Protein isotope effects in dihydrofolate reductase from geobacillus stearothermophilus show entropic-enthalpic compensatory effects on the rate constant

Catalysis by dihydrofolate reductase from the moderately thermophilic bacterium Geobacillus stearothermophilus (BsDHFR) was investigated by isotope substitution of the enzyme. The enzyme kinetic isotope effect for hydride transfer was close to unity at physiological temperatures but increased with decreasing temperatures to a value of 1.65 at 5 °C. This behavior is opposite to that observed for DHFR from Escherichia coli (EcDHFR), where the enzyme kinetic isotope effect increased slightly with increasing temperature. These experimental results were reproduced in the framework of variational transition-state theory that includes a dynamical recrossing coefficient that varies with the mass of the protein. Our simulations indicate that BsDHFR has greater flexibility than EcDHFR on the ps-ns time scale, which affects the coupling of the environmental motions of the protein to the chemical coordinate and consequently to the recrossing trajectories on the reaction barrier. The intensity of the dynamic coupling in DHFRs is influenced by compensatory temperature-dependent factors, namely the enthalpic barrier needed to achieve an ideal transition-state configuration with minimal nonproductive trajectories and the protein disorder that disrupts the electrostatic preorganization required to stabilize the transition state. Together with our previous studies of other DHFRs, the results presented here provide a general explanation why protein dynamic effects vary between enzymes. Our theoretical treatment demonstrates that these effects can be satisfactorily reproduced by including a transmission coefficient in the rate constant calculation, whose dependence on temperature is affected by the protein flexibility.