S3U

Science / Life science / Undergraduate / sld01

Enzyme Saturation and Michaelis-Menten Parameters

Interpret a saturation curve without turning its parameters into unsupported biological claims.

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5 questions0m 0s

Prerequisites

Functions, limits, derivatives, concentration units, and initial reaction rates.

Learn the skill

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.

1. What initial rate does the model predict at S=2?
2. What initial rate does it predict at S=4?
3. What value does v approach as S increases without bound?
4. What is the low-substrate slope Vmax/Km?
5. Can this fitted Km alone be reported as a binding dissociation constant?

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.