Prerequisites
Functions, limits, derivatives, concentration units, and initial reaction rates.
In the stated Michaelis-Menten model, v=Vmax*S/(Km+S). At S=Km, the initial rate is Vmax/2. Low-substrate behavior is approximately linear, while high-substrate behavior approaches a plateau. Km is not generally identical to a binding dissociation constant.
Worked example
For Vmax=90 and Km=3 in compatible units, S=3 gives v=45. Raising S from 3 to 6 gives v=60, not 90: doubling substrate does not double rate near saturation.
Model and Assumptions
Use invented initial-rate data represented exactly by v=120*S/(2+S). S and Km use the same concentration units; v and Vmax share rate units. Assume the model is applicable, enzyme amount is fixed, and product accumulation is negligible.
Further inquiry
Differentiate the rate law and show that the slope decreases with S. Derive the substrate concentration giving 90% of Vmax. Explain what changes in enzyme amount or model applicability would invalidate a direct comparison of fitted curves.
Review criteria
- Obtain dv/dS=Vmax*Km/(Km+S)^2.
- Show S=9Km for the 90% target.
- Distinguish an initial-rate model parameter from a universal measure of binding affinity.