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Secondary plot (kinetics)

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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 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 and :

1 v 0 = K M A v max [ A ] + K M B v max [ B ] + 1 v max {\displaystyle {\begin{aligned}{\frac {1}{v_{0}}}&={\frac {K_{M}^{A}}{v_{\max }{}}}+{\frac {K_{M}^{B}}{v_{\max }{}}}+{\frac {1}{v_{\max }}}\end{aligned}}}

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

y-intercept = K M B v max [ B ] + 1 v max {\displaystyle {\begin{aligned}{\mbox{y-intercept}}={\frac {K_{M}^{B}}{v_{\max }{}}}+{\frac {1}{v_{\max }}}\end{aligned}}}

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 {\displaystyle K_{M}^{B}} , as shown in the Figure to the right. The slope is equal to K M B {\displaystyle K_{M}^{B}} divided by v max {\displaystyle v_{\max }} and the intercept is equal to 1 over v max {\displaystyle v_{\max }} .

Secondary Plot of enzyme system Horseradish Peroxidase and o-Phenylenediamine (with hydrogen peroxide as the second substrate)

Secondary plot in inhibition studies

A secondary plot may also be used to find a specific inhibition constant, KI.

For a competitive enzyme inhibitor, the apparent Michaelis constant is equal to the following:

apparent  K m = K m × ( 1 + [ I ] K I ) {\displaystyle {\begin{aligned}{\mbox{apparent }}K_{m}=K_{m}\times \left(1+{\frac {}{K_{I}}}\right)\end{aligned}}}

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

slope = K m v max × ( 1 + [ I ] K I ) {\displaystyle {\begin{aligned}{\mbox{slope}}={\frac {K_{m}}{v_{\max }}}\times \left(1+{\frac {}{K_{I}}}\right)\end{aligned}}}

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/KI. This method allows one to find the KI constant, even when the Michaelis constant and vmax values are not known.

References

  1. A. Cornish-Bowden. Fundamentals of Enzyme kinetics Rev. ed., Portland: London, England, (1995) pp. 30-37, 56-57.
  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).
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