Wepy: A Flexible Software Framework for Simulating Rare Events with Weighted Ensemble Resampling

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.

Ligand Gaussian Accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional molecular dynamics (cMD), due to limited simulation time scales. Based on our previously developed ligand Gaussian accelerated molecular dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3″, in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding, and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as the model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 μs simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 were in agreement with the available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligands and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Ligand Gaussian accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional Molecular Dynamics (cMD), due to limited simulation timescales. Based on our previously developed Ligand Gaussian accelerated Molecular Dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3", in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 microsecond simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 agreed with available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligand and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Accurate Characterization of Binding Kinetics and Allosteric Mechanisms for the HSP90 Chaperone Inhibitors Using AI-Augmented Integrative Biophysical Studies

The binding kinetics of drugs to their targets are gradually being recognized as a crucial indicator of the efficacy of drugs in vivo, leading to the development of various computational methods for predicting the binding kinetics in recent years. However, compared with the prediction of binding affinity, the underlying structure and dynamic determinants of binding kinetics are more complicated. Efficient and accurate methods for predicting binding kinetics are still lacking. In this study, quantitative structure-kinetics relationship (QSKR) models were developed using 132 inhibitors targeting the ATP binding domain of heat shock protein 90α (HSP90α) to predict the dissociation rate constant (koff), enabling a direct assessment of the drug-target residence time. These models demonstrated good predictive performance, where hydrophobic and hydrogen bond interactions significantly influence the koff prediction. In subsequent applications, our models were used to assist in the discovery of new inhibitors for the N-terminal domain of HSP90α (N-HSP90α), demonstrating predictive capabilities on an experimental validation set with a new scaffold. In X-ray crystallography experiments, the loop-middle conformation of apo N-HSP90α was observed for the first time (previously, the loop-middle conformation had only been observed in holo-N-HSP90α structures). Interestingly, we observed different conformations of apo N-HSP90α simultaneously in an asymmetric unit, which was also observed in a holo-N-HSP90α structure, suggesting an equilibrium of conformations between different states in solution, which could be one of the determinants affecting the binding kinetics of the ligand. Different ligands can undergo conformational selection or alter the equilibrium of conformations, inducing conformational rearrangements and resulting in different effects on binding kinetics. We then used molecular dynamics simulations to describe conformational changes of apo N-HSP90α in different conformational states. In summary, the study of the binding kinetics and molecular mechanisms of N-HSP90α provides valuable information for the development of more targeted therapeutic approaches.

How Robust Is the Ligand Binding Transition State?

For many drug targets, it has been shown that the kinetics of drug binding (e.g., on rate and off rate) is more predictive of drug efficacy than thermodynamic quantities alone. This motivates the development of predictive computational models that can be used to optimize compounds on the basis of their kinetics. The structural details underpinning these computational models are found not only in the bound state but also in the short-lived ligand binding transition states. Although transition states cannot be directly observed experimentally due to their extremely short lifetimes, recent successes have demonstrated that modeling the ligand binding transition state is possible with the help of enhanced sampling molecular dynamics methods. Previously, we generated unbinding paths for an inhibitor of soluble epoxide hydrolase (sEH) with a residence time of 11 min. Here, we computationally modeled unbinding events with the weighted ensemble method REVO (resampling of ensembles by variation optimization) for five additional inhibitors of sEH with residence times ranging from 14.25 to 31.75 min, with average prediction accuracy within an order of magnitude. The unbinding ensembles are analyzed in detail, focusing on features of the ligand binding transition state ensembles (TSEs). We find that ligands with similar bound poses can show significant differences in their ligand binding TSEs, in terms of their spatial distribution and protein-ligand interactions. However, we also find similarities across the TSEs when examining more general features such as ligand degrees of freedom. Together these findings show significant challenges for rational, kinetics-based drug design.

SOURSOP: A Python Package for the Analysis of Simulations of Intrinsically Disordered Proteins

Conformational heterogeneity is a defining hallmark of intrinsically disordered proteins and protein regions (IDRs). The functions of IDRs and the emergent cellular phenotypes they control are associated with sequence-specific conformational ensembles. Simulations of conformational ensembles that are based on atomistic and coarse-grained models are routinely used to uncover the sequence-specific interactions that may contribute to IDR functions. These simulations are performed either independently or in conjunction with data from experiments. Functionally relevant features of IDRs can span a range of length scales. Extracting these features requires analysis routines that quantify a range of properties. Here, we describe a new analysis suite simulation analysis of unfolded regions of proteins (SOURSOP), an object-oriented and open-source toolkit designed for the analysis of simulated conformational ensembles of IDRs. SOURSOP implements several analysis routines motivated by principles in polymer physics, offering a unique collection of simple-to-use functions to characterize IDR ensembles. As an extendable framework, SOURSOP supports the development and implementation of new analysis routines that can be easily packaged and shared.

