Quantitative Exploration of the Molecular Origin of the Activation of Gtpase

Quantitative exploration of the molecular origin of the activation of GTPase

Ram Prasad Ba, Nikolay V. Plotnikova, Jeronimo Lameiraa,b, and Arieh Warshela,1

aDepartment of Chemistry, University of Southern California, Los Angeles, CA 90089; and bLaborátorio de Planejamento e Desenvolvimento de Fármacos, Faculdade de Biotecnologia, Universidade Federal do Pará, 66075-110 Belém, PA, Brazil

Contributed by Arieh Warshel, October 23, 2013 (sent for review September 1, 2013) GTPases play a major role in cellular processes, and gaining likely mechanism is a 2W mechanism with a major transition state quantitative understanding of their activation demands reliable stabilization due to electrostatic allosteric effect. free energy surfaces of the relevant mechanistic paths in solution, as well as the interpolation of this information to GTPases. Recently, Quantifying the Relationship Between Competing we generated ab initio quantum mechanical/molecular mechanical Mechanisms of Phosphate Monoester Hydrolysis in Solution free energy surfaces for the hydrolysis of phosphate monoesters in Phosphate hydrolysis reactions are arguably the most important solution, establishing quantitatively that the barrier for the reactions class of biological reactions (7–11), and it is thus important to with a proton transfer (PT) step from a single attacking water (1W) is elucidate the relevant mechanism in solution and proteins. In this higher than the one where the PT is assisted by a second water (2W). respect, it is now gradually realized that QM(ai)/MM studies are The implication of this finding on the activation of GTPases is perhaps the only way of resolving the fundamental mechanistic quantified here, by using the ab initio solution surfaces to calibrate controversies associated with phosphate hydrolysis (11). However, empirical valence bond surfaces and then exploring the origin of the this does not mean that just running uncritical black box QM/MM- activation effect. It is found that, although the 2W PT path is a new based calculations can be used to resolve deep mechanistic issues. element, this step is not rate determining, and the catalytic effect is That is, in addition to uncritical theoretical studies of phosphate actually due to the electrostatic stabilization of the pre-PT transition hydrolysis by irrelevant gas phase and energy minimization studies (for discussion see ref. 11), even recent studies that involve some state and the subsequent plateau. Thus, the electrostatic catalytic fi

