7. Enzyme Inhibition and Regulation

Inhibition Constant

1

concept

## Inhibition Constant

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So before we actually get into the details of all of the different types of reversible inhibitors, there's a couple things that would be helpful for us to cover first. And one of those things is the inhibition constant. And so in this video, we're going to begin our introduction to the inhibition constant. So before we actually define the inhibition constant, it's helpful for us to recall from our previous lesson videos that every single reaction has a rate constant K. And so we already know that the rate constant K indicates the reaction rate, efficiency or probability under set conditions. And so the higher the value of the rate constant K, the more likely it is that the reaction will be faster. And so again, every reaction has a rate constant K, including the reactions that form and break down the enzyme inhibitor complexes, including the E I as well as the E S I complexes. Now it turns out that there's actually no universal notation for the rate constants of these, uh, inhibitor complexes. And so here at clutch crap, we've chosen a very straightforward notation for these rate constants. And so, for the rate constant for the inhibitor complex formation or association. It's just going to be k e i or K E s. I depending on if the EI complex is forming or the E s I complexes forming. And so the rate constant for the inhibitor complex breakdown or dissociation is just going to be K minus E i or K minus s. I again depending on if the EI complex is breaking down or dissociating or if the s ky complex is breaking down or dissociating. So, essentially the little minus sign here indicates the breakdown or dissociation. And so, taking a look at our image down below over here on the left hand side. Notice we're showing the free enzyme associating with the inhibitor via this Ford Reaction arrow here, toe form the EI complex. And, of course, this reaction arrow. I's gonna have a rate constant that we're going to indicate as just k e for the formation of the EI complex. Now, over here on the right, notice that we're showing the enzyme substrate complex forming a complex with the inhibitor via this Ford reaction here to form the S I complex and this reaction rate constant here is just going to be K E s. I so e for the formation of the complex and s I for the formation of the complex. Now, for the dissociation of the EI complex backwards via this backwards reaction narrative form the free inhibitor in the free enzyme. Uh, this rate constant is just going to be k minus e i. And again, the minus indicates the dissociation of the EI complex. And so similarly, over here on the right, the dissociation of the S I complex via this backwards reactionary to form the free inhibitor complex or the free inhibitor and the enzyme substrate complex is just going to be this rate constants just going to be K minus e s I. So again, the minus indicates the dissociation. And so this here refreshes are memories of rate constants and introduces the fundamentals that we need toe understand the inhibition constant which we're going to define in our next lesson video. So I'll see you guys there

2

example

## Inhibition Constant Example 1

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all right, so here we have a two part example problem broken up into part A and part B. And so the example problem. In part, A. Says to consider the data in the chart down below over here, and it asks which enzyme has the strongest binding affinity for its substrate? And, of course, we know from our previous lesson videos that when it comes to the binding affinity that enzyme has for its substrate, that's going to be indicated by them. Achilles constant K M. And of course, the K M has an inverse relationship with the binding affinity. And so the smaller the value of the K m, the stronger the binding affinity. And so we want to look for the smallest K M. And the smallest K M of the three is going to be this one here 0.15 which corresponds with enzyme see. And so because Enzyme C has the smallest value for its McHale is constant. K M. Therefore, it has the strongest binding affinity, and so for part a up above, we can indicate that it's enzyme see, that has the strongest binding affinity and indicate that See, here is correct for part A. Now moving on to Part B. It's asking which enzyme has the strongest binding affinity not for its substrate but for its inhibitor. And of course, we know from our last lesson video that when it comes to the binding affinity that enzyme has for its inhibitor, that's gonna be indicated by the inhibition constant K I. And again, the K I has an inverse relationship to the binding affinity, just like the K M does. And so the smaller the value of the inhibition constant k I the greater or the stronger, the binding affinity. And so we wanna look for the smallest K I value and the smallest K I value is actually this value right here, 7.2 times 10 to the negative six. The greater the negative exponents here, the smaller the number is, and so enzyme A has the smallest value for the innovation constant K I, which therefore means that enzyme A has the strongest binding affinity for its inhibitor. And so, for Part B, we can indicate that it's enzyme a that has the strongest binding affinity for its inhibitor. And so this here concludes our example problem and we'll be able to get some practice in our next video, so I will see you guys there.

