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.

Mechanistic Insights into Passive Membrane Permeability of Drug-like Molecules from a Weighted Ensemble of Trajectories.

Passive permeability of a drug-like molecule is a critical property assayed early in a drug discovery campaign that informs a medicinal chemist how well a compound can traverse biological membranes, such as gastrointestinal epithelial or restrictive organ barriers, so it can perform a specific therapeutic function. However, the challenge that remains is the development of a method, experimental or computational, which can both determine the permeation rate and provide mechanistic insights into the transport process to help with the rational design of any given molecule. Typically, one of the following three methods are used to measure the membrane permeability: (1) experimental permeation assays acting on either artificial or natural membranes; (2) quantitative structure-permeability relationship models that rely on experimental values of permeability or related pharmacokinetic properties of a range of molecules to infer those for new molecules; and (3) estimation of permeability from the Smoluchowski equation, where free energy and diffusion profiles along the membrane normal are taken as input from large-scale molecular dynamics simulations. While all these methods provide estimates of permeation coefficients, they provide very little information for guiding rational drug design. In this study, we employ a highly parallelizable weighted ensemble (WE) path sampling strategy, empowered by cloud computing techniques, to generate unbiased permeation pathways and permeability coefficients for a set of drug-like molecules across a neat 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine membrane bilayer. Our WE method predicts permeability coefficients that compare well to experimental values from an MDCK-LE cell line and PAMPA assays for a set of drug-like amines of varying size, shape, and flexibility. Our method also yields a series of continuous permeation pathways weighted and ranked by their associated probabilities. Taken together, the ensemble of reactive permeation pathways, along with the estimate of the permeability coefficient, provides a clearer picture of the microscopic underpinnings of small-molecule membrane permeation.

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.

Accurate Modeling of Scaffold Hopping Transformations in Drug Discovery.

The accurate prediction of protein-ligand binding free energies remains a significant challenge of central importance in computational biophysics and structure-based drug design. Multiple recent advances including the development of greatly improved protein and ligand molecular mechanics force fields, more efficient enhanced sampling methods, and low-cost powerful GPU computing clusters have enabled accurate and reliable predictions of relative protein-ligand binding free energies through the free energy perturbation (FEP) methods. However, the existing FEP methods can only be used to calculate the relative binding free energies for R-group modifications or single-atom modifications and cannot be used to efficiently evaluate scaffold hopping modifications to a lead molecule. Scaffold hopping or core hopping, a very common design strategy in drug discovery projects, is critical not only in the early stages of a discovery campaign where novel active matter must be identified but also in lead optimization where the resolution of a variety of ADME/Tox problems may require identification of a novel core structure. In this paper, we introduce a method that enables theoretically rigorous, yet computationally tractable, relative protein-ligand binding free energy calculations to be pursued for scaffold hopping modifications. We apply the method to six pharmaceutically interesting cases where diverse types of scaffold hopping modifications were required to identify the drug molecules ultimately sent into the clinic. For these six diverse cases, the predicted binding affinities were in close agreement with experiment, demonstrating the wide applicability and the significant impact Core Hopping FEP may provide in drug discovery projects.

TCR triggering by pMHC ligands tethered on surfaces via poly(ethylene glycol) depends on polymer length.

Antigen recognition by T cells relies on the interaction between T cell receptor (TCR) and peptide-major histocompatibility complex (pMHC) at the interface between the T cell and the antigen presenting cell (APC). The pMHC-TCR interaction is two-dimensional (2D), in that both the ligand and receptor are membrane-anchored and their movement is limited to 2D diffusion. The 2D nature of the interaction is critical for the ability of pMHC ligands to trigger TCR. The exact properties of the 2D pMHC-TCR interaction that enable TCR triggering, however, are not fully understood. Here, we altered the 2D pMHC-TCR interaction by tethering pMHC ligands to a rigid plastic surface with flexible poly(ethylene glycol) (PEG) polymers of different lengths, thereby gradually increasing the ligands' range of motion in the third dimension. We found that pMHC ligands tethered by PEG linkers with long contour length were capable of activating T cells. Shorter PEG linkers, however, triggered TCR more efficiently. Molecular dynamics simulation suggested that shorter PEGs exhibit faster TCR binding on-rates and off-rates. Our findings indicate that TCR signaling can be triggered by surface-tethered pMHC ligands within a defined 3D range of motion, and that fast binding rates lead to higher TCR triggering efficiency. These observations are consistent with a model of TCR triggering that incorporates the dynamic interaction between T cell and antigen-presenting cell.

