Weighted-ensemble Brownian dynamics simulations for protein association reactions

Elucidating protein-ligand binding kinetics based on returning probability theory

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host-guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein-ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT.

Direct observation of negative cooperativity in a detoxification enzyme at the atomic level by Electron Paramagnetic Resonance spectroscopy and simulation

The catalytic activity of human glutathione S-transferase A1-1 (hGSTA1-1), a homodimeric detoxification enzyme, is dependent on the conformational dynamics of a key C-terminal helix α9 in each monomer. However, the structural details of how the two monomers interact upon binding of substrates is not well understood and the structure of the ligand-free state of the hGSTA1-1 homodimer has not been resolved. Here, we used a combination of electron paramagnetic resonance (EPR) distance measurements and weighted ensemble (WE) simulations to characterize the conformational ensemble of the ligand-free state at the atomic level. EPR measurements reveal a broad distance distribution between a pair of Cu(II) labels in the ligand-free state that gradually shifts and narrows as a function of increasing ligand concentration. These shifts suggest changes in the relative positioning of the two α9 helices upon ligand binding. WE simulations generated unbiased pathways for the seconds-timescale transition between alternate states of the enzyme, leading to the generation of atomically detailed structures of the ligand-free state. Notably, the simulations provide direct observations of negative cooperativity between the monomers of hGSTA1-1, which involve the mutually exclusive docking of α9 in each monomer as a lid over the active site. We identify key interactions between residues that lead to this negative cooperativity. Negative cooperativity may be essential for interaction of hGSTA1-1 with a wide variety of toxic substrates and their subsequent neutralization. More broadly, this work demonstrates the power of integrating EPR distances with WE rare-events sampling strategy to gain mechanistic information on protein function at the atomic level.

Perspectives on Ligand/Protein Binding Kinetics Simulations: Force Fields, Machine Learning, Sampling, and User-Friendliness

Computational techniques applied to drug discovery have gained considerable popularity for their ability to filter potentially active drugs from inactive ones, reducing the time scale and costs of preclinical investigations. The main focus of these studies has historically been the search for compounds endowed with high affinity for a specific molecular target to ensure the formation of stable and long-lasting complexes. Recent evidence has also correlated the in vivo drug efficacy with its binding kinetics, thus opening new fascinating scenarios for ligand/protein binding kinetic simulations in drug discovery. The present article examines the state of the art in the field, providing a brief summary of the most popular and advanced ligand/protein binding kinetics techniques and evaluating their current limitations and the potential solutions to reach more accurate kinetic models. Particular emphasis is put on the need for a paradigm change in the present methodologies toward ligand and protein parametrization, the force field problem, characterization of the transition states, the sampling issue, and algorithms' performance, user-friendliness, and data openness.

Kinetics from Metadynamics: Principles, Applications, and Outlook

Metadynamics is a popular enhanced sampling algorithm for computing the free energy landscape of rare events by using molecular dynamics simulation. Ten years ago, Tiwary and Parrinello introduced the infrequent metadynamics approach for calculating the kinetics of transitions across free energy barriers. Since then, metadynamics-based methods for obtaining rate constants have attracted significant attention in computational molecular science. Such methods have been applied to study a wide range of problems, including protein-ligand binding, protein folding, conformational transitions, chemical reactions, catalysis, and nucleation. Here, we review the principles of elucidating kinetics from metadynamics-like approaches, subsequent methodological developments in this area, and successful applications on chemical, biological, and material systems. We also highlight the challenges of reconstructing accurate kinetics from enhanced sampling simulations and the scope of future developments.

Worth the Weight: Sub-Pocket EXplorer (SubPEx), a Weighted Ensemble Method to Enhance Binding-Pocket Conformational Sampling

Structure-based virtual screening (VS) is an effective method for identifying potential small-molecule ligands, but traditional VS approaches consider only a single binding-pocket conformation. Consequently, they struggle to identify ligands that bind to alternate conformations. Ensemble docking helps address this issue by incorporating multiple conformations into the docking process, but it depends on methods that can thoroughly explore pocket flexibility. We here introduce Sub-Pocket EXplorer (SubPEx), an approach that uses weighted ensemble (WE) path sampling to accelerate binding-pocket sampling. As proof of principle, we apply SubPEx to three proteins relevant to drug discovery: heat shock protein 90, influenza neuraminidase, and yeast hexokinase 2. SubPEx is available free of charge without registration under the terms of the open-source MIT license: http://durrantlab.com/subpex/.

