What is the equation for kcat?

The correct equation for kcat is derived from the relationship between the maximum reaction velocity (Vmax) and the total enzyme concentration ([E]total). Specifically, kcat represents the turnover number, which indicates how many substrate molecules one enzyme molecule converts into product per unit of time when the enzyme is fully saturated with substrate.

When substrate concentration is sufficiently high, and the enzyme is at its maximum activity, Vmax can be expressed as:

[

Vmax = kcat \times [E]_{total}

]

To isolate kcat, you rearrange this equation as follows:

[

kcat = \frac{Vmax}{[E]_{total}}

]

This shows that kcat, the turnover number, directly correlates with the maximum velocity and inversely with the total enzyme concentration. Thus, the proper equation for kcat is indeed Vmax divided by the total enzyme concentration, which aligns with the correct choice. This understanding is essential for analyzing enzyme kinetics and the efficiency of enzymes in catalyzing reactions.