Protein-Ligand Fractional Saturation

in this video, we're going to begin our discussion on protein Ligon Fractional saturation. So first we need to define fractional saturation, which can actually be abbreviated with two different variables. The first is the Greek letter theta, and the second is the capital Letter. Why? And so some textbooks used data? Other textbooks use why, but on your exam or in some practice problems, you might find that either theta or why could be used to represent the fractional saturation. So it's important for us to be able to recognize both of these variables, however, moving forward in our course. I'm mainly going to be using data to represent the fractional saturation Onley because it's a little bit more unique and visually distinguishable. But I'll also be trying to remind you guys that every time you see Fada in our lesson, we could easily replace the theta with capital. Why? And so what exactly is this fractional saturation anyways? Well, it's just the fraction of occupied or, in other words, the fraction of saturated like in binding sites and a protein sample. And so when a ligand binding site on a protein is occupied or saturated, it just means that that, like and binding site is bound to a lie Gand. And so this fractional saturation theta or why is really just a ratio. And really, it's just the ratio of occupied proteins over the total protein content and so notice. That's exactly what we're saying down below in our image in our first box. So we can see that the fractional saturation theater, or why is really just equal to this ratio of the occupied proteins, which are just the proteins that are bound by like an over the total protein content. And so notice that that's exactly what this ratio over here is expressing is well, so the proteins that are bound by Lijun is just going to be the concentration of protein liking complex. And then the total protein is just going to be the concentration of protein liking complex, plus the concentration of free protein. Now it's also important to recognize that this expression right here for the fractional saturation actually resembles the rectangular hyperbole, a equation which recall that we covered way back when we talked about the meticulous meant in equation and so we can see that in this rectangular hyperbole equation, the access here represent the protein leg in concentration, and the B represents the concentration of free protein. And then, of course, this a right here must be equal to a value of one in our equation up above because it's not being shown. And so notice that because it resembles a rectangular hyperba that when we actually plot this data, we get a rectangular hyperbole like we see in this plot. Now, before we actually get down to this plot, it's important to note that this fractional saturation data or why can actually help us reveal the exact percentage of occupied, like and binding sites on a protein and the values of the fractional saturation theta, or why are going to range from zero at its minimum when there's absolutely no lie again, That's bound to the protein all the way up to the highest value of one when all of the protein binding sites are bound by lie game. And so at this point, we already know. So recall from our previous lesson videos that the dissociation equilibrium, constant capital, K d has units of molar ity, and it's equal to the exact lie again concentration that allows for 50% of all of the available, like in binding sites to be occupied. And so 50% corresponds with feta or the fractional saturation Equalling to a value of 0. and so down below. This plot that we see over here on the right is actually referred to as a saturation curve or ah, protein like and binding graph. And what it does is it plots the fractional saturation theta, Or why on the Y axis so we can put feta here, Or why on DSO, that's what's plotted on the Y axis and then on the X axis. Notice that it plots the lie again concentration. And so you can see that when the value of the fractional saturation theta, or why, is equal to 0.5. This is a very unique and critical point on these saturation curves or protein binding, like in binding graphs. And that's because when data is equal to 0.5, the lie again concentration that's associated with that reveals the K D, which is a measure of the affinity that the protein has for the lie again and so in our next video will be able to continue to talk more about the fractional saturation and how it applies directly to protein ligand interactions. And so I'll see you guys in that video.

So now that we've introduced Protein Ligon fractional saturation in this video, we're going to focus on the maximum fada or the maximum value of the fractional saturation. And so it's important to note that for all protein ligand interactions, the equivalent of the theoretical maximum reaction velocity V max is always going to be 100% ligand binding. And so you can't have any more than 100% like and binding. And so 100% like in binding is always going to correlate with the maximum value of theta, which we know is always gonna be equal toe one. And so what we need to recall from our previous lesson videos is that the V max is actually subject to change between different enzymes. So some enzymes have a smaller V max. Other enzymes have a much, much larger V max. However, when it comes to protein ligand interactions, all protein like in interactions are always gonna have a maximum fate, a value equal to one, because you could never have mawr than 100% like in binding Now also recall from our previous lesson videos that the McHale is constant. K M is very similar to the dissociation equilibrium, constant K d. And so what this means is that the smaller the value of the K d, the stronger the proteins, affinity for that lie again. And so taking a look at our image down below, notice that we have this saturation curve here where we have the fractional saturation on the Y axis, which is either Fada or why, and notice that it ranges from zero all the way upto one and then on the X axis. What we have is the lie again concentration and notice that we have these two different curves. Here we have this black curve here for protein A and then we have this blue curve here for protein B and noticed that both protein A and protein B have the same maximum value for the theta, which is, uh, maximum value of data is one. And so this shows that regardless of what protein like an interaction that we're looking at, all protein like in interactions are gonna have a Mac state of one. And so we also need to note that, uh, the example problem here is asking which protein has a stronger affinity to the lie game. Is it protein A or is it protein B? And so what we need to recall is that the smaller the value of the k d, the stronger the proteins affinity for that lie game. And so if we're looking for a stronger affinity, we want Thio look for the smaller KD value. And so notice that this Katie value corresponding with a black herb is smaller than this Katie value corresponding with the blue curve. And so for that reason, we can say that the smaller KD belongs to protein A and so protein A therefore has a stronger affinity, so we can indicate that option. And here is the correct answer for this example problem and our next lesson video. We'll be able to talk about a different way to express the fractional saturation, so I'll see you guys in that video.

