Inhibition Effects on Reaction Rate: Study with Video Lessons, Practice Problems & Examples

In enzyme kinetics, the presence of inhibitors modifies the Michaelis-Menten and Lineweaver-Burk equations by incorporating the degree of inhibition factors, alpha (α) and alpha prime (α'). These factors relate to inhibition constants (K_i and K'_i), allowing biochemists to assess the initial reaction velocity (V₀). Competitive, uncompetitive, and noncompetitive inhibitors alter the apparent Michaelis constant (K_m) and V_max differently, emphasizing the need to substitute these values in the equations to understand their effects on enzyme activity.

Inhibition Effects on Reaction Rate

Alright. So now that we've covered the degree of inhibition on the free enzyme and the enzyme-substrate complex, alpha and alpha prime, as well as the apparent Km and the apparent V_max, in this video we're going to talk about the inhibition effects on reaction rate. Way back in our previous lesson videos, we talked about two different equations that allowed us to calculate the initial reaction velocity or the V₀ of an enzyme-catalyzed reaction. Those two equations that we talked about were the Michaelis-Menten equation and the Lineweaver-Burk equation. If alpha and alpha prime are degree of inhibition factors that quantify the effect that an inhibitor has on this initial reaction velocity, then that must mean that these two equations, the Michaelis-Menten and the Lineweaver-Burk equations, must include the degree of inhibition factors specifically in the presence of inhibitors. In our next lesson video, we're going to talk about how both alpha and alpha prime can be included in the Michaelis-Menten and the Lineweaver-Burk equations, depending on the type of inhibitor. I'll see you guys in that video there.

Inhibition Effects on Reaction Rate

So from our last lesson video, we know that the Michaelis-Menten and the Lineweaver-Burk equations are going to change just a little bit in the presence of inhibitors because we know that alpha and alpha prime are going to be included into these equations in the presence of inhibitors. Now from our previous lesson videos, we know that the inhibition constants ki and ki' are very, very similar to the Michaelis constant km. And we know for sure that the Michaelis constant km is definitely included in the Michaelis-Menten and Lineweaver-Burk equations. But it turns out that the inhibition constants kI and or kI' can also be included into the Michaelis-Menten as well as the Lineweaver-Burk equations. And so, this allows biochemists to measure the inhibitor effects on the initial reaction velocity or the vn0 of an enzyme-catalyzed reaction in the presence of inhibitors. Now, even though kI and kI' are definitely included in these equations in the presence of inhibitors, they're not directly included and so they're actually going to be indirectly included via the degree of inhibition factors and so, there recall that the degree of inhibition factors are alpha and alpha prime. And so, recall from our previous lesson videos that alpha and alpha prime can be defined using the inhibition constants ki and ki'. And so even though when we look at our, equations down below, we're not going to see kI and kI'. But when we see that alpha and alpha prime are included, we know that they include kI and kI' indirectly. And so, we covered this in our previous lesson videos, but it's important to emphasize here that depending on the type of inhibitor, alpha and or alpha prime can impact the Kilometers and or the V Max in different ways and we'll be able to see that down below. But when it comes down to it, in the presence of inhibitors, all we need to do is simply substitute the normal Kilometers and Vmax that are present in the Michaelis-Menten equations with the apparent Kilometers and the apparent V Max from the appropriate inhibitor. And so we covered the different apparent KMs and apparent V Maxes in our previous lesson videos. And so, if you compare and contrast, you'll be able to see how these equations down below will change. Simply, by substituting the kilometers and the v max into these equations. And so there's a lot of information here in, this table. And so I definitely do not expect you guys to memorize all of these equations, in the presence of inhibitors right now. And, actually, as we move forward in our course, we're going to revisit each of these equations, in our future videos, for these different types of inhibitors. And so, right now, all I really want you guys to take away from this video is that again, depending on the type of inhibitor, the Michaelis-Menten as well as the Lineweaver-Burk equations can change in different ways. And so, all we need to do to figure out how they change is, simply by substituting the Kilometers, the apparent Kilometers, and the apparent V MAX. And so, this first row right here here is specifically, how, competitive inhibitors affect the Michaelis-Menten and the Lineweaver-Burk equation. And so notice really the only way that it changes is, we substitute the, Kilometers with the apparent Kilometers for the competitive inhibitor. And then, we just take the reciprocal of this equation and what we get is this equation here. Now, we can do the same for the next row here, which is specifically for uncompetitive inhibitors and how uncompetitive inhibitors, can, alter the Michaelis-Menten equation, in the presence of inhibitors. And so again, all we do is we substitute the Vmax with the apparent Vmax and we substitute the Kilometers with the apparent Kilometers. And then, all we need to do is take the reciprocal of this equation to get this equation over here. And so, down below, in this last row, what we have is how mixed as well as noncompetitive inhibitors, affect the Michaelis-Menten and Weinweaver equations. And, again, all we need to do is substitute the apparent V Max, here and then, of course the apparent Kilometers here. And then, if we want to get this equation, we just take the reciprocal of this equation here. And so, again, no need to memorize all of this. We're going to revisit everything that's here moving forward but one of the main takeaways is that again, depending on the type of inhibitor, the Michaelis-Menten and Lineweaver-Burk equations will be, different from one another and they're different because the apparent KMs and apparent Vmaxs are different. And so this concludes our introduction to how these equations can be modified in the presence of inhibitors and I'll see you guys in our next, video.

