arXiv subjects

Michael R. Shirts

Publications and source records attributed to Michael R. Shirts.

At least 19 recordsLinked to original sources

arXiv2026

Improving sampling of binding free energy differences between covalently bound ligands in alternate binding pockets using MT-REXEE

The primary limitation for the application of alchemical free energy methods to a wider variety of complex molecular systems is achieving reasonable sampling. Flexible binding complexes often have high free energy barriers, which require prohibitively long simulations or carefully tuned enhanced sampling methods in order to gather sufficient uncorrelated samples to obtain reliable free energy estimates. An example of such a flexible system is the complex formed between FabB, an elongating \b{eta}-ketoacyl-acyl carrier protein (ACP) synthase (KS) from Escherichia coli, and ACP, which carries acyl chains of varying lengths. Previous experimental evidence suggests that growing acyl chains can bind to at least two pockets in FabB. With the multiple topology replica exchange of expanded ensemble (MT-REXEE) enhanced sampling approach, we can obtain highly efficient sampling of both pockets by adaptively growing and shrinking the chains in the simulation ensemble, allowing each simulation to visit chain lengths where transitions between the pockets occur. This enables unbiased sampling of alternate configurational states for large complex systems without prior pocket definitions, as collective-variable based enhanced sampling methods would require. Using the new swapping approach gives significantly enhanced sampling even for this simpler problem, as demonstrated by faster convergence of free energy estimates of relative binding affinity between kinetically separated binding pockets. This case study demonstrates the utility of MT-REXEE and its open-source implementation for systems that feature high free energy barriers for a subset of ligands of interest, demonstrating a valuable addition to the existing stable of enhanced sampling methods.

physics.bio-ph↗

arXiv2025

Local ion environment in polyamide membranes revealed by molecular dynamics

In reverse osmosis (RO) and nanofiltration (NF) membranes, the polymer structure and interactions with solvent and solutes dictate the permeability and selectivity. However, these interactions have not been fully characterized within hydrated polymer membranes. In this study, we elucidate the local atomic neighborhood around ions within a RO membrane using molecular dynamics (MD). We built a MD model of a RO membrane closely following experimental synthesis and performed long time scale simulations of ions moving within the polymer. We find that the ion-oxygen nearest neighbor distance within the membrane is essentially the same as in solution, indicating that ions coordinate similarly in the confined membrane as in water. However, we do find that the average coordination number decreases in the polymer, which we attribute primarily to shifting the outer portion of the solvation shell beyond the cutoff, rather than being entirely stripped away. We find that cations bind tightly to both the carboxylate and amide oxygen atoms within the membrane. Even in ionized membranes, binding to amide oxygen atoms appears to play a substantial role in hindering ion mobility. Finally, we find that commonly used measures of ionic solvation structure such as coordination numbers do not fully capture the solvation structure, and we explore other measures such as the chemical composition of the nearest neighbors and the radial distribution function.

cond-mat.soft↗

arXiv2025

Force switching and potential shifting lead to significant cutoff dependence in alchemical free energies

The accurate treatment of long-range energy terms such as van der Waals interactions is crucial for reliable free energy calculations in molecular simulations. Methods like force switching, potential switching, potential shifting, and Ewald summation of van der Waals are commonly employed to smooth the truncation or otherwise manage these interactions at and beyond a cutoff distance, but their effects on free energy calculations are not always clear. In this study, we systematically explore the effects of these modifiers on the accuracy of free energy calculations using model systems: Lennard-Jones spheres, all-atom anthracene in water with GROMACS, and alkane chains in water with LAMMPS. Our results reveal that free energies of solvation using potential switching and particle-mesh Ewald summation of long-range Lennard-Jones are essentially independent of cutoff in solution, while force switching and potential shifting introduce cutoff-dependent behavior significant enough to affect the utility of the calculations.

physics.chem-ph↗

arXiv2025

Molecular details and free energy barriers of ion de-coordination at elevated salinity and pressure and their consequences for membrane separations

