Biomolecular free energy profiles by a shooting/umbrella sampling protocol, "BOLAS"

Transition Path Sampling Study of Engineered Enzymes That Catalyze the Morita-Baylis-Hillman Reaction: Why Is Enzyme Design so Difficult?

It is hoped that artificial enzymes designed in laboratories can be efficient alternatives to chemical catalysts that have been used to synthesize organic molecules. However, the design of artificial enzymes is challenging and requires a detailed molecular-level analysis to understand the mechanism they promote in order to design efficient variants. In this study, we computationally investigate the mechanism of proficient Morita-Baylis-Hillman enzymes developed using a combination of computational design and directed evolution. The powerful transition path sampling method coupled with in-depth post-processing analysis has been successfully used to elucidate the different chemical pathways, transition states, protein dynamics, and free energy barriers of reactions catalyzed by such laboratory-optimized enzymes. This research provides an explanation for how different chemical modifications in an enzyme affect its catalytic activity in ways that are not predictable by static design algorithms.

Comparing brute force to transition path sampling for gas hydrate nucleation with a flat interface: comments on time reversal symmetry

Fluid to solid nucleation is often investigated with the rare event method transition path sampling (TPS). I claim that the inherent irreversibility of solid nucleation, even at stationary conditions, calls into question TPS's applicability for determining solid nucleation mechanisms, especially for pre-critical behavior. Even when applied to a phenomenon which displays time reversal asymmetry like solid nucleation, TPS is a good means of exploring phase space and giving trends in post-critical structure, and its ability to facilitate nucleation rate and free energy calculations remains outstanding. Forward-only splitting and ratcheting methods such as forward flux sampling are more attractive for understanding nucleation mechanisms as they do not require time reversal symmetry, but at low driving forces may suffer from the same limitations as brute force: they may never make it to the first ratchet. Here I briefly summarize the TPS method and gas hydrate nucleation simulation literature, focusing on topics within both to facilitate a comparison of brute force hydrate nucleation to transition path sampling of hydrate nucleation. Perhaps anecdotally, the brute force technique results in more crystalline trajectories despite having higher driving forces than TPS. I maintain this difference is because of the inherent irreversibility of hydrate nucleation, meaning its pre-critical behavior cannot accurately be determined by the melting trajectories that comprise approximately half of the configurations in TPS's path ensemble.

Activating mutations drive human MEK1 kinase using a gear-shifting mechanism

There is an unmet need to classify cancer-promoting kinase mutations in a mechanistically cognizant way. The challenge is to understand how mutations stabilize different kinase configurations to alter function, and how this influences pathogenic potential of the kinase and its responses to therapeutic inhibitors. This goal is made more challenging by the complexity of the mutational landscape of diseases, and is further compounded by the conformational plasticity of each variant where multiple conformations coexist. We focus here on the human MEK1 kinase, a vital component of the RAS/MAPK pathway in which mutations cause cancers and developmental disorders called RASopathies. We sought to explore how these mutations alter the human MEK1 kinase at atomic resolution by utilizing enhanced sampling simulations and free energy calculations. We computationally mapped the different conformational stabilities of individual mutated systems by delineating the free energy landscapes, and showed how this relates directly to experimentally quantified developmental transformation potentials of the mutations. We conclude that mutations leverage variations in the hydrogen bonding network associated with the conformational plasticity to progressively stabilize the active-like conformational state of the kinase while destabilizing the inactive-like state. The mutations alter residue-level internal molecular correlations by differentially prioritizing different conformational states, delineating the various modes of MEK1 activation reminiscent of a gear-shifting mechanism. We define the molecular basis of conversion of this kinase from its inactive to its active state, connecting structure, dynamics, and function by delineating the energy landscape and conformational plasticity, thus augmenting our understanding of MEK1 regulation.

Atomistic description of the relationship between protein dynamics and catalysis with transition path sampling

Despite initial resistance, it has been increasingly accepted that protein dynamics plays a role in enzymatic catalysis. There have been two lines of research. Some works study slow conformational motions that are not coupled to the reaction coordinate, but guide the system towards catalytically competent conformations. Understanding at the atomistic level how this is accomplished has remained elusive except for a few systems. In this review we focus on fast sub-picosecond motions that are coupled to the reaction coordinate. The use of Transition Path Sampling has allowed us an atomistic description of how these rate-promoting vibrational motions are incorporated in the reaction mechanism. We will also show how we used insights from rate-promoting motions in protein design.

Protein Dynamics and Enzymatic Catalysis

This Perspective presents a review of our work and that of others in the highly controversial topic of the coupling of protein dynamics to reaction in enzymes. We have been involved in studying this topic for many years. Thus, this perspective will naturally present our own views, but it also is designed to present an overview of the variety of viewpoints of this topic, both experimental and theoretical. This is obviously a large and contentious topic.

