Lineweaver-Burk Plot Calculators

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The Lineweaver-Burk (double reciprocal) plot is a graphical method for analyzing enzyme kinetics data by linearizing the Michaelis-Menten equation. By plotting 1/v vs. 1/[S], the hyperbolic Michaelis-Menten curve becomes a straight line: y-intercept = 1/Vmax; x-intercept = −1/Km; slope = Km/Vmax. This linearization allows easy determination of Vmax and Km from the intercepts, and enables identification of enzyme inhibition types from the characteristic changes in intercepts when inhibitors are present.

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Lineweaver-Burk Equation

Starting from Michaelis-Menten: v = Vmax × [S] / (Km + [S]). Taking the reciprocal of both sides:

1/v = (Km/Vmax) × (1/[S]) + 1/Vmax

Linear form: y = slope × x + intercept, where: y = 1/v; x = 1/[S]; slope = Km/Vmax; y-intercept = 1/Vmax; x-intercept = −1/Km.

Determining Vmax and Km

From the Lineweaver-Burk plot: Vmax = 1 / (y-intercept); Km = −1 / (x-intercept) = slope × Vmax.

Inhibition Types on Lineweaver-Burk

  • Competitive inhibition: Lines with inhibitor have increased slope (higher Km) but same y-intercept (same Vmax). Lines intersect on y-axis.
  • Uncompetitive inhibition: Parallel lines — both Km and Vmax decrease proportionally. Same slope, different intercepts.
  • Noncompetitive inhibition: Lines intersect on x-axis (−1/Km unchanged; same Km). Different y-intercepts (different Vmax); different slopes.
  • Mixed inhibition: Lines intersect at a point in the second quadrant (neither on x-axis nor y-axis).

Limitations

Lineweaver-Burk gives unequal weight to data points: low [S] data (large 1/[S] values, which are most affected by experimental error) have disproportionate influence on slope and intercepts. Preferred modern methods: nonlinear regression of v vs. [S] directly using Michaelis-Menten equation, or Eadie-Hofstee plot (v vs. v/[S]), which distributes data points more evenly.

Glossary

Lineweaver-Burk Plot
A double reciprocal plot of 1/v vs. 1/[S]; linearizes Michaelis-Menten kinetics; y-intercept = 1/Vmax; x-intercept = −1/Km; slope = Km/Vmax; used to identify inhibition type.
Competitive Inhibition (Lineweaver-Burk)
Lines intersect on y-axis; increased slope (higher Km); same y-intercept (unchanged Vmax); inhibitor competes with substrate for the active site; overcome by high [S].
Uncompetitive Inhibition (Lineweaver-Burk)
Parallel lines on Lineweaver-Burk; both Km and Vmax decrease proportionally; inhibitor binds only the ES complex; not overcome by increasing substrate concentration.

Frequently Asked Questions

The Lineweaver-Burk plot linearizes the Michaelis-Menten equation by plotting 1/v (reciprocal reaction velocity) on the y-axis against 1/[S] (reciprocal substrate concentration) on the x-axis. The resulting line has: y-intercept = 1/Vmax; x-intercept = −1/Km; slope = Km/Vmax. To construct: measure initial velocities (v) at 5–8 different [S] values; calculate 1/v and 1/[S] for each; plot and draw a best-fit line by linear regression; read off y-intercept and x-intercept to determine Vmax and Km.

Competitive inhibition on Lineweaver-Burk: the inhibitor increases apparent Km without changing Vmax. On the plot: the line rotates — slope increases (higher Km/Vmax), but the y-intercept remains the same (1/Vmax unchanged). Lines with and without inhibitor intersect on the y-axis. Mechanistically: the competitive inhibitor competes with substrate for the active site; increasing [S] can overcome the inhibition; Vmax is achievable at saturating [S]; only the apparent Km (K_m_app = Km(1+[I]/Ki)) increases.

Noncompetitive inhibition: inhibitor binds both free enzyme and ES complex at a site other than the active site; Km is unchanged (same x-intercept = −1/Km); Vmax decreases (y-intercept = 1/Vmax increases); slope increases. Lines intersect on the x-axis. Uncompetitive inhibition: inhibitor binds only to the ES complex; both Km and Vmax decrease proportionally (apparent Km_app = Km/(1+[I]/Ki'); apparent Vmax_app = Vmax/(1+[I]/Ki')); the ratio Km/Vmax (slope) stays the same. Lines are parallel on Lineweaver-Burk.

The Lineweaver-Burk plot distorts experimental error: data points at low [S] (large 1/[S]) correspond to low v values that are most prone to experimental error — and taking reciprocals magnifies these errors. These inaccurate high-1/[S] points dominate the slope and intercept determination, giving biased estimates of Vmax and Km. Modern practice: measure v at multiple [S] values (at least 6–8), spanning 0.2–5× Km, and fit the Michaelis-Menten equation directly by nonlinear least-squares regression (GraphPad Prism, R). This weights all data points equally, gives unbiased parameter estimates, and provides proper confidence intervals.