On possible pitfalls in ab initio quantum mechanics/molecular mechanics minimization approaches for studies of enzymatic reactions

Abstract

Reliable studies of enzymatic reactions by combined quantum mechanics/molecular mechanics (QM/MM) approaches, with an ab initio description of the quantum region, presents a major challenge to computational chemists. The main problem is the need for a very large computer time for the evaluation of the QM energy, which in turn makes it extremely challenging to perform proper configurational sampling. A seemingly reasonable alternative is to perform energy minimization studies of the type used in gas-phase ab initio studies. However, it is hard to see why such an approach should give reliable results in protein active sites. To examine the problems with energy minimization QM/MM approaches, we chose the hypothetical reaction of a metaphosphate ion with water in the Ras.GAP complex. This hypothetical reaction served as a simple benchmark reaction. The possible problems with the QM/MM minimization were explored by generating several protein configurations from long MD simulations and using energy minimization and scanning of the reaction coordinates to evaluate the corresponding potential energy surfaces of the reaction for each of these different protein configurations. Comparing these potential energy surfaces, we found major variations of the corresponding minima. Furthermore, the reaction energies and activation energies also varied significantly even for similar protein configurations. The specific coordination of a magnesium ion, present in the active center of the protein complex, turned out to influence the energetics of the reaction in a major way, where a direct coordination to the reactant leads to an increase of the activation energy by 17 kcal/mol. Apparently, using energy minimization to generate potential surfaces for an enzymatic reaction, while starting from a single protein structure, could lead to major errors in calculations of activation free energies and binding free energies. Thus we believe that extensive samplings of the configurational space of the protein are essential for meaningful determination of the energetics of enzymatic reactions. The possible relevance of our conclusion with regard to a recent study of the RasGAP reaction is discussed.

Figure 1

Showing the substrate GTP and its hydrogen bonds to residues of the Ras•GAP complex as derived from the crystal structure of the hydrolysis transition state analogue of Scheffzek et al. (PDB code: 1WQ119).

Figure 2

Showing the two reaction coordinates R and r used in the present study.

Figure 3

Division of the simulated system into QM and MM regions. The upper part shows the QM region and a part of the MM region that contains the guanosine moiety. The rest of the MM region, which is not shown in the figure, contains the surrounding protein and solvent molecules. The lower part shows the QM fragment capped with a hydrogen link atom. The notations LABP and LAH designate, respectively, the link atom bond partner and the link atom host. The link atom host is replaced here by the hydrogen link atom (LA).

Figure 4

Showing the free energy surface for the reference reaction of metaphosphate with water in solution and dependency on the two reaction coordinates R and r. The solid lines are the equipotential lines of the surface with the corresponding free energy values given next to them. The dashed line represents the reaction pathway connecting the shallow reactant region (upper left corner) to the product valley (lower right corner) through the transition state (marked with a dot). The free energies of the ground, transition and product as well as the reaction and activation free energy are given on the right side of the figure. All energies are given in kcal/mol.

Figure 5

Showing the potential energy surface of the reaction of metaphosphate with water in the active site of Ras•GAP for one representative protein structure. The red line represents the reaction pathway connecting the reactant (on the left side) with the product (right side)

Figure 6

Showing the temporal development of the potential energy surface of the reaction metaphosphate with water in the active site of Ras•GAP. The generic surface is based on the two dimensional PES’s, like the one shown in Fig. 5, projected on an intrinsic reaction coordinate (IRC), determined at five different protein configurations taken from the MD trajectory after 600, 700, 800, 900 and 1000 ps. The reactant states are marked with squares, the product states with triangles and the transition states with circles. The inscribed numbers correspond to one of the five protein structures.

Figure 7

Showing the potential energy surfaces in the transition state region for the reaction of metaphosphate with water in Ras analogous to Fig. 4. The lower half displays the case where the Mg²⁺ ion is coordinated between the metaphosphate reactant and GDP. The upper half shows the PES for the case where the Mg²⁺ ion is coordinated to two GDP oxygens and not to the metaphosphate.