Perspective: Path Sampling Methods Applied to Enzymatic Catalysis

This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.

Transition Path Sampling Based Calculations of Free Energies for Enzymatic Reactions: The Case of Human Methionine Adenosyl Transferase and Plasmodium vivax Adenosine Deaminase

Transition path sampling (TPS) is widely used for the calculations of reaction rates, transition state structures, and reaction coordinates of condensed phase systems. Here we discuss a scheme for the calculation of free energies using the ensemble of TPS reactive trajectories in combination with a window-based sampling technique for enzyme-catalyzed reactions. We calculate the free energy profiles of the reactions catalyzed by the human methionine S-adenosyltransferase (MAT2A) enzyme and the Plasmodium vivax adenosine deaminase (pvADA) enzyme to assess the accuracy of this method. MAT2A catalyzes the formation of S-adenosine-l-methionine following a S_N2 mechanism, and using our method, we estimate the free energy barrier for this reaction to be 16 kcal mol^-1, which is in excellent agreement with the experimentally measured activation energy of 17.27 kcal mol^-1. Furthermore, for the pvADA enzyme-catalyzed reaction we estimate a free energy barrier of 21 kcal mol^-1, and the calculated free energy profile is similar to that predicted from experimental observations. Calculating free energies by employing our simple method within TPS provides significant advantages over methods such as umbrella sampling because it is free from any applied external bias, is accurate compared to experimental measurements, and has a reasonable computational cost.

Transition Path Sampling Study of the Feruloyl Esterase Mechanism

Serine hydrolases cleave peptide and ester bonds and are ubiquitous in nature, with applications in biotechnology, in materials, and as drug targets. The serine hydrolase two-step mechanism employs a serine-histidine-aspartate/glutamate catalytic triad, where the histidine residue acts as a base to activate poor nucleophiles (a serine residue or a water molecule) and as an acid to allow the dissociation of poor leaving groups. This mechanism has been the subject of debate regarding how histidine shuttles the proton from the nucleophile to the leaving group. To elucidate the reaction mechanism of serine hydrolases, we employ quantum mechanics/molecular mechanics-based transition path sampling to obtain the reaction coordinate using the Aspergillus niger feruloyl esterase A (AnFaeA) as a model enzyme. The optimal reaction coordinates include terms involving nucleophilic attack on the carbonyl carbon and proton transfer to, and dissociation of, the leaving group. During the reaction, the histidine residue undergoes a reorientation on the time scale of hundreds of femtoseconds that supports the "moving histidine" mechanism, thus calling into question the "ring flip" mechanism. We find a concerted mechanism, where the transition state coincides with the tetrahedral intermediate with the histidine residue pointed between the nucleophile and the leaving group. Moreover, motions of the catalytic aspartate toward the histidine occur concertedly with proton abstraction by the catalytic histidine and help stabilize the transition state, thus partially explaining how serine hydrolases enable poor nucleophiles to attack the substrate carbonyl carbon. Rate calculations indicate that the second step (deacylation) is rate-determining, with a calculated rate constant of 66 s^-1. Overall, these results reveal the pivotal role of active-site dynamics in the catalytic mechanism of AnFaeA, which is likely similar in other serine hydrolases.

A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects

Research problems in the domains of physical, engineering, biological sciences often span multiple time and length scales, owing to the complexity of information transfer underlying mechanisms. Multiscale modeling (MSM) and high-performance computing (HPC) have emerged as indispensable tools for tackling such complex problems. We review the foundations, historical developments, and current paradigms in MSM. A paradigm shift in MSM implementations is being fueled by the rapid advances and emerging paradigms in HPC at the dawn of exascale computing. Moreover, amidst the explosion of data science, engineering, and medicine, machine learning (ML) integrated with MSM is poised to enhance the capabilities of standard MSM approaches significantly, particularly in the face of increasing problem complexity. The potential to blend MSM, HPC, and ML presents opportunities for unbound innovation and promises to represent the future of MSM and explainable ML that will likely define the fields in the 21st century.

Efficient Conformational Sampling of Collective Motions of Proteins with Principal Component Analysis-Based Parallel Cascade Selection Molecular Dynamics

