Mechanical Free Energy Simulations Research Articles

Kinetic model for reversible radical transfer in ribonucleotide reductase

The enzyme ribonucleotide reductase (RNR), which catalyzes the reduction of ribonucleotides to deoxynucleotides, is vital for DNA synthesis, replication, and repair in all living organisms. Its mechanism requires long-range radical translocation over ∼32 Å through two protein subunits and the intervening aqueous interface. Herein, a kinetic model is designed to describe reversible radical transfer in Escherichia coli RNR. This model is based on experimentally studied photoRNR systems that allow the photochemical injection of a radical at a specific tyrosine residue, Y356, using a photosensitizer. The radical then transfers across the interface to another tyrosine residue, Y731, and continues until it reaches a cysteine residue, C439, which is primed for catalysis. This kinetic model includes radical injection, an off-pathway sink, radical transfer between pairs of residues along the pathway, and the conformational flipping motion of Y731 at the interface. Most of the input rate constants for this kinetic model are obtained from previous experimental measurements and quantum mechanical/molecular mechanical free-energy simulations. Ranges for the rate constants corresponding to radical transfer across the interface are determined by fitting to the experimentally measured Y356 radical decay times in photoRNR systems. This kinetic model illuminates the time evolution of radical transport along the tyrosine and cysteine residues following radical injection. Further analysis identifies the individual rate constants that may be tuned to alter the timescale and probability of the injected radical reaching C439. The insights gained from this kinetic model are relevant to biochemical understanding and protein-engineering efforts with potential pharmacological implications.

Multiscale molecular simulations to investigate adenylyl cyclase‐based signaling in the brain

AbstractAdenylyl cyclases (ACs) play a key role in many signaling cascades. ACs catalyze the production of cyclic AMP from ATP and this function is stimulated or inhibited by the binding of their cognate stimulatory or inhibitory Gα subunits, respectively. Here we used simulation tools to uncover the molecular and subcellular mechanisms of AC function, with a focus on the AC5 isoform, extensively studied experimentally. First, quantum mechanical/molecular mechanical free energy simulations were used to investigate the enzymatic reaction and its changes upon point mutations. Next, molecular dynamics simulations were employed to assess the catalytic state in the presence or absence of Gα subunits. This led to the identification of an inactive state of the enzyme that is present whenever an inhibitory Gα is associated, independent of the presence of a stimulatory Gα. In addition, the use of coevolution‐guided multiscale simulations revealed that the binding of Gα subunits reshapes the free‐energy landscape of the AC5 enzyme by following the classical population‐shift paradigm. Finally, Brownian dynamics simulations provided forward rate constants for the binding of Gα subunits to AC5, consistent with the ability of the protein to perform coincidence detection effectively. Our calculations also pointed to strong similarities between AC5 and other AC isoforms, including AC1 and AC6. Findings from the molecular simulations were used along with experimental data as constraints for systems biology modeling of a specific AC5‐triggered neuronal cascade to investigate how the dynamics of downstream signaling depend on initial receptor activation.This article is categorized under: Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Software > Molecular Modeling

Role of Water in Proton-Coupled Electron Transfer between Tyrosine and Cysteine in Ribonucleotide Reductase.

Ribonucleotide reductase (RNR) catalyzes the reduction of ribonucleotides to deoxyribonucleotides and is critical for DNA synthesis and repair in all organisms. Its mechanism requires radical transfer along a ∼32 Å pathway through a series of proton-coupled electron transfer (PCET) steps. Previous simulations suggested that a glutamate residue (E623) mediates the PCET reaction between two stacked tyrosine residues (Y730 and Y731) through a proton relay mechanism. This work focuses on the adjacent PCET reaction between Y730 and a cysteine residue (C439). Quantum mechanical/molecular mechanical free energy simulations illustrate that when Y730 and Y731 are stacked, E623 stabilizes the radical on C439 through hydrogen bonding with the Y730 hydroxyl group. When Y731 is flipped away from Y730, a water molecule stabilizes the radical on C439 through hydrogen bonding with Y730 and lowers the free energy barrier for radical transfer from Y730 to C439 through electrostatic interactions with the transferring hydrogen but does not directly accept the proton. These simulations indicate that the conformational motions and electrostatic interactions of the tyrosines, cysteine, glutamate, and water strongly impact the thermodynamics and kinetics of these two coupled PCET reactions. Such insights are important for protein engineering efforts aimed at altering radical transfer in RNR.

