Common Enzymological Experiments Allow Free Energy Profile Determination

The determination of a complete set of rate constants [free energy profiles (FEPs)] for a complex kinetic mechanism is challenging. Enzymologists have devised a variety of informative steady-state kinetic experiments (e.g., Michaelis–Menten kinetics, viscosity dependence of kinetic parameters, kinetic isotope effects, etc.) that each provide distinct information regarding a particular kinetic system. A simple method for combining steady-state experiments in a single analysis is presented here, which allows microscopic rate constants and intrinsic kinetic isotope effects to be determined. It is first shown that Michaelis–Menten kinetic parameters (<i>k</i>_cat and <i>K</i>_m values), kinetic isotope efffets, solvent viscosity effects, and intermediate partitioning measurements are sufficient to define the rate constants for a reversible uni-uni mechanism with an intermediate, EZ, between the ES and EP complexes. Global optimization provides the framework for combining the independent experimental measurements, and the search for rate constants is performed using algorithms implemented in the biochemical software COPASI. This method is applied to the determination of FEPs for both alanine racemase and triosephosphate isomerase. The FEPs obtained from global optimization agree with those in the literature, with important exceptions. The method opens the door to routine and large-scale determination of FEPs for enzymes