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This article explores the use of Neural Network Potentials (NNPs) to model prebiotic chemistries accurately and efficiently. The authors present a scalable and generalizable approach for designing NNPs that can handle chemical reactivity in solvated systems. Through active learning and enhanced sampling techniques, they generate free-energy landscapes and calculate committors, finding a preference for the dissociative mechanism and identifying HPO4 2− as the more reactive species under prebiotic conditions. This research has the potential to enhance our understanding of prebiotic chemistry and its connection to the origins of life. The study acknowledges the need for further improvements, such as incorporating machine learning approaches and training neural network potentials using collective variables. The work was supported by the US Department of Energy. [Extracted from the article]

The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations. [ABSTRACT FROM AUTHOR]

In this work, we revisit our recent iterative machine learning (ML)–molecular dynamics (MD) technique "Reweighted autoencoded variational Bayes for enhanced sampling" [J. M. L. Ribeiro et al., J. Chem. Phys. 149, 072301 (2018) and Y. Wang, J. M. L. Ribeiro, and P. Tiwary, Nat. Commun. 10, 3573 (2019)] and analyze and formalize some of its approximations. These include (a) the choice of a predictive time-delay, or how far into the future should the ML try to predict the state of a given system output from MD, and (b) that for short time-delays, how much of an error is made in approximating the biased propagator for the dynamics as the unbiased propagator. We demonstrate through a master equation framework as to why the exact choice of time-delay is irrelevant as long as a small non-zero value is adopted. We also derive a correction to reweight the biased propagator, and somewhat to our dissatisfaction but also to our reassurance, we find that it barely makes a difference to the intuitive picture we had previously derived and used. [ABSTRACT FROM AUTHOR]

We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For this we use our recently proposed method "spectral gap optimization of order parameters (SGOOP)" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. We show how available information about dynamical observables in addition to static information can be incorporated intoSGOOP, which can then be used to accurately determine the "best" reaction coordinate for arbitrary anisotropies.We compare our results with transmission coefficient calculations and published benchmarks wherever applicable or available, respectively. [ABSTRACT FROM AUTHOR]

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated. Nucleation rates spanning a range of 10 orders of magnitude are computed at moderate supersaturation levels, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems. [ABSTRACT FROM AUTHOR]

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom. [ABSTRACT FROM AUTHOR]

Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently, metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method. [ABSTRACT FROM AUTHOR]

In this brief review, we discuss the question of calculating the distance between different molecular configurations. We focus on the theoretical basis of different existing methods for this problem, including ones which are more physics-driven and ones which are more data-driven. We explain the key ideas behind these methods, and conclude with what we see as the central challenges. We hope this review will be helpful to someone aiming to understand these methods, many of which are new and have not been compared and reviewed together. We also hope it will help develop new methods that address the challenges we identify and others. [ABSTRACT FROM AUTHOR]

We consider the rate of transition for a particle between two metastable states coupled to a thermal environment for various magnitudes of the coupling strength using the recently proposed infrequent metadynamics approach [P. Tiwary and M. Parrinello, Phys. Rev. Lett. 111, 230602 (2013)]. We are interested in understanding how this approach for obtaining rate constants performs as the dynamics regime changes from energy diffusion to spatial diffusion. Reassuringly, we find that the approach works remarkably well for various coupling strengths in the strong coupling regime, and to some extent even in the weak coupling regime. [ABSTRACT FROM AUTHOR]

Biotin-streptavidin is a very popular system used to gain insight into protein-ligand interactions. In its tetrameric form, it is well-known for its exceptionally high kinetic stability, being one of the strongest known noncovalent interactions in nature, and it is heavily used across the biotechnological industry. In this work, we gain understanding of the molecular determinants and bottlenecks in the dissociation of the dimeric biotin-streptavidin system in wild type and with a point mutation. Using recently proposed enhanced sampling methods with full atomistic resolution, we reproduce the experimentally reported effect of the mutation on the dissociation rate. We also answer a longstanding question regarding cause/effect in the coupled events of bond stretching and bond hydration during dissociation and establish that in this system, it is the bond stretching and not hydration which forms the bottleneck in the early parts of the dissociation process. We believe these calculations represent a step forward in the use of atomistic simulations to study pharmacokinetics. An improved understanding of biotin-streptavidin dissociation dynamics should also have direct benefits in biotechnological and nanobiotechnological applications. [ABSTRACT FROM AUTHOR]

