When the substrate concentration ([S]) is equal to the Michaelis constant (Km), the initial velocity (V_o) of an enzyme-catalyzed reaction will be half of the maximum velocity (V_max).

Here's why:

* Michaelis-Menten Equation: The relationship between substrate concentration, initial velocity, and the kinetic parameters Km and Vmax is described by the Michaelis-Menten equation:

V_o = (V_max * [S]) / (Km + [S])

* When [S] = Km: If you substitute [S] with Km in the equation, you get:

V_o = (V_max * Km) / (Km + Km)

V_o = (V_max * Km) / (2 * Km)

V_o = V_max / 2

* Significance of Km: Km represents the substrate concentration at which the reaction proceeds at half its maximum velocity. This is a useful measure of an enzyme's affinity for its substrate. A lower Km indicates a higher affinity (the enzyme reaches half its maximum velocity at a lower substrate concentration).

In summary: When [S] = Km, the enzyme is working at half its maximum efficiency. This point is often used in enzyme kinetics experiments to determine the Km value and gain insight into the enzyme's behavior.