Understanding Animal Nervous Systems

Hi everyone, we have been talking about how animals expend their energy, how they get their food, and how they interact with the environment with regards to temperature. We're going to move on now to looking inside of animals and looking at the various systems that allow them to run. One of the things that we've seen with animals is that they tend to be very active and reactive to their environments. The nature of being heterotrophic means that they've got to go out and acquire and eat their food. Their food might be in different places at different times. They don't want to be food. So they're very active. And it is a benefit to be able to react to changes in the environment and act very, very quickly. And the system that animals have to do this, or most animals have, is the nervous system. The nervous system is a signaling system that... essentially sends signals from cell to cell and ultimately to an animal's muscles to allow it to behave. It's similar to the endocrine system, which is another signaling system we have in which signals are sent into the bloodstream and then activate various organs around the body. The nervous system does the same thing. It releases chemicals as messengers that activate receptors and tell cells to do things. The nervous system tends to be very very fast and very very specific in terms of where its targets are whereas the endocrine system is slower it relies on slow blood stream and it has sort of effects throughout the body whereas a single neuron has a response just in a few muscle cells ultimately. things that we'll see over the course of looking at the nervous system is that signals are transmitted within a cell, within a neuron, electrically. So we have a change in electrical signaling inside the cell, and we'll go through all of the mechanisms by which that happens. So inside a cell, signals travel electrically, and then typically, but not always, between cells, signals travel electrically. the transmission of information is chemical in nature and so the neuron will release chemicals onto another cell to signal that something interesting should happen. The stars of the show are the cells called neurons. We'll spend a little bit of time here just looking at sort of the anatomy of an individual neuron. Neurons have an enlarged area that houses the major organelles and the nucleus that we call the soma, which means the body. And it has a lot of things that stick out of the soma. And there are different types of neurons that all look a little bit different, but the general features are the same. A soma will have typically lots of branches that come off at what we call the receiving end. that kind of look like branches on a tree. We call those ones dendrites. This is the receiving end of a neuron. It's where input comes into a neuron. And those dendrites can be really, really branched, and there are usually lots and lots of them. The output side of a neuron has a single branch, a single output cable that we call the axon. And something interesting happens here electrically. The axon starts right where the axon joins the soma at what we call the axon hillock. It means little hill. That kind of looks like a little hill. So the axon is the output of a neuron. There's one axon that comes out of the soma. That axon may branch. A lot of axons branch many, many times. But there's only one typically that comes right out of the soma. Where one neuron meets another, it's for communication. we call a synapse. A synapse is a structure that sort of includes the end of one axon, which we call the axon terminal here, and then the dendrite or sometimes even the soma of the target cell. That whole structure we sometimes call the synapse. Sometimes we just call the synapse the space between the neurons, but usually the word synapse means two cells but just one small tiny part of each of the two cells. It's kind of a joining of the two neurons. They don't actually come in contact with each other. It was a decades-long fairly bitter argument between scientists in the late 1800s about whether neurons were individual separate cells or whether they were all sort of interconnected like a fungus. It turns out that they are all individual cells. Now the basic function of the nervous system, and I think it's always useful to remember this, is to allow an animal to contract its muscles. at the appropriate time and in the appropriate way, depending on what's going on in the environment. Right, that is literally what the nervous system is. The nervous system is ultimately for contracting muscles. It is ultimately for allowing an animal to behave. So the overall output of the nervous system goes through what we call motor neurons. These are neurons that are attached to your muscle fibers. It's kind of the end point of the nervous system. Basically, the whole point of an animal having a nervous system is to control muscles. Mostly those are skeletal muscles that allow us to move around. We do actually have muscles that control our digestive system and other smooth muscles, but we'll worry about those later. So the output of the nervous system goes through these motor neurons. Now, just sort of contracting our muscles randomly isn't going to help us. We need to know what's going on in the environment. And for that, we have sensory neurons. These are neurons that are bringing in... information from the environment, from sight, from sound, from taste, and other types of senses. And so basically the flow of information in our nervous system is typically sensory input comes in and motor output goes out. And this can be very, very simple. You can think of like a reflex. If I put my hand on a hot stove, I'm going to feel pain. That pain is going to be sent to my spinal cord. where almost immediately it's going to be sent to a motor neuron to cause me to react and withdraw my arm. And there's not a lot of sort of thinking that goes on with that. However, of course, not all behavior is so reflexive and so simple. If an animal wants to be able to behave flexibly, it needs to have some kind of set of neurons that go between the sensory neurons and the motor neurons, right? Otherwise, if the sensory neuron always activated the motor neuron, every time that sensory neuron was activated the motor neuron would be activated it'd be a very sort of rigid robotic kind of animal that you have and so what we have are what we call interneurons that sort of live between the sensory neurons and the motor neurons that allow for information to be spread out to be branched out to to go to different places to be remembered your brain in its entirety is in this definition of the word I'm using it interneuron There are other definitions where it's not all inter neurons, but your brain does not have neurons connected to muscle fibers and your brain does not have neurons that are directly attached to the sensory neurons. Since this is biology, there's always minor exceptions to those things, but we'll not talk about the retina right now. Really your brain is about allowing different kinds of information to go to different places to allow you to make your decisions more flexibly rather than reflexively. Okay, here's just an example of a really, really straightforward neuronal interaction. This cockroach here has these little things at the back of its body called circle organs that have little hairs on them. And when the wind blows, those hairs cause this red neuron, the sensory neuron, to change its voltage. It is activated in response to the wind. So if a predator is sneaking up on it, and it feels the wind of this predator, those hairs are going to be activated. And this red neuron is going to release chemicals onto this blue neuron, this what we call the giant interneuron. That giant interneuron is going to activate this motor neuron, this purple one, which is then going to activate the muscles and allow this thing to escape. And so we can see kind of over here, if you puff air on this animal's rear end, the sensory neuron begins responding immediately. The interneuron responds with some delay. The motor neuron responds a little bit after that, and this thing is responding less than 50 milliseconds. after the stimulus. Just for an example, a decently fast human reaction time is around 200 milliseconds way out here. This animal is going really, really fast in response to this stimulus. Okay, so that's just kind of an overview of what the nervous system does and a really simple example of what we call a reflex arc. Just a really simple example of taking sensory information. and then transferring it over to the motor system so that the animal can behave. What we're going to do now is talk about the system as a whole. I'm going to give you just an overview of how the nervous system works, how neurons communicate with each other, and then over the next few days we'll go into all of the details of how this works. But I think it's worthwhile to see the whole thing all at once before getting into the details. That way you can kind of have a sense for how everything fits together. So we're just going to be in the brain and we're just going to talk about one neuron in the brain talking to another neuron in the brain, which will probably talk to another neuron in the brain. Most of your neurons are just interneurons talking amongst themselves. We'll talk about sensory neurons and motor neurons when we talk about the sensory system and the motor system in later weeks. So we can kind of start anywhere, but let's start with a neuron receiving input. from another neuron, right? So one neuron is going to talk to another and it's going to send some kind of signal to it. Remember the nervous system is a signaling system. Okay, the input to this neuron that we're talking