Quantitative exploration of the molecular origin of the activation of GTPase

Significance

The origin of the activation of GTPases is explored considering the evidence that the transition state for the reference solution reaction involves a proton transfer between two water molecules. Ab initio quantum mechanical/molecular mechanical–based calibration of empirical valence bond surfaces of the solution reaction is used to simulate the GTPase activation process. The activation is found to reflect the same type of electrostatic stabilization obtained previously for the single water mechanism. The transition state proton transfer step does not appear to be rate limiting and thus is irrelevant to the catalytic effect. The calculated activation of RasGAP and EF-Tu reproduce the observed trend quantitatively and establishes its allosteric origin. We believe that our finding is general to all GTPases.

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 (1W) is higher than the one where the PT is assisted by a second water (2W). 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 2W 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 1W mechanism is still valid for the 2W 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.

Detailed understanding of many problems in biology boils down to the elucidation of the correct reaction mechanism in the protein and in solution and to the elucidation of the origin of the corresponding catalytic effect. However, this requires overcoming the challenge of obtaining accurate free energy surfaces in the condensed phase. Such a task can be accomplished, in principle, by the combined quantum mechanical/molecular mechanical (QM/MM) method (1–5). However, the implementation of this method is still very challenging. At present, we are not at the stage reached in studies of gas phase reactions, where the results of ab initio calculations are sometimes considered almost as substitutes for experimental results. Nevertheless, recent advances in ab initio QM/MM [QM(ai)/MM] studies (2, 4–6) brought us closer to having quantitative results for solution reactions and in some respects to quantitative results for enzymes, especially if one evaluates reliable QM(ai)/MM free energy surfaces for the solution reaction and then use the resulting surfaces to calibrate empirical valence bond (EVB) surfaces for studying the relevant enzymatic reaction. Here we exploit these advances by exploring the hydrolysis of phosphate monoesters that is the key to the activation of GTPases. That is, we start by quantifying the energetics of the solution reaction and then use the solution free energy surface to calibrate EVB surface that allow us to reliably explore the energetics in GTPases. We demonstrate that the origin of the catalytic effect obtained in our previous studies of Ras GTPase activating protein (RasGAP) is valid even with the two water (2W) path, but the fact that the single water (1W) path is high in energy forces the system to use either Gln or a water molecule as a proton transfer (PT) shuttle. We then apply the same analysis to the activation of EF-Tu, where we show that His-84 does not serve as a base and that the most likely mechanism is a 2W mechanism with a major transition state stabilization due to electrostatic allosteric effect.

Quantifying the Relationship Between Competing Mechanisms of Phosphate Monoester Hydrolysis in Solution

Phosphate hydrolysis reactions are arguably the most important class of biological reactions (7–11), and it is thus important to elucidate the relevant mechanism in solution and proteins. In this respect, it is now gradually realized that QM(ai)/MM studies are perhaps the only way of resolving the fundamental mechanistic controversies associated with phosphate hydrolysis (11). However, this does not mean that just running uncritical black box QM/MM-based calculations can be used to resolve deep mechanistic issues. That is, in addition to uncritical theoretical studies of phosphate hydrolysis by irrelevant gas phase and energy minimization studies (for discussion see ref. 11), even recent studies that involve some configurational sampling (12, 13), or path search approaches (14) (see Exploring the Activation of EF-Tu and SI Text), have not provided yet reliable mechanistic picture. The difficulty to elucidate the mechanism reflected several problems including the most studies have not explored all of the possible options (including key earlier proposals). In the case of phosphate monoester hydrolysis, the debate involves two issues; first, it is not clear whether the hydrolysis follows an associative or a dissociative path (unfortunately, as discussed in ref. 11, most of the recent studies failed to realize correctly the clear distinction between these two), and second, it has not been clear whether the PT from the attacking nucleophilic water molecule to the γ-phosphate oxygen occurs in a direct manner or with the assistance of several water molecules. Thus, it has not been sufficient (or useful) to explore a PT between several water molecules while not carefully examining a transfer from a single water molecule in a direct manner.

The basic major issues associated with the determination of the mechanism of the hydrolysis of phosphate monoesters and related systems can be formulated by considering the structural models presented in Fig. 1, where R₁ represents the nuclear reaction coordinate between the P_γ and the leaving O_w atom, R₂ describes the nuclear reaction coordinate between the P_γ and the attacking nucleophilic O_w atom, and the PT reaction coordinate is designated by X. Apparently, the PT can occur along the associative or dissociative paths in either a direct manner (1W) or with the assistance of the second water molecule (2W) (this case is also taken as a representation of PT involving more water molecules).

