Resting Potentials and Action Potentials

today we're going to continue our discussion about action potentials and wrestling potentials getting a little more detail the history of nerve action potentials and the way in which they are involved in the information encoding and propagation in the nervous system goes back more than 80 years ago with the development of modern-day electronic instrumentation techniques amplifiers and the like and these studies would provide really fundamental insights were done on a seemingly unpromising lookin

g species anybody recognize this animal so horseshoe crab so if you spent any time on the east coast of the United States this animal has been around for a 100 million years it's been called a living fossil it was inhabited earth before the dinosaurs so it's a very primitive creature but nevertheless this primitive creature like will and like all animals have nerve cells and resting potentials and action potentials and what these investigators did 80 years ago was to place electrodes on the surf

ace of the nerve these are so-called extracellular recording techniques and this is just one example of many different types of extracellular so-called extracellular recording techniques because we can put electrodes on the surface of an excitable membrane and measure reflections of the potential changes that are taking place across the membrane anybody tell me the names of some other extracellular recording techniques that are heavily utilized in medicine EKG right put electrodes or the chest a

nd you can measure the electrical activity to heart I'll give you a hint they all start with E and they all end in G EEG put electrodes on the scalp and you measure brain electrical activity EMG put electrodes on the muscle you measure electrical activity muscle it's three it's more than three what if I were to put two electrodes right here Yoji electro ocula gram we're if I were to put electrodes on the eyeball itself electroretinogram electro goes that ii ii ii i G maybe that's the good one el

ectro right never electroretinogram so you'll hear about these throughout your careers but it's all basically the same phenomenology you put electrodes on the surface of the structure that you're interested in there's electrical activity of some sort underneath and these electrodes pick it up so here's what happened when you put these electrodes on the surface of the optic nerve and you connect these electrodes through some recording device and this recording device will also be connected to a s

peaker so we can actually hear what happens so if you make a light very dim at the case here so this have different buttons here you can make a dim light and a brighter light depending upon where you put your cursor and you can do this on the online so online syllabus the dim light you don't see anything on a recording device but if you make that light a little now all of a sudden you're like and you record the events on the recording device these little blip or spike like events and what's inte

resting here is that when you turn the light on so it's a little bit brighter and brighter but the thing is that the frequency another of the type life event changes as a function of the intensity of the elimination these insights are applicable not just to how the nerve system of abortion CREB works but how our nervous system works as well there's three principles that come from these recordings and I don't even need to Sam I think you're no more ready so what's principle number one what can yo

u say about these nerve impulses or action potentials one thing is about the timing note this is a one second duration stimulus you can say that these events are very brief right this is a one second time scale here so these events are very brief you can't tell how brief they are but you already know they're about a millisecond or so in duration right second you can see as these investigators did that these action potentials or impulses are elicited in an all-or-nothing fashion either you have a

n impulse or you don't have an impulse you never see half an impulse right so they're elicited in an all-or-nothing fashion and as you also know they are propagated in at all in nothing fashion so an action potential listed here at the eye is going to be propagated to the central nervous system in uncollected fashion and then the third principle that emerge from these studies is the principle of frequency coding in the nervous system the greater the intensity of the stimulus here a visual stimul

us the greater is the frequency the firing of [Music] okay so we have to move from these extracellular recordings after that very informative but at the same time they're relatively crude to the intracellular recordings I introduced you to the technique on Monday here is an idealized nerve cell you learned about some of the features of this reductive way Marty you're going to learn more later on you have this micro electrode which is no more than a thin piece of glass tubing stretch on cookie fi

lled with a conducting solution and when it's in the extracellular environment the potential that's recorded is 0 because the extracellular environment is ISO potential so let's go freeport 0 you take the electrode and you penetrate the cell so that the inside tip of the electrode is now inside the cell and now there's this sharp reflection on the recording device and this is the so-called resting potential its characteristic of all cells in the body nerve cells have as well as all other cells b

