Reaction Free Energy Surface Research Articles

Ligand and solvent effects on the kinetics of the electrochemical reduction of Ni(II) complexes: Experiment and quantum chemical modeling

The two-electron reduction of some Ni(II) complexes with α-diimine ligands ([Ni(bpy)3]2+ and [Ni(pybox)2]2+) at a platinum electrode from acetonitrile (AN) and dimethylformamide (DMF) solutions is investigated by cyclic voltammetry (CV). Digisim simulations are employed to determine kinetic parameters. For [Ni(bpy)3]2+ in AN the first electron transfer (ET) step was found to be rate-controlling. The rate constants of the first and second steps (k1 and k2) are practically the same in the DMF solution. In contrast, the second ET step is rate controlling for the [Ni(pybox)2]2+ complex in AN, while the difference between k1 and k2 for this complex reactant in DMF becomes less noticeable. Molecular modeling based on the quantum mechanical theory of electron transfer and on density functional theory (DFT) calculations is performed for the first time to predict the activation barriers of the two-step heterogeneous redox processes and to elucidate the role of the ligands and solvents in the kinetics of these processes. Three-dimensional reaction free energy surfaces are constructed along the solvent and intramolecular coordinates. The electronic transmission coefficients are estimated as well. The results of model calculations are in qualitative agreement with the experimental data.

Rate of Insulin Dimer Dissociation: Interplay between Memory Effects and Higher Dimensionality

We calculate the rate of dissociation of an insulin dimer into two monomers in water. The rate of this complex reaction is determined by multiple factors that are elucidated. By employing advanced sampling techniques, we first obtain the reaction free energy surface for the dimer dissociation as a function of two order parameters, namely, the distance between the center-of-mass of two monomers (R) and the number of cross-contacts (Q) among the backbone Cα atoms of two monomers. We then construct an orthogonal 2D reaction energy surface by introducing the reaction coordinate X to denote the minimum energy pathway and a conjugate coordinate Y that spans the orthogonal direction. The free energy landscape is rugged with multiple maxima and minima. We calculate the rate by employing not only the non-Markovian multidimensional rate theory but also several other theoretical approaches. The necessary reaction frequencies and the frictions are calculated from the time correlation function formalism. Our best estimate of the rate is 0.4 μs-1. Our study reveals interesting opposite influences of dimensionality and memory in determining the rate constant of the reaction. We gain interesting insights into the dimer dissociation process by looking directly at the trajectories obtained from molecular dynamics simulation.

Kinetics of the Reactions between the Criegee Intermediate CH2OO and Alcohols.

Reactions of the simplest Criegee intermediate (CH2OO) with a series of alcohols have been studied in a flash photolysis flow reactor. Laser photolysis of diiodomethane at 355 nm in the presence of molecular oxygen was used to produce CH2OO, and the absolute number densities were determined as a function of delay time from analysis of broadband transient absorption spectra obtained using a pulsed LED. The kinetics for the reactions of CH2OO with methanol, ethanol, and 2-propanol were measured under pseudo-first-order conditions at 295 K, yielding rate constants of (1.4 ± 0.4) × 10-13 cm3 s-1, (2.3 ± 0.6) × 10-13 cm3 s-1, and (1.9 ± 0.5) × 10-13 cm3 s-1, respectively. Complementary ab initio calculations were performed at the CCSD(T)/aug-cc-pVTZ//CCSD/cc-pVDZ level of theory to characterize stationary points on the reaction enthalpy and free energy surfaces and to elucidate the thermochemistry and mechanisms. The reactions proceed over free energy barriers of ∼8 kcal mol-1 to form geminal alkoxymethyl hydroperoxides: methoxymethyl hydroperoxide (MMHP), ethoxymethyl hydroperoxide (EMHP), and isopropoxymethyl hydroperoxide (PMHP). The experimental and theoretical results are compared to reactions of CH2OO with other hydroxylic compounds, such as water and carboxylic acids, and trends in reactivity are discussed.