about causes a transient and decaying voltage change in the dendrites. So what does that mean? Transient means it doesn't last very long and decaying means that this voltage change doesn't last very long. We will, after all of this is done, spend a little bit more time defining what voltage change means. But voltage change just means a change in how much charge, how much electric charge there is. This here is an example of this change in voltage. The voltage inside the cell, when it's not being signaled, is usually around minus 70 millivolts or something. We'll talk about all this later. And when the input comes in, right, here's a neuron who's activating by squirting chemicals on the cell, the target neuron, you end up with an increase in voltage that goes up, then it goes down, and that voltage spreads out along the dendrites. So if it came in up here, it's going to travel down the dendrite and through the soma until it gets to the axon hillock. And so those changes in voltage... they're typically in the positive direction, but not always, are going to travel along the length of the axon, and interestingly, they decay as they go. And what we mean by decay is that they get smaller. So at the point of its source, it's a pretty high change in voltage, but as we measure it over here in the soma, it's much lower, and by the time it gets to the axon hillock, it is... probably pretty, pretty small. So it decays as it travels and then it ends up at the axon helix. So that's what one neuron does to another. It makes it change its voltage and that voltage then sort of diffuses throughout the target cell. Now a neuron typically has lots of inputs coming in all the time, right? This thing, this neuron has lots of dendrites, it has lots of other neurons that are trying to tell it things. And so here's a neuron called A1 that's coming in, another one called A2. These are all individual neurons that form connections, synapses with this target neuron. And so if they come in at the same time, if input A1, which causes this transient increase in voltage, comes in and then A2 comes in right after it, both of those changes are going to kind of funnel down towards the axon hillock and and come in at near the same time. And what happens is if they come in close enough, they add together, shown down here. We call that summation. And so these inputs get added together. And if two positive inputs come in, you can get a bigger one. If a positive one and a negative one comes in, they can kind of subtract from each other. But basically, inputs coming in throughout the net of dendrites and even on the soma itself are all coming in together. And they all funnel into the axon hillock where they are sort of added together in real time. Now, something changes at the axon hillock. There are changes in the cell membrane that allow all this to happen. At the axon hillock, if you sum all these voltages together and they get high enough, if they get high enough to a voltage that we call the threshold, here I said neurons are typically around minus 70, threshold tends to be around minus 55 or so. These numbers are all different depending on the cell. If you get to this threshold, the voltage doesn't decay and go back. If you get to this threshold, something new happens. You get a huge burst of electricity, a large voltage pulse that we call the action potential. This action potential can only be generated in the axon. Always exceptions, but in our cartoon neuron here. It is generated at the start of the axon, right where the axon hillock joins with the soma. The action potential is sent along the length of the axon. Now these axons can be really short, they can be a few hundred microns and be targeting nearby cells. They can be millimeters away, they can be centimeters away. The largest, longest axon in your body probably goes from your toe. all the way up to your brainstem. So some of these axons can be many feet in length. Imagine a giraffe or a blue whale has axons that go many, many, many meters. So axons can be really long. And the interesting thing about the action potential is that as it travels a potentially really long cable, right, the axon is like a wire, it is what we call actively propagated. What this means is that it does not get any smaller. It doesn't decay. It remains the same height. So if this is the length of my axon here, it's the same height here, it's the same height in the middle, it's the same height over here. You can even have more than one action potential traveling along the action axon at one time. It is actively propagated. Don't confuse that with active transport. It turns out that all the mechanisms of making an action potential are passive and don't directly require the use of ATP. Okay, so it's very good news that this doesn't decay as it travels because now it can go long distances, right? If it if it decayed as it traveled you wouldn't be able to send a signal from your toe up to your brain, right? It would decay too fast and so by actively propagating an action potential can essentially be sent long distances without loss of any signal. Okay, now wherever the axon ends, and it might branch, but it's going to end somewhere. It's going to end in a synaptic terminal, which is often like a little enlargement of the axon. And it is positioned next to the dendrites of another neuron. It could be a muscle cell or there are some other exceptions, but usually it's positioned next to the dendrite, the input area of another neuron. So this neuron is going to tell its target, hey, I have information to send to you. and that information is transmitted in the form of chemicals. The action potential in the axon terminal causes the release of chemicals called neurotransmitters from the axon terminal to the dendrite of the target cell. So the action potential kind of has two jobs. It carries information potentially long distances, and then finally the action potential actually causes the release. neurotransmitters from one cell to the other. Once the neurotransmitters are released, they cross the space between the neurons, the synaptic cleft. It is a tiny, tiny, tiny space, so small that you can't even see it with a light microscope. You need an EM microscope to see it, which is why it took decades for scientists to even know that these were separate cells. You can imagine why that distance is so small, why it really makes neural transmission very efficient if the distance is very small. The neurotransmitters cross the synapse very, very quickly for this reason, where they then bind to what we call post-synaptic receptors. These are receptors that you find on the dendrites of the target cell, right, that have binding sites for the particular neurotransmitters that are released. Now, when those... neurotransmitters bind to the receptors, it typically causes a transient and decaying voltage change in the dendrite. And now we're back to where we started. And this is basically how the nervous system works. It's how one neuron gets input. It takes all of the different kinds of inputs that it's getting, right? It's not usually just a single input that causes it to reach threshold and cause an output, but multiple inputs all coming in together. Neurons actually integrate information. Once the neuron is raised to threshold, it will generate its own output. That output is sent to multiple targets typically. But when it reaches a particular target, it will cause the release of neurotransmitter, which causes then this sort of transient decaying voltage change in the target. And so that's the same same slide that we started with up here. Okay, that is the overview. The way we're going to start this, so we'll go over all of that in more detail, and we're going to start at the beginning with where a neuron sits when it's not doing anything. We're going to start with what we call the resting potential. The resting potential is the charge on the membrane of a neuron that is not actively signaling. What we will see is that neurons are kept kind of imbalanced at rest when they're not signaling. so that when they need to respond, they do so really, really quickly. If you think about it, if response is moving a big rock, right, either up or down, I can keep the rock at the bottom, and then when I hear the signal, I can then use my energy to push the rock to the top, and now everyone sees the rock and I've signaled something. That's going to take a lot of time and energy. The other opportunity maybe if I'm going to signal with my rock is keep it at the top of a cliff. And then when I see the signal, I push it off and it falls very rapidly. It doesn't take very much energy to do so. It makes a loud noise and it is very rapid. And I don't have to expend a lot of energy at the moment of signaling. I've expended the energy setting it up like that. And that's the way your nervous system works. It is set up to be kind of far away from equilibrium. far away from certain types of equilibriums, so that signaling can be really, really rapid. Okay, so your neuronal resting potential is the voltage, the separation of charge that we find inside of a cell. And before we begin, we actually need to define these terms. So what is a potential? You'll also hear it called a voltage. This is an electric potential. It's something from physics. It's a separation of electrical charge. So remember there are two kinds of charge. There are negative charges and there are positive charges. Typically they are all sort of intermixed in a solution that has charges in it. Like if I dump sodium chloride into a solution, right, positive sodiums will be mixing around and sort of bouncing around and negative chlorides will be mixed as well. But if I can keep... them separated, if I can get more positives over here and more negatives