ut we'll seen ourselves as special as our other excitable membranes like muscle cells new muscle skeletal muscle and cardiac muscle cells in that they're capable of changing their resting potential nerve cells for the process of encoding and transmitting information and in muscle cells through the process of producing a contraction now how do you actually trigger an action potential we talked about that in the last lecture you can impale a neuron with another electrode and artificially stimulate

d we'll see just next week that's the physiological way that nerve cells are stimulated or through synapses excitatory synaptic connections we've already heard a little bit about them we'll say much more so here is a showing a strategy for stimulating a neuron it will give a show two examples with a stimulating electrode the stimulating electrode is going to be connected to a battery and the battery in turn can be connected to the circuit in two different ways course when you put a battery into

a device you can put the battery in the device so just a negative pole is going one way or you can connect it so that the positive pole is going one way right you know they've got a little plus and a minus and you got to make sure you get it right for the circuit to work we got to get it right in a nerve cell as well when you get two different kinds of responses depending upon whether you puts a battery this way or you put the battery this way so the pole the battery is connected as shown here a

nd by the way just the terminology for batteries is the big plate is always the positive plate it's not particularly important to you you know that already so what do you think would happen if we record the membrane potential which is initially going to be minus 60 millivolts we impale the other the other electrode into the cell and we connect it to a battery what's going to happen when we close the switch we're going to make VF because the pole of the battery here is oriented such that when the

switch is closed the inside of the cell is going to be more negative than it is and depending upon the size of the battery now we have different sized batteries right you have 1.5 volt battery you have a 9-volt battery you have a 12-volt battery so by different sized batteries are going to make the inside of the cell you know progressively more negative so what you going to see in this little animation is that the switch is going to be repeatedly closed and opened and each time it happens the b

attery is going to be replaced with a larger battery right so here's the animation see the different batteries that'll even bigger so the different sized batteries you close the switch are making the inside of the cell progressively more negative now anytime you make the inside of the cell more negative that potential is called a hyper-polarization right the membrane is more polarized than it normally is hyper right membranes hyperpolarize you need to know a little bit about this nomenclature in

order to follow it we're going to be saying throughout the rest of the course by the way is back the way Maier indicated this material is all cumulative so if you don't understand and remember what I'm talking about today you're not going to understand virtually anything that's talked about next week so you have to stay up on the material okay so this is with the negative pole of battery now let's flip it around put a positive pole of the battery connected to the switch and let's just start dur

ing larger right same thing but we get very different results okay the inside the cell becomes more positive as you expect but then you get to a certain potential where something totally you get to that potential the threshold where you get this all-or-nothing signal and this is the nerve action potential or impulse there's an interesting difference between this stimulus these the size of these pulses by the way are representative of the size of the battery so this stimulus was sufficient to rea

ch threshold and fire an action potential and this stimulus which was a greater intensity also fired an action potential but note the fact that despite the fact that the stimulus is larger here than it is here the action potential is the same amplitude so this again just a restatement of this all-or-nothing law of the action potential either you have an action potential or you don't and if you use a greater intensity stimulus to get the action potential you still have an action potential all rig

ht I like to think of an action potential in terms of a thermal analogue an action potential is kind of like the ignition of gunpowder so if you have a flame and you put it to a fuse a gunpowder fuse you need a certain intensity of that flame in order to ignite the Gunpowder right if you use a more intense flame you know instead of using a match using acetylene torch whose isn't going to burn any faster or brighter than when you light it with a match right so there's a certain threshold for keep

necessary to ignite gunpowder and there's a certain threshold of depolarization necessary to initiate an action potential now there's some nomenclature that you need to know about so note interestingly that the action potential when you have an action potential the membrane potential changes from its resting potential of about minus 60 to a new value of about plus 55 millivolts that's called the peak for obvious reasons right so the membrane potential almost totally reverses in its polarity fro

