Inhibition Constant - Online Tutor, Practice Problems & Exam Prep

The inhibition constant (K_I) quantifies the binding affinity of an enzyme for an inhibitor, paralleling the Michaelis constant (K_M) for substrate affinity. K_I is derived from the dissociation constant of the enzyme-inhibitor complex (E_I), where a lower K_I indicates stronger binding. For the enzyme-substrate complex, the inhibition constant is denoted as K'_I, measuring the affinity of the enzyme-substrate-inhibitor complex (E_SI). Both constants reflect the dynamics of enzyme inhibition and are crucial for understanding enzyme kinetics.

Inhibition Constant

So before we actually get into the details of all the different types of reversible inhibitors, there are a couple of things that would be helpful for us to cover first, and one of those things is the inhibition constant. In this video, we're going to begin our introduction to the inhibition constant. 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 we already know that the rate constant k indicates the reaction rate efficiency or probability under set conditions, and the higher the value of the rate constant k, the more likely it is that the reaction will be faster.

Again, every reaction has a rate constant k, including the reactions that form and break down the enzyme inhibitor complexes, including the EI as well as the ESI complexes. It turns out that there is actually no universal notation for the rate constants of these inhibitor complexes. Here at Clutch Prep, we've chosen a very straightforward notation for these rate constants. For the rate constant for the inhibitor complex formation or association, it's just going to be KEI or KESI depending on if the EI complex is forming or the ESI complex is forming.

And the rate constant for the inhibitor complex breakdown or dissociation is just going to be K−EI or K−ESI. Again, depending on if the EI complex is breaking down or dissociating, or if the ESI complex is breaking down or dissociating. Essentially, the small minus sign here indicates the breakdown or dissociation.

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 forward reaction arrow here to form the EI complex. This reaction arrow is going to have a rate constant that we're going to indicate as just KEI 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 forward reaction here to form the ESI complex, and this reaction rate constant here is just going to be KESI.

Now, for the dissociation of the EI complex backwards via this backward reaction arrow to form the free inhibitor and the free enzyme, this rate constant is just going to be K−EI. And again, the minus indicates the dissociation of the EI complex. And so, similarly, over here on the right, the dissociation of the ESI complex via this backward reaction arrow to form the free inhibitor complex or the free inhibitor and the enzyme substrate complex is just going to be this rate constant is just going to be K−ESI. So again, the minus indicates the dissociation.

This here refreshes our memories of rate constants and introduces the fundamentals that we need to understand the inhibition constant, which we're going to define in our next lesson video. So I'll see you guys there.

Inhibition Constant Example 1

Alright, so here we have a 2-part example problem broken up into part a and part b. 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? We know from our previous lesson videos that when it comes to the binding affinity that an enzyme has for its substrate, that's going to be indicated by the Michaelis constant \( K_M \). The \( K_M \) has an inverse relationship with the binding affinity, so the smaller the value of the \( K_M \), the stronger the binding affinity. We want to look for the smallest \( K_M \). The smallest \( K_M \) of the three is going to be this one here, 0.015, which corresponds with enzyme C. Because enzyme C has the smallest value for its Michaelis constant \( K_M \), it therefore has the strongest binding affinity. For part a, we can indicate that it's enzyme C that has the strongest binding affinity and indicate that C 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. We know from our last lesson video that when it comes to the binding affinity that an enzyme has for its inhibitor, that's going to be indicated by the inhibition constant \( K_I \). Again, the \( K_I \) has an inverse relationship to the binding affinity just like the \( K_M \) does, so the smaller the value of the inhibition constant \( K_I \), the greater or the stronger the binding affinity. We want to look for the smallest \( K_I \) value, and the smallest \( K_I \) value is actually this value right here, \( 7.2 \times 10^{-6} \). The greater the negative exponent here, the smaller the number is. Enzyme A has the smallest value for the inhibition constant \( K_I \) which therefore means that enzyme A has the strongest binding affinity for its inhibitor. For part b, we can indicate that it's enzyme A that has the strongest binding affinity for its inhibitor. 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.

