On the interpretation of the observed linear free energy relationship in phosphate hydrolysis: a thorough computational study of phosphate diester hydrolysis in solution

Unveiling the Cleavage Mechanism of an RNA Model Compound on the whole pH Scale: Computations Meet Experiments in the Determination of Reaction Rates

The knowledge of the mechanism of reactions occurring in solution is a primary research line both in the context of theoretical-computational chemistry and in the field of organic and bio-organic chemistry. Given the importance of the hydrolysis of nucleic acids in life-related phenomena, here we present a combined experimental and computational study on the cleavage of an RNA model compound. This phosphodiester features a cleavage rate strictly dependent on the pH with three different dependence domains. Such experimental evidence, highlighted by an in-depth kinetic investigation, unequivocally suggests a change in the reaction mechanism along the pH scale. In order to interpret the data and to explain the experimental behavior, we have applied a theoretical-computational procedure, involving a hybrid quantum/classical approach, able to model chemical reactions in complex environments, i. e. in solution. This study turns out to quantitatively reproduce the experimental data with accuracy and, in addition, provides useful mechanistic insight into the transesterification process of the investigated compound. The study indicates that the cleavage can occur through anA N D N ${A_N D_N }$ , anA N + D N ${A_N + D_N }$ , and aD N A N ${D_N A_N }$ mechanism depending on the pH values.

Structure and Ultrafast X-ray Diffraction of the Hydrated Metaphosphate

We study the pathway of metaphosphate hydration when a metaphosphate anion is dissolved in liquid water with an explicit water model. For this purpose, we propose a sequential Monte Carlo algorithm incorporated with the ab initio quantum mechanics/molecular mechanics (QM/MM) method, which can reduce the amount of ab initio QM/MM sampling while retaining the accuracy of the simulation. We demonstrate the numerical calculation of the standard enthalpy change for the successive addition reaction PO3-·2H2O + H2O ⇌ PO3-·3H2O in the liquid phase, which helps to clarify the hydration pathway of the metaphosphate. With the obtained hydrated structure of the metaphosphate anion, we perform ab initio calculations for its relaxation dynamics upon vibrational excitation and characterize the energy transfer process in solution with simulated ultrafast X-ray diffraction signals, which can be experimentally implemented with X-ray free-electron lasers.

Systematic QM/MM Study for Predicting 31P NMR Chemical Shifts of Adenosine Nucleotides in Solution and Stages of ATP Hydrolysis in a Protein Environment

NMR (nuclear magnetic resonance) spectroscopy allows for important atomistic insights into the structure and dynamics of biological macromolecules; however, reliable assignments of experimental spectra are often difficult. Herein, quantum mechanical/molecular mechanical (QM/MM) calculations can provide crucial support. A major problem for the simulations is that experimental NMR signals are time-averaged over much longer time scales, and since computed chemical shifts are highly sensitive to local changes in the electronic and structural environment, sufficiently large averages over representative structural ensembles are essential. This entails high computational demands for reliable simulations. For NMR measurements in biological systems, a nucleus of major interest is 31P since it is both highly present (e.g., in nucleic acids) and easily observable. The focus of our present study is to develop a robust and computationally cost-efficient framework for simulating 31P NMR chemical shifts of nucleotides. We apply this scheme to study the different stages of the ATP hydrolysis reaction catalyzed by p97. Our methodology is based on MM molecular dynamics (MM-MD) sampling, followed by QM/MM structure optimizations and NMR calculations. Overall, our study is one of the most comprehensive QM-based 31P studies in a protein environment and the first to provide computed NMR chemical shifts for multiple nucleotide states in a protein environment. This study sheds light on a process that is challenging to probe experimentally and aims to bridge the gap between measured and calculated NMR spectroscopic properties.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

What Does the Brønsted Slope Measure in the Phosphoryl Transfer Transition State?

The structural and energetic features of phosphate and phosphonate hydrolysis in Protein Phosphatase-1 (PP1) and water are studied using quantum mechanical (QM) cluster models. The calculations are able to reproduce observed kinetic isotope effects and capture several key trends in the experimental Brønsted plots: the β l g values are rather different for phosphate and phosphonate ester hydrolysis in solution but are similar in PP1. Detailed analyses of structure, charge distribution and bond order of computed transition states support the general conclusion from experimental study that phosphoryl transfer transition states are different for the two classes of substrates in solution but similar in PP1. On the other hand, the microscopic models also highlight notable differences between the phosphate and phosphonate transition states, which are manifested in not only structure but also kinetic isotope effects. Overall, we find that while β l g / β E Q , l g generally correlates with the partial charge on leaving group oxygen and the fractional bond order of the breaking P- O l g bond, the precise mapping between β l g / β E Q , l g and P- O l g bond order in the transition state is difficult due largely to the cross talk between breaking and forming P-O bonds. Therefore, further supporting previous analyses of limitations of free energy relations, our results suggest that while free energy relation is a valuable tool for probing the nature of transition state, a quantitative mapping of β l g and β l g / β E Q , l g values to structure or charge in the transition state should be conducted with great care.

