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

    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.

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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 10.1101/2023.10.03.560706v2 on bioRxiv
  2. Version published to 10.7554/elife.93099.1 on eLife
  3. Version published to 10.7554/elife.93099 on eLife
  4. 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.

  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 (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.

  6. 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.

  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.

    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 10.1101/2023.10.03.560706v1 on bioRxiv