Targeted Protein Degradation: Advances, Challenges, and Prospects for Computational Methods

The therapeutic approach of targeted protein degradation (TPD) is gaining momentum due to its potentially superior effects compared with protein inhibition. Recent advancements in the biotech and pharmaceutical sectors have led to the development of compounds that are currently in human trials, with some showing promising clinical results. However, the use of computational tools in TPD is still limited, as it has distinct characteristics compared with traditional computational drug design methods. TPD involves creating a ternary structure (protein-degrader-ligase) responsible for the biological function, such as ubiquitination and subsequent proteasomal degradation, which depends on the spatial orientation of the protein of interest (POI) relative to E2-loaded ubiquitin. Modeling this structure necessitates a unique blend of tools initially developed for small molecules (e.g., docking) and biologics (e.g., protein-protein interaction modeling). Additionally, degrader molecules, particularly heterobifunctional degraders, are generally larger than conventional small molecule drugs, leading to challenges in determining drug-like properties like solubility and permeability. Furthermore, the catalytic nature of TPD makes occupancy-based modeling insufficient. TPD consists of multiple interconnected yet distinct steps, such as POI binding, E3 ligase binding, ternary structure interactions, ubiquitination, and degradation, along with traditional small molecule properties. A comprehensive set of tools is needed to address the dynamic nature of the induced proximity ternary complex and its implications for ubiquitination. In this Perspective, we discuss the current state of computational tools for TPD. We start by describing the series of steps involved in the degradation process and the experimental methods used to characterize them. Then, we delve into a detailed analysis of the computational tools employed in TPD. We also present an integrative approach that has proven successful for degrader design and its impact on project decisions. Finally, we examine the future prospects of computational methods in TPD and the areas with the greatest potential for impact.

Uncertainties in Markov State Models of Small Proteins

Markov state models are widely used to describe and analyze protein dynamics based on molecular dynamics simulations, specifically to extract functionally relevant characteristic time scales and motions. Particularly for larger biomolecules such as proteins, however, insufficient sampling is a notorious concern and often the source of large uncertainties that are difficult to quantify. Furthermore, there are several other sources of uncertainty, such as choice of the number of Markov states and lag time, choice and parameters of dimension reduction preprocessing step, and uncertainty due to the limited number of observed transitions; the latter is often estimated via a Bayesian approach. Here, we quantified and ranked all of these uncertainties for four small globular test proteins. We found that the largest uncertainty is due to insufficient sampling and initially increases with the total trajectory length T up to a critical tipping point, after which it decreases as 1 / T , thus providing guidelines for how much sampling is required for given accuracy. We also found that single long trajectories yielded better sampling accuracy than many shorter trajectories starting from the same structure. In comparison, the remaining sources of the above uncertainties are generally smaller by a factor of about 5, rendering them less of a concern but certainly not negligible. Importantly, the Bayes uncertainty, commonly used as the only uncertainty estimate, captures only a relatively small part of the true uncertainty, which is thus often drastically underestimated.

AlphaFold2-RAVE: From Sequence to Boltzmann Ranking

While AlphaFold2 is rapidly being adopted as a new standard in protein structure predictions, it is limited to single structures. This can be insufficient for the inherently dynamic world of biomolecules. In this Letter, we propose AlphaFold2-RAVE, an efficient protocol for obtaining Boltzmann-ranked ensembles from sequence. The method uses structural outputs from AlphaFold2 as initializations for artificial intelligence-augmented molecular dynamics. We release the method as an open-source code and demonstrate results on different proteins.

15 Years of molecular simulation of drug-binding kinetics

INTRODUCTION

Drug-binding kinetics has been increasingly recognized as an important factor to be considered in drug discovery. Long residence time could prolong the action of some drugs while produce toxicity on others. Early evaluation of the binding kinetics of drug candidates could reduce attrition rate late in the drug discovery process. Computational prediction of drug-binding kinetics is useful as compounds can be evaluated even before they are made. However, simulation of drug-binding kinetics is a challenging problem because of the long-time scale involved. Nevertheless, significant progress has been made.

AREAS COVERED

This review illustrates the rapid evolution of qualitative to quantitative molecular dynamics-based methods that have been developed over the last 15 years.

EXPERT OPINION

The development of new methods based on molecular dynamics simulations now enables computation of absolute association/dissociation rate constants. Cheaper methods capable of identifying candidates with fast or slow binding kinetics, or rank-ordering rate constants are also available. Together, these methods have generated useful insights into the molecular mechanisms of drug-binding kinetics, and the design of drug candidates with therapeutically favorable kinetics. Although predicting absolute rate constants is still expensive and challenging, rapid improvement is expected in the coming years with the continuing refinement of current technologies, development of new methodologies, and the utilization of machine learning.

