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Our ability to calculate rates of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barriers. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables. This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the collective variable biasing efficiency $\gamma$. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect collective variable, $\gamma=1$. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different collective variables to bias, but which is sufficiently simple that we are able to compute the unbiased rate dire ctly. For this system, we demonstrate that our new Exponential Average Time-Dependent Rate (EATR) estimator converges to the true rate more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the $\gamma$ parameter can serve as a good metric for assessing the quality of the biasing coordinate. Finally, we demonstrate that the approach works when combining multiple less-than-optimal bias coordinates., Comment: 14 pages, 5 figures; 4 pages of supporting information with 2 tables and 6 additional figures

In this article we give our perspective on the successes and promise of various molecular and coarse-grained simulation approaches to probing the effect of mechanical forces in the actin cytoskeleton., Comment: 14 pages, 4 pages

Small mechanical forces play important functional roles in many crucial cellular processes, including in the dynamical behavior of the cytoskeleton and in the regulation of osmotic pressure through membrane-bound proteins. Molecular simulations offer the promise of being able to design the behavior of proteins that sense and respond to these forces. However, it is difficult to predict and identify the effect of the relevant piconewton (pN) scale forces due to their small magnitude. Previously, we introduced the Infinite Switch Simulated Tempering in Force (FISST) method which allows one to estimate the effect of a range of applied forces from a single molecular dynamics simulation, and also demonstrated that FISST additionally accelerates sampling of a molecule's conformational landscape. For some problems, we find that this acceleration is not sufficient to capture all relevant conformational fluctuations, and hence here we demonstrate that FISST can be combined with either temperature replica exchange or solute tempering approaches to produce a hybrid method that enables more robust prediction of the effect of small forces on molecular systems., Comment: 15 Pages with 6 figures, plus 7 supplemental figures and one supplemental table

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium ``quench'' process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of $N$-independent harmonic springs, and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling.= We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach, but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications., Comment: 18 pages, with 8 figures, 1 table, and 9 supplemental figures

In this work, we demonstrate that Linear Discriminant Analysis (LDA) applied to atomic positions in two different states of a biomolecule produces a good reaction coordinate between those two states. Atomic coordinates of a macromolecule are a direct representation of a macromolecular configuration, and yet they have not been used in enhanced sampling studies due to a lack of rotational and translational invariance. We resolve this issue using the technique of our prior work, where a molecular configuration is considered a member of an equivalence class in size-and-shape space, which is the set of all configurations that can be translated and rotated to a single point within a reference multivariate Gaussian distribution characterizing a single molecular state. The reaction coordinates produced by LDA applied to positions are shown to be good reaction coordinates both in terms of characterizing the transition between two states of a system within a long molecular dynamics (MD) simulation, and also ones that allow us to readily produce free energy estimates along that reaction coordinate using enhanced sampling MD techniques., Comment: 11 pages, 5 figures (plus 2 SI pages and 3 SI figures)

Colloidal particles with mobile binding molecules constitute a powerful platform for probing the physics of self-assembly. Binding molecules are free to diffuse and rearrange on the surface, giving rise to spontaneous control over the number of droplet-droplet bonds, i.e., valence, as a function of the concentration of binders. This type of valence control has been realized experimentally by tuning the interaction strength between DNA-coated emulsion droplets. Optimizing for valence two yields droplet polymer chains, termed `colloidomers', which have recently been used to probe the physics of folding. To understand the underlying self-assembly mechanisms, here we present a coarse-grained molecular dynamics (CGMD) model to study the self-assembly of this class of systems using explicit representations of mobile binding sites. We explore how valence of assembled structures can be tuned through kinetic control in the strong binding limit. More specifically, we optimize experimental control parameters to obtain the highest yield of long linear colloidomer chains. Subsequently tuning the dynamics of binding and unbinding via a temperature-dependent model allows us to observe the heptamer chain collapse into all possible rigid structures, in good agreement with recent folding experiments. Our CGMD platform and dynamic bonding model (implemented as an open-source custom plugin to HOOMD-Blue) reveal the molecular features governing the binding patch size and valence control, and opens the study of pathways in colloidomer folding. This model can therefore guide programmable design in experiments., Comment: 14 pages + 11 pages SI. 10 figures + 9 supplemental figures + 6 supplemental tables

Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the innate rotational and translational invariance of these features. The vast number of possible internal coordinates necessitates a feature space supervision step to make clustering tractable, but yields a protocol that can be system type specific. Particle positions offer an appealing alternative to internal coordinates, but suffer from a lack of rotational and translational invariance, as well as a perceived insensitivity to regions of structural dissimilarity. Here, we present a method, denoted shape-GMM, that overcomes the shortcomings of particle positions using a weighted maximum likelihood (ML) alignment procedure. This alignment strategy is then built into an expectation maximization Gaussian mixture model (GMM) procedure to capture metastable states in the free energy landscape. The resulting algorithm distinguishes between a variety of different structures, including those indistinguishable by RMSD and pair-wise distances, as demonstrated on several model systems. Shape-GMM results on an extensive simulation of the the fast-folding HP35 Nle/Nle mutant protein support a 4-state folding/unfolding mechanism which is consistent with previous experimental results and provides kinetic detail comparable to previous state of the art clustering approaches, as measured by the VAMP-2 score. Currently, training of shape-GMMs is recommended for systems (or subsystems) that can be represented by $\lesssim$ 200 particles and $\lesssim$ 100K configurations to estimate high-dimensional covariance matrices and balance computational expense. Once a shape-GMM is trained, it can be used to predict the cluster identities of millions of configurations., Comment: 20 pages, 8 figures

Protein-ligand interactions are crucial for a wide range of physiological processes. Many cellular functions result in these non-covalent `bonds' being mechanically strained, and this can be integral to proper cellular function. Broadly, two classes of force dependence have been observed -- slip bonds, where unbinding rate increases, and catch bonds where unbinding rate decreases. Despite much theoretical work, we cannot we predict for which protein-ligand pairs, pulling coordinates, and forces a particular rate dependence will appear. Here, we assess the ability of MD simulations combined with enhanced sampling techniques to probe the force dependence of unbinding rates. We show that the infrequent metadynamics technique correctly produces both catch and slip bonding kinetics for model potentials. We then apply it to the well-studied case of a buckyball in a hydrophobic cavity, which appears to exhibit an ideal slip bond. Finally, we compute the force-dependent unbinding rate of biotin-streptavidin. Here, the complex nature of the unbinding process causes the infrequent metadynamics method to begin to break down due to the presence of unbinding intermediates, despite use of a previously optimized sampling coordinate. Allowing for this limitation, a combination of kinetic and free energy computations predict an overall slip bond for larger forces consistent with prior experimental results, although there are substantial deviations at small forces that require further investigation. This work demonstrates the promise of predicting force-dependent unbinding rates using enhanced sampling MD techniques, while also revealing the methodological barriers that must be overcome to tackle more complex targets in the future., Comment: 16 pages. 9 figures, 1 table, 5 supplemental figures

Natural language processing models have emerged that can generate usable software and automate a number of programming tasks with high fidelity. These tools have yet to have an impact on the chemistry community. Yet, our initial testing demonstrates that this form of Artificial Intelligence is poised to transform chemistry and chemical engineering research. Here, we review developments that brought us to this point, examine applications in chemistry, and give our perspective on how this may fundamentally alter research and teaching., Comment: 6 pages, 3 figures, plus 8 page SI with additional examples and extended figure details

Understanding the role of non-equilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and non-equilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle crosslinked by two competing types of actin binding proteins, we construct a minimal model for such a system and show that the dynamics are subject to a set of thermodynamic constraints that relate the non-equilibrium driving, bundle morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes, and offer a route to estimating microscopic driving forces from microscopy experiments., Comment: 5 Figs + SI