Glutamate Mediates Proton-Coupled Electron Transfer Between Tyrosines 730 and 731 in Escherichia coli Ribonucleotide Reductase.

Ribonucleotide reductase (RNR) is an essential enzyme in DNA synthesis for all living organisms. It reduces ribonucleotides to the corresponding deoxyribonucleotides by a reversible radical transfer mechanism. The active form of E. coli Ia RNR is composed of two subunits, α and β, which form an active asymmetric α2β2 complex. The radical transfer pathway involves a series of proton-coupled electron transfer (PCET) reactions spanning α and β over ∼32 Å. Herein, quantum mechanical/molecular mechanical free energy simulations of PCET between tyrosine residues Y730 and Y731 are performed on the recently solved cryo-EM structure of the active α2β2 complex, which includes a pre-turnover α/β pair with an ordered PCET pathway and a post-turnover α'/β' pair. The free energy surfaces in both the pre- and post-turnover states are computed. According to the simulations, forward radical transfer from Y731 to Y730 is thermodynamically favored in the pre-turnover state, and backward radical transfer is favored in the post-turnover state, consistent with the reversible mechanism. E623, a glutamate residue that is near these tyrosines only in the pre-turnover state, is discovered to play a key role in facilitating forward radical transfer by thermodynamically stabilizing the radical on Y730 through hydrogen-bonding and electrostatic interactions and lowering the free energy barrier via a proton relay mechanism. Introduction of fluorinated Y731 exhibits expected thermodynamic trends without altering the basic mechanism. These simulations suggest that E623 influences the directionality of PCET between Y731 and Y730 and predict that mutation of E623 will impact catalysis.

Environmental Effects on Guanine-Thymine Mispair Tautomerization Explored with Quantum Mechanical/Molecular Mechanical Free Energy Simulations.

DNA bases can adopt energetically unfavorable tautomeric forms that enable the formation of Watson-Crick-like (WC-like) mispairs, which have been proposed to give rise to spontaneous mutations in DNA and misincorporation errors in DNA replication and translation. Previous NMR and computational studies have indicated that the population of WC-like guanine-thymine (G-T) mispairs depends on the environment, such as the local nucleic acid sequence and solvation. To investigate these environmental effects, herein G-T mispair tautomerization processes are studied computationally in aqueous solution, in A-form and B-form DNA duplexes, and within the active site of a DNA polymerase λ variant. The wobble G-T (wG-T), WC-like G-T*, and WC-like G*-T forms are considered, where * indicates the enol tautomer of the base. The minimum free energy paths for the tautomerization from the wG-T to the WC-like G-T* and from the WC-like G-T* to the WC-like G*-T are computed with mixed quantum mechanical/molecular mechanical (QM/MM) free energy simulations. The reaction free energies and free energy barriers are found to be significantly influenced by the environment. The wG-T→G-T* tautomerization is predicted to be endoergic in aqueous solution and the DNA duplexes but slightly exoergic in the polymerase, with Arg517 and Asn513 providing electrostatic stabilization of G-T*. The G-T*→G*-T tautomerization is also predicted to be slightly more thermodynamically favorable in the polymerase relative to these DNA duplexes. These simulations are consistent with an experimentally driven kinetic misincorporation model suggesting that G-T mispair tautomerization occurs in the ajar polymerase conformation or concertedly with the transition from the ajar to the closed polymerase conformation. Furthermore, the order of the associated two proton transfer reactions is predicted to be different in the polymerase than in aqueous solution and the DNA duplexes. These studies highlight the impact of the environment on the thermodynamics, kinetics, and fundamental mechanisms of G-T mispair tautomerization, which plays a role in a wide range of biochemically important processes.

