# How to Calculate Km ••• seb_ra/iStock/GettyImages

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 KM, 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. KM 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 Michaelis-Menten Plot

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 KM = [S], this equation reduces to:

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

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

## The Lineweaver-Burk Plot

Although it's possible to read KM 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 = KM/Vmax
• b = 1/[S]
• x-intercept = -1/KM

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

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