Final answer:
The substrate concentration at which an enzyme shows one-quarter of its maximum rate can be calculated using the Michaelis-Menten equation and the enzyme's kcat and Km values. In this case, the enzyme's kcat is 30 s-1 and Km is 0.3 M. Therefore, one-quarter of the maximum rate would occur at a substrate concentration of 0.075 M.
Step-by-step explanation:
The Michaelis-Menten equation describes the relationship between substrate concentration and enzyme activity. The Km value is the substrate concentration at which the reaction rate is half the maximum rate. To find the substrate concentration at which the enzyme shows one-quarter of its maximum rate, we can rearrange the Michaelis-Menten equation.
Km = (Vmax / 2) * (1 / kcat)
We know that kcat is 30 s-1, so we can substitute this value into the equation:
Km = (Vmax / 2) * (1 / 30)
Assuming the maximum rate (Vmax) is reached at a high substrate concentration, we can estimate Km to be approximately 0.3 M. Therefore, one-quarter of the maximum rate would occur at one-quarter of the Km value, which is 0.075 M.