Transition Path Sampling Based Calculations of Free Energies for Enzymatic Reactions: The Case of Human Methionine Adenosyl Transferase and Plasmodium vivax Adenosine Deaminase

Transition path sampling (TPS) is widely used for the calculations of reaction rates, transition state structures, and reaction coordinates of condensed phase systems. Here we discuss a scheme for the calculation of free energies using the ensemble of TPS reactive trajectories in combination with a window-based sampling technique for enzyme-catalyzed reactions. We calculate the free energy profiles of the reactions catalyzed by the human methionine S-adenosyltransferase (MAT2A) enzyme and the Plasmodium vivax adenosine deaminase (pvADA) enzyme to assess the accuracy of this method. MAT2A catalyzes the formation of S-adenosine-l-methionine following a S_N2 mechanism, and using our method, we estimate the free energy barrier for this reaction to be 16 kcal mol^-1, which is in excellent agreement with the experimentally measured activation energy of 17.27 kcal mol^-1. Furthermore, for the pvADA enzyme-catalyzed reaction we estimate a free energy barrier of 21 kcal mol^-1, and the calculated free energy profile is similar to that predicted from experimental observations. Calculating free energies by employing our simple method within TPS provides significant advantages over methods such as umbrella sampling because it is free from any applied external bias, is accurate compared to experimental measurements, and has a reasonable computational cost.