Magnesium-dependent RNA binding to the PA endonuclease domain of the avian influenza polymerase.

Influenza A viruses are highly pathogenic and pose an unpredictable public health danger to humans. An attractive target for developing new antiviral drugs is the PA N-terminal domain (PAN) of influenza polymerase, which is responsible for the endonuclease activity and essential for viral replication. Recently, the crystal structures of the holo form of PAN as well as PAN bound to different inhibitors have been reported, but the potency and selectivity of these inhibitors still need to be improved. New drug design can be guided by a better understanding of the endonuclease activity of PAN. However, this requires the structure of PAN in complex with the host mRNA, which has not been determined yet. In particular, divalent metal ions are known to be essential for RNA cleavage, but it is not clear whether there is either one or two Mg ions in the PAN active site. In the present work, we have modeled the complex of the PAN endonuclease domain with the host mRNA in the presence of either one or two Mg(2+) by using all-atom molecular dynamics. These simulations identify crucial interactions between the enzyme and the nucleic acid. Moreover, they validate a previous hypothesis that a second metal ion binds in the presence of the RNA substrate and therefore support a two-metal ion mechanism, in which K134 decreases the pKa of the nucleophilic water. Nevertheless, at low Mg concentrations an alternative, one-metal ion mechanism is possible, with K137 as the catalytic lysine and H41 as the general base, rationalizing previous unexpected mutagenesis results. The RNA-enzyme interactions determined here could likely be used to design more specific endonuclease inhibitors to fight influenza viral infections.

Exploring volatile general anesthetic binding to a closed membrane-bound bacterial voltage-gated sodium channel via computation.

Despite the clinical ubiquity of anesthesia, the molecular basis of anesthetic action is poorly understood. Amongst the many molecular targets proposed to contribute to anesthetic effects, the voltage gated sodium channels (VGSCs) should also be considered relevant, as they have been shown to be sensitive to all general anesthetics tested thus far. However, binding sites for VGSCs have not been identified. Moreover, the mechanism of inhibition is still largely unknown. The recently reported atomic structures of several members of the bacterial VGSC family offer the opportunity to shed light on the mechanism of action of anesthetics on these important ion channels. To this end, we have performed a molecular dynamics "flooding" simulation on a membrane-bound structural model of the archetypal bacterial VGSC, NaChBac in a closed pore conformation. This computation allowed us to identify binding sites and access pathways for the commonly used volatile general anesthetic, isoflurane. Three sites have been characterized with binding affinities in a physiologically relevant range. Interestingly, one of the most favorable sites is in the pore of the channel, suggesting that the binding sites of local and general anesthetics may overlap. Surprisingly, even though the activation gate of the channel is closed, and therefore the pore and the aqueous compartment at the intracellular side are disconnected, we observe binding of isoflurane in the central cavity. Several sampled association and dissociation events in the central cavity provide consistent support to the hypothesis that the "fenestrations" present in the membrane-embedded region of the channel act as the long-hypothesized hydrophobic drug access pathway.

General anesthetics predicted to block the GLIC pore with micromolar affinity.

Although general anesthetics are known to modulate the activity of ligand-gated ion channels in the Cys-loop superfamily, there is at present neither consensus on the underlying mechanisms, nor predictive models of this modulation. Viable models need to offer quantitative assessment of the relative importance of several identified anesthetic binding sites. However, to date, precise affinity data for individual sites has been challenging to obtain by biophysical means. Here, the likely role of pore block inhibition by the general anesthetics isoflurane and propofol of the prokaryotic pentameric channel GLIC is investigated by molecular simulations. Microscopic affinities are calculated for both single and double occupancy binding of isoflurane and propofol to the GLIC pore. Computations are carried out for an open-pore conformation in which the pore is restrained to crystallographic radius, and a closed-pore conformation that results from unrestrained molecular dynamics equilibration of the structure. The GLIC pore is predicted to be blocked at the micromolar concentrations for which inhibition by isofluorane and propofol is observed experimentally. Calculated affinities suggest that pore block by propofol occurs at signifcantly lower concentrations than those for which inhibition is observed: we argue that this discrepancy may result from binding of propofol to an allosteric site recently identified by X-ray crystallography, which may cause a competing gain-of-function effect. Affinities of isoflurane and propofol to the allosteric site are also calculated, and shown to be 3 mM for isoflurane and 10 µM for propofol; both anesthetics have a lower affinity for the allosteric site than for the unoccupied pore.

