Vmax Enzyme - Online Tutor, Practice Problems & Exam Prep

The maximum reaction velocity (Vmax) of an enzyme represents the theoretical peak rate achievable at saturating substrate concentrations, where all active sites are occupied. Vmax can be expressed through a rate law, linking it to the total enzyme concentration (ET), which directly influences Vmax; higher ET results in a greater Vmax. The initial reaction velocity (v₀) approaches Vmax under these conditions, allowing for effective analysis of enzyme kinetics. Understanding these relationships is crucial for studying enzyme behavior and catalysis in biochemical reactions.

Vmax Enzyme

In this video, we're going to begin talking about the maximum reaction velocity, or the V_max, of an enzyme. So already from our previous lesson videos, we've mentioned the V_max a good handful of times. So we already kinda know that the V_max is just the maximum reaction velocity of an enzyme. But really the V_max is more than just that. And the V_max is actually better defined as the theoretical maximum reaction velocity of an enzyme that can only occur at infinitely large substrate concentrations graphically. And by infinitely large substrate concentrations, what we really mean are substrate concentrations that are so large that the substrate is completely saturating all of the active sites that are available on all of the available enzymes. And so by theoretical maximum reaction velocity, what we mean is that the reaction velocities of enzyme catalyzed reactions can only approach the V_max or get really, really close to the V_max, but the V_max can actually never be attained by any enzyme, and so that's why it's better suited as the theoretical maximum velocity.

Now, recall from our previous lesson videos on the initial velocity of an enzyme catalyzed reaction that the initial velocity, or the V₀, is actually a reaction's best chance at approaching the maximum velocity V_max, and that's partially why biochemists tend to focus on measuring the initial velocity of enzyme catalyzed reactions. Now, in our typical enzyme kinetics plot, the V_max acts as a horizontal asymptote to limit the reaction velocity.

And so, let's take a look down below at our image to clear some of this up. Now, notice over here on the left what we have is an enzyme kinetics plot where we have the initial reaction rate or the V₀ on the y-axis and we have the substrate concentration on the x-axis. And, of course, we've got our typical curve that we tend to see for so many different enzymes. And so notice that at low substrate concentrations, we have a pretty low initial reaction rate. At medium substrate concentrations, we tend to have a medium initial reaction rate. However, at really, really high substrate concentrations, notice that our initial reaction rate begins to approach this horizontal asymptote line right here, which actually indicates the maximal reaction velocity or the V_max of our enzyme.

And so if we take a look and zoom in on each of these different images here, we get this image that we see here on the right. And so, notice that if we look at low substrate concentrations and zoom in on low substrate concentrations over here, we have the substrate in this pink little dot and then we have the enzyme in these red, brownish structures here. And so notice that at low substrate concentrations, most of the enzymes are actually not occupied. Their active sites are empty, and we only have a very little bit of enzymes that are actually occupied and forming the enzyme-substrate complex. And so what this means is that at low substrate concentrations, we're going to have a low initial reaction rate.

Now, if we increase the concentration just a little bit so that we have medium substrate concentration, notice that if we zoom in on that, that we have still, some enzymes are not occupied with substrate. And, even though we have more enzymes that are forming the enzyme-substrate complex, not all of them are forming the enzyme-substrate complex, and for that reason we just have a medium amount of initial reaction rate.

Now, notice that when we increase the substrate concentration to a point where it's really really high, we will get this box right here that has high substrate concentrations. And so notice all of these pink little dots that we see that represent our substrate. It's really, really high concentration. And when our concentration is high enough to the point where the enzyme is actually saturated with the substrate, that is a point where all of the enzyme that is present is forming the enzyme-substrate complex. And so what we can say is that the total amount of enzyme here, notice e_T, is going to be equal to the concentration of the enzyme-substrate complex. And so when this becomes true, then the enzyme is capable of approaching its V_max, its maximal reaction velocity.

And so this here concludes our introduction to the V_max and the maximum reaction velocity, and as we move forward in our course we're going to be able to continue to utilize all of these different concepts that we've learned here. So I'll see you guys in our next video.