over there, that is a voltage. And that is potential energy. That is like pushing the rock to the top of the hill. That's potential energy. A battery has a voltage, right? Those charges, right? Positive charges want to be where it's negative and negative charges want to be where it's positive. Remember, opposites attract. And so by separating these charges, Right. we have created kind of a potential for the movement of things. And so that is what potential or voltage means. We measure it typically and biologically in millivolts. This is how many charges per unit area are separated. A typical resting potential in a neuron is minus 70 millivolts. A typical AAA battery I think is 1.5 volts, so a lot more. Okay, so potential is the separation of charge. If you separate those charges, they are going to want to flow. It's like pushing water up a hill. It wants to flow downhill. Okay, current is defined as the flow of charge. So when charged things like ions or in our electronics, electrons move around, that is what we call electrical current. It is different. than potential. Potential is the potential for things to move. Current is charge actually moving. In your electronics, Current is going to be driven by the movement of electrons in wire, in metal. In biology, we find that current is typically carried by ions. And so we're going to see that the star players in the nervous system are sodium ions and potassium ions. You can learn a lot about the nervous system by only looking at those two ions. So when they move... from one side of the membrane to the other, they carry charge with them, and we call that movement of charge, positive charge current. And finally, we have something that's called resistance. Resistance is the resistance to the flow of charge. Its inverse is conductance. And conductance is anything that allows charge to flow. In electronics, those are going to be like copper wires have a high conductance. What about in biology? In biology, the lipid bilayer is extremely resistant to the flow of ions, right? Ions don't go through a lipid bilayer very easily. But what does allow conductance of ions through a membrane? There's my lipid bilayer. Ion channels, right? Embedded proteins can allow ions through. And so conductance resistance is R. We measure it in something called ohms. Oh, by the way, current is measured in amps, amperes. For some reason, conductance is little g, and it's the inverse of. resistance. All right, let's look at an example here. There are certain animals that have very, very large neurons, large with large axons that make them particularly well suited to studying this. One of these animals is these little squids. Squids, these small squids have what is called a giant axon in them that's part of their escape reflex. They can be up to a millimeter wide, like you can see these cells with the naked eye. We record voltage with something that we call an electrode. An electrode is going to measure the charge in one area relative to the charge in another. So whenever we talk about a potential, it's always a relative measure, right? It's how much charge is over here. relative to over here. And so we typically have a recording electrode and then what we call a reference electrode, sometimes called a ground electrode as well. And so here's an axon, a neuron that's in a saline bath. It's essentially created the saline bath to mimic extracellular fluid. And so when the recording electrode and the reference electrode are in the same solution, we don't read any voltage change because... they're part of the same solution. Now what happens if we drop that electrode into the cell and we make them really sharp and they actually sort of pierce into the cell, what we record is the membrane potential. And in this case it's minus 65 millivolts. That means the inside of the cell is negative relative to the outside. And just to be clear, the inside of the cell in total doesn't really have tons and tons of extra negative charge. We'll see the numbers here. It just means that there are slightly more negative charges lined up on the inside of the membrane than there are positive charges on the outside. It turns out, as we will see, that there isn't really that huge of a difference in the number of charges. If there were huge differences in positive and negative charges inside and outside your cell, you'd have like lightning shooting out of you. So these differences are relatively subtle. generate electrical fields that we can measure. Now once we have a resting potential, there are a couple of other terms that we want to just make sure that we get into our heads to think about how neuronal signaling works. Because a neuron at rest has a membrane potential, it's not neutral, we call it polar, right? In the same way that a water molecule is polar, and it has partially positive hydrogens and partially charged negative. or partially negative oxygens, right? A neuron is polar in the same way. It is negative on the inside relative to the outside. So at rest, it is polarized. If we ever raise the membrane up, potential up closer to zero, we call that depolarization. It kind of means you're getting closer to zero. If we go even more polarized than the rest, we call that hyperpolarization. Just a couple of terms that we'll run into in the future. All right. The last portion of this, I'm going to... just go over here in the video and then definitely go over again in class because this is confusing and definitely works best when we go over it multiple times. We will also work on problems doing this kind of thing in class as well. But I'm going to sort of discuss where the membrane potential comes from. And to start by thinking about where this membrane potential, this resting potential comes from, we're going to look at a really, really simplified situation. We're going to look at a situation that only has one ion of interest, and that ion is going to be potassium. And the reason that I say that there's only one ion of interest is because we have a system that has two containers, left and right, that could be inside and outside the cell. that are separated by an ion-selective membrane. And of course your cell membranes are the very same, right? They can allow different ions through. This membrane is only permeable to potassium, right? And so the membrane will allow potassium through, but no water and no chloride, no other ion. Only allows potassium through. And this is mimicking kind of how our cells work. So we only have one ion. that we need to worry about when we're looking at this. Now we are going to be dumping a salt into the different solutions in this system. So we have a left system and a right system. We're dumping potassium chloride salt in there. It looks a lot like table salt, but we're not going to worry about the chlorides because it can't cross the membrane. And if it can't cross the membrane, it actually does not participate in any of the things that we're going to talk about. So what's going to happen if I put the same amount potassium chloride on the left and the right side. Is there going to be no movement of potassium across this membrane at all? That's not technically true. Some potassiums are going to cross from the left to the right, but the same number that are going to cross from the right to the left. Remember this is all random bouncing, random molecular motion. you're going to get no net movement of potassium, even though some small number of potassiums are going across the membrane, right? Okay, so this is fairly straightforward. The other thing to remember, though, is that every time a potassium moves across the membrane, it brings with it a positive charge. And so if positive charges start to move in one direction or the other, it's going to start to make one side more positive and the other side more negative. And that's actually what we see. if instead of putting equal amounts of potassium chloride in these two sides of the speaker, we put 10 times more on the left, right? That's 0.1. On the right, it's 0.01. So now we have 10 times more potassium chloride on the left than on the right. And as you can imagine, we're going to have a net flow of potassiums across this membrane, which allows potassium across from the left to the right. This is exactly what you'd expect. This is going to happen if I dump more glucose on the left and the membrane allows glucose to go through. You're just going to get these things to diffuse. However, potassium is not going to behave in the same way glucose does. Glucose, when it goes across the membrane, does not change the membrane potential. Glucose does not bring along, it's not charged, does not bring along a positive charge with it. When potassium moves across, it brings a positive charge. Now, what difference does that make? Well, first of all, it makes the right side more positive and the left side more negative relative to each other. But what effect does that have on how much potassium wants to go to the right? And to answer that question, we need to remember... that like charges repel each other and opposite charges attract each other. Positive charges are repelled by other positive charges. So once enough potassium goes from the left to the right, the right side of these beakers is going to be too positive. And it's going to be so positive over here that it's going to keep the positively charged potassiums out. And you will end up with two interesting things. You will end up with the right side being more positive than the left. This thing here is a voltmeter, and this side is more positive, this side is more negative, and you will end up with an imbalance. of potassiums, they will not reach the same concentration in both sides. At some point in time you are going to have a electrical force that repels