Wide Transition-State Ensemble as Key Component for Enzyme Catalysis

  1. Gabriel Ernesto Jara
  2. Francesco Pontiggia
  3. Renee Otten
  4. Roman V. Agafonov
  5. Marcelo A. Martí
  6. Dorothee Kern

  • Curated by eLife

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    eLife assessment

    In this potentially important study, the authors report results of QM/MM simulations and kinetic measurements for the phosphoryl-transfer step in adenylate kinase. The results point to the mechanistic proposal that the transition state ensemble is broader in the most efficient form of the enzyme (i.e., in the presence of Mg2+ in the active site) and thus a different activation entropy. With a broad set of computations and experimental analyses, the level of evidence is considered solid by some reviewers. On the other hand, there remain limitations in the computational analyses, especially regarding free energy profiles using different methodologies and the activation entropy, leading some reviewers to the evaluation that the level of evidence is incomplete.

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Abstract

Transition-state theory has provided the theoretical framework to explain the enormous rate accelerations of chemical reactions by enzymes. Given that proteins display large ensembles of conformations, unique transition states would pose a huge entropic bottleneck for enzyme catalysis. To shed light on this question, we studied the nature of the enzymatic transition state for the phosphoryl-transfer step in adenylate kinase by quantum-mechanics/molecular-mechanics calculations. We find a structurally wide set of energetically equivalent configurations that lie along the reaction coordinate and hence a broad transition-state ensemble (TSE). A conformationally delocalized ensemble, including asymmetric transition states, is rooted in the macroscopic nature of the enzyme. The computational results are buttressed by enzyme kinetics experiments that confirm the decrease of the entropy of activation predicted from such wide TSE. Transition-state ensembles as a key for efficient enzyme catalysis further boosts a unifying concept for protein folding and conformational transitions underlying protein function.

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  1. Version published to 10.7554/elife.93099.2 on eLife
  2. Version published to 10.7554/elife.93099 on eLife
  3. eLife

    Author response:

    The following is the authors’ response to the original reviews.

    eLife assessment

    This is a potentially important study that integrates QM/MM free energy simulations and experimental kinetic analyses to probe the nature of phosphoryl transfer transition state in adenylate kinase. The idea that the transition state ensemble encompasses conformations with substantially different structural features (including the breaking/forming bonds) is interesting and potentially applicable to many other enzyme systems. In the current form, however, the study is considered incomplete since the connection between the putative transition state ensemble from the computations and key experimental observables, such as the activation entropy, is not well established.

    Thank you so much for your great professional work as the senior editor. We thank you and the reviewers for carefully reading our manuscript and for very valuable suggestions. In response, we have performed the recommended additional calculations and modified the manuscript as suggested, in order to improve the connection between the transition state ensemble obtained from simulations and experimental observables. Importantly, the new simulations fully corroborate our original findings, and thanks to your work made the revised manuscript stronger and better.

    Below are our point-to-point responses:

    Public Reviews:

    Reviewer #1 (Public Review):

    Summary:

    This study investigated the phosphoryl transfer mechanism of the enzyme adenylate kinase, using SCC-DFTB quantum mechanical/molecular mechanical (QM/MM) simulations, along with kinetic studies exploring the temperature and pH dependence of the enzyme's activity, as well as the effects of various active site mutants. Based on a broad free energy landscape near the transition state, the authors proposed the existence of wide transition states (TS), characterized by the transferring phosphoryl group adopting a meta-phosphate-like geometry with asymmetric bond distances to the nucleophilic and leaving oxygens. In support of this finding, kinetic experiments were conducted with Ca2+ ions (instead of Mg2+) at different temperatures, which revealed a negative entropy of activation. Overall, in its present form, the manuscript has more weaknesses in terms of interpretation of the simulation results than strengths, which need to be addressed by the authors.

    We thank the reviewer for carefully reviewing our manuscript and the great suggestions for the revisions. Thanks to these points raised we are able to submit a revised manuscript addressing all questions.

    There are several major concerns:

    First, the authors' claim that the catalytic mechanism of adenylate kinase (Adk) has not been previously studied by QM/MM free energy simulations is somewhat inaccurate. In fact, two different groups have previously investigated the catalytic mechanism of Adk. The first study, cited by the authors themselves, used the string method to determine the minimum free energy profile, but resulted in an unexpected intermediate; note that they obtained a minimum free energy profile, not a minimum energy profile. The second study (Ojedat-May et al., Biochemistry 2021 and Dulko-Smith et al., J Chem Inf Model 2023) overlaps substantially with the present study, but its main conclusions differ from those of the present study. Therefore, a thorough discussion comparing the results of these studies is needed.

