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:

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

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):

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.

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About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.