Examining the Mechanism of Phosphite Dehydrogenase with Quantum Mechanical/Molecular Mechanical Free Energy Simulations

The projected decline of available phosphorus necessitates alternative methods to derive usable phosphate for fertilizer and other applications. Phosphite dehydrogenase oxidizes phosphite to phosphate with the cofactor NAD+ serving as the hydride acceptor. In addition to producing phosphate, this enzyme plays an important role in NADH cofactor regeneration processes. Mixed quantum mechanical/molecular mechanical free energy simulations were performed to elucidate the mechanism of this enzyme and to identify the protonation states of the substrate and product. Specifically, the finite temperature string method with umbrella sampling was used to generate the free energy surfaces and determine the minimum free energy paths for six different initial conditions that varied in the protonation state of the substrate and the position of the nucleophilic water molecule. In contrast to previous studies, the mechanism predicted by all six independent strings is a concerted but asynchronous dissociative mechanism in which hydride transfer from the phosphite substrate to NAD+ occurs prior to attack by the nucleophilic water molecule. His292 is identified as the most likely general base that deprotonates the attacking water molecule. However, Arg237 could also serve as this base if it were deprotonated and His292 were protonated prior to the main chemical transformation, although this scenario is less probable. The simulations indicate that the phosphite substrate is monoanionic in its active form and that the most likely product is dihydrogen phosphate. These mechanistic insights may be helpful for designing mutant enzymes or artificial constructs that convert phosphite to phosphate and NAD+ to NADH more effectively.

Confluence of theory and experiment reveals the catalytic mechanism of the Varkud satellite ribozyme

The Varkud Satellite (VS) ribozyme catalyzes site-specific RNA cleavage and ligation, and serves as an important model system to understand RNA catalysis. Here we combine stereospecific phosphorothioate substitution, precision nucleobase mutation and linear free energy relationship measurements with molecular dynamics, molecular solvation theory, and ab initio quantum mechanical/molecular mechanical free energy simulations to gain insight into catalysis. Through this confluence of theory and experiment, we unify the existing body of structural and functional data to unveil the catalytic mechanism in unprecedented detail, including the degree of proton transfers in the transition state. Further, we provide evidence for a critical Mg2+ ion in the active site that interacts with the scissile phosphate and anchors the general base guanine in position for nucleophile activation. This novel role for Mg2+ adds to the diversity of known catalytic RNA strategies and unifies functional features observed in the VS, hairpin, and hammerhead ribozyme classes.

How Does the Spliceosome Catalyze Intron Lariat Formation? Insights from Quantum Mechanics/Molecular Mechanics Free-Energy Simulations.

The spliceosome catalyzes nuclear pre-mRNA splicing via formation of an intron lariat and is arguably the most complex macromolecular machine in eukaryotic cells. Intron lariat formation is a conservative feature of the splicing reaction for both spliceosomal and group II introns. Despite the importance of the lariat formation in pre-mRNA splicing, an atomic-level understanding of the reaction mechanism remains elusive. In this work, a quantum mechanics and molecular mechanics method with thermodynamic integration is used to calculate the free-energy profile along the reaction pathway. The results demonstrate that the catalytic Mg2+ ion does not act as a Lewis acid to activate the nucleophile and the intron lariat is formed via a dissociative transition state stabilized by electrostatic interactions with two catalytic Mg2+ ions. Proton transfer occurs from the nucleophile to the leaving oxygen group through the phosphate substrate after the transition state is reached, which is important for stabilization of the intron-lariat product and the efficiency of pre-mRNA splicing. The two-metal-ion mechanism proposed in this study provides a novel insight into understanding of the splicing reaction catalyzed by the spliceosome.

Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations.

The proton-coupled electron transfer (PCET) reaction catalyzed by soybean lipoxygenase has served as a prototype for understanding hydrogen tunneling in enzymes. Herein this PCET reaction is studied with mixed quantum mechanical/molecular mechanical (QM/MM) free energy simulations. The free energy surfaces are computed as functions of the proton donor-acceptor (C-O) distance and the proton coordinate, and the potential of mean force is computed as a function of the C-O distance, inherently including anharmonicity. The simulation results are used to calculate the kinetic isotope effects for the wild-type enzyme (WT) and the L546A/L754A double mutant (DM), which have been measured experimentally to be ∼80 and ∼700, respectively. The PCET reaction is found to be exoergic for WT and slightly endoergic for the DM, and the equilibrium C-O distance for the reactant is found to be ∼0.2 Å greater for the DM than for WT. The larger equilibrium distance for the DM, which is due mainly to less optimal substrate binding in the expanded binding cavity, is primarily responsible for its higher kinetic isotope effect. The calculated potentials of mean force are anharmonic and relatively soft at shorter C-O distances, allowing efficient thermal sampling of the shorter distances required for effective hydrogen tunneling. The primarily local electrostatic field at the transferring hydrogen is ∼100 MV/cm in the direction to facilitate proton transfer and increases dramatically as the C-O distance decreases. These simulations suggest that the overall protein environment is important for conformational sampling of active substrate configurations aligned for proton transfer, but the PCET reaction is influenced primarily by local electrostatic effects that facilitate conformational sampling of shorter proton donor-acceptor distances required for effective hydrogen tunneling.

The role of the Met20 loop in the hydride transfer in Escherichia coli dihydrofolate reductase

A key question concerning the catalytic cycle of Escherichia coli dihydrofolate reductase (ecDHFR) is whether the Met20 loop is dynamically coupled to the chemical step during catalysis. A more basic, yet unanswered question is whether the Met20 loop adopts a closed conformation during the chemical hydride transfer step. To examine the most likely conformation of the Met20 loop during the chemical step, we studied the hydride transfer in wild type (WT) ecDHFR using hybrid quantum mechanics-molecular mechanics free energy simulations with the Met20 loop in a closed and disordered conformation. Additionally, we investigated three mutant forms (I14X; X = Val, Ala, Gly) of the enzyme that have increased active site flexibility and donor-acceptor distance dynamics in closed and disordered Met20 loop states. We found that the conformation of the Met20 loop has a dramatic effect on the ordering of active site hydration, although the Met20 loop conformation only has a moderate effect on the hydride transfer rate and donor-acceptor distance dynamics. Finally, we evaluated the pKa of the substrate N5 position in closed and disordered Met20 loop states and found a strong correlation between N5 basicity and the conformation of the Met20 loop.

Electrostatic Control of Chemistry in Terpene Cyclases

Electrostatic interactions play a major role in stabilizing transition states in enzymes. A crucial question is how general this electrostatic stabilization principle is. To address this point, we study a key common C–C bond formation step in a family of enzymes that is responsible for the biosynthesis of 60% of all natural products. In these terpene cyclases, we have previously shown that the enzymes gain chemical control by raising the energy of initial carbocation intermediates along the reaction coordinate to bypass the formation of unwanted side products. Here we employ hybrid quantum mechanics–molecular mechanics free energy simulations to show that this energy tuning is achieved by modulation of electrostatic interactions. The tempering of electrostatic interactions allows enzymatically directed chemical control that slows down the reaction temporarily by introducing thermodynamic and activation barriers. We show that this electrostatic control in terpene cyclases is achieved by a unique binary act...

Role of the active site guanine in the glmS ribozyme self-cleavage mechanism: quantum mechanical/molecular mechanical free energy simulations.