Atomistic simulations play a central role in many fields of science. However, their usefulness is often limited by the fact that many systems are characterized by several metastable states separated by high barriers, leading to kinetic bottlenecks. Transitions between metastable states are thus rare events that occur on significantly longer timescales than one can simulate in practice. Numerous enhanced sampling methods have been introduced to alleviate this timescale problem, including methods based on identifying a few crucial order parameters or collective variables and enhancing the sampling of these variables. Metadynamics is one such method that has proven successful in a great variety of fields. Here we review the conceptual and theoretical foundations of metadynamics. As demonstrated, metadynamics is not just a practical tool but can also be considered an important development in the theory of statistical mechanics. [ABSTRACT FROM AUTHOR]

Mutations in the gatekeeper residue of kinases have emerged as a key way through which cancer cells develop resistance to treatment. As such, the design of gatekeeper mutation resistant kinase inhibitors is a crucial way forward in increasing the efficacy of a broad range of anticancer drugs. In this work we use atomistic simulations to provide detailed thermodynamic and structural insight into how two inhibitors of cSrc kinase, namely, a commercial drug and type 1 kinase inhibitor Dasatinib and the type II inhibitor RL45, respectively fail and succeed in being effective against the T338M gatekeeper residue mutation in the kinase binding site. Given the well-known limitations of atomistic simulations in sampling biomolecular systems, we use an enhanced sampling technique called free energy perturbation with replica exchange solute tempering (FEP/REST). Our calculations find that the type I inhibitor Dasatinib binds favorably to the wild type but unfavorably to T338M mutated kinase, while RL45 binds favorably to both. The predicted relative binding free energies are well within 1 kcal/ mol accuracy compared to experiments. We find that Dasatinib's impotency against gatekeeper residue mutations arises from a loss of ligand-kinase hydrogen bonding due to T338M mutation and from steric hindrance due to the presence of an inflexible phenyl ring close to the ligand. On the other hand, in the type II binding RL45, the central phenyl ring has very pronounced flexibility. This leads to the inhibitor overcoming effects of steric clashes on mutation and maintaining an electrostatically favorable "edge-to-face" orientation with a neighboring phenylalanine residue. Our work provides useful insight into the mechanisms of mutation resistant kinase inhibitors and demonstrates the usefulness of enhanced sampling techniques in computational drug design. [ABSTRACT FROM AUTHOR]

In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhanced-sampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs. [ABSTRACT FROM AUTHOR]

Herein, we demonstrate a convenient approach to systematically investigate chemical reaction dynamics using the metadynamics (MetaD) family of enhanced sampling methods. Using a symmetric SN2 reaction as a model system, we applied infrequent metadynamics, a theoretical framework based on acceleration factors, to quantitatively estimate the rate of reaction from biased and unbiased simulations. A systematic study of the algorithm and its application to chemical reactions was performed by sampling over 5000 independent reaction events. Additionally, we quantitatively reweighed exhaustive free-energy calculations to obtain the reaction potential-energy surface and showed that infrequent metadynamics works to effectively determine Arrhenius-like activation energies. Exact agreement with unbiased high-temperature kinetics is also shown. The feasibility of using the approach on actual ab initio molecular dynamics calculations is then presented by using Car-Parrinello MD+MetaD to sample the same reaction using only 10-20 calculations of the rare event. Owing to the ease of use and comparatively low-cost of computation, the approach has extensive potential applications for catalysis, combustion, pyrolysis, and enzymology. [ABSTRACT FROM AUTHOR]

