Allosteric Enzyme Conformations: Videos & Practice Problems

Allosteric enzymes exist in two conformations: the tense (T) state, which is catalytically inactive with low substrate affinity, and the relaxed (R) state, which is catalytically active with high substrate affinity. The allosteric constant (L₀) represents the ratio of T to free R states in the absence of substrate, influencing the sigmoidal kinetics of enzyme activity. Positive cooperativity occurs when substrate binding to the R state facilitates further substrate binding, enhancing reaction velocity as substrate concentration increases, ultimately approaching V_max.

Allosteric Enzyme Conformations

In this video, we're going to begin our lesson on allosteric enzyme conformations. So recall that protein conformations are really just alternative three-dimensional states or forms that a protein can achieve. And so recall from our previous lesson videos where we covered protein structure that proteins are not completely rigid structures. Instead, we know that protein structures can be induced to changes. And again, we know that from our previous lesson videos where we covered the induced fit model that enzymes and proteins can display. It is important to note that different conformations that proteins can take on can actually have different abilities and/or functions. In our next lesson video, we're going to introduce the two conformations that allosteric enzymes can take on, and those two conformations are going to have different abilities and/or functions. I'll see you guys there.

Allosteric Enzyme Conformations

So from our last lesson video, we know that allosteric enzymes have 2 protein confirmations or states. And those 2 protein confirmations are the T state and the R state. And so allosteric enzymes can exist in either one of these 2 states. And so again, the 2 states are the T state, which stands for the tense state, and the R state, which stands for the relaxed state. And so, the allosteric enzyme confirmation T state is a catalytically inactive state. And so because it is catalytically inactive, that means that it's going to have a low affinity for the substrate. And so when the allosteric enzyme is in the T state confirmation, the allosteric enzyme is going to bind substrates very inefficiently. So the other allosteric enzyme confirmation is the R state, and the R state is essentially the opposite of the T state. And so the R state is a catalytically active state and of course, this means that the R state is going to have a high affinity for the substrate. And so when the allosteric enzyme is in the R state confirmation, the allosteric enzyme is going to bind substrates very, very efficiently.

And so notice down below in our example on the left-hand side over here, what we have is an allosteric enzyme that has 2 different subunits. One subunit right here and a second subunit right here. And so notice that this is actually the T state, confirmation of the allosteric enzyme. And, of course, the T state is the tense state. And so notice that the active sites here that are supposed to be binding substrate represented by this blue circle. The active sites are in a tense confirmation that are very, very small and therefore, the allosteric enzyme in the T state is not going to be able to bind substrate very, very efficiently. And so that means that the allosteric enzyme is going to be inactive and bind with low affinity to the substrates. And so that's why we have these x's here to show that the substrate cannot bind very efficiently to the T state.

Now, over here on the right-hand side, what we have is the same exact allosteric enzyme just in a different confirmation. This time, it's in the R state confirmation, and the R state is the relaxed state. And so notice that the enzyme's active site is in a more relaxed confirmation. It's much more open. And for that reason, the R state is the catalytically active state that binds substrates very, very efficiently. And so notice that the substrate can easily bind into the enzyme's active site when, the enzyme is in the R state.

And so notice down below, we have these images to help you guys better understand the T state and the R state. And again, recall that the T state is really the tense state. And so when you think about the tense state, you can think about Arthur's tense fist right here. And so Arthur's fist is so tight, there's no way he's going to be able to grab onto anything. And so, there's no way that a substrate is going to be able to fit in here because it is simply so tense. And so you can also think of the T state of the allosteric enzyme as a balled-up piece of paper, which is also very, very tensely balled up. And when it's so tense, again, it's pretty hard for a substrate to get to the inside and bind to this, balled-up tense state. Now, notice over here, what we have is the relaxed state. And so notice that Arthur's fist has actually become much more relaxed and it looks like that Arthur even got himself a nice looking manicure. And so when the, enzyme is in this relaxed R state, it's much easier for a substrate to fit into the enzyme's active site. And so the R state binds substrates very, very efficiently. And also notice what we have is in, a piece of paper that is a little bit uncrinkled. It's not as balled up and tense as it was over here. So again, it's much easier for a substrate to make its way into and, bind to the active site. And so hopefully all of these memory tools here will help you guys distinguish, the T state from the R state. And we'll be able to get some more practice utilizing all of these concepts as we move along through our course. So this concludes our introduction to the T state and R state, and I'll see you guys in our next video.