Inhibition Constant

Alright, so in this video, we're going to define the inhibition constant, but it's important to know that because inhibitors can bind to either the free enzyme E and or the enzyme-substrate complex ES, 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 only 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 are referring to the set of conditions where the concentration of the enzyme-substrate complex remains exactly the same during an enzyme-catalyzed reaction, but it turns out that steady state conditions do not only apply to the enzyme-substrate complex. It also applies to the enzyme inhibitor complexes including the EI and the ESI complexes, but again, here we're only going to focus on the free enzyme and the EI complex. And so, what this means is that the steady state conditions applied to the EI complex means that the rate of formation of the EI complex is going to be exactly equal to the rate of the breakdown of the EI complex. And so in our previous lesson videos, just like how we were able to derive the Michaelis constant Km, under these steady state conditions, we're also able to derive the inhibition constant, Ki from these same exact steady state conditions. And so the inhibition Ki is just the dissociation constant for the free enzyme inhibitor complex or the EI complex. And as we'll see as we move forward in this video, the inhibition constant Ki is really parallel to the Michaelis constant Km and they are very similar to one another. And so, similar to how the Michaelis constant Km is equal to a substrate concentration and we know from our previous lesson videos that the Km is equal to the exact substrate concentration that allows for the initial reaction velocity V0 to equal half of the Vmax. The inhibition constant Ki 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 Michaelis constant Km is a measure and a representation of the enzyme-substrate binding affinity, the inhibition constant Ki is also a measure and a representation of the enzyme inhibitor binding affinity. And just like the Michaelis constant Km has an inverse relationship with the binding affinity, the inhibition constant Ki also has an inverse relationship with the binding affinity. And so what this means is that the smaller the value of the inhibition constant Ki, the stronger or the greater the binding affinity an enzyme will have for that particular inhibitor. And so you can really see here how the inhibition constant Ki has a lot of similarities to the Michaelis constant Km, 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 Michaelis constant Km 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 Km 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 Ki which we know is very similar and comparable to the Km. And so notice that the inhibition constant Ki is also equal to the dissociation over the association. But instead of the enzyme-substrate complex, instead of the ES, it is the enzyme inhibitor complex or the EI. And so we already know from our last lesson video that the rate constant for the EI dissociation is just going to be k-ei. 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 the inhibitor interacting with the free enzyme. And of course, this association here is going to occur via the KEI rate constant and that forms the EI complex. And then of course we know that really, but, when it comes to comparing the Km and the Ki all we really need to do is substitute the substrate that we see here with the inhibitor. And so that's exactly what we're going to 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 × the enzyme inhibitor complex, the EI complex concentration. I'm sorry, over the EI concentration. And so, really here what we can take away from all of this is that the inhibition constant Ki is a representation of the binding affinity that an enzyme has for its inhibitor and it's very comparable to the Michaelis constant Km except instead of the ES it is all about the EI. And so moving forward in our course, we're going to be able to get some practice applying these concepts. So, I'll see you guys in our next video.

Use 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 → weakest affinity).

a) A → B → C. 

b) C → A → B. 

c) C → B → A. 

d) B → A → C.

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

a) A → B → C. 

b) B → C → A. 

c) C → B → A. 

d) B → A → C.

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

a) Enzyme A. 

b) Enzyme B. 

c) Enzyme C.

Alright. So here we have a 3 part practice problem broken up into part a, b, and c. The problem says to use the data in the chart below to determine the answer to the following. Taking a look at our chart down below, notice that we are given these 3 different enzymes, enzyme a, b, and c, and then we are given the catalytic constant or the kcat or the turnover number in units of inverse seconds for each of the 3 enzymes, the Michaelis constant or the Km in units of molarity for each of the 3 enzymes, the specificity constant ratio or the kcat/Km in units of inverse molarity inverse seconds for each of these 3 enzymes as well as the inhibition constant of the free enzyme Ki in units of molarity for each of these 3 enzymes. And so part a here wants us to rank the enzymes in order of their binding affinity to their substrate, ranking them from their strongest affinity to their weakest affinity. We know from our previous lesson videos that an enzyme's binding affinity to its substrate is indicated by the Michaelis constant Km. We also know that the Km has an inverse relation with the binding affinity, so the smaller the value of the Km, the stronger the binding affinity. We want to look for the smallest Km, and the smallest Km is enzyme C followed by enzyme B, and then enzyme A has the greatest Km making it have the weakest affinity, and so the ranking for these enzymes will be enzyme C has the strongest, enzyme B the next, and then enzyme A has the weakest affinity. The answer option that indicates this order is answer option C. We can go ahead and indicate that C here is the correct answer for part a. Moving on to the next part, part b, it also wants us to rank the enzymes in order of their binding affinities. But this time, it's not about the binding affinity to the substrate, it's about the binding affinity to the inhibitor. It wants us to rank the enzymes in terms of their binding affinity to the inhibitor from strongest affinity to the weakest affinity. From our previous lesson videos, we know that an enzyme's binding affinity to the inhibitor is indicated by the inhibition constant Ki and the Ki is very comparable to the Michaelis constant Km and has an inverse relationship with the binding affinity. The smaller the value of the Ki, the stronger the binding affinity. The enzyme that has the smallest Ki is enzyme A. Enzyme A has the smallest, the next smallest would be enzyme B, and then enzyme C has the greatest Ki making it have the weakest affinity. The order here is going to be enzyme A followed by B followed by C. That order is indicated by answer option A. We can go ahead and highlight A here and indicate A is the correct answer for part b. Moving on to our final part, part c, it asks which enzyme you would expect the inhibitor to affect the most and why? Well, when we take a look at our previous two answer options, notice that enzyme A has the weakest affinity to the substrate and it has the strongest affinity to the inhibitor. If it has a very weak affinity to the substrate and a strong affinity to the inhibitor, then it is going to be inhibited the most. Thus, we would expect for these reasons enzyme A to be the enzyme that is inhibited the most by this inhibitor. The reasons for this is because enzyme A has the weakest affinity for its substrate yet the strongest affinity for its inhibitor. This here concludes our answers to our practice problem, and I'll see you guys in our next video.

