Simulate Michaelis-Menten kinetics and reversible inhibition models in real time · v = Vmax·[S] / (Km + [S])
Substrate concentration
Maximum reaction velocity
Substrate concentration at which v = Vmax/2
Total enzyme concentration (optional)
35.71
µmol/(L·min)71.43
%It is the model that describes how fast an enzyme works. An enzyme (E) first binds its substrate (S) to form an enzyme-substrate complex (ES), then converts it to product (P) and is released to repeat the cycle:
The key idea is that an enzyme can be saturated: with little substrate, the rate grows almost proportionally; but once every active site is occupied, adding more substrate no longer speeds things up and the rate plateaus at a ceiling, Vmax.
The model was proposed by Michaelis & Menten (1913) and generalized by Briggs & Haldane (1925) with the steady-state approximation: after a brief initial transient, [ES] stays roughly constant. It remains the foundation of modern enzymology.
There are only two protagonists. Vmax is the maximum rate (enzyme saturated). Km (the Michaelis constant) is the substrate concentration at which the enzyme runs at half of its maximum rate; it acts as an inverse measure of affinity: small Km → high affinity.
It helps to think in three regimes:
An inhibitor is a molecule that slows the enzyme down. In reversible inhibition, what matters is what it binds to: the free enzyme (E), the ES complex, or both. The four classic types all fit into a single equation with two factors:
Inhibitor bound to the free enzyme. Affects the Km term.
Inhibitor bound to the ES complex. Affects the [S] term.
Ki and Ki′ are the inhibition constants (smaller = more potent inhibitor). With no inhibitor, α = α′ = 1 and the original equation is recovered. Each type leaves a distinct fingerprint on the apparent parameters:
| Type | Binds to | Vmax,app | Km,app | Lineweaver-Burk |
|---|---|---|---|---|
| Competitive | free enzyme (E) | = | ↑ rises | lines pivot on the Y-axis |
| Uncompetitive | ES complex | ↓ drops | ↓ drops | parallel lines |
| Non-competitive | E and ES equally | ↓ drops | = | lines pivot on the X-axis |
| Mixed | E and ES (differently) | ↓ drops | ↑ or ↓ | cross away from the axes |
Non-competitive is the special case of mixed with Ki = Ki′ (α = α′). The ratio kcat/Km changes only with α (the competitive component).
The equation describes the initial velocity very well, but it rests on several assumptions:
How many substrate molecules each active site converts per second when the enzyme is saturated. It is the intrinsic rate of the catalytic step — which is why you must enter the enzyme concentration [ET] to compute it.
The specificity constant combines affinity and catalysis: it measures how good the enzyme is at low [S]. It has a physical ceiling, the diffusion limit in water (~10⁸–10⁹ M⁻¹s⁻¹): you cannot catalyze faster than substrate and enzyme can meet. Enzymes like carbonic anhydrase brush against that limit — so-called catalytic perfection.
Taking reciprocals turns the hyperbola into a straight line: the y-intercept is 1/Vmax, the x-intercept is −1/Km, and the slope is Km/Vmax. Its great use is diagnosing inhibition at a glance: how the lines move (pivot on Y, pivot on X, or run parallel) tells you which type it is.
Today nonlinear regression is preferred for fitting parameters, because the linearization amplifies error at low [S] (Srinivasan, 2022).
| Enzyme | Km | kcat (s⁻¹) | kcat/Km |
|---|---|---|---|
| Carbonic anhydrase | 12 mM | 1×10⁶ | 8×10⁷ |
| Catalase | 25 mM | 1×10⁷ | 4×10⁸ |
| Acetylcholinesterase | 95 µM | 1.4×10⁴ | 1.5×10⁸ |
| Fumarase | 5 µM | 800 | 1.6×10⁸ |
Typical values from Berg, Tymoczko & Stryer, Biochemistry (8th ed.). All of them approach the diffusion limit (catalytic perfection).