Monte Carlo simulations of heterogeneous electron transfer: New challenges

We report results of MC simulations of electron transfer across a metal electrode/electrolyte solution interface. The model presumes the Landau–Zener theory and a random walk on a two-dimensional lattice formed by crossing parabolic reaction free energy surfaces along the solvent coordinate. Emphasis is put on investigating the activationless discharge regime; the bridge-assisted electron transfer is also partially addressed. We have calculated effective electronic transmission coefficient as a function of the electrode overpotential and temperature in a wide range of orbital overlap. The dependence of the transmission coefficient on the electronic density of states is analyzed as well.

Simulating Protein Mediated Hydrolysis of ATP and Other Nucleoside Triphosphates by Combining QM/MM Molecular Dynamics with Advances in Metadynamics.

The protein mediated hydrolysis of nucleoside triphosphates such as ATP or GTP is one of the most important and challenging biochemical reactions in nature. The chemical environment (water structure, catalytic metal, and amino acid residues) adjacent to the hydrolysis site contains hundreds of atoms, usually greatly limiting the amount of the free energy sampling that one can achieve from computationally demanding electronic structure calculations such as QM/MM simulations. Therefore, the combination of QM/MM molecular dynamics with the recently developed transition-tempered metadynamics (TTMetaD), an enhanced sampling method that can provide a high-quality free energy estimate at an early stage in a simulation, is an ideal approach to address the biomolecular nucleoside triphosphate hydrolysis problem. In this work the ATP hydrolysis process in monomeric and filamentous actin is studied as an example application of the combined methodology. The performance of TTMetaD in these demanding QM/MM simulations is compared with that of the more conventional well-tempered metadynamics (WTMetaD). Our results show that TTMetaD exhibits much better exploration of the hydrolysis reaction free energy surface in two key collective variables (CVs) during the early stages of the QM/MM simulation than does WTMetaD. The TTMetaD simulations also reveal that a key third degree of freedom, the O–H bond-breaking and proton transfer from the lytic water, must be biased for TTMetaD to converge fully. To perturb the NTP hydrolysis dynamics to the least extent and to properly focus the MetaD free energy sampling, we also adopt here the recently developed metabasin metadynamics (MBMetaD) to construct a self-limiting bias potential that only applies to the lytic water after its nucleophilic attack of the phosphate of ATP. With these new, state-of-the-art enhanced sampling metadynamics techniques, we present an effective and accurate computational strategy for combining QM/MM molecular dynamics simulation with free energy sampling methodology, including a means to analyze the convergence of the calculations through robust numerical criteria.

Quantifying the Risks of Asparagine Deamidation and Aspartate Isomerization in Biopharmaceuticals by Computing Reaction Free-Energy Surfaces.

Early identification of asparagine deamidation and aspartate isomerization degradation sites can facilitate the successful development of biopharmaceuticals. Several knowledge-based models have been proposed to assess these degradation risks. In this study, we propose a physics-based approach to identify the degradation sites on the basis of the free-energy barriers along the prechemical conformational step and the chemical reaction pathway. These contributions are estimated from classical and quantum mechanics/molecular mechanics molecular dynamics simulations. The computed barriers are compared to those for reference reactions in water within GNG and GDG sequence motifs in peptides (which demonstrate the highest degradation rates). Two major factors decreasing the degradation rates relative to the reference reactions are steric hindrance toward accessing reactive conformations and replacement of water by less polar side chains in the solvation shell of transition states. Among the potential degradation sites in the complementarity-determining region of trastuzumab and between two DK sites in glial cell-derived neurotropic factor, this method identified N30T, N55G, D102G, and D95K, respectively, in agreement with experiments. This approach can be incorporated in early computational screening of chemical degradation sites in biopharmaceuticals.

Molecular Origin of Mechanical Sensitivity of the Reaction Rate in Anthracene Cyclophane Isomerization Reveals Structural Motifs for Rational Design of Mechanophores

The observed pressure sensitivity of the isomerization reaction rate of bis-anthracene cyclophane photoisomer has attracted significant attention in the rational design of mechanically sensitive materials. However, the molecular origin of this sensitivity remains unclear. We developed an ab initio molecular model to quantify the effect of pressure on the reaction rate and to elucidate its molecular origin. Pressure-induced deformations and changes along the reaction free-energy surfaces are estimated from ab initio molecular dynamics trajectories. Our model predicts a barrier reduction of ∼2 kcal/mol at 0.9 GPa (in agreement with experiment). The barrier reduction is linear in the low-pressure regime (up to 2 GPa) but has a nonlinear dependence at higher pressures. We find that pressure alters the reaction path and that the mechanical sensitivity of the reaction rate is caused by an uneven distribution of the free-energy increase along the reaction surface. The uneven distribution primarily results from d...

