Degree of Inhibition: Videos & Practice Problems

Enzyme inhibitors decrease the initial reaction velocity (v₀) of enzyme-catalyzed reactions, quantified by the degree of inhibition. For the free enzyme, this is represented by α = 1 + (I/K_I), where I is the inhibitor concentration and K_I is the inhibition constant. An α value of 1 indicates no inhibitor, while values greater than 1 signify inhibition. Similarly, the degree of inhibition on the enzyme-substrate complex is denoted as α' = 1 + (I/K'_I), modifying Michaelis-Menten and Lineweaver-Burk equations in the presence of inhibitors.

Degree of Inhibition

Alright. So now that we've introduced the inhibition constant, the next topic that we're going to cover before we actually get into the details of the different types of reversible inhibitors is the degree of inhibition. Recall from our previous lesson videos, we said that enzyme inhibitors, by definition, will decrease the initial reaction rate or velocity \( v_0 \) of an enzyme-catalyzed reaction. But here we have a question, and really it's just asking how can biochemists measure the inhibitor effects on the initial reaction velocity \( v_0 \) of an enzyme-catalyzed reaction? It turns out that the answer to this question is the degree of inhibition. And so the degree of inhibition is really just a factor that measures and quantifies how much an enzyme is being inhibited by the inhibitor.

Recall from our previous lesson videos that enzyme inhibitors can either bind to the free enzyme to form the \( E\cdot I \) complex or enzyme inhibitors could also bind to the enzyme-substrate complex to form the \( E\cdot S\cdot I \) complex. Because enzyme inhibitors can bind to either the free enzyme or the enzyme-substrate complex, biochemists can actually separately measure the degree of inhibition on the free enzyme and the enzyme-substrate complex.

In our next lesson video, we're going to focus on the degree of inhibition on the free enzyme, but later in a separate video, we'll talk about the degree of inhibition on the enzyme-substrate complex. And so I'll see you guys in our next video.

Degree of Inhibition

Alright. So in this video, we're going to talk about the degree of inhibition on the free enzyme. And so the degree of inhibition on the free enzyme is represented with the Greek variable alpha. And so the degree of inhibition on the free enzyme alpha is just equal to α=1+concentration of inhibitorinhibition constant. And so this degree of inhibition on the free enzyme alpha is a unitless factor that is always greater than or equal to 1. And so here you can see that alpha will always be greater than or equal to 1. Now when there's no inhibitor present at all, that means that alpha is going to equal exactly 1. And then as alpha begins to increase, then the concentration of inhibitor will also increase. So a value of alpha greater than 1 means that there is an inhibitor present. And, of course, the greater alpha is, the more inhibitor is present.

And so if we take a look at our image down below, notice over here on the left hand side what we have is the same enzyme catalyzed reaction that we've seen so many times before in our previous lesson videos. And so here in this video, we're specifically focusing on, again, the degree of inhibition on the free enzyme alpha. And so that means that the inhibitor here is going to be only inhibiting the free enzyme as we see here. And so, of course, we know that when the inhibitor is bound to the enzyme, no reaction is able to take place. And so, here what we can see, again, what we're emphasizing is that the degree of inhibition on the free enzyme is equal to the variable alpha. And alpha is just equal to, again, α=1+concentration of inhibitorinhibition constant.

And so, if we take a second and think about what this here actually means, we know that, of course, the concentration of inhibitor is either going to be 0 or some positive number. We're never going to have a negative number for the concentration of inhibitor. We know from our previous lesson videos that the inhibition constant \( K_I \) also represents a specific concentration of inhibitor. It's the exact concentration of inhibitor that allows for half of maximum inhibition. And so, if we have 2 concentrations here that are both positive, then that means that this ratio here is going to be positive. And of course, any positive number here, plus 1, is going to be greater than 1. And in this equation right here, there's no way that alpha is going to be less than 1. And so here, in our chart below where it says alpha is less than 1, what we can write is that it's simply not possible to have an alpha less than 1. We're never going to see that, in our course.

And so also notice that, if alpha is exactly equal to 1, as we mentioned up above in our lesson, if alpha is equal to 1, that means that there's going to be no inhibitor present. So essentially the inhibitor is going to be absent or we could just say that there's no inhibitor present when alpha is equal to 1. Now in our last scenario here we can see if alpha is greater than 1, that means that the inhibitor is indeed present and it will be inhibiting the enzyme. And so, we'll be able to show you guys an example of how to utilize this degree of inhibition on the free enzyme alpha, in our next video. So I will see you guys there.

Degree of Inhibition Example 1

Alright. So, here we have an example problem that's asking according to the data in the table below shown right here, which enzyme is affected most by the inhibitor? Is it enzyme A, enzyme B, or enzyme C? And so taking a look at this table over here, notice that for each of these three enzymes, we're given the degree of inhibition that the inhibitor has on each enzyme. And so, of course, the enzyme that has the greatest degree of inhibition is going to be the one that's going to be inhibited the most. And so enzyme B, because it has the greatest degree of inhibition here, it's going to be the one that's inhibited the most. And so we can go ahead and say that it's enzyme B here that is the correct answer for this example. Now, of course, we know that if the degree of inhibition is equal to 1, then what that means is, alpha will be equal to 1. And, if this is the case, that means that there will be essentially no inhibitor present, essentially as if the inhibitor were absent. And so, notice here that enzyme C has an alpha that is, really close to equaling 1. It's 1.02. And so what this means is that really the inhibitor has a very, very small effect on enzyme C and it doesn't really inhibit enzyme C that much. And so the main takeaway here that we want to get is that the greater the degree of inhibition, the more that enzyme will be inhibited by that enzyme inhibitor. And so, this here concludes our example, and I'll see you guys in our next video where we'll be able to get some practice.

