Weighted Ensemble Path Sampling Research Articles

Gating residues govern ligand unbinding kinetics from the buried cavity in HIF-2α PAS-B.

While transcription factors have been generally perceived as "undruggable," an exception is the HIF-2 hypoxia-inducible transcription factor, which contains an internal cavity that is sufficiently large to accommodate a range of small-molecules, including the therapeutically used inhibitor belzutifan. Given the relatively long ligand residence times of these small molecules and the lack of any experimentally observed pathway connecting the cavity to solvent, there has been great interest in understanding how these drug ligands exit the buried receptor cavity. Here, we focus on the relevant PAS-B domain of hypoxia-inducible factor 2α (HIF-2α) and examine how one such small molecule (THS-017) exits from the buried cavity within this domain on the seconds-timescale using atomistic simulations and ZZ-exchange NMR. To enable the simulations, we applied the weighted ensemble path sampling strategy, which generates continuous pathways for a rare-event process [e.g., ligand (un)binding] with rigorous kinetics in orders of magnitude less computing time compared to conventional simulations. Results reveal the formation of an encounter complex intermediate and two distinct classes of pathways for ligand exit. Based on these pathways, we identified two pairs of conformational gating residues in the receptor: one for the major class (N288 and S304) and another for the minor class (L272 and M309). ZZ-exchange NMR validated the kinetic importance of N288 for ligand unbinding. Our results provide an ideal simulation dataset for rational manipulation of ligand unbinding kinetics.

How does a ligand exit from a buried receptor cavity? Atomistic simulations of unbinding pathways with rigorous kinetics.

Hypoxia-inducible factors (HIFs) are heterodimeric transcription factors that can promote cancer growth. The development of small-molecule drugs that can inhibit the formation of the dimer is therefore a promising route to the treatment of cancer. Here, we focus on the relevant domain of the protein, the HIF2α PAS-B domain, which contains a preformed, buried cavity that binds artificial small-molecule ligands that allosterically perturb the formation of the HIF heterodimer. We examine how a representative ligand (THS-017) dissociates and re-enters the buried cavity using atomistic simulations. To enable these simulations, we applied the weighted ensemble path sampling strategy, which can generate continuous pathways with rigorous kinetics (i.e., rate constants) in orders of magnitude less computing time compared to standard simulations. Results reveal a diverse set of pathways for both the ligand unbinding and rebinding processes with estimated rate constants and methyl order parameters that are consistent with experiment.

The RED scheme: Rate-constant estimation from pre-steady state weighted ensemble simulations.

We present the Rate from Event Durations (RED) scheme, a new scheme that more efficiently calculates rate constants using the weighted ensemble path sampling strategy. This scheme enables rate-constant estimation from shorter trajectories by incorporating the probability distribution of event durations, or barrier-crossing times, from a simulation. We have applied the RED scheme to weighted ensemble simulations of a variety of rare-event processes that range in complexity: residue-level simulations of protein conformational switching, atomistic simulations of Na+/Cl- association in explicit solvent, and atomistic simulations of protein-protein association in explicit solvent. Rate constants were estimated with up to 50% greater efficiency than the original weighted ensemble scheme. Importantly, our scheme accounts for the systematic error that results from statistical bias toward the observation of events with short durations and reweights the event duration distribution accordingly. The RED scheme is relevant to any simulation strategy that involves unbiased trajectories of similar length to the most probable event duration, including weighted ensemble, milestoning, and standard simulations as well as the construction of Markov state models.

A Minimal, Adaptive Binning Scheme for Weighted Ensemble Simulations.

A promising approach for simulating rare events with rigorous kinetics is the weighted ensemble path sampling strategy. One challenge of this strategy is the division of configurational space into bins for sampling. Here we present a minimal adaptive binning (MAB) scheme for the automated, adaptive placement of bins along a progress coordinate within the framework of the weighted ensemble strategy. Results reveal that the MAB binning scheme, despite its simplicity, is more efficient than a manual, fixed binning scheme in generating transitions over large free energy barriers, generating a diversity of pathways, estimating rate constants, and sampling conformations. The scheme is general and extensible to any rare-events sampling strategy that employs progress coordinates.