con gurational sampling (12, 13), or path search approaches (14) BIOPHYSICS AND effect found in our previous studies of the Ras GTPase activating (see Exploring the Activation of EF-Tu and SI Text), have not protein (RasGAP) and the elongation factor-Tu (EF-Tu) with a 1W provided yet reliable mechanistic picture. The difficulty to eluci- COMPUTATIONAL BIOLOGY mechanism is still valid for the 2W path. Furthermore, as found date the mechanism reflected several problems including the before, the corresponding activation appears to involve a major most studies have not explored all of the possible options (in- fi allosteric effect. Overall, we believe that our nding is general to cluding key earlier proposals). In the case of phosphate mono- both GTPases and ATPases. In addition to the biologically relevant ester hydrolysis, the debate involves two issues; first, it is not clear finding, we also provide a critical discussion of the requirements whether the hydrolysis follows an associative or a dissociative from reliable surfaces for enzymatic reactions. path (unfortunately, as discussed in ref. 11, most of the recent studies failed to realize correctly the clear distinction between etailed understanding of many problems in biology boils down these two), and second, it has not been clear whether the PT from γ to the elucidation of the correct reaction mechanism in the the attacking nucleophilic water molecule to the -phosphate D oxygen occurs in a direct manner or with the assistance of several protein and in solution and to the elucidation of the origin of the fi corresponding catalytic effect. However, this requires overcoming water molecules. Thus, it has not been suf cient (or useful) to explore a PT between several water molecules while not carefully the challenge of obtaining accurate free energy surfaces in the examining a transfer from a single water molecule in a direct- condensed phase. Such a task can be accomplished, in principle, by manner. the combined quantum mechanical/molecular mechanical (QM/ The basic major issues associated with the determination of MM) method (1–5). However, the implementation of this method is the mechanism of the hydrolysis of phosphate monoesters and still very challenging. At present, we are not at the stage reached in studies of gas phase reactions, where the results of ab initio calcu- Significance lations are sometimes considered almost as substitutes for experimental results. Nevertheless, recent advances in ab initio QM/MM The origin of the activation of GTPases is explored considering [QM(ai)/MM] studies (2, 4–6) brought us closer to having quanti- the evidence that the transition state for the reference solution tative results for solution reactions and in some respects to quan- reaction involves a proton transfer between two water mole- titative results for enzymes, especially if one evaluates reliable QM cules. Ab initio quantum mechanical/molecular mechanical– (ai)/MM free energy surfaces for the solution reaction and then use based calibration of empirical valence bond surfaces of the so- the resulting surfaces to calibrate empirical valence bond (EVB) lution reaction is used to simulate the GTPase activation process. surfaces for studying the relevant enzymatic reaction. Here we ex- The activation is found to reflect the same type of electrostatic ploit these advances by exploring the hydrolysis of phosphate stabilization obtained previously for the single water mecha- monoesters that is the key to the activation of GTPases. That is, we nism. The transition state proton transfer step does not appear start by quantifying the energetics of the solution reaction and then to be rate limiting and thus is irrelevant to the catalytic effect. use the solution free energy surface to calibrate EVB surface that The calculated activation of RasGAP and EF-Tu reproduce the allow us to reliably explore the energetics in GTPases. We dem- observed trend quantitatively and establishes its allosteric fi onstrate that the origin of the catalytic effect obtained in our origin. We believe that our nding is general to all GTPases. previous studies of Ras GTPase activating protein (RasGAP) is Author contributions: A.W. designed research; R.P.B., N.V.P., and A.W. performed research; valid even with the two water (2W) path, but the fact that the R.P.B., N.V.P., J.L., and A.W. analyzed data; and R.P.B. and A.W. wrote the paper. single water (1W) path is high in energy forces the system to use The authors declare no conflict of interest. either Gln or a water molecule as a proton transfer (PT) shuttle. 1To whom correspondence should be addressed. E-mail: [email protected]. We then apply the same analysis to the activation of EF-Tu, where This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. we show that His-84 does not serve as a base and that the most 1073/pnas.1319854110/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1319854110 PNAS Early Edition | 1of6 Downloaded by guest on September 24, 2021 + 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). Having a reliable EVB surface for the solution reaction allowed us to explore the surface in the protein without the ex- Fig. 1. Mechanistic options for the hydrolysis of phosphate monoester in tremely challenging need to obtain fully converging QM(ai)/MM free energy surfaces in the protein, which at present is probably solution. R1,R2, and X define the reaction coordinates. (A) Structural model where the proton has been directly transferred from the attacking nucleo- not the most effective way of reaching concrete conclusions. The philic water molecule to the substrate phosphate oxygen atom (1W mech- corresponding study is described below. anism). (B) Structural model where the proton transfer occurs through the assistance of an additional water molecule (2W mechanism). Using the Calibrated EVB in Moving Form Solution to the Ras/GAP System The activation of Ras by GAP has been arguably the most prom- related systems can be formulated by considering the structural inent model for the activation of GTPases. Here the question has models presented in Fig. 1, where R1 represents the nuclear been: what are the features of the active site of the Ras/GAP reaction coordinate between the Pγ and the leaving Ow atom, R2 complex that makes the reaction seven orders of magnitude faster describes the nuclear reaction coordinate between the Pγ and the than in the isolated Ras (16, 17). Although the electrostatic role of attacking nucleophilic Ow atom, and the PT reaction coordinate is the so-called arginine finger (18) has been easy to reproduce (19, designated by X. Apparently, the PT can occur along the associative 20), interest and controversy focused on the role of Gln-61 that was or dissociative paths in either a direct manner (1W) or with the originally proposed to serve as a base (21, 22). In this case, we have assistance of the second water molecule (2W) (this case is also been able to show as early as in 1992 (23) that Gln-61 cannot be the taken as a representation of PT involving more water molecules). base in the ground state (because the barrier for ground state PT to Considering the crucial importance of the above issue, we re- Gln-61 is higher than the overall actual barrier and thus the ultimate cently invested (5) a major effort in obtaining reliable QM(ai)/MM base must be the GTP) (24). Furthermore, we found that Gln-61 free energy surfaces for different mechanistic options, focusing on does not affect the reaction in a direct way, at least in the 1W the difference between the 1W and 2W mechanisms. Our study mechanism (the obvious option to explore at that stage). Thus, it found that the hydrolysis of phosphate monoesters proceeds was concluded that Gln-61 serves indirectly in an allosteric mech- through a plateau in the R1/R2 space, where the attacking water anism by changing the P-loop interaction with the TS (19). Now, approach the γ-phosphate and the leaving group start to move away because our recent QM(ai)/MM free energy calculations determined to around 2.8−3.0 Å (see discussion in the SI Text and Fig. S1), and that in solution the 2W mechanism has a lower barrier than the 1W, then a PT step along either the 2W or 1W path. It was found that it is important to explore the corresponding implications on the the barrier along the 2W PT path is only 2–3 kcal/mol from the reaction in Ras/GAP, and such a study is reported below. plateau, whereas the 1W barrier is higher by more than 5–7kcal/ Starting with the WT Ras/GAP, we considered the options mol than the 2W barrier. Interestingly, widely used lower level (Fig. 3) of concerted and stepwise (2W type) PT from the functionals like Becke−Lee−Yang−Parr (BLYP) gave a smaller attacking water through Gln-61 to the phosphate oxygen, as well difference between the 1W and 2W barriers. as the 2W mechanism without participation of Gln and the 1W + Adding an Mg 2 ion to the QM(ai)/MM simulation system, with mechanism (Fig. S2, schemes I–III and Table S1). In all cases, we the needed additional QM water molecules, made the evaluation calibrated the relevant EVB surfaces on the reference solution of a reliable surface more challenging, but the conclusion that the reaction (SI Text) and explored the energetics of the reaction in 2W barrier is lower than that of the 1W remains a robust con- Ras/GAP. The surfaces in the protein were evaluated along the + clusion. The inclusion of the Mg 2 ion led to a more associative TS 2W assisted type path while moving to TS1, and the plateau path with a small barrier before the plateau, followed by a bar- and then performing the PT step from both the TS1 and the rierless 2W PT at the R1/R2 transition state (TS). This finding is plateau. The calculated free energy profiles are summarized in most probably reliable, despite the fact that the actual activation Fig. 3 (the corresponding energetics are presented in Table S5), + barrier for the surface with Mg 2 is an overestimate (SI Text). At where it is shown that the main catalytic effect is due to the any rate, considering the fact that the observed activation barrier drastic reduction in the free energy of TS1 and the plateau. The + in solution is found to be very similar with and without the Mg 2 PT step can occur both in concerted and stepwise paths. In- ion [31.2 vs. 30.4 kcal/mol, respectively (15)], we took the shape terestingly, however, because this PT step is already close to zero

