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

BAD-NEUS: Rapidly converging trajectory stratification

An issue for molecular dynamics simulations is that events of interest often involve timescales that are much longer than the simulation time step, which is set by the fastest timescales of the model. Because of this timescale separation, direct simulation of many events is prohibitively computationally costly. This issue can be overcome by aggregating information from many relatively short simulations that sample segments of trajectories involving events of interest. This is the strategy of Markov state models (MSMs) and related approaches, but such methods suffer from approximation error because the variables defining the states generally do not capture the dynamics fully. By contrast, once converged, the weighted ensemble (WE) method aggregates information from trajectory segments so as to yield unbiased estimates of both thermodynamic and kinetic statistics. Unfortunately, errors decay no faster than unbiased simulation in WE as originally formulated and commonly deployed. Here, we introduce a theoretical framework for describing WE that shows that the introduction of an approximate stationary distribution on top of the stratification, as in nonequilibrium umbrella sampling (NEUS), accelerates convergence. Building on ideas from MSMs and related methods, we generalize the NEUS approach in such a way that the approximation error can be reduced systematically. We show that the improved algorithm can decrease the simulation time required to achieve the desired precision by orders of magnitude.

WEDAP: A Python Package for Streamlined Plotting of Molecular Simulation Data

Given the growing interest in path sampling methods for extending the time scales of molecular dynamics (MD) simulations, there has been great interest in software tools that streamline the generation of plots for monitoring the progress of large-scale simulations. Here, we present the WEDAP Python package for simplifying the analysis of data generated from either conventional MD simulations or the weighted ensemble (WE) path sampling method, as implemented in the widely used WESTPA software package. WEDAP facilitates (i) the parsing of WE simulation data stored in highly compressed, hierarchical HDF5 files and (ii) incorporates trajectory weights from WE simulations into all generated plots. Our Python package consists of multiple user-friendly interfaces: a command-line interface, a graphical user interface, and a Python application programming interface. We demonstrate the plotting features of WEDAP through a series of examples using data from WE and conventional MD simulations that focus on the HIV-1 capsid protein's C-terminal domain dimer as a showcase system. The source code for WEDAP is freely available on GitHub at https://github.com/chonglab-pitt/wedap.

Weighted ensemble: Recent mathematical developments

Weighted ensemble (WE) is an enhanced sampling method based on periodically replicating and pruning trajectories generated in parallel. WE has grown increasingly popular for computational biochemistry problems due, in part, to improved hardware and accessible software implementations. Algorithmic and analytical improvements have played an important role, and progress has accelerated in recent years. Here, we discuss and elaborate on the WE method from a mathematical perspective, highlighting recent results that enhance the computational efficiency. The mathematical theory reveals a new strategy for optimizing trajectory management that approaches the best possible variance while generalizing to systems of arbitrary dimension.

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.

Predicting the structural basis of targeted protein degradation by integrating molecular dynamics simulations with structural mass spectrometry

Targeted protein degradation (TPD) is a promising approach in drug discovery for degrading proteins implicated in diseases. A key step in this process is the formation of a ternary complex where a heterobifunctional molecule induces proximity of an E3 ligase to a protein of interest (POI), thus facilitating ubiquitin transfer to the POI. In this work, we characterize 3 steps in the TPD process. (1) We simulate the ternary complex formation of SMARCA2 bromodomain and VHL E3 ligase by combining hydrogen-deuterium exchange mass spectrometry with weighted ensemble molecular dynamics (MD). (2) We characterize the conformational heterogeneity of the ternary complex using Hamiltonian replica exchange simulations and small-angle X-ray scattering. (3) We assess the ubiquitination of the POI in the context of the full Cullin-RING Ligase, confirming experimental ubiquitinomics results. Differences in degradation efficiency can be explained by the proximity of lysine residues on the POI relative to ubiquitin.

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.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

Gaussian-Accelerated Molecular Dynamics with the Weighted Ensemble Method: A Hybrid Method Improves Thermodynamic and Kinetic Sampling

Gaussian-accelerated molecular dynamics (GaMD) is a well-established enhanced sampling method for molecular dynamics simulations that effectively samples the potential energy landscape of the system by adding a boost potential, which smoothens the surface and lowers the energy barriers between states. GaMD is unable to give time-dependent properties such as kinetics directly. On the other hand, the weighted ensemble (WE) method can efficiently sample transitions between states with its many weighted trajectories, which directly yield rates and pathways. However, convergence to equilibrium conditions remains a challenge for the WE method. Hence, we have developed a hybrid method that combines the two methods, wherein GaMD is first used to sample the potential energy landscape of the system and WE is subsequently used to further sample the potential energy landscape and kinetic properties of interest. We show that the hybrid method can sample both thermodynamic and kinetic properties more accurately and quickly compared to using either method alone.

The Next Frontier for Designing Switchable Proteins: Rational Enhancement of Kinetics

Designing proteins that can switch between active (ON) and inactive (OFF) conformations in response to signals such as ligand binding and incident light has been a tantalizing endeavor in protein engineering for over a decade. While such designs have yielded novel biosensors, therapeutic agents, and smart biomaterials, the response times (times for switching ON and OFF) of many switches have been too slow to be of practical use. Among the defining properties of such switches, the kinetics of switching has been the most challenging to optimize. This is largely due to the difficulty of characterizing the structures of transient states, which are required for manipulating the height of the effective free energy barrier between the ON and OFF states. We share our perspective of the most promising new experimental and computational strategies over the past several years for tackling this next frontier for designing switchable proteins.

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.