Concerted (MWC) Model: Videos & Practice Problems

The concerted model, or MWC model, describes allosteric enzymes' behavior, emphasizing simultaneous transitions between the T state (inactive) and R state (active). This model adheres to the symmetry rule, ensuring all subunits are in the same conformation. Positive cooperativity occurs as substrate binding to one R state subunit increases the likelihood of other subunits transitioning to the R state, enhancing reaction velocity. This phenomenon explains the sigmoidal kinetics observed in allosteric enzymes, where initial reaction velocity sharply increases with substrate concentration, reflecting the dynamic equilibrium between enzyme states.

Concerted (MWC) Model

So now that we've covered allosteric effectors, in this video, we're going to introduce the first model that explains positive cooperativity and the sigmoidal kinetics of allosteric enzymes, and that first model is the concerted model. The concerted model is also sometimes referred to as just the MWC model, where MWC represents the abbreviations of the last names of the three scientists that discovered the concerted model. However, this model is more commonly referred to simply as the concerted model than the MWC model, and so, moving forward in our course, I will mainly refer to it as the concerted model. Recall from your previous organic chemistry courses that the word "concerted" means jointly happening all together at the same exact time. So, "concerted" really just means simultaneous. The concerted model suggests that there are simultaneous, T state to R state conversions, and all of the subunits of an allosteric enzyme. In other words, the concerted model states that the T state to R state conversions encompass the entire allosteric enzyme as a whole so that all of the subunits are simultaneously converting from the T state to the R state and vice versa. This ties directly into what is known as the symmetry rule. The symmetry rule states that all of the subunits of an allosteric enzyme must always be in the same conformation or state. This means that all of the subunits of an allosteric enzyme must either be in the T state or all of the subunits must be in the R state, but no hybrids are allowed.

Looking at our image down below on the left-hand side, we have an allosteric enzyme with four different subunits. Notice that all four subunits of the allosteric enzyme are in the same exact state; they are all in the T state, and that is part of the symmetry rule. Notice that no matter how we cut this allosteric enzyme in half, we're going to have perfect symmetry. The green circles represent the allosteric enzyme with all four subunits in the free R state. Again, all of the subunits of an allosteric enzyme, when it comes to the concerted model, must always be in the same state. They must always be in the T state or must always be in the R state. When the allosteric enzyme converts from the T state to the R state, the conversions encompass the entire enzyme as a whole, so that all four of its subunits will convert simultaneously. This means that all of the subunits of an allosteric enzyme are always going to be in the same exact state.

It is also important to note that absolutely no substrate is needed or required to induce the fit and induce the conversion of the allosteric enzyme from the T state to the R state, which means that the allosteric enzyme is able to convert from the T state to the R state even in the absence of substrate, so even when no substrate is present. Instead, what controls the conversion of the enzyme from the T state to the R state and vice versa is just a natural equilibrium that exists between the two states, allowing them to convert between the two states. Although no substrate is required to induce the T state to R state conversion, changing the substrate, specifically increasing the substrate concentration, will affect this T state to R state equilibrium. This equilibrium is actually going to be shifted when we increase the substrate concentration, as we will see in our next lesson video. When we increase the substrate concentration, this T state to R state equilibrium is shifted towards the R state, allowing the allosteric enzyme to bind more substrate more easily and therefore allowing for positive cooperativity. We will talk more about this idea in our next lesson video. For now, down below in this portion of our image, notice that it reminds us that because all of the subunits are always going to be in the same state in the concerted model, no hybrids are allowed whatsoever. We can't have, within the same allosteric enzyme, one subunit in the R state while the other subunits are in the T state, and we can't have any combination of T state and R state subunits. All of the subunits must either be in the T state or all of the subunits must be in the R state. These are the fundamentals to understanding the concerted MWC model. In our next lesson video, we will discuss how the concerted model allows for positive cooperativity and the sigmoidal kinetics of allosteric enzymes, so I'll see you guys in that video.