Differences in the Nature of the Phosphoryl Transfer Transition State in Protein Phosphatase 1 and Alkaline Phosphatase: Insights from QM Cluster Models

Quantum mechanical (QM) cluster models are used to probe effects on the catalytic properties of protein phosphatase 1 (PP1) and alkaline phosphatase (AP) due to metal ions and active site residues. The calculations suggest that the phosphoryl transfer transition states in PP1 are synchronous in nature with a significant degree of P-Olg cleavage, while those in AP are tighter with a modest degree of P-Olg cleavage and a range of P-Onuc formation. Similar to observations made in our recent work, a significant degree of cross talk between the forming and breaking P-O bonds complicates the interpretation of the Brønsted relation, especially in regard to AP for which the computed βlg/βEQ,lg value does not correlate with the degree of P-Olg cleavage regardless of the metal ions in the active site. By comparison, the correlation between βlg/βEQ,lg and the P-Olg bond order is more applicable to PP1, which generally exhibits less variation in the transition state than AP. Results for computational models with swapped metal ions between PP1 and AP suggest that the metal ions modulate both the nature of the transition state and the degrees of sensitivity of the transition state to the leaving group. In the reactant state, the degree of the scissile bond polarization is also different in the two enzymes, although this difference appears to be largely determined by the active site residues rather than the metal ions. Therefore, both the identity of the metal ion and the positioning of polar or charged residues in the active site contribute to the distinct catalytic characteristics of these enzymes. Several discrepancies observed between the QM cluster results and the available experimental data highlight the need for further QM/MM method developments for the quantitative analysis of metalloenzymes that contain open-shell transition metal ions.

Modeling the Alkaline Hydrolysis of Diaryl Sulfate Diesters: A Mechanistic Study

Phosphate and sulfate esters have important roles in regulating cellular processes. However, while there has been substantial experimental and computational investigation of the mechanisms and the transition states involved in phosphate ester hydrolysis, there is far less work on sulfate ester hydrolysis. Here, we report a detailed computational study of the alkaline hydrolysis of diaryl sulfate diesters, using different DFT functionals as well as mixed implicit/explicit solvation with varying numbers of explicit water molecules. We consider the impact of the computational model on computed linear free-energy relationships (LFER) and the nature of the transition states (TS) involved. We obtain good qualitative agreement with experimental LFER data when using a pure implicit solvent model and excellent agreement with experimental kinetic isotope effects for all models used. Our calculations suggest that sulfate diester hydrolysis proceeds through loose transition states, with minimal bond formation to the nucleophile and bond cleavage to the leaving group already initiated. Comparison to prior work indicates that these TS are similar in nature to those for the alkaline hydrolysis of neutral arylsulfonate monoesters or charged phosphate diesters and fluorophosphates. Obtaining more detailed insights into the transition states involved assists in understanding the selectivity of enzymes that hydrolyze these reactions.

Molecular Mechanism of ATP Hydrolysis in an ABC Transporter

Hydrolysis of nucleoside triphosphate (NTP) plays a key role for the function of many biomolecular systems. However, the chemistry of the catalytic reaction in terms of an atomic-level understanding of the structural, dynamic, and free energy changes associated with it often remains unknown. Here, we report the molecular mechanism of adenosine triphosphate (ATP) hydrolysis in the ATP-binding cassette (ABC) transporter BtuCD-F. Free energy profiles obtained from hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations show that the hydrolysis reaction proceeds in a stepwise manner. First, nucleophilic attack of an activated lytic water molecule at the ATP γ-phosphate yields ADP + HPO₄ ^2- as intermediate product. A conserved glutamate that is located very close to the γ-phosphate transiently accepts a proton and thus acts as catalytic base. In the second step, the proton is transferred back from the catalytic base to the γ-phosphate, yielding ADP + H₂PO₄ ^-. These two chemical reaction steps are followed by rearrangements of the hydrogen bond network and the coordination of the Mg²⁺ ion. The rate constant estimated from the computed free energy barriers is in very good agreement with experiments. The overall free energy change of the reaction is close to zero, suggesting that phosphate bond cleavage itself does not provide a power stroke for conformational changes. Instead, ATP binding is essential for tight dimerization of the nucleotide-binding domains and the transition of the transmembrane domains from inward- to outward-facing, whereas ATP hydrolysis resets the conformational cycle. The mechanism is likely relevant for all ABC transporters and might have implications also for other NTPases, as many residues involved in nucleotide binding and hydrolysis are strictly conserved.

Phosphoryl-Transfer Reaction in RNA under Alkaline Conditions

The phosphoryl-transfer reaction in RNA under alkaline conditions by exploring the influence of several solvents theoretically was studied. The calculations were carried out by using the M06-2X functional and the solvents were taken as a continuum by using the solvent model density (SMD) method. The main findings show that the O2'-P-O5' angle in the reactants, the free activation energies, and the reaction mechanism are clearly dependent on the dielectric constant of the environment, thus showing that the electrostatic term is the determining factor for this chemical system with two negative charges. Our study seems to indicate that water, the solvent with the greatest dielectric constant, would be the solvent that increases the reaction rate the most. As this outcome was not the case in enzymatic catalysis, one has to conclude that, in the case of proteins as well as for ribozymes, the enzymatic catalysis is not mainly due to the solvent reaction field, but to local electrical fields as a result of enzyme preorganization.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Allostery in the dengue virus NS3 helicase: Insights into the NTPase cycle from molecular simulations

The C-terminus domain of non-structural 3 (NS3) protein of the Flaviviridae viruses (e.g. HCV, dengue, West Nile, Zika) is a nucleotide triphosphatase (NTPase) -dependent superfamily 2 (SF2) helicase that unwinds double-stranded RNA while translocating along the nucleic polymer. Due to these functions, NS3 is an important target for antiviral development yet the biophysics of this enzyme are poorly understood. Microsecond-long molecular dynamic simulations of the dengue NS3 helicase domain are reported from which allosteric effects of RNA and NTPase substrates are observed. The presence of a bound single-stranded RNA catalytically enhances the phosphate hydrolysis reaction by affecting the dynamics and positioning of waters within the hydrolysis active site. Coupled with results from the simulations, electronic structure calculations of the reaction are used to quantify this enhancement to be a 150-fold increase, in qualitative agreement with the experimental enhancement factor of 10–100. Additionally, protein-RNA interactions exhibit NTPase substrate-induced allostery, where the presence of a nucleotide (e.g. ATP or ADP) structurally perturbs residues in direct contact with the phosphodiester backbone of the RNA. Residue-residue network analyses highlight pathways of short ranged interactions that connect the two active sites. These analyses identify motif V as a highly connected region of protein structure through which energy released from either active site is hypothesized to move, thereby inducing the observed allosteric effects. These results lay the foundation for the design of novel allosteric inhibitors of NS3.