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).

Considering the crucial importance of the above issue, we recently invested (5) a major effort in obtaining reliable QM(ai)/MM free energy surfaces for different mechanistic options, focusing on the difference between the 1W and 2W mechanisms. Our study found that the hydrolysis of phosphate monoesters proceeds through a plateau in the R₁/R₂ space, where the attacking water approach the γ-phosphate and the leaving group start to move away to around 2.8−3.0 Å (see discussion in the SI Text and Fig. S1), and then a PT step along either the 2W or 1W path. It was found that the barrier along the 2W PT path is only 2–3 kcal/mol from the plateau, whereas the 1W barrier is higher by more than 5–7 kcal/mol than the 2W barrier. Interestingly, widely used lower level functionals like Becke−Lee−Yang−Parr (BLYP) gave a smaller difference between the 1W and 2W barriers.

Adding an Mg⁺² ion to the QM(ai)/MM simulation system, with the needed additional QM water molecules, made the evaluation of a reliable surface more challenging, but the conclusion that the 2W barrier is lower than that of the 1W remains a robust conclusion. The inclusion of the Mg⁺² ion led to a more associative path with a small barrier before the plateau, followed by a barrierless 2W PT at the R₁/R₂ transition state (TS). This finding is most probably reliable, despite the fact that the actual activation barrier for the surface with Mg⁺² is an overestimate (SI Text). At any rate, considering the fact that the observed activation barrier in solution is found to be very similar with and without the Mg⁺² ion [31.2 vs. 30.4 kcal/mol, respectively (15)], we took the shape of the surface with Mg⁺² as the shape of a consensus reference solution reaction for studies of GTPases while using the observed activation barrier (about 30.4 kcal/mol) as our reference barrier. Thus, we calibrated an EVB solution surface in the presence of Mg⁺² while considering the shape of the surface of Fig. 2 and using Table S1 as a guide in obtaining calibrated EVB parameters (Tables S2–S4).

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. 5. The corresponding surfaces for the case without Mg⁺² are given in Fig. S1.

Having a reliable EVB surface for the solution reaction allowed us to explore the surface in the protein without the extremely challenging need to obtain fully converging QM(ai)/MM free energy surfaces in the protein, which at present is probably not the most effective way of reaching concrete conclusions. The corresponding study is described below.

Using the Calibrated EVB in Moving Form Solution to the Ras/GAP System

The activation of Ras by GAP has been arguably the most prominent model for the activation of GTPases. Here the question has been: what are the features of the active site of the Ras/GAP complex that makes the reaction seven orders of magnitude faster than in the isolated Ras (16, 17). Although the electrostatic role of the so-called arginine finger (18) has been easy to reproduce (19, 20), interest and controversy focused on the role of Gln-61 that was originally proposed to serve as a base (21, 22). In this case, we have been able to show as early as in 1992 (23) that Gln-61 cannot be the base in the ground state (because the barrier for ground state PT to Gln-61 is higher than the overall actual barrier and thus the ultimate base must be the GTP) (24). Furthermore, we found that Gln-61 does not affect the reaction in a direct way, at least in the 1W mechanism (the obvious option to explore at that stage). Thus, it was concluded that Gln-61 serves indirectly in an allosteric mechanism by changing the P-loop interaction with the TS (19). Now, because our recent QM(ai)/MM free energy calculations determined that in solution the 2W mechanism has a lower barrier than the 1W, it is important to explore the corresponding implications on the reaction in Ras/GAP, and such a study is reported below.