A key factor influencing a drug's efficacy is its residence time in the binding pocket of the host protein. Using atomistic computer simulation to predict this residence time and the associated dissociation process is a desirable but extremely difficult task due to the long timescales involved. This gets further complicated by the presence of biophysical factors such as steric and solvation effects. In this work, we perform molecular dynamics (MD) simulations of the unbinding of a popular prototypical hydrophobic cavity-ligand system using a metadynamics-based approach that allows direct assessment of kinetic pathways and parameters. When constrained to move in an axial manner, the unbinding time is found to be on the order of 4,000 s. In accordance with previous studies, we find that the cavity must pass through a region of sharp wetting transition manifested by sudden and high fluctuations in solvent density. When we remove the steric constraints on ligand, the unbinding happens predominantly by an alternate pathway, where the unbinding becomes 20 times faster, and the sharp wetting transition instead becomes continuous. We validate the unbinding timescales from metadynamics through a Poisson analysis, and by comparison through detailed balance to binding timescale estimates from unbiased MD. This work demonstrates that enhanced sampling can be used to perform explicit solvent MD studies at timescales previously unattainable, to our knowledge, obtaining direct and reliable pictures of the underlying physiochemical factors including free energies and rate constants. [ABSTRACT FROM AUTHOR]

The ability to predict the mechanisms and the associated rate constants of protein-ligand unbinding is of great practical importance in drug design. In this work we demonstrate how a recently introduced metadynamics-based approach allows exploration of the unbinding pathways, estimation of the rates, and determination of the rate-limiting steps in the paradigmatic case of the trypsin- benzamidine system. Protein, ligand, and solvent are described with full atomic resolution. Using metadynamics, multiple unbinding trajectories that start with the ligand in the crystallographic binding pose and end with the ligand in the fully solvated state are generated. The unbinding rate koff is computed from the mean residence time of the ligand. Using our previously computed binding affinity we also obtain the binding rate kon. Both rates are in agreement with reported experimental values. We uncover the complex pathways of unbinding trajectories and describe the critical ratelimiting steps with unprecedented detail. Our findings illuminate the role played by the coupling between subtle protein backbone fluctuations and the solvation by water molecules that enter the binding pocket and assist in the breaking of the shielded hydrogen bonds. We expect our approach to be useful in calculating rates for general protein-ligand systems and a valid support for drug design. [ABSTRACT FROM AUTHOR]

Metadynamicsis a powerful and well-established enhanced samplingmethod for exploring and quantifying free energy surfaces of complexsystems as a function of appropriately chosen variables. In the limitof long simulation time, metadynamics converges to the exact freeenergy surface plus a time-dependent constant. In this article, weanalyze in detail this time-dependent constant. We show an easy wayto calculate it, and by explicitly calculating the time dependenceof this constant, we are able to derive a time-independent and locallyconvergent free energy estimator for metadynamics. We also derivean alternate procedure for obtaining the full unbiased distributionsof generic operators from biased metadynamics simulations and explicitlytest its usefulness. [ABSTRACT FROM AUTHOR]

In this work, we revisit the classic problem of homogeneous nucleation of a liquid droplet in a supersaturated vapor phase. We consider this at different extents of the driving force, or equivalently the supersaturation, and calculate a reaction coordinate (RC) for nucleation as the driving force is varied. The RC is constructed as a linear combination of three order parameters, where one accounts for the number of liquidlike atoms and the other two for local density fluctuations. The RC is calculated from biased and unbiased molecular dynamics (MD) simulations using the spectral gap optimization approach "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. Our key finding is that as the supersaturation decreases, the RC ceases to simply be the number of liquidlike atoms, and instead, it becomes important to explicitly consider local density fluctuations that correlate with shape and density variations in the nucleus. All three order parameters are found to have similar barriers in their respective potentials of mean force; however, as the supersaturation decreases, the density fluctuations decorrelate slower and thus carry longer memory. Thus, at lower supersaturations, density fluctuations are non-Markovian and cannot be simply ignored from the RC by virtue of being noise. Finally, we use this optimized RC to calculate nucleation rates in the infrequent metadynamics framework and show that it leads to a more accurate estimate of the nucleation rate with four orders of magnitude acceleration relative to unbiased MD. [ABSTRACT FROM AUTHOR]

