120
umol/(L·min)
7
umol/L
5.83333e-2
min
8.33333e-3
L·min/umol
-1.42857e-1
L/umol
2
1
120
umol/(L·min)
7
umol/L
5.83333e-2
min
8.33333e-3
L·min/umol
-1.42857e-1
L/umol
2
1
The Lineweaver-Burk Plot Calculator determines Vmax and Km from experimental enzyme kinetics data using the double-reciprocal linearization of the Michaelis-Menten equation. Introduced by Hans Lineweaver and Dean Burk in 1934, this method transforms the hyperbolic Michaelis-Menten curve into a straight line by plotting 1/v versus 1/[S], making it possible to extract kinetic parameters using linear regression. While modern practice favors nonlinear fitting, the Lineweaver-Burk plot remains invaluable for visualizing inhibition patterns (competitive, uncompetitive, mixed) and is a standard tool in biochemistry education. Enter your experimental substrate concentration and velocity data points, and the calculator determines Vmax and Km from the best-fit line.
The Michaelis-Menten equation is inverted to obtain the Lineweaver-Burk (double-reciprocal) equation:
$$\frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$$
This has the linear form y = mx + b, where:
The calculator performs linear regression on the reciprocal data points (1/[S], 1/v) to find the best-fit slope and intercept. From these:
$$V_{max} = \frac{1}{\text{y-intercept}}, \quad K_m = \text{slope} \times V_{max}$$
With 2 data points, the line is exact. With 3+ points, the calculator uses least-squares regression for the best fit.
Vmax is found from the y-intercept (1/Vmax) — where the line crosses the y-axis. Km is found from the x-intercept (−1/Km) or from the slope. The slope (Km/Vmax) indicates the enzyme's overall efficiency at low substrate. When comparing uninhibited and inhibited data on the same Lineweaver-Burk plot: competitive inhibition shows lines intersecting on the y-axis (same Vmax, different slopes), uncompetitive inhibition shows parallel lines (different intercepts, same slope), and mixed inhibition shows lines intersecting above or below the x-axis.
Inputs
Results
Data points: (1, 15), (5, 50), (10, 66.67). Reciprocals: (1.0, 0.0667), (0.2, 0.02), (0.1, 0.015). Linear regression gives slope = 0.05, intercept = 0.01. Vmax = 1/0.01 = 100, Km = 0.05 × 100 = 5.0 μmol/L.
Inputs
Results
With just two data points: reciprocals are (0.5, 0.025) and (0.125, 0.0125). Slope = (0.025-0.0125)/(0.5-0.125) = 0.0333. Intercept = 0.025 - 0.0333×0.5 = 0.00833. Vmax ≈ 120, Km ≈ 4.0.
It is a double-reciprocal plot of 1/v versus 1/[S] that linearizes the Michaelis-Menten equation. The y-intercept gives 1/Vmax, the x-intercept gives −1/Km, and the slope gives Km/Vmax. It was the standard method for determining enzyme kinetic parameters before nonlinear regression became routine.
It distorts experimental errors unequally: data at low [S] (high 1/[S]) are magnified, giving disproportionate weight to the least accurate measurements. This can lead to biased parameter estimates. Nonlinear regression of the untransformed data is statistically superior.
The Eadie-Hofstee plot (v vs v/[S]) and Hanes-Woolf plot ([S]/v vs [S]) provide better statistical properties. The direct linear plot (Eisenthal & Cornish-Bowden) is the most robust to experimental error. However, Lineweaver-Burk remains popular for visualizing inhibition patterns.
Competitive inhibition shows lines that intersect on the y-axis: Vmax stays the same (same y-intercept) but the apparent Km increases (steeper slope). The inhibitor competes with substrate for the active site.
Uncompetitive inhibition produces parallel lines: both Vmax and Km decrease proportionally, keeping the slope (Km/Vmax) constant. The y-intercept increases and the x-intercept becomes more negative.
A minimum of 2 points defines the line exactly but provides no error estimate. At least 5-7 data points spanning a wide range of substrate concentrations (from well below Km to well above) are recommended for reliable parameter estimation.
Ideally, data should span from 0.2×Km to 5×Km. Data at very low [S] (high 1/[S]) are noisy and overly influential. Data at very high [S] (low 1/[S]) cluster near the y-axis and don't help distinguish slopes.
Yes, by keeping one substrate at saturating concentration and varying the other. This gives apparent Km and Vmax values for the varied substrate. Full characterization requires varying both substrates systematically.
Nonlinearity in a Lineweaver-Burk plot indicates deviation from simple Michaelis-Menten kinetics: substrate inhibition, cooperativity, multiple binding sites, enzyme inactivation, or mixed inhibition. Investigate the cause before forcing a linear fit.
Published in 1934, it provided an easy graphical method to determine Vmax and Km before computers were available. A straight line could be drawn through data points with a ruler, making enzyme kinetic analysis accessible to any biochemistry laboratory.
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