Molecular dynamics (MD) simulation has become a powerful tool because it provides a time series of protein dynamics at high temporal-spatial resolution. However, the accessible timescales of MD simulation are shorter than those of the biologically rare events. Generally, long-time MD simulations over microseconds are required to detect the rare events. Therefore, it is desirable to develop rare-event-sampling methods. For a rare-event-sampling method, we have developed parallel cascade selection MD (PaCS-MD). PaCS-MD generates transition pathways from a given source structure to a target structure by repeating short-time MD simulations. The key point in PaCS-MD is how to select reasonable candidates (protein configurations) with high potentials to make transitions toward the target structure. In the present study, based on principal component analysis (PCA), we propose PCA-based PaCS-MD to detect rare events of collective motions of a given protein. Here, the PCA-based PaCS-MD is composed of the following two steps. At first, as a preliminary run, PCA is performed using an MD trajectory from the target structure to define a principal coordinate (PC) subspace for describing the collective motions of interest. PCA provides principal modes as eigenvectors to project a protein configuration onto the PC subspace. Then, as a production run, all the snapshots of short-time MD simulations are ranked by inner products (IPs), where an IP is defined between a snapshot and the target structure. Then, snapshots with higher values of the IP are selected as reasonable candidates, and short-time MD simulations are independently restarted from them. By referring to the values of the IP, the PCA-based PaCS-MD repeats the short-time MD simulations from the reasonable candidates that are highly correlated with the target structure. As a demonstration, we applied the PCA-based PaCS-MD to adenylate kinase and detected its large-amplitude (open-closed) transition with a nanosecond-order computational cost.

Nucleation and growth of 2D covalent organic frameworks: polymerization and crystallization of COF monomers

First computational study of the nucleation of a prototypical covalent organic framework from its building blocks.

Insertion of oxidized nucleotide triggers rapid DNA polymerase opening

A novel mechanism is unveiled to explain why a pro-mutagenic nucleotide lesion (oxidized guanine, 8-oxoG) causes the mammalian DNA repair polymerase-β (pol-β) to rapidly transition to an inactive open conformation. The mechanism involves unexpected features revealed recently in time-lapse crystallography. Specifically, a delicate water network associated with a lesion-stabilizing auxilliary product ion Mg(p) triggers a cascade of events that leads to poor active site geometry and the rupture of crucial molecular interactions between key residues in both the anti(8-oxoG:C) and syn(8-oxoG:A) systems. Once the base pairs in these lesioned systems are broken, dislocation of both Asp192 (a metal coordinating ligand) and the oxoG phosphate group (PO₄) interfere with the hydrogen bonding between Asp192 and Arg258, whose rotation toward Asp192 is crucial to the closed-to-open enzyme transition. Energetically, the lesioned open states are similar in energy to those of the corresponding closed complexes after chemistry, in marked contrast to the unlesioned pol-β anti(G:C) system, whose open state is energetically higher than the closed state. The delicate surveillance system offers a fundamental protective mechanism in the cell that triggers DNA repair events which help deter insertion of oxidized lesions.

Reaction coordinate of incipient methane clathrate hydrate nucleation

Nucleation from solution is a ubiquitous phenomenon with relevance to myriad scientific disciplines, including pharmaceuticals, biomineralization, and disease. One prominent example is the nucleation of clathrate hydrates, multicomponent crystalline inclusion compounds relevant to the energy industry where they block pipelines and also constitute a potential vast energy resource. Despite their importance, the molecular mechanism of incipient hydrate formation remains unknown. Herein, we employ advanced molecular simulation tools (pB histogram, equilibrium path sampling) to provide a statistical-mechanical basis for extracting physical insight into the molecular steps by which clathrates form. Through testing the Mutually Coordinated Guest (MCG) order parameter, we demonstrate that both guest (methane) and host (water) structuring are crucial to accurately describe the nucleation of hydrates and determine a critical nucleus size of MCG-1 = 16 at 255 K and 500 bar. Equipped with a validated (and novel) reaction coordinate, subsequent equilibrium path sampling simulations yield the free energy barrier and nucleation rate. The resulting quantitative nucleation process is described by the MCG clustering mechanism. This constitutes a significant advance in the field of hydrates research, as the fitness of a molecular descriptor has never been statistically verified. More broadly, this work has significance to a wide range of multicomponent nucleation contexts wherein the formation mechanism depends on contributions from both solute and solvent.

How Accurate Are Transition States from Simulations of Enzymatic Reactions?

The rate expression of traditional transition state theory (TST) assumes no recrossing of the transition state (TS) and thermal quasi-equilibrium between the ground state and the TS. Currently, it is not well understood to what extent these assumptions influence the nature of the activated complex obtained in traditional TST-based simulations of processes in the condensed phase in general and in enzymes in particular. Here we scrutinize these assumptions by characterizing the TSs for hydride transfer catalyzed by the enzyme Escherichia coli dihydrofolate reductase obtained using various simulation approaches. Specifically, we compare the TSs obtained with common TST-based methods and a dynamics-based method. Using a recently developed accurate hybrid quantum mechanics/molecular mechanics potential, we find that the TST-based and dynamics-based methods give considerably different TS ensembles. This discrepancy, which could be due equilibrium solvation effects and the nature of the reaction coordinate employed and its motion, raises major questions about how to interpret the TSs determined by common simulation methods. We conclude that further investigation is needed to characterize the impact of various TST assumptions on the TS phase-space ensemble and on the reaction kinetics.