The study of rare events in molecular and atomic systems such as conformal changes and cluster rearrangements has been one of the most important research themes in chemical physics. Key challenges are associated with long waiting times rendering molecular simulations inefficient, high dimensionality impeding the use of PDE-based approaches, and the complexity or breadth of transition processes limiting the predictive power of asymptotic methods. Diffusion maps are promising algorithms to avoid or mitigate all these issues. We adapt the diffusion map with Mahalanobis kernel proposed by Singer and Coifman (2008) for the SDE describing molecular dynamics in collective variables in which the diffusion matrix is position-dependent and, unlike the case considered by Singer and Coifman, is not associated with a diffeomorphism. We offer an elementary proof showing that one can approximate the generator for this SDE discretized to a point cloud via the Mahalanobis diffusion map. We use it to calculate the committor functions in collective variables for two benchmark systems: alanine dipeptide, and Lennard-Jones-7 in 2D. For validating our committor results, we compare our committor functions to the finite-difference solution or by conducting a "committor analysis" as used by molecular dynamics practitioners. We contrast the outputs of the Mahalanobis diffusion map with those of the standard diffusion map with isotropic kernel and show that the former gives significantly more accurate estimates for the committors than the latter. [ABSTRACT FROM AUTHOR]

Metadynamics is a commonly used and successful enhanced sampling method. By the introduction of a history dependent bias which depends on a restricted number of collective variables it can explore complex free energy surfaces characterized by several metastable states separated by large free energy barriers. Here we extend its scope by introducing a simple yet powerful method for calculating the rates of transition between different metastable states. The method does not rely on a previous knowledge of the transition states or reaction coordinates, as long as collective variables are known that can distinguish between the various stable minima in free energy space. We demonstrate that our method recovers the correct escape rates out of these stable states and also preserves the correct sequence of state-to-state transitions, with minimal extra computational effort needed over ordinary metadynamics. We apply the formalism to three different problems and in each case find excellent agreement with the results of long unbiased molecular dynamics runs. [ABSTRACT FROM AUTHOR]

We present a method called SISYPHUS (stochastic iterations to strengthen yield of path hopping over upper states) for extending accessible time scales in atomistic simulations. The method proceeds by separating phase space into basins and transition regions between the basins based on a general collective variable (CV) criterion. The transition regions are treated via traditional molecular dynamics (MD) while Monte Carlo (MC) methods are used to (i) estimate the expected time spent in each basin and (ii) thermalize the system between two MD episodes. In particular, an efficient adiabatic switching based scheme is used to estimate the time spent inside the basins. The method offers various advantages over existing approaches in terms of (i) providing an accurate real time scale, (ii) avoiding reliance on harmonic transition state theory, and (iii) avoiding the need to enumerate all possible transition events. Applications of SISYPHUS to low-temperature vacancy diffusion in bcc Ta and adatom island ripening in fcc Al are presented. A CV appropriate for such condensed phases, especially for transitions involving collective motions of several atoms, is also introduced. [ABSTRACT FROM AUTHOR]

We extend our recently developed interatomic potentials for UO2 to the fuel system (U,Pu,Np)O2. We do so by fitting against an extensive database of ab initio results as well as to experimental measurements. The applicability of these interactions to a variety of mixed environments beyond the fitting domain is also assessed. The employed formalism makes these potentials applicable across all interatomic distances without the need for any ambiguous splining to the well-established short-range Ziegler-Biersack-Littmark universal pair potential. We therefore expect these to be reliable potentials for carrying out damage simulations (and molecular dynamics simulations in general) in nuclear fuels of varying compositions for all relevant atomic collision energies. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and analytical results are used to demonstrate that the hexagonal close-packed (h.c.p.) pair correlation functions for different values of randomly distributed growth and deformation faults can be collapsed into master curves when plotted against a spatial variable, scaled with respect to a characteristic length ( L). The functional dependences of L on different types of faults are found to be non-universal. A simple method for the determination of L from the measured intensity distributions is also outlined. [ABSTRACT FROM AUTHOR]