3

concept

## Inhibition Constant

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all right, so in this video, we're going to define the inhibition constant. But it's important to know that because inhibitors combined to either the free enzyme E and or the enzyme substrate complex E. S, there's actually a separate inhibition constant for the free enzyme E and for the enzyme substrate complex. And so, in this lesson video, we're on Lee going to focus on the inhibition constant for the free enzyme E. But then later, in a separate video, we'll talk about the inhibition constant for the enzyme substrate complex. And so now that we know that there's a separate inhibition constant for the free enzyme and the enzyme substrate complex, let's continue forward with the inhibition constant for the free enzyme. And so recall from our previous lesson videos that steady state conditions is referring to the set of conditions where the concentration of the enzyme substrate complex remains exactly the same during an enzyme catalyzed reactions. But it turns out that steady state conditions does not Onley apply to the enzyme substrate complex. It also applies to the enzyme inhibitor complexes, including the EI and the E S I complexes. But again here we're on Lee gonna focus on the free enzyme and e complex. And so what this means is that the steady state conditions apply to the EI complex means that the rate of formation of the EI complex is gonna be exactly equal to the rate of the breakdown of the eye complex. And so, in our previous lesson videos just like how we were able to derive the McHale is constant. K m. Under these steady state conditions were also able to derive these inhibition constant K I from these same exact steady state conditions. And so the inhibition constant k I is just the dissociation constant for the free enzyme inhibitor complex or the E I complex. And as we'll see as we move forward in this video, the inhibition constant K I is really parallel to the Michaelis constant K m. And they are very, very similar to one another and so similar to how the Michaelis constant K M is equal to a substrate concentration. And we know from our previous lesson videos that the K M is equal to the exact substrate concentration that allows for the initial reaction Velocity V not to equal half of the V Max. The the Inhibition Constant K I is also equal to a concentration, but it's not the substrate concentration. It's actually the inhibitor concentration, and it's the exact inhibitor concentration that allows for half of the maximum inhibition and also similar to how the McHale is constant. K M is a measure and a representation of the enzyme substrate binding affinity, the inhibition constant K I is also a measure and a representation of the enzyme inhibitor binding affinity. And just like the Michaelis constant, K M has an inverse relationship with the binding affinity, the inhibition constant K. I also has an inverse relationship with the binding affinity. And so what this means is that the smaller the value of the inhibition constant k I the stronger or the greater the binding affinity and enzyme will have for that particular inhibitor. And so you can really see here how the inhibition constant K I has a lot of similarities to the McKeel is constant, K m. And really, as we'll see moving forward in our course, it's really just swapping out the substrate with the inhibitor. And so if we take a look at our image down below notice up above here. What we have is the same enzyme catalyzed reaction that we've seen so many times before in our previous lesson videos and again, over here on the right, what we have is just some review from our previous lesson videos. And we know that the McHale is constant. K m is equal to the ratio of the enzyme substrate complex dissociation over the enzyme substrate complex association. And so we know that the Michaelis constant K M is defined as these two ratios that we see over here from our previous lesson videos. And so really, in this video, what we're learning that's new is the inhibition constant K I, which we know is very, very similar and comparable to the K. And and so notice that the inhibition constant K I is also equal to the dissociation over the association. But instead of the enzyme substrate complex instead of the E s, it is the enzyme inhibitor complex or the e I. And so we already know from our last lesson video that the rate constant for the E I dissociation is just going to be K minus e i. And that's exactly what we see over here as well. So you can see over here on the left hand side, what we have is the free enzyme and, uh, the inhibitor interacting with the free enzyme. And of course, this association here is going to occur via the K E I rate constant and that forms the E I complex. And then, of course, once the inhibitor is bound to the enzyme, no reaction is capable of taking place. And so, uh, we know that the association is just going to be k e I. And so we can put that down below here. Okay, e i And then, of course, we know that, really. But when it comes to comparing the k m and the K I, all we really need to do is substitute the, uh, substrate that we see here with the inhibitor. And so that's exactly what we're gonna do over here as well. Just substitute the substrate with the inhibitor. And so what we get is the free enzyme concentration times, the free inhibitor concentration times, the enzyme inhibitor complex e I complex concentration. I'm sorry. Over the ei uh, concentration. And so really hear what we can take away from all of this is that the inhibition constant K I is a representation of the binding affinity that enzyme has for its inhibitor. And it's very, very, very comparable to the meticulous, constant K m except instead of E s. It is all about the e I, and so moving forward in our course, we're gonna be able to get some practice applying these concepts, so I'll see you guys in our next video.

