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 [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]:
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 }{[}A{]}}}+{\frac {K_{M}^{B}}{v_{\max }{[}B{]}}}+{\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 }{[}B{]}}}+{\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/[B] 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 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 {[I]}{K_{I}}}\right)\end{aligned}}}
The slope of the Lineweaver-Burk plot is therefore equal to:
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