Abstract: The cluster variation method (CVM) coupled with the constrained simulated annealing (CSA) algorithm for global free energy minimization is proposed as an efficient approach for the study of alloy phase diagram. The chemical order–disorder transitions in Fe–Co alloy system between 300 and 1100K are investigated using the proposed CSA–CVM approach using the irregular tetrahedron approximation in a bcc lattice. The calculations have been carried out for a hypothetical paramagnetic Fe–Co alloy, i.e. with chemical interactions only, as well as for Fe–Co alloy with both magnetic and chemical interactions acting simultaneously, i.e., considering the quaternary Fe↑Fe↓Co↑Co↓ system. The calculated A2/B2 boundary is found to match well with that determined experimentally. The incorporation of magnetic interaction is also found to have a large influence on the order–disorder transitions. The main advantages of the CSA–CVM approach is that it works efficiently with no initial value dependence on optimization parameters, and in contrast to some of the previously used minimization techniques, it is always found to converge to the global minimum. Another new aspect of the present investigation is that the phase diagram is obtained here by plotting long range order versus composition for the most ordered phase (B2 in this study) and not the commonly used grand potential versus chemical potential curves for various phases, thereby saving a lot of labor. Precise predictions for the variation of heat capacity with temperature have also been made. [Copyright &y& Elsevier]

The ability to predict accurate thermodynamic and kinetic properties in biomolecular systems is of both scientific and practical utility. While both remain very difficult, predictions of kinetics are particularly difficult because rates, in contrast to free energies, depend on the route taken. For this reason, specific enhanced sampling methods are needed to calculate long-time scale kinetics. It has recently been demonstrated that it is possible to recover kinetics through the so-called “infrequent metadynamics” simulations, where the simulations are biased in a way that minimally corrupts the dynamics of moving between metastable states. This method, however, requires the bias to be added slowly, thus hampering applications to processes with only modest separations of time scales. Here we present a frequency-adaptive strategy which bridges normal and infrequent metadynamics. We show that this strategy can improve the precision and accuracy of rate calculations at fixed computational cost and should be able to extend rate calculations for much slower kinetic processes. [ABSTRACT FROM AUTHOR]

Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework based on statistical mechanics and generative artificial intelligence that allows solving this problem. Specifically, we work with denoising diffusion probabilistic models and show how these models in combination with replica exchange molecular dynamics achieve superior sampling of the biomolecular energy landscape at temperatures that were never simulated without assuming any particular slow degrees of freedom. The key idea is to treat the temperature as a fluctuating random variable and not a control parameter as is usually done. This allows us to directly sample from the joint probability distribution in configuration and temperature space. The results here are demonstrated for a chirally symmetric peptide and single-strand RNA undergoing conformational transitions in all-atom water. We demonstrate how we can discover transition states and metastable states that were previously unseen at the temperature of interest and even bypass the need to perform further simulations for a wide range of temperatures. At the same time, any unphysical states are easily identifiable through very low Boltzmann weights. The procedure while shown here for a class of molecular simulations should be more generally applicable to mixing information across simulations and experiments with varying control parameters. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) enables the study of physical systems with excellent spatiotemporal resolution but suffers from severe timescale limitations. To address this, enhanced sampling methods have been developed to improve the exploration of configurational space. However, implementing these methods is challenging and requires domain expertise. In recent years, integration of machine learning (ML) techniques into different domains has shown promise, prompting their adoption in enhanced sampling as well. Although ML is often employed in various fields primarily due to its data-driven nature, its integration with enhanced sampling is more natural with many common underlying synergies. This review explores the merging of ML and enhanced MD by presenting different shared viewpoints. It offers a comprehensive overview of this rapidly evolving field, which can be difficult to stay updated on. We highlight successful strategies such as dimensionality reduction, reinforcement learning, and flow-based methods. Finally, we discuss open problems at the exciting ML-enhanced MD interface. [ABSTRACT FROM AUTHOR]

• Machine learning and artificial intelligence approaches have been leveraged for MD. • One machine learning contribution is in removing noise to make MD data human accessible. • Yet another contribution is in helping to enhance sampling to make MD simulations more ergodic. • The problem of making MD data human accessible and enhancing MD sampling requires overlapping ideas. Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex biophysical systems, there remain methodological difficulties to be surmounted. First, how to make the deluge of data generated in running even a microsecond long MD simulation human comprehensible. Second, how to efficiently sample the underlying free energy surface and kinetics. In this short perspective, we summarize machine learning based ideas that are solving both of these limitations, with a focus on their key theoretical underpinnings and remaining challenges. [ABSTRACT FROM AUTHOR]