Adrenomedullin 2/intermedin is a slow off-rate, long-acting endogenous agonist of the adrenomedullin2 G protein-coupled receptor

Adrenomedullin 2/intermedin (AM2/IMD), adrenomedullin (AM), and calcitonin gene-related peptide (CGRP) have signaling functions in the cardiovascular, lymphatic, and nervous systems by activating three heterodimeric receptors comprised of the class B GPCR CLR and a RAMP1, -2, or -3 modulatory subunit. CGRP and AM prefer the RAMP1 and RAMP2/3 complexes, respectively, whereas AM2/IMD is thought to be relatively non-selective. Accordingly, AM2/IMD exhibits overlapping actions with CGRP and AM, so the rationale for this third agonist for the CLR-RAMP complexes is unclear. Here, we report that AM2/IMD is kinetically selective for CLR-RAMP3, known as the AM₂R, and we define the structural basis for its distinct kinetics. In live cell biosensor assays, AM2/IMD-AM₂R elicited substantially longer duration cAMP signaling than the eight other peptide-receptor combinations. AM2/IMD and AM bound the AM₂R with similar equilibrium affinities, but AM2/IMD had a much slower off-rate and longer receptor residence time, thus explaining its prolonged signaling capacity. Peptide and receptor chimeras and mutagenesis were used to map the regions responsible for the distinct binding and signaling kinetics to the AM2/IMD mid-region and the RAMP3 extracellular domain (ECD). Molecular dynamics simulations revealed how the former forms stable interactions at the CLR ECD-transmembrane domain interface and how the latter augments the CLR ECD binding pocket to anchor the AM2/IMD C-terminus. These two strong binding components only combine in the AM₂R. Our findings uncover AM2/IMD-AM₂R as a cognate pair with unique temporal features, reveal how AM2/IMD and RAMP3 collaborate to shape CLR signaling, and have significant implications for AM2/IMD biology.

Quality over quantity: Sampling high probability rare events with the weighted ensemble algorithm

The prediction of (un)binding rates and free energies is of great significance to the drug design process. Although many enhanced sampling algorithms and approaches have been developed, there is not yet a reliable workflow to predict these quantities. Previously we have shown that free energies and transition rates can be calculated by directly simulating the binding and unbinding processes with our variant of the WE algorithm "Resampling of Ensembles by Variation Optimization", or "REVO". Here, we calculate binding free energies retrospectively for three SAMPL6 host-guest systems and prospectively for a SAMPL9 system to test a modification of REVO that restricts its cloning behavior in quasi-unbound states. Specifically, trajectories cannot clone if they meet a physical requirement that represents a high likelihood of unbinding, which in the case of this work is a center-of-mass to center-of-mass distance. The overall effect of this change was difficult to predict, as it results in fewer unbinding events each of which with a much higher statistical weight. For all four systems tested, this new strategy produced either more accurate unbinding free energies or more consistent results between simulations than the standard REVO algorithm. This approach is highly flexible, and any feature of interest for a system can be used to determine cloning eligibility. These findings thus constitute an important improvement in the calculation of transition rates and binding free energies with the weighted ensemble method.

Predicting Biomolecular Binding Kinetics: A Review

Biomolecular binding kinetics including the association (k_on) and dissociation (k_off) rates are critical parameters for therapeutic design of small-molecule drugs, peptides, and antibodies. Notably, the drug molecule residence time or dissociation rate has been shown to correlate with their efficacies better than binding affinities. A wide range of modeling approaches including quantitative structure-kinetic relationship models, Molecular Dynamics simulations, enhanced sampling, and Machine Learning has been developed to explore biomolecular binding and dissociation mechanisms and predict binding kinetic rates. Here, we review recent advances in computational modeling of biomolecular binding kinetics, with an outlook for future improvements.

SOURSOP: A Python package for the analysis of simulations of intrinsically disordered proteins

Conformational heterogeneity is a defining hallmark of intrinsically disordered proteins and protein regions (IDRs). The functions of IDRs and the emergent cellular phenotypes they control are associated with sequence-specific conformational ensembles. Simulations of conformational ensembles that are based on atomistic and coarse-grained models are routinely used to uncover the sequence-specific interactions that may contribute to IDR functions. These simulations are performed either independently or in conjunction with data from experiments. Functionally relevant features of IDRs can span a range of length scales. Extracting these features requires analysis routines that quantify a range of properties. Here, we describe a new analysis suite SOURSOP, an object-oriented and open-source toolkit designed for the analysis of simulated conformational ensembles of IDRs. SOURSOP implements several analysis routines motivated by principles in polymer physics, offering a unique collection of simple-to-use functions to characterize IDR ensembles. As an extendable framework, SOURSOP supports the development and implementation of new analysis routines that can be easily packaged and shared.