the potassium and keeps them from going down their concentration gradient. And those two forces, the concentration gradient force, which is not really a force but we can think of it like that, and the electrical force will be equal and opposite. And so let me ask you this question, just for you to guess. If I have 10 times more potassium chloride over here than over here, how much potassium has to cross over to this side before there's enough force to repel them, right? What will the ending concentration be if it started at 0.1 molar? How much will I have to decrease that left-hand concentration? before the electrical gradient stops it from coming in? Is it going to go down to 0.09, 0.05? Actually, 0.05 would be pretty close to being in equilibrium. It's not going to do that. How far do you think it's going to have to go? Well, if you're looking at the entire slide here, and my text, and these numbers, a shocking thing happens. it is almost none. It is a tiny handful of potassium that cross this membrane that create a repelling positive force field, essentially, that keeps any more potassium from coming over. The number is so small that it has almost no effect on the concentration, not a measurable effect. Technically, yes. It's gone from 0.1 to 0.099999, something like that. That's amazing. It hardly takes any ions to move across the membrane to cause a change in voltage that then repels any more movement of ions. In fact, if you do the physics of this, here is a membrane potential of minus 90 millivolts. right? The amount of potassium that needs to cross one cubic or one square micron of membrane with one cubic micron of fluid on either side out of a total of a hundred thousand potassium ions that are in that cubic micron of fluid, it is literally six. Six out of a hundred thousand. So that is not really... measurable change in concentration, right? It is technically a change in concentration, but it is not a change in concentration that a biologist really cares about. So that's amazing. So as soon as a few ions cross the membrane, they essentially set up an opposing gradient, an electrical gradient, right? Because it's so positive out here and so negative in here that potassium, these positive ions, want to stay where it's negative. and they don't want to go where it's positive. And it keeps them in. It keeps them in way against their concentration gradient, right? The concentration gradient is 50 to 1 here, right? 100,000 to 2. It's a huge concentration gradient. But if you make the inside negative 90, which means the outside is, you know, plus 90. This is actually, I prefer this at plus 90 outside. It's all relative, so it kind of depends what you're talking about, but it's more positive on the outside. That's enough to stop all of this potassium from wanting to leave, right? So that electrical gradient is much, much stronger essentially than the concentration. In fact, there's a mathematical relationship that tells us for any given concentration gradient, 10 to 1, 100 to 1, 1000 to 1, whatever our concentration gradient is, those ions want to go down their concentration gradient. How much electrical gradient do you need to counteract the concentration gradient in order to stop the ion from flowing down its concentration gradient? I'm going to ask that question here. If we had a 10 to 1 ratio, right, lots of potassium outside, not very much potassium inside, I'm going to need some number of millivolts to stop it from coming over. If I have a thousand to one, there's way more potassium, and I always draw bigger letters if I need higher concentration. I'm going to need a lot more positive charge to stop it from coming over. Well, it turns out that there's a very simple mathematical relationship that tells us exactly how much electrical force we need to counteract an ion's tendency to flow down its concentration gradient. And it's given by this equation here, the Nernst equation, which you may have seen in chemistry, but it's way more interesting here in biology. And that's just me being objective, that's just a fact. The equation is this. It is 60 times the log base 10. These are concentration out over concentration in. Now there are lots of ways you can memorize this. You will, if you look this up, there are different formulations of it. There are lots of different ways to show it. This 60 actually comes from a lot of different things. It takes into account temperature and all sorts of other things. This is the simplified version of it. Oh yeah, here's the, you got the gas constant, the temperature, Faraday constant. This is the valence. This is the natural log. The important things here... are the concentration ratio, the fact that you're taking the log of it and you multiply it by 60. Let's go through a couple of examples and we'll do this in more in class. All right, here is a neuron. It's got sodium inside that equals 100 and outside Sodium is going to equal 10. These are the concentrations. So the way I would solve this is a couple ways. First of all, you can do the equation and I will have you solve equations, but as if you probably know me, I'm less interested in seeing that you understand or that you can plug numbers into an equation because that's super easy. and you don't need to learn anything. But I'm interested in having you understand the concepts. And so if this membrane is permeable to sodium and sodium only, and these are the numbers, will the inside the cell end up positive or will it end up negative? And the way we think about this is there are a couple ways you can think about it. One is if I just sort of magic these sodiums in here, you know. just poof them into existence. What's the first thing that's going to happen? Right, let's assume there's no, there's no electrical gradient here, there's no charge separation. Well, sodiums are going to want to flow down their concentration gradient, and they're going to make the outside more positive, right? But very, very quickly, enough sodiums are going to make the outside more positive, which means the inside is negative. If positive charge leaves, the inside becomes more negative, and very soon It's going to be so positive out here that sodium is going to stop wanting to leave, essentially leaving the concentrations the same, but leaving the inside negative. The voltage that I end up with is going to be negative. Now to find the value of it, that's easy. I just take the ratio of the two, ratio is 10, and then I take the log of 10. The log of 10 is 1. and 1 times 60 is 60 millivolts. And so the inside of the cell will be negative. 60 millivolts. That number, negative 60, we call the equilibrium potential. The equilibrium potential is the voltage that you need to stop a single ion from moving down its concentration gradient. It's the voltage you need inside the cell to stop an ion from flowing down its concentration gradient. It's an opposition. It's basically a complete balancing of the concentration gradient, but with electrical force, right? And so if I want to keep sodium from leaving the cell, right, sodium is positive, I need to make the inside negative so it likes to stay in, right? And keeping the inside negative means that the outside is positive. If I have a negatively charged ion, let's say I have chloride in here, negatively charged, let's say it's 50 inside, and let's say the concentration of chloride outside is 500. Yeah, let's use a slightly different set of numbers, 5 and 500. So there's two things I'm going to do. I am going to think about what the sign is going to be, and this is a negative ion. How do I stop chloride from moving down its concentration gradient? Well, chloride wants to come in, right? It's negative, and it wants to come in because it's more concentrated outside. So to stop it from coming in, I need to make the inside more negative, right? That's one way of thinking about it is what do I need to do to stop it from coming in? The other way of thinking about it is if I just magic these into existence, a couple of chlorides are going to come in, bringing their negative charge, making the inside negative, but not enough are going to come in to change this concentration. So this thing will remain at 5 and 500. The inside will be negative if this cell is only permeable to chloride. And the ratio is 500 to 5. That's 100, the log of 100. It's 2 10 squared, and 2 times 60 is 120. Negative 120 millivolts. So you notice that I didn't really do too much with any of this business here with logs. Sorry, with valences or temperatures. We're always assuming it's kind of at whatever temperature it's at. You will see sometimes that it's outside over inside. Sometimes you will see that it's negative times the log. I am going to have you learn how to do this without having to worry about any of that. I just divide the bigger number by the smaller number. What happens if I divide 5 by 500? What if I did the inside divided by the outside? I end up with 0.01. The log of 0.01 is negative 2. Well guess what? The only difference there is the negative. And so the flip the log of 1 over 100 is the same as the negative log of 100. So I don't actually worry about where my negative sign is because I understand why the sign is the way it is. And you can guarantee that on the test, I'm not just going to have you plug numbers into the equation. I could go online and find Nernst equation calculators in two seconds. You're going to have to tell me why. the inside of a cell would be negative or positive given a particular ratio of ions. The answer is the equilibrium potential is the voltage you need to stop an ion from flowing down its concentration gradient. Okay, we will go over this again in class and we will do some problems in class and we'll think about it more more deeply there. All right.