    We thank the reviewer for pointing out two additional articles to the one we had discussed. Accordingly, we have changed the claim that the Adk mechanism was not previously studied using QM/MM, and added a discussion of the latter two citations. Notably, although the general outcome is consistent with our results, the conclusions and details of findings differ. The two additional papers agree with our findings of a concerted TS, and not the metastable intermediate as observed in the QM/MM simulation of Shibanuma et al., 2020.

    The difference of the two papers by Nam/Wolf-Watz and our manuscript pointed out by the reviewer is mainly in the interpretation. Importantly, the authors do not primarily focus on the nature of the Transition State for the P-transfer reaction, but on the connection between the chemical and conformational steps. We have extensively reported on the fact that the conformational changes of lid opening and closing are obviously unrelated to the chemical step, see also our free energy landscape in Fig. 1a. Consequently, there cannot be a coupling. We note that our group had extensively studied the lid opening step both experimentally and computationally before. In contrast, we discover here a fundamental concept for rate enhancement by an optimal enzyme: the reduction in the activation entropy by a wide TSE. New experiments were triggered by this finding, that then delivered experimental validation of this concept.

    In the revised version of the manuscript, and according to the reviewer’s suggestion we expanded our discussion to these two additional papers.

    Second, the interpretation of the TS ensemble needs deeper scrutiny. In general, the TS is defined as the hypersurface separating the reactant and product states. Consequently, if a correct reaction coordinate is defined, trajectories initiated at the TS should have equal probabilities of reaching either the reactant or product state; if an approximate reaction coordinate, such as the distance difference used in this study, is used, recrossing may be introduced as a correction into the probabilities. Thus, in order to establish the presence of a wide TS region, it is necessary to characterize the TS ensemble through a commitment analysis across the TS region.

    We thank the reviewer for suggesting to add a commitment analysis to our calculations. The newly performed commitment analysis is shown in Fig. 4b. The corresponding analysis further strengthens our original findings of the wide TS in the fully active enzyme.

    The relatively flat free energy surface observed near TS in Figures 1c and 2a, may be attributed to the cleavage and formation of P-O bonds relative to the marginally stable phosphorane intermediate, as described in Zhou et al.'s work (Chem Rev 1998, 98:991). This scenario is clearly different from a wide TS ensemble concept. In addition, given the inherent similarity in reactivity of the two oxygens towards the phosphoryl atom, it is reasonable to expect a single TS as shown in Figure 1 - supplement 9, rather than two TSs with a marginally stable intermediate as shown in Figure 1c. Consequently, it remains uncertain whether the elongated P-O bonds observed near the TS and their asymmetry are realistic or potentially an artifact of the pulling/non-equilibrium MD simulations. Further validation in this regard is required.

    The reviewer raises the key issue of how realistic the observation of the wide TSE is, and the possibility of it being a potential artifact of the simulation strategy, and suggests that further validation is required in this regard. According to his/her suggestion, in the revised version we have further validated this key observation by two additional simulations. First, we performed a commitment analysis (see above), and second, we also performed Umbrella Sampling, see Fig. 4a. We consistently observe one wide TSE in the presence of Mg2+, but not in the absence of Mg2+. The fact that this wide TSE is observed with the three strategies (i.e pulling/nonequilibrium MD, commitment analysis, and umbrella sampling) most likely rules out the possibility of an artifact related to the simulation strategy.

    Third, there are several inconsistencies in the free energy results and their discussion. First, the data from Kerns et al. (Kerns, NSMB, 2015, 22:124) indicate that the ATP/AMP -> ADP/ADP reaction proceeds at a faster rate than the ADP/ADP -> ATP/AMP reaction, suggesting that the ADP/ADP state has a lower free energy (approximately -1.0 kcal/mol) compared to the ATP/ATP state. This contrasts with Figure 1c, which shows a higher free energy of 6.0 kcal/mol for the ATP/ADP state. This discrepancy needs to be discussed.

    The reviewer correctly found our experimental result on the equilibrium of about -1 kcal/mol for ADP/ADP relative to ATP/AMP with Mg. Importantly, that was measured at a pH of 7. With a pKA of about 7.2 for ADP, under these experimental conditions more than 50% is in the monoprotonated state. As we found in our QM/MM simulations, for the monoprotonated state the ADP/ADP is much more stable than ATP/AMP (see Figure 1 – supplement 4, about 8 kcal/mol). In contrast, as shown in Fig. 1c and highlighted by the reviewer, for the nonprotonated state the equilibrium is flipped. Consequently our QM/MM simulations roughly recapitulate the ensemble equilibrium of substrates/products measured at pH 7.