m being highly negative to being positive then there's a region of the action potential let's call the overshoot so here's the zero millivolt so the region of the action potential between the zero millivolt level and its it's called the overshoot that's the shaded region then we also can characterize the up stroke phase of the action potential in the down stroke phase so this is the depolarizing phase of the action potential also called the upstroke and this is the repolarizing phase of the acti

on potential sometimes called the down stroke right goal so you're going to be hearing this terminology and you just need to know what it means now there's also a very interesting phenomenon that occurs with action potentials and that is when the stimulus is terminated when the action potential finishes its repolarizing phase it just doesn't return back to the resting potential there's a period of time where the membrane potential is actually more negative than the resting potential and that is

called the undershoot for obvious reasons and it's also called the hyperpolarizing after potential so it's a potential it's really not after the action potential it's part of the action potential but it's a potential where the membrane potential is more negative more it's hyperpolarizing compared to the resting potential so here now the duration of the stimulus was relatively brief the stimulus is 5 milliseconds or less there was only time for an only enough time for a single action potential to

be triggered but as I showed you in the previous lecture on Monday if you use a longer duration stimulus so as shown here I think this is a 1 second stimulus notes I think it's less but it's longer than one millisecond we're going to use different batteries here and what this animation is just going to recapitulate is the frequency photo so here's a small battery it produces a depolarization but that depolarization is sub-threshold you use a larger battery and then the stimulus produces a depol

arization physics threshold but only one action potential to go through so this this stimulus duration here is what about 5 10 to 20 milliseconds a larger battery produces greater depolarization a greater great a number of actions acceptance so this is a recapitulation of the frequency coding business in the nervous system action potentials are all or nothing the action potential here the same intensity of the action potential here the action potential here is the same amplitude is here but what

differs as a function of stimulus intensity is the number or frequency of action potentials okay this is just this little summary of what we said so far on lecture physics in a handout but pieces of it are there before you record the membrane potential you can inject a cell with a current either depolarizing or hyperpolarizing current the magnitude of the hyperpolarization is proportional to the stimulus and for depolarizing stimuli it's proportional to a certain range until you reach a thresho

ld when you elicit in a willing an action potential you have the overshoot you have the hyperpolarizing after potential or undershoot if the stimulus is brief you can get just a single action potential if you use a longer duration stimulus now you get multiple action potentials the frequency of which is dependent upon the intensity of the stimulus okay so now we want to find out what accounts for the initiation of these action potentials what accounts for the repolarization of the action potenti

al and what accounts for the hyperpolarizing after potential so in order to answer that question we need to know a little bit more about the resting potential so in order to understand the ionic mechanisms of the action potential you need to know about the ionic mechanisms was a resting potential now that has a long history it goes back to more than hundred years ago where the first satisfactory hypothesis for the generation of the resting potential was put forward by an early physiologist by th

e name of Julius Bernstein working in Germany and Bernstein knew from analyses that the interior of cells nerve cells but all cells had high concentrations of potassium there was unequal distribution of ions between the inside and outside and in particular there was a high concentration of potassium inside the cells compared the outside and he also knew based on chemical analyses that cell membranes seemed to be highly permeable to potassium but not so permeable to other ions and finally he knew

of the work of the physical chemist Nernst and Nernst had developed a mathematical equation called the Nernst equilibrium potential equation that theoretically predicted a potential that would be generated of course a membrane if the membrane was variable to a single island so based on that what Bernstein suggested was that you could predict the membrane potential of a cell based on the Nernst potential let's just say have a membrane and this is the outside and this is the inside and what Berns

tein knew was that the membrane had a high concentration of potassium inside the cell and there was a relatively low concentration of potassium outside the cell so if this membrane is permeable to potassium what is potassium going to do what if you were potassium inside the cell what would you want to do want to go out it's crowded don't like it in there you want to get out and go to a place where it's not so crowded so potassium is going to try to would like to move just on the principle diffus