In a Michaelis-Menten kinetics plot (V0 vs. [S]), what is the reason that the curve reaches a plateau and V0 cannot increase any further upon adding more substrate?

• A. The enzyme becomes locked in an inactive conformation.
• B. Enzymes match rate of catalysis & rate of ES formation.
• C. The active site of all the enzymes are saturated with substrate.
• D. There is an inhibitor present.
• E. Vmax can only be attained by some enzymes.
• F. Enzyme is locked in an inactive conformation.

Vmax Enzyme

Alright. So now that we've covered a little bit about the \( V_{\text{max}} \) of an enzyme, in this video, we're going to talk about a different way to express the \( V_{\text{max}} \), and that is by expressing the \( V_{\text{max}} \) with a rate law. Now, we know from our previous lesson videos on rate laws that the rate law is just an alternative way to express the reaction rate or the reaction velocity. And because the \( V_{\text{max}} \) is a reaction velocity, then we kind of should have already known that \( V_{\text{max}} \) could be expressed with a rate law. And so, what we need to recall from our previous lesson video, is that \( V_{\text{max}} \) or the maximum reaction velocity can only occur at saturating substrate concentrations where all of the available enzyme active sites are 100% full or 100% occupied with substrate. And so, what we can say is that under saturating substrate concentrations, the total concentration of enzyme will equal the concentration of enzyme substrate complex.

And so, what's really important to note is that the \( V_{\text{max}} \) and the total enzyme concentration relationship is actually expressed via substituting variables into the rate law that we're already familiar with from our previous lesson videos, and that is the rate law of the product formation step. Notice down below in our image, we have broken it up into two different sections. We have this section over here on the left, which is essentially review information from our previous lesson videos, no new information over there. And, this image over here on the right is the new information that we're introducing in this video.

And so, just to do some review from our previous lesson videos, recall that the reaction rate or the reaction velocity, including the initial reaction velocity, can commonly be expressed as the change in the product concentration over the change in time. Initially, during a typical enzyme catalyzed reaction, this is how it can be expressed. And we know, initially there's only one rate constant that actually affects the change in the product concentration as we see up above. And that rate constant that affects the change in product concentration directly is \( k_2 \). If we focus on drawing, or writing the rate law for this product formation step here, it's going to include the rate constant. And so we already know that the rate law for the product formation step, is just going to be the initial reaction velocity \( v_0 \), which is equal to the rate constant for the product formation step, which is \( k_2 \) times the reactant for this particular reaction arrow, and the reactant for this arrow is actually the enzyme substrate complex. And because this is going to be a simple reaction, we know that the coefficient of 1 is going to equal the reaction order, so it's just 1. So essentially, this here is the rate law for the product formation step. All of these rate laws, be sure to go back and check out our rate law videos and those topics.

Now over here on the right, we're going to cover the new information that we're introducing here and that is that we can actually variable, do variable substitution into this rate law right here in order to get the rate law for the \( V_{\text{max}} \). And so what we need to recall is that under saturating substrate concentrations, we know that the initial reaction velocity \( v_0 \) can actually approach the maximum reaction velocity \( V_{\text{max}} \). And so they're going to be approximately equal to each other under saturating substrate concentrations. And what we also need to know is that also under saturating substrate concentrations, the total concentration of enzyme \( E_T \) is going to equal the concentration of enzyme substrate complex just like what we said up above here.

And so, essentially by substituting these variables here into the rate law down below, we can actually get the rate law for the \( V_{\text{max}} \). And so if we take this \( v_0 \) here and substitute it with the \( V_{\text{max}} \), then we can place \( V_{\text{max}} \) right here in this position. And if we take the enzyme substrate complex concentration and substitute that with the total enzyme substrate concentration, then we can place it in here. And so, the rate constant is still going to be \( k_2 \). Essentially what we're saying is that this right here is the rate constant for \( V_{\text{max}} \), and so this is an alternative way to express \( V_{\text{max}} \). And so, later in our course, we're going to talk about different ways to be able to calculate the \( V_{\text{max}} \), in different types of practice problems. But for now all I want you guys to realize is that through understanding that under saturating substrate concentrations, these variables will be equal to each other, we can actually get the rate law, for the \( V_{\text{max}} \) and express \( V_{\text{max}} \) with a rate law. And so that concludes our lesson on how \( V_{\text{max}} \) can be expressed with a rate law and I'll see you guys in our next video.