    We should have better described these facts in the manuscript, and we thank the reviewer for noting this point, as it promoted us to better explaining this agreement between experiments and computation for this on enzyme equilibrium between the substrate and product states (see page 11 in the revised manuscript).

    Furthermore, the barrier for ATP/AMP -> ADP/ADP, calculated to be 20 kcal/mol for the fully charged state, exceeds the corresponding barrier for the monoprotonated state. This cautions against the conclusion that the fully charged state is the reactive state. In addition, the difference in the barrier for the no-Mg2+ system compared to the barriers with Mg2+ is substantially too large (21 kcal/mol from the calculation versus 7 kcal/mol from the experimental values). These inconsistencies raise questions as to their origins, whether they result from the use of the pulling/non-equilibrium MD simulation approach, which may yield unrealistic TS geometries, or from potential issues related to the convergence of the determined free energy values. To address this issue, a comparison of results obtained by umbrella sampling and similar methodologies is necessary.

    We agree that these points need to be clarified. For the resubmission, we performed an umbrella sampling for the fully charged nucleotide with Mg2+, and for the noMg2+ systems, and added these new figures to the manuscript (new Fig. 4). We agree with the reviewer that the obtained free energy profiles from the umbrella sampling are more reliable; the original simulations for the monoprotonated state have larger errors, see Fig. 1, supplement 4. Importantly, we experimentally measured the pH dependence of the reaction in the direction ADP/ADP to AMP and ATP, and hence compare the corresponding barriers in this direction.

    In respect to the comparison of the simulated (9.5 kcal/mol) to the experimental barriers with and without Mg, the experimental barrier is 7 kcal/mol for Ca2+ versus no metal, but larger for Mg2+ versus no metal, for which the simulations were performed. The P-transfer with Mg2+ is faster than 500 sec-1, meaning the experimental barrier for the no Mg versus magnesium is ≥ 11 kcal/mol, which is in quite good agreement with our umbrella sampling barrier differences (Fig. 4a). In response to this reviewer’s question, we added these points into the revised manuscript.

    Reviewer #2 (Public Review):

    Summary:

    The authors report the results of QM/MM simulations and kinetic measurements for the phosphoryl-transfer step in adenylate kinase. The main assertion of the paper is that a wide transition state ensemble is a key concept in enzyme catalysis as a strategy to circumvent entropic barriers. This assertion is based on the observation of a "structurally wide" set of energetically equivalent configurations that lie along the reaction coordinate in QM/MM simulations, together with kinetic measurements that suggest a decrease in the entropy of activation.

    We thank the reviewer for the endorsement, and very useful suggestions to improve the manuscript in an revised manuscript. Thanks to the questions, we have edited our manuscript accordingly. All suggested additional simulations and analysis further support our original findings.

    Strengths:

    The study combines theoretical calculations and supporting experiments.

    Weaknesses:

    The role(s) of entropy in enzyme catalysis has been discussed extensively in the literature, from the Circe effect proposed by Jencks and many other works. The current paper hypothesizes a "wide" transition state ensemble as a catalytic strategy and key concept in enzyme catalysis. Overall, it is not clear the degree to which this hypothesis is supported by the data. The reasons are as follows:

    (1) Enzyme catalysis reflects a rate enhancement with respect to a baseline reaction in solution. In order to assert that something is part of a catalytic strategy of an enzyme, it would be necessary to demonstrate from simulations that the activation entropy for the baseline reaction is indeed greater and the transition state ensemble less "wide". Alternatively stated, when indicating there is a "wide transition state ensemble" for the enzyme system - one needs to indicate that is with respect to the non-enzymatic reaction. However, these simulations were not performed and the comparisons were not demonstrated.

    We agree with the reviewer, that the ideal comparison to address enzyme catalytic power is to compare with the baseline reaction in solution. However, as is the case for many biological relevant reactions, in solution the reactions are too slow (i.e have too high barriers) and thus cannot be measured (this reaction would take about 7000 years without the enzyme). Moreover, in many cases, the reaction mechanism in solution is too different to that observed in the enzyme.

    To overcome this problem, another reference reaction is used instead of that in solution, such as a mutant enzyme, or the enzyme lacking a key cofactor, hence a non-optimized enzyme. In the present case, this baseline reaction corresponds to enzyme reaction in the absence of the Mg ion. Consistently, our results clearly show that the reaction without Mg which displays a larger barrier, has a narrower TS. We want to highlight that the extensive and excellent literature about QM/MM calculations of the hydrolysis of ATP hydrolysis in solution, which shows narrow transitions state ensembles, just to mention a few: Klähn, M., Rosta, E., & Warshel, A. (2006).

