Derive Michaelis-Menten equation for a non-competitive inhibitor reactions.
The Michaelis-Menten equation is fundamental in enzymology, describing the rate of enzymatic reactions as a function of substrate concentration. When an enzyme is inhibited by a non-competitive inhibitor, the situation becomes slightly more complex, but it can still be described by a modified version of the Michaelis-Menten equation. In the case of non-competitive inhibition, the inhibitor binds to an allosteric site on the enzyme, distinct from the active site, and does not affect substrate binding directly. However, it affects the overall catalytic activity of the enzyme.
### Derivation of the Michaelis-Menten Equation for Non-Competitive Inhibition
For an enzyme-catalyzed reaction in the presence of a non-competitive inhibitor, the reaction can be represented as follows:
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