Final answer:
The MM equation for mixed inhibition accounts for an inhibitor that can bind both the free enzyme and the enzyme-substrate complex, affecting both Vmax and Km. The modified equation introduces alpha and alpha-prime terms, which are a function of inhibitor concentration and its dissociation constants. This equation helps understand how mixed inhibitors alter enzyme kinetics.
Step-by-step explanation:
The Michaelis-Menten (MM) equation for mixed inhibition can be derived by considering the impact of an inhibitor that can bind to both the enzyme (E) alone and the enzyme-substrate complex (ES). Mixed inhibitors alter the maximum velocity (Vmax) and the Michaelis constant (Km) of the enzymatic reaction. In the presence of a mixed inhibitor, the enzyme's affinity for the substrate can either increase or decrease, which is reflected in the change in Km.
In the derivation, traditionally we start with the assumption that the binding of inhibitor to the enzyme (E) and enzyme-substrate (ES) complex is reversible. Let's denote the inhibitor as I, the enzyme-inhibitor complex as EI, and the enzyme-substrate-inhibitor complex as ESI. The Michaelis-Menten equation for mixed inhibition can be represented as:
Velocity (V) = (Vmax * [S]) / (alpha * Km + alpha-prime * [S])
where:
- [S] is the substrate concentration,
- alpha = 1 + [I]/Ki,
- alpha-prime = 1 + [I]/Ki',
- Ki and Ki' are the dissociation constants of the inhibitor with the enzyme and the enzyme-substrate complex, respectively.
This modified equation indicates how the presence of a mixed inhibitor affects the normal MM equation, introducing additional terms alpha and alpha-prime that alter both Vmax and Km. The scale of the change in Vmax and Km depends on the concentration of the inhibitor and its dissociation constants.