In enzyme kinetics, a secondary plot uses the intercept or slope from several Lineweaver–Burk plots to find additional kinetic constants. For example, when a set of v by curves from an

enzyme Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. A ...

with a ping–pong mechanism (varying substrate A, fixed substrate B) are plotted in a Lineweaver–Burk plot, a set of parallel lines will be produced. The following Michaelis–Menten equation relates the initial reaction rate ''v''₀ to the

substrate Substrate may refer to: Physical layers *Substrate (biology), the natural environment in which an organism lives, or the surface or medium on which an organism grows or is attached ** Substrate (locomotion), the surface over which an organism lo ...

concentrations and :

\begin 
\frac &= \frac+\frac+\frac
\end

The y-intercept of this equation is equal to the following: :

\begin
\mbox = \frac+\frac
\end

The y-intercept is determined at several different fixed concentrations of substrate B (and varying substrate A). The y-intercept values are then plotted versus 1/ to determine the Michaelis constant for substrate B,

K_M^B

, as shown in the Figure to the right.The Horseradish Peroxidase/ o-Phenylenediamine (HRP/OPD) System Exhibits a Two-Step Mechanism. M. K. Tiama and T. M. Hamilton, ''Journal of Undergraduate Chemistry Research'', 4, 1 (2005). The slope is equal to

K_M^B

divided by

v_\max

and the intercept is equal to 1 over

v_\max

Secondary plot in inhibition studies

A secondary plot may also be used to find a specific inhibition constant, K_I. For a competitive

enzyme inhibitor An enzyme inhibitor is a molecule that binds to an enzyme and blocks its activity. Enzymes are proteins that speed up chemical reactions necessary for life, in which substrate molecules are converted into products. An enzyme facilitates a sp ...

, the apparent Michaelis constant is equal to the following: :

\begin
\mbox K_m=K_m\times \left(1+\frac\right)
\end

The slope of the Lineweaver-Burk plot is therefore equal to: :

\begin
\mbox =\frac\times \left(1+\frac\right)
\end

If one creates a secondary plot consisting of the slope values from several Lineweaver-Burk plots of varying inhibitor concentration the competitive inhbition constant may be found. The slope of the secondary plot divided by the intercept is equal to 1/K_I. This method allows one to find the K_I constant, even when the Michaelis constant and v_max values are not known.

References

{{refbegin Enzyme kinetics