Starting with the WT Ras/GAP, we considered the options (Fig. 3) of concerted and stepwise (2W type) PT from the attacking water through Gln-61 to the phosphate oxygen, as well as the 2W mechanism without participation of Gln and the 1W mechanism (Fig. S2, schemes I–III and Table S1). In all cases, we calibrated the relevant EVB surfaces on the reference solution reaction (SI Text) and explored the energetics of the reaction in Ras/GAP. The surfaces in the protein were evaluated along the TS 2W assisted type path while moving to TS1, and the plateau and then performing the PT step from both the TS1 and the plateau. The calculated free energy profiles are summarized in Fig. 3 (the corresponding energetics are presented in Table S5), where it is shown that the main catalytic effect is due to the drastic reduction in the free energy of TS1 and the plateau. The PT step can occur both in concerted and stepwise paths. Interestingly, however, because this PT step is already close to zero barriers in solution, there is no significant catalytic effect at this step. This finding implies that our previous calculations (19, 20, 25) that considered a concerted 1W path have captured the correct catalytic effect. That is, our previous studies calibrated the EVB surface in a way that the TS of the 1W path would reproduce the observed barrier in water (which turned out to be TS1). Thus, the corresponding barrier in the protein is similar to that of the TS1 or the plateau in the 2W PT model. The same is true for the catalytic effect, which is the difference between the barriers in the protein and in water.

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).

After considering the catalytic effect in the WT enzyme (with Gln-61), we explored the origin of the enormous (about 9 kcal/mol) effect of the Gln61Leu mutation of Ras/GAP. Here we had to consider the 2W mechanism while exploring the energetics of inserting additional water molecule plus the intrinsic effect of the mutation. The results of the corresponding simulations are summarized in Fig. 4 and Table S5. As seen from Table S5, the insertion and movement of the second water does not cost much energy; either the water is already in the site (more stable than in bulk water) or it can go in for around 1 kcal/mol. However, the energetics of reaching the plateau and TS1 increases significantly relative to the WT enzyme. Finally, as before, the 2W PT step is not rate limiting and thus does not contribute to the change in the relevant activation energy. Apparently the present results are very similar to those obtained with our previous 1W TS (19).

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.

We also explored the energetics of the reaction in the Gln61Ala mutant. In this case, we examined the participation of a second water in a 2W path, and the corresponding energetics are considered in Fig. 5 (Table S5). Here the effect of the mutation is not large, in agreement with qualitative experimental studies (19). Finally, we explored the involvement of a second water in the WT enzyme (Fig. 3) and found that the corresponding barrier is comparable to that with direct Gln-61 involvement.

Fig. 5.

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

At this stage, it is important to see if our previous conclusions about the allosteric effect are still valid. To examine this issue, we evaluated the electrostatic contributions of the protein amino acid residues going from the reactant state (RS) to the plateau in the WT and the Gln61Leu mutant, and the corresponding results are presented in Fig. 6. As seen in the figure (and in agreement with ref. 19), the group contributions for the P- loop, switch I, switch II, and Mg²⁺ ion appear to be very different. The changes in group contributions strongly supports our allosteric proposal where the mutation changes the active site preorganization.

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.

Overall, we concluded that the catalytic effect of using the 2W path (or the related use of Gln-61 as a “TS-PT shuttle” in Ras/GAP) is negligible and that the main role of the enzyme is to stabilize the plateau and TS1, where the main shift of the negative substrate charge occurs. In principle, if there is no residue, or a water molecule, which can support a 2W-type mechanism, the system will have to use the higher-energy 1W path that may become the rate-limiting step. However, even in the Gln61Leu mutant, the energetics of bringing a second water do not seem to be a major effect, and the main mutational effect already occurs before the PT step.

Exploring the Activation of EF-Tu

Another interesting and unresolved questions about G-proteins is the action of the elongation factor EF-Tu (26) and the related elongation factor G (EF-G) (27, 28). The GTP hydrolysis rate in this system increases by seven orders of magnitude (29) on activation by the ribosome. Here, as in the Ras/GAP GTPase case, the question is what is so special about the activated system? In particular, because the activation process involves the movement of His-84 to the proximity of the γ-phosphate of the GTP, it has been suggested by some (e.g., ref. 26) that the activation involves a histidine (His-84) as a base mechanism. On the other hand, our study that considered the structures of both the active ribosome-bound (EF-Tu′) and inactive (EF-Tu) forms (29) concluded that the His-84 cannot act as a base. We also concluded, using the 1W surfaces, that the direct effect of His-84 on the TS energy is only around 2 kcal/mol and that its effect is thus allosteric. We also reproduced, using calculations, the change in the pK_a of His-84 due to its interaction with the sarcin–ricin loop.