ion from its region of high concentration to a region of low concentration so what will happen if potassium diffuses is that there will be a distribution of charge established on the outside of the membrane and if potassium is the only ion that can move it's going to leave behind negative charge and so there will be a charge distribution that will be established across the membrane with the inside surface of the membrane being negative and the outside surface being positive so what will that pot

ential be well here's where you get into the equilibrium they quote the Nernst equilibrium potential equation where is the equilibrium I don't see any equilibrium here you would think that potassium is just going to go from outside in high concentration here to there and ultimately the concentration the outside of the inside would be the same and there'd be no potential right so where's the equilibrium come from because of the gradient the high concentration of potassium here is going to want to

move out side it's going to leave negative charge behind but that negative charge is going to try to pull back the positive charge that's leaving right because unlike charges attract each other so these negative guys in here are going to say hey hold it a second potassium you can't leave I'm going to attach to you I'm going to pull you back so there's going to be this force that tends to move the potassium out of the cell because based on the concentration gradient but there'll be an equal and

opposite force an electrical force that tends to pull the potassium back and the equilibrium is established when this force is equal to this force and not said there's a potential it's going to be generated and for potassium it's going to be equal to 60 times the log of the outside potassium concentration divided by the inside potassium concentration and this gives you an answer in millivolts so if you know what the concentration is outside and you know what the concentration is inside you can g

et out your calculator and calculate exactly what that equilibrium potential will be that's pretty neat right so what Bernstein said was hey I think because we have a high concentration of potassium inside we have a low concentration of potassium outside the membrane is permeable to potassium so I'm going to say that the membrane potential is equal I'm going to put a question mark here equal to the potassium equilibrium potential so that's the hypothesis of Bernstein but he couldn't test it beca

use he didn't have electrode recording techniques so but we'd have them now so how could you test the Bernstein hypothesis so what was done was that the membrane potential was recorded and the potassium concentration in the extracellular medium was systematically altered and each one of these dots and enters an experimental measurement you can do this experiment can come up to my lab and do this experiment this afternoon if you to this we can have ourselves and we can change the potassium concen

tration it's really easy it just make up a whole bunch of different concentrations of potassium and then you stick the electrode in the cell and you measure the potential so up here by the way this is a semi-log plot what's shown here also is the equation for the Nernst equilibrium potential for potassium sixty times the log of the outside concentration divided by the inside concentration which was 140 which we assumed in this experiment is stable all right so what you can do is you can use your

calculator and make a plot of this equation if you put in different values here you get this nice green line right now here's the data points and what you see is there's a remarkable correspondence between how the membrane potential changes with changing potassium concentration and what you predict by the Nernst equation so this then gives strong experimental support fact the membrane potential is due to the fact that there's this unequal distribution of potassium ions membres permeable to pota

ssium and that accounts for the resting potential so by the way if you put the electrode in the cell and you recorded minus 60 millivolts that's necessary but why isn't it sufficient because it could be that the resting potential is due to the equilibrium potential to some other ion maybe hydrogen ions have an equilibrium potential of minus 60 millivolts maybe calcium ions have an equilibrium potential of minus 60 so just because you get minus 60 and that's the value for the equilibrium potentia

l of potassium it's not sufficient you need to change the potassium concentrations to see if it changes as predicted okay is that the end of the story if it is we could we could stop and finish the lecture it's not the end of the story what's what why not you're shaking your head you don't like it I failed to account for sodium okay how do you know about sodium you see any sodium here there's a cyst he says there's a systematic difference well I think this looks pretty damn good don't you not we

