Stochastic steps in secondary active sugar transport.

Secondary active transporters, such as those that adopt the leucine-transporter 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.

Expression of three topologically distinct membrane proteins elicits unique stress response pathways in the yeast Saccharomyces cerevisiae.

Misfolded membrane proteins are retained in the endoplasmic reticulum (ER) and are subject to ER-associated degradation, which clears the secretory pathway of potentially toxic species. While the transcriptional response to environmental stressors has been extensively studied, limited data exist describing the cellular response to misfolded membrane proteins. To this end, we expressed and then compared the transcriptional profiles elicited by the synthesis of three ER retained, misfolded ion channels: The α-subunit of the epithelial sodium channel, ENaC, the cystic fibrosis transmembrane conductance regulator, CFTR, and an inwardly rectifying potassium channel, Kir2.1, which vary in their mass, membrane topologies, and quaternary structures. To examine transcriptional profiles in a null background, the proteins were expressed in yeast, which was previously used to examine the degradation requirements for each substrate. Surprisingly, the proteins failed to induce a canonical unfolded protein response or heat shock response, although messages encoding several cytosolic and ER lumenal protein folding factors rose when αENaC or CFTR was expressed. In contrast, the levels of these genes were unaltered by Kir2.1 expression; instead, the yeast iron regulon was activated. Nevertheless, a significant number of genes that respond to various environmental stressors were upregulated by all three substrates, and compared with previous microarray data we deduced the existence of a group of genes that reflect a novel misfolded membrane protein response. These data indicate that aberrant proteins in the ER elicit profound yet unique cellular responses.

Structural determinants of water permeation through the sodium-galactose transporter vSGLT.

Sodium-glucose transporters (SGLTs) facilitate the movement of water across the cell membrane, playing a central role in cellular homeostasis. Here, we present a detailed analysis of the mechanism of water permeation through the inward-facing state of vSGLT based on nearly 10 µs of molecular dynamics simulations. These simulations reveal the transient formation of a continuous water channel through the transporter that permits water to permeate the protein. Trajectories in which spontaneous release of galactose is observed, as well as those in which galactose remains in the binding site, show that the permeation rate, although modulated by substrate occupancy, is not tightly coupled to substrate release. Using a, to our knowledge, novel channel-detection algorithm, we identify the key residues that control water flow through the transporter and show that solvent gating is regulated by side-chain motions in a small number of residues on the extracellular face. A sequence alignment reveals the presence of two insertion sites in mammalian SGLTs that flank these outer-gate residues. We hypothesize that the absence of these sites in vSGLT may account for the high water permeability values for vSGLT determined via simulation compared to the lower experimental estimates for mammalian SGLT1.

Simulating rare events using a weighted ensemble-based string method.

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.

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.

Constraint-based, homology model of the extracellular domain of the epithelial Na+ channel α subunit reveals a mechanism of channel activation by proteases.

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 α 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 α subunit-derived inhibitory peptide affects channel gating by constraining motions within two major domains in the extracellular region, the thumb and finger domains.

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.

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.

The mechanical properties of PCNA: implications for the loading and function of a DNA sliding clamp.

Sliding clamps are toroidal proteins that encircle DNA and act as mobile platforms for DNA replication and repair machinery. To be loaded onto DNA, the eukaryotic sliding clamp Proliferating Cell Nuclear Antigen (PCNA) must be splayed open at one of the subunit-subunit interfaces by the ATP-dependent clamp loader, Replication Factor C, whose clamp-interacting sites form a right-handed spiral. Earlier molecular dynamics (MD) studies suggested that when PCNA opens, it preferentially adopts a right-handed spiral to match the spiral of the clamp loader. Here, analysis of considerably longer MD simulations shows that although the opened form of PCNA can achieve conformations matching the helical pitch of Replication Factor C, it is not biased toward a right-handed spiral structure. A coarse-grained elastic model was also built; its strong correspondence to the all-atom MD simulations of PCNA suggests that the behavior of the open clamp is primarily due to elastic deformation governed by the topology of the clamp domains. The elastic model was further used to construct the energy landscape of the opened PCNA clamp, including conformations that would allow binding to the clamp loader and loading onto double-stranded DNA. A picture of PCNA emerges of a rather flexible protein that, once opened, is mechanically compliant in the clamp opening process.

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.

Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models.

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.

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.

Simulating Current-Voltage Relationships for a Narrow Ion Channel Using the Weighted Ensemble Method.

Ion channels are responsible for a myriad of fundamental biological processes via their role in controlling the flow of ions through water-filled membrane-spanning pores in response to environmental cues. Molecular simulation has played an important role in elucidating the mechanism of ion conduction, but connecting atomistically detailed structural models of the protein to electrophysiological measurements remains a broad challenge due to the computational cost of reaching the necessary time scales. Here, we introduce an enhanced sampling method for simulating the conduction properties of narrow ion channels using the Weighted ensemble (WE) sampling approach. We demonstrate the application of this method to calculate the current­voltage relationship as well as the nonequilibrium ion distribution at steady-state of a simple model ion channel. By direct comparisons with long brute force simulations, we show that the WE simulations rigorously reproduce the correct long-time scale kinetics of the system and are capable of determining these quantities using significantly less aggregate simulation time under conditions where permeation events are rare.

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.

Structure-guided simulations illuminate the mechanism of ATP transport through VDAC1.

The voltage-dependent anion channel (VDAC) mediates the flow of metabolites and ions across the outer mitochondrial membrane of all eukaryotic cells. The open channel passes millions of ATP molecules per second, whereas the closed state exhibits no detectable ATP flux. High-resolution structures of VDAC1 revealed a 19-stranded ß-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 simulations to construct a Markov state model of ATP permeation. These simulations indicate that ATP flows through VDAC through multiple pathways, in agreement with our structural data and experimentally determined physiological rates.

Mechanochemistry of transcription termination factor Rho.

Rho is a ring-shaped hexameric motor protein that translocates along nascent mRNA transcript and terminates transcription of select genes in bacteria. Using a numerical optimization algorithm that simultaneously fits all of the presteady-state ATPase kinetic data, we determine how Rho utilizes the chemical energy of ATP hydrolysis to translocate RNA. A random hydrolysis mechanism is ruled out by the observed inhibition of ATPase in a mixed hexamer containing wt and an inactive Rho mutant. We propose a mechanism in which (1) all six subunits are catalytically competent and hydrolyze ATP sequentially, (2) translocation of RNA is driven by the weak to tight binding transition of nucleotide in the catalytic site, (3) hydrolysis is coordinated between adjacent subunits by the transmission of stress via the catalytic arginine finger, (4) hydrolysis weakens the affinity of a subunit for RNA, and (5) the slow release of inorganic phosphate is controlled by changes in circumferential stress around the ring.