Non-structural protein 3 (NS3) is a Flaviviridae (e.g. Hepatitis C, dengue, and Zika viruses) helicase that unwinds double stranded RNA while translocating along the nucleic polymer during viral genome replication. As a member of superfamily 2 (SF2) helicases, NS3 utilizes the free energy of nucleotide triphosphate (NTP) binding, hydrolysis, and product unbinding to perform its functions. While much is known about SF2 helicases, the pathways and mechanisms through which free energy is transduced between the NTP hydrolysis active site and RNA binding cleft remains elusive. Here we present a multiscale computational study to characterize the allosteric effects induced by the RNA and NTPase substrates (ATP, ADP, and P_i) as well as the pathways of short-range, residue-residue interactions that connect the two active sites. Results from this body of molecular dynamics simulations and electronic structure calculations are highlighted in context to the NTPase enzymatic cycle, allowing for development of testable hypotheses for validation of these simulations. Our insights, therefore, provide novel details about the biophysics of NS3 and guide the next generation of experimental studies.

Challenges and advances in the computational modeling of biological phosphate hydrolysis

Phosphate ester hydrolysis is fundamental to many life processes, and has been the topic of substantial experimental and computational research effort. However, even the simplest of phosphate esters can be hydrolyzed through multiple possible pathways that can be difficult to distinguish between, either experimentally, or computationally. Therefore, the mechanisms of both the enzymatic and non-enzymatic reactions have been historically controversial. In the present contribution, we highlight a number of technical issues involved in reliably modeling these computationally challenging reactions, as well as proposing potential solutions. We also showcase examples of our own work in this area, discussing both the non-enzymatic reaction in aqueous solution, as well as insights obtained from the computational modeling of organophosphate hydrolysis and catalytic promiscuity amongst enzymes that catalyze phosphoryl transfer.

Phosphoryl Transfer Reaction in RNA: Is the Substrate-Assisted Catalysis a Possible Mechanism in Certain Solvents?

A proton shuttle mechanism for the phosphoryl transfer reaction in RNA, in which a proton is transferred from the nucleophile to the leaving group through a nonbridged oxygen atom of the phosphate, was explored using the MO6-2X density functional method and the solvent continuum model. This reaction is the initial step of the RNA hydrolysis. We used different solvents characterized by their dielectric constant, and, for each of them, we studied the nuclear and electronic relaxation, produced by the solvent reaction field, for the stationary points. Given that RNA has a poor leaving group, the bond breaking corresponds to the rate-determining step. If the O atom is substituted by a S atom, the leaving group is now good, and the rate-determining step is now the nucleophilic attack concerted with the proton transfer. The most relevant result we found is that none of the solvents we studied has a free energy of activation that is smaller than the one in water. This suggests that the enzyme catalysis following this mechanism must be due to the permanent electric field that is created by a preorganized charge distribution but not to the solvent reaction field.

Effect of protonation on the mechanism of phosphate monoester hydrolysis and comparison with the hydrolysis of nucleoside triphosphate in biomolecular motors

Hydrolysis of phosphate groups is a crucial reaction in living cells. It involves the breaking of two strong bonds, i.e. the O_aH bond of the attacking water molecule, and the PO_l bond of the substrate (O_a and O_l stand for attacking and leaving oxygen atoms). Mechanism of the hydrolysis reaction can proceed either by a concurrent or a sequential mechanism. In the concurrent mechanism, the breaking of O_aH and PO_l bonds occurs simultaneously, whereas in the sequential mechanism, the O_aH and PO_l bonds break at different stages of the reaction. To understand how protonation affects the mechanism of hydrolysis of phosphate monoester, we have studied the mechanism of hydrolysis of protonated and deprotonated phosphate monoester at M06-2X/6-311+G**//M06-2X/6-31+G*+ZPE level of theory (where ZPE stands for zero point energy). Our calculations show that in both protonated and deprotonated cases, the breaking of the water O_aH bond occurs before the breaking of the PO_l bond. Because the two events are not separated by a stable intermediate, the mechanism can be categorized as semi-concurrent. The overall energy barrier is 41kcalmol^-1 in the unprotonated case. Most (5/6th) of this is due to the initial breaking of the water O_aH bond. This component is lowered from 34 to 25kcalmol^-1 by adding one proton to the phosphate. The rest of the overall energy barrier comes from the subsequent breaking of the PO_l bond and is not sensitive to protonation. This is consistent with previous findings about the effect of triphosphate protonation on the hydrolysis, where the equivalent protonation (on the γ-phosphate) was seen to lower the barrier of breaking the water O_aH bond and to have little effect on the PO_l bond breaking. Hydrolysis pathways of phosphate monoester with initial breaking of the PO_l bond could not be found here. This is because the leaving group in phosphate monoester cannot be protonated, unlike in triphosphate hydrolysis, where protonation of the β- and γ-phosphates had been shown to promote a mechanism where the PO_l bond breaks before the O_aH bond does. We also point out that the charge shift due to PO_l bond breaking during sequential ATP hydrolysis in bio-molecular motors onsets the week unbinding of hydrolysis product that finally leads to the product release during power stroke.

