So now that we've introduced protein like and interactions as well as protein like and rate constants in this video, we're going to talk about the first of two different protein like and equilibrium constants. So again, it turns out that there are actually two protein like an equilibrium constants. And so in this video we're really only going to talk about the very first protein like and equilibrium constant. And then later in our next video, we'll talk about the second protein like and equilibrium constant. Now it's important to note now that equilibrium constants are different than rate constants. And so, in our last lesson video, we talked about rate constants, and in this video we're focusing on equilibrium, constants, and so the first protein, like an equilibrium constant is the protein like in association equilibrium constant, which is Capital K A. Not to be confused with lower case K A, which is again the rate constant that we talked about in our last couple of lesson videos and so recall that the equilibrium constant is abbreviated as just k e. Q. And really all it is is just the ratio of the concentration of products over the concentration of react. It's and so this association equilibrium Constant Capital K is really just an equilibrium constant itself. It's the exact equilibrium constant for the association of the free protein and free lie again into the protein logging complex. Now you might recognize this capital K a variable from way back in our previous lesson videos. And that's because we use the same exact capital K a variable to represent the acid dissociation constant, which again also uses the variable capital K. And so it's very, very important not to confuse. So do not confuse this protein like in association constant K A that we just introduced now with the acid dissociation constant that we talked about way back in our previous lesson videos. And we kind of already knew to do that anyways, because we know that not all proteins are going to be acids anyways. And so this association equilibrium Constant Capital K is actually a measure of protein affinity for a lie again. And so the k A and protein affinity for lie again are actually directly proportional to each other, which therefore means that the greater the value of this K, the stronger the affinity a protein has for that particular lie game. Now, this K also has units of inverse molar ity, and it turns out that it's actually going to be the reciprocal of the second protein, like an equilibrium constant that we'll talk more about in our next lesson video. And so, essentially, what we're saying is that the K is the reciprocal of the dissociation constant K d, which again we'll talk more about and our next video. And so here. What you can see is that the k A can be defined as the reciprocal of the K d. So essentially one over K d. And again we'll revisit this idea mawr when we talk about the dissociation constant k d n our next lesson video. Now notice down below in our image Over here on the far left, what we have is a, um, reminder of how protein ligand interactions work. And so notice that this lower case K and this lower case K d represent rate constants which we again talked about and our last few lesson videos. And so these particular rate constants are different than the equilibrium constants that we're learning about in this video and so over here what we have is the equilibrium constant the association equilibrium constant capital K A, which is again different than this rate constant over here with lower case K. And so again, we already know from our previous awesome videos that equilibrium constants are just the ratio of the product over the reactive. And so, for the association here of the protein legging complex, the product is just going to be pl and the reactant they're gonna be p and L. And so it's going to be, uh, the two of these concentrations multiplied by each other. And so this is one way to express this association equilibrium constant K, a capital K. But it can also be defined by the ratio of the rate constant lower case K over the rate constant lower case, K d. And so here What we can say is that lower case K A, as well as lower case k d. A. Za ratio. Just like this K over k d. Also, rip is a representation of the association equilibrium constant Capital K. And then, of course, as we said up above in this line, the K is the reciprocal of the dissociation constant. And so we can also define the K A as the reciprocal of the k d the capital k d, which again we're going to talk more about and our next lesson video. And so over here on the far right, what we have is a reminder that the capital K a is going to have units of inverse molar ity. So over here we can put an inverse polarity. And so this here is ah, lot of information. And as we move forward in our course and continue to talk about these protein leg in equilibrium constants, we'll be able to piece a lot of this information together and make it make even mawr sense. And so this here is the conclusion to our introduction of the protein leg in association equilibrium Constant Capital K. And I'll see you guys in our next lesson. Video. We'll we'll talk about the dissociation equilibrium, constant capital, K d

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Protein-Ligand Equilibrium Constants