Steady-state nucleation rate and flux of composite nucleus at saddle point

The steady-state nucleation rate and flux of composite nucleus at the saddle point is studied by extending the theory of binary nucleation. The Fokker-Planck equation that describes the nucleation flux is derived using the Master equation for the growth of the composite nucleus, which consists of the core of the final stable phase surrounded by a wetting layer of the intermediate metastable phase nucleated from a metastable parent phase recently evaluated by Iwamatsu [J. Chem. Phys. 134, 164508 (2011)]. The Fokker-Planck equation is similar to that used in the theory of binary nucleation, but the non-diagonal elements exist in the reaction rate matrix. First, the general solution for the steady-state nucleation rate and the direction of nucleation flux is derived. Next, this information is then used to study the nucleation of composite nucleus at the saddle point. The dependence of steady-state nucleation rate as well as the direction of nucleation flux on the reaction rate in addition to the free-energy surface is studied using a model free-energy surface. The direction of nucleation current deviates from the steepest-descent direction of the free-energy surface. The results show the importance of two reaction rate constants: one from the metastable environment to the intermediate metastable phase and the other from the metastable intermediate phase to the stable new phase. On the other hand, the gradient of the potential Φ or the Kramers crossover function (the commitment or splitting probability) is relatively insensitive to reaction rates or free-energy surface.

Multidimensional free energy volumes offer unique insights into reaction mechanisms, molecular conformation and association

Free energy is a central measure in statistical mechanics and the means by which other thermodynamic properties of a system may be accessed. Using an efficient numerical method referred to as the Free Energy from Adaptive Reaction Coordinate Forces (FEARCF) method it is shown that multidimensional free energy volumes (FEVs) are computable and that they are critical to the understanding of reactions, conformational analysis and molecular association. Specifically the FEV of the hydrolysis reaction catalysed by a cellobiohydrolase I is shown to reveal molecular details of the reaction mechanism. The reaction is understood from a combination of the two dimensional reaction free energy surface, W(ξ(1), ξ(2)) and the three dimensional glucopyranose ring pucker FEV, W(ξ(1), ξ(2), ξ(3)). These studies provide for the first time details of the evolution of the oxocarbenium ion, which is a key to characterizing transition state structures seen in carbohydrate chemistry. A long-standing challenge has been the unambiguous assignment of the relative orientation of molecular pairs in solution. Here we describe how the molecular association of the benzene dimer in water and their relative orientational attraction are found from four dimensional, FEVs W(ξ(1), ξ(2), ξ(3), ξ(4)).

QM/MM Reweighting Free Energy SCF for Geometry Optimization on Extensive Free Energy Surface of Enzymatic Reaction.

We developed a quantum mechanical/molecular mechanical (QM/MM) free energy geometry optimization method by which the geometry of a quantum chemically treated (QM) molecule is optimized on a free energy surface defined with thermal distribution of the surrounding molecular environment obtained by molecular dynamics simulation with a molecular mechanics (MM) force field. The method called QM/MM reweighting free energy self-consistent field combines a mean field theory of QM/MM free energy geometry optimization developed by Yamamoto (Yamamoto, T. J. Chem. Phys.2008, 129, 244104) with a reweighting scheme for updating the MM distribution introduced by Hu et al. (Hu, H., et al. J. Chem. Phys.2008, 128, 034105) and features high computational efficiency suitable for exploring the reaction free energy surface of extensive protein conformational space. The computational efficiency with improved treatment of a long-range electrostatic (ES) interaction using the Ewald summation technique permits one to take into account global conformational relaxation of an entire protein of an enzyme in the free energy geometry optimization of its reaction center. We applied the method to an enzymatic reaction of a substrate complex of psychrophilic α-amylase from Antarctic bacterium Pseudoalteromonas haloplanktis and succeeded in geometry optimizations of the reactant and the product of the catalytic reaction that involve large conformational changes of protein loops adjacent to the reaction center on time scales reaching sub-microseconds. We found that the adjacent loops in the reactant and the product form in different conformations and produce catalytic ES potentials on the reaction center.