Surfactant concentration effects on micellar properties.

A hydrophobic theory is combined with a Debye-Hückel approximation to calculate surfactant micellization properties such as the critical micelle concentration (cmc) and concentration effects. The predictive power of the theory is validated by comparison with experimental data of various ionic surfactant types in presence of salt. The theory is also used to describe micellar properties of surfactant models developed for molecular simulations for which cmc computations become infeasible. The theory allows such computations and helps to evaluate the quality of models used in simulations.

Micellization Studied by GPU-Accelerated Coarse-Grained Molecular Dynamics.

The computational design of advanced materials based on surfactant self-assembly without ever stepping foot in the laboratory is an important goal, but there are significant barriers to this approach, because of the limited spatial and temporal scales accessible by computer simulations. In this paper, we report our work to bridge the gap between laboratory and computational time scales by implementing the coarse-grained (CG) force field previously reported by Shinoda et al. [Shinoda, W.; DeVane, R.; Klein, M. L. Mol. Simul. 2007, 33, 27-36] into the HOOMD-Blue graphical processing unit (GPU)-accelerated molecular dynamics (MD) software package previously reported by Anderson et al. [Anderson, J. A.; Lorenz, C. D.; Travesset, A. J. Comput. Phys. 2008, 227, 5342-5359]. For a system of 25 750 particles, this implementation provides performance on a single GPU, which is superior to that of a widely used parallel MD simulation code running on an optimally sized CPU-based cluster. Using our GPU setup, we have collected 0.6 ms of MD trajectory data for aqueous solutions of 7 different nonionic polyethylene glycol (PEG) surfactants, with most of the systems studied representing ∼1 000 000 atoms. From this data, we calculated various properties as a function of the length of the hydrophobic tails and PEG head groups. Specifically, we determined critical micelle concentrations (CMCs), which are in good agreement with experimental data, and characterized the size and shape of micelles. However, even with the microsecond trajectories employed in this study, we observed that the micelles composed of relatively hydrophobic surfactants are continuing to grow at the end of our simulations. This suggests that the final micelle size distributions of these systems are strongly dependent on initial conditions and that either longer simulations or advanced sampling techniques are needed to properly sample their equilibrium distributions. Nonetheless, the combination of coarse-grained modeling and GPU acceleration marks a significant step toward the computational prediction of the thermodynamic properties of slowly evolving surfactant systems.

Protein-water electrostatics and principles of bioenergetics.

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.

Multiple binding sites for the general anesthetic isoflurane identified in the nicotinic acetylcholine receptor transmembrane domain.

An extensive search for isoflurane binding sites in the nicotinic acetylcholine receptor (nAChR) and the proton gated ion channel from Gloebacter violaceus (GLIC) has been carried out based on molecular dynamics (MD) simulations in fully hydrated lipid membrane environments. Isoflurane introduced into the aqueous phase readily partitions into the lipid membrane and the membrane-bound protein. Specifically, isoflurane binds persistently to three classes of sites in the nAChR transmembrane domain: (i) An isoflurane dimer occludes the pore, contacting residues identified by previous mutagenesis studies; analogous behavior is observed in GLIC. (ii) Several nAChR subunit interfaces are also occupied, in a site suggested by photoaffinity labeling and thought to positively modulate the receptor; these sites are not occupied in GLIC. (iii) Isoflurane binds to the subunit centers of both nAChR alpha chains and one of the GLIC chains, in a site that has had little experimental targeting. Interpreted in the context of existing structural and physiological data, the present MD results support a multisite model for the mechanism of receptor-channel modulation by anesthetics.

Ferroelectric hydration shells around proteins: electrostatics of the protein-water interface.

Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric layer with large values of the average dipole moment magnitude and the dipole moment variance. The emergence of the new polarized mesophase dramatically alters the statistics of electrostatic fluctuations at the protein-water interface. The linear response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic fluctuations far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a slow (approximately = 1 ns) component that freezes in at the temperature of the dynamical transition of proteins. The ferroelectric shell propagates 3-5 water diameters into the bulk.