Calculate the degree of inhibition of an inhibitor on the free enzyme if the [I] = 3 μM and the K_I = 6 μM.

• A. α = 1.5
• B. α = 2
• C. α = 4
• D. α = 3.5
• E. α = 0.5

Answer: (A)

Degree of Inhibition

Alright. So now that we've covered the degree of inhibition on the free enzyme, in this video we're going specifically talk about the degree of inhibition on the enzyme-substrate complex. The degree of inhibition on the enzyme-substrate complex or the substrate complex or the ES complex is represented as α_′, and the prime is this little apostrophe that we see here. The degree of inhibition on the enzyme-substrate complex α_′, of course, is going to quantify the effect that an inhibitor has on the enzyme-substrate complex.

Looking down at our image below, notice what we have is the same enzyme-catalyzed reaction that we've seen so many times before in our previous lessons. Notice that this time, the inhibitor is affecting the enzyme-substrate complex to form the ESI complex. And, of course, we know that anytime the inhibitor is bound to the enzyme like it is here, the reaction is not going to be able to take place.

Here in this video, what we're emphasizing is that the degree of inhibition on the enzyme-substrate complex is represented as α_′. And, of course, it's going to be very, very similar to the degree of inhibition on the free enzyme. It can be represented as 1+concentration of inhibitorinhibition constant. But notice that it actually uses the inhibition constant on the enzyme-substrate complex k_′I instead of the inhibition constant on the free enzyme, k_I.

So, you might be wondering why we are talking about these degrees of inhibitions, α and α_′? Well, it turns out that both α and α_′, degree of inhibitions, are going to be used as factors to modify the Michaelis-Menten and the Lineweaver-Burk equations that we're already familiar with from our previous lesson videos. α and α_′ will modify these two equations specifically in the presence of inhibitors. We'll be able to talk more about how α and α_′ can be used as factors in these two equations a little bit later in our course.

But for now, this concludes our introduction to the degree of inhibition on the enzyme-substrate complex, α_′, and we'll be able to get some practice utilizing these concepts in our next couple of videos. So I'll see you guys there.

Calculate the degree of inhibition of an inhibitor on the ES-complex if the [I] = 8 μM and the K'_I = 0.03 mM.

• A. α = 0.87
• B. α = 1.08
• C. α = 1.27
• D. α = 2.39
• E. α = 0.27

Answer: (C)

Here’s what students ask on this topic:

What is the degree of inhibition in enzyme kinetics?

The degree of inhibition in enzyme kinetics quantifies how much an enzyme's activity is reduced by an inhibitor. For the free enzyme, it is represented by the Greek letter α (alpha), calculated as:

$\alpha =1+\frac{I}{\mathrm{K_I}}$

where I is the inhibitor concentration and K_I is the inhibition constant. An α value of 1 indicates no inhibition, while values greater than 1 signify the presence of an inhibitor. For the enzyme-substrate complex, the degree of inhibition is denoted as α' (alpha prime) and is calculated similarly but uses a different inhibition constant, K'_I.

How do you calculate the degree of inhibition for a free enzyme?

The degree of inhibition for a free enzyme is calculated using the formula:

$\alpha =1+\frac{I}{\mathrm{K_I}}$

Here, I represents the concentration of the inhibitor, and K_I is the inhibition constant. This formula provides a unitless factor that is always greater than or equal to 1. When α equals 1, it indicates no inhibitor is present. As α increases, it signifies a higher concentration of the inhibitor, thus greater inhibition of the enzyme.

What is the difference between α and α' in enzyme inhibition?

In enzyme inhibition, α (alpha) and α' (alpha prime) represent the degree of inhibition for different enzyme states. α quantifies the inhibition of the free enzyme and is calculated as:

$\alpha =1+\frac{I}{\mathrm{K_I}}$

where I is the inhibitor concentration and K_I is the inhibition constant. α' quantifies the inhibition of the enzyme-substrate complex and is calculated similarly but uses a different inhibition constant, K'_I:

$\mathrm{\alpha \text{'}}=1+\frac{I}{\mathrm{K\text{'}_I}}$

Both factors modify the Michaelis-Menten and Lineweaver-Burk equations in the presence of inhibitors.

How does the degree of inhibition affect the Michaelis-Menten equation?

The degree of inhibition affects the Michaelis-Menten equation by modifying the apparent kinetic parameters in the presence of inhibitors. For competitive inhibition, the Michaelis-Menten equation is adjusted as:

$v=\frac{\mathrm{V_max}\mathrm{[S]}}{\alpha \mathrm{K_m}+\mathrm{[S]}}$

where α is the degree of inhibition for the free enzyme. For non-competitive inhibition, both α and α' modify the equation:

$v=\frac{\mathrm{V_max}\mathrm{[S]}}{\alpha \mathrm{K_m}+\mathrm{\alpha \text{'}}\mathrm{[S]}}$

These modifications help in understanding how inhibitors affect enzyme kinetics.

What does an α value of 1 indicate in enzyme inhibition?

An α value of 1 in enzyme inhibition indicates that no inhibitor is present. The formula for the degree of inhibition is:

$\alpha =1+\frac{I}{\mathrm{K_I}}$

When I, the inhibitor concentration, is zero, α equals 1. This means the enzyme is functioning without any inhibition. As the inhibitor concentration increases, α becomes greater than 1, indicating the presence and effect of the inhibitor on the enzyme's activity.