Revisiting Textbook Azide-Clock Reactions: A "Propeller-Crawling" Mechanism Explains Differences in Rates.

An ongoing challenge to chemists is the analysis of pathways and kinetics for chemical reactions in solution, including transient structures between the reactants and products that are difficult to resolve using laboratory experiments. Here, we enabled direct molecular dynamics simulations of a textbook series of chemical reactions on the hundreds of ns to µs time scale using the weighted ensemble (WE) path sampling strategy with hybrid quantum mechanical/molecular mechanical (QM/MM) models. We focused on azide-clock reactions involving addition of an azide anion to each of three long-lived trityl cations in an acetonitrile-water solvent mixture. Results reveal a two-step mechanism: (1) diffusional collision of reactants to form an ion-pair intermediate; (2) "activation" or rearrangement of the intermediate to the product. Our simulations yield not only reaction rates that are within error of experiment but also rates for individual steps, indicating the activation step as rate-limiting for all three cations. Further, the trend in reaction rates is due to dynamical effects, i.e., differing extents of the azide anion "crawling" along the cation's phenyl-ring "propellers" during the activation step. Our study demonstrates the power of analyzing pathways and kinetics to gain insights on reaction mechanisms, underscoring the value of including WE and other related path sampling strategies in the modern toolbox for chemists.

A Suite of Tutorials for the WESTPA 2.0 Rare-Events Sampling Software [Article v2.0].

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations.

WESTPA 2.0: High-Performance Upgrades for Weighted Ensemble Simulations and Analysis of Longer-Timescale Applications.

The weighted ensemble (WE) family of methods is one of several statistical mechanics-based path sampling strategies that can provide estimates of key observables (rate constants and pathways) using a fraction of the time required by direct simulation methods such as molecular dynamics or discrete-state stochastic algorithms. WE methods oversee numerous parallel trajectories using intermittent overhead operations at fixed time intervals, enabling facile interoperability with any dynamics engine. Here, we report on the major upgrades to the WESTPA software package, an open-source, high-performance framework that implements both basic and recently developed WE methods. These upgrades offer substantial improvements over traditional WE methods. The key features of the new WESTPA 2.0 software enhance the efficiency and ease of use: an adaptive binning scheme for more efficient surmounting of large free energy barriers, streamlined handling of large simulation data sets, exponentially improved analysis of kinetics, and developer-friendly tools for creating new WE methods, including a Python API and resampler module for implementing both binned and "binless" WE strategies.

A Suite of Tutorials for the WESTPA Rare-Events Sampling Software [Article v1.0].

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present five tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. Users are expected to already have significant experience with running standard molecular dynamics simulations using the underlying dynamics engine of interest (e.g. Amber, Gromacs, OpenMM). The tutorials range from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding.

Efficient Atomistic Simulation of Pathways and Calculation of Rate Constants for a Protein-Peptide Binding Process: Application to the MDM2 Protein and an Intrinsically Disordered p53 Peptide.

The characterization of protein binding processes - with all of the key conformational changes - has been a grand challenge in the field of biophysics. Here, we have used the weighted ensemble path sampling strategy to orchestrate molecular dynamics simulations, yielding atomistic views of protein-peptide binding pathways involving the MDM2 oncoprotein and an intrinsically disordered p53 peptide. A total of 182 independent, continuous binding pathways were generated, yielding a kon that is in good agreement with experiment. These pathways were generated in 15 days using 3500 cores of a supercomputer, substantially faster than would be possible with "brute force" simulations. Many of these pathways involve the anchoring of p53 residue F19 into the MDM2 binding cleft when forming the metastable encounter complex, indicating that F19 may be a kinetically important residue. Our study demonstrates that it is now practical to generate pathways and calculate rate constants for protein binding processes using atomistic simulation on typical computing resources.

WESTPA: an interoperable, highly scalable software package for weighted ensemble simulation and analysis.

