenient instead of talking about the physical chemistry of ions entering the pathway or going out to talk about the open channel as a conductor now this and so each open channel then is a conductor and furthermore because it's gated and can be either open or closed but not intermediate each of these little open channels has a switch associated with it when the switch is straight up then the channel is open when the switch is slanted then the channel is closed and the the reason that we use conductors rather than resistors is that as you learned in fizz one conductors add in parallel resistors don't there's this complex form resistors do add in series but we won't mention that again conductors and in parallel so each channel has associated with it its conductance its switch and it's got a little battery associated with it and that battery is the Nernst potential for the ion that's permeate through that channel so if all and so there is a macroscopic conductance which is simply the sum of all of the little single channel conductances and now we make the macroscopic conductance look like a rheostat potentiometer but we understand that it's actually just how many of these little switches are up or to the side at any point and then the battery associated with that macroscopic conductance is the battery for all of these little channels the sodium we usually use sodium in red and so the Nernst potential for sodium is plus 60 millivolts there are more sodium ions on the outside than on the inside and we derived that from first principles at the beginning of last week and there are mostly potassium ions on the inside so electrically it's very convenient to talk about this combination of phenomena physical chemistry down here ions going through electricity up here within equivalent circuit would anyone like me to use more words or different words to describe this but there's complications the complications are that there are several types of channels in the memory in particular not only are there sodium channels but there are also potassium channels and each potassium channel has its own conductance which may differ from the conductance from for the sodium channel has its own switch whether that potassium channel is open or closed and has its own battery which is the Nernst potential for the potassium channel and so we some all of the potassium channels as well in a macroscopic symbol like a potentiometer like a variable conductance when we call that conductance G the we typically use for the microscopic conductance is a little gamma and for the macroscopic conductance is a large G well we had to call them something so as you know conductances are usually called G's G equals 1 over R and so we have a G sodium which consists of a sum of all of the little gamma sodiums that are open at the time and a G potassium which equals the sum of all the potassium conductances that are open at any time in the membrane we have this green potassium conductance and this red sodium channel and most of the time here is a key all of the time since time immemorial in memorial these circuits obey Kirchhoff's law that is charges neither created nor destroyed that means that a current that flows inward through a sodium channel has to flow outward some other way and typically since there are potassium channels inside the cell and sodium channels outside the cell the simple the most likely event is that charge gets conserved by sodium ions flowing into the cell and potassium ions flowing out of the cell now the charge carriers change their identity sodium flowing in potassium flowing out the brain the cell needs to pump those back up again using transporters and splitting ATP in between action potentials but take my word for it we can serve charge any complications or questions okay so these principles variable resistors voltages Kirchhoff's law allow one to make an equivalent circuit now we take the entire cell and I think I probably will not talk about little gammas anymore we're only going to talk about large macroscopic G's that okay so we take now from Kirchhoff's law it is possible on the back of an envelope or on a sketch pad or however to deduce that the membrane potential will be dominated by the conductance which is largest at any time all this has to do with Kirchhoff's law and being sure that what flows into any of these junctions also flows out conservation of charge so what works out is that the membrane potential at any time is a weighted sum of each of the can of each of the Nernst potentials e k or chloride we haven't we haven't talked about chloride much well we did when we talked about the ivermectin channel on Monday after the Nobel Prize that's a chloride channel so if GK is largest then this first term and the bottom term term dominate if GNA is largest then this term dominates etc all right now that you see this little C here you remember we talked about the fact that the membrane has a very high electric field in its dielectric and is very which is very small that means that the membrane has a large capacitance and so as you know current through a capacitor is equal to the capacitance times the first derivative of the voltage so here for the moment we are talking about only steady state where dv by dt equals zero and so the current through the capacitor which is in parallel with the resistors is zero and that's one of the great things about the voltage clamp the voltage is clamped dv bed dt equals zero and then as instantaneously as the electronics will allow the voltage is stepped to another area to another place