Optimal and variant metal-ion routes in DNA polymerase β's conformational pathways

To interpret recent structures of the R283K mutant of human DNA repair enzyme DNA polymerase β (pol β) differing in the number of Mg(2+) ions, we apply transition path sampling (TPS) to assess the effect of differing ion placement on the transition from the open one-metal to the closed two-metal state. We find that the closing pathway depends on the initial ion position, both in terms of the individual transition states and associated energies. The energy barrier of the conformational pathway varies from 25 to 58 kJ/mol, compared to the conformational energy barrier of 42 kJ/mol for the wild-type pol β reported previously. Moreover, we find a preferred ion route located in the center of the enzyme, parallel to the DNA. Within this route, the conformational pathway is similar to that of the overall open to closed transition of pol β, but outside it, especially when the ion starts near active site residues Arg258 and Asp190, the conformational pathway diverges significantly. Our findings should apply generally to pol β, since R283K is relatively far from the active site; further experimental and computational work are required to confirm this. Our studies also underscore the common feature that less active mutants have less stable closed states than their open states, in marked contrast to the wild-type enzyme, where the closed state is significantly more stable than the open form.

Unfavorable electrostatic and steric interactions in DNA polymerase β E295K mutant interfere with the enzyme's pathway

Mutations in DNA polymerase β (pol β) have been associated with approximately 30% of human tumors. The E295K mutation of pol β has been linked to gastric carcinoma via interference with base excision repair. To interpret the different behavior of E295K as compared to wild-type pol β in atomic and energetic detail, we resolve a binary crystal complex of E295K at 2.5 Å and apply transition path sampling (TPS) to delineate the closing pathway of the E295K pol β mutant. Conformational changes are important components in the enzymatic pathway that lead to and ready the enzyme for the chemical reaction. Our analyses show that the closing pathway of E295K mutant differs from the wild-type pol β in terms of the individual transition states along the pathway, associated energies, and the active site conformation in the final closed form of the mutant. In particular, the closed state of E295K has a more distorted active site than the active site in the wild-type pol β. In addition, the total energy barrier in the conformational closing pathway is 65 ± 11 kJ/mol, much higher than that estimated for both correct (e.g., G:C) and incorrect (e.g., G:A) wild-type pol β systems (42 ± 8 and 45 ± 7 kJ/mol, respectively). In particular, the rotation of Arg258 is the rate-limiting step in the conformational pathway of E295K due to unfavorable electrostatic and steric interactions. The distorted active site in the closed relative to open state and the high energy barrier in the conformational pathway may explain in part why the E295K mutant is observed to be inactive. Interestingly, however, following the closing of the thumb but prior to the rotation of Arg258, the E295K mutant complex has a similar energy level as compared to the wild-type pol β. This suggests that the E295K mutant may associate with DNA with similar affinity, but it may be hampered in continuing the process of chemistry. Supporting experimental data come from the observation that the catalytic activity of wild-type pol β is hampered when E295K is present: this may arise from the competition between E295K and wild-type enzyme for the DNA. These combined results suggest that the low insertion efficiency of E295K mutant as compared to wild-type pol β may be related to a closed form distorted by unfavorable electrostatic and steric interactions between Arg258 and other key residues. The active site is thus less competent for proceeding to the chemical reaction, which may also involve a higher reaction barrier than the wild-type or may not be possible in this mutant. Our analysis also suggests further experiments for other mutants to test the above hypothesis and dissect the roles of steric and electrostatic factors on enzyme behavior.

Revisiting and computing reaction coordinates with Directional Milestoning

The method of Directional Milestoning is revisited. We start from an exact and more general expression and state the conditions and validity of the memory-loss approximation. An algorithm to compute a reaction coordinate from Directional Milestoning data is presented. The reaction coordinate is calculated as a set of discrete jumps between Milestones that maximizes the flux between two stable states. As an application we consider a conformational transition in solvated adenosine. We compare a long molecular dynamic trajectory with Directional Milestoning and discuss the differences between the maximum flux path and minimum energy coordinates.