Select the option below that best fills in the blanks in order of their appearance in the following sentence:

In terms of the effects that the common types of reversible inhibitors can have on an enzyme's kinetic variables such as K_m and V_max, notice that regardless of the type of inhibitor used, the ______ is always either unaltered or ______________, whereas the ______ can either be increased, decreased or remain unchanged depending on the type of inhibitor.

• A. K_m ; increased ; V_max.
• B. K_m ; decreased ; V_max.
• C. V_max ; increased ; K_m.
• D. V_max ; decreased ; K_m.

Here’s what students ask on this topic:

How do competitive inhibitors affect the Michaelis-Menten equation?

Competitive inhibitors increase the apparent Michaelis constant (Km) without affecting the maximum reaction velocity (Vmax). In the presence of a competitive inhibitor, the Michaelis-Menten equation is modified to include the degree of inhibition factor, α. The modified equation is:

$\frac{V=\frac{V\_\max \left[S\right]}{K\_m+\alpha \left[S\right]}}{}$

Here, α is defined as 1 + [I]/Ki, where [I] is the inhibitor concentration and Ki is the inhibition constant. This modification reflects the increased Km, indicating that a higher substrate concentration is needed to reach half of Vmax in the presence of a competitive inhibitor.

What is the difference between competitive and noncompetitive inhibition in enzyme kinetics?

Competitive inhibition occurs when an inhibitor competes with the substrate for binding to the active site of the enzyme. This increases the apparent Km (Michaelis constant) but does not affect Vmax (maximum reaction velocity). Noncompetitive inhibition, on the other hand, occurs when an inhibitor binds to an allosteric site on the enzyme, not the active site. This type of inhibition decreases the apparent Vmax without changing the Km. In the presence of noncompetitive inhibitors, the enzyme's efficiency is reduced regardless of substrate concentration.

How do you calculate the degree of inhibition (α and α') in enzyme kinetics?

The degree of inhibition factors, α and α', quantify the effect of inhibitors on enzyme activity. They are calculated using the inhibition constants Ki and K'i. For competitive inhibitors, α is defined as:

$\alpha =1+\frac{\left[I\right]}{K\_i}$

For uncompetitive inhibitors, α' is defined as:

$\alpha \text{'}=1+\frac{\left[I\right]}{K\text{'}i}$

Here, [I] is the inhibitor concentration, Ki is the inhibition constant for competitive inhibition, and K'i is the inhibition constant for uncompetitive inhibition. These factors are used to modify the Michaelis-Menten and Lineweaver-Burk equations in the presence of inhibitors.

What are the effects of uncompetitive inhibitors on the Michaelis-Menten equation?

Uncompetitive inhibitors bind only to the enzyme-substrate complex, not to the free enzyme. This type of inhibition decreases both the apparent Km and Vmax. The modified Michaelis-Menten equation in the presence of an uncompetitive inhibitor includes the degree of inhibition factor, α', and is given by:

$\frac{V=\frac{V\_\max \left[S\right]}{\frac{K\_m}{\alpha }}}{}$

Here, α' is defined as 1 + [I]/K'i, where [I] is the inhibitor concentration and K'i is the inhibition constant. This modification reflects the simultaneous decrease in Km and Vmax, indicating that the enzyme's efficiency is reduced in the presence of an uncompetitive inhibitor.

How do mixed inhibitors affect enzyme kinetics?

Mixed inhibitors can bind to both the free enzyme and the enzyme-substrate complex, but with different affinities. This type of inhibition affects both the apparent Km and Vmax. The degree of inhibition factors, α and α', are used to modify the Michaelis-Menten equation:

$\frac{V=\frac{V\_\max \left[S\right]}{\frac{K\_m\alpha }{\alpha }}}{}$

Here, α is defined as 1 + [I]/Ki and α' is defined as 1 + [I]/K'i, where [I] is the inhibitor concentration, Ki is the inhibition constant for binding to the free enzyme, and K'i is the inhibition constant for binding to the enzyme-substrate complex. Mixed inhibition results in a decrease in Vmax and a change in Km, depending on the relative values of α and α'.