pyCHARMM: Embedding CHARMM Functionality in a Python Framework

CHARMM is rich in methodology and functionality as one of the first programs addressing problems of molecular dynamics and modeling of biological macromolecules and their partners, e.g., small molecule ligands. When combined with the highly developed CHARMM parameters for proteins, nucleic acids, small molecules, lipids, sugars, and other biologically relevant building blocks, and the versatile CHARMM scripting language, CHARMM has been a trendsetting platform for modeling studies of biological macromolecules. To further enhance the utility of accessing and using CHARMM functionality in increasingly complex workflows associated with modeling biological systems, we introduce pyCHARMM, Python bindings, functions, and modules to complement and extend the extensive set of modeling tools and methods already available in CHARMM. These include access to CHARMM function-generated variables associated with the system (psf), coordinates, velocities and forces, atom selection variables, and force field related parameters. The ability to augment CHARMM forces and energies with energy terms or methods derived from machine learning or other sources, written in Python, CUDA, or OpenCL and expressed as Python callable routines is introduced together with analogous functions callable during dynamics calculations. Integration of Python-based graphical engines for visualization of simulation models and results is also accessible. Loosely coupled parallelism is available for workflows such as free energy calculations, using MBAR/TI approaches or high-throughput multisite λ-dynamics (MSλD) free energy methods, string path optimization calculations, replica exchange, and molecular docking with a new Python-based CDOCKER module. CHARMM accelerated platform kernels through the CHARMM/OpenMM API, CHARMM/DOMDEC, and CHARMM/BLaDE API are also readily integrated into this Python framework. We anticipate that pyCHARMM will be a robust platform for the development of comprehensive and complex workflows utilizing Python and its extensive functionality as well as an optimal platform for users to learn molecular modeling methods and practices within a Python-friendly environment such as Jupyter Notebooks.

Molecular Mechanism of Ligand Binding to the Minor Groove of DNA

Although DNA-ligand binding is pervasive in biology, little is known about molecular-level binding mechanisms. Using all-atom, explicit-solvent molecular dynamics simulations in conjunction with weighted ensemble (WE)-enhanced sampling, an ensemble of 2562 binding trajectories of Hoechst 33258 (H33258) to d(CGC AAA TTT GCG) was generated from which the binding mechanism was extracted. In particular, the electrostatic interaction between the positively charged H33258 and the negatively charged DNA backbone drives the formation of initial H33258-DNA contacts. After this initial contact, a hinge-like intermediate state is formed in which one end of H33258 inserts into the minor groove of DNA. Following hinge state formation is a concerted motion whereby the second end of H33258 swings into the minor groove and the spine of hydration along the minor groove causing dehydration. This study illustrates how WE-enhanced simulations of biomolecular ligation processes can offer novel mechanistic insights by generating ensembles of binding events.

Machine Learning-Driven Multiscale Modeling: Bridging the Scales with a Next-Generation Simulation Infrastructure

Interdependence across time and length scales is common in biology, where atomic interactions can impact larger-scale phenomenon. Such dependence is especially true for a well-known cancer signaling pathway, where the membrane-bound RAS protein binds an effector protein called RAF. To capture the driving forces that bring RAS and RAF (represented as two domains, RBD and CRD) together on the plasma membrane, simulations with the ability to calculate atomic detail while having long time and large length- scales are needed. The Multiscale Machine-Learned Modeling Infrastructure (MuMMI) is able to resolve RAS/RAF protein-membrane interactions that identify specific lipid-protein fingerprints that enhance protein orientations viable for effector binding. MuMMI is a fully automated, ensemble-based multiscale approach connecting three resolution scales: (1) the coarsest scale is a continuum model able to simulate milliseconds of time for a 1 μm2 membrane, (2) the middle scale is a coarse-grained (CG) Martini bead model to explore protein-lipid interactions, and (3) the finest scale is an all-atom (AA) model capturing specific interactions between lipids and proteins. MuMMI dynamically couples adjacent scales in a pairwise manner using machine learning (ML). The dynamic coupling allows for better sampling of the refined scale from the adjacent coarse scale (forward) and on-the-fly feedback to improve the fidelity of the coarser scale from the adjacent refined scale (backward). MuMMI operates efficiently at any scale, from a few compute nodes to the largest supercomputers in the world, and is generalizable to simulate different systems. As computing resources continue to increase and multiscale methods continue to advance, fully automated multiscale simulations (like MuMMI) will be commonly used to address complex science questions.

Worth the weight: Sub-Pocket EXplorer (SubPEx), a weighted-ensemble method to enhance binding-pocket conformational sampling

Structure-based virtual screening (VS) is an effective method for identifying potential small-molecule ligands, but traditional VS approaches consider only a single binding-pocket conformation. Consequently, they struggle to identify ligands that bind to alternate conformations. Ensemble docking helps address this issue by incorporating multiple conformations into the docking process, but it depends on methods that can thoroughly explore pocket flexibility. We here introduce Sub-Pocket EXplorer (SubPEx), an approach that uses weighted ensemble (WE) path sampling to accelerate binding-pocket sampling. As proof of principle, we apply SubPEx to three proteins relevant to drug discovery: heat shock protein 90, influenza neuraminidase, and yeast hexokinase 2. SubPEx is available free of charge without registration under the terms of the open-source MIT license: http://durrantlab.com/subpex/.

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.