Ion dehydration has been hypothesized to strongly influence separation performance in membrane systems and ion transport in nanoscale channels. However, the molecular details of ion dehydration in membranes are not well understood, in particular under the high pressures and concentrations required for brine treatment. In this study, we define \textit{de-coordination} as the process by which an ion decreases its total coordination number, including both water molecules and counterions. We estimate the de-coordination free energies in bulk solution for a range of different ions at high pressure and salinity relevant to brine treatment using molecular simulation. We also propose alternatives to the coordination number as the size constraint for traversing nanoscale constrictions, such as the maximum cross-sectional area of the complexed ion. We show that high operating pressures do not significantly change cation hydration shell stability nor the shell size, while high ionic concentrations lower the free energy barrier to reduce the cation coordination number. We find that anion de-coordination free energies are largely unaffected by elevated salinity and pressure conditions. Finally, we discuss the implications on ion-ion selectivity in separations membranes (e.g. extracting lithium from salt-lake brines) due to the effects of elevated pressure and salinity on ion de-coordination.

cond-mat.mes-hall↗

arXiv2024

Multiple Topology Replica Exchange of Expanded Ensembles (MT-REXEE) for Multidimensional Alchemical Calculations

Relative free energy calculations are now widely used in academia and industry, but the accuracy is often limited by poor sampling of the complexes conformational ensemble. To address this, we have developed a novel method termed Multi-Topology Replica Exchange of Expanded Ensembles (MT-REXEE). This method enables parallel expanded ensemble calculations, facilitating iterative relative free energy computations while allowing conformational exchange between parallel transformations. These iterative transformations are adaptable to any set of systems with a common backbone or central substructure. We demonstrate that the MT-REXEE method maintains thermodynamic cycle closure to the same extent as standard expanded ensemble for both solvation free energy and relative binding free energy. The transformations tested involve simple systems that incorporate diverse heavy atoms and multi-site perturbations of a small molecule core resembling multi-site $λ$ dynamics, without necessitating modifications to the MD code, which in our initial implementation is GROMACS. We outline a systematic approach for topology set-up and provide instructions on how to perform inter-replicate coordinate modifications. This work shows that MT-REEXE can be used to perform accurate and reproducible free energy estimates and prompts expansion to more complex test systems and other molecular dynamics simulation infrastructures.

physics.chem-ph↗

arXiv2024

Interpreting effective energy barriers to membrane permeation in terms of a heterogeneous energy landscape

Major efforts in recent years have been directed towards understanding molecular transport in polymeric membranes, in particular reverse osmosis and nanofiltration membranes. Transition-state theory is an increasingly common approach to explore mechanisms of transmembrane permeation with molecular details, but most applications treat all free energy barriers to transport within the membrane as equal. This assumption neglects the inherent structural and chemical heterogeneity in polymeric membranes. In this work, we expand the transition-state theory framework to include distributions of membrane free energy barriers. We show that the highest free energy barriers along the most permeable paths, rather than typical paths, provide the largest contributions to the experimentally-observed effective free energy barrier. We show that even moderate, random heterogeneity in molecular barriers will significantly impact how we interpret the mechanisms of transport through membranes. Simplified interpretations of experimentally measured barriers can lead to incorrect assumptions about the underlying mechanisms governing transport and miss the mechanisms most relevant to the overall permeability.

cond-mat.soft↗

arXiv2024

Replica exchange of expanded ensembles: A generalized ensemble approach with enhanced flexibility and parallelizability

Generalized ensemble methods such as Hamiltonian replica exchange (HREX) and expanded ensemble (EE) have been shown effective in free energy calculations for various contexts, given their ability to circumvent free energy barriers via nonphysical pathways defined by states with different modified Hamiltonians. However, both HREX and EE methods come with drawbacks, such as limited flexibility in parameter specification, or the lack of parallelizability for more complicated applications. To address this challenge, we present the method of replica exchange of expanded ensembles (REXEE), which integrates the principles of HREX and EE methods by periodically exchanging coordinates of EE replicas sampling different yet overlapping sets of alchemical states. With the solvation free energy calculation of anthracene and binding free energy calculation of the CB7-10 binding complex, we show that the REXEE method achieves the same level of accuracy in free energy calculations as the HREX and EE methods, while offering enhanced flexibility and parallelizability. Additionally, we examined REXEE simulations with various setups to understand how different exchange frequencies and replica configurations influence the sampling efficiency in the fixed-weight phase and the weight convergence in the weight-updating phase. The REXEE approach can be further extended to support asynchronous parallelization schemes, allowing looser communications between larger numbers of loosely coupled processors such as cloud computing and therefore promising much more scalable and adaptive executions of alchemical free energy calculations. All algorithms for the REXEE method are available in the Python package ensemble_md, which offers an interface for REXEE simulation management without modifying the source code in GROMACS.

