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The Biology Project > Biomath > Linear Functions > Applications > Enzyme Kinetics

Linear Functions Applications

Enzyme Kinetics

One of the ways biochemists characterize enzymes is to study the rates of enzyme-catalyzed reactions, a field known as enzyme kinetics. The study of enzyme kinetics provides researchers with clues as to how enzymes work. In 1913, Leonor Michaelis and Maud Menten derived a rate law that governs enzyme kinetics.

Michaelis-Menten enzyme kinetics can be modeled by the following equation,

V = Vmax[S]/Km + [S],

where V represents the reaction velocity, Vmax represents the maximum reaction velocity, Km represents the Michaelis-Menten constant, and [S] represents the substrate concentration.

Note of caution

This equation assumes that during the reaction the concentration of the enzyme-substrate complex remains constant and is lower than the concentrations of unbound substrate. These conditions are known as steady-state.


Looking at the equation, one can readily see that the velocity of the reaction, V , is dependent on the substrate concentration, [S]. In fact, the Michaelis-Menten equation is a rational function. As rational functions can be difficult to work with graphically, the Michaelis-Menten equation can be transformed into a linear equation by taking the reciprocal of both sides as,

1/V = (Km + [S])/Vmax[S] = (km/vmax)(1/[S]) + 1/vmax.

This new equation is called the Lineweaver-Burk equation after the researchers who derived it in 1934. The Lineweaver-Burk equation is a linear equation, where 1/V is a linear function of 1/[S] instead of V being a rational function of [S]. The Lineweaver-Burk equation can be readily represented graphically to determine the values of Km and Vmax.


Now use the Lineweaver-Burk equation to answer the following questions:

Determine the slope of the line represented by the Lineweaver-Burk equation.

Determine the 1/V -intercept of the Lineweaver-Burk equation.

Given a Lineweaver-Burk plot, determine the Vmax of a particular enzyme.

Given a Lineweaver-Burk plot, determine the Km of a particular enzyme.

Determine the 1/[S]-intercept of the Lineweaver-Burk equation.

Compare a Lineweaver-Burk plot to a Michaelis-Menten plot for the same data set.




The Biology Project > Biomath > Linear Functions > Applications > Enzyme Kinetics

The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

May 2006
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