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# 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).

## In detail

- 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.

**Also called**
Km and Vmax, Michaelis–Menten, Lineweaver–Burk

## Clinical notes

- 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.

## Related

- [Types of enzyme inhibition](https://durgical.com/en/biochemistry/topics/types-of-enzyme-inhibition/)
- [Allosteric and covalent regulation of enzymes](https://durgical.com/en/biochemistry/topics/allosteric-and-covalent-regulation-of-enzymes/)
- [Isoenzymes](https://durgical.com/en/biochemistry/topics/isoenzymes/)
- [Hexokinase](https://durgical.com/en/biochemistry/enzymes/hexokinase/)
- [Phosphofructokinase-1 (PFK-1)](https://durgical.com/en/biochemistry/enzymes/phosphofructokinase-1/)
- [Glucose](https://durgical.com/en/biochemistry/molecules/glucose/)

## Test yourself

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.

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

Sources: [Enzyme: MedlinePlus Medical Encyclopedia](https://medlineplus.gov/ency/article/002353.htm) (MedlinePlus, US National Library of Medicine, 2026); [What are proteins and what do they do?: MedlinePlus Genetics](https://medlineplus.gov/genetics/understanding/howgeneswork/protein/) (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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