cond-mat.stat-mech↗

arXiv2023

Machine-learned molecular mechanics force field for the simulation of protein-ligand systems and beyond

The development of reliable and extensible molecular mechanics (MM) force fields -- fast, empirical models characterizing the potential energy surface of molecular systems -- is indispensable for biomolecular simulation and computer-aided drug design. Here, we introduce a generalized and extensible machine-learned MM force field, \texttt{espaloma-0.3}, and an end-to-end differentiable framework using graph neural networks to overcome the limitations of traditional rule-based methods. Trained in a single GPU-day to fit a large and diverse quantum chemical dataset of over 1.1M energy and force calculations, \texttt{espaloma-0.3} reproduces quantum chemical energetic properties of chemical domains highly relevant to drug discovery, including small molecules, peptides, and nucleic acids. Moreover, this force field maintains the quantum chemical energy-minimized geometries of small molecules and preserves the condensed phase properties of peptides, self-consistently parametrizing proteins and ligands to produce stable simulations leading to highly accurate predictions of binding free energies. This methodology demonstrates significant promise as a path forward for systematically building more accurate force fields that are easily extensible to new chemical domains of interest.

physics.chem-ph↗

arXiv2022

Adding alchemical variables to metadynamics to enhance sampling in free energy calculations

Performing alchemical transformations, in which one molecular system is nonphysically changed to another system, is a popular approach adopted in performing free energy calculations associated with various biophysical processes, such as protein-ligand binding or the transfer of a molecule between environments. While the sampling of alchemical intermediate states in either parallel (e.g. Hamiltonian replica exchange) or serial manner (e.g. expanded ensemble) can bridge the high-probability regions in the configurational space between two end states of interest, alchemical methods can fail in scenarios where the most important slow degrees of freedom in the configurational space are in large part orthogonal to the alchemical variable, or if the system gets trapped in a deep basin extending in both the configurational and alchemical space. To alleviate these issues, we propose to use alchemical variables as an additional dimension in metadynamics, augmenting the ability both to sample collective variables and to enhance sampling in free energy calculations. In this study, we validate our implementation of alchemical metadynamics in PLUMED with test systems and alchemical processes with varying complexities and dimensions of collective variable space, including the interconversion between the torsional metastable states of a toy system and the methylation of a nucleoside both in the isolated form and in a duplex. We show that multi-dimensional alchemical metadynamics can address the challenges mentioned above and further accelerate sampling by introducing configurational collective variables. The method can trivially be combined with other metadynamics-based algorithms implemented in PLUMED. The necessary PLUMED code changes have already been released for general use in PLUMED 2.8.

cond-mat.stat-mech↗

arXiv2022

Enhanced sampling methods for molecular dynamics simulations

Enhanced sampling algorithms have emerged as powerful methods to extend the utility of molecular dynamics simulations and allow the sampling of larger portions of the configuration space of complex systems in a given amount of simulation time. This review aims to present the unifying principles and differences of many of the computational methods currenly used for enhanced sampling in molecular simulations of biomolecules, soft matter and molecular crystals. Indeed, despite the apparent abundance and divergence of such methods, the principles at their core can be boiled down to a relatively limited number of statistical and physical principles. To enable comparisons, the various methods are introduced using similar terminology and notation. We then illustrate in which ways many different methods combine principles from a smaller class of enhanced sampling concepts. This review is intended for scientists with an understanding of the basics of molecular dynamics simulations and statistical physics who want a deeper understanding of the ideas that underlie various enhanced sampling methods and the relationships between them. This living review is intended to be updated to continue to reflect the wealth of sampling methods as they continue to emerge in the literature.

cond-mat.stat-mech↗

arXiv2022

How cooperatively folding are homopolymer molecular knots?

Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work we derive a heat capacity decomposition comprising contributions from each individual configurational state, which together sum to a baseline heat capacity, and contributions from each state-to-state transition. We apply this analysis framework to a series of replica exchange molecular dynamics simulations of linear and 1-1 coarse-grained homo-oligomer models which fold into stable, configurationally well-defined molecular knots, in order to better understand the parameters leading to stable and cooperative folding of these knots. We find that a stiff harmonic backbone bending angle potential is key to achieving knots with specific 3D structures. Tuning the backbone equilibrium angle in small increments yields a variety of knot topologies, including $3_1$, $5_1$, $7_1$, and $8_{19}$ types. Populations of different knotted states as functions of temperature can also be manipulated by tuning backbone torsion stiffness or by adding side chain beads. We find that sharp total heat capacity peaks for the homo-oligomer knots are largely due to a coil-to-globule transition, rather than a cooperative knotting step. However, in some cases the cooperativity of globule-to-knot and coil-to-globule transitions are comparable, suggesting that highly cooperative folding to knotted structures can be achieved by refining the model parameters or adding sequence specificity.

cond-mat.stat-mech↗

arXiv2021

Bayesian inference-driven model parameterization and model selection for 2CLJQ fluid models

A high level of physical detail in a molecular model improves its ability to perform high accuracy simulations, but can also significantly affect its complexity and computational cost. In some situations, it is worthwhile to add additional complexity to a model to capture properties of interest; in others, additional complexity is unnecessary and can make simulations computationally infeasible. In this work we demonstrate the use of Bayes factors for molecular model selection, using Monte Carlo sampling techniques to evaluate the evidence for different levels of complexity in the two-centered Lennard-Jones + quadrupole (2CLJQ) fluid model. Examining three levels of nested model complexity, we demonstrate that the use of variable quadrupole and bond length parameters in this model framework is justified only sometimes. We also explore the effect of the Bayesian prior distribution on the Bayes factors, as well as ways to propose meaningful prior distributions. This Bayesian Markov Chain Monte Carlo (MCMC) process is enabled by the use of analytical surrogate models that accurately approximate the physical properties of interest. This work paves the way for further atomistic model selection work via Bayesian inference and surrogate modeling

physics.comp-ph↗

arXiv2020

Probing the force field sensitivity of entropy and enthalpy differences in organic polymorphs using classical potentials

We evaluate the effectiveness of different classical potentials to predict the thermodynamics of a number of organic solid form polymorphs relative to experimentally reported values using the quasi-harmonic approximation. Using the polarizable potential AMOEBA we are able to predict the correct sign of the enthalpy difference for 71+/-12 % of the polymorphs. Alternatively, all point charge potentials perform on par with random chance of correcting the correct sign (50%) for enthalpy. We find that the entropy is less sensitive to the accuracy of the potential with all force fields, excluding CGenFF, reporting the correct sign of the entropy for 64+/-13 - 75+/-11 % of the systems. Predicting the correct sign of the enthalpy and entropy differences can help indicate the low and high temperature stability of the polymorphs, unfortunately the error relative to experiment in these predicted values can be as large as 1 - 2.5 kcal/mol at the transition temperature.

cond-mat.mtrl-sci↗

arXiv2020

Best Practices for Alchemical Free Energy Calculations

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing \emph{alchemical} intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations, including relative and absolute small molecule binding free energy calculations to biomolecular targets.

q-bio.BM↗

arXiv2020

Statistical mechanical approximations to more efficiently determine polymorph free energy differences for small organic molecules

Methods to efficiently determine the relative stability of polymorphs of organic crystals are highly desired in crystal structure predictions (CSPs). Current methodologies include use of static lattice phonons, quasi-harmonic approximation (QHA), and computing the full thermodynamic cycle using replica exchange molecular dynamics (REMD). We found that 13 out of the 29 systems minimized from experiment restructured to a lower energy minima when heated using REMD, a phenomena that QHA cannot capture. Here, we present a series of methods that are intermediate in accuracy and expense between QHA and computing the full thermodynamic cycle which can save 42-80% of the computational cost and introduces, on this benchmark, a relatively small (0.16 +/- 0.04 kcal/mol) error relative to the full pseudosupercritical path approach. In particular, a method that Boltzmann weights the harmonic free energy of the trajectory of an REMD replica appears to be an appropriate intermediate between QHA and full thermodynamic cycle using MD when screening crystal polymorph stability.

cond-mat.mtrl-sci↗

arXiv2020

Statistically optimal continuous free energy surfaces from biased simulations and multistate reweighting