They don't want to be food. So they're very active. And it is a benefit to be able to react to changes in the environment and act very, very quickly.

And the system that animals have to do this, or most animals have, is the nervous system. The nervous system is a signaling system that... essentially sends signals from cell to cell and ultimately to an animal's muscles to allow it to behave.

It's similar to the endocrine system, which is another signaling system we have in which signals are sent into the bloodstream and then activate various organs around the body. The nervous system does the same thing. It releases chemicals as messengers that activate receptors and tell cells to do things.

The nervous system tends to be very very fast and very very specific in terms of where its targets are whereas the endocrine system is slower it relies on slow blood stream and it has sort of effects throughout the body whereas a single neuron has a response just in a few muscle cells ultimately. things that we'll see over the course of looking at the nervous system is that signals are transmitted within a cell, within a neuron, electrically. So we have a change in electrical signaling inside the cell, and we'll go through all of the mechanisms by which that happens. So inside a cell, signals travel electrically, and then typically, but not always, between cells, signals travel electrically. the transmission of information is chemical in nature and so the neuron will release chemicals onto another cell to signal that something interesting should happen.

The stars of the show are the cells called neurons. We'll spend a little bit of time here just looking at sort of the anatomy of an individual neuron. Neurons have an enlarged area that houses the major organelles and the nucleus that we call the soma, which means the body.

And it has a lot of things that stick out of the soma. And there are different types of neurons that all look a little bit different, but the general features are the same. A soma will have typically lots of branches that come off at what we call the receiving end.

that kind of look like branches on a tree. We call those ones dendrites. This is the receiving end of a neuron. It's where input comes into a neuron. And those dendrites can be really, really branched, and there are usually lots and lots of them.

The output side of a neuron has a single branch, a single output cable that we call the axon. And something interesting happens here electrically. The axon starts right where the axon joins the soma at what we call the axon hillock. It means little hill.

That kind of looks like a little hill. So the axon is the output of a neuron. There's one axon that comes out of the soma. That axon may branch.

A lot of axons branch many, many times. But there's only one typically that comes right out of the soma. Where one neuron meets another, it's for communication.

we call a synapse. A synapse is a structure that sort of includes the end of one axon, which we call the axon terminal here, and then the dendrite or sometimes even the soma of the target cell. That whole structure we sometimes call the synapse. Sometimes we just call the synapse the space between the neurons, but usually the word synapse means two cells but just one small tiny part of each of the two cells.

It's kind of a joining of the two neurons. They don't actually come in contact with each other. It was a decades-long fairly bitter argument between scientists in the late 1800s about whether neurons were individual separate cells or whether they were all sort of interconnected like a fungus. It turns out that they are all individual cells. Now the basic function of the nervous system, and I think it's always useful to remember this, is to allow an animal to contract its muscles.

at the appropriate time and in the appropriate way, depending on what's going on in the environment. Right, that is literally what the nervous system is. The nervous system is ultimately for contracting muscles. It is ultimately for allowing an animal to behave. So the overall output of the nervous system goes through what we call motor neurons.

These are neurons that are attached to your muscle fibers. It's kind of the end point of the nervous system. Basically, the whole point of an animal having a nervous system is to control muscles. Mostly those are skeletal muscles that allow us to move around.

We do actually have muscles that control our digestive system and other smooth muscles, but we'll worry about those later. So the output of the nervous system goes through these motor neurons. Now, just sort of contracting our muscles randomly isn't going to help us.

We need to know what's going on in the environment. And for that, we have sensory neurons. These are neurons that are bringing in... information from the environment, from sight, from sound, from taste, and other types of senses.

And so basically the flow of information in our nervous system is typically sensory input comes in and motor output goes out. And this can be very, very simple. You can think of like a reflex. If I put my hand on a hot stove, I'm going to feel pain.

That pain is going to be sent to my spinal cord. where almost immediately it's going to be sent to a motor neuron to cause me to react and withdraw my arm. And there's not a lot of sort of thinking that goes on with that.

However, of course, not all behavior is so reflexive and so simple. If an animal wants to be able to behave flexibly, it needs to have some kind of set of neurons that go between the sensory neurons and the motor neurons, right? Otherwise, if the sensory neuron always activated the motor neuron, every time that sensory neuron was activated the motor neuron would be activated it'd be a very sort of rigid robotic kind of animal that you have and so what we have are what we call interneurons that sort of live between the sensory neurons and the motor neurons that allow for information to be spread out to be branched out to to go to different places to be remembered your brain in its entirety is in this definition of the word I'm using it interneuron There are other definitions where it's not all inter neurons, but your brain does not have neurons connected to muscle fibers and your brain does not have neurons that are directly attached to the sensory neurons. Since this is biology, there's always minor exceptions to those things, but we'll not talk about the retina right now.

Really your brain is about allowing different kinds of information to go to different places to allow you to make your decisions more flexibly rather than reflexively. Okay, here's just an example of a really, really straightforward neuronal interaction. This cockroach here has these little things at the back of its body called circle organs that have little hairs on them.

And when the wind blows, those hairs cause this red neuron, the sensory neuron, to change its voltage. It is activated in response to the wind. So if a predator is sneaking up on it, and it feels the wind of this predator, those hairs are going to be activated. And this red neuron is going to release chemicals onto this blue neuron, this what we call the giant interneuron.

That giant interneuron is going to activate this motor neuron, this purple one, which is then going to activate the muscles and allow this thing to escape. And so we can see kind of over here, if you puff air on this animal's rear end, the sensory neuron begins responding immediately. The interneuron responds with some delay.

The motor neuron responds a little bit after that, and this thing is responding less than 50 milliseconds. after the stimulus. Just for an example, a decently fast human reaction time is around 200 milliseconds way out here.

This animal is going really, really fast in response to this stimulus. Okay, so that's just kind of an overview of what the nervous system does and a really simple example of what we call a reflex arc. Just a really simple example of taking sensory information.

and then transferring it over to the motor system so that the animal can behave. What we're going to do now is talk about the system as a whole. I'm going to give you just an overview of how the nervous system works, how neurons communicate with each other, and then over the next few days we'll go into all of the details of how this works. But I think it's worthwhile to see the whole thing all at once before getting into the details.

That way you can kind of have a sense for how everything fits together. So we're just going to be in the brain and we're just going to talk about one neuron in the brain talking to another neuron in the brain, which will probably talk to another neuron in the brain. Most of your neurons are just interneurons talking amongst themselves.

We'll talk about sensory neurons and motor neurons when we talk about the sensory system and the motor system in later weeks. So we can kind of start anywhere, but let's start with a neuron receiving input. from another neuron, right? So one neuron is going to talk to another and it's going to send some kind of signal to it.

Remember the nervous system is a signaling system. Okay, the input to this neuron that we're talking about causes a transient and decaying voltage change in the dendrites. So what does that mean?

Transient means it doesn't last very long and decaying means that this voltage change doesn't last very long. We will, after all of this is done, spend a little bit more time defining what voltage change means. But voltage change just means a change in how much charge, how much electric charge there is.

