The Lineweaver–Burk plot (or double-reciprocal plot) is a linear graphical representation of enzyme kinetics. It is created by taking the reciprocal of both sides of the Michaelis–Menten equation, transforming a hyperbolic curve into a straight line. This linearization makes it much easier to determine key kinetic parameters and identify types of enzyme inhibition. The Mathematical Equation
The standard Michaelis–Menten equation models initial velocity (V₀) against substrate concentration (
V0=Vmax[S]Km+[S]cap V sub 0 equals the fraction with numerator cap V sub m a x end-sub open bracket cap S close bracket and denominator cap K sub m plus open bracket cap S close bracket end-fraction
Taking the reciprocal yields the Lineweaver–Burk equation:
1V0=(KmVmax)1[S]+1Vmaxthe fraction with numerator 1 and denominator cap V sub 0 end-fraction equals open paren the fraction with numerator cap K sub m and denominator cap V sub m a x end-sub end-fraction close paren the fraction with numerator 1 and denominator open bracket cap S close bracket end-fraction plus the fraction with numerator 1 and denominator cap V sub m a x end-sub end-fraction
This matches the slope-intercept form of a straight line (y = mx + b), where: y-variable:
1V0the fraction with numerator 1 and denominator cap V sub 0 end-fraction x-variable:
1[S]the fraction with numerator 1 and denominator open bracket cap S close bracket end-fraction Slope (m):
KmVmaxthe fraction with numerator cap K sub m and denominator cap V sub m a x end-sub end-fraction y-intercept (b):
1Vmaxthe fraction with numerator 1 and denominator cap V sub m a x end-sub end-fraction Key Intercepts on the Graph
Instead of reading values directly, you calculate parameters using the reciprocals of where the line crosses the axes: y-intercept: Equals
1Vmaxthe fraction with numerator 1 and denominator cap V sub m a x end-sub end-fraction . (A lower intercept means a higher maximum velocity). x-intercept: Equals
−1Kmnegative the fraction with numerator 1 and denominator cap K sub m end-fraction
. (Extrapolated into the negative quadrant; a point closer to zero means a higher Kmcap K sub m value, indicating lower enzyme affinity). Diagnosing Enzyme Inhibition
According to AK Lectures and standard biochemistry profiles, the plot visually differentiates the three main types of reversible enzyme inhibition: Inhibition Type Vmaxcap V sub m a x end-sub Kmcap K sub m Line Shift Behavior on Plot Competitive
Lines intersect at the exact same point on the y-axis; slope steepens. Noncompetitive
Lines intersect at the exact same point on the x-axis; y-intercept rises. Uncompetitive
Parallel lines; both intercepts shift away from zero by the same ratio. Limitations and Modern Usage
While historically vital before advanced computing, the Lineweaver–Burk plot has a major statistical flaw: YouTube·Moof University Enzymes (Part 3 of 5) – Lineweaver Burk Plot
Leave a Reply