The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid–base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mechanical/molecular mechanical free energy simulations and pKa calculations, as well as experimental measurements of the rate constant for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calculations suggest that an external base deprotonates either G40(N1) or possibly A-1(O2′), which would be followed by proton transfer from G40(N1) to A-1(O2′). After this initial deprotonation, A-1(O2′) starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2′) to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2′) to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calculated rate constant for the favored mechanism is in agreement with the experimental rate constant measured at biological Mg2+ ion concentration. According to these calculations, catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa’s of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40.

Quantum Mechanical/Molecular Mechanical Free Energy Simulations of the Self-Cleavage Reaction in the Hepatitis Delta Virus Ribozyme

The hepatitis delta virus (HDV) ribozyme catalyzes a self-cleavage reaction using a combination of nucleobase and metal ion catalysis. Both divalent and monovalent ions can catalyze this reaction, although the rate is slower with monovalent ions alone. Herein, we use quantum mechanical/molecular mechanical (QM/MM) free energy simulations to investigate the mechanism of this ribozyme and to elucidate the roles of the catalytic metal ion. With Mg2+ at the catalytic site, the self-cleavage mechanism is observed to be concerted with a phosphorane-like transition state and a free energy barrier of ∼13 kcal/mol, consistent with free energy barrier values extrapolated from experimental studies. With Na+ at the catalytic site, the mechanism is observed to be sequential, passing through a phosphorane intermediate, with free energy barriers of 2–4 kcal/mol for both steps; moreover, proton transfer from the exocyclic amine of protonated C75 to the nonbridging oxygen of the scissile phosphate occurs to stabilize the phosphorane intermediate in the sequential mechanism. To explain the slower rate observed experimentally with monovalent ions, we hypothesize that the activation of the O2′ nucleophile by deprotonation and orientation is less favorable with Na+ ions than with Mg2+ ions. To explore this hypothesis, we experimentally measure the pKa of O2′ by kinetic and NMR methods and find it to be lower in the presence of divalent ions rather than only monovalent ions. The combined theoretical and experimental results indicate that the catalytic Mg2+ ion may play three key roles: assisting in the activation of the O2′ nucleophile, acidifying the general acid C75, and stabilizing the nonbridging oxygen to prevent proton transfer to it.

Computing pKa Values with a Mixing Hamiltonian Quantum Mechanical/Molecular Mechanical Approach

Accurate computation of the pKa value of a compound in solution is important but challenging. Here, a new mixing quantum mechanical/molecular mechanical (QM/MM) Hamiltonian method is developed to simulate the free-energy change associated with the protonation/deprotonation processes in solution. The mixing Hamiltonian method is designed for efficient quantum mechanical free-energy simulations by alchemically varying the nuclear potential, i.e., the nuclear charge of the transforming nucleus. In pKa calculation, the charge on the proton is varied in fraction between 0 and 1, corresponding to the fully deprotonated and protonated states, respectively. Inspired by the mixing potential QM/MM free energy simulation method developed previously [H. Hu and W. T. Yang, J. Chem. Phys. 2005, 123, 041102], this method succeeds many advantages of a large class of λ-coupled free-energy simulation methods and the linear combination of atomic potential approach. Theory and technique details of this method, along with the calculation results of the pKa of methanol and methanethiol molecules in aqueous solution, are reported. The results show satisfactory agreement with the experimental data.

QM/MM and free-energy simulations of deacylation reaction catalysed by sedolisin, a serine-carboxyl peptidase

Quantum mechanical/molecular mechanical free-energy simulations were performed to understand the deacylation reaction catalysed by sedolisin (a serine-carboxyl peptidase) and to elucidate the catalytic mechanism and the role of the active-site residues during the process. The results given here demonstrate that Asp170 may act as a general acid/base catalyst for the deacylation reaction. It is also shown that the electrostatic oxyanion hole interactions involving Asp170 may be less effective in transition state stabilisation for the deacylation step in the sedolisin-catalysed reaction compared to the general acid/base mechanism. The proton transfer processes during the enzyme-catalysed process were examined, and their role in the catalysis was discussed.