This here is an example of this change in voltage. The voltage inside the cell, when it's not being signaled, is usually around minus 70 millivolts or something. We'll talk about all this later. And when the input comes in, right, here's a neuron who's activating by squirting chemicals on the cell, the target neuron, you end up with an increase in voltage that goes up, then it goes down, and that voltage spreads out along the dendrites. So if it came in up here, it's going to travel down the dendrite and through the soma until it gets to the axon hillock.

And so those changes in voltage... they're typically in the positive direction, but not always, are going to travel along the length of the axon, and interestingly, they decay as they go. And what we mean by decay is that they get smaller. So at the point of its source, it's a pretty high change in voltage, but as we measure it over here in the soma, it's much lower, and by the time it gets to the axon hillock, it is... probably pretty, pretty small.

So it decays as it travels and then it ends up at the axon helix. So that's what one neuron does to another. It makes it change its voltage and that voltage then sort of diffuses throughout the target cell. Now a neuron typically has lots of inputs coming in all the time, right? This thing, this neuron has lots of dendrites, it has lots of other neurons that are trying to tell it things.

And so here's a neuron called A1 that's coming in, another one called A2. These are all individual neurons that form connections, synapses with this target neuron. And so if they come in at the same time, if input A1, which causes this transient increase in voltage, comes in and then A2 comes in right after it, both of those changes are going to kind of funnel down towards the axon hillock and and come in at near the same time.

And what happens is if they come in close enough, they add together, shown down here. We call that summation. And so these inputs get added together.

And if two positive inputs come in, you can get a bigger one. If a positive one and a negative one comes in, they can kind of subtract from each other. But basically, inputs coming in throughout the net of dendrites and even on the soma itself are all coming in together. And they all funnel into the axon hillock where they are sort of added together in real time.

Now, something changes at the axon hillock. There are changes in the cell membrane that allow all this to happen. At the axon hillock, if you sum all these voltages together and they get high enough, if they get high enough to a voltage that we call the threshold, here I said neurons are typically around minus 70, threshold tends to be around minus 55 or so.

These numbers are all different depending on the cell. If you get to this threshold, the voltage doesn't decay and go back. If you get to this threshold, something new happens. You get a huge burst of electricity, a large voltage pulse that we call the action potential. This action potential can only be generated in the axon.

Always exceptions, but in our cartoon neuron here. It is generated at the start of the axon, right where the axon hillock joins with the soma. The action potential is sent along the length of the axon.

Now these axons can be really short, they can be a few hundred microns and be targeting nearby cells. They can be millimeters away, they can be centimeters away. The largest, longest axon in your body probably goes from your toe.

all the way up to your brainstem. So some of these axons can be many feet in length. Imagine a giraffe or a blue whale has axons that go many, many, many meters. So axons can be really long.

And the interesting thing about the action potential is that as it travels a potentially really long cable, right, the axon is like a wire, it is what we call actively propagated. What this means is that it does not get any smaller. It doesn't decay.

It remains the same height. So if this is the length of my axon here, it's the same height here, it's the same height in the middle, it's the same height over here. You can even have more than one action potential traveling along the action axon at one time. It is actively propagated. Don't confuse that with active transport.

It turns out that all the mechanisms of making an action potential are passive and don't directly require the use of ATP. Okay, so it's very good news that this doesn't decay as it travels because now it can go long distances, right? If it if it decayed as it traveled you wouldn't be able to send a signal from your toe up to your brain, right? It would decay too fast and so by actively propagating an action potential can essentially be sent long distances without loss of any signal. Okay, now wherever the axon ends, and it might branch, but it's going to end somewhere.

It's going to end in a synaptic terminal, which is often like a little enlargement of the axon. And it is positioned next to the dendrites of another neuron. It could be a muscle cell or there are some other exceptions, but usually it's positioned next to the dendrite, the input area of another neuron. So this neuron is going to tell its target, hey, I have information to send to you.

and that information is transmitted in the form of chemicals. The action potential in the axon terminal causes the release of chemicals called neurotransmitters from the axon terminal to the dendrite of the target cell. So the action potential kind of has two jobs.

It carries information potentially long distances, and then finally the action potential actually causes the release. neurotransmitters from one cell to the other. Once the neurotransmitters are released, they cross the space between the neurons, the synaptic cleft.

It is a tiny, tiny, tiny space, so small that you can't even see it with a light microscope. You need an EM microscope to see it, which is why it took decades for scientists to even know that these were separate cells. You can imagine why that distance is so small, why it really makes neural transmission very efficient if the distance is very small.

The neurotransmitters cross the synapse very, very quickly for this reason, where they then bind to what we call post-synaptic receptors. These are receptors that you find on the dendrites of the target cell, right, that have binding sites for the particular neurotransmitters that are released. Now, when those... neurotransmitters bind to the receptors, it typically causes a transient and decaying voltage change in the dendrite.

And now we're back to where we started. And this is basically how the nervous system works. It's how one neuron gets input.

It takes all of the different kinds of inputs that it's getting, right? It's not usually just a single input that causes it to reach threshold and cause an output, but multiple inputs all coming in together. Neurons actually integrate information.

Once the neuron is raised to threshold, it will generate its own output. That output is sent to multiple targets typically. But when it reaches a particular target, it will cause the release of neurotransmitter, which causes then this sort of transient decaying voltage change in the target.

And so that's the same same slide that we started with up here. Okay, that is the overview. The way we're going to start this, so we'll go over all of that in more detail, and we're going to start at the beginning with where a neuron sits when it's not doing anything.

We're going to start with what we call the resting potential. The resting potential is the charge on the membrane of a neuron that is not actively signaling. What we will see is that neurons are kept kind of imbalanced at rest when they're not signaling.

so that when they need to respond, they do so really, really quickly. If you think about it, if response is moving a big rock, right, either up or down, I can keep the rock at the bottom, and then when I hear the signal, I can then use my energy to push the rock to the top, and now everyone sees the rock and I've signaled something. That's going to take a lot of time and energy. The other opportunity maybe if I'm going to signal with my rock is keep it at the top of a cliff. And then when I see the signal, I push it off and it falls very rapidly.

It doesn't take very much energy to do so. It makes a loud noise and it is very rapid. And I don't have to expend a lot of energy at the moment of signaling.

I've expended the energy setting it up like that. And that's the way your nervous system works. It is set up to be kind of far away from equilibrium. far away from certain types of equilibriums, so that signaling can be really, really rapid. Okay, so your neuronal resting potential is the voltage, the separation of charge that we find inside of a cell.

And before we begin, we actually need to define these terms. So what is a potential? You'll also hear it called a voltage. This is an electric potential.

It's something from physics. It's a separation of electrical charge. So remember there are two kinds of charge.

There are negative charges and there are positive charges. Typically they are all sort of intermixed in a solution that has charges in it. Like if I dump sodium chloride into a solution, right, positive sodiums will be mixing around and sort of bouncing around and negative chlorides will be mixed as well.

But if I can keep... them separated, if I can get more positives over here and more negatives over there, that is a voltage. And that is potential energy.

That is like pushing the rock to the top of the hill. That's potential energy. A battery has a voltage, right? Those charges, right?

Positive charges want to be where it's negative and negative charges want to be where it's positive. Remember, opposites attract. And so by separating these charges, Right. we have created kind of a potential for the movement of things.

And so that is what potential or voltage means. We measure it typically and biologically in millivolts. This is how many charges per unit area are separated.

