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

Abstract

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.

Figure 1.

Reaction catalyzed by the human MAT2A enzyme between ATP and l-methionine, resulting in the formation of S-adenosyl l-methionine and triphosphate leaving group.

Figure 2.

Reaction catalyzed by the pvADA enzyme between adenosine and hydroxide ion, resulting in the formation of inosine and ammonia.

Figure 3.

Equilibrated structure of the MAT2A enzyme in complex with ATP and MET along with two Mg²⁺ ions.

Figure 4.

Bond breaking (d_OC) and bond forming (d_SC) distances for a typical reactive trajectory for the reaction catalyzed by the MAT2A enzyme.

Figure 5.

Transition state structure of the reaction catalyzed by the human MAT2A enzyme. The bond parameters d_SC and d_OC are 2.31 Å and 2.09 Å, respectively.

Figure 6.

Committor distribution analysis for obtaining the reaction coordinate of the MAT2A-catalyzed reaction. The figure on the left has the QM region constrained, and the figure on the right has the QM region along with the Gln113, Ser114, Arg249, and Arg264 residues constrained.

Figure 7.

Free energy as a function of the order parameter for the reaction catalyzed by the human MAT2A enzyme. The activation barrier is calculated to be 16 kcal mol⁻¹. The solid colored disks represent the free energies calculated within the individual windows which is adjusted to make the free energy as a function of the order parameter a continuous function.

Figure 8.

Equilibrated structure of pvADA enzyme complexed with adenosine, an OH⁻ anion, and Zn²⁺.

Figure 9.

Bond breaking (d_NC), bond forming (d_OC) distances for a typical reactive trajectory for the reaction catalyzed by the pvADA enzyme.

Figure 10.

Transition state structure of the reaction catalyzed by the ADA enzyme. The formation of the Meisenheimer complex like structure with d_NC = 1.62 Å and d_OC = 1.49 Å is observed.

Figure 11.

Free energy as a function of the reaction parameter for the ADA-catalyzed reaction. The activation barrier is calculated as 21 kcal mol⁻¹. The solid colored disks represent the free energies calculated within the individual windows which are adjusted to make the free energy as a function of the order parameter a continuous function.