're not on the left yeah okay so there this looks great but when the potassium concentration starts getting lower you start to see deviations from what you predicted that you would get and actually what you do get and what you see is that the membrane potential is more depolarized than you would expect to have from a membrane which is exclusively permeable to potassium so this tells you that you need more than two points because if you just look two points right here you would be fooled into thi

nking that this is you proved it but if you look at these points down here you start to see there's something wrong with this hypothesis it doesn't completely work so how do we explain the deviation between the Nernst equation and Bernstein's beautiful hypothesis and the reality well that's because we didn't account for sodium so this is the distribution for potassium what's the distribution for sodium like opposite so sodium is in high concentration outside the cell and relatively low concentra

tion inside the cell so if you were sodium if you were sodium what would you want to do you want to go in okay let's assume so sodium is in high concentration here it's a positively charged ion you want to go in for two reasons you'd want to go in because there's a concentration gradient but you also want to go in because the inside of the cell is negative and you want to find a partner who is negative which you're positive assume that there is some small permeability to sodium as a result becau

se of the concentration gradient sodium ions will tend to go inside the cell and make the inside of the cell positive with respect to the outside so the because if you assume some permeability to sodium not a lot that will tend to subtract from the negative polarity produced by the diffusion of peski now we have a membrane that's permeable to more than one ion so the Nernst equation can no longer be used to predict the membrane potential we have to introduce a new equation called the Goldman Hod

gkin Katz equation also called the ghk equation actually Goldman was a medical student at Columbia University when he developed this equation so the ghk equation says that a potential across a membrane is permeable to two ions in this case we're going to talk about sodium and potassium you can extrapolate this to include lots of other ions but we're just going to talk about the form that counts for sodium and potassium because they are the ones that have the permeability that we're interested in

it's got a 60 in it it's got a log in it it's got outside potassium concentration it's got the inside potassium concentration so it looks kind of similar so far right then it has this term alpha I'll say what alpha is in a moment the outside sodium concentration plus alpha times the inside sodium concentration and that gives an answer in millivolts that's the ghk equation alpha is equal to the ratio of the sodium permeability divided by the potassium permeability so this looks complicated but i

t's really not and it can be simplified you know if you take some extreme cases so take the case where the sodium permeability is zero that means you have a membrane essentially that's only permeable to potassium the sodium permeability is zero what's alpha and what is the Goldman Hodgkin Katz equation revert to the Nernst equation and it better write it better do that take the other extreme let's just say the sodium permeability is very high relative to the potassium permeability what is the Go

ldman Hodgkin Katz equation revert to the Nernst equilibrium potential for sodium right so on one extreme of the golden Hodgkin test equation is the Nernst equation for potassium and the other extremists of Nernst equation sodium and you can see that you get any potential in-between simply by adjusting the relative permeability of these two ions so we need to test this the next slide just simply shows the same experiment with now the same data points but now showing a plot of both the Nernst equ

ation and the Goldman Hodgkin Katz equation here so the outside potassium concentration that's what's varied and here's the equation here's the equation for the nurse and you see now you get a much better fit still not perfect but with an experimental variability it's pretty darn good and it reflects the general consensus that the resting potential is due to the combined permeability of potassium and sodium with the potassium permeability being much much greater than the sodium permeability and

in fact what is the ratio of those two certain probabilities so what you see here is that this fit was obtained by this value here 0.01 what is a 0.01 the 0.01 is our friend the ratio of the sodium potassium permeability so if alpha is 0.01 what does that tell you about the relative contribution of the sodium permeability system and the potassium permeability system potassium is much much more in fact you can say exactly how much more it is it's a hundred times more so the potassium permeability

is a hundred times greater than the sodium permanently don't need to know exactly what the numbers are but you need to know about the ratios right okay so that's the story of the resting potential now we know how the resting potential works we can move on to a discussion of the action potential by the way in your electronic online syllabus there is something called the membrane potential laboratory and what this membrane potential laboratory does let me just do something here so here is a plot

of the Nernst equation for potassium so this blue line here is the Goldman Hodgkin cat's equation and what this program allows you to do is put in different values of the extracellular concentration of potassium and different values of alpha and make a plot and see how it affects the predicted membrane potential so you can use these laboratories to sort of test your understanding okay so what we're going to do then next time we meet is talk about the ionic mechanisms of the action potential okay

let's see you this [Applause] you