A typical resting potential in a neuron is minus 70 millivolts. A typical AAA battery I think is 1.5 volts, so a lot more. Okay, so potential is the separation of charge.

If you separate those charges, they are going to want to flow. It's like pushing water up a hill. It wants to flow downhill.

Okay, current is defined as the flow of charge. So when charged things like ions or in our electronics, electrons move around, that is what we call electrical current. It is different. than potential.

Potential is the potential for things to move. Current is charge actually moving. In your electronics, Current is going to be driven by the movement of electrons in wire, in metal. In biology, we find that current is typically carried by ions. And so we're going to see that the star players in the nervous system are sodium ions and potassium ions.

You can learn a lot about the nervous system by only looking at those two ions. So when they move... from one side of the membrane to the other, they carry charge with them, and we call that movement of charge, positive charge current.

And finally, we have something that's called resistance. Resistance is the resistance to the flow of charge. Its inverse is conductance. And conductance is anything that allows charge to flow.

In electronics, those are going to be like copper wires have a high conductance. What about in biology? In biology, the lipid bilayer is extremely resistant to the flow of ions, right?

Ions don't go through a lipid bilayer very easily. But what does allow conductance of ions through a membrane? There's my lipid bilayer. Ion channels, right? Embedded proteins can allow ions through.

And so conductance resistance is R. We measure it in something called ohms. Oh, by the way, current is measured in amps, amperes.

For some reason, conductance is little g, and it's the inverse of. resistance. All right, let's look at an example here. There are certain animals that have very, very large neurons, large with large axons that make them particularly well suited to studying this. One of these animals is these little squids.

Squids, these small squids have what is called a giant axon in them that's part of their escape reflex. They can be up to a millimeter wide, like you can see these cells with the naked eye. We record voltage with something that we call an electrode. An electrode is going to measure the charge in one area relative to the charge in another. So whenever we talk about a potential, it's always a relative measure, right?

It's how much charge is over here. relative to over here. And so we typically have a recording electrode and then what we call a reference electrode, sometimes called a ground electrode as well. And so here's an axon, a neuron that's in a saline bath.

It's essentially created the saline bath to mimic extracellular fluid. And so when the recording electrode and the reference electrode are in the same solution, we don't read any voltage change because... they're part of the same solution. Now what happens if we drop that electrode into the cell and we make them really sharp and they actually sort of pierce into the cell, what we record is the membrane potential.

And in this case it's minus 65 millivolts. That means the inside of the cell is negative relative to the outside. And just to be clear, the inside of the cell in total doesn't really have tons and tons of extra negative charge. We'll see the numbers here. It just means that there are slightly more negative charges lined up on the inside of the membrane than there are positive charges on the outside.

It turns out, as we will see, that there isn't really that huge of a difference in the number of charges. If there were huge differences in positive and negative charges inside and outside your cell, you'd have like lightning shooting out of you. So these differences are relatively subtle. generate electrical fields that we can measure.

Now once we have a resting potential, there are a couple of other terms that we want to just make sure that we get into our heads to think about how neuronal signaling works. Because a neuron at rest has a membrane potential, it's not neutral, we call it polar, right? In the same way that a water molecule is polar, and it has partially positive hydrogens and partially charged negative. or partially negative oxygens, right? A neuron is polar in the same way.

It is negative on the inside relative to the outside. So at rest, it is polarized. If we ever raise the membrane up, potential up closer to zero, we call that depolarization. It kind of means you're getting closer to zero.

If we go even more polarized than the rest, we call that hyperpolarization. Just a couple of terms that we'll run into in the future. All right. The last portion of this, I'm going to...

just go over here in the video and then definitely go over again in class because this is confusing and definitely works best when we go over it multiple times. We will also work on problems doing this kind of thing in class as well. But I'm going to sort of discuss where the membrane potential comes from.

And to start by thinking about where this membrane potential, this resting potential comes from, we're going to look at a really, really simplified situation. We're going to look at a situation that only has one ion of interest, and that ion is going to be potassium. And the reason that I say that there's only one ion of interest is because we have a system that has two containers, left and right, that could be inside and outside the cell.

that are separated by an ion-selective membrane. And of course your cell membranes are the very same, right? They can allow different ions through.

This membrane is only permeable to potassium, right? And so the membrane will allow potassium through, but no water and no chloride, no other ion. Only allows potassium through.

And this is mimicking kind of how our cells work. So we only have one ion. that we need to worry about when we're looking at this. Now we are going to be dumping a salt into the different solutions in this system. So we have a left system and a right system.

We're dumping potassium chloride salt in there. It looks a lot like table salt, but we're not going to worry about the chlorides because it can't cross the membrane. And if it can't cross the membrane, it actually does not participate in any of the things that we're going to talk about. So what's going to happen if I put the same amount potassium chloride on the left and the right side.

Is there going to be no movement of potassium across this membrane at all? That's not technically true. Some potassiums are going to cross from the left to the right, but the same number that are going to cross from the right to the left. Remember this is all random bouncing, random molecular motion. you're going to get no net movement of potassium, even though some small number of potassiums are going across the membrane, right?

Okay, so this is fairly straightforward. The other thing to remember, though, is that every time a potassium moves across the membrane, it brings with it a positive charge. And so if positive charges start to move in one direction or the other, it's going to start to make one side more positive and the other side more negative. And that's actually what we see. if instead of putting equal amounts of potassium chloride in these two sides of the speaker, we put 10 times more on the left, right?

That's 0.1. On the right, it's 0.01. So now we have 10 times more potassium chloride on the left than on the right.

And as you can imagine, we're going to have a net flow of potassiums across this membrane, which allows potassium across from the left to the right. This is exactly what you'd expect. This is going to happen if I dump more glucose on the left and the membrane allows glucose to go through.

You're just going to get these things to diffuse. However, potassium is not going to behave in the same way glucose does. Glucose, when it goes across the membrane, does not change the membrane potential.

Glucose does not bring along, it's not charged, does not bring along a positive charge with it. When potassium moves across, it brings a positive charge. Now, what difference does that make?

Well, first of all, it makes the right side more positive and the left side more negative relative to each other. But what effect does that have on how much potassium wants to go to the right? And to answer that question, we need to remember... that like charges repel each other and opposite charges attract each other. Positive charges are repelled by other positive charges.

So once enough potassium goes from the left to the right, the right side of these beakers is going to be too positive. And it's going to be so positive over here that it's going to keep the positively charged potassiums out. And you will end up with two interesting things.

You will end up with the right side being more positive than the left. This thing here is a voltmeter, and this side is more positive, this side is more negative, and you will end up with an imbalance. of potassiums, they will not reach the same concentration in both sides. At some point in time you are going to have a electrical force that repels the potassium and keeps them from going down their concentration gradient.

And those two forces, the concentration gradient force, which is not really a force but we can think of it like that, and the electrical force will be equal and opposite. And so let me ask you this question, just for you to guess. If I have 10 times more potassium chloride over here than over here, how much potassium has to cross over to this side before there's enough force to repel them, right?

What will the ending concentration be if it started at 0.1 molar? How much will I have to decrease that left-hand concentration? before the electrical gradient stops it from coming in? Is it going to go down to 0.09, 0.05?