The effect of magnesium ions on triphosphate hydrolysis

The role of metal ions in catalyzing phosphate ester hydrolysis has been the subject of much debate, both in terms of whether they change the transition state structure or mechanistic pathway. Understanding the impact of metal ions on these biologically critical reactions is central to improving our understanding of the role of metal ions in the numerous enzymes that facilitate them. In the present study, we have performed density functional theory studies of the mechanisms of methyl triphosphate and acetyl phosphate hydrolysis in aqueous solution to explore the competition between solvent- and substrate-assisted pathways, and examined the impact of Mg2+ on the energetics and transition state geometries. In both cases, we observe a clear preference for a more dissociative solvent-assisted transition state, which is not significantly changed by coordination of Mg2+. The effect of Mg2+ on the transition state geometries for the two pathways is minimal. While our calculations cannot rule out a substrate-assisted pathway as a possible solution for biological phosphate hydrolysis, they demonstrate that a significantly higher energy barrier needs to be overcome in the enzymatic reaction for this to be an energetically viable reaction pathway.

Simulating the fidelity and the three Mg mechanism of pol η and clarifying the validity of transition state theory in enzyme catalysis

Pol η belongs to the important Y family of DNA polymerases that can catalyze translesion synthesis across sites of damaged DNA. This activity involves the reduced fidelity of Pol η for 8-oxo-7,8-dhyedro-2'-deoxoguanosin(8-oxoG). The fundamental interest in Pol η has grown recently with the demonstration of the importance of a 3rd Mg2+ ion. The current work explores both the fidelity of Pol η and the role of the 3rd metal ion, by using empirical valence bond (EVB) simulations. The simulations reproduce the observed trend in fidelity and shed a new light on the role of the 3rd metal ion. It is found that this ion does not lead to a major catalytic effect, but most probably plays an important role in reducing the product release barrier. Furthermore, it is concluded, in contrast to some implications, that the effect of this metal does not violate transition state theory, and the evaluation of the catalytic effect must conserve the molecular composition upon moving from the reactant to the transition state. Proteins 2017; 85:1446-1453. © 2017 Wiley Periodicals, Inc.

Simulating the reactions of substituted pyridinio-N-phosphonates with pyridine as a model for biological phosphoryl transfer

This work provides a comprehensive model for non-enzymatic phosphoryl transfer, as a baseline for understanding biological phosphoryl transfer reactions.

Uniform Free-Energy Profiles of the P-O Bond Formation and Cleavage Reactions Catalyzed by DNA Polymerases β and λ

Human X-family DNA polymerases β (Polβ) and λ (Polλ) catalyze the nucleotidyl-transfer reaction in the base excision repair pathway of the cellular DNA damage response. Using empirical valence bond and free-energy perturbation simulations, we explore the feasibility of various mechanisms for the deprotonation of the 3′-OH group of the primer DNA strand, and the subsequent formation and cleavage of P–O bonds in four Polβ, two truncated Polλ (tPolλ), and two tPolλ Loop1 mutant (tPolλΔL1) systems differing in the initial X-ray crystal structure and nascent base pair. The average calculated activation free energies of 14, 18, and 22 kcal mol^–1 for Polβ, tPolλ, and tPolλΔL1, respectively, reproduce the trend in the observed catalytic rate constants. The most feasible reaction pathway consists of two successive steps: specific base (SB) proton transfer followed by rate-limiting concerted formation and cleavage of the P–O bonds. We identify linear free-energy relationships (LFERs) which show that the differences in the overall activation and reaction free energies among the eight studied systems are determined by the reaction free energy of the SB proton transfer. We discuss the implications of the LFERs and suggest pK_a of the 3′-OH group as a predictor of the catalytic rate of X-family DNA polymerases.

Substrate and Transition State Binding in Alkaline Phosphatase Analyzed by Computation of Oxygen Isotope Effects

Enzymes are powerful catalysts, and a thorough understanding of the sources of their catalytic power will facilitate many medical and industrial applications. Here we have studied the catalytic mechanism of alkaline phosphatase (AP), which is one of the most catalytically proficient enzymes known. We have used quantum mechanics calculations and hybrid quantum mechanics/molecular mechanics (QM/MM) simulations to model a variety of isotope effects relevant to the reaction of AP. We have calculated equilibrium isotope effects (EIEs), binding isotope effects (BIEs), and kinetic isotope effects (KIEs) for a range of phosphate mono- and diester substrates. The results agree well with experimental values, but the model for the reaction's transition state (TS) differs from the original interpretation of those experiments. Our model indicates that isotope effects on binding make important contributions to measured KIEs on V/K, which complicated interpretation of the measured values. Our results provide a detailed interpretation of the measured isotope effects and make predictions that can test the proposed model. The model indicates that the substrate is deformed in the ground state (GS) of the reaction and partially resembles the TS. The highly preorganized active site preferentially binds conformations that resemble the TS and not the GS, which induces the substrate to adapt to the enzyme, rather than the other way around-as with classic "induced fit" models. The preferential stabilization of the TS over the GS is what lowers the barrier to the chemical step.

Exploring the mechanism of DNA polymerases by analyzing the effect of mutations of active site acidic groups in Polymerase β

Elucidating the catalytic mechanism of DNA polymerase is crucial for a progress in the understanding of the control of replication fidelity. This work tries to advance the mechanistic understanding by analyzing the observed effect of mutations of the acidic groups in the active site of Polymerase β as well as the pH effect on the rate constant. The analysis involves both empirical valence bond (EVB) free energy calculations and considerations of the observed pH dependence of the reaction. The combined analysis indicates that the proton transfer (PT) from the nucleophilic O3' has two possible pathways, one to D256 and the second to the bulk. We concluded based on calculations and the experimental pH profile that the most likely path for the wild-type (WT) and the D256E and D256A mutants is a PT to the bulk, although the WT may also use a PT to Asp 256. Our analysis highlights the need for very extensive sampling in the calculations of the activation barrier and also clearly shows that ab initio QM/MM calculations that do not involve extensive sampling are unlikely to give a clear quantitative picture of the reaction mechanism. Proteins 2016; 84:1644-1657. © 2016 Wiley Periodicals, Inc.