The weighted ensemble (WE) path sampling approach orchestrates an ensemble of parallel calculations with intermittent communication to enhance the sampling of rare events, such as molecular associations or conformational changes in proteins or peptides. Trajectories are replicated and pruned in a way that focuses computational effort on underexplored regions of configuration space while maintaining rigorous kinetics. To enable the simulation of rare events at any scale (e.g., atomistic, cellular), we have developed an open-source, interoperable, and highly scalable software package for the execution and analysis of WE simulations: WESTPA (The Weighted Ensemble Simulation Toolkit with Parallelization and Analysis). WESTPA scales to thousands of CPU cores and includes a suite of analysis tools that have been implemented in a massively parallel fashion. The software has been designed to interface conveniently with any dynamics engine and has already been used with a variety of molecular dynamics (e.g., GROMACS, NAMD, OpenMM, AMBER) and cell-modeling packages (e.g., BioNetGen, MCell). WESTPA has been in production use for over a year, and its utility has been demonstrated for a broad set of problems, ranging from atomically detailed host­guest associations to nonspatial chemical kinetics of cellular signaling networks. The following describes the design and features of WESTPA, including the facilities it provides for running WE simulations and storing and analyzing WE simulation data, as well as examples of input and output.

Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories.

Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many nonequilibrium processes can be described by suitable subsets of the equilibrium ensemble. Here, we employ the "weighted ensemble" (WE) simulation protocol [Huber and Kim, Biophys. J.1996, 70, 97-110] to generate equilibrium trajectory ensembles and extract nonequilibrium subsets for computing kinetic quantities. States do not need to be chosen in advance. The procedure formally allows estimation of kinetic rates between arbitrary states chosen after the simulation, along with their equilibrium populations. We also describe a related history-dependent matrix procedure for estimating equilibrium and nonequilibrium observables when phase space has been divided into arbitrary non-Markovian regions, whether in WE or ordinary simulation. In this proof-of-principle study, these methods are successfully applied and validated on two molecular systems: explicitly solvated methane association and the implicitly solvated Ala4 peptide. We comment on challenges remaining in WE calculations.

Simulations of the alternating access mechanism of the sodium symporter Mhp1.

Sodium coupled cotransporters of the five-helix inverted repeat (5HIR) superfamily use an alternating access mechanism to transport a myriad of small molecules across the cell membrane. One of the primary steps in this mechanism is the conformational transition from a state poised to bind extracellular substrates to a state that is competent to deliver substrate to the cytoplasm. Here, we construct a coarse-grained model of the 5HIR benzylhydantoin transporter Mhp1 that incorporates experimental structures of the outward- and inward-open states to investigate the mechanism of this conformational change. Using the weighted ensemble path-sampling method, we rigorously sample the outward- to inward-facing transition path ensemble. The transition path ensemble reveals a heterogeneous set of pathways connecting the two states and identifies two modes of transport: one consistent with a strict alternating access mechanism and another where decoupling of the inner and outer gates causes the transient formation of a continuous permeation pathway through the transporter. We also show that the conformational switch between the outward- and inward-open states results from rigid body motions of the hash motif relative to the substrate bundle, supporting the rocking bundle hypothesis. Finally, our methodology provides the groundwork for more chemically detailed investigations of the alternating mechanism.

Direct observations of conformational distributions of intrinsically disordered p53 peptides using UV Raman and explicit solvent simulations.

We report the first experimental measurements of Ramachandran Ψ-angle distributions for intrinsically disordered peptides: the N-terminal peptide fragment of tumor suppressor p53 and its P27S mutant form. To provide atomically detailed views of the conformational distributions, we performed classical, explicit-solvent molecular dynamics simulations on the microsecond time scale. Upon binding its partner protein, MDM2, wild-type p53 peptide adopts an α-helical conformation. Mutation of Pro27 to serine results in the highest affinity yet observed for MDM2-binding of the p53 peptide. Both UV resonance Raman spectroscopy (UVRR) and simulations reveal that the P27S mutation decreases the extent of PPII helical content and increases the probability for conformations that are similar to the α-helical MDM2-bound conformation. In addition, UVRR measurements were performed on peptides that were isotopically labeled at the Leu26 residue preceding the Pro27 in order to determine the conformational distributions of Leu26 in the wild-type and mutant peptides. The UVRR and simulation results are in quantitative agreement in terms of the change in the population of non-PPII conformations involving Leu26 upon mutation of Pro27 to serine. Finally, our simulations reveal that the MDM2-bound conformation of the peptide is significantly populated in both the wild-type and mutant isolated peptide ensembles in their unbound states, suggesting that MDM2 binding of the p53 peptides may involve conformational selection.