Actually, 0.05 would be pretty close to being in equilibrium. It's not going to do that. How far do you think it's going to have to go? Well, if you're looking at the entire slide here, and my text, and these numbers, a shocking thing happens. it is almost none.

It is a tiny handful of potassium that cross this membrane that create a repelling positive force field, essentially, that keeps any more potassium from coming over. The number is so small that it has almost no effect on the concentration, not a measurable effect. Technically, yes.

It's gone from 0.1 to 0.099999, something like that. That's amazing. It hardly takes any ions to move across the membrane to cause a change in voltage that then repels any more movement of ions. In fact, if you do the physics of this, here is a membrane potential of minus 90 millivolts.

right? The amount of potassium that needs to cross one cubic or one square micron of membrane with one cubic micron of fluid on either side out of a total of a hundred thousand potassium ions that are in that cubic micron of fluid, it is literally six. Six out of a hundred thousand. So that is not really... measurable change in concentration, right?

It is technically a change in concentration, but it is not a change in concentration that a biologist really cares about. So that's amazing. So as soon as a few ions cross the membrane, they essentially set up an opposing gradient, an electrical gradient, right? Because it's so positive out here and so negative in here that potassium, these positive ions, want to stay where it's negative.

and they don't want to go where it's positive. And it keeps them in. It keeps them in way against their concentration gradient, right? The concentration gradient is 50 to 1 here, right?

100,000 to 2. It's a huge concentration gradient. But if you make the inside negative 90, which means the outside is, you know, plus 90. This is actually, I prefer this at plus 90 outside. It's all relative, so it kind of depends what you're talking about, but it's more positive on the outside. That's enough to stop all of this potassium from wanting to leave, right? So that electrical gradient is much, much stronger essentially than the concentration.

In fact, there's a mathematical relationship that tells us for any given concentration gradient, 10 to 1, 100 to 1, 1000 to 1, whatever our concentration gradient is, those ions want to go down their concentration gradient. How much electrical gradient do you need to counteract the concentration gradient in order to stop the ion from flowing down its concentration gradient? I'm going to ask that question here. If we had a 10 to 1 ratio, right, lots of potassium outside, not very much potassium inside, I'm going to need some number of millivolts to stop it from coming over. If I have a thousand to one, there's way more potassium, and I always draw bigger letters if I need higher concentration.

I'm going to need a lot more positive charge to stop it from coming over. Well, it turns out that there's a very simple mathematical relationship that tells us exactly how much electrical force we need to counteract an ion's tendency to flow down its concentration gradient. And it's given by this equation here, the Nernst equation, which you may have seen in chemistry, but it's way more interesting here in biology.

And that's just me being objective, that's just a fact. The equation is this. It is 60 times the log base 10. These are concentration out over concentration in.

Now there are lots of ways you can memorize this. You will, if you look this up, there are different formulations of it. There are lots of different ways to show it.

This 60 actually comes from a lot of different things. It takes into account temperature and all sorts of other things. This is the simplified version of it. Oh yeah, here's the, you got the gas constant, the temperature, Faraday constant.

This is the valence. This is the natural log. The important things here... are the concentration ratio, the fact that you're taking the log of it and you multiply it by 60. Let's go through a couple of examples and we'll do this in more in class. All right, here is a neuron.

It's got sodium inside that equals 100 and outside Sodium is going to equal 10. These are the concentrations. So the way I would solve this is a couple ways. First of all, you can do the equation and I will have you solve equations, but as if you probably know me, I'm less interested in seeing that you understand or that you can plug numbers into an equation because that's super easy.

and you don't need to learn anything. But I'm interested in having you understand the concepts. And so if this membrane is permeable to sodium and sodium only, and these are the numbers, will the inside the cell end up positive or will it end up negative?

And the way we think about this is there are a couple ways you can think about it. One is if I just sort of magic these sodiums in here, you know. just poof them into existence.

What's the first thing that's going to happen? Right, let's assume there's no, there's no electrical gradient here, there's no charge separation. Well, sodiums are going to want to flow down their concentration gradient, and they're going to make the outside more positive, right?

But very, very quickly, enough sodiums are going to make the outside more positive, which means the inside is negative. If positive charge leaves, the inside becomes more negative, and very soon It's going to be so positive out here that sodium is going to stop wanting to leave, essentially leaving the concentrations the same, but leaving the inside negative. The voltage that I end up with is going to be negative. Now to find the value of it, that's easy.

I just take the ratio of the two, ratio is 10, and then I take the log of 10. The log of 10 is 1. and 1 times 60 is 60 millivolts. And so the inside of the cell will be negative. 60 millivolts.

That number, negative 60, we call the equilibrium potential. The equilibrium potential is the voltage that you need to stop a single ion from moving down its concentration gradient. It's the voltage you need inside the cell to stop an ion from flowing down its concentration gradient. It's an opposition. It's basically a complete balancing of the concentration gradient, but with electrical force, right?

And so if I want to keep sodium from leaving the cell, right, sodium is positive, I need to make the inside negative so it likes to stay in, right? And keeping the inside negative means that the outside is positive. If I have a negatively charged ion, let's say I have chloride in here, negatively charged, let's say it's 50 inside, and let's say the concentration of chloride outside is 500. Yeah, let's use a slightly different set of numbers, 5 and 500. So there's two things I'm going to do.

I am going to think about what the sign is going to be, and this is a negative ion. How do I stop chloride from moving down its concentration gradient? Well, chloride wants to come in, right?

It's negative, and it wants to come in because it's more concentrated outside. So to stop it from coming in, I need to make the inside more negative, right? That's one way of thinking about it is what do I need to do to stop it from coming in? The other way of thinking about it is if I just magic these into existence, a couple of chlorides are going to come in, bringing their negative charge, making the inside negative, but not enough are going to come in to change this concentration. So this thing will remain at 5 and 500. The inside will be negative if this cell is only permeable to chloride.

And the ratio is 500 to 5. That's 100, the log of 100. It's 2 10 squared, and 2 times 60 is 120. Negative 120 millivolts. So you notice that I didn't really do too much with any of this business here with logs. Sorry, with valences or temperatures. We're always assuming it's kind of at whatever temperature it's at. You will see sometimes that it's outside over inside.

Sometimes you will see that it's negative times the log. I am going to have you learn how to do this without having to worry about any of that. I just divide the bigger number by the smaller number.

What happens if I divide 5 by 500? What if I did the inside divided by the outside? I end up with 0.01.

The log of 0.01 is negative 2. Well guess what? The only difference there is the negative. And so the flip the log of 1 over 100 is the same as the negative log of 100. So I don't actually worry about where my negative sign is because I understand why the sign is the way it is. And you can guarantee that on the test, I'm not just going to have you plug numbers into the equation.

I could go online and find Nernst equation calculators in two seconds. You're going to have to tell me why. the inside of a cell would be negative or positive given a particular ratio of ions. The answer is the equilibrium potential is the voltage you need to stop an ion from flowing down its concentration gradient. Okay, we will go over this again in class and we will do some problems in class and we'll think about it more more deeply there.

All right.

Transcript for:Understanding Animal Nervous Systems

Transcript for:
Understanding Animal Nervous Systems