Concerted (MWC) Model

So in our last lesson video, we explained the basics of the concerted model. In this video, we're going to talk about how the model allows for positive cooperativity, and therefore explains the sigmoidal kinetics of allosteric enzymes. Recall from our previous lesson videos, we had defined positive cooperativity. We have somewhat of an idea that positive cooperativity states r state equilibrium in the t state, r state equilibrium favors the r state to essentially increase the initial reaction velocity or the vnaught of the enzyme-catalyzed reaction. It's this positive cooperativity that accounts for the sharp increase that we see with the initial reaction sigmoidal kinetics curve of allosteric enzymes.

If we take a look at our enzyme kinetics plot below in our image, notice that we have our sigmoidal curve right here for the allosteric enzyme. We're indicating positive cooperativity right here, which explains the sharp increase in the initial reaction velocity at this stage. How it increases so sharply is explained by positive cooperativity. Again, the concerted model allows for positive cooperativity.

To understand how the concerted model enables positive cooperativity, recall from our previous lesson videos that, when there is no substrate concentration, essentially at very low substrate concentrations, the equilibrium of the t state and the r state actually favors the inactive t state. If the t state is favored, it means that the t state will be in high concentration at these low substrate concentrations. If there is a high concentration of the t state, then the allosteric constant L0 will be very large. There will be a large allosteric constant L0 at low substrate concentrations. Under cellular conditions, even when there is low substrate concentration, it's important to note that the allosteric enzyme can still sometimes spontaneously convert from the t state, which is going to be, again, in high abundance, to the r state. Even at these low substrate concentrations, even when there's no substrate present, there's still going to be some small percentage of the allosteric enzyme in the r state, though most of the allosteric enzymes will be in the t state.

Further down in our image, we're showing you the concerted or the MWC model. Notice over here we have a key, and these pink squares represent the allosteric enzyme with 4 subunits all in the t state. Here we have the allosteric enzyme with 4 subunits all in the free r state. We know the r state is going to bind substrate more efficiently. These individual subunits are capable of binding substrates. So these yellow circles represent the subunits with substrate bound and this would be the allosteric enzyme with 1 subunit binding substrate. This one has 2 subunits binding substrate, 3 subunits binding substrate, and this one has all 4 subunits binding substrate. At very low substrate concentrations, essentially when the substrate concentration is equal to 0, the equilibrium favors the t state. That's why we have most of the allosteric enzymes here present in the t state and we still have a small percentage of the allosteric enzyme in the free r state when there's no substrate present.

As we start to increase substrate concentrations to higher levels, it becomes more likely that the substrate molecules are going to bind to an r state subunit. As soon as a substrate molecule binds to one r state subunit, it traps all the other subunits of the allosteric enzyme in the r state as well. This means that they are more likely to bind substrate. This is exactly what we mean by positive cooperativity. The binding of 1 substrate molecule leads to making it a lot easier for other substrates, so for other enzymes to bind substrate.

As we increase the substrate concentration even higher, this leads to more substrate binding, which traps allosteric enzyme subunits in the r state. An increase in the concentration of the r state decreases the allosteric constant. Since we have more enzymes in the r state binding substrate, this ultimately leads to an increase in the initial reaction velocity. This sharp increase is all related to the positive cooperativity. Notice that, as on the scale, the substrate concentration is increasing, we start to get more of the r state enzymes, and more of the r state enzymes binding substrates. We start to see more yellow as we move to the right showing more enzyme-substrate complex, signalling a higher reaction velocity. This explains the sharp increase in the reaction velocity.

Notice that at this point on our curve, half of all the active sites are going to be occupied with substrate. When the initial reaction velocity approaches Vmax, all the present enzymes are going to be bound with substrate, looking like this, all yellow, at this point up here where it approaches Vmax. This concludes our lesson on how the concerted model can explain positive cooperativity and, therefore, explain the sigmoidal kinetics of allosteric enzymes. In our next lesson video, we'll be able to talk about the other model that explains positive cooperativity as well, the sequential model. I'll see you guys in our next video.