Free energies as a function of a selected set of collective variables are commonly computed in molecular simulation and of significant value in understanding and engineering molecular behavior. These free energy surfaces are most commonly estimated using variants of histogramming techniques, but such approaches obscure two important facets of these functions. First, the empirical observations along the collective variable are defined by an ensemble of discrete observations and the coarsening of these observations into a histogram bins incurs unnecessary loss of information. Second, the free energy surface is itself almost always a continuous function, and its representation by a histogram introduces inherent approximations due to the discretization. In this study, we relate the observed discrete observations from biased simulations to the inferred underlying continuous probability distribution over the collective variables and derive histogram-free techniques for estimating this free energy surface. We reformulate free energy surface estimation as minimization of a Kullback-Leibler divergence between a continuous trial function and the discrete empirical distribution and show that this is equivalent to likelihood maximization of a trial function given a set of sampled data. We then present a fully Bayesian treatment of this formalism, which enables the incorporation of powerful Bayesian tools such as the inclusion of regularizing priors, uncertainty quantification, and model selection techniques. We demonstrate this new formalism in the analysis of umbrella sampling simulations for the $χ$ torsion of a valine sidechain in the L99A mutant of T4 lysozyme with benzene bound in the cavity.

cond-mat.stat-mech↗

arXiv2020

Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling

Mathematically modeling complex transport phenomena at the molecular level can be a powerful tool for identifying transport mechanisms and predicting macroscopic properties. We use two different stochastic time series models, parameterized from long molecular dynamics (MD) simulation trajectories of a cross-linked HII phase lyotropic liquid crystal (LLC) membrane, in order to predict solute mean squared displacements (MSDs) and solute flux, and thus solute selectivity, in macroscopic length pores. First, using anomalous diffusion theory, we show how solute dynamics can be modeled as a fractional diffusion process subordinate to a continuous time random walk. From the MD simulations, we parameterize the distribution of dwell times, hop lengths between dwells and correlation between hops. We explore two variations of the anomalous diffusion modeling approach. The first applies a single set of parameters to the solute displacements and the second applies two sets of parameters based on the solute's radial distance from the closest pore center. Next, we generalize Markov state models, treating the configurational states of the system as a Markov process where each state has distinct transport properties. For each state and transition between states, we parameterize the distribution and temporal correlation structure of positional fluctuations as a means of characterization and to allow us to predict solute MSDs. Qualitative differences between MD and Markov state dependent model-generated trajectories may limit its usefulness. Finally, we demonstrate how one can use these models to estimate flux of a solute across a macroscopic-length pore and, based on those quantities, the membrane's selectivity towards each solute. This work helps to connect microscopic chemically-dependent solute motions that do not follow simple diffusive behavior with macroscopic membrane performance.

cond-mat.soft↗

arXiv2019

Adding anisotropy to the standard quasi-harmonic approximation still fails in several ways to capture organic crystal thermodynamics

We evaluate the accuracy of varying thermal expansion models for the quasi-harmonic approximation (QHA) relative to molecular dynamics (MD) for 10 sets of enantiotropic organic polymorphs. Relative to experiment we find that MD, using an off-the-shelf point charge potential gets the sign of the enthalpic contributions correct for 6 of the 10 pairs of polymorphs and the sign of the entropic contributions correct for all pairs. We find that anisotropic QHA provides little improvement to the error in free energy differences from MD relative to isotropic QHA, but does a better job capturing the thermal expansion of the crystals. A form of entropy-enthalpy compensation allows the free energy differences of QHA to deviate less than 0.1 kcal/mol from MD for most polymorphic pairs, despite errors up to 0.4 kcal/mol in the entropy and enthalpy. Much of the error previously found between QHA and MD for these flexible molecules is reduced when QHA is run from a lattice minimum consistent with the same basin as MD, rather than the energy-minimized experimental crystal structure. Specifically, performing anisotropic QHA on lattice minimum quenched from low-temperature replica exchange simulations reduced the error previously found by 0.2 kcal/mol on average. However, these conformationally flexible molecules can have many low-temperature conformational minima, and the choice of an inconsistent minima causes free energies estimated from QHA to deviate from MD at temperatures as low as 10 K. The errors between MD and experiment are 1-2 orders of magnitude larger than those seen between QHA and MD, so the quality of the force field used is still of primary concern, but this study illustrates a number of other important factors that must be considered to obtain quantitative organic crystal thermodynamics.

cond-mat.mtrl-sci↗