Engineering & Scientific
Lineweaver-Burk & Hanes-Woolf Enzyme Kinetics: Vmax, Km & Inhibitor Diagnosis
Extract catalytic maximum velocity V_max and Michaelis constant K_m from substrate-velocity assays using double-reciprocal Lineweaver-Burk (1/v vs 1/[S]) and Hanes-Woolf ([S]/v vs [S]) OLS regression.
Comparing Lineweaver-Burk double-reciprocal plots against Hanes-Woolf variance weighting
Inverting the hyperbolic Michaelis-Menten rate law v = (V_max * [S]) / (K_m + [S]) yields Hans Lineweaver and Dean Burk’s (1934) double-reciprocal linear equation: 1 / v = (K_m / V_max) * (1 / [S]) + (1 / V_max). Regressing Y = 1/v against X = 1/[S] recovers V_max = 1 / INTERCEPT(Y, X) and K_m = SLOPE(Y, X) / INTERCEPT(Y, X).
Because taking 1/[S] amplifies experimental error at the lowest substrate concentrations, biochemists cross-check estimates with the Hanes-Woolf transformation [S] / v = (1 / V_max) * [S] + (K_m / V_max), where V_max = 1 / SLOPE([S]/v, [S]) and K_m = INTERCEPT([S]/v, [S]) / SLOPE([S]/v, [S]). Comparing inhibited vs uninhibited runs diagnoses Competitive Inhibition (V_max unchanged, apparent K_m increases) vs Non-Competitive Inhibition (V_max drops, K_m unchanged).
| Linearization | Y vs X Axes | V_max Extraction | K_m Extraction |
|---|---|---|---|
| Lineweaver-Burk | 1/v vs 1/[S] | 1 / INTERCEPT(1/v, 1/[S]) | SLOPE(1/v, 1/[S]) / INTERCEPT(1/v, 1/[S]) |
| Hanes-Woolf | [S]/v vs [S] | 1 / SLOPE([S]/v, [S]) | INTERCEPT([S]/v, [S]) / SLOPE([S]/v, [S]) |
Lineweaver-Burk V_max & K_m Regression Formulas
Compute reciprocal columns C2:C5 (=1/A2) and D2:D5 (=1/B2), then invert INTERCEPT(D2:D5, C2:C5) for V_max and divide SLOPE by INTERCEPT for K_m.
=ROUND(SLOPE(D2:D5, C2:C5) / INTERCEPT(D2:D5, C2:C5), 2)Hanes-Woolf Cross-Check Formula ([S]/v vs [S])
Regress E2:E5 (=A2/B2) against substrate concentration A2:A5 directly to verify agreement across low- and high-substrate points.
=ROUND(1 / SLOPE(E2:E5, A2:A5), 2)Try the example
Use the original values or change them to test your understanding.