In the Concerted model for allosteric enzymes:

• A. Relative affinities of substrate for the T & R states play a crucial role in reaction cooperativity.
• B. Equilibrium between T and R states plays a minor role.
• C. Enzymatic activity of the T state is considerably higher than that of the R state.
• D. It is possible to describe the reactions of all allosteric enzymes accurately.

Answer: (A)

Which of the following is true concerning the symmetry rule & the Concerted model of allosterism?

• A. The protein is an oligomer of symmetrically related proteins.
• B. Though not with the same affinity, the ligand can bind to a subunit in either conformation.
• C. The oligomer can only exist in one of two conformational states (T & R), which are in equilibrium.
• D. All the above are true.

Answer: (D)

According to the Concerted model & symmetry rule for allosteric proteins, which of the following statements is true for hemoglobin?

• A. Each of the 4 subunits in hemoglobin changes one at a time from the low affinity to high affinity state.
• B. First hemoglobin's α-subunits, then β subunits change from the low to the high affinity state.
• C. Each of the four subunits in the hemoglobin tetramer is either in the low affinity or the high affinity state.
• D. Hemoglobin's α-subunits have a low affinity state while the β subunits have high affinity for oxygen.

Answer: (C)

Here’s what students ask on this topic:

What is the concerted model in biochemistry?

The concerted model, also known as the MWC model, describes the behavior of allosteric enzymes. It posits that all subunits of an allosteric enzyme transition simultaneously between two states: the T state (inactive) and the R state (active). This model adheres to the symmetry rule, which ensures that all subunits are in the same conformation at any given time. The concerted model explains positive cooperativity, where the binding of a substrate to one R state subunit increases the likelihood of other subunits transitioning to the R state, thereby enhancing the enzyme's reaction velocity. This phenomenon accounts for the sigmoidal kinetics observed in allosteric enzymes.

How does the concerted model explain positive cooperativity?

The concerted model explains positive cooperativity by suggesting that all subunits of an allosteric enzyme transition between the T state (inactive) and the R state (active) simultaneously. At low substrate concentrations, the equilibrium favors the T state. However, as substrate concentration increases, the likelihood of substrate binding to an R state subunit also increases. Once a substrate binds to one R state subunit, it traps all other subunits in the R state, making them more likely to bind additional substrate molecules. This cooperative binding leads to a sharp increase in reaction velocity, which is characteristic of the sigmoidal kinetics observed in allosteric enzymes.

What is the symmetry rule in the concerted model?

The symmetry rule in the concerted model states that all subunits of an allosteric enzyme must be in the same conformation or state at any given time. This means that all subunits must either be in the T state (inactive) or the R state (active), with no hybrids allowed. This rule ensures that the enzyme transitions as a whole between these states, maintaining symmetry. The symmetry rule is crucial for the concerted model's explanation of positive cooperativity and the sigmoidal kinetics of allosteric enzymes.

What is the difference between the T state and the R state in the concerted model?

In the concerted model, the T state (tense state) and the R state (relaxed state) represent two different conformations of an allosteric enzyme. The T state is the inactive form of the enzyme, where substrate binding is less favorable. In contrast, the R state is the active form, where substrate binding is more favorable. The model posits that all subunits of the enzyme transition simultaneously between these two states. The equilibrium between the T state and the R state is influenced by substrate concentration, with higher substrate levels favoring the R state, thereby enhancing enzyme activity and promoting positive cooperativity.

How does substrate concentration affect the T state to R state equilibrium in the concerted model?

In the concerted model, substrate concentration significantly affects the equilibrium between the T state (inactive) and the R state (active). At low substrate concentrations, the equilibrium favors the T state, meaning most enzyme subunits are in the inactive form. As substrate concentration increases, the likelihood of substrate binding to an R state subunit also increases. Once a substrate binds to one R state subunit, it traps all other subunits in the R state, shifting the equilibrium towards the active form. This shift enhances the enzyme's ability to bind more substrate, leading to positive cooperativity and a sharp increase in reaction velocity, characteristic of sigmoidal kinetics.