An analytical expression for the characteristic length scale (L) of the pair correlation functions for randomly faulted hexagonal close-packed structures is derived for the case when the roots of the characteristic equation are all real. The values of L obtained by this analytical treatment are in good agreement with those obtained numerically. [ABSTRACT FROM AUTHOR]

With the advent of faster computer processors and especially graphics processing units (GPUs) over the last few decades, the use of data-intensive machine learning (ML) and artificial intelligence (AI) has increased greatly, and the study of crystal nucleation has been one of the beneficiaries. In this review, we outline how ML and AI have been applied to address four outstanding difficulties of crystal nucleation: how to discover better reaction coordinates (RCs) for describing accurately non-classical nucleation situations; the development of more accurate force fields for describing the nucleation of multiple polymorphs or phases for a single system; more robust identification methods for determining crystal phases and structures; and as a method to yield improved course-grained models for studying nucleation. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems. [ABSTRACT FROM AUTHOR]

Understanding the structural and energetic requisites of ligand binding toward its molecular target is of paramount relevance in drug design. In recent years, atomistic free energy calculations have proven to be a valid tool to complement experiments in characterizing the thermodynamic and kinetic properties of protein/ligand interaction. Here, we investigate, through a recently developed metadynamics-based protocol, the unbinding mechanism of an inhibitor of the pharmacologically relevant target p38 MAP kinase. We provide a thorough description of the ligand unbinding pathway identifying the most stable binding mode and other thermodynamically relevant poses. From our simulations, we estimated the unbinding rate as koff = 0.020 ± 0.011 s –1 . This is in good agreement with the experimental value ( koff = 0.14 s –1 ). Next, we developed a Markov state model that allowed identifying the rate-limiting step of the ligand unbinding process. Our calculations further show that the solvation of the ligand and that of the active site play crucial roles in the unbinding process. This study paves the way to investigations on the unbinding dynamics of more complex p38 inhibitors and other pharmacologically relevant inhibitors in general, demonstrating that metadynamics can be a powerful tool in designing new drugs with engineered binding/unbinding kinetics. [ABSTRACT FROM AUTHOR]

Crystal nucleation is relevant across the domains of fundamental and applied sciences. However, in many cases, its mechanism remains unclear due to a lack of temporal or spatial resolution. To gain insights into the molecular details of nucleation, some form of molecular dynamics simulations is typically performed; these simulations, in turn, are limited by their ability to run long enough to sample the nucleation event thoroughly. To overcome the timescale limits in typical molecular dynamics simulations in a manner free of prior human bias, here, we employ the machine learningaugmented molecular dynamics framework "reweighted autoencoded variational Bayes for enhanced sampling (RAVE)."Westudy two molecular systems--urea and glycine--in explicit all-atom water, due to their enrichment in polymorphic structures and common utility in commercial applications. From our simulations, we observe multiple back-and-forth nucleation events of different polymorphs from homogeneous solution; from these trajectories, we calculate the relative ranking of finite-sized polymorph crystals embedded in solution, in terms of the free-energy difference between the finite-sized crystal polymorph and the original solution state. We further observe that the obtained reaction coordinates and transitions are highly nonclassical. [ABSTRACT FROM AUTHOR]