    On the mechanism of hydrolysis of phosphate monoesters dianions in solutions and proteins.

    Journal of the American Chemical Society, 128(47), 15310–15323. https://doi.org/10.1021/ja065470t; Wang, C., Huang, W., & Liao, J. lou. (2015). QM/MM investigation of ATP hydrolysis in aqueous solution. Journal of Physical Chemistry B, 119(9), 3720–3726. https://doi.org/10.1021/jp512960e.

    (2) The observation of a "wide conformational ensemble" is not a quantitative measure ofentropy. In order to make a meaningful computational prediction of the entropic contribution to the activation of free energy, one would need to perform free energy simulations over a range of temperatures (for the enzymatic and non-enzymatic systems). Such simulations were not performed, and the entropy of activation was thus not quantified by the computational predictions.

    In the present work we do not intend to quantify entropy from the simulations, since such calculations are known to have too large errors. However, even if not strictly quantified, a wider TS ensemble is a proxy for a larger entropy.

    (3) The authors indicate that lid-opening, essential for product release, and not P-transfer is therate-limiting step in the catalytic cycle and Mg2+ accelerates both steps. How is it certain that the kinetic measurements are reporting on the chemical steps of the reaction, and not other factors such as metal ion binding or conformational changes?

    These questions were indeed the absolute critically ones we needed to answer early for studying how adenylate kinase is catalyzing the reaction by more than 14 orders of magnitude. This was done by a combination of pre-steady state, steady-state experiments combined with NMR dynamics, published in (Kerns et al., 2015), and described in the beginning of this manuscript in Fig. 1a. We agree with the reviewer that for many other enzymes such experimental examination of all microscopic steps for the enzymatic cycle had not been performed, leading to the risk of wrong interpretation of observed kinetic rates.

    (4) The authors explore different starting states for the chemical steps of the reaction (e.g.,different metal ion binding and protonation states), and conclude that the most reactive enzyme configuration is the one with the more favorable reaction-free energy barrier. However, it is not clear what is the probability of observing the system in these different states as a function of pH and metal ion concentration without performing appropriate pKa and metal ion binding calculations. This was not done, and hence these results seem somewhat inconclusive.

    As noted by the reviewer, in the present work our aim was to compare the chemical step of the reaction in different metal ion and protonation states. Our computational results show that the most reactive enzyme configuration is the nonprotonated state with Mg2+ in our forward reaction.

    We actually know what the probability of the metal-bound states are for this enzyme. The experimental data were described in (Kerns et al., 2015), we directly experimentally determined the concentration needed to fully occupy the Mg site with Mg or Ca, therefore no metal binding calculations are needed as the experiments are a direct measurement. From our x-ray structures we know the accurate binding site, and also see full occupancy. This is also true for the pH dependence of the chemical step, measured in this manuscript and shown in Fig. 5b. We note that the excellent agreement between our simulations and the experiments are one of the key features of the current manuscript. As stated in the manuscript, we analyzed the pH dependence of the P-transfer step and showed that the rate increases with higher pH in the presence of Ca2+, while without a metal the opposite trend is observed. These results further support the QM/MM results showing that the fully-charged nucleotides state was the most reactive in the presence of the metal, whereas in the absence of the cation, only the monoprotonated nucleotides (low pH) were reactive.

    Reviewer #3 (Public Review):

    Summary:

    By conducting QM/MM free energy simulations, the authors aimed to characterize the mechanism and transition state for the phosphoryl transfer in adenylate kinase. The qualitative reliability of the QM/MM results has been supported by several interesting experimental kinetic studies. However, the interpretation of the QM/MM results is not well supported by the current calculations.

    Strengths:

    The QM/MM free energy simulations have been carefully conducted. The accuracy of the semiempirical QM/MM results was further supported by DFT/MM calculations, as well as qualitatively by several experimental studies.

    We thank the reviewer for the positive comments on the manuscript, particularly highlighting the support of the QM/MM results by additional DFT/MM calculations and several experiments.

    Weaknesses:

    (1) One key issue is the definition of the transition state ensemble. The authors appear to define this by simply considering structures that lie within a given free energy range from the barrier. However, this is not the rigorous definition of transition state ensemble, which should be defined in terms of committor distribution. This is not simply an issue of semantics, since only a rigorous definition allows a fair comparison between different cases - such as the transition state in an enzyme vs in solution, or with and without the metal ion. For a chemical reaction in a complex environment, it is also possible that many other variables (in addition to the breaking and forming P-O bonds) should be considered when one measures the diversity in the conformational ensemble.