Computational approaches for the design of modulators targeting protein-protein interactions

BACKGROUND

Protein-protein interactions (PPIs) are intriguing targets for designing novel small-molecule inhibitors. The role of PPIs in various infectious and neurodegenerative disorders makes them potential therapeutic targets . Despite being portrayed as undruggable targets, due to their flat surfaces, disorderedness, and lack of grooves. Recent progresses in computational biology have led researchers to reconsider PPIs in drug discovery.

AREAS COVERED

In this review, we introduce in-silico methods used to identify PPI interfaces and present an in-depth overview of various computational methodologies that are successfully applied to annotate the PPIs. We also discuss several successful case studies that use computational tools to understand PPIs modulation and their key roles in various physiological processes.

EXPERT OPINION

Computational methods face challenges due to the inherent flexibility of proteins, which makes them expensive, and result in the use of rigid models. This problem becomes more significant in PPIs due to their flexible and flat interfaces. Computational methods like molecular dynamics (MD) simulation and machine learning can integrate the chemical structure data into biochemical and can be used for target identification and modulation. These computational methodologies have been crucial in understanding the structure of PPIs, designing PPI modulators, discovering new drug targets, and predicting treatment outcomes.

DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling

Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.

Dissecting the general mechanisms of protein cage self-assembly by coarse-grained simulations

The development of artificial protein cages has recently gained massive attention due to their promising application prospect as novel delivery vehicles for therapeutics. These nanoparticles are formed through a process called self-assembly, in which individual subunits spontaneously arrange into highly ordered patterns via non-covalent but specific interactions. Therefore, the first step toward the design of novel engineered protein cages is to understand the general mechanisms of their self-assembling dynamics. Here we have developed a new computational method to tackle this problem. Our method is based on a coarse-grained model and a diffusion-reaction simulation algorithm. Using a tetrahedral cage as test model, we showed that self-assembly of protein cage requires of a seeding process in which specific configurations of kinetic intermediate states are identified. We further found that there is a critical concentration to trigger self-assembly of protein cages. This critical concentration allows that cages can only be successfully assembled under a persistently high concentration. Additionally, phase diagram of self-assembly has been constructed by systematically testing the model across a wide range of binding parameters. Finally, our simulations demonstrated the importance of protein's structural flexibility in regulating the dynamics of cage assembly. In summary, this study throws lights on the general principles underlying self-assembly of large cage-like protein complexes and thus provides insights to design new nanomaterials.

Sampling rare event energy landscapes via birth-death augmented dynamics

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the presences of high kinetic barriers that hinder transitions between metastable states on typical simulation time scales. Many enhanced sampling methods have been developed to address this sampling problem and more efficiently sample rare event systems. An interesting idea, coming from the field of statistics, was introduced in a recent work [Lu, Lu, and Nolen, Accelerating Langevin sampling with birth-death, arXiv:1905.09863] in the form of a novel sampling algorithm that augments overdamped Langevin dynamics with a birth-death process. In this work, we expand on this idea and show that this birth-death sampling scheme can efficiently sample prototypical rare event energy landscapes, and that the speed of equilibration is independent of the barrier height. We amend a crucial shortcoming of the original algorithm that leads to incorrect sampling of barrier regions by introducing an alternative approximation of the birth-death term. We establish important theoretical properties of the modified algorithm and prove mathematically that the relevant convergence results still hold. We investigate via numerical simulations the effect of various parameters, and we investigate ways to reduce the computational effort of the sampling scheme. We show that the birth-death mechanism can be used to accelerate sampling in the more general case of underdamped Langevin dynamics that is more commonly used in simulating physical systems. Our results show that this birth-death scheme is a promising method for sampling rare event energy landscapes.

Translocation of a single Arg[Formula: see text] peptide across a DOPC/DOPG(4:1) model membrane using the weighted ensemble method

It is difficult to observe a spontaneous translocation of cell-penetrating peptides(CPPs) within a short time scale (e.g., a few hundred ns) in all-atom molecular dynamics(MD) simulations because the time required for the translocation of usual CPPs is on the order of minutes or so. In this work, we report a spontaneous translocation of a single Arg[Formula: see text](R9) across a DOPC/DOPG(4:1) model membrane within an order of a few tens ns scale by using the weighted ensemble(WE) method. We identify how water molecules and the orientation of Arg[Formula: see text] play a role in translocation. We also show how lipid molecules are transported along with Arg[Formula: see text]. In addition, we present free energy profiles of the translocation across the membrane using umbrella sampling and show that a single Arg[Formula: see text] translocation is energetically unfavorable. We expect that the WE method can help study interactions of CPPs with various model membranes within MD simulation approaches.