Allosteric Enzyme Conformations

In this video, we're going to introduce the allosteric constant, \( L_0 \). The allosteric constant is represented with the variable \( L_0 \), and it is simply a ratio. It's the ratio of the concentration of T states over the concentration of free R states. Essentially, it is the ratio of the concentration of T over the concentration of R, but specifically when there is no substrate present. The reason for this is because it turns out that this ratio of the T states over the R states can change when we alter the concentration of substrate, but we'll talk more about that idea later in our course. For now, all I want you to know is that the allosteric constant, \( L_0 \), is just this ratio of T over R when there is no substrate present. Under these conditions, when there's no substrate and at very low substrate concentrations, the T state is more thermodynamically favorable than the free R state. This means that at these low substrate concentrations when there's no substrate present, the equilibrium between the T state and the R state will favor the T state.

If we look at our image below, notice on the left hand side, what we have is the same allosteric enzyme from our previous lesson videos, and we know that it's in the T state since the active site does not bind substrate efficiently. On the right hand side, what we have is the R state of the allosteric enzyme. But notice specifically that this is the free R state of the allosteric enzyme, which means that it has not yet bound any substrate. The active sites are in a relaxed state, but they're not yet binding to any substrate. As soon as a substrate binds to these active sites, it becomes a substrate-bound R state. These substrate-bound R states are different from the free R state. This is important because the allosteric constant, which we know is abbreviated as \( L_0 \), is the ratio of the concentration of T states over the concentration of free R states, not the concentration of substrate-bound R states. Specifically, \( L_0 \) tells us about this particular equilibrium and it does not involve the substrate-bound R state.

Now, at low substrate concentrations, essentially when there's no substrate present, the equilibrium between the T state and the free R state favors the T state. If the equilibrium favors the T state under these conditions, then it means there will be a lot more T state than free R state. Thus, the ratio \( L_0 \) will be quite large if there is a lot of T state and not much R state. Below, the enzyme in the T state is represented by pink boxes, and the enzyme in the free R state by green circles. Notice that at low substrate concentrations where there's no substrate, there are significantly more T states than free R states, demonstrating that the equilibrium favors the T states. Here, \( L_0 \) will be large.

Below, we have a memory tool for the allosteric constant \( L_0 \) to help you remember it's the ratio of the concentration of T states over the concentration of free R states and not vice versa. This line can remind you of a tightrope, helping you remember that Lauren is tightroping over a relaxed crowd. This memory tool should assist you in recalling that the allosteric constant, \( L_0 \), is just the ratio of the T states over the concentration of R states and not vice versa. Utilizing this memory tool can aid your understanding moving forward.

This concludes our introduction to the allosteric constant \( L_0 \) and how it relates to allosteric enzyme conformations. Moving forward in our course, we'll learn even more about allosteric enzyme conformations, so I'll see you in our next video.

Which of the following is true about allosteric enzyme conformational states?

• A. The T state is more stable than the R state of the enzyme when no substrate is present.
• B. Rearrangement of the protein's secondary structure dictates T vs. R states.
• C. The R state of the enzyme has a higher affinity for substrate molecules than the T state.
• D. When a substrate is released from the R state, the enzyme remains in that state indefinitely.
• E. All of the above are correct.
• F. Only A and D are correct.
• G. Only A and C are correct.

Answer: (G)