A molecular mechanism of hydrolysis of peptide bonds at neutral pH using a model compound

The covalent stability of peptide bonds is a critical aspect of biological chemistry and therapeutic protein applications. In this computational study, the hydrolytic reaction of peptide bonds at neutral pH was studied using a model compound, N-MAA. The most probable reaction pathway and intermediate(s) involved are controversial in previous studies. In addition, most previous computational studies focus on the energetics of chemical species involved, rather than providing a dynamic picture of the reaction process in aqueous conditions. However, fluctuations at finite temperatures are quite important, as we show. Thus, a path sampling method was used to generate an ensemble of trajectories according to their statistical weights in trajectory space. An ab initio molecular dynamics technique was applied to advance the time of the reaction in order to collect trajectories. The likelihood maximization procedure and its modification were used in extracting dynamically relevant degrees of freedom in the system, and approximations of the reaction coordinate were compared. It was found that this hydrolytic reaction is very complex because it involves many degrees of freedom. The reaction coordinate C-O distance previously assumed was found to be inadequate in describing the dynamic progress of the reaction. In addition to affecting atoms directly involved in bond-making and -breaking processes, the water network also has determining effects on the hydrolytic reaction, a fact which is manifest in the expression of the best one-dimensional reaction coordinate that we found, which includes five geometric quantities. p(B) histograms were computed to verify the results of the likelihood maximization and to evaluate the accuracy of our best reaction coordinate to the "true" reaction coordinate. The relation with previous suggested reaction pathways and intermediate(s) is discussed in terms of computational system, method, and accuracy.

Investigating Molecular Mechanisms of Activation and Mutation of the HER2 Receptor Tyrosine Kinase through Computational Modeling and Simulation

Human epidermal growth factor receptor 2 (HER2)/ErbB2 is a receptor tyrosine kinase belonging to the EGFR/ErbB family and is overexpressed in 20-30% of human breast cancers. Since there is a growing effort to develop pharmacological inhibitors of the HER2 kinase for the treatment of breast cancer, it is clinically valuable to rationalize how specific mutations impact the molecular mechanism of receptor activation. Although several crystal structures of the ErbB kinases have been solved, the precise mechanism of HER2 activation remains unknown, and it has been suggested that HER2 is unique in its requirement for phosphorylation of Y877, a key tyrosine residue located in the activation loop (A-loop). In our studies, discussed here, we have investigated the mechanisms that are important in HER2 kinase domain regulation and compared them with the other ErbB family members, namely EGFR and ErbB4, to determine the molecular basis for HER2's unique mode of activation. We apply computational simulation techniques at the atomic level and at the electronic structure (quantum mechanical) level to elucidate details of the mechanisms governing the kinase domains of these ErbB members. Through analysis of our simulation results, we have discovered potential regulatory mechanisms common to EGFR, HER2, and ErbB4, including a tight coupling between the A-loop and catalytic loop that may contribute to alignment of residues required for catalysis in the active kinase. We further postulate an autoinhibitory mechanism whereby the inactive kinase is stabilized through sequestration of catalytic residues. In HER2, we also predict a role for phosphorylated Y877 in bridging a network of hydrogen bonds that fasten the A-loop in its active conformation, suggesting that HER2 may be unique among the ErbB members in requiring A-loop tyrosine phosphorylation for functionality. In EGFR, HER2, and ErbB4, we discuss the possible effects of activating mutations. Delineation of the activation mechanism of HER2 in the context of the other ErbB members is crucial for understanding how the activated kinase might interact with downstream molecules and couple to signaling cascades that promote cancer. Our comparative analysis furthers insight into the mechanics of activation of the HER2 kinase and enables us to predict the effect of an identified insertion mutation on HER2 activation. Further understanding of the mechanism of HER2 kinase activation at the atomic scale and how it couples to downstream signaling at the cellular scale will elucidate predictive molecular phenotypes that may indicate likelihood of response to specific therapies for HER2-mediated cancers.

Molecular mechanism of acid-catalyzed hydrolysis of peptide bonds using a model compound

The stability of peptide bonds is a critical aspect of biological chemistry and therapeutic protein applications. Recent studies found elevated nonenzymatic hydrolysis in the hinge region of antibody molecules, but no mechanism was identified. As a first step in providing a mechanistic interpretation, this computational study examines the rate-determining step of the hydrolytic reaction of a peptide bond under acidic pH by a path sampling technique using a model compound N-MAA. Most previous computational studies did not include explicit water molecules, whose effects are significant in solution chemistry, nor did they provide a dynamic picture for the reaction process in aqueous conditions. Because no single trajectory can be used to describe the reaction dynamics due to fluctuations at finite temperatures, a variant version of the transition path sampling technique, the aimless shooting algorithm, was used to sample dynamic trajectories and to generate an ensemble of transition trajectories according to their statistical weights in the trajectory space. Each trajectory was computed as the time evolution of the molecular system using the Car-Parrinello molecular dynamics technique. The likelihood maximization procedure and its modification were used in extracting dynamically relevant degrees of freedom in the system, and approximations of the reaction coordinate were compared. Its low log-likelihood score and poor p(B) histogram indicate that the C-O distance previously assumed as the reaction coordinate for the rate-determining step is inadequate in describing the dynamics of the reaction. More than one order parameter in a candidate set including millions of geometric quantities was required to produce a convergent reaction coordinate model; its involvement of many degrees of freedom suggests that this hydrolytic reaction step is very complex. In addition to affecting atoms directly involved in bond-making and -breaking processes, the water network also has determining effects on the hydrolytic reaction, a fact that is manifest in the expression of the one-dimensional best-ranked reaction coordinate, which includes three geometric quantities. The p(B) histograms were computed to verify the results of the likelihood maximization and to verify the accuracy of approximation to the "true" reaction coordinate.

