kcat, Km and Catalytic Efficiency (kcat/Km): Comparing Enzymes

k_cat (turnover number) is how many substrate molecules one enzyme active site converts to product per second when saturated: k_cat = V_max / [E]_total. Catalytic efficiency is k_cat/K_m, which combines speed (k_cat) with how well the enzyme grabs substrate (low K_m means high apparent affinity). Bigger is better for both.

Reading the pieces

At low substrate, v ≈ (k_cat/K_m)[E][S]. That is why k_cat/K_m is the number to compare when substrate is scarce, as it often is in cells. The theoretical ceiling is diffusion, roughly 10⁸ to 10⁹ M^-1s^-1, and enzymes near that limit (such as carbonic anhydrase) are called catalytically perfect.

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Worked example 1: finding k_cat

An assay with 2.0 nM enzyme reaches V_max = 6.0 μM/s.

k_cat = (6.0 × 10^-6 M/s) / (2.0 × 10^-9 M) = 3,000 s^-1.

Worked example 2: comparing two enzymes

B turns over four times faster when saturated, but A is four times more efficient at low substrate because its K_m is 16 times lower. At [S] well above both K_m values, B wins. At low [S], A wins.

Effect of inhibitors

• Competitive: K_m rises, V_max and k_cat unchanged, so apparent efficiency falls.
• Noncompetitive: V_max falls, K_m unchanged.
• Uncompetitive: both V_max and K_m fall.

Common traps

• Equating low K_m with fast. K_m is about affinity, not speed.
• Forgetting units. k_cat is s^-1, k_cat/K_m is M^-1s^-1.
• Using total enzyme mass. k_cat needs the concentration of active sites.
• Treating K_m as a true K_d. They match only when product release is slow relative to binding.

One-minute recap

k_cat = V_max/[E]_total is turnover per active site. k_cat/K_m is catalytic efficiency, the best single number for comparing enzymes at low substrate, and diffusion caps it near 10⁸ to 10⁹ M^-1s^-1.