Enzymology

Enzyme activity: units, katal, specific activity and kinetics

From a raw absorbance slope to kcat — with the unit conversions that trip people up in between.

Reaction rate from an absorbance slope

Turn a ΔA/Δt from a plate reader or spectrophotometer into mol/s and enzyme units.

rate (M/s) = (ΔA/Δt) / (ε × l)  ·  activity = rate × assay volume

Enzyme units ↔ katal

1 U converts 1 µmol of substrate per minute; 1 katal converts 1 mol per second.

1 U = 1 µmol/min = 16.67 nkat  ·  1 kat = 6 × 10⁷ U
UnitValue

Specific activity and purification table

Total activity per milligram of protein — the number that should rise at every purification step.

specific activity = total activity / total protein  ·  fold purification = SAstep / SAstart

kcat and catalytic efficiency

Turnover number per active site, and kcat/Km — the number to compare enzymes with.

kcat = Vmax / [E]total  ·  efficiency = kcat / Km

Michaelis–Menten velocity

Rate at a given substrate concentration, with optional competitive, uncompetitive or non-competitive inhibition.

v = Vmax[S] / (Kmα + [S]α′)  ·  α = 1 + [I]/Ki
[S] / Km[S]v% Vmax

Enzyme activity units, defined

UnitDefinitionIn katal
katal (kat)1 mol of substrate converted per second — the SI unit1
U (enzyme unit, IUB)1 µmol per minute1.667 × 10⁻⁸
mU1 nmol per minute1.667 × 10⁻¹¹
nkat1 nmol per second10⁻⁹
kcatMolecules of substrate per active site per second (s⁻¹)

The katal is the official SI derived unit, but the enzyme unit refuses to die because 1 U is a conveniently human-scale amount of activity — one katal is roughly the entire enzymatic capacity of a small bioreactor.

Reading a purification table

ColumnHow to compute itWhat it tells you
Total protein (mg)concentration × volumeHow much material is left
Total activity (U)activity per mL × volumeHow much enzyme is left
Specific activity (U/mg)total activity / total proteinPurity
Yield (%)100 × total activity / starting total activityWhat you lost
Fold purificationSA / starting SAHow much contaminant you removed

A step that increases fold purification while destroying yield is often worse than a gentler step that does both modestly. Report both.

Diagnosing kinetics

  • kcat/Km near 10⁸–10⁹ M⁻¹s⁻¹ means the enzyme is diffusion-limited — catalytically perfect. Triosephosphate isomerase, carbonic anhydrase and catalase all sit there.
  • Competitive inhibitors raise the apparent Km and leave Vmax alone; uncompetitive inhibitors lower both by the same factor; non-competitive inhibitors lower Vmax only.
  • Work at [S] ≥ 10 Km if you want to measure Vmax, and at [S] ≤ 0.1 Km if you want kcat/Km directly from the initial slope.
  • Fit the hyperbola, not a Lineweaver–Burk plot. The double-reciprocal transformation inflates the weight of the least reliable low-[S] points.

Frequently asked questions

What is one enzyme unit (U)?

The amount of enzyme that converts 1 µmol of substrate per minute under defined assay conditions. In SI, 1 U = 16.67 nkat, and 1 katal = 6 × 10⁷ U.

How is specific activity calculated?

Total activity divided by total protein: U/mg. It rises during purification and is the standard measure of enzyme purity.

What is kcat and how does it differ from Vmax?

Vmax is the maximum rate for the enzyme amount present; kcat = Vmax / [E]ₜ is the per-active-site turnover number in s⁻¹, so it is independent of how much enzyme you added and can be compared between preparations.

How do I convert an absorbance slope to a reaction rate?

Rate (M/s) = (ΔA/Δt) / (ε × l). Multiply by the assay volume for mol/s, then divide by the enzyme mass for specific activity. NADH at 340 nm has ε = 6220 M⁻¹cm⁻¹.

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