    We thank the reviewer for noting this issue and for this great suggestion, as this led to a strengthening of the key findings in the revised manuscript version. According to his/her suggestion, we performed a commitment analysis to properly define the TSE and compare the results between the enzyme in the presence/absence of Mg2+ (see new Fig. 4b). The results further strengthen our previous finding and interpretation of a wider TSE for the reaction with Mg relative to without Mg.

    (2) While the experimental observation that the activation entropy differs significantly with and without the Ca2+ ion is interesting, it is difficult to connect this result with the "wide" transition state ensemble observed in the QM/MM simulations so far. Even without considering the definition of the transition state ensemble mentioned above, it is unlikely that a broader range of P-O distances would explain the substantial difference in the activation entropy measured in the experiment. Since the difference is sufficiently large, it should be possible to compute the value by repeating the free energy simulations at different temperatures, which would lead to a much more direct evaluation of the QM/MM model/result and the interpretation.

    In the present work we do not intend to quantify entropy from the simulations, since such calculations are known to have too large errors. However, even if not strictly quantified, a wider TS ensemble is a proxy for a larger entropy. We believe that the additional committor calculations and the umbrella sampling (new Fig. 4a) are a strong support of our original findings, and better suited for supporting our findings as compared to repeating the free energy simulations at different temperatures.

    Recommendations for the authors:

    Reviewer #1 (Recommendations For The Authors):

    Minor comments:

    Make sure consistent units are used, either kJ/mol or kcal/mol.

    Thanks, we made the changes.

    In the case of the mono-protonated simulation, where does the proton transfer between AD(T)P and AMP occur in both the forward and reverse reactions? It is worthwhile to note that the proton transfer may take place at different reaction coordinate values (between the two reactions), as it is not explicitly defined in the reaction coordinate. In this context, it is also necessary to discuss how to combine the results to generate a single free energy profile.

    We agree with the reviewer on this point. Accordingly, we have analyzed for the monoprotonated reaction when (or where in terms of RC) the proton transfer occurs in both forward and reverse reactions. The proton transfer occurs at -0.7 of the reaction coordinate (average value, figures 3-supplement 5 e and f).

    The methods section needs improvements:

    (1) Computational setup of the system: Were the systems neutralized? If so, what types of ions were used, and how many of them were included? If systems were not neutralized, discuss a potential artifact in the results. In addition, if the system for the reverse reaction (and no-Mg2+ systems) was prepared separately, provide details regarding their preparation.

    We thank the reviewer for noting this issue. Accordingly, we have provided the requested additional details of the computational setup in the revised version.

    (2) Simulation parameters: Clarify how non-bonded interactions were treated in both MM and QM/MM simulations. For the QM/MM simulation, specify the time step used, whether the Shake was applied; whether the NPT simulations were performed, and any other relevant parameters.

    We thank the reviewer for noting this issue. Accordingly, we have provided the requested additional details of the simulation parameters.

    (3) Free energy determination strategy: Describe how the two profiles (forward and reverse profiles) were combined and provide a theoretical justification for this approach. Additionally, include a comment on whether Jarzynski's inequality equation is directly applicable to the NPT simulation.

    According to the reviewer request, in the revised version of the manuscript we have described how the two profiles where combined and provided a theoretical justification for this approach.

    Reviewer #3 (Recommendations For The Authors):

    See recommendations in the Public Review regarding the analysis of transition state ensemble and activation entropy.

  4. eLife

    eLife assessment

    In this potentially important study, the authors report results of QM/MM simulations and kinetic measurements for the phosphoryl-transfer step in adenylate kinase. The results point to the mechanistic proposal that the transition state ensemble is broader in the most efficient form of the enzyme (i.e., in the presence of Mg2+ in the active site) and thus a different activation entropy. With a broad set of computations and experimental analyses, the level of evidence is considered solid by some reviewers. On the other hand, there remain limitations in the computational analyses, especially regarding free energy profiles using different methodologies and the activation entropy, leading some reviewers to the evaluation that the level of evidence is incomplete.