The Competing Mechanisms of Phosphate Monoester Dianion Hydrolysis

Despite the numerous experimental and theoretical studies on phosphate monoester hydrolysis, significant questions remain concerning the mechanistic details of these biologically critical reactions. In the present work we construct a linear free energy relationship for phosphate monoester hydrolysis to explore the effect of modulating leaving group pK_a on the competition between solvent- and substrate-assisted pathways for the hydrolysis of these compounds. Through detailed comparative electronic-structure studies of methyl phosphate and a series of substituted aryl phosphate monoesters, we demonstrate that the preferred mechanism is dependent on the nature of the leaving group. For good leaving groups, a strong preference is observed for a more dissociative solvent-assisted pathway. However, the energy difference between the two pathways gradually reduces as the leaving group pK_a increases and creates mechanistic ambiguity for reactions involving relatively poor alkoxy leaving groups. Our calculations show that the transition-state structures vary smoothly across the range of pK_as studied and that the pathways remain discrete mechanistic alternatives. Therefore, while not impossible, a biological catalyst would have to surmount a significantly higher activation barrier to facilitate a substrate-assisted pathway than for the solvent-assisted pathway when phosphate is bonded to good leaving groups. For poor leaving groups, this intrinsic preference disappears.

The control of the discrimination between dNTP and rNTP in DNA and RNA polymerase

Understanding the origin of discrimination between rNTP and dNTP by DNA/RNA polymerases is important both for gaining fundamental knowledge on the corresponding systems and for advancing the design of specific drugs. This work explores the nature of this discrimination by systematic calculations of the transition state (TS) binding energy in RB69 DNA polymerase (gp43) and T7 RNA polymerase. The calculations reproduce the observed trend, in particular when they included the water contribution obtained by the water flooding approach. Our detailed study confirms the idea that the discrimination is due to the steric interaction between the 2'OH and Tyr416 in DNA polymerase, while the electrostatic interaction is the source of the discrimination in RNA polymerase. Proteins 2016; 84:1616-1624. © 2016 Wiley Periodicals, Inc.

Leaving Group Ability Observably Affects Transition State Structure in a Single Enzyme Active Site

A reaction's transition state (TS) structure plays a critical role in determining reactivity and has important implications for the design of catalysts, drugs, and other applications. Here, we explore TS structure in the enzyme alkaline phosphatase using hybrid Quantum Mechanics/Molecular Mechanics simulations. We find that minor perturbations to the substrate have major effects on TS structure and the way the enzyme stabilizes the TS. Substrates with good leaving groups (LGs) have little cleavage of the phosphorus-LG bond at the TS, while substrates with poor LGs have substantial cleavage of that bond. The results predict nonlinear free energy relationships for a single rate-determining step, and substantial differences in kinetic isotope effects for different substrates; both trends were observed in previous experimental studies, although the original interpretations differed from the present model. Moreover, due to different degrees of phosphorus-LG bond cleavage at the TS for different substrates, the LG is stabilized by different interactions at the TS: while a poor LG is directly stabilized by an active site zinc ion, a good LG is mainly stabilized by active site water molecules. Our results demonstrate the considerable plasticity of TS structure and stabilization in enzymes. Furthermore, perturbations to reactivity that probe TS structure experimentally (i.e., substituent effects) may substantially perturb the TS they aim to probe, and thus classical experimental approaches such as free energy relations should be interpreted with care.

Theoretical Insights on the Mechanism of the GTP Hydrolysis Catalyzed by the Elongation Factor Tu (EF-Tu)

The purpose of this work is to have a better understanding of the mechanism of GTP hydrolysis catalyzed by the elongation factor Tu. Two main aspects are being discussed in the literature: the associative or dissociative character of the process and the nature of nucleophile activation. The calculations of the QM subsystem have been done by means of the M06-2X density functional and the split valence triple-ζ 6-311+G(d,p) basis set. The environmental effect has been introduced through the continuum SMD method. We have studied three models of increasing complexity in order to analyze the different factors that intervene in the catalytic action. The results obtained in this paper confirm that the protonated His84 plays a fundamental role in the catalytic mechanism, but we have also found that the crystallographic sodium ion has a notable effect in the catalysis. So, our work has permitted a new insight, complementary to those obtained with QM/MM calculations, into this very complex process.

Theoretical Modeling on the Reaction Mechanism of p-Nitrophenylmethylphosphate Alkaline Hydrolysis and its Kinetic Isotope Effects

We have studied the alkaline hydrolysis of p-nitrophenylmethylphosphate (p-NPmP) in aqueous solution by means of polarizable continuum models and by hybrid quantum-mechanical/molecular-mechanical (QM/MM) methods. The theoretical predictions of kinetic isotope effects (KIEs) are in very good agreement with the experimental data, confirming a concerted asynchronous molecular mechanism. In addition, comparison of high level DFT theory with semiempirical AM1/d Hamiltonian has allowed checking the reliability of the later to be used in modeling very large molecular models containing phosphorus atoms.

Understanding thio-effects in simple phosphoryl systems: role of solvent effects and nucleophile charge

Recent experimental work (J. Org. Chem., 2012, 77, 5829) demonstrated pronounced differences in measured thio-effects for the hydrolysis of (thio)phosphodichloridates by water and hydroxide nucleophiles. In the present work, we have performed detailed quantum chemical calculations of these reactions, with the aim of rationalizing the molecular bases for this discrimination. The calculations highlight the interplay between nucleophile charge and transition state solvation in SN2(P) mechanisms as the basis of these differences, rather than a change in mechanism.