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 H2O16× 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 deﬁ- nition 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.

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1319854110 Betal. Downloaded by guest on September 24, 2021 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. 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 Fig. 3. The EVB free energy profiles for the hydrolysis of GTP in solution and is the action of the elongation factor EF-Tu (26) and the related in the active site of RasGAP. The figure provides the profiles for different elongation factor G (EF-G) (27, 28). The GTP hydrolysis rate in feasible paths (as explained in SI Text). React* is used to indicate that all of this system increases by seven orders of magnitude (29) on ac- the energy barriers and reaction energies are with respect to their corre- ’ tivation by the ribosome. Here, as in the Ras/GAP GTPase case, sponding reference GS s energy regardless of whether it is for the 1W or 2W the question is what is so special about the activated system? In case. Taking such a reference is justified because the energy of inserting

particular, because the activation process involves the move- BIOPHYSICS AND a second water is negative in this case (Table S5). The notation Pro′ indicates ment of His-84 to the proximity of the γ-phosphate of the GTP, that we are not dealing with the real product but with a state where the COMPUTATIONAL BIOLOGY proton has just been transferred to the oxygen of the corresponding acceptor it has been suggested by some (e.g., ref. 26) that the activation oxygen and not the final product, which is at lower energy (see main text). involves a histidine (His-84) as a base mechanism. On the other hand, our study that considered the structures of both the active 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 ribosome-bound (EF-Tu ) and inactive (EF-Tu) forms (29) (squares for reference solution reactions and filled in circles for the corre- concluded that the His-84 cannot act as a base. We also con- sponding reaction in protein environment). cluded, 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 barriers in solution, there is no significant catalytic effect at this the pKa of His-84 due to its interaction with the sarcin–ricin loop. step. This finding implies that our previous calculations (19, 20, Recent works (14, 30) questioned some of the findings in our 25) that considered a concerted 1W path have captured the previous study of EF-Tu′. However, one of those works (14) had 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. 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). 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 Fig. 4. The energetics of the GTP hydrolysis in the Gln61Leu mutant of Ras/ large, in agreement with qualitative experimental studies (19). GAP. Notation as in Fig. 3. Note that the calculated barrier in protein envi- Finally, we explored the involvement of a second water in the WT ronment might be overestimated, and more sampling is probably needed. enzyme (Fig. 3) and found that the corresponding barrier is The description of React* and Prod′ are the same as described in Fig. 3. The + comparable to that with direct Gln-61 involvement. 2W path involves an H3O formation.