Thermal nanostructure: an order parameter multiscale ensemble approach

Deductive all-atom multiscale techniques imply that many nanosystems can be understood in terms of the slow dynamics of order parameters that coevolve with the quasiequilibrium probability density for rapidly fluctuating atomic configurations. The result of this multiscale analysis is a set of stochastic equations for the order parameters whose dynamics is driven by thermal-average forces. We present an efficient algorithm for sampling atomistic configurations in viruses and other supramillion atom nanosystems. This algorithm allows for sampling of a wide range of configurations without creating an excess of high-energy, improbable ones. It is implemented and used to calculate thermal-average forces. These forces are then used to search the free-energy landscape of a nanosystem for deep minima. The methodology is applied to thermal structures of Cowpea chlorotic mottle virus capsid. The method has wide applicability to other nanosystems whose properties are described by the CHARMM or other interatomic force field. Our implementation, denoted SIMNANOWORLD, achieves calibration-free nanosystem modeling. Essential atomic-scale detail is preserved via a quasiequilibrium probability density while overall character is provided via predicted values of order parameters. Applications from virology to the computer-aided design of nanocapsules for delivery of therapeutic agents and of vaccines for nonenveloped viruses are envisioned.

Biomolecular Structure and Modeling: Historical Perspective

physics, chemistry, and biology have been connected by a web of causal explanation organized by induction-based theories that telescope into one another. … Thus, quantum theory underlies atomic physics, which is the foundation of reagent chemistry and its specialized offshoot biochemistry, which interlock with molecular biology — essentially, the chemistry of organic macromolecules — and hence, through successively higher levels of organization, cellular, organismic, and evolutionary biology. … Such is the unifying and highly productive understanding of the world that has evolved in the natural sciences.

The energy landscape for the interaction of the family 1 carbohydrate-binding module and the cellulose surface is altered by hydrolyzed glycosidic bonds

A multiscale simulation model is used to construct potential and free energy surfaces for the carbohydrate-binding module [CBM] from an industrially important cellulase, Trichoderma reesei cellobiohydrolase I, on the hydrophobic face of a coarse-grained cellulose Ibeta polymorph. We predict from computation that the CBM alone exhibits regions of stability on the hydrophobic face of cellulose every 5 and 10 A, corresponding to a glucose unit and a cellobiose unit, respectively. In addition, we predict a new role for the CBM: specifically, that in the presence of hydrolyzed cellulose chain ends, the CBM exerts a thermodynamic driving force to translate away from the free cellulose chain ends. This suggests that the CBM is not only required for binding to cellulose, as has been known for two decades, but also that it has evolved to both assist the enzyme in recognizing a cellulose chain end and exert a driving force on the enzyme during processive hydrolysis of cellulose.

Molecular dynamics-based approaches for enhanced sampling of long-time, large-scale conformational changes in biomolecules

The rugged energy landscape of biomolecules together with shortcomings of traditional molecular dynamics (MD) simulations require specialized methods for capturing large-scale, long-time configurational changes along with chemical dynamics behavior. In this report, MD-based methods for biomolecules are surveyed, involving modification of the potential, simulation protocol, or algorithm as well as global reformulations. While many of these methods are successful at probing the thermally accessible configuration space at the expense of altered kinetics, more sophisticated approaches like transition path sampling or Markov chain models are required to obtain mechanistic information, reaction pathways, and/or reaction rates. Divide-and-conquer methods for sampling and for piecing together reaction rate information are especially suitable for readily available computer cluster networks. Successful applications to biomolecules remain a challenge.

A theoretical study on the detection of proton transfer pathways in some mutants of human carbonic anhydrase II

Structural and kinetic studies of mutants can give much insight into the function of an enzyme. We report the detection of possible proton transfer pathways into the active site of a number of mutants of the enzyme human carbonic anhydrase II (HCA II). Using a recently developed method of path search in the protein conformational space, we identify hydrogen-bonded networks (or proton paths) that can dynamically connect the protein surface to the active site through fluctuations in protein structure and hydration. The feasibility of establishing such dynamical connectivities is assessed by computing the change in free energy of conformational fluctuations and compared to those identified earlier in the wild type enzyme. It is found that the point mutation facilitates or suppresses one or more of the alternative pathways. Our results allow the use of a generic set of pathways to correlate qualitatively the residual activity in the mutants to the molecular mechanism of proton transfer in the absence of His at position 64. We also demonstrate how the detected pathways may be used to compare the efficiencies of the mutants His-64-Ala/Asn-62-His and His-64-Ala/Asn-67-His using the empirical valence bond theory.