Vmax Enzyme

So it's also important to note that the theoretical maximal reaction velocity or the V_max is actually directly impacted; the greater the total enzyme concentration, the greater the V_max will be. Before we get to our example down below, I want to point out that we should have already known this from our previous lesson video on the rate law. Recall that the V_max rate law is expressed right here. We covered this in our last lesson video, and we can clearly see that the total enzyme concentration will directly impact the V_max of the reaction; the greater this total enzyme concentration is, the greater the V_max will be.

If we take a look at our example down below to analyze the graph and get a more visual understanding of what this looks like, notice here in this graph that we have an enzyme kinetics plot where we have the initial reaction rates or the V₀ on the y-axis and the substrate concentration on the x-axis. We see two different curves here: a red curve and a green curve. This green curve has double the total concentration of enzymes compared to the red curve. Because it has double the total concentration, the theoretical maximum reaction velocity or the V_max is also doubled since the total enzyme concentration is also doubled.

We can see that by increasing the total enzyme concentration, this will also increase not only the initial reaction velocity but also the maximal reaction velocity, V_max. This is important to note as we move forward in our course when we're trying to compare the V_max of different enzyme-catalyzed reactions fairly. That concludes our lesson, and I'll see you guys in our next video.

V₀ for an enzyme-catalyzed reaction:

• A. Increases when pH increases.
• B. Is limited by the [S].
• C. Is limited by the [E].
• D. Is limited by the reaction's slowest step.
• E. b & c.
• F. b, c & d.

What kind of kinetics is observed initially in an enzymatic reaction under conditions where [S] is saturating?

• A. Cooperative kinetics.
• B. First order kinetics.
• C. Zero order kinetics.
• D. Second order kinetics.
• E. The system is at equilibrium and reaction proceeds equally in both directions.

Here’s what students ask on this topic:

What is Vmax in enzyme kinetics?

Vmax, or maximum reaction velocity, represents the theoretical peak rate of an enzyme-catalyzed reaction when the substrate concentration is so high that all enzyme active sites are fully occupied. It is an asymptotic value that the reaction rate approaches but never actually reaches. Vmax is crucial for understanding enzyme efficiency and behavior under different conditions. It is influenced by the total enzyme concentration (E_T), with higher E_T leading to a greater Vmax.

How is Vmax related to enzyme concentration?

Vmax is directly proportional to the total enzyme concentration (E_T). This relationship is expressed in the rate law for Vmax, where Vmax = k₂ [E_T]. As the total enzyme concentration increases, the Vmax also increases. This is because more enzyme molecules are available to form enzyme-substrate complexes, thereby increasing the maximum possible reaction rate.

Why can Vmax never be truly attained in enzyme-catalyzed reactions?

Vmax is considered a theoretical maximum because it represents the reaction rate at infinitely high substrate concentrations, where all enzyme active sites are fully occupied. In practical terms, it is impossible to achieve such infinite substrate concentrations. Therefore, the reaction rate can only approach Vmax asymptotically but never actually reach it.

How can Vmax be expressed using a rate law?

Vmax can be expressed using a rate law by substituting variables into the rate law for the product formation step. Under saturating substrate conditions, the initial reaction velocity (v₀) approaches Vmax, and the total enzyme concentration (E_T) equals the enzyme-substrate complex concentration. The rate law for Vmax is given by Vmax = k₂ [E_T], where k₂ is the rate constant for the product formation step.

What factors influence the Vmax of an enzyme-catalyzed reaction?

The primary factor influencing Vmax is the total enzyme concentration (E_T). Higher E_T results in a greater Vmax. Additionally, the rate constant (k₂) for the product formation step also affects Vmax. Environmental factors such as pH, temperature, and the presence of inhibitors or activators can indirectly influence Vmax by affecting enzyme activity and stability.