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Rapid-Equilibrium Rate Equations for A + B -> Products and Determinationf of Kinetic Paarameters

Robert A. Alberty
Organization: Massachusetts Institute of Technology
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Rate equations for enzyme-catalyzed reactions may be quite complicated and may involve a number of kinetic parameters. The rapid-equilibrium rate equations for the enzyme-catalyzed reaction A + B -> products may involve 4 kinetic parameters. When a single inhibitor is involved, the number of kinetic parameters may be 6. These rate equations are polynomials. The kinetic parameters can be determined by plotting reciprocal velocities versus reciprocal substrate concentrations, and the plotting these slopes and intercepts versus reciprocal concentrations. In 1979, Duggleby pointed out that when a rate equation involves N parameters, only N reaction rates need to be measured to determine all the kinetic parameters, but he did not have a computer that could solve systems of simultaneous equations. Solve in Mathematica makes it possible to solve N polynomial rate equations for N kinetic parameters. Solve can also be used to derive rapid-equilibrium rate equations for enzyme-catalyzed reactions and to calculate the effects of experimental errors in measured velocities and substrate concentration on the values of kinetic parameters obtained. That is all done in this Mathematica Package for ordered A + B -> products, random A + B -> products, competetitive inhibition, uncompetitive inhibition, and mixed inhibition.

The objective here is not just to determine kinetic parameters, but to identify the mechanism of catalysis; that is the series of reactions by which the catalysis is accomplished.

The use of the minimum number of measured velocities is especially important in studying more complex enzymatic catalysis (for example, A + B + C -> products and A + nB -> products), and in studying the effect of pH and temperature on kinetic parameters, because of the very large number of velocities that have to be measured to make Lineweaver-Burk plots. In this package, rapid-equilibrium rate equations are considered, but this method can also be applied to steady-state rate equations.

*Science > Biochemistry

Biochemistry, enzyme-catalyzed reactions, kinetics, kinetic parameters, enzyme mechanisms
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