A Comparison of Weighted Stochastic Simulation Methods for the Analysis of Genetic Circuits

Rare events are of particular interest in synthetic biology because rare biochemical events may be catastrophic to a biological system by, for example, triggering irreversible events such as off-target drug delivery. To estimate the probability of rare events efficiently, several weighted stochastic simulation methods have been developed. Under optimal parameters and model conditions, these methods can greatly improve simulation efficiency in comparison to traditional stochastic simulation. Unfortunately, the optimal parameters and conditions cannot be deduced a priori. This paper presents a critical survey of weighted stochastic simulation methods. It shows that the methods considered here cannot consistently, efficiently, and exactly accomplish the task of rare event simulation without resorting to a computationally expensive calibration procedure, which undermines their overall efficiency. The results suggest that further development is needed before these methods can be deployed for general use in biological simulations.

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.

Binding and Unbinding Pathways of Peptide Substrates on the SARS-CoV-2 3CL Protease

Based on many crystal structures of ligand complexes, much study has been devoted to understanding the molecular recognition of SARS-CoV-2 3C-like protease (3CL^pro), a potent drug target for COVID-19. In this research, to extend this present static view, we examined the kinetic process of binding/unbinding of an eight-residue substrate peptide to/from 3CL^pro by evaluating the path ensemble with the weighted ensemble simulation. The path ensemble showed the mechanism of how a highly flexible peptide folded into the bound form. At the early stage, the dominant motion was the diffusion on the protein surface showing a broad distribution, whose center was led into the cleft of the chymotrypsin fold. We observed a definite sequential formation of the hydrogen bonds at the later stage occurring in the cleft, initiated between Glu166 (3CL^pro) and P3_Val (peptide), followed by binding to the oxyanion hole and completed by the sequence-specific recognition at P1_Gln.

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.

#COVIDisAirborne: AI-enabled multiscale computational microscopy of delta SARS-CoV-2 in a respiratory aerosol

We seek to completely revise current models of airborne transmission of respiratory viruses by providing never-before-seen atomic-level views of the SARS-CoV-2 virus within a respiratory aerosol. Our work dramatically extends the capabilities of multiscale computational microscopy to address the significant gaps that exist in current experimental methods, which are limited in their ability to interrogate aerosols at the atomic/molecular level and thus obscure our understanding of airborne transmission. We demonstrate how our integrated data-driven platform provides a new way of exploring the composition, structure, and dynamics of aerosols and aerosolized viruses, while driving simulation method development along several important axes. We present a series of initial scientific discoveries for the SARS-CoV-2 Delta variant, noting that the full scientific impact of this work has yet to be realized.

Protein Structure Validation Derives a Smart Conformational Search in a Physically Relevant Configurational Subspace

Since proteins perform biological functions through their dynamic properties, molecular dynamics (MD) simulation is a sophisticated strategy for investigating their functions. Analyses of trajectories provide statistical information about a specific protein as a free-energy landscape (FEL). However, the timescale of normal MD is shorter than that of biological functions, resulting in statistically insufficient conformational sampling, finally leading to unreliable FEL calculation. To search for a broad configurational subspace, an external bias is imposed on a target protein as biased sampling. However, its regulation is challenging because the optimal strength of the perturbation is unknown. Furthermore, a physically irrelevant configurational subspace was searched when imposing an inappropriate external bias. To address this issue, we newly proposed an external biased regulation scheme known as the G-factor external bias limiter (GERBIL). In GERBIL, protein configurations generated by external bias are structurally validated by an indicator (G-factor), enabling the search for a physically relevant subspace. In addition to biased sampling, nonbiased sampling might search for a physically irrelevant configurational subspace because repeating multiple MD simulations from several initial structures tends to search for an overly broad configurational subspace. For this issue, the structural qualities of configurations generated by nonbiased sampling have not been investigated. Therefore, we confirmed whether the G-factor screened the collapsed (low-quality) configurations generated by nonbiased sampling. To address this issue, the outlier flooding method (OFLOOD) was adopted in GERBIL as a nonbiased sampling method, which is referred to as OFLOOD-GERBIL. OFLOOD rapidly expands a configurational subspace by resampling the rarely occurring states of a given protein and tends to search an overly broad subspace. Thus, we considered that GERBIL might improve the excessive conformational search of OFLOOD for a physically irrelevant configurational subspace. As a demonstration, OFLOOD and OFLOOD-GERBIL were applied to a globular protein (T4 lysozyme) and their conformational search qualities were assessed. Based on our assessment, normal OFLOOD without the outlier validation frequently sampled low-quality configurations, whereas OFLOOD-GERBIL with the outlier validation intensively sampled high-quality configurations. In conclusion, OFLOOD-GERBIL derives a smart conformational search in a physically relevant configurational subspace, indicating that protein structure validation works in both nonbiased and biased sampling methods.