Allosteric Enzyme Conformations

In this video, we're going to talk about how allosteric enzyme confirmations, essentially the T and the R state confirmations, allow for cooperative kinetics. And so recall from our previous lesson videos that allosteric enzymes display sigmoidal kinetics, which means that on an enzyme kinetics plot, they display an S-shaped curve, just like the enzyme kinetics plot down below showing the S-shaped curve right here in blue. And so what we haven't yet mentioned is that the sigmoidal kinetics displayed by allosteric enzymes actually suggest that substrate binding to the allosteric enzyme is a cooperative process. Now, it turns out that there are actually multiple types of cooperativity. There's negative cooperativity and positive cooperativity. Later in our course, we'll talk about negative cooperativity, but it turns out that the sigmoidal kinetics displayed by allosteric enzymes actually suggest positive cooperativity. And so, positive cooperativity is just this idea that binding of one substrate molecule to the allosteric enzyme ends up making it a lot easier for other substrate molecules to bind to the allosteric enzyme. But how exactly does cooperative substrate binding work? How is it that the binding of one substrate molecule could make it a lot easier for other substrate molecules to bind? Well, in order to understand that, we need to recall from our previous lesson that when there's no substrate concentration, essentially at very, very low substrate concentrations, the equilibrium between the T state, which notice over here we have the T state of our allosteric enzyme, and the free R state over here, this equilibrium at very, very low substrate concentrations favors the T state, as we already discussed in our previous lesson videos. However, it's important to note that increasing the substrate shifts the equilibrium between the T state and the free R state, essentially this equilibrium right here. And so ultimately, what we'll see is that substrate binding to the free R state will produce substrate bound R state. Notice here we have the free R state that does not have any substrate bound to it. And so when we start to increase the substrate concentration, the substrate is more likely to bind to the free R state and when it binds to the free R state, it forms the substrate bound R state down below. Now, of course, substrate binding to the free R state does produce the substrate bound R state, but it also consequently decreases the concentration of free R state. And so if the concentration of free R state is being decreased, going down to form substrate bound R state, then that means that this equilibrium right here is going to shift to the right to compensate for this decrease, and that is explained by Le Chatelier's principle. And so, lowering the concentration of free R state right here is going to cause the reaction to shift to the right here towards the production of more free R state. And so you can see that the binding of a substrate molecule to the free R state is going to decrease the concentration of R state and cause other proteins in the T state to shift into the R state. So, essentially, the binding of a substrate molecule makes it easier for these enzymes to shift into the R state and bind substrate molecules as well, and that is exactly what explains positive cooperativity. Binding of one substrate molecule makes it easier for other substrate molecules to bind to the enzymes. And so, notice over here in this enzyme kinetics plot on the right again, we have the sigmoidal kinetics of our allosteric enzyme. Notice that the ES concentration here, the enzyme substrate complex concentration, is actually representative of the substrate bound R state. The concentration of the substrate bound R state is really, really low, and much, much less than the total enzyme concentration represented by the concentration of ET here. Now as we start to increase the substrate concentration towards the right, notice that the initial reaction velocity begins to increase. The initial reaction velocity here begins to increase and, at this point right here, notice that the concentration of enzyme substrate complex, which is again the concentration of substrate bound R state, is actually increasing. And now at this point, it's equal to half of the total enzyme concentration instead of being much, much less than the total enzyme concentration. And then, of course, if we continue to increase the substrate concentration even further to the right, then the initial reaction velocity starts to approach the maximum reaction velocity, vmax, and, at saturating substrate concentrations, the concentration of enzyme substrate complex, which is again the substrate bound R state, is going to equal the total enzyme concentration, which means that all of the enzyme will be bound to substrate in this form. And then again, that's going to allow the reaction to proceed at its near maximum velocity vmax. And so, this here is our introduction to how allosteric enzyme confirmations, T and R confirmations, allow for cooperative kinetics. But later in our course, we're going to talk more about even more details about cooperative kinetics, specifically negative and positive cooperativity. And, again, this is just our introduction. So as we move forward in our course, we're going to continue to learn more and more about our allosteric enzymes. So I'll see you guys in our next video.

Allosteric Enzyme Conformations

In this video, we're going to talk about how the allosteric constant, l₀, really dictates the extent of an allosteric enzyme sigmoidal curve. And so the greater the value of the allosteric constant l₀, the more sigmoidal the curve will be on an enzyme kinetics plot of the initial reaction velocity versus the substrate concentration. And so, of course, what this means is that the smaller the value of the allosteric constant l₀, the less sigmoidal the curve will be and the more the curve will resemble Michaelis-Menten kinetics.

And so if we take a look at our enzyme kinetics plot down below, notice that we've got these 3 different curves. We've got this green curve right here. We've got the pink curve right here, and we've got the black curve over here. And so, notice that we're also given the allosteric constant for each of these 3 curves. And notice that as the allosteric constant increases, the more sigmoidal the curve becomes. And so because, the green curve here has the largest allosteric constant, it is the most sigmoidal. Of course, the pink curve has an intermediate allosteric constant between the three curves and, that makes it have a slightly less sigmoidal curve. And then, the lowest allosteric constant here is going to be the one that is, least sigmoidal and most resembles the Michaelis-Menten Kinetics showing a rectangular hyperbola. And so if the Allosteric constant goes even lower than 1, then that just means that it's just going to come up even, earlier, but it's still going to resemble Michaelis-Menten kinetics.

