>> Welcome back. Let's begin by asking what is computational neuroscience? According to Terry Sejnowski, who was one of the founding fathers of the field and was also my postdoctoral advisers, the goal of computation neuroscience is to explain in computational terms how brains generate behaviors. Now, let's dissect this definition a little bit. This leads us to a definition proposed by Peter Dayan and Larry Abbott. According to them, computational neuroscience is the field that provides us with the tools and methods for doing three different things. One is characterizing what nervous systems do. The second is Determining how they function. And finally, the third is, understanding why they operate in particular ways. Now, this actually corresponds quite nicely to the three types of computational models that we looked at earlier in the, in a previous lecture. This corresponds to descriptive models, mechanistic models and interpretive models. Now to understand these three types of models in a little bit more detail with an example, let's look at the concept of receptor fields. In order to understand the concept of receptive fields it is useful to go back to some early experiments performed by Hubel and Wiesel back in the 1960s. Now, they were interested in trying to understand the visual system of the cat. In order to do so, they implanted tiny electrodes, or tiny wires. Into the visual area of the cat's brain. So this is this an area that's in the very rear of the cat's brain and by using these electrodes, they were able to record some electrical signals from particular brain cells. So these electrical signals that they record are due to the output of the brain cells and these outputs are in the form of Tiny digital pulses. which are also called spikes or action potentials. We'll learn more about them in a later lecture. And in order to get these cells to respond, they show different types of stimuli to the animal. And on the right hand side, you see one of these, stimuli. So this is a bar of light that's oriented at approximately 45 degrees, and I'm going to show you a movie that will have this bar of light moving in a particular direction. And what you're going to hear are the responses of one particular brain cell in a cat's brain. And you're going to hear the responses because Hubel and Wiesel have converted the electrical signals that they're recording into sound signals. So are you ready? Here we go. [SOUND] So the crackling sound that you're hearing are the responses of a brain cell, a visual cortical brain cell. [SOUND] In the cat's brain. And you'll notice that this particular brain cell likes bars of light that are oriented at this 45 degree angle. But it doesn't like broad field illumination, like this big square of light that they are showing. So it doesn't really respond when this big square of light is being turned on. On or off, but it does respond to the edge of that square when it's oriented at this 45 degree angle. Okay, so what did we see in the previous slide? We saw that when the bar of light was horizontal, there was not much of a response from the cells so this is a way of representing There being not much of a response. Each of these vertical lines is a spike. So you were hearing the crackling noise that responded to one little pop for each of these vertical lines. And that's the spike from the recorded neuron. And we found that in the particular movie that we say in the previous slide The cat's cell, the one that we were recording from, responded the most when the bar of light was at a 45-degree angle. So we got a very robust response. So here's where the light, the bar of light, was in a particular location at that particular orientation. And so we got a very robust response as shown by. These vertical lines which correspond to the output of neuron, also called a spike. And similarly when the bar of light was at a different angle, you would not expect much of a response. That the response is lesser than it is for the 45 degree angle. So what this leads us to is a notion called A receptive field. So here is the definition. So the receptive field is defined by neuroscientists as comprising of all these specific properties of a sensory stimulus that generates a very robust or a strong response from any cell that you're recording from. So examples could be that, for example, you're, recording from a cell. In the retina, and you might find that the cell responds really robustly to spots of light that are turned on at a particular location. Similarly, as we saw in the Hubel and Wiesel experiments, a bar of light that is at a particular orientation and at a particular location on the retina. Might cause a robust response in a visual cortex cell in the cat's brain. So what we'll do now is we'll look at the three different types of computational models that we mentioned earlier, descriptive, mechanistic and interpretive models. And we're going to build these models for The concept of Receptive Fields. So first, let's look at Descriptive Models. So how do you build a Descriptive Model of a Receptive Field? Well let's take the case of the Retina. So the Retina is the layer of tissue that's at the back of your eyes. And when you for example are looking at a particular object, let's say this pencil, the inverted image is projected to the back of your eyes and on the retina. And if you're recording from a particular group of cells called the retinal ganglion cells, you will find that it is conveying information about the image. To the other areas of the brain. Particularly, this area called the lateral geniculate nucleus. And so you can do an experiment to try to understand the receptive fields of cells in the retina. So how would you do that? Well, you could try to flash spots of light that are circular, as shown by the yellow circle here. different locations on the retina. And what you'll find is that for any particular cell that you're recording from, let's say, this particular cell over here. You might find that the cell only responds when you turn on a spot of light. So when you turn on a spot of light in this particular location. And that generates a robust response, as shown by these spikes over here. And interestingly enough, when you turn on the spot of light in the surrounding area. In this annulus around the center. You might find that the cell stops responding. So it does not generate these spikes. This allows us to define the concept of center surround receptive fields in the retina. So as we saw in the previous slide, when you turn on a spot of light in the central region, you get an increase in the activity of the cell in the retina. And when you turn off a spot of light in the surrounding region, you also get an increase in the activity of the retinal cell. So this leads us to the concept of its On-Center, Off-Surround, Receptive Field. And this basically means that the cell responds when you turn on a spot of light in the center or when you turn off a spot of light in the surrounding region. Now, the counterpart to this type of a receptive field is the off-center. On-surround type receptive field. And so as you might expect, in this case the cell likes it when you turn off a spot of light in the center region. And also it will respond with increased activity when you turn on a spot of light in the surrounding region. So the plus indicates on, and the minus indicates off. Now the information from the retina is passed on to a nucleus. As I mentioned earlier, called the Lateral Geniculate Nucleus or LGN for short. And, this in turn passes information, to the back of your brain, to an area called the Primary Visual Cortex, and so one might ask What happens if you record from cells in the primary visual cortex? What kind of receptive fields do you observe in the primary visual cortex? Well, remember what happened in the Hubel and Wiesel movie that I showed you earlier? In that movie we saw that a particular cell responded robustly, to an oriented bar of light that was oriented in a 45 degree angle. So this gives rise to, receptive fields, that look like this in the visual cortex. So these are called oriented receptive fields, because they're oriented at different angles. And the, neurons are cells in the visual cortex, in this particular case, the primary visual cortex. Tend to respond the best to bars, such as this one, bright bar in a dark background. So the black or the gray over here represents a dark background. And so we have a bar that's bright that is oriented at 45 degrees, and that is what the particular cell that we saw in the movie responded to best. And so this corresponds to a descriptive model. Of the oriented receptive field of the neuron, in that case in the primary visual cortex of a cat. Now, obviously these are not the only types of receptive fields that are found not just at one orientation. What you'll find if you recall from a whole bunch of cells in the primary visual cortex is that the receptive fields vary in their orientation such as shown over here. Some might be vertically oriented or at 90 degrees, some might be horizontal, some might be at a different angle, such as the one shown here. But you would also find that there are cells that respond to dark bars such as one shown over here, or the one shown over here, it's oriented at a 45 degree angle but it likes dark bars. As opposed to this one over here, which likes the bright bar, oriented at 45 degrees. So we'll later learn in the course how to quantitatively estimate these types of receptive fields using a technique called reverse correlation. Now, the second question we can ask is. We know that there are center surround receptive fields in the retina. And also, it turns out, in the LGN, or or lateral geniculate nucleus. But when you come up to the cortex, you find this oriented receptive fields. So, how do we get from center-surround type of receptive fields to oriented receptive fields? And that leads us to a Mechanistic Model of Receptive Fields. And that'll be covered in the next lecture. So, see you then.