Ligand Gaussian Accelerated Molecular Dynamics 2 (LiGaMD2): Improved Calculations of Ligand Binding Thermodynamics and Kinetics with Closed Protein Pocket

Ligand binding thermodynamics and kinetics are critical parameters for drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics from molecular simulations due to limited simulation timescales. Protein dynamics, especially in the ligand binding pocket, often plays an important role in ligand binding. Based on our previously developed Ligand Gaussian accelerated molecular dynamics (LiGaMD), here we present LiGaMD2 in which a selective boost potential was applied to both the ligand and protein residues in the binding pocket to improve sampling of ligand binding and dissociation. To validate the performance of LiGaMD2, the T4 lysozyme (T4L) mutants with open and closed pockets bound by different ligands were chosen as model systems. LiGaMD2 could efficiently capture repetitive ligand dissociation and binding within microsecond simulations of all T4L systems. The obtained ligand binding kinetic rates and free energies agreed well with available experimental values and previous modeling results. Therefore, LiGaMD2 provides an improved approach to sample opening of closed protein pockets for ligand dissociation and binding, thereby allowing for efficient calculations of ligand binding thermodynamics and kinetics.

Adrenomedullin 2/intermedin is a slow off-rate, long-acting endogenous agonist of the adrenomedullin 2 G protein-coupled receptor

The signaling peptides adrenomedullin 2/intermedin (AM2/IMD), adrenomedullin (AM), and CGRP have overlapping and distinct functions in the cardiovascular, lymphatic, and nervous systems by activating three shared receptors comprised of the class B GPCR CLR in complex with a RAMP1, -2, or -3 modulatory subunit. Here, we report that AM2/IMD, which is thought to be a non-selective agonist, is kinetically selective for CLR-RAMP3, known as the AM 2 R. AM2/IMD-AM 2 R elicited substantially longer duration cAMP signaling than the eight other peptide-receptor combinations due to AM2/IMD slow off-rate binding kinetics. The regions responsible for the slow off-rate were mapped to the AM2/IMD mid-region and the RAMP3 extracellular domain. MD simulations revealed how these bestow enhanced stability to the complex. Our results uncover AM2/IMD-AM 2 R as a cognate pair with unique temporal features, define the mechanism of kinetic selectivity, and explain how AM2/IMD and RAMP3 collaborate to shape the signaling output of a clinically important GPCR.

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.

CHARMM-GUI Implicit Solvent Modeler for Various Generalized Born Models in Different Simulation Programs

Implicit solvent models are widely used because they are advantageous to speed up simulations by drastically decreasing the number of solvent degrees of freedom, which allows one to achieve long simulation time scales for large system sizes. CHARMM-GUI, a web-based platform, has been developed to support the setup of complex multicomponent molecular systems and prepare input files. This study describes an Implicit Solvent Modeler (ISM) in CHARMM-GUI for various generalized Born (GB) implicit solvent simulations in different molecular dynamics programs such as AMBER, CHARMM, GENESIS, NAMD, OpenMM, and Tinker. The GB models available in ISM include GB-HCT, GB-OBC, GB-neck, GBMV, and GBSW with the CHARMM and Amber force fields for protein, DNA, RNA, glycan, and ligand systems. Using the system and input files generated by ISM, implicit solvent simulations of protein, DNA, and RNA systems produce similar results for different simulation packages with the same input information. Protein-ligand systems are also considered to further validate the systems and input files generated by ISM. Simple ligand root-mean-square deviation (RMSD) and molecular mechanics generalized Born surface area (MM/GBSA) calculations show that the performance of implicit simulations is better than docking and can be used for early stage ligand screening. These reasonable results indicate that ISM is a useful and reliable tool to provide various implicit solvent simulation applications.

