So I just told you about the time constant, tau 0, or tau n, sorry. And I told you that this is a very important parameter that determines the buildup, the time constant for buildup of voltage. Following current injection, so I inject the current here. A get a time constant for the buildup of voltage, following i. And at the end of the current, as I said, there is a voltage continuation which is also controlled by this membrane time constant. Let me show you what is the consequence, very important consequence of the fact that we have a time constant and this is called the Temporal Summation. Let's do the following exercise. Instead of injecting a continuous current, I now will inject intermitant current. So I will inject the current. I and I will stop it, and then I will wait a little bit and then I will inject another, exactly the same current and I will stop it. So this will be a repeated current but with intermissions and then there will be another one here, injected current, and stop it. So this will be my I. And now I want to show you what would be the voltage response. After you have learned all what you've learned, you will see that the voltage is now, will build up, will summate, due to this repetetive current. So let's see what happens in the beginning. You just inject current I and you already know that following this current I there will be voltage V. But now you stop this current here. By stopping injecting current, and the voltage starts to attenuate. Attenuate it back to resting. But suddenly there is another current here. So, due to the second current, this is current number two, this is current number one, due to the second current, because there is time constant to the membrane and the voltage did not have enough time to attenuate completely to rest to the basic. Then you would have a buildup of voltage. So following the second pass, second step you will get a buildup of the second voltage perturbation on top of the remainders of the previous one. And now you stop the current, it will start to attenuate again. But then, it will feel the third current here, and then there will be another buildup. And then you stop completely injecting the current. There will be a attenuation until you drop back to the initial condition which we will later call it resting potential. So, what we saw here is something very important. Really, really important for cells. The fact that when you have a consequence of several inputs, several currents, one after the other with the appropriate time difference. If it's not too long the time difference, then the reminiscence the remainders of the previous voltage here will be the initial condition for the next buildup. And you can see that the voltage is buildup, so this amplitude will be smaller than the next amplitude, which will be smaller than the third amplitude, because they build one on top of the other. This phenomena is called Temporal Summation, because I summate in time. One response, and then the second one on top of the first response, and then the third one on top of the second response, and they summate one on top of the other. And this is because you have a memory to the system, electrical memory. There is some memory to the first input. Here is the first input. There is some memory to it because it takes time to get rid of it. And then you get the second input on top of the memory of the first one, and you build up. This is called Temporal Summation. And it's all due to the fact that you have time constant. Let me just say one thing that is very important, and that of course, if you would inject, if you would inject continuously the current. Unlike what we did, if I would have injected the current continuously, then of course, I will get a buildup [SOUND]. That is larger than what you would get if you had these intermissions. Though the maximal you can get, of course, is when you continuously inject the current. Whenever you stop the current, you, of course, lose something of the voltage because of this attenuation. So this IR that we mentioned before, is the maximum that you can get. And if you inject in some intermissions, you will get the peak will be always less than the voltage if you would have injected continously. That's one important aspect. But still, the fact that there, there is not too long a difference in time between the first, and the second and the third. And meaning that the time difference here is on the order of tao, so this is on the order of the time constant of the membrane. It could be two time constant but not too long because then the voltage will attenuate back to rest, to, to the initial state. If this, if the intermission here between the currents is on the order of the time constant, then there will be this Temporal Summation. There will be buildup of one voltage on top of the shoulder of the previous voltage, and this is Temporal Summation. And this means that when you have consequence input like synaptic inputs. One after the other after the other, that will tend, the voltage response, will tend to summate one on top of the other. What would have happened for example if I would inject here a negative current, like this? What would have happened if my current number four would be not positive inside, but rather I inject negative current inside the cell. This would mean that at that point, here, I will push the voltage down. Because I now push the voltage in the negative direction. Indeed, if this is strong enough, I may go very, very much below, even below the resting potential depending how this strong this voltage this current is. This is hyperpolarizing current, this is current that makes the cell more negative inside. This is carrying the voltage toward negativity. And when I complete, when I cease injecting the current, [SOUND] then the voltage will attenuate back, [SOUND] into the resting potential here, into the reference potential. So this will be also a summation of a positive response. Depolarization. And a negative response, hyper-polarization due to hyper-polarization current. So this interplay between positive currents trying to depolarize the cell, negative currents trying to carry the voltage back or even more negative relative to the initial state. This interplay between positive and negative is exactly what synapses are doing. Because as we'll hear soon, some synapses inject positive current, some synapses inject negative current in the cell. And this will be a Temporal Summation of consequence of several currents. One positive, second positive, third positive, fourth negative and so on in time. This is Temporal Summation. It's a very, very critical important, machinery. The way that neuron work when they summate inputs is governed by this Temporal Summation principle. Which is eventually all results from the fact that you have a membrane time constant memory that takes time, because of this memory, takes time to get rid of the previous input. And that's why you can summate the next one on top of it. If the time difference is correct. So you have to remember the notion of Temporal Summation.
