Undergraduate · 35 min

Michaelis–Menten assay: spotting the inhibitor type

Run virtual rate measurements at eight substrate concentrations, then classify an unknown inhibitor by how Km and Vmax respond — the core skill of enzyme kinetics.

Goal

Distinguish competitive, non-competitive and uncompetitive inhibition on the curve $v = V_\mathrm{max}[S]/(K_m^{\mathrm{app}} + [S])$ and predict what each does to a Lineweaver–Burk plot.

Apparatus and reagents

Virtual assay: substrate stock (0–8 mM), the same enzyme batch ( $V_\mathrm{max} = 10$ , $K_m = 1$ mM), and an inhibitor added at fixed $[I]$ ; the simulation replays idealized curves.

Procedure

Select “none” and hover at $[S] = 1$ mM: confirm $v = V_\mathrm{max}/2 = 5$ , reading off $K_m$ .
Switch to the competitive inhibitor: the plateau is unchanged but the half-saturation point moved right — measure the new apparent $K_m$ .
Select non-competitive: now the plateau dropped to half while $K_m$ stayed at 1 mM.
Try uncompetitive: both $K_m^{\mathrm{app}}$ and $V_\mathrm{max}^{\mathrm{app}}$ halved — a rare signature where inhibition needs the ES complex.
Sketch 1/v versus 1/[S] for each case by hand: parallel lines signal uncompetitive, a shared y-intercept competitive.

What to observe

Competitive: $K_m^{\mathrm{app}}$ rises while $V_\mathrm{max}$ is untouched — the inhibitor only competes for the free enzyme.
Non-competitive: $V_\mathrm{max}^{\mathrm{app}}$ falls but $K_m$ is fixed — inhibitor binds E and ES equally, removing active enzyme.
Uncompetitive: the curve gets both lower and steeper near the origin — binding to ES removes complex and pulls more ES forward.

Explanation

The three textbook mechanisms differ in where the inhibitor binds: to E (competitive, so extra substrate outcompetes it and $K_m^{\mathrm{app}} = K_m(1+[I]/K_i)$ ), to E and ES equally (non-competitive, $V_\mathrm{max}^{\mathrm{app}} = V_\mathrm{max}/(1+[I]/K_i)$ ), or to ES only (uncompetitive, dividing both constants by $1+[I]/K_i$ ). On a double-reciprocal plot these become intersecting lines at the y-axis, parallel lines, and lines sharing the x-intercept — which is why Lineweaver–Burk plots still teach mechanism even though fitting is now done non-linearly.

History of the experiment

Leonor Michaelis and Maud Menten published their equation in 1913 after studying invertase; Maud Menten, one of Canada’s first women MDs, is honoured by the equation bearing both names.

Chemists behind it

Frances Arnold Emil Fischer