According to Michaelis–Menten kinetics, when the substrate concentration equals K m (that is, [S] = K m), what fraction of V max is the reaction velocity approximately?

Introduction / Context:The Michaelis–Menten model describes how reaction velocity v depends on substrate concentration [S] given a maximum velocity V max and a constant K m. A classic, testable consequence is the speed at [S] = K m.

Given Data / Assumptions:

• Rate law: v = (Vmax * [S]) / (Km + [S]).
• At the condition of interest, [S] = Km.
• Single-substrate, steady-state assumptions apply.

Concept / Approach:Substitute [S] = K m into the Michaelis–Menten equation and simplify to find v as a fraction of V max.

Step-by-Step Solution:

Verification / Alternative check:Half-saturation property: by definition, K m is the [S] at which v reaches half of V max in this model, confirming the result.

Why Other Options Are Wrong:

• 0.1, 0.2, 0.75, 0.9 * Vmax: incompatible with the defining property of K m.

Common Pitfalls:Confusing K m with a dissociation constant in all cases; while related, K m is operationally defined via rate constants and the velocity curve.

Final Answer:0.5 * Vmax