Undergraduate · 20 min

Enzyme catalysis: the Michaelis–Menten curve

Plot the initial rate v of an enzyme reaction against substrate concentration and see why the curve saturates at Vmax.

Goal

Read $K_m$ and $V_\mathrm{max}$ off the curve $v = V_\mathrm{max}[S]/(K_m + [S])$ and connect them to enzyme–substrate affinity and enzyme amount.

Apparatus and reagents

Virtual bench: stock substrate solution, catalase-like enzyme, stopwatch and $v$ readout; the simulation supplies the full curve.

Procedure

Start with the reference preset (Km = 1.0, Vmax = 1). Hover at [S] = Km and confirm that v = Vmax/2.
Switch to Km = 4.0 (low affinity): how much substrate do you now need to reach half of Vmax?
Compare Km = 1.0, Vmax = 0.5 with the reference: what stays the same and what shrinks? Link that to halving the enzyme.
For each preset, estimate the apparent efficiency near [S] → 0: it approaches Vmax/Km.

What to observe

At low [S] the curve is nearly linear with slope Vmax/Km; at high [S] it flattens because every enzyme active site is occupied.
Doubling Km from 1.0 to 4.0 pushes the half-saturation point fourfold to the right without changing the plateau.
Halving Vmax lowers the plateau but leaves Km — the half-saturation substrate level — unchanged.

Explanation

The enzyme E binds substrate S reversibly to form ES, which releases product: $\ce{E + S <=> ES -> E + P}$ . When most active sites are empty, doubling [S] roughly doubles v. When [S] ≫ Km, every site is busy and the rate plateaus at $V_\mathrm{max} = k_\mathrm{cat}[E]_\mathrm{total}$ : only adding more enzyme raises it. $K_m$ is the substrate level giving half that rate, so a small Km means productive binding even at low [S].

History of the experiment

In 1913 Leonor Michaelis and Maud Menten derived their rate law by measuring invertase in a Berlin lab, building on Victor Henri's earlier formulation. The hyperbolic equation became the backbone of enzymology, later refined by Briggs and Haldane's steady-state treatment in 1925.

Chemists behind it

Emil Fischer Wilhelm Ostwald Frances Arnold