Iterative Landmark-Based Umbrella Sampling (ILBUS) Protocol for Sampling of Conformational Space of Biomolecules

Computer simulations of biomolecules such as molecular dynamics often suffer from insufficient sampling. Due to limited computational resources, insufficient sampling prevents obtaining proper equilibrium distributions of observed properties. To deal with this problem, we proposed a simulation protocol for efficient resampling of collected off-equilibrium trajectories. These trajectories are utilized for the initial mapping of the conformational space, which is later properly resampled by the introduced Iterative Landmark-Based Umbrella Sampling (ILBUS) method. Reconstruction of static equilibrium properties is achieved by the multistate Bennett acceptance ratio (MBAR) method, which enables efficient use of simulated data. The ILBUS protocol is geometry-based and does not demand any additional collective variable or a dimensional-reduction technique. The only requirement is a set of suitably spaced reference conformations, which serve as landmarks in the mapped conformational space. Additionally, the ILBUS protocol encompasses an iterative process that optimizes the force constant used in the umbrella sampling simulation. Such tuning is an inherent feature of the protocol and does not need to be performed by the user in advance. Furthermore, even the simulations with suboptimal force constants can be used in estimates by MBAR. We demonstrate the feasibility and the performance of this approach in the study of the conformational landscape of the alanine dipeptide, met-enkephalin, and adenylate kinase.

Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.

Local Ion Densities can Influence Transition Paths of Molecular Binding

Improper reaction coordinates can pose significant problems for path-based binding free energy calculations. Particularly, omission of long timescale motions can lead to over-estimation of the energetic barriers between the bound and unbound states. Many methods exist to construct the optimal reaction coordinate using a pre-defined basis set of features. Although simulations are typically conducted in explicit solvent, the solvent atoms are often excluded by these feature sets—resulting in little being known about their role in reaction coordinates, and ultimately, their role in determining (un)binding rates and free energies. In this work, analysis is done on an extensive set of host-guest unbinding trajectories, working to characterize differences between high and low probability unbinding trajectories with a focus on solvent-based features, including host-ion interactions, guest-ion interactions and location-dependent ion densities. We find that differences in ion densities as well as guest-ion interactions strongly correlate with differences in the probabilities of reactive paths that are used to determine free energies of (un)binding and play a significant role in the unbinding process.

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.

Creating Maps of the Ligand Binding Landscape for Kinetics-Based Drug Discovery

Simulations of ligand-protein interactions can be very useful for drug design and to gain biological insight. Full pathways of ligand-protein binding can be used to get information about ligand binding transition states, which form the rate-limiting step of the binding and release processes. However, these simulations are typically limited by the presence of large energy barriers that separate stable poses of interest. Here we describe a simulation protocol for exploring and analyzing landscapes of ligand-protein interactions that makes use of molecular docking, enhanced molecular simulation with the weighted ensemble algorithm, and network analysis. It can be accomplished using a modest cluster of graphics processing units and freely accessible software. This protocol focuses on the construction and analysis of a network model of ligand binding poses and provides links to resources that describe the other steps in more detail. The end result of this protocol is a map of the ligand-protein binding landscape that identifies transition states of the ligand binding pathway, as well as alternative bound poses that could be stabilized with modifications to the ligand.

Molecular Paradigms for Biological Mechanosensing

Many proteins in living cells are subject to mechanical forces, which can be generated internally by molecular machines, or externally, e.g., by pressure gradients. In general, these forces fall in the piconewton range, which is similar in magnitude to forces experienced by a molecule due to thermal fluctuations. While we would naively expect such moderate forces to produce only minimal changes, a wide variety of "mechanosensing" proteins have evolved with functions that are responsive to forces in this regime. The goal of this article is to provide a physical chemistry perspective on protein-based molecular mechanosensing paradigms used in living systems, and how these paradigms can be explored using novel computational methods.

Ligand unbinding mechanisms and kinetics for T4 lysozyme mutants from τRAMD simulations

The protein-ligand residence time, τ, influences molecular function in biological networks and has been recognized as an important determinant of drug efficacy. To predict τ, computational methods must overcome the problem that τ often exceeds the timescales accessible to conventional molecular dynamics (MD) simulation. Here, we apply the τ-Random Acceleration Molecular Dynamics (τRAMD) method to a set of kinetically characterized complexes of T4 lysozyme mutants with small, engineered binding cavities. τRAMD yields relative ligand dissociation rates in good accordance with experiments across this diverse set of complexes that differ with regard to measurement temperature, ligand identity, protein mutation and binding cavity. τRAMD thereby allows a comprehensive characterization of the ligand egress routes and determinants of τ. Although ligand dissociation by multiple egress routes is observed, we find that egress via the predominant route determines the value of τ. We also find that the presence of a greater number of metastable states along egress pathways leads to slower protein-ligand dissociation. These physical insights could be exploited in the rational optimization of the kinetic properties of drug candidates.

•

Relative residence times are computed for T4 lysozyme mutant-ligand complexes.

•

τ-Random Acceleration Molecular Dynamics provide efficient sampling of unbinding.

•

Computed dissociation rates show good agreement with all available measured values.

•

Ligand egress via the predominant route determines the value of the residence time.

•

The presence of metastable states along egress pathways slows down dissociation.