ScMiles2: A Script to Conduct and Analyze Milestoning Trajectories for Long Time Dynamics

Milestoning is a theory and an algorithm that computes kinetics and thermodynamics at long time scales. It is based on partitioning the (phase) space into cells and running a large number of short trajectories between the boundaries of the cells. The termination points of the trajectories are analyzed with the Milestoning theory to obtain kinetic and thermodynamic information. Managing the tens to hundreds of thousands of Milestoning trajectories is a challenge, which we handle with a python script, ScMiles. Here, we introduce a new version of the python script ScMiles2 to conduct Milestoning simulations. Major enhancements are: (i) post analysis of Milestoning trajectories to obtain the free energy, mean first passage time, the committor function, and exit times; (ii) similar to (i) but the post analysis is for a single long trajectory; (iii) we support the use of the GROMACS software in addition to NAMD; (iv) a restart option; (v) the automated finding, sampling, and launching trajectories from new milestones that are found on the fly; and (vi) support Milestoning calculations with several coarse variables and for complex reaction coordinates. We also evaluate the simulation parameters and suggest new algorithmic features to enhance the rate of convergence of observables. We propose the use of an iteration-averaged kinetic matrix for a rapid approach to asymptotic values. Illustrations are provided for small systems and one large example.

Simulation of ligand dissociation kinetics from the protein kinase PYK2

Early-stage drug discovery projects often focus on equilibrium binding affinity to the target alongside selectivity and other pharmaceutical properties. The kinetics of drug binding are ignored but can have significant influence on drug efficacy. Therefore, increasing attention has been paid on evaluating drug-binding kinetics early in a drug discovery process. Simulating drug-binding kinetics at the atomic level is challenging for the long time scale involved. Here, we used the transition-based reweighting analysis method (TRAM) with the Markov state model to study the dissociation of a ligand from the protein kinase PYK2. TRAM combines biased and unbiased simulations to reduce computational costs. This work used the umbrella sampling technique for the biased simulations. Although using the potential of mean force from umbrella sampling simulations with the transition-state theory over-estimated the dissociation rate by three orders of magnitude, TRAM gave a dissociation rate within an order of magnitude of the experimental value.

Rare Event Kinetics from Adaptive Bias Enhanced Sampling

We introduce a novel enhanced sampling approach named on-the-fly probability enhanced sampling (OPES) flooding for calculating the kinetics of rare events from atomistic molecular dynamics simulation. This method is derived from the OPES approach [Invernizzi and Parrinello, J. Phys. Chem. Lett. 2020, 11, 7, 2731-2736], which has been recently developed for calculating converged free energy surfaces for complex systems. In this paper, we describe the theoretical details of the OPES flooding technique and demonstrate the application on three systems of increasing complexity: barrier crossing in a two-dimensional double-well potential, conformational transition in the alanine dipeptide in the gas phase, and the folding and unfolding of the chignolin polypeptide in an aqueous environment. From extensive tests, we show that the calculation of accurate kinetics not only requires the transition state to be bias-free, but the amount of bias deposited should also not exceed the effective barrier height measured along the chosen collective variables. In this vein, the possibility of computing rates from biasing suboptimal order parameters has also been explored. Furthermore, we describe the choice of optimum parameter combinations for obtaining accurate results from limited computational effort.

Ligand Unbinding Pathway and Mechanism Analysis Assisted by Machine Learning and Graph Methods

We present two methods to reveal protein-ligand unbinding mechanisms in biased unbinding simulations by clustering trajectories into ensembles representing unbinding paths. The first approach is based on a contact principal component analysis for reducing the dimensionality of the input data, followed by identification of unbinding paths and training a machine learning model for trajectory clustering. The second approach clusters trajectories according to their pairwise mean Euclidean distance employing the neighbor-net algorithm, which takes into account input data bias in the distances set and is superior to dendrogram construction. Finally, we describe a more complex case where the reaction coordinate relevant for path identification is a single intraligand hydrogen bond, highlighting the challenges involved in unbinding path reaction coordinate detection.

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.

Fluctuations and first-passage properties of systems of Brownian particles with reset

We study, analytically and numerically, stationary fluctuations in two models involving N Brownian particles undergoing stochastic resetting in one dimension. We start with the well-known reset model where the particles reset to the origin independently (model A). Then we introduce nonlocal interparticle correlations by postulating that only the particle farthest from the origin can be reset to the origin (model B). At long times, models A and B approach nonequilibrium steady states. In the limit of N→∞, the steady-state particle density in model A has an infinite support, whereas in model B, it has a compact support, like the recently studied Brownian bees model. A finite system radius, which scales at large N as lnN, appears in model A when N is finite. In both models, we study stationary fluctuations of the center of mass of the system and of the radius of the system due to the random character of the Brownian motion and of the resetting events. In model A, we determine exact distributions of these two quantities. The variance of the center of mass for both models scales as 1/N. The variance of the radius is independent of N in model A and exhibits an unusual scaling (lnN)/N in model B. The latter scaling is intimately related to the 1/f noise in the radius autocorrelation. Finally, we evaluate the mean first-passage time (MFPT) to a distant target in model A, model B, and the Brownian bees model. For model A, we obtain an exact asymptotic expression for the MFPT which scales as 1/N. For model B and the Brownian bees model, we propose a sharp upper bound for the MFPT. The bound assumes an evaporation scenario, where the first passage requires multiple attempts of a single particle, which breaks away from the rest of the particles, to reach the target. The resulting MFPT for model B and the Brownian bees model scales exponentially with sqrt[N]. We verify this bound by performing highly efficient weighted-ensemble simulations of the first passage in model B.