And so, really, the main point here that we're trying to make is that the greater the value of the allosteric constant l₀, the more sigmoidal the curve will be, as we see here with, this green curve being the most sigmoidal.

And so, it turns out that amongst all biochemists, there are really 2 popular models that, really explain the sigmoidal kinetics of allosteric enzymes. And so, the first model is referred to as the concerted model, also known as the MWC model, which MWC, by the way, are the first letters of the last names of the 3 scientists, that discovered this concerted model, And then the second model that scientists believe can explain sigmoidal kinetics of allosteric enzymes is, the sequential model, also known as the KNF model. And again, KNF are the letters of the last names of the 3 scientists that discovered the sequential model. More commonly, these are referred to as the concerted and the sequential model. And so, it turns out that in both of these models, allosteric enzymes, reaction activity are going to be affected by allosteric effectors.

And so before we actually get into talking about the details of the concerted model and the sequential model, we're first going to talk about these allosteric effectors that can affect the enzymes in both of these models. So in our next lesson video, I'll see you guys, where we'll talk more about these allosteric effectors.

An allosteric enzyme that follows the concerted model mechanism has a L ₀ = 10,000 in the absence of substrate. A mutation in this enzyme caused the L₀ to now be 1/10,000 (reciprocal to its original value). What affect does this mutation have on the reaction rate of the enzymatic reaction?

• A. The enzyme will retain the T state and the reaction will not occur.
• B. Reaction rate remains independent of the substrate concentration.
• C. The association constant (Ka) for formation of the enzyme-substrate complex will not change with the mutation.
• D. Kinetics will appear to be similar to Michaelis-Menten kinetics, since the enzyme is nearly always in its R state.

Answer: (D)

Here’s what students ask on this topic:

What are the two conformations of allosteric enzymes?

Allosteric enzymes exist in two conformations: the tense (T) state and the relaxed (R) state. The T state is catalytically inactive and has a low affinity for the substrate, meaning it binds substrates inefficiently. In contrast, the R state is catalytically active and has a high affinity for the substrate, allowing it to bind substrates very efficiently. These conformations are crucial for the regulation of enzyme activity and are influenced by various factors, including substrate concentration and allosteric effectors.

How does the allosteric constant (L0) affect enzyme kinetics?

The allosteric constant (L0) is the ratio of the concentration of T states to free R states in the absence of substrate. A higher L0 value indicates a greater proportion of T states, leading to more sigmoidal enzyme kinetics. This means the enzyme activity shows a more pronounced S-shaped curve on a plot of initial reaction velocity versus substrate concentration. Conversely, a lower L0 value results in less sigmoidal kinetics, making the curve resemble Michaelis-Menten kinetics. Thus, L0 plays a critical role in determining the extent of cooperativity and the overall shape of the enzyme kinetics curve.

What is positive cooperativity in allosteric enzymes?

Positive cooperativity in allosteric enzymes refers to the phenomenon where the binding of one substrate molecule to the enzyme makes it easier for additional substrate molecules to bind. This is often observed in enzymes that display sigmoidal kinetics. As the substrate concentration increases, the initial binding of substrate to the R state decreases the concentration of free R states, shifting the equilibrium from the T state to the R state. This shift facilitates further substrate binding, enhancing the reaction velocity and leading to a cooperative increase in enzyme activity.

What is the difference between the T state and the R state in allosteric enzymes?

The T state (tense state) and the R state (relaxed state) are two conformations of allosteric enzymes. The T state is catalytically inactive and has a low affinity for the substrate, meaning it binds substrates inefficiently. The active sites in the T state are less accessible to substrates. In contrast, the R state is catalytically active and has a high affinity for the substrate, allowing it to bind substrates very efficiently. The active sites in the R state are more open and accessible, facilitating substrate binding and catalysis.

How do allosteric enzymes exhibit cooperative kinetics?

Allosteric enzymes exhibit cooperative kinetics through the interplay between their T and R states. At low substrate concentrations, the equilibrium favors the T state. As substrate concentration increases, substrates preferentially bind to the R state, forming substrate-bound R states. This binding reduces the concentration of free R states, causing a shift in equilibrium from the T state to the R state, as explained by Le Chatelier's principle. This shift makes it easier for additional substrate molecules to bind, resulting in a sigmoidal (S-shaped) curve on an enzyme kinetics plot, indicative of positive cooperativity.