Experiment Directed Simulations (EDS) is a method within a class of techniques seeking to improve molecular simulations by minimally biasing the system Hamiltonian to reproduce certain experimental observables. In a previous application of EDS to ab initio molecular dynamics (AIMD) simulation-based on electronic density functional theory (DFT), the AIMD simulations of water were biased to reproduce its experimentally derived solvation structure. In particular, by solely biasing the O-O pair correlation functions, other structural and dynamical properties that were not biased were improved. In this work, the hypothesis is tested that directly biasing the OH pair correlation, will provide an even better improvement of DFT-based water properties in AIMD simulations. The logic behind this hypothesis is that for most electronic DFT descriptions of water the hydrogen bonding is known to be deficient due to anomalous charge transfer and over polarization in the DFT. Using recent advances to the EDS learning algorithm, we thus train a minimal bias on AIMD water that reproduces the O-H radial distribution function derived from the highly accurate MB-pol model of water. It is then confirmed that biasing the O-H pair correlation alone can lead to improved AIMD water properties, with structural and dynamical properties in even closer to experiment than the previous EDS-AIMD model., Comment: 28 pages, 10 total figures

Many proteins in cells are capable of sensing and responding to piconewton scale forces, a regime in which conformational changes are small but significant for biological processes. In order to efficiently and effectively sample the response of these proteins to small forces, enhanced sampling techniques will be required. In this work, we derive, implement, and evaluate an efficient method to simultaneously sample the result of applying any constant pulling force within a specified range to a molecular system of interest. We start from Simulated Tempering in Force, whereby force is applied as a linear bias on a collective variable to the system's Hamiltonian, and the coefficient is taken as a continuous auxiliary degree of freedom. We derive a formula for an average collective-variable-dependent force, which depends on a set of weights, learned on-the-fly throughout a simulation, that reflect the limit where force varies infinitely quickly. These weights can then be used to retroactively compute averages of any observable at any force within the specified range. This technique is based on recent work deriving similar equations for Infinite Switch Simulated Tempering in Temperature, that showed the infinite switch limit is the most efficient for sampling. Here, we demonstrate that our method accurately and simultaneously samples molecular systems at all forces within a user defined force range, and show how it can serve as an enhanced sampling tool for cases where the pulling direction destabilizes states of low free-energy at zero-force. This method is implemented in, and will be freely-distributed with, the PLUMED open-source sampling library, and hence can be readily applied to problems using a wide range of molecular dynamics software packages., Comment: 15 pages w/ 4 figures + Appendix of 7 pages w/ 6 figures

Living cells dynamically modulate the local morphologies of their actin cytoskeletons to perform biological functions, including force transduction, intracellular transport, and cell division. A major challenge is to understand how diverse structures of the actin cytoskeleton are assembled from a limited set of molecular building blocks. Here we study the spontaneous self-assembly of a minimal model of cytoskeletal materials, consisting of semiflexible actin filaments, crosslinkers, and molecular motors. Using coarse-grained simulations, we demonstrate that by changing concentrations and kinetics of crosslinkers and motors we can generate three distinct structural phases of actomyosin assemblies: bundled, polarity-sorted, and contracted. We introduce new metrics to distinguish these structural phases and demonstrate their functional roles. We find that the binding kinetics of motors and crosslinkers can be tuned to optimize contractile force generation, motor transport, and mechanical response. By quantitatively characterizing the relationships between modes of cytoskeletal self-assembly, the resulting structures, and their functional consequences, our work suggests new principles for the design of active materials., Comment: 17 pages, 15 figures

Computer simulations can aid in understanding how collective materials properties emerge from interactions between simple constituents. Here, we introduce a coarse-grained model that enables simulation of networks of actin filaments, myosin motors, and crosslinking proteins at biologically relevant time and length scales. We demonstrate that the model qualitatively and quantitatively captures a suite of trends observed experimentally, including the statistics of filament fluctuations, mechanical responses to shear, motor motilities, and network rearrangements. We use the simulation to predict the viscoelastic scaling behavior of crosslinked actin networks, characterize the trajectories of actin in a myosin motility assay, and develop order parameters to measure contractility of a simulated actin network. The model can thus serve as a platform for interpretation and design of cytoskeletal materials experiments, as well as for further development of simulations incorporating active elements., Comment: 26 pages, 7 figures

