Quantitative exploration of the molecular origin of the activation of GTPase

Abstract

GTPases play a major role in cellular processes, and gaining quantitative understanding of their activation demands reliable free energy surfaces of the relevant mechanistic paths in solution, as well as the interpolation of this information to GTPases. Recently, we generated ab initio quantum mechanical/molecular mechanical free energy surfaces for the hydrolysis of phosphate monoesters in solution, establishing quantitatively that the barrier for the reactions with a proton transfer (PT) step from a single attacking water (1 W) is higher than the one where the PT is assisted by a second water (2 W). The implication of this finding on the activation of GTPases is quantified here, by using the ab initio solution surfaces to calibrate empirical valence bond surfaces and then exploring the origin of the activation effect. It is found that, although the 2 W PT path is a new element, this step is not rate determining, and the catalytic effect is actually due to the electrostatic stabilization of the pre-PT transition state and the subsequent plateau. Thus, the electrostatic catalytic effect found in our previous studies of the Ras GTPase activating protein (RasGAP) and the elongation factor-Tu (EF-Tu) with a 1 W mechanism is still valid for the 2 W path. Furthermore, as found before, the corresponding activation appears to involve a major allosteric effect. Overall, we believe that our finding is general to both GTPases and ATPases. In addition to the biologically relevant finding, we also provide a critical discussion of the requirements from reliable surfaces for enzymatic reactions.

Fig. 1.

Mechanistic options for the hydrolysis of phosphate monoester in solution. R₁, R₂, and X define the reaction coordinates. (A) Structural model where the proton has been directly transferred from the attacking nucleophilic water molecule to the substrate phosphate oxygen atom (1W mechanism). (B) Structural model where the proton transfer occurs through the assistance of an additional water molecule (2W mechanism).

Fig. 2.

(A) The free energy surface in the R₁, R₂ space for the first step of the phosphate monoester hydrolysis (the cleavage of the P−O bond) in solution. The system is modeled by considering the hydrolysis of MDP using B3LYP functional with 6–31G(d) basis for P and 6–31G for other elements, with a QM region that includes the MDP plus Mg⁺² ion and 6 QM H₂O 16 × 16 10 ps QM/MM trajectories. (B) The surface for the 2W PT step (PT from the attacking water to the 2W at the TS/Plateau), showing that this step occurs spontaneously near TS1. Here ξ is the 2W PT coordinate, defined as the difference between the proton-donor and proton-acceptor distances. Further details about the definition and construction of the PT coordinate are discussed in ref. . The corresponding surfaces for the case without Mg⁺² are given in Fig. S1.

Fig. 3.

The EVB free energy profiles for the hydrolysis of GTP in solution and in the active site of RasGAP. The figure provides the profiles for different feasible paths (as explained in SI Text). React* is used to indicate that all of the energy barriers and reaction energies are with respect to their corresponding reference GS’s energy regardless of whether it is for the 1W or 2W case. Taking such a reference is justified because the energy of inserting a second water is negative in this case (Table S5). The notation Pro′ indicates that we are not dealing with the real product but with a state where the proton has just been transferred to the oxygen of the corresponding acceptor oxygen and not the final product, which is at lower energy (see main text). The positions of the critical states [React*, TS1, Int, TS(PT), etc.] on the free energy surfaces along the reaction coordinate are highlighted using markers (squares for reference solution reactions and filled in circles for the corresponding reaction in protein environment).

Fig. 4.

The energetics of the GTP hydrolysis in the Gln61Leu mutant of Ras/GAP. Notation as in Fig. 3. Note that the calculated barrier in protein environment might be overestimated, and more sampling is probably needed. The description of React* and Prod′ are the same as described in Fig. 3. The 2W path involves an H₃O⁺ formation.

Fig. 5.

The energetics of the GTP hydrolysis Gln61Ala mutant of Ras/GAP. Notation as in Fig. 3.

Fig. 6.

Demonstrating the allosteric effect in Ras/GAP and EF-Tu′. The changes in the group contributions associated with moving form the RS to the INT on mutating (A) WT Ras/GAP to Q61L and (B) EF-Tu′ to EF-Tu. The group contributions are obtained by dividing the LRA results for charged residues by 10 and those for polar groups by 2. The rational for the scaling is given in SI Text.

Fig. 7.

The EVB free energy profiles (associated with the 2W PT pathway) corresponding to the hydrolysis of GTP in solution, as well as at the active sites of EF-Tu′ and EF-Tu. Notation as in Fig. 3.