Computing transition path theory quantities with trajectory stratification

Transition path theory computes statistics from ensembles of reactive trajectories. A common strategy for sampling reactive trajectories is to control the branching and pruning of trajectories so as to enhance the sampling of low probability segments. However, it can be challenging to apply transition path theory to data from such methods because determining whether configurations and trajectory segments are part of reactive trajectories requires looking backward and forward in time. Here, we show how this issue can be overcome efficiently by introducing simple data structures. We illustrate the approach in the context of nonequilibrium umbrella sampling, but the strategy is general and can be used to obtain transition path theory statistics from other methods that sample segments of unbiased trajectories.

Structural Validation by the G-Factor Properly Regulates Boost Potentials Imposed in Conformational Sampling of Proteins

Free energy landscapes (FELs) of proteins are indispensable for evaluating thermodynamic properties. Molecular dynamics (MD) simulation is a computational method for calculating FELs; however, conventional MD simulation frequently fails to search a broad conformational subspace due to its accessible timescale, which results in the calculation of an unreliable FEL. To search a broad subspace, an external bias can be imposed on a protein system, and biased sampling tends to cause a strong perturbation that might collapse the protein structures, indicating that the strength of the external bias should be properly regulated. This regulation can be challenging, and empirical parameters are frequently employed to impose an optimal bias. To address this issue, several methods regulate the external bias by referring to system energies. Herein, we focused on protein structural information for this regulation. In this study, a well-established structural indicator (the G-factor) was used to obtain structural information. Based on the G-factor, we proposed a scheme for regulating biased sampling, which is referred to as a G-factor-based external bias limiter (GERBIL). With GERBIL, the configurations were structurally validated by the G-factor during biased sampling. As an example of biased sampling, an accelerated MD (aMD) simulation was adopted in GERBIL (aMD-GERBIL), whereby the aMD simulation was repeatedly performed by increasing the strength of the boost potential. Furthermore, the configurations sampled by the aMD simulation were structurally validated by their G-factor values, and aMD-GERBIL stopped increasing the strength of the boost potential when the sampled configurations were regarded as low-quality (collapsed) structures. This structural validation is regarded as a "Brake" of the boost potential. For demonstrations, aMD-GERBIL was applied to globular proteins (ribose binding and maltose-binding proteins) to promote their large-amplitude open-closed transitions and successfully identify their domain motions.

SEEKR2: Versatile Multiscale Milestoning Utilizing the OpenMM Molecular Dynamics Engine

We present SEEKR2 (simulation-enabled estimation of kinetic rates version 2)—the latest iteration in the family of SEEKR programs for using multiscale simulation methods to computationally estimate the kinetics and thermodynamics of molecular processes, in particular, ligand-receptor binding. SEEKR2 generates equivalent, or improved, results compared to the earlier versions of SEEKR but with significant increases in speed and capabilities. SEEKR2 has also been built with greater ease of usability and with extensible features to enable future expansions of the method. Now, in addition to supporting simulations using NAMD, calculations may be run with the fast and extensible OpenMM simulation engine. The Brownian dynamics portion of the calculation has also been upgraded to Browndye 2. Furthermore, this version of SEEKR supports hydrogen mass repartitioning, which significantly reduces computational cost, while showing little, if any, loss of accuracy in the predicted kinetics.

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.

Sampling rare trajectories using stochastic bridges

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. Further, we also compare the stochastic bridges we produce to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the generated paths, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that the method can also be used to judge the accuracy of the WKB approximation at finite levels of noise.

Practical guide to replica exchange transition interface sampling and forward flux sampling

Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of the so-called rare events that are characterized by transitions between metastable states separated by sizable free energy barriers. Their practical application, in particular to ever more complex molecular systems, is, however, not entirely trivial. Focusing on replica exchange transition interface sampling (RETIS) and forward flux sampling (FFS), we discuss a range of analysis tools that can be used to assess the quality and convergence of such simulations, which is crucial to obtain reliable results. The basic ideas of a step-wise evaluation are exemplified for the study of nucleation in several systems with different complexities, providing a general guide for the critical assessment of RETIS and FFS simulations.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

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.

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.