Efficient Explicit-Solvent Molecular Dynamics Simulations of Molecular Association Kinetics: Methane/Methane, Na(+)/Cl(-), Methane/Benzene, and K(+)/18-Crown-6 Ether.

Atomically detailed views of molecular recognition events are of great interest to a variety of research areas in biology and chemistry. Here, we apply the weighted ensemble path sampling approach to improve the efficiency of explicit solvent molecular dynamics (MD) simulations in sampling molecular association events between two methane molecules, Na(+) and Cl(-) ions, methane and benzene, and the K(+) ion and 18-crown-6 ether. Relative to brute force simulation, we obtain efficiency gains of at least 300 and 1100-fold for the most challenging system, K(+)/18-crown-6 ether, in terms of sampling the association rate constant k and distribution of times required to traverse transition paths, respectively. Our results indicate that weighted ensemble sampling is likely to allow for even greater efficiencies for more complex systems with higher barriers to molecular association.

Reaching biological timescales with all-atom molecular dynamics simulations.

Molecular dynamics (MD) simulations can provide atomically detailed views of protein motions, sampling multiple timescales ranging from femtoseconds to nanoseconds on typical computing resources. The 'reach' of these computer simulations toward biologically relevant timescales (microseconds and beyond) has been improving with advances in hardware and software, as well as the development of enhanced sampling techniques. This review outlines these advances, focusing on techniques that also provide realistic, unperturbed kinetics. These longer-timescale MD simulations can provide detailed insights into the mechanisms of biological events, potentially aiding the design of pharmaceuticals.

Hybrid molecular dynamics-quantum mechanics simulations of solute spectral properties in the condensed phase: evaluation of simulation parameters.

We have explored the impact of a number of basic simulation parameters on the results of a recently developed hybrid molecular dynamics-quantum mechanics (MD-QM) method (Mercer et al., J Phys Chem B 1999, 103, 7720). The method utilizes MD simulations to explore the ground-state configuration space of the system and QM evaluation of those structures to yield the time-dependent electronic transition energy, which is transformed into the optical line-broadening function using the second-order cumulant expansion. Both linear and nonlinear optical spectra can then be generated for comparison to experiment. The dependence of the resulting spectra on the length of the MD trajectory, the QM sampling rate, and the QM model chemistry have all been examined. In particular, for the system of oxazine-4 in methanol studied here, at least 20 ps of MD trajectory are needed for qualitative convergence of linear spectral properties, and >100 ps is needed for quantitative convergence. Surprisingly, little difference is found between the 3-21G and 6-31G(d) basis sets, and the CIS and TD-B3LYP methods yield remarkably similar spectra. The semiempirical INDO/s method yields the most accurate results, reproducing the experimental Stokes shift to within 5% and the FWHM to within 20%. Nonlinear 3-pulse photon echo peak shift (3PEPS) decays have also been simulated. Decays are generally poorly reproduced, though the initial peak shift which depends on the overall coupling of motions to the solute transition energy is within 15% of experiment for all model chemistries other than those using the STO-3G basis.

Fretting about FRET: correlation between kappa and R.

Molecular dynamics simulations were used to examine the structural dynamics of two fluorescent probes attached to a typical protein, hen egg-white lysozyme (HEWL). The donor probe (D) was attached via a succinimide group, consistent with the commonly-used maleimide conjugation chemistry, and the acceptor probe (A) was bound into the protein as occurs naturally for HEWL and the dye Eosin Y. The is found to deviate significantly from the theoretical value and high correlation between the orientation factor kappa and the distance R is observed. The correlation is quantified using several possible fixed A orientations and correlation as high as 0.80 is found between kappa and R and as high as 0.68 between kappa(2) and R. The presence of this correlation highlights the fact that essentially all fluorescence-detected resonance energy transfer studies have assumed that kappa and R are independent--an assumption that is clearly not justified in the system studied here. The correlation results in the quantities and < R(-)(6)> differing by a factor of 1.6. The observed correlation between kappa and R is caused by the succinimide linkage between the D and HEWL, which is found to be relatively inflexible.