Enzyme kinetics (Michaelis–Menten and Lineweaver–Burk) !

An enzyme's rate rises with substrate until it reaches a maximum; two numbers, Km and Vmax, sum up how it works and how drugs change it.

Updated 2026-11-01

Key facts

Michaelis–Menten: v = Vmax·[S] / (Km + [S]). The plot of v against [S] is a hyperbola.
Km is the substrate concentration that gives half of Vmax; a low Km generally means high affinity for the substrate.
Vmax is the rate with the enzyme saturated; it depends on how much enzyme there is. kcat (turnover number) = Vmax / [total enzyme]; kcat/Km measures efficiency.
Lineweaver–Burk (double reciprocal): 1/v = (Km/Vmax)·(1/[S]) + 1/Vmax. Y-intercept = 1/Vmax; X-intercept = −1/Km; slope = Km/Vmax.
Allosteric enzymes do not follow this equation: their curve is sigmoidal (cooperativity).

The enzyme (E) binds the substrate (S) to form the ES complex, which turns into product (P) and releases the enzyme: E + S ⇌ ES → E + P.
With [S] far below Km, the rate rises almost in proportion to substrate (first-order kinetics).
With [S] far above Km, the enzyme is saturated and the rate no longer depends on substrate (zero-order kinetics).
When [S] = Km, the rate is exactly half of Vmax; when [S] = 9 × Km, it reaches 90 %.
The Lineweaver–Burk plot turns the hyperbola into a straight line, which makes Km and Vmax easy to read and the type of inhibition easy to recognise.
Isoenzyme example: hexokinase (Km for glucose ≈ 0.1 mM) is always saturated in tissues; liver glucokinase (Km ≈ 10 mM) speeds up when blood glucose rises after a meal.
Temperature and pH have an optimum; away from it the enzyme loses activity and, at the extremes, denatures.

Ethanol is cleared with zero-order kinetics because alcohol dehydrogenase saturates at low alcohol levels: a fixed amount is metabolised per hour.
Phenytoin and high-dose aspirin switch to zero-order kinetics, so small dose increases raise their blood level a lot.
Genetic variants that raise an enzyme's Km (lower affinity) can sometimes be offset by giving more cofactor, as in some vitamin-responsive diseases.

Think of the answer, then tap the question to see it.

What does a low Km mean?

The enzyme reaches half its maximum rate with little substrate: generally, high affinity for it.

On a Lineweaver–Burk plot, what does the Y-intercept show?

1/Vmax: the reciprocal of the maximum rate.

Why is ethanol cleared at a constant rate?

Alcohol dehydrogenase has a low Km and saturates at small concentrations, so it works at zero order.

What rate does an enzyme reach when [S] equals Km?

Half of Vmax; that is the definition of Km in the Michaelis–Menten equation.

Educational information, not medical advice. For any symptom, see a health professional.

Sources: Enzyme: MedlinePlus Medical Encyclopedia (MedlinePlus, US National Library of Medicine, 2026); What are proteins and what do they do?: MedlinePlus Genetics (MedlinePlus, US National Library of Medicine, 2026); Textbook of Biochemistry for Medical Students, 6th ed. (Jaypee Brothers Medical Publishers (Vasudevan DM, Sreekumari S, Vaidyanathan K), 2011).

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Representative model, for educational purposes only.