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So now that we've introduced the first protein like an association equilibrium Constant Capital K A in our last lesson video In this video, we're going to move on to our second protein like an equilibrium constant, which is the protein like an dissociation equilibrium constant capital K d, which again is different than lower case K D, which is the dissociation rate constant, not equilibrium constant. And so this dissociation equilibrium, constant capital K d is literally an equilibrium, constant itself. Except this time, instead of being the equilibrium constant for the association, it's going to be the equilibrium constant for the dissociation of the protein like and complex backwards to form the free protein and the free like. And now, at this point, we already know from our last lesson video that the k d and the k a r just reciprocal of each other. And so because we already know that K A has units of inverse molar ity, this means that the K D is just gonna have units of molar ity. And so again, we already know that both the K D as well as the K A r used to express the proteins, affinity for the lie game. But it turns out that the K D is actually used much, much mawr often then the K A to express protein affinity for like it. But why is it that the K D would be used more often than the K? Well, one of the reasons has to do with the fact that the K A has units of inverse polarity and inverse mole arat e is a little bit tough for our brains to process, whereas the K D has units of just molar ity, and we know that mole Arat E is just a unit of concentration, and it's much easier for our brains to process units of molar ity than units of inverse molar ity. And so the second reason why the K D is used more often than the K A is because the K D actually ends up resembling one of the variables that we already covered in our previous lesson videos, which is the Michaelis constant K M. And we'll talk about this a little bit more after we digest this image down below. And so notice over here on the left hand side of this image, what we have is the protein, like an interaction that we had in our previous lesson videos and notice again that lower case K and lower case K d. R the rate constants, whereas Capital K A and Capital K D are going to be the equilibrium constant. So these air different than each other. And so over here on the right, what we have is the dissociation, equilibrium, constant capital, K d. And so it's going to be an equilibrium constant. So we know it's gonna be the ratio of the concentration of products over the concentration of react. It's. And so for this backwards dissociation, the products are going to be the free protein and the free lie again so we can add those in here free protein and free lie game. And then, of course, the reactant is going to be the protein like game complex. And, of course, because the K D we know is really just the reciprocal of the K, then it's also going to be expressed as the dissociation rate constant over the association rate concept. So it's gonna be K lower case K d over lower case K A. And of course, because again the K D and the KR reciprocal of each other. We can say that the K D is just going to be the reciprocal of the K A. So the reciprocal of the K is just one over K. And this is the capital K. And of course, as we already indicated, up above, the K D is going to have units of just molar ITI, which is again much easier for us to process than units of inverse similarity. So moving forward in our course were mainly going to be talking about the K D and not so much the K A. And so, as we briefly mentioned earlier in our video, it turns out that this K D is very, very similar to the McHale is constant from our previous lesson videos, which is the K M. And so the K D and the K M are going to be very, very similar to each other as we'll see uh, here in a moment. And so both the K D and the K M are inversely proportional to the affinities that they represent. And so the k D and protein affinity for the lie again are going to be inversely proportional instead of being directly proportional, like the K a waas. And so therefore, what this means is that the smaller the value of the k d, the stronger the affinity the protein is gonna have for that lie again, which is a very similar relationship that the K M has to an enzymes affinity for substrate now also similar to the way that the McHale is constant. K M is equal to an exact substrate concentration that allows the initial reaction velocity Thio equal half of the V max the k D. Because it's also in units of polarity, it also represents a specific concentration. It represents the exact concentration of Lagan that allows for half of the ligand binding sites to be occupied and so we can actually see this down below and our image over here on the left. So notice that we have a bunch of these proteins here and notice that we also have some lie again that's present. And so when the ligand concentration is exactly equal to the K D, which is units and units of molar ity, that means that exactly 50% of all of the protein binding sites are going to be full. And we can see here that this is exactly true, that we have three of the six protein binding sites occupied or full of like and when the concentration of, like n equals the K d. And so you can see graphically here if we grab the binding percentage of the protein over here on the Y axis and lagging concentration on the X axis that the K D has a very similar relationship to the K M. So it represents the exact LaGon concentration that allows for the binding to be at 50%. And so again, this is very, very similar to the meticulous, constant K M from our previous lesson videos. And so, uh, our next video will be able to talk Maura about this relationship of K d with protein binding affinity. But for now, this concludes our introduction to protein lying in dissociation equilibrium constant, and we'll be able to get some practice later in our course. So I'll see you guys in our next video

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Problem

Protein A has a binding site for ligand X with a K _{d} of 54 mM. Protein B has a binding site for ligand X with a K_{d} of 58 mM. Answer the following questions based on this information:

A) Which protein has a stronger affinity for ligand X?

B) Convert the K_{d} to K_{a} for both proteins.

K_{a} for Protein A: __________

K_{a} for Protein B: __________

A

Protein A.

B

Protein B.

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Problem

You prepare a solution of protein and its ligand where the initial concentrations are [P] = 10 mM and [L] = 10 mM. At equilibrium you measure the concentration of the complex [PL] = 5 mM. If the protein-ligand reaction can be represented by P + L ⇌ PL, what is the K_{d} of the reaction under these conditions?