How To Calculate Km

In biological reactions, enzymes function much like catalysts, providing alternative pathways for reactions to occur and speeding up the overall process. An enzyme works within a substrate, and its ability to increase the velocity of the reaction depends on how well it binds with the substrate. The Michaelis constant, denoted by K_M, is a measure of enzyme/substrate affinity. A smaller value indicates tighter binding, which means the reaction will reach its maximum velocity at a lower concentration. K_M has the same units as substrate concentration and is equal to the substrate concentration when the velocity of the reaction is at half its maximum value.

The velocity of an enzyme-catalyzed reaction is a function of substrate concentration. To derive a plot for a particular reaction, researchers prepare several samples of substrate at different concentrations and record the rate of product formation for each sample. A plot of velocity (V) vs. concentration ([S]) produces a curve that climbs rapidly and levels off at the maximum velocity, which is the point at which the enzyme is working as fast as it can. This is called a saturation plot or Michaelis-Menten plot.

The equation that defines the Michaelis-Menten plot is:

\(V=\frac{V_{max}[S]}{K_M+[S]}\)

At the point at which K_M = [S], this equation reduces to:

\(V=\frac{V_{max}}{2}\)

so K_M is equal to the concentration of the substrate when the velocity is half its maximum value. This makes it theoretically possible to read K_M off the graph.

Although it's possible to read K_M from a Michaelis-Menten plot, it isn't easy or necessarily accurate. An alternative is to plot the reciprocal of the Michaelis-Menten equation, which is (after all terms have been rearranged):

\(\frac{1}{V}=\frac{K_M}{V_{max}[S]}+\frac{1}{V_{max}}\)

This equation has the form y = mx + b, where

•y = 1/V
•x = 1/S
•m = K_M/V_max 
•b = 1/[S]
•x-intercept = -1/K_M

This is the equation biochemists normally use to determine K_M. They prepare various concentrations of substrate (because it's a straight line, they technically need only two), plot the results and read K_M directly off the graph.