Recent works (14, 30) questioned some of the findings in our previous study of EF-Tu′. However, one of those works (14) had some problems, including the presumption that our 1W mechanism would give an about 50-kcal/mol barrier (overlooking the facts that the method used by them cannot give the 1W barrier even in bulk water and that the barrier in the enzyme should be about 20 kcal/mol with proper sampling). This overestimate reflected the unjustified assumption that just running basically guided QM/MM energy minimization in proteins from classically obtained starting points (without careful convergence analysis) can give quantitative information about catalysis. Thus, the work of ref. 14 will be considered here and in the SI Text mainly in a discussion of the possible problems with some emerging QM/MM studies. The second and by far more careful work (30) attempted to explore the origin of the GTPase activation while focusing mainly on the electrostatic interaction between the His-84 and the nucleophilic OH⁻, which would be produced in a stepwise mechanism that involves a direct PT from the attacking water to the phosphate oxygen (basically our earliest 1W mechanism, with a fully stepwise phosphate as a base mechanism). This work used a similar strategy to that introduced in our early study of Ras (23) and concluded that the catalysis is due to the very large electrostatic interaction between the protonated His-84 and the OH⁻ ion. Note, however, that the OH⁻ formed before the actual TS and an attempt to model the effect of His-84 on a dissociative type TS gave a far smaller effect (only about 4–3 kcal/mol with the reported estimate of the effect of moving to the inactive form). Ref. 30 also suggested that the allosteric effect from the P-loop and other parts of the protein is unlikely to be important. However, this assertion has been based on structural rather than energy considerations (SI Text). The work of ref. 30 has also been consistent with our conclusion that the His-84 cannot serve as a base and our finding that the protonated His-84 is pulled near the substrate in the cognate configuration due to the interaction with the sarcin–ricin loop. Now, although it is very reasonable to challenge some of our finding by simple and in some cases reliable calculations of PT energies (as well as by logical arguments), some of the points brought to support the arguments of ref. 30 are unjustified. Thus, we will provide the main details of the clarifications in the SI Text and allow the reader to focus on the actual open issues here. That is, we will examine below what is the origin of the activation of EF-Tu, using the emerging improved knowledge about the corresponding reference solution reaction.

We started our EF-Tu study by exploring the possibility that His-84 can serve as a PT shuttle as in a 2W-type mechanism (Figs. S3, scheme I′, and S4, scheme III′), examining the possibility of early PT from a protonated His-84 to the phosphate oxygen and reprotonation from the attacking water [Fig. S4, scheme III′(c)]. Here, the calibrated EVB surface produced too high of a barrier in EF-Tu′, and a similar high barrier occurred with more concerted paths [Fig. S4, scheme III′(b,c)]. We also examined the possibility of having unprotonated His-84 serving as a proton acceptor in TS1 or the plateau [Fig. S3, scheme I′(f)], as well as the other possibilities that His-84 is directly involved in PT step at TS/plateau [Fig. S3, scheme I′(b,e)]. However, here the energy of deprotonating His-84 leads to a 6-kcal/mol destabilization of the reactant state in the protein, and the overall barriers for the different possible paths (including His-84 as a base) become too high (SI Text). Finally, we also explored the mechanism of ref. 14 and found it to be unfavorable (SI Text). Furthermore, we found the corresponding calculations to be insufficiently reliable (SI Text).

In view of the above findings, we returned to the likely possibilities that His-84 is protonated and is not directly involved. Here we have three options: (i) the 2W mechanism, where a second water has to be inserted near His-84; (ii) the regular 1W mechanism with its inherent high barrier for PT; and (iii) the stepwise water mechanism with an early PT to the phosphate oxygen.

Starting with the 2W mechanism, we used the calibrated EVB surface and the energetics of inserting additional water and obtained the results summarized in Fig. 7 and Table S6. As seen from the figure, the energetics of reaching the plateau are very similar to what was obtained in our previous study with the calibrated 1W mechanism (the same point as in the above Ras/GAP study). The profile for the 2W PT step appears to be almost flat, and the energy of inserting additional water appears to be quite small. The rate-determining barrier for this path was found to be around 15 kcal/mol, in a good agreement with the observed barrier of around 14 kcal/mol.

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.

Next we explored the stepwise single water mechanism of ref. 30 (the original phosphate as a base mechanism), and the corresponding results are summarized in Table S6. The calculations (see SI Text) avoid the instability involved in evaluating the PT step that leads to the formation of an OH⁻ ion (which is strongly interacting with the protonated His84), and went directly to the TS through the plateau. We also consider a direct transition from the reactant state. This analysis (Table S6) indicates that, although the 1W stepwise mechanism is feasible, the corresponding barrier is higher by a few kilocalories per mole than that of the 2W mechanism.