Betal. PNAS Early Edition | 3of6 Downloaded by guest on September 24, 2021 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′,andS4, 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 possi- Fig. 5. The energetics of the GTP hydrolysis Gln61Ala mutant of Ras/GAP. bilities that His-84 is directly involved in PT step at TS/plateau Notation as in Fig. 3. [Fig. S3, scheme I′(b,e)]. However, here the energy of deproto- nating His-84 leads to a 6-kcal/mol destabilization of the reactant some problems, including the presumption that our 1W mecha- state in the protein, and the overall barriers for the different nism would give an about 50-kcal/mol barrier (overlooking the possible paths (including His-84 as a base) become too high (SI facts that the method used by them cannot give the 1W barrier Text). Finally, we also explored the mechanism of ref. 14 and found even in bulk water and that the barrier in the enzyme should be it to be unfavorable (SI Text). Furthermore, we found the corresponding calculations to be insufficiently reliable (SI Text). about 20 kcal/mol with proper sampling). This overestimate fi reflected the unjustified assumption that just running basically In view of the above ndings, we returned to the likely possibil- guided QM/MM energy minimization in proteins from classically ities that His-84 is protonated and is not directly involved. Here we obtained starting points (without careful convergence analysis) can have three options: (i) the 2W mechanism, where a second water give quantitative information about catalysis. Thus, the work of ref. has to be inserted near His-84; (ii) the regular 1W mechanism with 14 will be considered here and in the SI Text mainly in a discussion its inherent high barrier for PT; and (iii) the stepwise water of the possible problems with some emerging QM/MM studies. mechanism with an early PT to the phosphate oxygen. The second and by far more careful work (30) attempted to ex- Starting with the 2W mechanism, we used the calibrated EVB plore the origin of the GTPase activation while focusing mainly on surface and the energetics of inserting additional water and the electrostatic interaction between the His-84 and the nucleo- obtained the results summarized in Fig. 7 and Table S6. As seen − philic OH , which would be produced in a stepwise mechanism from the figure, the energetics of reaching the plateau are very that involves a direct PT from the attacking water to the phosphate similar to what was obtained in our previous study with the oxygen (basically our earliest 1W mechanism, with a fully stepwise calibrated 1W mechanism (the same point as in the above Ras/ phosphate as a base mechanism). This work used a similar strategy GAP study). The profile for the 2W PT step appears to be almost to that introduced in our early study of Ras (23) and concluded flat, and the energy of inserting additional water appears to be that the catalysis is due to the very large electrostatic interaction quite small. The rate-determining barrier for this path was found − between the protonated His-84 and the OH ion. Note, however, to be around 15 kcal/mol, in a good agreement with the observed − that the OH formed before the actual TS and an attempt to barrier of around 14 kcal/mol. model the effect of His-84 on a dissociative type TS gave a far Next we explored the stepwise single water mechanism of ref. smaller effect (only about 4–3 kcal/mol with the reported estimate 30 (the original phosphate as a base mechanism), and the cor- of the effect of moving to the inactive form). Ref. 30 also suggested responding results are summarized in Table S6. The calculations that the allosteric effect from the P-loop and other parts of the (see SI Text) avoid the instability involved in evaluating the PT − protein is unlikely to be important. However, this assertion has step that leads to the formation of an OH ion (which is strongly been based on structural rather than energy considerations (SI interacting with the protonated His84), and went directly to the Text). The work of ref. 30 has also been consistent with our con- TS through the plateau. We also consider a direct transition clusion that the His-84 cannot serve as a base and our finding that from the reactant state. This analysis (Table S6) indicates that,

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.

