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 under-explored 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 host-guest associations to non-spatial chemical kinetics of cellular signaling networks. The following describes the design and features of WESTPA, including the facilities it provides for running WE simulations, storing and analyzing WE simulation data, as well as examples of input and output.

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.

The voltage-dependent anion channel (VDAC) mediates metabolite and ion flow across the outer mitochondrial membrane of all eukaryotic cells. The open channel passes millions of ATP molecules per second, while the closed state exhibits no detectable ATP flux. High-resolution structures of VDAC1 revealed a 19-stranded β-barrel with an α-helix partially occupying the central pore. To understand ATP permeation through VDAC, we solved the crystal structure of mouse VDAC1 (mVDAC1) in the presence of ATP, revealing a low-affinity binding site. Guided by these coordinates, we initiated hundreds of molecular dynamics (MD) simulations to construct a Markov State Model (MSM) of ATP permeation. These simulations indicate that ATP flows through VDAC using multiple pathways, consistent with our structural data and experimentally determined physiological rates.

Because standard molecular dynamics (MD) simulations are unable to access time scales of interest in complex biomolecular systems, it is common to “stitch together” information from multiple shorter trajectories using approximate Markov state model (MSM) analysis. However, MSMs may require significant tuning and can yield biased results. Here, by analyzing some of the longest protein MD data sets available (>100 μs per protein), we show that estimators constructed based on exact non-Markovian (NM) principles can yield significantly improved mean first-passage times (MFPTs) for protein folding and unfolding. In some cases, MSM bias of more than an order of magnitude can be corrected when identical trajectory data are reanalyzed by non-Markovian approaches. The NM analysis includes “history” information, higher order time correlations compared to MSMs, that is available in every MD trajectory. The NM strategy is insensitive to fine details of the states used and works well when a fine time-discretization (i.e., small “lag time”) is used.

The epithelial Na ؉ channel (ENaC) mediates Na ؉ transport across high resistance epithelia. This channel is assembled from three homologous subunits with the majority of the protein's mass found in the extracellular domains. Acid-sensing ion channel 1 (ASIC1) is homologous to ENaC, but a key functional domain is highly divergent. Here we present molecular models of the extracellular region of ␣ ENaC based on a large data set of mutations that attenuate inhibitory peptide binding in combination with comparative modeling based on the resolved structure of ASIC1. The models successfully rationalized the data from the peptide binding screen. We engineered new mutants that had not been tested based on the models and successfully predict sites where mutations affected peptide binding. Thus, we were able to confirm the overall general fold of our structural models. Further analysis suggested that the ␣ subunit-derived inhibitory peptide affects channel gating by constraining motions within two major domains in the extracellular region, the thumb and finger domains.Epithelial Na ϩ channels (ENaCs) 3 are members of the ENaC/degenerin family of ion channels, of which the high resolution structure of acid-sensing ion channel 1 (ASIC1) has been reported. These channels are probably trimers (1, 2) with each subunit having two transmembrane helices, large extracellular regions, and short cytosolic amino and carboxyl termini (3). The resolved structure of the extracellular region of ASIC1 is composed of core ␤-sheet domains (termed palm and ␤-ball) surrounded by peripheral ␣-helical domains (termed finger, thumb, and knuckle) (1). Channels in the ENaC/degenerin family are Na ϩ -permeable and are gated by a diverse set of stimuli, including external ligands and mechanical forces (4). As such, ENaC/degenerin family members play diverse roles in biology. For ENaC, these include the regulation of extracellular volume and blood pressure by mediating Na ϩ transport in the distal nephron of the kidney, regulation of airway surface liquid volume and mucociliary clearance by facilitating Na ϩ transport in airways, and facilitation of salt taste by transporting Na ϩ in lingual epithelium (4). ENaC is assembled from homologous ␣, ␤, and ␥ subunits and is allosterically inhibited by extracellular Na ϩ by a phenomenon referred to as Na ϩ self-inhibition (5-7). Within the ENaC/degenerin family, sequence conservation is conspicuously lacking within the finger domains of the extracellular regions of these channels (1). This fact may partly account for the diversity in the regulation of channel gating observed among gene family members and is an obstacle in building comparative models of ENaC subunits based on the resolved ASIC1 structure.Among the panoply of ENaC properties is its activation by proteolytic cleavage, which is unusual for ion channels (8). Proteolytic activation of ENaC occurs through the cleavage of both the ␣ and ␥ subunits at multiple sites within their finger domains, leading to the release of inhibitory tracts (9 -12). Pe...

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.

We introduce an extension to the weighted ensemble (WE) path sampling method to restrict sampling to a one-dimensional path through a high dimensional phase space. Our method, which is based on the finite-temperature string method, permits efficient sampling of both equilibrium and non-equilibrium systems. Sampling obtained from the WE method guides the adaptive refinement of a Voronoi tessellation of order parameter space, whose generating points, upon convergence, coincide with the principle reaction pathway. We demonstrate the application of this method to several simple, two-dimensional models of driven Brownian motion and to the conformational change of the nitrogen regulatory protein C receiver domain using an elastic network model. The simplicity of the two-dimensional models allows us to directly compare the efficiency of the WE method to conventional brute force simulations and other path sampling algorithms, while the example of protein conformational change demonstrates how the method can be used to efficiently study transitions in the space of many collective variables.

Secondary active transporters, such as those that adopt the leucinetransporter fold, are found in all domains of life, and they have the unique capability of harnessing the energy stored in ion gradients to accumulate small molecules essential for life as well as expel toxic and harmful compounds. How these proteins couple ion binding and transport to the concomitant flow of substrates is a fundamental structural and biophysical question that is beginning to be answered at the atomistic level with the advent of high-resolution structures of transporters in different structural states. Nonetheless, the dynamic character of the transporters, such as ion/substrate binding order and how binding triggers conformational change, is not revealed from static structures, yet it is critical to understanding their function. Here, we report a series of molecular simulations carried out on the sugar transporter vSGLT that lend insight into how substrate and ions are released from the inward-facing state of the transporter. Our simulations reveal that the order of release is stochastic. Functional experiments were designed to test this prediction on the human homolog, hSGLT1, and we also found that cytoplasmic release is not ordered, but we confirmed that substrate and ion binding from the extracellular space is ordered. Our findings unify conflicting published results concerning cytoplasmic release of ions and substrate and hint at the possibility that other transporters in the superfamily may lack coordination between ions and substrate in the inward-facing state.T ransport of sugar molecules across membranes is virtually ubiquitous in biology, and it is of central importance in human health. The uptake of glucose is especially crucial due to its pivotal role in cellular metabolism and energy production. In mammals, glucose is absorbed in the small intestine and kidney via sodium-dependent glucose transporters (SGLTs), which localize to the apical membrane and concentrate glucose in the epithelia. SGLTs fall into the large leucine-transporter (LeuT) structural family of secondary active transporters that have evolved to concentrate a wide array of substrates across membranes using the energy stored in the Na + electrochemical potential gradient. For symporters in this family, transport occurs by an alternating access mechanism (1) in which the transporter first binds ligands in an outward-facing conformation, and then transitions to an inwardfacing conformation that releases the cargo to the cytoplasm. The order of ion and substrate binding and unbinding is likely tied to the function of the transporter, making it possible to convert the energy stored in the ion gradient into a substrate gradient, and vice versa when these proteins operate in reverse.Extensive biochemical uptake assays and electrophysiological studies of SGLTs have led to a view of Na + /glucose cotransport in which Na + binding precedes sugar binding on the external face of the transporter. Kinetic models adhering to this mechanism satisfactorily account fo...