QM/MM investigation of ATP hydrolysis in aqueous solution

Adenosine-5'-triphosphate (ATP) hydrolysis represents a most important reaction in biology. Despite extensive research efforts, the mechanism for ATP hydrolysis in aqueous solution still remains under debate. Previous theoretical studies often predefined reaction coordinates to characterize the mechanism for ATP hydrolysis in water with Mg(2+) by evaluating free energy profiles through these preassumed reaction paths. In the present work, a nudged elastic band method is applied to identify the minimum energy path calculated with a hybrid quantum mechanics and molecular mechanics approach. Along the reaction path, the free energy profile was obtained to have a single transition state and the activation energy of 32.5 kcal/mol. This transition state bears a four-centered structure that describes a concerted nature of the reaction. In the More-O'Ferrall-Jencks diagram, the results show that the reaction proceeds through a concerted path before the system reaches the transition state and along an associative path after the transition state. In addition, the calculated reaction free energy is -7.0 kcal/mol, in good agreement with experiment, capturing the exothermic feature of MgATP(2-) hydrolysis in aqueous solution, whereas the reaction was often shown to be endothermic in the previous theoretical studies. As Mg(2+) is required for ATP hydrolysis in cells, its role in the reaction is also elucidated.

Resolving apparent conflicts between theoretical and experimental models of phosphate monoester hydrolysis

Understanding phosphoryl and sulfuryl transfer is central to many biochemical processes. However, despite decades of experimental and computational studies, a consensus concerning the precise mechanistic details of these reactions has yet to be reached. In this work we perform a detailed comparative theoretical study of the hydrolysis of p-nitrophenyl phosphate, methyl phosphate and p-nitrophenyl sulfate, all of which have served as key model systems for understanding phosphoryl and sulfuryl transfer reactions, respectively. We demonstrate the existence of energetically similar but mechanistically distinct possibilities for phosphate monoester hydrolysis. The calculated kinetic isotope effects for p-nitrophenyl phosphate provide a means to discriminate between substrate- and solvent-assisted pathways of phosphate monoester hydrolysis, and show that the solvent-assisted pathway dominates in solution. This preferred mechanism for p-nitrophenyl phosphate hydrolysis is difficult to find computationally due to the limitations of compressing multiple bonding changes onto a 2-dimensional energy surface. This problem is compounded by the need to include implicit solvation to at least microsolvate the system and stabilize the highly charged species. In contrast, methyl phosphate hydrolysis shows a preference for a substrate-assisted mechanism. For p-nitrophenyl sulfate hydrolysis there is only one viable reaction pathway, which is similar to the solvent-assisted pathway for phosphate hydrolysis, and the substrate-assisted pathway is not accessible. Overall, our results provide a unifying mechanistic framework that is consistent with the experimentally measured kinetic isotope effects and reconciles the discrepancies between theoretical and experimental models for these biochemically ubiquitous classes of reaction.

Modeling the role of G12V and G13V Ras mutations in the Ras-GAP-catalyzed hydrolysis reaction of guanosine triphosphate

Cancer-associated point mutations in Ras, in particular, at glycine 12 and glycine 13, affect the normal cycle between inactive GDP-bound and active GTP-bound states. In this work, the role of G12V and G13V replacements in the GAP-stimulated intrinsic GTP hydrolysis reaction in Ras is studied using molecular dynamics (MD) simulations with quantum mechanics/molecular mechanics (QM/MM) potentials. A model molecular system was constructed by motifs of the relevant crystal structure (Protein Data Bank entry 1WQ1 ). QM/MM optimization of geometry parameters in the Ras-GAP-GTP complex and QM/MM-MD simulations were performed with a quantum subsystem comprising a large fraction of the enzyme active site. For the system with wild-type Ras, the conformations fluctuated near the structure ready to be involved in the efficient chemical reaction leading to the cleavage of the phosphorus-oxygen bond in GTP upon approach of the properly aligned catalytic water molecule. Dynamics of the system with the G13V mutant is characterized by an enhanced flexibility in the area occupied by the γ-phosphate group of GTP, catalytic water, and the side chains of Arg789 and Gln61, which should somewhat hinder fast chemical steps. Conformational dynamics of the system with the G12V mutant shows considerable displacement of the Gln61 side chain and catalytic water from their favorable arrangement in the active site that may lead to a marked reduction in the reaction rate. The obtained computational results correlate well with the recent kinetic measurements of the Ras-GAP-catalyzed hydrolysis of GTP.

Quantum mechanical analysis of nonenzymatic nucleotidyl transfer reactions: kinetic and thermodynamic effects of β-γ bridging groups of dNTP substrates

Rate (k) and equilibrium (K) constants for the reaction of tetrahydrofuranol with a series of Mg²⁺ complexes of methyl triphosphate analogues, CH₃O-P(O₂)-O-P(O₂)-X-PO₃^4–, X = O, CH₂, CHCH₃, C(CH₃)₂, CFCH₃, CHF, CHCl, CHBr, CFCl, CF₂, CCl₂, and CBr₂, forming phosphate diester and pyrophosphate or bisphosphonate in aqueous solution were evaluated by B3LYP/TZVP//HF/6-31G* quantum chemical calculations and Langevin dipoles and polarized continuum solvation models. The calculated log k and log K values were found to depend linearly on the experimental pK_a4 of the conjugate acid of the corresponding pyrophosphate or bisphosphonate leaving group. The calculated slopes of these Brønsted linear free energy relationships were β_lg = −0.89 and β_eq = −0.93, respectively. The studied compounds also followed the linear relationship Δlog k = 0.8Δlog K, which became less steep, Δlog k = 0.6Δlog K, after the range of studied compounds was extended to include analogues that were doubly protonated on γ-phosphate, CH₃O-P(O₂)-O-P(O₂)-X-PO₃H₂^2–. The scissile P_α–O_lg bond length in studied methyl triphosphate analogues slightly increases with decreasing pK_a of the leaving group; concomitantly, the CH₃OP_α(O₂) moiety becomes more positive. These structural effects indicate that substituents with low pK_a can facilitate both P_α–O_lg bond breaking and the P_α–O_nuc bond forming process, thus explaining the large negative β_lg calculated for the transition state geometry that has significantly longer P_α–O_nuc distance than the P_α–O_lg distance.