Accounting for electrons and nuclei simultaneously is a powerful capability of ab initio molecular dynamics (AIMD). However, AIMD is often unable to accurately reproduce properties of systems such as water due to inaccuracies in the underlying electronic density functionals. This shortcoming is often addressed by added empirical corrections and/or increasing the simulation temperature. We present here a maximum-entropy approach to directly incorporate limited experimental data via a minimal bias. Biased AIMD simulations of water and an excess proton in water are shown to give significantly improved properties both for observables which were biased to match experimental data and for unbiased observables. This approach also yields new physical insight into inaccuracies in the underlying density functional theory as utilized in the unbiased AIMD., Comment: 30 pages, 9 figures, 1 table

Ultrastable glasses have risen to prominence due to their potentially useful material properties and the tantalizing possibility of a general method of preparation via vapor deposition. Despite the importance of this novel class of amorphous materials, numerical studies have been scarce because achieving ultrastability in atomistic simulations is an enormous challenge. Here we bypass this difficulty and establish that randomly pinning the position of a small fraction of particles inside an equilibrated supercooled liquid generates ultrastable configurations at essentially no numerical cost, while avoiding undesired structural changes due to the preparation protocol. Building on the analogy with vapor-deposited ultrastable glasses, we study the melting kinetics of these configurations following a sudden temperature jump into the liquid phase. In homogeneous geometries, we find that enhanced kinetic stability is accompanied by large scale dynamic heterogeneity, while a competition between homogeneous and heterogeneous melting is observed when a liquid boundary invades the glass at constant velocity. Our work demonstrates the feasibility of large-scale, atomistically resolved, and experimentally relevant simulations of the kinetics of ultrastable glasses., Comment: 9 pages, 5 figures

We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced., Comment: 6 pages, 3 figures and 6 page sup. with 5 figures and 1 table

We study the relaxation dynamics of a binary Lennard-Jones liquid in the presence of an amorphous wall generated from equilibrium particle configurations. In qualitative agreement with the results presented in Nature Phys. {\bf 8}, 164 (2012) for a liquid of harmonic spheres, we find that our binary mixture shows a saturation of the dynamical length scale close to the mode-coupling temperature $T_c$. Furthermore we show that, due to the broken symmetry imposed by the wall, signatures of an additional change in dynamics become apparent at a temperature well above $T_c$. We provide evidence that this modification in the relaxation dynamics occurs at a recently proposed dynamical crossover temperature $T_s > T_c$, which is related to the breakdown of the Stokes-Einstein relation. We find that this dynamical crossover at $T_s$ is also observed for a system of harmonic spheres as well as a WCA liquid, showing that it may be a general feature of glass-forming systems., Comment: 10 pages, 8 figures

In this work, we study the nature of transitions between inherent structures of a two-dimensional model supercooled liquid. We demonstrate that these transitions occur predominately along a small number of directions on the energy landscape. Moreover, we show that the number of such directions decreases as the temperature of the liquid is decreased in the mildly supercooled regime, in concert with earlier studies on an athermal jamming system. We show that this decrease happens in parallel with a change in character of the transitions as dynamics in the system become more heterogeneous and localized. We investigate the origin of these trends, which suggests interesting connections between jamming and thermal glassy phenomena., Comment: 9 pages, 11 figures, 1 table. Appears in the "Special Topic Issue on the Glass Transition"

It has been demonstrated recently that supercooled liquids sharing simple structural features (e.g. pair distribution functions) may exhibit strikingly distinct dynamical behavior. Here we show that a more subtle structural feature correlates with relaxation times in three simulated systems that have nearly identical radial distribution functions but starkly different dynamical behavior. In particular, for the first time we determine the thermodynamic "point-to-set" length scale in several canonical model systems and demonstrate the quantitative connection between this length scale and the growth of relaxation times. Our results provide clues necessary for distinguishing competing theories of the glass transition., Comment: 8 pages, 5 figures, 1 table