Extensions to the likelihood maximization approach for finding reaction coordinates

This paper extends our previous work on obtaining reaction coordinates from aimless shooting and likelihood maximization. We introduce a simplified version of aimless shooting and a half-trajectory likelihood score based on the committor probability. Additionally, we analyze and compare the absolute log-likelihood score for perfect and approximate reaction coordinates. We also compare the aimless shooting and likelihood maximization approach to the earlier genetic neural network (GNN) approach of Ma and Dinner [J. Phys. Chem. B 109, 6769 (2005)]. For a fixed number of total trajectories in the GNN approach, the accuracy of the transition state ensemble decreases as the number of trajectories per committor probability estimate increases. This quantitatively demonstrates the benefit of individual committor probability realizations over committor probability estimates. Furthermore, when the least squares score of the GNN approach is applied to individual committor probability realizations, the likelihood score still provides a better approximation to the true transition state surface. Finally, the polymorph transition in terephthalic acid demonstrates that the new half-trajectory likelihood scheme estimates the transition state location more accurately than likelihood schemes based on the probability of being on a transition path.

Synergistic approach to improve "alchemical" free energy calculation in rugged energy surface

The authors present an integrated approach to "alchemical" free energy simulation, which permits efficient calculation of the free energy difference on rugged energy surface. The method is designed to obtain efficient canonical sampling for rapid free energy convergence. The proposal is motivated by the insight that both the exchange efficiency in the presently designed dual-topology alchemical Hamiltonian replica exchange method (HREM), and the confidence of the free energy determination using the overlap histogramming method, depend on the same criterion, viz., the overlaps of the energy difference histograms between all pairs of neighboring states. Hence, integrating these two techniques can produce a joint solution to the problems of the free energy convergence and conformational sampling in the free energy simulations, in which lambda parameter plays two roles to simultaneously facilitate the conformational sampling and improve the phase space overlap for the free energy determination. Specifically, in contrast with other alchemical HREM based free energy simulation methods, the dual-topology approach can ensure robust conformational sampling. Due to these features (a synergistic solution to the free energy convergence and canonical sampling, and the improvement of the sampling efficiency with the dual-topology treatment), the present approach, as demonstrated in the model studies of the authors, is highly efficient in obtaining accurate free energy differences, especially for the systems with rough energy landscapes.

Phase-space overlap measures. I. Fail-safe bias detection in free energies calculated by molecular simulation

We consider ways to quantify the overlap of the parts of phase space important to two systems, labeled A and B. Of interest is how much of the A-important phase space lies in that important to B, and how much of B lies in A. Two measures are proposed. The first considers four total-energy distributions, formed from all combinations made by tabulating either the A-system or the B-system energy when sampling either the A or B system. Measures for A in B and B in A are given by two overlap integrals defined on pairs of these distributions. The second measure is based on information theory, and defines two relative entropies which are conveniently expressed in terms of the dissipated work for free-energy perturbation (FEP) calculations in the A-->B and B-->A directions, respectively. Phase-space overlap is an important consideration in the performance of free-energy calculations. To demonstrate this connection, we examine bias in FEP calculations applied to a system of independent particles in a harmonic potential. Systems are selected to represent a range of overlap situations, including extreme subset, subset, partial overlap, and nonoverlap. The magnitude and symmetry of the bias (A-->B vs B-->A) are shown to correlate well with the overlap, and consequently with the overlap measures. The relative entropies are used to scale the amount of sampling to obtain a universal bias curve. This result leads to develop a simple heuristic that can be applied to determine whether a work-based free-energy measurement is free of bias. The heuristic is based in part on the measured free energy, but we argue that it is fail-safe inasmuch as any bias in the measurement will not promote a false indication of accuracy.

Surface-Mediated Nucleation in the Solid-State Polymorph Transformation of Terephthalic Acid

A molecular mechanism for nucleation for the solid-state polymorph transformation of terephthalic acid is presented. New methods recently developed in our group, aimless shooting and likelihood maximization, are employed to construct a model for the reaction coordinate for the two system sizes studied. The reaction coordinate approximation is validated using the committor probability analysis. The transformation proceeds via a localized, elongated nucleus along the crystal edge formed by fluctuations in the supramolecular synthons, suggesting a nucleation and growth mechanism in the macroscopic system.

Distinct energetics and closing pathways for DNA polymerase beta with 8-oxoG template and different incoming nucleotides

Background

8-Oxoguanine (8-oxoG) is a common oxidative lesion frequently encountered by DNA polymerases such as the repair enzyme DNA polymerase β (pol β). To interpret in atomic and energetic detail how pol β processes 8-oxoG, we apply transition path sampling to delineate closing pathways of pol β 8-oxoG complexes with dCTP and dATP incoming nucleotides and compare the results to those of the nonlesioned G:dCTP and G:dATPanalogues.