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1319854110 Betal. Downloaded by guest on September 24, 2021 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 fi the corresponding very high PT barrier. Fig. 7. The EVB free energy pro les (associated with the 2W PT pathway) Similar insight has been provided for the reaction of EF-Tu′. corresponding to the hydrolysis of GTP in solution, as well as at the active Here we find that the most likely mechanism is also a concerted sites of EF-Tu′ and EF-Tu. Notation as in Fig. 3. 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 although the 1W stepwise mechanism is feasible, the correspond- (even not as a TS proton shuttle) and that the allosteric effect found ing barrier is higher by a few kilocalories per mole than that of the in our previous work is the major catalytic effect. Of course, our 2W mechanism. mechanism requires an additional water molecule and thus we explored the energy associated with the insertion of an additional 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 molecule to the active sites of Ras/GAP and EF-Tu .Hereit water. Our first finding (Fig. S5) was that using the EF-Tu′ and EF- was found that the insertion energy is rather small. Note that this BIOPHYSICS AND finding is supported by the recent observation of two resolved water Tu structures give very different results. In this case, the catalytic γ COMPUTATIONAL BIOLOGY contributions come from the rest of the protein (see the change in molecules in a close distance to the -phosphate of EF-G (27). the calculated group contributions on moving from EF-Tu and EF- In trying to resolve the origin of the activity of enzymes, one is faced with the question of what is the most reliable current com- Tu′). Here, in contrast to the implication of ref. 30, it seems that the putational strategy. Here it may be tempting to assume that QM TS stabilization is different in EF-Tu and EF-Tu′ due to the change (ai)/MM free energy calculations in the protein offer the most in interaction with the active site groups (Fig. 6B). As discussed in reliable option. However, despite major recent progress, including SI Text, the assertion of ref. 30 about the absence of allosteric effect the development of the paradynamics (PD) approach (5, 31), we is based on structural observations that are less conclusive than believe that we are still not at a point where the corresponding our energy-based analysis, which does support the allosteric idea. results can be considered sufficiently reliable. That is, the sampling To further explore the role of the His-84 charges, we performed problems in evaluating free energy surfaces are very serious, es- calculations where the His-84 residual charges were set to zero. fi pecially when we have large electrostatic effects, and this means The calculations with the nonpolar (NP) His-84 involved signi - that one needs to use very long simulations with different starting cant instability, due in part to the fact (29, 30) that the NP His points and a correct long range treatment. Doing so with a reliable prefers to be in the EF-Tu structure. Using constraints to keep the QM level requires major computational resources (as well as val- NP His in the EF-Tu′ structure gave different results with different − idation of the corresponding reliability). We would like to point constraints, with an increase in the barrier between 10.0 and 2.0 out that earlier finding of the 2W-type mechanism in Ras/GAP kcal/mol, depending on the constraint and the initial conditions. (32, 33) has provided important insight but unrealistic barriers Most importantly, in the cases where we obtained large increases fi fi (due to the dif culties of performing proper sampling). In fact, in the activation barrier, we also obtained a very signi cant change even attempts to obtain QM(ai)/MM activation free energies with in the contributions from other groups (this is an allosteric effect sampling strategies that can work in principle have not been able to that is consistent with the concept that the charged His-84 plays provide a reliable analysis of the catalytic effect (11). As will be a major role in changing the preorganization of the active site than pointed out below, the QM(ai)/MM is very useful for obtaining the of EF-Tu). Interestingly, the group contribution from His-84 (Fig. reliable EVB surfaces for the reference solution reaction but at S5) is large, but it is similar in RS and in INT, which results in present is not the best option for calculations in the protein. a small overall direct effect. Furthermore, even the large effect of Although we repeatedly addressed the risk in the assumption the His-84 charge found in ref. 30 was only for the interaction with − that just running QM/MM calculations should give the correct the OH (which does not occur at the TS) and not for their model result to major biological problems, we find it useful to discuss here of the dissociative TS. as an example of a recent work on EF-Tu′ (14). As stated in section Finally, we also explored the effect of the His84Ala mutation Exploring the Activation of EF-Tu, this work concluded that the and reproduced the large observed anticatalytic effect (Table barrier for the 1W mechanism in EF-Tu′ is around 50 kcal/mol, not S6); however, more careful studies of this and other mutants are recognizing that obtaining the 1W barrier in water is already far left to subsequent studies. above the ability of what is in some respects a minimization-type mapping that does not attempt to produce any 2D surface of the Concluding Remarks type obtained in the careful study of ref. 5. The other problems of This work explored the implications of our recent careful QM(ai)/ this work include not providing any information on the calculated MM free energy surfaces for the hydrolysis of phosphate mono- hydrolysis path, and more importantly, the inability to properly esters on the activation of GTPases. Particular attention was placed samples of the protein along the solute path or to validate the on the possible impact of a 2W-type TS path on the activation presumed conclusions by performing calculations with different process. It was found that the major catalytic effect that leads to starting points, as well as the missing validations of the reaction in the activation does not change from what was obtained in our water. The problems with the approach of ref. 14 are further dis- earlier work, and it is associated with the electrostatic interaction cussed in the in SI Text.

