Common Enzymological Experiments Allow Free Energy Profile Determination

Abstract

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, KIEs, 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 (kcat and KM 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 to combine 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.

Is the catalytic activity of triosephosphate isomerase fully optimized? An investigation based on maximization of entropy production

“…These results could be used to check the usefulness of entropy production maximization for other enzymes with cyclic reaction schemes [53]. Free-energy transduction from driving to driven thermodynamic force is possible by enzymes associated with kinetic schemes having a greater number of functional states connected with more than one cycle [7,18].…”

Carbon Acidity in Enzyme Active Sites

“…The procedure used here does not involve time-consuming numerical integration of differential rate equations. Instead, the adjustable parameters (rate constants) are altered by the chosen algorithm and the new parameters are used to calculated a new value of the target function (see below) (Toney, 2013). This is much less computationally demanding than fitting to primary kinetic data via numerical integration, allowing essentially exhaustive exploration of parameter space.…”

“…Here, a recently introduced method for free energy profile (FEP) determination (Toney, 2013) is applied to five enzymes, employing experimental data reported in the literature. The FEPs allow calculation of proton transfer equilibrium constants in active sites.…”

Effects of Glycosylation on the Enzymatic Activity and Mechanisms of Proteases

“…The distinct conformational states of these reaction steps were calculated for trypsin with a combined approach of quantum mechanics/molecular mechanics with molecular dynamics/free energy perturbation calculations, resulting in a free energy profile, which was extended by analyzing the role of Asp102 [118,144]. In addition, free energy profiles for the single steps of this mechanism have been determined, including enzyme product complexes, using rate constants from Michaelis−Menten kinetics, viscosity and isotope kinetic parameters (Figure 4) [145]. Although K M , k cat , and k cat / K M do not directly correspond to free energies in the reaction profile, they correlate, such as a low K M with a high ∆ G bind of the enzyme substrate complex formation, a high k cat with a low ∆ G ‡ , and k cat / K M with the overall change of the free energy ∆ G = ∆ G ‡ − ∆ G ES [146,147].…”