FEARCF a multidimensional free energy method for investigating conformational landscapes and chemical reaction mechanisms

The development and implementation of a computational method able to produce free energies in multiple dimensions, descriptively named the free energies from adaptive reaction coordinate forces (FEARCF) method is described in this paper. While the method can be used to calculate free energies of association, conformation and reactivity here it is shown in the context of chemical reaction landscapes. A reaction free energy surface for the Claisen rearrangement of chorismate to prephenate is used as an illustration of the method’s efficient convergence. FEARCF simulations are shown to achieve flat histograms for complex multidimensional free energy volumes. The sampling efficiency by which it produces multidimensional free energies is demonstrated on the complex puckering of a pyranose ring, that is described by a three dimensional W(θ1, θ2, θ3) potential of mean force.

An Abridged Transition State Model To Derive Structure, Dynamics, and Energy Components of DNA Polymerase β Fidelity

We show how a restricted reaction surface can be used to facilitate the calculation of biologically important contributions of active site geometries and dynamics to DNA polymerase fidelity. Our analysis, using human DNA polymerase beta (pol β), is performed within the framework of an electrostatic linear free energy response (EFER) model. The structure, dynamics, and energetics of pol β-DNA-dNTP interactions are computed between two points on the multidimensional reaction free energy surface. "Point 1" represents a ground state activation intermediate (GSA), which is obtained by deprotonating the terminal 3'OH group of the primer DNA strand. "Point 2" is the transition state (PTS) for the attack of the 3'O(-) (O(nuc)) on the P(α) atom of dNTP substrate, having the electron density of a dianionic phosphorane intermediate. Classical molecular dynamics simulations are used to compute the geometric and dynamic contributions to the formation of right and wrong O(nuc)-P chemical bonds. Matched dCTP·G and mismatched dATP·G base pairs are used to illustrate the analysis. Compared to the dCTP·G base pair, the dATP·G mismatch has fewer GSA configurations with short distances between O(nuc) and P(α) atoms and between the oxygen in the scissile P-O bond (O(lg)) and the nearest structural water. The thumb subdomain conformation of the GSA complex is more open for the mismatch, and the H-bonds in the mispair become more extended during the nucleophilic attack than in the correct pair. The electrostatic contributions of pol β and DNA residues to catalysis of the right and wrong P-O(nuc) bond formation are 5.3 and 3.1 kcal/mol, respectively, resulting in an 80-fold contribution to fidelity. The EFER calculations illustrate the considerable importance of Arg183 and an O(lg)-proximal water molecule to pol β fidelity.

An AIMD Study of the CPD Repair Mechanism in Water: Reaction Free Energy Surface and Mechanistic Implications

In a series of two papers, we report the detailed mechanism of cyclobutane pyrimidine dimer repair in aqueous solvent using ab initio molecular dynamics simulations (AIMD). Umbrella sampling is used to determine the free energy surface for dimer splitting. The two-dimensional free energy surface for splitting of the C5-C5' and C6-C6' bonds on the anion surface is reported. The splitting of the C5-C5' and C6-C6' bonds occurs on a picosecond time scale. The transition state along the splitting coordinate in the anion state coincides with a maximum in the free energy along the same coordinate on the neutral surface. The implication is that back electron transfer occurring before the anion reaches the transition state leads to reformation of the cyclobutane dimer, while back electron transfer after transit through the transition state, leads to successful repair. On the basis of our calculations for CPD splitting in water, we propose a framework for understanding how various factors, such as solvent polarity, can control repair efficiency. This framework explains why back electron transfer leads predominantly to unsuccessful repair in some situations, and successful repair in others. A key observation is that the same free energy surfaces that control dimer splitting also govern how the back electron transfer rate changes during the splitting process. Configurational changes of the dimer along the splitting coordinate are also documented.

