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 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 = (V _{max} [S]) ÷ (K_{M }+ [S})**.

At the point at which K_{M} = [S], this equation reduces to **V = 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.

## The Lineweaver-Burk Plot

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):

**1/V = {K _{M}/(V_{max} × [S])} + (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.