At this point, we explored again the issue of the His-84 charge and the allosteric effect for both the 2W and the stepwise single water. Our first finding (Fig. S5) was that using the EF-Tu′ and EF-Tu structures give very different results. In this case, the catalytic contributions come from the rest of the protein (see the change in the calculated group contributions on moving from EF-Tu and EF-Tu′). Here, in contrast to the implication of ref. 30, it seems that the TS stabilization is different in EF-Tu and EF-Tu′ due to the change in interaction with the active site groups (Fig. 6B). As discussed in SI Text, the assertion of ref. 30 about the absence of allosteric effect is based on structural observations that are less conclusive than our energy-based analysis, which does support the allosteric idea.

To further explore the role of the His-84 charges, we performed calculations where the His-84 residual charges were set to zero. The calculations with the nonpolar (NP) His-84 involved significant instability, due in part to the fact (29, 30) that the NP His prefers to be in the EF-Tu structure. Using constraints to keep the NP His in the EF-Tu′ structure gave different results with different constraints, with an increase in the barrier between 10.0 and −2.0 kcal/mol, depending on the constraint and the initial conditions. Most importantly, in the cases where we obtained large increases in the activation barrier, we also obtained a very significant change in the contributions from other groups (this is an allosteric effect that is consistent with the concept that the charged His-84 plays a major role in changing the preorganization of the active site than of EF-Tu). Interestingly, the group contribution from His-84 (Fig. S5) is large, but it is similar in RS and in INT, which results in a small overall direct effect. Furthermore, even the large effect of the His-84 charge found in ref. 30 was only for the interaction with the OH⁻ (which does not occur at the TS) and not for their model of the dissociative TS.

Finally, we also explored the effect of the His84Ala mutation and reproduced the large observed anticatalytic effect (Table S6); however, more careful studies of this and other mutants are left to subsequent studies.

Concluding Remarks

This work explored the implications of our recent careful QM(ai)/MM free energy surfaces for the hydrolysis of phosphate monoesters on the activation of GTPases. Particular attention was placed on the possible impact of a 2W-type TS path on the activation process. It was found that the major catalytic effect that leads to the activation does not change from what was obtained in our earlier work, and it is associated with the electrostatic interaction between the protein and the shift of negative charge toward the leaving group (20). Nevertheless, the need for a PT path through additional water or another residue introduces a unique twist, because the additional group should have the correct proton affinity and correct position. Thus, for example, Gln-61 in the Ras/GAP system does allow for a TS PT shuttle (or through an additional water molecule). Nevertheless, the TS PT shuttle does not contribute to catalysis. Interestingly the Gln61Leu mutant slows the reaction in a drastic way, not because of the need for second water but almost entirely because of the increase in the energy of the plateau. This energy increase has the same electrostatic allosteric origin as that found in our previous studies.

The mechanism of a concerted TS shuttle, where Gln-61 helps in the PT from the attacking water to the phosphate, should not be confused with the Gln as a base proposal. The Gln as a base proposal has been defined exactly as a ground state PT from the attacking water to Gln-61, and this proposal has been shown by our early works (see discussion in ref. 11) to be inconsistent with the corresponding very high PT barrier.

Similar insight has been provided for the reaction of EF-Tu′. Here we find that the most likely mechanism is also a concerted water attack and P−O bond stretch and then a 2W PT at the TS. Interestingly, we find again that His-84 does not play a direct role (even not as a TS proton shuttle) and that the allosteric effect found in our previous work is the major catalytic effect. Of course, our mechanism requires an additional water molecule and thus we explored the energy associated with the insertion of an additional water molecule to the active sites of Ras/GAP and EF-Tu′. Here it was found that the insertion energy is rather small. Note that this finding is supported by the recent observation of two resolved water molecules in a close distance to the γ-phosphate of EF-G (27).