Mechanism of Xylobiose Hydrolysis by GH43 β-Xylosidase

Glycoside hydrolases cleave the glycosidic linkage between two carbohydrate moieties. They are among the most efficient enzymes currently known. β-Xylosidases from glycoside hydrolase family 43 hydrolyze the nonreducing ends of xylooligomers using an inverting mechanism. Although the general mechanism and catalytic amino acid residues of β-xylosidases are known, the nature of the reaction's transition state and the conformations adopted by the glycon xylopyranosyl ring along the reaction pathway are still elusive. In this work, the xylobiose hydrolysis reaction catalyzed by XynB3, a β-xylosidase produced by Geobacillus stearothermophilus T-6, was explicitly modeled using first-principles quantum mechanics/molecular mechanics Car-Parrinello metadynamics. We present the reaction's free energy surface and its previously undetermined reaction pathway. The simulations also show that the glycon xylopyranosyl ring proceeds through a (2,5)B-type transition state with significant oxacarbenium ion character.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.

Medium and Interfacial Effects in the Multistep Reduction of Binuclear Complexes with Robson-Type Ligand

We present a combined experimental and computational approach to the modeling and prediction of reactivity in multistep processes of heterogeneous electron transfer. The approach is illustrated by the study of a Robson-type binuclear complex (-Cu(II)-Cu(II)-) undergoing four-electron reduction in aqueous media and water-acetonitrile mixtures. The observed effects of solvent, pH, buffer capacity, and supporting electrolyte are discussed in the framework of a general reaction scheme involving two main routes; one of them includes protonation of intermediate species. The main three problems are addressed on the basis of modern charge transfer theory: (1) the effect of the nature of reactant and intermediate species (protonated/deprotonated, bare or associated with supporting anion/solvent molecule) on the standard redox potential, the electronic transmission coefficient, and the intramolecular reorganization; (2) possible effect of protonation on the shape of the reaction free energy surfaces which are built using the Anderson Hamiltonian; (3) electron transfer across an adsorbed chloride anion. Quantum chemical calculations were performed at the density functional theory level.

Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis

We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.

Structure and Dynamics of DNA−Dendrimer Complexation: Role of Counterions, Water, and Base Pair Sequence

We study sequence-dependent complexation between oligonucleotides (single-strand DNA) and various generation ethylene diamine (EDA) cored poly amido amide (PAMAM) dendrimers through atomistic molecular dynamics simulations accompanied by free energy calculations and inherent structure determination. Simulations reveal formation of a stable complex and provide a detailed molecular level understanding of the structure and dynamics of such a complexation. The reaction free energy surface in the initial stage is found to be funnel-like, with a significant barrier arising in the late stage due to the occurrence of misfolded states of DNA. Complexation shows surprisingly strong sensitivity to the ssDNA sequence, which is found to arise from a competition between enthalpic versus entropic rigidity of ssDNA.

Theoretical modeling of chemical reactions in complex environments: the intramolecular proton transfer in aqueous malonaldehyde

AbstractThe free energy profile and the (classical) kinetics of chemical reactions in (soft) condensed phase are modeled theoretically by means of molecular dynamics simulations, the Perturbed Matrix Method (PMM) and the quasi Gaussian entropy (QGE) theory. In this paper we describe the theoretical framework and apply the model to the intramolecular proton transfer reaction of aqueous malonaldehyde. Although in the present application we disregard the quantum effects for the proton dynamics along the reaction coordinate (i.e., tunneling), the classical‐like view of the proton transition over the reaction free energy surface seems to properly describe the kinetic process and shows that water acts lowering the reaction free energy barrier. Moreover, a weak temperature dependence of the free energy surface is obtained, implying small entropy variations in the transition. Interestingly the activation entropy, as provided by the QGE model, is negative in the whole temperature range considered, thus indicating an entropy reduction at the transition structure. Finally, by comparing our results with theoretical and experimental literature data, we critically address the actual role of tunneling in this reaction and discuss the emerging kinetic scheme. Copyright © 2006 John Wiley & Sons, Ltd.

Statistical Mechanical Modeling of Chemical Reactions in Complex Systems: The Reaction Free Energy Surface

In this paper, the perturbed matrix method (PMM) is used in combination with basic statistical mechanics, to develop a general theoretical method to model chemical reactions and related molecular processes in complex systems, i.e., liquids, biochemical systems, macromolecules, etc. The main feature of this approach consists of the explicit treatment of the coupling between the reaction center and the fluctuating atomic−molecular environment, providing a rigorous statistical mechanical description of the chemical event. A special attention is dedicated to the approximations and assumptions necessary to use such a theoretical procedure in combination with simulation data.