dv by dt becomes very large and the capacitive current become very large but so fast that it doesn't bother the experiment and then the voltage remains clamped at another membrane potential so that's why the voltage clamp is so useful now technically it's steady state not equilibrium because as we mentioned those ions are replacing each other and the extracellular solution need to be pumped back in again and the sodium potassium ATPase is working so if only one set of channels were open say the sodium potassium channel we would have equilibrium but with two of them fighting against each other everything begins to run down we need to eat and two-thirds of the ATP consumed in the brain is consumed by the sodium potassium ATPase which pumps us back up again and my friend Chris Miller is fond of saying that potassium channels are highly selective for potassium about a factor of a thousand to one and if they were not so highly selective for potassium if a little sodium leaked through them your brain would have to work much harder than it does and it would be much hotter than it is so thank goodness that those potassium channels are completely selective to potassium everybody with us so far any questions okay so at the resting potential only potassium channels are open EK dominates at the peak of the action potential as we'll see the GK doesn't don't close but there are many more sodium channels open a larger sodium conductance and it open they open to and they dominate and so during that peak of the action potential the flow currents are flowing into the sodium channels out of the potassium channels and there's lots and lots of ions going back and forth curcoughs law gets obeyed but those ions are flexing in and flexing out and so we're running down the potential the ion gradients and in between action potentials the sodium potassium pump needs to clean things up now this is a lot easier for a squid axon to do and we're going to be talking about the squid axon then it is for a little a small diameter cell in the brain we'll talk about that and then it rise we're going to see after the action potential more potassium channels open we get a little bit of a hyper polarization and we go even further toward the potassium equilibrium the potassium endurance potential all righty now we are going to simulate the nerve impulse and we're going to simulate the nerve impulse as though we were doing a macroscopic version of the microscopic simulations that I showed you on Monday same types of Markov probabilities now transformed in the macroscopic case into differential equations that change the G's the macroscopic G's and we're going to go to the same website which is pun show betzanyas website at the University of Chicago all right so we turn off David McCormick's website and we go to punch in you puncture of betzanyas website now and he just redid his website to avoid using Java it doesn't work very well so we're going to go back to the Java Java version all right so the first thing we're going to do is that we are going to use a squid axon a squid axon is enormous it is I think I showed you very briefly what a squid axon looks like here it is here's the squid its axon runs from the brain to the end of the mantle it gives these squid and because it's so large it conducts very rapidly invertebrates have not yet invented myelin so they have to use large axons to conduct rapidly and in one of your problem sets you're actually going to experimentally verify using simulations the dependence of conduction velocity on the diameter of the axon so the escape response of the squid is that the mantle contracts simultaneously squirts water out of the siphon squid escapes sometimes a little ink to confuse the predator and this happens rapidly enough so that the squid survives to do it again the next time in order to contract simultaneously all of the muscles in the mantle need to get stimulated at the same time and so the action potential needs to get to the end of the mantle as as quickly as it gets to the beginning of the mantle so that longest fibers need to conduct more rapidly and they have a larger diameter and they are the ones that neuro physiologists use in the 30s and 40s and 50s to get a good idea about the permeability of the membrane they are so large half a millimeter in diameter that you can actually stick a wire down the middle sticking a wire down the middle for passing current had the great advantage of being easy and microscopic and you could get large currents but also when you stick a wire down the middle then because the wires conductor the membrane potential doesn't vary doesn't propagate and so that's called the space clamped version and so we are going to look at we're going to reset the parameters their vimpose turn this guy off just to make sure we are in the right place and unfortunately we are not going to use the new version that runs without java can everybody instead we are going to use the older version which runs on when did this get grayed out you know the number of times that you rehearse this and it still doesn't work just in three hours rehearsing this non java work version worked very poorly for me it was a good sign how many devices ran java billions so membrane so we have our wire inside a squid axon we have we're measuring the voltage between the outside and the inside this particular case is when we give a little pulse of current and we get an action potential we're going to build up to that what we're going to do now is simply a lot simpler which is that we are going to show the passive