Enzymes and kinetics

How enzymes speed reactions, the Michaelis–Menten equation and types of inhibition.

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After this guide you should be able to:

Explain how enzymes speed up reactions
Use the Michaelis–Menten equation
Interpret Km, Vmax, kcat and kcat/Km
Distinguish competitive, uncompetitive and noncompetitive inhibition

Key concepts

Enzymes speed reactions by lowering the activation energy. They do not change the overall free-energy change or the equilibrium position, only how fast equilibrium is reached.

Michaelis–Menten

v = Vmax [S] / (Km + [S])

Vmax: the maximum rate when the enzyme is saturated with substrate.
Km: the substrate concentration that gives half of Vmax. A lower Km generally means higher apparent affinity.
kcat = Vmax ÷ total enzyme: the turnover number, reactions per enzyme per second.
kcat/Km: catalytic efficiency.

Lineweaver–Burk

1/v = (Km/Vmax)(1/[S]) + 1/Vmax

A double-reciprocal plot gives a straight line: y-intercept 1/Vmax, x-intercept −1/Km.

Inhibition

Competitive: binds the active site. Apparent Km rises; Vmax is unchanged. More substrate overcomes it.
Uncompetitive: binds only the enzyme–substrate complex. Apparent Km and Vmax both fall.
Noncompetitive (pure): binds equally to enzyme and complex. Vmax falls; Km is unchanged. Mixed inhibition changes both.

Allosteric enzymes often show S-shaped (sigmoidal) curves rather than hyperbolic ones.

Worked example

Problem: An enzyme has Km = 2 mM and Vmax = 100 µmol/min. What is the rate at [S] = 2, 6 and 18 mM?

Solution: At 2 mM, v = 100 × 2/(2 + 2) = 50. At 6 mM, v = 100 × 6/8 = 75. At 18 mM, v = 100 × 18/20 = 90 µmol/min. Note how slowly v approaches Vmax.

Common mistakes

Saying a high Km means high affinity. It is the opposite.
Thinking enzymes shift equilibrium. They only change the rate.
Mixing up which inhibitor type changes Km versus Vmax.

Check yourself

When [S] = Km, what is v?

Vmax ÷ 2.

Which type of inhibition raises apparent Km but leaves Vmax unchanged?

Competitive inhibition.

What does the y-intercept of a Lineweaver–Burk plot equal?

1/Vmax.

Flashcards for this guide

18 cards on enzymes & kinetics.

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Cite this page

VALREXA Biosciences. (2026, November 7). Enzymes and kinetics: study guide. VALREXA Biosciences. https://valrexa.com/study/enzymes-kinetics.html

APA style · Last reviewed November 7, 2026 · Our editorial standards

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