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Problem

ProblemUse the data in the chart below to determine the answer to the following:

A) Rank the enzymes in order of their binding affinity to their substrate (strongest affinity â†’ weakest affinity).

a) A â†’ B â†’ C.

b) C â†’ A â†’ B.

c) C â†’ B â†’ A.

d) B â†’ A â†’ C.

B) Rank the enzymes in order of their binding affinity to the inhibitor (strongest affinity â†’ weakest affinity).

a) A â†’ B â†’ C.

b) B â†’ C â†’ A.

c) C â†’ B â†’ A.

d) B â†’ A â†’ C.

C) Which enzyme would you expect the inhibitor to affect the most? Why?

a) Enzyme A.

b) Enzyme B.

c) Enzyme C.

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5

concept

## Inhibition Constant

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So in our previous lesson videos, we cover the inhibition constant of the free enzyme. But in this lesson video, we're going to cover the inhibition constant of the enzyme substrate complex. And so the inhibition constant of the enzyme substrate complex is denoted by the variable K prime I where the prime is this little apostrophe that we see right here. And really it's this prime or this apostrophe that distinguishes the two inhibition constants. And so the inhibition constant of the enzyme substrate complex K prime I is the dissociation constant for the enzyme substrate inhibitor complex or the E s I complex. Now the k prime. I is really the same exact thing as K I. The Onley riel difference is that k prime I measures the enzyme substrate complex affinity instead of just the free enzyme affinity for the inhibitor. And of course, this is going to form the E s I complex instead of just the e i complex. And so if we take a look at our image down below notice that k prime I, which is again the inhibition constant of the enzyme substrate complex, is denote it by this ratio of the e s I dissociation over the e s I association. And of course, the rate constant for the dissociation is just k minus s. I just like what we see over here and then the s association rate constant is gonna be K s. I just like what we see over here. And so notice that over here in our image that when the inhibitor interacts with the enzyme substrate complex, it forms the S. I. And when the inhibitor is bound to the enzyme in any way, the reaction is not going to be able to proceed. And, of course, as we already said, the rial difference between K. I and K Prime I is that k prime. I measures three es complex affinity instead of just the the free ends. I'm affinity. And so really, all we need to do for this ratio right years substitute the free ends. I'm with the enzyme substrate complex. And so what we end up getting is the concentration of enzyme substrate, complex times the concentration of free inhibitor, uh, over the concentration of the enzyme substrate inhibitor complex or the complex. And so it's these two ratios here that really define uh, k prime I and again K Prime. I is just a measure of the affinity that the enzyme substrate complex has for the inhibitor and three k prime. I is very, very comparable to the K I, which we know is very, very comparable to the McHale is constant. K m. And so moving forward in our course will be able to apply these concepts more and more. So I'll see you guys in our next video.

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Problem

ProblemCalculate the Michaelis constant (K_{m}) and the inhibition constant (K _{I}) given the following information:

[E] = 20 mM. [S] = 15 mM. [ES] = 5 mM. [I] = 8 mM. [EI] = 2 mM.

A

K

_{m}= 7 mM ; K_{I}= 14 mM.B

K

_{m}= 10 mM ; K_{I}= 20 mM.C

K

_{m}= 20 mM ; K_{I}= 80 mM.D

K

_{m}= 60 mM ; K_{I}= 80 mM.E

K

_{m}= 60 mM ; K_{I}= 20 mM.