Concerted (MWC) Model: Videos & Practice Problems

The concerted model, also known as the MWC model, is a key framework for understanding positive cooperativity and the sigmoidal kinetics of allosteric enzymes. This model posits that all subunits of an allosteric enzyme transition simultaneously between two states: the tense (T) state and the relaxed (R) state. The term "concerted" implies that these transitions occur jointly, meaning that if one subunit changes state, all others must do so at the same time, adhering to what is known as the symmetry rule. This rule dictates that all subunits must be in the same conformation—either all in the T state or all in the R state—without any hybrid states allowed.

In the concerted model, the conversion from the T state to the R state does not require the presence of substrate; rather, it is governed by a natural equilibrium between these two states. This equilibrium can be influenced by substrate concentration, which, when increased, shifts the balance towards the R state. This shift enhances the enzyme's ability to bind additional substrate, thereby facilitating positive cooperativity.

To visualize this, consider an allosteric enzyme with four subunits. If all subunits are in the T state, they maintain perfect symmetry. When the enzyme transitions to the R state, all subunits again change simultaneously, ensuring that the enzyme remains in a uniform state throughout the process. This characteristic of the concerted model is crucial for understanding how allosteric enzymes function and respond to changes in substrate concentration, leading to their unique kinetic behavior.

In summary, the concerted model emphasizes the simultaneous nature of state transitions in allosteric enzymes, the importance of the symmetry rule, and the role of substrate concentration in modulating enzyme activity. Understanding these principles lays the groundwork for exploring the implications of positive cooperativity and the sigmoidal kinetics associated with allosteric enzymes.

The concerted model of enzyme kinetics provides a framework for understanding positive cooperativity, which is crucial for explaining the sigmoidal kinetics observed in allosteric enzymes. Positive cooperativity occurs when the binding of a substrate to one subunit of an enzyme increases the likelihood of substrate binding to other subunits. This phenomenon leads to a sharp increase in the initial reaction velocity, denoted as \( V_0 \), as substrate concentration rises.

At very low substrate concentrations, the equilibrium between the tense state (T state) and the relaxed state (R state) favors the T state, resulting in a high concentration of inactive enzyme. The allosteric constant, \( L_0 \), is large under these conditions due to the predominance of the T state. However, even in the absence of substrate, a small fraction of the enzyme can spontaneously convert to the R state, allowing for some activity.

As substrate concentration increases, the likelihood of substrate binding to an R state subunit rises. When a substrate molecule binds to an R state subunit, it stabilizes the R state across the enzyme's subunits, enhancing the overall binding affinity for additional substrate molecules. This cooperative binding effect is what characterizes positive cooperativity.

As more substrate binds, the concentration of the R state increases, which in turn decreases the allosteric constant. This dynamic leads to a significant increase in the initial reaction velocity as more enzyme-substrate complexes form. The sigmoidal curve observed in enzyme kinetics plots reflects this relationship, where the steep rise indicates the transition from low to high substrate binding efficiency.

Ultimately, when the substrate concentration reaches a point where all active sites are occupied, the reaction velocity approaches its maximum, \( V_{max} \). This behavior illustrates how the concerted model effectively accounts for the cooperative interactions among enzyme subunits, resulting in the characteristic sigmoidal kinetics of allosteric enzymes.