So now that we know that the Max Fada value is equal toe one in this video, we're going to talk about an alternative way to express Fada. And so, through algebraic rearrangements and substitution of previous equations, Fada can also be defined in another way. And this way mathematically relates feta to the K D. And it also resembles the Mackay list meant an equation from our previous lesson videos. And so down below on the right hand side, you can see that we have the fractional saturation, which is data, or why. And we already know that it's equal to the ratio of the proteins bound by Lagan over the total concentration of protein. And so really, everything up to this point right here is review from our previous lesson video. And so here in this video, what we're saying is that this equation through algebraic rearrangements and substitution of previous equation, we can actually rearrange it to, uh, this equation right here. And this equation mathematically relates feta to the K D. So we can see we can relate theta to the value of the K. D. And it noticed that this equation here actually resembles the McHale is meant in equation from our previous lesson videos. And so notice that all we need to do is substitute the substrate concentrations with lie game concentrations substitute. The McHale is constant K m with the dissociation equilibrium, constant k d. And then, of course, the V Max. We know that the equivalent of the V max is the max data. And from our last lesson video, we know Max data is equal toe one, and so technically, here we're supposed to have Max data. But we know Max data is equal toe one. So we could just put a one here. And, of course, one times anything is just going to be that thing. And so what we can do is cross this off here because it's being multiplied by one, so it doesn't really matter. And so, really, this equation right here is the alternative way to express the fractional saturation. And so, in our next few videos will be able to get some practice utilizing all of these concepts. So I'll see you guys in our next video

all right. So here we have an example problem that's asking us about antibodies, which we haven't yet talked about, but we will talk about them or later and our course. But antibodies air just proteins that display protein, leg and interactions. And so this example, Problem says that if an antibody binds to an anti gin, which is it's lying in with a K d of five times 10 to the negative eighth Moeller What concentration of antigen or what concentration of lie gone Will fada equals 0.2 and we've got these four potential answer options down below. And so notice down below. Here in the box. What we've got is the equation from our last lesson video for the fractional saturation and so notice here we are actually given the value of data and were also given the value of the K d. And so really, what we need to solve for is the concentration of antigen or the concentration of lie again, which is this variable down below. And so essentially, what we can do is just use our algebra skills and use our algebra skills to essentially isolate this concentration of Ligon all by itself. And so we can do that by first moving this entire denominator up to the left hand side of the equation by multiplying both sides of the equation by the entire denominator. So on the left hand side, what we end up getting his data times the concentration of Ligon plus K d. And then on the right hand side of the equation, we're getting rid of this whole thing. So we're just left with concentration of live game and so we can fill in these, like and here. All right, And then next, What we can do is distribute this Fada here right here and right here, so just multiply it through. So that's pretty simple. So we could go ahead and do that, so we'll get data times the concentration of, like, an plus Fada times K d. And then on the right hand side of the equation, we have the same exact thing. And so now what we can do is again we're trying to isolate for this lie again. So we wanna put it on the same side of the equation so we can take this and subtract it from both sides of the equation. So when we do that, we get data times K d all by itself is equal to the concentration of Lagan minus this portion right here that we're subtracting off data times the concentration of Lagan. And so now what? We have eyes, the ability to factor out this concentration of lie again from this term. And so when we do that, what we get is the concentration of Ligand, Uh, times when we factor it out from this component is just gonna be one. And then when we factor out from this component were just loved with data on DSO, the the left hand side of the equation is gonna be exactly the same data times K d. And so essentially what you'll see when we factored out this concentration of lie again to get it out front. Uh, you can check to see if it's the same as the top here by distributing it here. So concentration of Lagan times one gives you the concentration of lie again and then a concentration of law again, Times data gives you data times the concentration of like and so this is the same thing as this just different format and So now you can see we have one variable for the concentration of lie again. And so we just want to get rid of this whole thing. So we can do that by dividing both sides of the equation by one minus data. And so what we end up getting is, uh we get data times k d over one minus. Data is equal to the concentration of Liggan. And so now we've got our equation rearranged eso that all we need to do is plug in the variables that were given, and we'll get the concentration of log in. And so again for the variable Fada were given to it as 0.2. So let's take this and we're gonna plug in up here. So, uh, fatal were given as 0.2 so we could go ahead and plug that in 0.2. And then the KD were given as five times 10 to the negative eighth so we can plug that in times five times 10. Let's put this in a different color here. Let's put this in red five times 10 to the negative eight. Uh, negative eighth Moeller And that is the K D down here and then this is all gonna be one minus fatal, which is given to us a 0.2. And this is all gonna be equal to the concentration of lying in that we're looking for. And so, really, all we need to do is use our calculators at this point and just crunch these numbers. So if you do 0.2 times five times 10 to the negative eighth and take the answer of that and divided by one minus zero point to what you'll get is our concentration of lie again, which is going to be equal to one 0.25 times 10 to the negative eighth Moeller. And of course, this is equal to the concentration of lie again. So this is the answer to our example problem, and that matches with answer option A. So we can indicate that a is the correct answer for this example problem. And basically, you could just see how this equation here can be used and just rearranged to solve for whatever variable that we need to solve for, in this case, the concentration of like and so we'll be able to get some practice utilizing uh, this thes concepts that we've learned moving forward. So I'll see you guys in our next video