properties of the membrane as there were as though there were no voltage gated channels and to do that we go to our control panel for the axon do this pharmacologically sodium channels or you would do it genetically with a knockout for the sodium channels i'm going to do it digitally do the same thing to the potassium channels okay now we no longer have the action potential we have something that looks a lot simpler and we are going to go to the pulses make the pulses first of all a bit delayed make them smaller very simple boring waveform here is the current it's just a little pulse of current that we are telling the axon to put in jonathan thanks for the hint that was good and um we are seeing this rc resistance capacitance depolarization the change in voltage doesn't occur instantaneously because the membrane has a capacitance which needs to be charged up but everything is linear and you can see that it's linear the easiest way to see that it's linear is to make this guy negative it goes the other way but is as large for a negative pulse as for a positive pulse so this is really boring the next thing we're going to do is to make things more lively by resetting the parameters is to we once again have a axon that fires an action potential just one and we note that here is the resting potential before we have put the current in here's a little blippeting through the wire it takes a little while but the axon finally does get to threshold and fires the spike which overshoots from zero and then after the spike it actually goes below its normal resting potential that is the after hyperpolarization or the overshoot or other terms and you'll remember that at this point only potassium channels are open at this point sodium channels are open in addition to the potassium channels and that makes the membrane potential go to ENA and at this point the sodium channels have again closed mostly through inactivation but also because they are voltage dependent and the membrane has gone back to zero and as an extra kick more potassium channels have opened and this has the selective advantage of rapidly terminating the action potential so that it's clean and fast so now we are going to do an experiment that fascinated physiologists for roughly the first year 50 years or so neuro physiology and that was to define threshold and so here we have a current pulse that is about 10 milliseconds long and let's see what happens when we make it only one millisecond long we don't get an action potential let's go to four milliseconds long we do get an action potential oh sorry that's 41 we don't get an action potential well let's go try five but we finally get an action potential let's go to 4.9 4.99 we'll try that etc so there is a well-defined well there is a reasonably well-defined threshold it depends on the amount of current we put through depends on lots of parameters of the axon but when we get a spike it's always the same size no matter how long we had to wait and that is because of the regenerative nature of the action potential so now how could a Markov process which depends only on the history of things turn into a regenerative event which is a sodium channel sodium spike that turns on and then off well you need to get deeply into the models for the sodium channel and it's in activation and the models for the potassium channel and its activation to understand it now one thing that we can do is that we can look at the refractory period and the way we look at the refractory period oh you know what we can plot we can plot in gk right so now what we're going to do is actually so the number of sodium and potassium channels open at any given time that's not really good that really doesn't show very well so let's try plotting the currents instead no that doesn't show either well we could actually see the conductance for gk and gna and remember that's the total number of channels open at any one point if we could expand things and i'm not sure how to do that let's turn off we would actually see this spatial evolution of the sodium channels opening and then closing and of the potassium channels opening and closing let's look at another interesting point which is the refractory period okay so the refractory period uh to do that the total time of 30 milliseconds two pulses and the third pulse is going to be rather strong it's going to be 30 microamps and the first one is going to be back to 10 and we are actually going to let's say 12 milliseconds here there's a bunch of things that we're plotting that we don't want to be able to plot yeah now actually seeing gna and inna but i'm going to turn those off so now we've given two stimuli and we have two because of this hyperpolarization that takes a while and because sodium channels get inactivated uh another action potential cannot follow instantaneously after the first so let's go to five milliseconds we don't see another action potential let's go to seven milliseconds now this is a violation of what i told you what i told you is that action potentials always have the same amplitude well obviously that's not always the case but it's pretty robust and uh let's go to 20 things are fine and so there's this period of time after which an action an axon can fire an action potential can't fire another one well if it could uh it would just go into spasms we call that the refractory period uh and so here's my screen so we have been to spatially homogeneous membrane the membrane action potential which can be simulated here by our wire and an axon but it's also pretty well approached by having a