Spectral gap optimization of order parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)] is a method for constructing the reaction coordinate (RC) in molecular systems, especially when they are plagued with hard to sample rare events, given a larger dictionary of order parameters or basis functions and limited static and dynamic information about the system. In its original formulation, SGOOP is designed to construct a 1-dimensional RC. Here we extend its scope by introducing a simple but powerful extension based on the notion of conditional probability factorization where known features are effectively washed out to learn additional and possibly hidden features of the energy landscape. We show how SGOOP can be used to proceed in a sequential and bottom-up manner to (i) systematically probe the need for extending the dimensionality of the RC and (ii) if such a need is identified, learn additional coordinates of the RC in a computationally efficient manner. We formulate the method and demonstrate its utility through three illustrative examples, including the challenging and important problem of calculating the kinetics of benzene unbinding from the protein T4L99A lysozyme, where we obtain excellent agreement in terms of dissociation pathway and kinetics with other sampling methods and experiments. In this last case, starting from a larger dictionary of 11 order parameters that are generic for ligand unbinding processes, we demonstrate how to automatically learn a 2-dimensional RC, which we then use in the infrequent metadynamics protocol to obtain 16 independent unbinding trajectories. We believe our method will be a big step in increasing the utility of SGOOP in performing intuition-free sampling of complex systems. Finally, we believe that the utility of our protocol is amplified by its applicability to not just SGOOP but also other generic methods for constructing the RC. [ABSTRACT FROM AUTHOR]

Here we propose the reweighted autoencoded variational Bayes for enhanced sampling (RAVE) method, a new iterative scheme that uses the deep learning framework of variational autoencoders to enhance sampling in molecular simulations. RAVE involves iterations between molecular simulations and deep learning in order to produce an increasingly accurate probability distribution along a low-dimensional latent space that captures the key features of the molecular simulation trajectory. Using the Kullback-Leibler divergence between this latent space distribution and the distribution of various trial reaction coordinates sampled from the molecular simulation, RAVE determines an optimum, yet nonetheless physically interpretable, reaction coordinate and optimum probability distribution. Both then directly serve as the biasing protocol for a new biased simulation, which is once again fed into the deep learning module with appropriate weights accounting for the bias, the procedure continuing until estimates of desirable thermodynamic observables are converged. Unlike recent methods using deep learning for enhanced sampling purposes, RAVE stands out in that (a) it naturally produces a physically interpretable reaction coordinate, (b) is independent of existing enhanced sampling protocols to enhance the fluctuations along the latent space identified via deep learning, and (c) it provides the ability to easily filter out spurious solutions learned by the deep learning procedure. The usefulness and reliability of RAVE is demonstrated by applying it to model potentials of increasing complexity, including computation of the binding free energy profile for a hydrophobic ligand–substrate system in explicit water with dissociation time of more than 3 min, in computer time at least twenty times less than that needed for umbrella sampling or metadynamics. [ABSTRACT FROM AUTHOR]

Understanding how mutations render a drug ineffective is a problem of immense relevance. Often the mechanism through which mutations cause drug resistance can be explained purely through thermodynamics. However, the more perplexing situation is when two proteins have the same drug binding affinities but different residence times. In this work, we demonstrate how all‐atom molecular dynamics simulations using recent developments grounded in statistical mechanics can provide a detailed mechanistic rationale for such variances. We discover dissociation mechanisms for the anti‐cancer drug Imatinib (Gleevec) against wild‐type and the N368S mutant of Abl kinase. We show how this point mutation triggers far‐reaching changes in the protein's flexibility and leads to a different, much faster, drug dissociation pathway. We believe that this work marks an efficient and scalable approach to obtain mechanistic insight into resistance mutations in biomolecular receptors that are hard to explain using a structural perspective. [ABSTRACT FROM AUTHOR]

Understanding how mutations render a drug ineffective is a problem of immense relevance. Often the mechanism through which mutations cause drug resistance can be explained purely through thermodynamics. However, the more perplexing situation is when two proteins have the same drug binding affinities but different residence times. In this work, we demonstrate how all‐atom molecular dynamics simulations using recent developments grounded in statistical mechanics can provide a detailed mechanistic rationale for such variances. We discover dissociation mechanisms for the anti‐cancer drug Imatinib (Gleevec) against wild‐type and the N368S mutant of Abl kinase. We show how this point mutation triggers far‐reaching changes in the protein's flexibility and leads to a different, much faster, drug dissociation pathway. We believe that this work marks an efficient and scalable approach to obtain mechanistic insight into resistance mutations in biomolecular receptors that are hard to explain using a structural perspective. [ABSTRACT FROM AUTHOR]

We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways. [ABSTRACT FROM AUTHOR]