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Biology · Simulator 035

Enzyme Kinetics

An enzyme turns substrate into product. Raise the substrate concentration and the reaction speeds up, until every enzyme is busy. Add an inhibitor and see how competitive and non-competitive inhibition change the curve in different ways.

How the model works

The Michaelis–Menten equation gives the initial reaction velocity v at substrate concentration [S]:

v = Vmax [S] / (Km + [S])

Vmax is the top speed when the enzyme is saturated. Km is the substrate concentration that gives half of Vmax; a low Km means high affinity.

Inhibitors at concentration [I] with dissociation constant Ki act through the factor α = 1 + [I]/Ki:

  • Competitive (competes for the active site): apparent Km becomes αKm, and Vmax is unchanged. Enough substrate overcomes it.
  • Non-competitive (binds elsewhere): apparent Vmax becomes Vmax/α, and Km is unchanged.
  • Uncompetitive (binds only the enzyme–substrate complex): both Km and Vmax are divided by α.

The Lineweaver–Burk (double-reciprocal) plot of 1/v against 1/[S] is a straight line. Its intercepts are 1/Vmax and −1/Km, which makes inhibition types easy to tell apart. “Measured” points include optional seeded noise, as in a real assay.

Steady-state, single-substrate kinetics; ignores product inhibition, cooperativity and enzyme denaturation.

Guided experiments

  1. Find Km. Vmax = 100, Km = 2 mM. Prediction: at [S] = 2 mM, v = 50 (half of Vmax). At 18 mM, v = 90.
  2. Competitive inhibitor. [I] = Ki. Prediction: α = 2, so apparent Km doubles to 4 mM. The curve still reaches 100 at high [S], and the Lineweaver–Burk lines cross on the y-axis.
  3. Non-competitive inhibitor. [I] = Ki. Prediction: Vmax halves to 50 and Km stays at 2. The lines cross on the x-axis.

Challenge

A drug is a competitive inhibitor of an enzyme. A patient's tissue has a substrate concentration far above Km. Will the drug work well? What about a non-competitive drug?

Reveal the explanation

At [S] ≫ Km, v ≈ Vmax for a competitive inhibitor, because substrate outcompetes it, so it has little effect. A non-competitive inhibitor lowers Vmax itself, so it still slows the reaction by the factor α, however much substrate there is.

References

  • OpenStax, Biology 2e, §6.5 “Enzymes”.
  • Berg, Tymoczko & Stryer, Biochemistry, ch. 8 “Enzymes: Basic Concepts and Kinetics”.