The Michaelis constant, K_{m}, is a parameter in the Michaelis-Menten equation. K_{m} is equal to the substrate concentration where the corresponding reaction rate is ½ • V_{max}. An enzyme with a low K_{m}, therefore, achieves its half-maximal velocity at a low substrate concentration, while an enzyme with a high K_{m} needs high substrate concentrations to achieve this velocity. It has been experimentally shown, that K_{m} of an enzyme is usually close to the cellular concentration of its substrate. For an enzymatic reaction involving 2 steps, where the second step is rate-limiting, K_{m} is approximately equal to the dissociation constant of the ES complex. In this case, a low K_{m} implies a high affinity for the substrate; however this interpretation of K_{m} is only valid for a few enzymes [1].
Figure 1: Figure 1.a; Michaelis-Menten equation fitted to a plot of initial rates against substrate concentration. When the substrate concentration equals K_{m}, the reaction rate is ½*V_{max}. Figure 1.b; An illustration of the Lineweaver-Burk equation fitted to a double-reciprocal transformation of an enzyme kinetic dataset.
Several methods for determining Km exist. The most direct method is to plot V_{0} against [S] and use curve fitting software to fit the Michaelis-Menten equation directly. However, certain transformations allow determination via linear regression, and these transformations are also useful when analyzing enzyme inhibition. Several transformations are possible; however, a simple one is obtained by taking the reciprocal on both sides of the Michaelis-Menten equation. This leads to the following expression, called the Lineweaver-Burk equation:
1/V_{0} = 1/V_{max} + K_{m}/V_{max} • 1/[S]
This equation shows, that a plot of 1/V_{0} against 1/[S] should give a plot that can be fitted by a straight line with the y-intercept 1/V_{max} and slope K_{m}/V_{max}. Thus, K_{m} can be obtained using linear regression. Figure 1.b shows an illustration of how to interpret the slope and intersects on a Lineweaver-Burk plot. [1]
Notable, the Lineweaver-Burk transformation is not the only option. For example, a plot of [S]/V_{0} against [S] (a Hanes–Woolf plot) will also result in a straight line [2]. However, in this case, we will use the Lineweaver-Burk transformation.
Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008). Principles of Biochemistry (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 978-0-7167-7108-1.
Atkins, G.L. and Nimmo, I.A. (1975) A comparison of seven methods for fitting the Michaelis-Menten equation. Biochem. J. 149, 775-777.