In trying to resolve the origin of the activity of enzymes, one is faced with the question of what is the most reliable current computational strategy. Here it may be tempting to assume that QM(ai)/MM free energy calculations in the protein offer the most reliable option. However, despite major recent progress, including the development of the paradynamics (PD) approach (5, 31), we believe that we are still not at a point where the corresponding results can be considered sufficiently reliable. That is, the sampling problems in evaluating free energy surfaces are very serious, especially when we have large electrostatic effects, and this means that one needs to use very long simulations with different starting points and a correct long range treatment. Doing so with a reliable QM level requires major computational resources (as well as validation of the corresponding reliability). We would like to point out that earlier finding of the 2W-type mechanism in Ras/GAP (32, 33) has provided important insight but unrealistic barriers (due to the difficulties of performing proper sampling). In fact, even attempts to obtain QM(ai)/MM activation free energies with sampling strategies that can work in principle have not been able to provide a reliable analysis of the catalytic effect (11). As will be pointed out below, the QM(ai)/MM is very useful for obtaining the reliable EVB surfaces for the reference solution reaction but at present is not the best option for calculations in the protein.

Although we repeatedly addressed the risk in the assumption that just running QM/MM calculations should give the correct result to major biological problems, we find it useful to discuss here as an example of a recent work on EF-Tu′ (14). As stated in section Exploring the Activation of EF-Tu, this work concluded that the barrier for the 1W mechanism in EF-Tu′ is around 50 kcal/mol, not recognizing that obtaining the 1W barrier in water is already far above the ability of what is in some respects a minimization-type mapping that does not attempt to produce any 2D surface of the type obtained in the careful study of ref. 5. The other problems of this work include not providing any information on the calculated hydrolysis path, and more importantly, the inability to properly samples of the protein along the solute path or to validate the presumed conclusions by performing calculations with different starting points, as well as the missing validations of the reaction in water. The problems with the approach of ref. 14 are further discussed in the in SI Text.

At any rate, we would like to reemphasize that approaches that cannot quantify the difference between 1W and 2W energetics in solution provide inadequate tools for determining the corresponding difference in the protein. In our experience, by far the most reliable current option is the use of a very careful QM(ai)/MM in exploring the reference solution reaction and then using the EVB with its powerful sampling ability to explore the change in energy in moving from the QM(ai)/MM solution to the protein. Of course, we can also use the PD approach (31) in moving from the EVB to the QM(ai)/MM surface, but the change in the QM(ai)/MM barrier in the protein on mutation or another effect is likely (once they converge) to be very similar to the corresponding change in the EVB reference potential. In fact, the quantitative power of the EVB is that it very reliably evaluates the free energy for moving from a known ground state and transition state (as well as the corresponding profile) in a water reaction to the same states in the protein active site.

The finding that the 2W-type mechanism has a significantly lower barrier than that of the 1W mechanism in water is also relevant to the action of ATPase. Here there were several works that suggested that the 2W mechanism is responsible to catalysis, but those studies have not been quantitative and have not attempted to explore the alternative 1W path (11). Furthermore, the challenge of obtaining realistic and converging activation free energies in the protein has not been overcome; our experience has been that starting from different initial structures can give very different results, and thus it is essential to average over starting structures. Here, as in the case of GTPases, we reproduced by calibrated EVB simulations the observed catalytic effect with a 1W mechanism (34). Thus, although further studies are needed, it is almost certain (by the same arguments presented in this work) that the catalytic effect in ATPase is due entirely to the reduction of the energy of the plateau and not due to the PT step that may well occur through a 2W mechanism.

In conclusion, it might be useful to comment again on the allosteric, catalytic, and mechanistic issues. In Ras/GAP, the reaction is most likely to involve either Gln assisted or water assisted (2W type) TS, with electrostatic allosteric activation. In EF-Tu′, we may have either a 2W TS path or a less likely stepwise 1W path (with higher estimated barrier). However, all of the mechanistic options without direct participation of His-84 involve an electrostatic allosteric effect. Thus, the actual question is whether the allosteric effect is due to just the generation of the electrostatic interaction between His-84 and the substrate on moving to EF-Tu′ or to additional changes in group contributions. The present study of the TS energetics seems to support the second option. Overall, it seems that the key to activation of GTPase-related systems is the electrostatic TS/plateau stabilization.

Methods

All the EVB simulations presented in this study were carried out by MOLARIS simulations program, using the ENZYMIX force field. The specific details about the setting of the simulations, the simulation conditions, and the EVB parameters sets used are given in the SI Text. The details of the QM(ai)/MM calculations are described in ref. 5.