Effects of Cholesterol on Fengycin, an Antimicrobial Lipopeptide Using Weighted Ensemble Path Sampling Method

Fengycin is an antimicrobial lipopeptide synthesized by the bacteria Bacillus subtilis and commercially available as an agricultural fungicide. One of the ways fengycin kills fungal cells is by binding and damaging their cell membranes. Previous all-atom simulations suggested aggregation of lipopeptides is the first step that leads to membrane deformation. Here we attempt to explain fengycin's selectivity for fungal over mammalian cells by examining the effects of cholesterol on its aggregation. Using weighted ensemble path sampling, we found that fengycin causes membrane demixing to some extent in the membrane consisting of POPC and cholesterol, with the latter being clustered around the lipopeptides. We also found that the free energy of a single fengycin binding to a membrane is independent of the presence of cholesterol. We are currently generalizing these calculations to examine fengycin aggregates in solution and their affinity for membranes. The results will help us understand the implications of cholesterol on fengycin's fungicidal properties and possibly indicate whether fengycin can be a potential drug candidate.

Protein-protein binding pathways and calculations of rate constants using fully-continuous, explicit-solvent simulations.

A grand challenge in the field of biophysics has been the complete characterization of protein-protein binding processes at atomic resolution. This characterization requires the direct simulation of binding pathways starting from the initial, unbound state and proceeding through states that are too transient to be captured by experiment. Here, we applied the weighted ensemble path sampling strategy to orchestrate atomistic simulation of protein-protein binding pathways. Our simulation generated 203 fully-continuous and independent pathways along with rate constants for the binding process involving the barnase and barstar proteins. Results reveal multiple binding pathways along a "funnel-like" free energy landscape in which the formation of the "encounter complex" intermediate is rate-limiting followed by a relatively rapid rearrangement of the encounter complex to the bound state. Among all diffusional collisions, only ∼11% were productive. In the most probable binding pathways, the proteins rotated to a large extent (likely via electrostatic steering) in order to collide productively followed by "rolling" of the proteins along each other's binding interfaces to reach the bound state. Consistent with experiment, R59 was identified as the most kinetically important barnase residue for the binding process. Furthermore, protein desolvation occurs late in the binding process during the rearrangement of the encounter complex to the bound state. Notably, the positions of crystallographic water molecules that bridge hydrogen bonds between barnase and barstar are occupied in the bound-state ensemble. Our simulation was completed in a month using 1600 CPU cores at a time, demonstrating that it is now practical to carry out atomistic simulations of protein-protein binding.

Highly Efficient Computation of the Basal kon using Direct Simulation of Protein-Protein Association with Flexible Molecular Models.

An essential baseline for determining the extent to which electrostatic interactions enhance the kinetics of protein–protein association is the “basal” kon, which is the rate constant for association in the absence of electrostatic interactions. However, since such association events are beyond the milliseconds time scale, it has not been practical to compute the basal kon by directly simulating the association with flexible models. Here, we computed the basal kon for barnase and barstar, two of the most rapidly associating proteins, using highly efficient, flexible molecular simulations. These simulations involved (a) pseudoatomic protein models that reproduce the molecular shapes, electrostatic, and diffusion properties of all-atom models, and (b) application of the weighted ensemble path sampling strategy, which enhanced the efficiency of generating association events by >130-fold. We also examined the extent to which the computed basal kon is affected by inclusion of intermolecular hydrodynamic interactions in the simulations.

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.

Steady-state simulations using weighted ensemble path sampling.

We extend the weighted ensemble (WE) path sampling method to perform rigorous statistical sampling for systems at steady state. A straightforward steady-state implementation of WE is directly practical for simple landscapes, but not when significant metastable intermediates states are present. We therefore develop an enhanced WE scheme, building on existing ideas, which accelerates attainment of steady state in complex systems. We apply both WE approaches to several model systems, confirming their correctness and efficiency by comparison with brute-force results. The enhanced version is significantly faster than the brute force and straightforward WE for systems with WE bins that accurately reflect the reaction coordinate(s). The new WE methods can also be applied to equilibrium sampling, since equilibrium is a steady state.

Weighted Ensemble Path Sampling for Efficient Calculation of Steady State Properties

Steady states are common in biological processes, most famously in enzymatic catalysis. We present a rigorous path sampling procedure, generalizing the “weighted ensemble” (WE) method, to attain a steady state (SS) efficiently. We apply this procedure to several different systems, from toy models to the folding of the atomistic Trp cage mini-protein. For systems without significant intermediates, we find that the SS-WE procedure is able to attain steady state fairly efficiently. However, for systems with significant intermediates, we develop an enhanced version of SS-WE that shifts probability to speed-up the establishment of a steady state, without perturbing the system's natural dynamics. The enhanced SS-WE approach is able to attain a steady state in significantly less time for systems with significant intermediates, and gives correct results for the steady state rates and probability distribution. First-passage rates are also obtained simultaneously.