Results

Our analyses show that the closing pathways of the 8-oxoG complexes are different from one another and from the nonlesioned analogues in terms of the individual transition states along each pathway, associated energies, and the stability of each pathway's closed state relative to the corresponding open state. In particular, the closed-to-open state stability difference in each system establishes a hierarchy of stability (from high to low) as G:C > 8-oxoG:C > 8-oxoG:A > G:A, corresponding to -3, -2, 2, 9 k_BT, respectively. This hierarchy of closed state stability parallels the experimentally observed processing efficiencies for the four pairs. Network models based on the calculated rate constants in each pathway indicate that the closed species are more populated than the open species for 8-oxoG:dCTP, whereas the opposite is true for 8-oxoG:dATP.

Conclusion

These results suggest that the lower insertion efficiency (larger K_m) for dATP compared to dCTP opposite 8-oxoG is caused by a less stable closed-form of pol β, destabilized by unfavorable interactions between Tyr271 and the mispair. This stability of the closed vs. open form can also explain the higher insertion efficiency for 8-oxoG:dATP compared to the nonlesioned G:dATP pair, which also has a higher overall conformational barrier. Our study offers atomic details of the complexes at different states, in addition to helping interpret the different insertion efficiencies of dATP and dCTP opposite 8-oxoG and G.

Obtaining reaction coordinates by likelihood maximization

We present a new approach for calculating reaction coordinates in complex systems. The new method is based on transition path sampling and likelihood maximization. It requires fewer trajectories than a single iteration of existing procedures, and it applies to both low and high friction dynamics. The new method screens a set of candidate collective variables for a good reaction coordinate that depends on a few relevant variables. The Bayesian information criterion determines whether additional variables significantly improve the reaction coordinate. Additionally, we present an advantageous transition path sampling algorithm and an algorithm to generate the most likely transition path in the space of collective variables. The method is demonstrated on two systems: a bistable model potential energy surface and nucleation in the Ising model. For the Ising model of nucleation, we quantify for the first time the role of nuclei surface area in the nucleation reaction coordinate. Surprisingly, increased surface area increases the stability of nuclei in two dimensions but decreases nuclei stability in three dimensions.

Exploring reaction pathways with transition path and umbrella sampling: Application to methyl maltoside

The transition path sampling (TPS) method is a powerful approach to study chemical reactions or transitional properties on complex potential energy landscapes. One of the main advantages of the method over potential of mean force methods is that reaction rates can be directly accessed without knowledge of the exact reaction coordinate. We have investigated the complementary nature of these two differing approaches, comparing transition path sampling with the weighted histogram analysis method to study a conformational change in a small model system. In this case study, the transition paths for a transition between two rotational conformers of a model disaccharide molecule, methyl beta-D-maltoside, were compared with a free energy surface constrained by the two commonly used glycosidic (phi,psi) torsional angles. The TPS method revealed a reaction channel that was not apparent from the potential of mean force method, and the suitability of phi and psi as reaction coordinates to describe the isomerization in vacuo was confirmed by examination of the transition path ensemble. Using both transition state theory and transition path sampling methods, the transition rate was estimated. We have estimated a characteristic time between transitions of approximately 160 ns for this rare isomerization event between the two conformations of the carbohydrate. We conclude that transition path sampling can extract subtle information about the dynamics not apparent from the potential of mean force method. However, in calculating the reaction rate, the transition path sampling method required 27.5 times the computational effort than was needed by the potential of mean force method.

Fidelity discrimination in DNA polymerase beta: differing closing profiles for a mismatched (G:A) versus matched (G:C) base pair

Understanding fidelity-the faithful replication or repair of DNA by polymerases-requires tracking of the structural and energetic changes involved, including the elusive transient intermediates, for nucleotide incorporation at the template/primer DNA junction. We report, using path sampling simulations and a reaction network model, strikingly different transition states in DNA polymerase beta's conformational closing for correct dCTP versus incorrect dATP incoming nucleotide opposite a template G. The cascade of transition states leads to differing active-site assembly processes toward the "two-metal-ion catalysis" geometry. We demonstrate that these context-specific pathways imply different selection processes: while active-site assembly occurs more rapidly with the correct nucleotide and leads to primer extension, the enzyme remains open longer, has a more transient closed state, and forms product more slowly when an incorrect nucleotide is present. Our results also suggest that the rate-limiting step in pol beta's conformational closing is not identical to that for overall nucleotide insertion and that the rate-limiting step in the overall nucleotide incorporation process for matched as well as mismatched systems occurs after the closing conformational change.