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Dissociation Pathways of the p53 DNA Binding Domain from DNA and Critical Roles of Key Residues Elucidated by dPaCS-MD/MSM

p53 is a transcriptional factor that regulates cell response to a variety of stresses. About a half of all human tumors contain p53 mutations, and the accumulation of mutations in the DNA binding domain of p53 (p53-DBD) can cause destabilization of p53 and its complex with DNA. To identify the key residues of the p53-DBD/DNA binding and to understand the dissociation mechanisms of the p53-DBD/DNA complex, the dissociation process of p53-DBD from a DNA duplex that contains the consensus sequence (the specific target of p53-DBD) was investigated by a combination of dissociation parallel cascade selection molecular dynamics (dPaCS-MD) and the Markov state model (MSM). This combination (dPaCS-MD/MSM) enabled us to simulate dissociation of the two large molecules based on an all-atom model with a short simulation time (11.2 ± 2.2 ns per trial) and to analyze dissociation pathways, free energy landscape (FEL), and binding free energy. Among 75 trials of dPaCS-MD, p53-DBD dissociated first from the major groove and then detached from the minor groove in 93% of the cases, while 7% of the cases unbinding from the minor groove occurred first. Minor groove binding is mainly stabilized by R248, identified as the most important residue that tightly binds deep inside the minor groove. The standard binding free energy calculated from the FEL was -10.9 ± 0.4 kcal/mol, which agrees with an experimental value of -11.1 kcal/mol. These results indicate that the dPaCS-MD/MSM combination can be a powerful tool to investigate dissociation mechanisms of two large molecules. Analysis of the p53 key residues for DNA binding indicates high correlations with cancer-related mutations, confirming that impairment of the interactions between p53-DBD and DNA can be frequently related to cancer.

Simulation of receptor triggering by kinetic segregation shows role of oligomers and close-contacts

The activation of T cells, key players of the immune system, involves local evacuation of phosphatase CD45 from a region of the T cell's surface, segregating it from the T cell receptor. What drives this evacuation? In the presence of antigen, what ensures evacuation happens in the subsecond timescales necessary to initiate signaling? In the absence of antigen, what mechanisms ensure that evacuation does not happen spontaneously, which could cause signaling errors? Phenomena known to influence spatial organization of CD45 or similar surface molecules include diffusive motion in the lipid bilayer, oligomerization reactions, and mechanical compression against a nearby surface, such as that of the cell presenting the antigen. Computer simulations can investigate hypothesized spatiotemporal mechanisms of T cell signaling. The challenge to computational studies of evacuation is that the base process, spontaneous evacuation by simple diffusion, is in the extreme rare event limit, meaning direct stochastic simulation is unfeasible. Here, we combine particle-based spatial stochastic simulation with the weighted ensemble method for rare events to compute the mean first passage time for cell surface availability by surface reorganization of CD45. We confirm mathematical estimates that, at physiological concentrations, spontaneous evacuation is extremely rare, roughly 300 years. We find that dimerization decreases the time required for evacuation. A weak bimolecular interaction (dissociation constant estimate 460 μM) is sufficient for an order of magnitude reduction of spontaneous evacuation times, and oligomerization to hexamers reduces times to below 1 s. This introduces a mechanism whereby externally induced CD45 oligomerization could significantly modify T cell function. For large regions of close contact, such as those induced by large microvilli, molecular size and compressibility imply a nonzero reentry probability of 60%, decreasing evacuation times. Simulations show that these reduced evacuation times are still unrealistically long (even with a fourfold variation centered around previous estimates of parameters), suggesting that a yet-to-be-described mechanism, besides compressional exclusion at a close contact, drives evacuation.

Binding free energy of protein/ligand complexes calculated using dissociation Parallel Cascade Selection Molecular Dynamics and Markov state model

We recently proposed a computational procedure to simulate the dissociation of protein/ligand complexes using the dissociation Parallel Cascade Selection Molecular Dynamics simulation (dPaCS-MD) method and to analyze the generated trajectories using the Markov state model (MSM). This procedure, called dPaCS-MD/MSM, enables calculation of the dissociation free energy profile and the standard binding free energy. To examine whether this method can reproduce experimentally determined binding free energies for a variety of systems, we used it to investigate the dissociation of three protein/ligand complexes: trypsin/benzamine, FKBP/FK506, and adenosine A_2A receptor/T4E. First, dPaCS-MD generated multiple dissociation pathways within a reasonable computational time for all the complexes, although the complexes differed significantly in the size of the molecules and in intermolecular interactions. Subsequent MSM analyses produced free energy profiles for the dissociations, which provided insights into how each ligand dissociates from the protein. The standard binding free energies obtained by dPaCS-MD/MSM are in good agreement with experimental values for all the complexes. We conclude that dPaCS-MD/MSM can accurately calculate the binding free energies of these complexes.

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.

Modeling biomolecular kinetics with large-scale simulation

The molecular details of biomolecular kinetics present a challenging estimation problem because the identities of relevant intermediates and the rates of exchange between them must be determined. These can be derived from prior knowledge, but in recent years, great advances have been made in the development and application of methods to systematically determine states and rates using biomolecular simulation. Doing this for biological systems of reasonable complexity requires substantial computational power, and contemporary methods leverage distributed computing or leadership-class computing resources to accomplish this. The result has been substantial insight into pressing contemporary problems, including structural activation of pandemic viruses. Here, we highlight recent developments in both methodology and exciting applications.