Energetics of bacterial photosynthesis.

We report the results of extensive numerical simulations and theoretical calculations of electronic transitions in the reaction center of Rhodobacter sphaeroides photosynthetic bacterium. The energetics and kinetics of five electronic transitions related to the kinetic scheme of primary charge separation have been analyzed and compared to experimental observations. Nonergodic formulation of the reaction kinetics is required for the calculation of the rates due to a severe breakdown of the system ergodicity on the time scale of primary charge separation, with the consequent inapplicability of the standard canonical prescription to calculate the activation barrier. Common to all reactions studied is a significant excess of the charge-transfer reorganization energy from the width of the energy gap fluctuations over that from the Stokes shift of the transition. This property of the hydrated proteins, breaking the linear response of the thermal bath, allows the reaction center to significantly reduce the reaction free energy of near-activationless electron hops and thus raise the overall energetic efficiency of the biological charge-transfer chain. The increase of the rate of primary charge separation with cooling is explained in terms of the temperature variation of induction solvation, which dominates the average donor-acceptor energy gap for all electronic transitions in the reaction center. It is also suggested that the experimentally observed break in the Arrhenius slope of the primary recombination rate, occurring near the temperature of the dynamical transition in proteins, can be traced back to a significant drop of the solvent reorganization energy close to that temperature.

Energetics and kinetics of primary charge separation in bacterial photosynthesis.

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Redox entropy of plastocyanin: developing a microscopic view of mesoscopic polar solvation.

We report applications of analytical formalisms and molecular dynamics (MD) simulations to the calculation of redox entropy of plastocyanin metalloprotein in aqueous solution. The goal of our analysis is to establish critical components of the theory required to describe polar solvation at the mesoscopic scale. The analytical techniques include a microscopic formalism based on structure factors of the solvent dipolar orientations and density and continuum dielectric theories. The microscopic theory employs the atomistic structure of the protein with force-field atomic charges and solvent structure factors obtained from separate MD simulations of the homogeneous solvent. The MD simulations provide linear response solvation free energies and reorganization energies of electron transfer in the temperature range of 280-310 K. We found that continuum models universally underestimate solvation entropies, and a more favorable agreement is reported between the microscopic calculations and MD simulations. The analysis of simulations also suggests that difficulties of extending standard formalisms to protein solvation are related to the inhomogeneous structure of the solvation shell at the protein-water interface combining islands of highly structured water around ionized residues along with partial dewetting of hydrophobic patches. Quantitative theories of electrostatic protein hydration need to incorporate realistic density profile of water at the protein-water interface.

Glassy protein dynamics and gigantic solvent reorganization energy of plastocyanin.

We report the results of molecular dynamics simulations of electron-transfer activation parameters of plastocyanin metalloprotein involved as an electron carrier in natural photosynthesis. We have discovered that slow, non-ergodic conformational fluctuations of the protein, coupled to hydrating water, result in a very broad distribution of donor-acceptor energy gaps far exceeding those observed for commonly studied inorganic and organic donor-acceptor complexes. The Stokes shift is not affected by these fluctuations and can be calculated from solvation models in terms of the linear response of the solvent dipolar polarization. The non-ergodic character of large-amplitude protein/water mobility breaks the strong link between the Stokes shift and the reorganization energy characteristic of equilibrium (ergodic) theories of electron transfer. This mechanism might be responsible for fast electronic transitions in natural electron-transfer proteins characterized by low reaction free energy.

Dynamical transition, hydrophobic interface, and the temperature dependence of electrostatic fluctuations in proteins.

Molecular dynamics simulations have revealed a dramatic increase, with increasing temperature, of the amplitude of electrostatic fluctuations caused by water at the active site of metalloprotein plastocyanin. The increased breadth of electrostatic fluctuations, expressed in terms of the reorganization energy of changing the redox state of the protein, is related to the formation of the hydrophobic protein-water interface, allowing large-amplitude collective fluctuations of the water density in the protein's first solvation shell. On top of the monotonic increase of the reorganization energy with increasing temperature, we have observed a spike at approximately 220 K also accompanied by a significant slowing of the exponential collective Stokes shift dynamics. In contrast to the local density fluctuations of the hydration-shell waters, these spikes might be related to the global property of the water solvent crossing the Widom line or undergoing a weak first-order transition.