spherical cell with an electrode in the middle or it can also be approached by having a very small region of the membrane that would be a patch in a patch clamp and i showed you the passive properties of the membrane i turned off all the conductance and then i showed you threshold and we talked about the hyperpolarization caused by the potassium conductance and the refractory period now we are going to look at the frequency code so in order to do that we're going to go we won't be able to get through everything reset all the parameters and we will do the frequency code and and what we're going to discover is that this is an imperfect frequency encoder which is pretty interesting time 40 milliseconds which it is now and we are going to lengthen the pulse from one to 30 milliseconds we're going to go to 30 milliseconds why is the total time not 40 milliseconds you can see here is again a if we keep the pulse on all the time we do see a train of action potentials and in fact if we did this in a real cell the subsequent action potentials might be slightly smaller than the first but not so much smaller as simulated here and that's because the real cell has not just one type of sodium channel or one type of potassium channel but several types of potassium channels which really tailor the repetitive firing frequencies of those cells which need to fire now a squid axon does not need to fire repetitively or pacemaker on its own it does so by having synapses excited and each time there's a presynaptic potential each time there's a synapse firing it the action potential gets propagated and the mantle conducts and the mantle contracts but you remember the cells that I showed you at the beginning of the talk and David McCormick's lab at Yale were pacemaking on their own and had variable frequencies depending on what kind of input they were getting and so those cells have an additional complement of channels not simulated here that enabled them to fire repetitively as a function of how much current they're getting let's turn this down to five microamps and we don't see repeat that's 50 we see repetitive firing but at a lower frequency and if we go down to four get to threshold yeah we did we we again we get a lower frequency now this is a poor approximation of the encoding properties of a real axon of a real cell body not an axon but a cell body which is much more complex and there's one other point that I want to make and this is that I've told you about unpropagated action potentials and now we are going to look at the propagated action potential and let's do it x versus y let's try it at the voltage we're putting a little current through this now we no longer have a clamped axon we no longer have a wire down it but we're looking at regions of the axon that have sodium channels open those sodium channels then shock the next region of the axon producing a threshold there shock a neighboring region producing threshold there etc and so if we start this we put some current through we get a spike and it propagates with distance along the axon instead of plotting x versus t we can plot sorry voltage versus distance we can plot voltage versus time which is in some ways much more interesting so what we have here is a stimulating electrode a recording electrode right next to it one two and a half centimeters away and one five centimeters away from it and so what happens what happens then is that just reset the parameters again we'll try it again using jonathan lou's law we'll try versus v versus t closing the browser so so the question was it seemed to be a propagating backwards you know that's a great question but it is an illusion we're looking at it with and so if you think about it yes the beginning of the action potential is sharp at any one point but if you go back toward the beginning it looks like the end of the action potential and so that is a an impression that you get from doing it versus x it's much easier to do it versus t when you don't get that impression so here now we are stimulating at point at the point on the left and we are recording from three different positions we get this nice stimulating pulse and we get the action potential propagating two and a half centimeters and five centimeters let's start it again so in one of your problem sets you are actually going to run this simulation and you are going to vary the parameters of the axon and ask how the conduction velocity varies with those parameters to give you a very simple example we can use the temperature this squid axon was measured at six point three degrees centigrade at the end of the forties people had these vacuum tube electronics their electronics was working really hard these um processes were pretty fast and in order to make them measurable they cooled down the animal cooled down the axon and measured it as as cool as possible but we live at 37 degrees centigrade so let's compute this at 37 degrees centigrade pretend we're turtles it propagates much faster and these are built into the simulations is the temperature dependence of those transition rate constants the differential equations that i've been telling you about all of those rate constants get faster at higher temperatures so we think faster both because we're at higher temperatures than a squid and also because we have myelin which makes little jumps rather than propagating from one square micron of the membrane to the next uh let's see now let's go back voltage versus time uh we'll talk about this next part next time and uh we will also have a quiz next time so see you on Friday