Computing the Free Energy Barriers for Less by Sampling with a Coarse Reference Potential while Retaining Accuracy of the Target Fine Model

Proposed in this contribution is a protocol for calculating fine-physics (e.g., ab initio QM/MM) free-energy surfaces at a high level of accuracy locally (e.g., only at reactants and at the transition state for computing the activation barrier) from targeted fine-physics sampling and extensive exploratory coarse-physics sampling. The full free-energy surface is still computed but at a lower level of accuracy from coarse-physics sampling. The method is analytically derived in terms of the umbrella sampling and the free-energy perturbation methods which are combined with the thermodynamic cycle and the targeted sampling strategy of the paradynamics approach. The algorithm starts by computing low-accuracy fine-physics free-energy surfaces from the coarse-physics sampling in order to identify the reaction path and to select regions for targeted sampling. Thus, the algorithm does not rely on the coarse-physics minimum free-energy reaction path. Next, segments of high-accuracy free-energy surface are computed locally at selected regions from the targeted fine-physics sampling and are positioned relative to the coarse-physics free-energy shifts. The positioning is done by averaging the free-energy perturbations computed with multistep linear response approximation method. This method is analytically shown to provide results of the thermodynamic integration and the free-energy interpolation methods, while being extremely simple in implementation. Incorporating the metadynamics sampling to the algorithm is also briefly outlined. The application is demonstrated by calculating the B3LYP//6-31G*/MM free-energy barrier for an enzymatic reaction using a semiempirical PM6/MM reference potential. These modifications allow computing the activation free energies at a significantly reduced computational cost but at the same level of accuracy compared to computing full potential of mean force.

The alkaline hydrolysis of sulfonate esters: challenges in interpreting experimental and theoretical data

Sulfonate ester hydrolysis has been the subject of recent debate, with experimental evidence interpreted in terms of both stepwise and concerted mechanisms. In particular, a recent study of the alkaline hydrolysis of a series of benzene arylsulfonates (Babtie et al., Org. Biomol. Chem. 10, 2012, 8095) presented a nonlinear Brønsted plot, which was explained in terms of a change from a stepwise mechanism involving a pentavalent intermediate for poorer leaving groups to a fully concerted mechanism for good leaving groups and supported by a theoretical study. In the present work, we have performed a detailed computational study of the hydrolysis of these compounds and find no computational evidence for a thermodynamically stable intermediate for any of these compounds. Additionally, we have extended the experimental data to include pyridine-3-yl benzene sulfonate and its N-oxide and N-methylpyridinium derivatives. Inclusion of these compounds converts the Brønsted plot to a moderately scattered but linear correlation and gives a very good Hammett correlation. These data suggest a concerted pathway for this reaction that proceeds via an early transition state with little bond cleavage to the leaving group, highlighting the care that needs to be taken with the interpretation of experimental and especially theoretical data.

Phosphate monoester hydrolysis by trinuclear alkaline phosphatase; DFT study of transition States and reaction mechanism

Alkaline phosphatase (AP) is a trinuclear metalloenzyme that catalyzes the hydrolysis of a broad range of phosphate monoesters to form inorganic phosphate and alcohol (or phenol). In this paper, by using density functional theory with a model based on a crystal structure, the AP-catalyzed hydrolysis of phosphate monoesters is investigated by calculating two substrates, that is, methyl and p-nitrophenyl phosphates, which represent alkyl and aryl phosphates, respectively. The calculations confirm that the AP reaction employs a "ping-pong" mechanism involving two chemical displacement steps, that is, the displacement of the substrate leaving group by a Ser102 alkoxide and the hydrolysis of the phosphoseryl intermediate by a Zn2-bound hydroxide. Both displacement steps proceed via a concerted associative pathway no matter which substrate is used. Other mechanistic aspects are also studied. Comparison of our calculations with linear free energy relationships experiments shows good agreement.

Modeling catalytic promiscuity in the alkaline phosphatase superfamily

In recent years, it has become increasingly clear that promiscuity plays a key role in the evolution of new enzyme function. This finding has helped to elucidate fundamental aspects of molecular evolution. While there has been extensive experimental work on enzyme promiscuity, computational modeling of the chemical details of such promiscuity has traditionally fallen behind the advances in experimental studies, not least due to the nearly prohibitive computational cost involved in examining multiple substrates with multiple potential mechanisms and binding modes in atomic detail with a reasonable degree of accuracy. However, recent advances in both computational methodologies and power have allowed us to reach a stage in the field where we can start to overcome this problem, and molecular simulations can now provide accurate and efficient descriptions of complex biological systems with substantially less computational cost. This has led to significant advances in our understanding of enzyme function and evolution in a broader sense. Here, we will discuss currently available computational approaches that can allow us to probe the underlying molecular basis for enzyme specificity and selectivity, discussing the inherent strengths and weaknesses of each approach. As a case study, we will discuss recent computational work on different members of the alkaline phosphatase superfamily (AP) using a range of different approaches, showing the complementary insights they have provided. We have selected this particular superfamily, as it poses a number of significant challenges for theory, ranging from the complexity of the actual reaction mechanisms involved to the reliable modeling of the catalytic metal centers, as well as the very large system sizes. We will demonstrate that, through current advances in methodologies, computational tools can provide significant insight into the molecular basis for catalytic promiscuity, and, therefore, in turn, the mechanisms of protein functional evolution.

