Secondary plot (kinetics) explained

In enzyme kinetics, a secondary plot uses the intercept or slope from several Lineweaver–Burk plots to find additional kinetic constants.^{[1] [2]}

For example, when a set of v by [S] curves from an enzyme 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 v₀ to the substrate concentrations [A] and [B]:

\begin{align} (1)/(v _{0}) & = (K ^{A} _{M})/(A{]}} + v _{max} {[) (K ^{B} _{M})/(B{]}} + v _{max} {[) (1)/(v _{max}) \end{align} The y-intercept of this equation is equal to the following:\begin{align} y-intercept = (K ^{B} _{M})/(B{]}} + v _{max} {[) (1)/(v _{max}) \end{align} 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/[B] to determine the Michaelis constant for substrate B, K ^{B} _{M} , as shown in the Figure to the right.^[3] The slope is equal to K ^{B} _{M} 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, the apparent Michaelis constant is equal to the following:

\begin{align} apparent K _{m=K} _{m x} \left( 1+ ([I])/(K _{I}) \right) \end{align}

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

\begin{align} slope = (K _{m})/(v _{max}) x \left( 1+ ([I])/(K _{I}) \right) \end{align}

If one creates a secondary plot consisting of the slope values from several Lineweaver-Burk plots of varying inhibitor concentration [I], 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.

Notes and References

1. [A. Cornish-Bowden]
2. J. N. Rodriguez-Lopez, M. A. Gilabert, J. Tudela, R. N. F. Thorneley, and F. Garcia-Canovas. Biochemistry, 2000, 39, 13201-13209.
3. 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).