  5. eLife

    Reviewer #1 (Public Review):

    Summary:

    This study investigated the phosphoryl transfer mechanism of the enzyme adenylate kinase, using SCC-DFTB quantum mechanical/molecular mechanical (QM/MM) simulations, along with kinetic studies exploring the temperature and pH dependence of the enzyme's activity, as well as the effects of various active site mutants. Based on a broad free energy landscape near the transition state, the authors proposed the existence of wide transition states (TS), characterized by the transferring phosphoryl group adopting a meta-phosphate-like geometry with asymmetric bond distances to the nucleophilic and leaving oxygens. In support of this finding, kinetic experiments were conducted with Ca2+ ions at different temperatures and pH, which revealed a reduced entropy of activation and unique pH-dependence of the catalyzed reaction.

    Strengths:

    A combined application of simulation and experiments is a strength.

    Weaknesses:

    The conclusion that the enzyme-catalyzed reaction involves a wide transition state is not sufficiently clarified with some concerns about the determined free energy profiles compared to the experimental estimate. (See Recommendations for the authors.)

  6. eLife

    Reviewer #2 (Public Review):

    Summary:

    The authors report results of QM/MM simulations and kinetic measurements for the phosphoryl-transfer step in adenylate kinase. The main assertion of the paper is that a wide transition state ensemble is a key concept in enzyme catalysis as a strategy to circumvent entropic barriers. This assertion is based on observation of a "structurally wide" set of energetically equivalent configurations that lie along the reaction coordinate in QM/MM simulations, together with kinetic measurements that suggest a decrease of the entropy of activation.

    Strengths:

    The study combines theoretical calculations and supporting experiments.

    Weaknesses:

    The current paper hypothesizes a "wide" transition state ensemble as a catalytic strategy and key concept in enzyme catalysis. Overall, it is not clear the degree to which this hypothesis is fully supported by the data. The reasons are as follows:

    (1) Enzyme catalysis reflects a rate enhancement with respect to a baseline reaction in solution. In order to assert that something is part of a catalytic strategy of an enzyme, it would be necessary to demonstrate from simulations that the activation entropy for the baseline reaction is indeed greater and the transition state ensemble less "wide". Alternatively stated, when indicating there is a "wide transition state ensemble" for the enzyme system - one needs to indicate that is with respect to the non-enzymatic reaction. However, these simulations were not performed and the comparisons not demonstrated. The authors state "This chemical step would take about 7000 years without the enzyme" making it impossible to measure; nonetheless, the simulations of the nonenzymatic reaction would be fairly straight forward to perform in order to demonstrate this key concept that is central to the paper. Rather, the authors examine the reaction in the absence of a catalytically important Mg ion.

    (2) The observation of a "wide conformational ensemble" is not a quantitative measure of entropy. In order to make a meaningful computational prediction of the entropic contribution to the activation free energy, one would need to perform free energy simulations over a range of temperatures (for the enzymatic and non-enzymatic systems). Such simulations were not performed, and the entropy of activation was thus not quantified by the computational predictions. The authors instead use a wider TS ensemble as a proxy for larger entropy, and miss an opportunity to compare directly to the experimental measurements.

  7. eLife

    Reviewer #3 (Public Review):

    Summary:

    By conducting QM/MM free energy simulations, the authors aimed to characterize the mechanism and transition state for the phosphoryl transfer in adenylate kinase. The qualitative reliability of the QM/MM results has been supported by several interesting experimental kinetic studies. However, the interpretation of the QM/MM results is not well supported by the current calculations.

    Strengths:

    The QM/MM free energy simulations have been carefully conducted. The accuracy of the semi-empirical QM/MM results was further supported by DFT/MM calculations, as well as qualitatively by several experimental studies.

    Weaknesses:

    (1) One key issue is the definition of the transition state ensemble. The authors appear to define this by simply considering structures that lie within a given free energy range from the barrier. However, this is not the rigorous definition of transition state ensemble, which should be defined in terms of committor distribution. This is not simply an issue of semantics, since only a rigorous definition allows a fair comparison between different cases - such as the transition state in an enzyme vs in solution, or with and without the metal ion. For a chemical reaction in a complex environment, it is also possible that many other variables (in addition to the breaking and forming P-O bonds) should be considered when one measures the diversity in the conformational ensemble.

    In the revised ms, the authors included committor analysis. However, the discussion of the result is very brief. In particular, if we use the common definition of the transition state ensemble (TSE) as those featuring the committor around 0.5, the reaction coordinate of the TSE would span a much narrower range than those listed in Table 1. This point should be carefully addressed.

    (2) While the experimental observation that the activation entropy differs significantly with and without the Ca2+ ion is interesting, it is difficult to connect this result with the "wide" transition state ensemble observed in the QM/MM simulations so far. Even without considering the definition of the transition state ensemble mentioned above, it is unlikely that a broader range of P-O distances would explain the substantial difference in the activation entropy measured in the experiment. Since the difference is sufficiently large, it should be possible to compute the value by repeating the free energy simulations at different temperatures, which would lead to a much more direct evaluation of the QM/MM model/result and the interpretation.