Stabilization of different types of transition states in a single enzyme active site: QM/MM analysis of enzymes in the alkaline phosphatase superfamily

The first step for the hydrolysis of a phosphate monoester (pNPP(2-)) in enzymes of the alkaline phosphatase (AP) superfamily, R166S AP and wild-type NPP, is studied using QM/MM simulations based on an approximate density functional theory (SCC-DFTBPR) and a recently introduced QM/MM interaction Hamiltonian. The calculations suggest that similar loose transition states are involved in both enzymes, despite the fact that phosphate monoesters are the cognate substrates for AP but promiscuous substrates for NPP. The computed loose transition states are clearly different from the more synchronous ones previously calculated for diester reactions in the same AP enzymes. Therefore, our results explicitly support the proposal that AP enzymes are able to recognize and stabilize different types of transition states in a single active site. Analysis of the structural features of computed transition states indicates that the plastic nature of the bimetallic site plays a minor role in accommodating multiple types of transition states and that the high degree of solvent accessibility of the AP active site also contributes to its ability to stabilize diverse transition-state structures without the need of causing large structural distortions of the bimetallic motif. The binding mode of the leaving group in the transition state highlights that vanadate may not always be an ideal transition state analog for loose phosphoryl transfer transition states.

Empirical valence bond simulations of the chemical mechanism of ATP to cAMP conversion by anthrax edema factor

The two-metal catalysis by the adenylyl cyclase domain of the anthrax edema factor toxin was simulated using the empirical valence bond (EVB) quantum mechanical/molecular mechanical approach. These calculations considered the energetics of the nucleophile deprotonation and the formation of a new P-O bond in aqueous solution and in the enzyme-substrate complex present in the crystal structure models of the reactant and product states of the reaction. Our calculations support a reaction pathway that involves metal-assisted transfer of a proton from the nucleophile to the bulk aqueous solution followed by subsequent formation of an unstable pentavalent intermediate that decomposes into cAMP and pyrophosphate (PPi). This pathway involves ligand exchange in the first solvation sphere of the catalytic metal. At 12.9 kcal/mol, the barrier for the last step of the reaction, the cleavage of the P-O bond to PPi, corresponds to the highest point on the free energy profile for this reaction pathway. However, this energy is too close to the value of 11.4 kcal/mol calculated for the barrier of the nucleophilic attack step to reach a definitive conclusion about the rate-limiting step. The calculated reaction mechanism is supported by reasonable agreement between the experimental and calculated catalytic rate constant decrease caused by the mutation of the active site lysine 346 to arginine.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Bovine brain myelin glycerophosphocholine choline phosphodiesterase is an alkaline lysosphingomyelinase of the eNPP-family, regulated by lysosomal sorting

Glycerophosphocholine choline phosphodiesterase (GPC-Cpde) is a glycosylphosphatidylinositol (GPI)-anchored alkaline hydrolase that is expressed in the brain and kidney. In brain the hydrolase is synthesized by the oligodendrocytes and expressed on the myelin membrane. There are two forms of brain GPC-Cpde, a membrane-linked (mGPC-Cpde) and a soluble (sGPC-Cpde). Here we report the characterisation sGPC-Cpde from bovine brain. The amino acid sequence was identical to ectonucleotide pyrophosphatase/phosphodiesterase 6 (eNPP6) precursor, lacking the N-terminal signal peptide region and a C-terminal stretch, suggesting that the hydrolase was solubilised by C-terminal proteolysis, releasing the GPI-anchor. sGPC-Cpde existed as two isoforms, a homodimer joined by a disulfide bridge linking C414 from each monomer, and a monomer resulting from proteolysis N-terminally to this disulfide bond. The only internal disulfide bridge, linking C142 and C154, stabilises the choline-binding pocket. sGPC-Cpde was specific for lysosphingomyelin, displaying 1 to 2 orders of magnitude higher catalytic activity than towards GPC and lysophosphatidylcholine, suggesting that GPC-Cpde may function in the sphingomyelin signaling, rather than in the homeostasis of acylglycerophosphocholine metabolites. The truncated high mannose and bisected hybrid type glycans linked to N118 and N341 of sGPC-Cpde is a hallmark of glycans in lysosomal glycoproteins, subjected to GlcNAc-1-phosphorylation en route through Golgi. Thus, sGPC-Cpde may originate from the lysosomes, suggesting that lysosomal sorting contributes to the level of mGPC-Cpde on the myelin membrane.

A modified QM/MM Hamiltonian with the Self-Consistent-Charge Density-Functional-Tight-Binding Theory for highly charged QM regions

To improve the description of electrostatic interaction between QM and MM atoms when the QM is SCC-DFTB, we adopt a Klopman-Ohno (KO) functional form which considers the finite size of the QM and MM charge distributions. Compared to the original implementation that used a simple Coulombic interaction between QM Mulliken and MM point charges, the KO based QM/MM scheme takes charge penetration effect into consideration and therefore significantly improves the description of QM/MM interaction at short range, especially when the QM region is highly charged. To be consistent with the third-order formulation of SCC-DFTB, the Hubbard parameter in the KO functional is dependent on the QM charge. As a result, the effective size of the QM charge distribution naturally adjusts as the QM region undergoes chemical transformations, making the KO based QM/MM scheme particularly attractive for describing chemical reactions in the condensed phase. Together with the van der Waals parameters for the QM atom, the KO based QM/MM model introduces four parameters for each element type. They are fitted here based on microsolvation models of small solutes, focusing on negatively charged molecular ions, for elements O, C, H and P with a specific version of SCC-DFTB (SCC-DFTBPR). Test calculations confirm that the KO based QM/MM scheme significantly improves the interactions between QM and MM atoms over the original point charge based model and it is transferable due to the small number of parameters. The new form of QM/MM Hamiltonian will greatly improve the applicability of SCC-DFTB based QM/MM methods to problems that involve highly charged QM regions, such as enzyme catalyzed phosphoryl transfers.