Inhibition Constant

So in our previous lesson videos, we covered 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', 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', is the dissociation constant for the enzyme-substrate-inhibitor complex or the ESI complex. Now, the k' is really the same exact thing as k_I. The only real difference is that k' 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 ESI complex instead of just the EI complex. And so, if we take a look at our image down below, notice that k', which is again the inhibition constant of the enzyme-substrate complex, is denoted by this ratio of the ESI dissociation over the ESI association. And of course, the rate constant for the ESI dissociation is just k_-ESI just like what we see over here. And then the ESI association rate constant is going to be k_ESI 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 ESI 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 real difference between k_I and k' is that k' measures the ES complex affinity instead of just the enzyme the free enzyme affinity. And so really all we need to do for this ratio right here is substitute the free enzyme 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 over the concentration of the enzyme-substrate-inhibitor complex or the ESI complex. And so, it's these two ratios here that really define, k'. And again, k' is just a measure of the affinity that the enzyme-substrate complex has for the inhibitor. And, the k' is very comparable to k_I which we know is very comparable to the Michaelis constant, k_m. And so, moving forward in our course, we'll be able to apply these concepts more and more. So, I'll see you guys in our next video.

Calculate 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.

Here’s what students ask on this topic:

What is the inhibition constant (KI) in enzyme kinetics?

The inhibition constant (KI) in enzyme kinetics quantifies the binding affinity of an enzyme for an inhibitor. It is derived from the dissociation constant of the enzyme-inhibitor complex (EI). A lower KI value indicates a stronger binding affinity between the enzyme and the inhibitor. Mathematically, KI is represented as the ratio of the rate constant for the dissociation of the EI complex (k-1) to the rate constant for the formation of the EI complex (k1). This concept is crucial for understanding how inhibitors affect enzyme activity and is comparable to the Michaelis constant (KM), which measures substrate affinity.

How is the inhibition constant (KI) related to the Michaelis constant (KM)?

The inhibition constant (KI) is related to the Michaelis constant (KM) in that both measure binding affinities, but for different molecules. KI measures the binding affinity of an enzyme for an inhibitor, while KM measures the binding affinity of an enzyme for its substrate. Both constants are derived from the dissociation constants of their respective complexes. A lower KI or KM indicates a higher binding affinity. The mathematical expressions for KI and KM are similar, with KI being the ratio of the dissociation rate constant to the association rate constant for the enzyme-inhibitor complex, and KM being the same ratio for the enzyme-substrate complex.

What is the difference between KI and K'I in enzyme inhibition?

KI and K'I are both inhibition constants but measure different affinities. KI quantifies the binding affinity of an enzyme for an inhibitor when the enzyme is free, forming the enzyme-inhibitor complex (EI). K'I, on the other hand, measures the binding affinity of the enzyme-substrate complex (ES) for an inhibitor, forming the enzyme-substrate-inhibitor complex (ESI). The primary difference lies in the state of the enzyme: KI is for the free enzyme, while K'I is for the enzyme already bound to a substrate. Both constants are crucial for understanding different types of enzyme inhibition.

How do you calculate the inhibition constant (KI) in enzyme kinetics?

The inhibition constant (KI) in enzyme kinetics is calculated using the steady-state conditions of the enzyme-inhibitor complex (EI). Under these conditions, the rate of formation of the EI complex equals the rate of its dissociation. Mathematically, KI is given by the ratio of the dissociation rate constant (k-1) to the association rate constant (k1) for the EI complex. The formula is:

$K{I}_{}=\frac{k_{-}}{k_1}$

This calculation helps determine the binding affinity of the enzyme for the inhibitor.

Why is the inhibition constant (KI) important in drug design?

The inhibition constant (KI) is crucial in drug design because it provides a measure of how effectively a potential drug (inhibitor) can bind to its target enzyme. A lower KI value indicates a stronger binding affinity, which generally translates to more effective inhibition of the enzyme's activity. Understanding KI helps researchers design inhibitors that can effectively modulate enzyme activity, leading to the development of drugs with higher efficacy and specificity. This is particularly important in targeting enzymes involved in disease pathways, where precise inhibition can lead to better therapeutic outcomes.