  8. Version published to 10.1101/2023.10.03.560706v2 on bioRxiv
  9. Version published to 10.7554/elife.93099.1 on eLife
  10. eLife

    eLife assessment

    This is a potentially important study that integrates QM/MM free energy simulations and experimental kinetic analyses to probe the nature of phosphoryl transfer transition state in adenylate kinase. The idea that the transition state ensemble encompasses conformations with substantially different structural features (including the breaking/forming bonds) is interesting and potentially applicable to many other enzyme systems. In the current form, however, the study is considered incomplete since the connection between the putative transition state ensemble from the computations and key experimental observables, such as the activation entropy, is not well established.

  11. eLife

    Reviewer #1 (Public Review):

    Summary:
    This study investigated the phosphoryl transfer mechanism of the enzyme adenylate kinase, using SCC-DFTB quantum mechanical/molecular mechanical (QM/MM) simulations, along with kinetic studies exploring the temperature and pH dependence of the enzyme's activity, as well as the effects of various active site mutants. Based on a broad free energy landscape near the transition state, the authors proposed the existence of wide transition states (TS), characterized by the transferring phosphoryl group adopting a meta-phosphate-like geometry with asymmetric bond distances to the nucleophilic and leaving oxygens. In support of this finding, kinetic experiments were conducted with Ca2+ ions (instead of Mg2+) at different temperatures, which revealed a negative entropy of activation. Overall, in its present form, the manuscript has more weaknesses in terms of interpretation of the simulation results than strengths, which need to be addressed by the authors.

    There are several major concerns:

    First, the authors' claim that the catalytic mechanism of adenylate kinase (Adk) has not been previously studied by QM/MM free energy simulations is somewhat inaccurate. In fact, two different groups have previously investigated the catalytic mechanism of Adk. The first study, cited by the authors themselves, used the string method to determine the minimum free energy profile, but resulted in an unexpected intermediate; note that they obtained a minimum free energy profile, not a minimum energy profile. The second study (Ojedat-May et al., Biochemistry 2021 and Dulko-Smith et al., J Chem Inf Model 2023) overlaps substantially with the present study, but its main conclusions differ from those of the present study. Therefore, a thorough discussion comparing the results of these studies is needed.

    Second, the interpretation of the TS ensemble needs deeper scrutiny. In general, the TS is defined as the hypersurface separating the reactant and product states. Consequently, if a correct reaction coordinate is defined, trajectories initiated at the TS should have equal probabilities of reaching either the reactant or product state; if an approximate reaction coordinate, such as the distance difference used in this study, is used, recrossing may be introduced as a correction into the probabilities. Thus, in order to establish the presence of a wide TS region, it is necessary to characterize the TS ensemble through a commitment analysis across the TS region.

    The relatively flat free energy surface observed near TS in Figures 1c and 2a, may be attributed to the cleavage and formation of P-O bonds relative to the marginally stable phosphorane intermediate, as described in Zhou et al.'s work (Chem Rev 1998, 98:991). This scenario is clearly different from a wide TS ensemble concept. In addition, given the inherent similarity in reactivity of the two oxygens towards the phosphoryl atom, it is reasonable to expect a single TS as shown in Figure 1 - supplement 9, rather than two TSs with a marginally stable intermediate as shown in Figure 1c. Consequently, it remains uncertain whether the elongated P-O bonds observed near the TS and their asymmetry are realistic or potentially an artifact of the pulling/non-equilibrium MD simulations. Further validation in this regard is required.

    Third, there are several inconsistencies in the free energy results and their discussion. First, the data from Kerns et al. (Kerns, NSMB, 2015, 22:124) indicate that the ATP/AMP -> ADP/ADP reaction proceeds at a faster rate than the ADP/ADP -> ATP/AMP reaction, suggesting that the ADP/ADP state has a lower free energy (approximately -1.0 kcal/mol) compared to the ATP/ATP state. This contrasts with Figure 1c, which shows a higher free energy of 6.0 kcal/mol for the ATP/ADP state. This discrepancy needs to be discussed. Furthermore, the barrier for ATP/AMP -> ADP/ADP, calculated to be 20 kcal/mol for the fully charged state, exceeds the corresponding barrier for the monoprotonated state. This cautions against the conclusion that the fully charged state is the reactive state. In addition, the difference in the barrier for the no-Mg2+ system compared to the barriers with Mg2+ is substantially too large (21 kcal/mol from the calculation versus 7 kcal/mol from the experimental values). These inconsistencies raise questions as to their origins, whether they result from the use of the pulling/non-equilibrium MD simulation approach, which may yield unrealistic TS geometries, or from potential issues related to the convergence of the determined free energy values. To address this issue, a comparison of results obtained by umbrella sampling and similar methodologies is necessary.