Betal. PNAS Early Edition | 5of6 Downloaded by guest on September 24, 2021 At any rate, we would like to reemphasize that approaches that the plateau and not due to the PT step that may well occur through cannot quantify the difference between 1W and 2W energetics in a2Wmechanism. solution provide inadequate tools for determining the correspond- In conclusion, it might be useful to comment again on the allo- ing difference in the protein. In our experience, by far the most steric, catalytic, and mechanistic issues. In Ras/GAP, the reaction is reliable current option is the use of a very careful QM(ai)/MM in most likely to involve either Gln assisted or water assisted (2W type) exploring the reference solution reaction and then using the EVB TS, with electrostatic allosteric activation. In EF-Tu′,wemayhave with its powerful sampling ability to explore the change in energy in either a 2W TS path or a less likely stepwise 1W path (with higher moving from the QM(ai)/MM solution to the protein. Of course, we estimated barrier). However, all of the mechanistic options without can also use the PD approach (31) in moving from the EVB to the direct participation of His-84 involve an electrostatic allosteric ef- QM(ai)/MM surface, but the change in the QM(ai)/MM barrier in fect. Thus, the actual question is whether the allosteric effect is due the protein on mutation or another effect is likely (once they con- to just the generation of the electrostatic interaction between His-84 verge) to be very similar to the corresponding change in the EVB ′ reference potential. In fact, the quantitative power of the EVB is andthesubstrateonmovingtoEF-Tu or to additional changes in that it very reliably evaluates the free energy for moving from group contributions. The present study of the TS energetics seems a known ground state and transition state (as well as the corre- to support the second option. Overall, it seems that the key to ac- sponding profile) in a water reaction to the same states in the pro- tivation of GTPase-related systems is the electrostatic TS/ tein active site. plateau stabilization. The finding that the 2W-type mechanism has a significantly lower barrier than that of the 1W mechanism in water is also rel- Methods evant to the action of ATPase. Here there were several works that All the EVB simulations presented in this study were carried out by MOLARIS suggested that the 2W mechanism is responsible to catalysis, but simulations program, using the ENZYMIX force field. The specific details those studies have not been quantitative and have not attempted about the setting of the simulations, the simulation conditions, and the EVB to explore the alternative 1W path (11). Furthermore, the chal- parameters sets used are given in the SI Text. The details of the QM(ai)/MM lenge of obtaining realistic and converging activation free energies calculations are described in ref. 5. in the protein has not been overcome; our experience has been that starting from different initial structures can give very different ACKNOWLEDGMENTS. We acknowledge the University of Southern results, and thus it is essential to average over starting structures. California’s High Performance Computing and Communications Center Here, as in the case of GTPases, we reproduced by calibrated EVB for computer time. We also thank the Extreme Science and Engineering simulations the observed catalytic effect with a 1W mechanism Discovery Environment for computer time. J.L. thanks the Conselho Nacional de Desenvolvimento Científico e Tecnológico and Programa Ciên- (34). Thus, although further studies are needed, it is almost certain cia sem Fronteiras. This work was supported by National Science Foundation (by the same arguments presented in this work) that the catalytic Grant MCB-0342276, National Cancer Institute Grant 1U19CA105010, and effect in ATPase is due entirely to the reduction of the energy of National Institutes of Health Grant R01 AI055926.

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