Question

Michaelis and Menten equation for simple enzyme kinetics is.....

• A. \(\frac{V_{\text{max}} \cdot S}{K_m + S}\)
• B. \(V_{\text{max}} \cdot S \times K_m + S\)
• C. \(\frac{K_m + S}{V_{\text{max}} \cdot S}\)
• D. \(\frac{V_{\text{max}} \cdot K_m}{S + S}\)

Hint:

A low \(K_m\) value indicates high affinity of the enzyme for its substrate, meaning the reaction can reach half-maximum velocity at very low substrate concentrations.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Michaelis-Menten equation is the fundamental mathematical model of one-substrate enzyme-catalyzed reactions, relating the initial reaction rate to substrate concentration.

Step 2: Key Formula or Approach:
The rate equation is given by:
\[ v = \frac{V_{\text{max}} [S]}{K_m + [S]} \]
where:
- \(v\) is the initial reaction velocity.
- \(V_{\text{max}}\) is the maximum reaction velocity at saturating substrate levels.
- \([S]\) is the substrate concentration.
- \(K_m\) is the Michaelis constant (representing the substrate concentration at which \(v = \frac{1}{2} V_{\text{max}}\)).

Step 3: Detailed Explanation:
The equation represents a hyperbolic curve:
- At low substrate concentrations (\([S] \ll K_m\)), the reaction rate is first-order with respect to substrate.
- At high substrate concentrations (\([S] \gg K_m\)), the rate is zero-order (saturated, approaching \(V_{\text{max}}\)).
The algebraic expression is represented as:
\[ \frac{V_{\text{max}} \cdot S}{K_m + S} \]

Step 4: Final Answer:
The correct equation is option (A).