  12. eLife

    Reviewer #2 (Public Review):

    Summary:
    The authors report the results of QM/MM simulations and kinetic measurements for the phosphoryl-transfer step in adenylate kinase. The main assertion of the paper is that a wide transition state ensemble is a key concept in enzyme catalysis as a strategy to circumvent entropic barriers. This assertion is based on the observation of a "structurally wide" set of energetically equivalent configurations that lie along the reaction coordinate in QM/MM simulations, together with kinetic measurements that suggest a decrease in the entropy of activation.

    Strengths:
    The study combines theoretical calculations and supporting experiments.

    Weaknesses:
    The role(s) of entropy in enzyme catalysis has been discussed extensively in the literature, from the Circe effect proposed by Jencks and many other works. The current paper hypothesizes a "wide" transition state ensemble as a catalytic strategy and key concept in enzyme catalysis. Overall, it is not clear the degree to which this hypothesis is supported by the data. The reasons are as follows:

    1. Enzyme catalysis reflects a rate enhancement with respect to a baseline reaction in solution. In order to assert that something is part of a catalytic strategy of an enzyme, it would be necessary to demonstrate from simulations that the activation entropy for the baseline reaction is indeed greater and the transition state ensemble less "wide". Alternatively stated, when indicating there is a "wide transition state ensemble" for the enzyme system - one needs to indicate that is with respect to the non-enzymatic reaction. However, these simulations were not performed and the comparisons were not demonstrated.

    2. The observation of a "wide conformational ensemble" is not a quantitative measure of entropy. In order to make a meaningful computational prediction of the entropic contribution to the activation of free energy, one would need to perform free energy simulations over a range of temperatures (for the enzymatic and non-enzymatic systems). Such simulations were not performed, and the entropy of activation was thus not quantified by the computational predictions.

    3. The authors indicate that lid-opening, essential for product release, and not P-transfer is the rate-limiting step in the catalytic cycle and Mg2+ accelerates both steps. How is it certain that the kinetic measurements are reporting on the chemical steps of the reaction, and not other factors such as metal ion binding or conformational changes?

    4. The authors explore different starting states for the chemical steps of the reaction (e.g., different metal ion binding and protonation states), and conclude that the most reactive enzyme configuration is the one with the more favorable reaction-free energy barrier. However, it is not clear what is the probability of observing the system in these different states as a function of pH and metal ion concentration without performing appropriate pKa and metal ion binding calculations. This was not done, and hence these results seem somewhat inconclusive.

  13. eLife

    Reviewer #3 (Public Review):

    Summary:
    By conducting QM/MM free energy simulations, the authors aimed to characterize the mechanism and transition state for the phosphoryl transfer in adenylate kinase. The qualitative reliability of the QM/MM results has been supported by several interesting experimental kinetic studies. However, the interpretation of the QM/MM results is not well supported by the current calculations.

    Strengths:
    The QM/MM free energy simulations have been carefully conducted. The accuracy of the semi-empirical QM/MM results was further supported by DFT/MM calculations, as well as qualitatively by several experimental studies.

    Weaknesses:
    1. One key issue is the definition of the transition state ensemble. The authors appear to define this by simply considering structures that lie within a given free energy range from the barrier. However, this is not the rigorous definition of transition state ensemble, which should be defined in terms of committor distribution. This is not simply an issue of semantics, since only a rigorous definition allows a fair comparison between different cases - such as the transition state in an enzyme vs in solution, or with and without the metal ion. For a chemical reaction in a complex environment, it is also possible that many other variables (in addition to the breaking and forming P-O bonds) should be considered when one measures the diversity in the conformational ensemble.

    2. While the experimental observation that the activation entropy differs significantly with and without the Ca2+ ion is interesting, it is difficult to connect this result with the "wide" transition state ensemble observed in the QM/MM simulations so far. Even without considering the definition of the transition state ensemble mentioned above, it is unlikely that a broader range of P-O distances would explain the substantial difference in the activation entropy measured in the experiment. Since the difference is sufficiently large, it should be possible to compute the value by repeating the free energy simulations at different temperatures, which would lead to a much more direct evaluation of the QM/MM model/result and the interpretation.

  14. Version published to 10.1101/2023.10.03.560706v1 on bioRxiv