Driving and characterizing nucleation of urea and glycine polymorphs in water.

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 learning-augmented molecular dynamics framework "reweighted autoencoded variational Bayes for enhanced sampling (RAVE)." We study 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.

Enhanced Sampling with Machine Learning.

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.

From data to noise to data for mixing physics across temperatures with generative artificial intelligence.

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.

Exploring Kinase Asp-Phe-Gly (DFG) Loop Conformational Stability with AlphaFold2-RAVE.

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular, cancers. The ubiquitousness and structural similarities of kinases make specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved Asp-Phe-Gly (DFG) motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticeably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learned order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations (Meller, A.; Bhakat, S.; Solieva, S.; Bowman, G. R. Accelerating Cryptic Pocket Discovery Using AlphaFold. J. Chem. Theory Comput. 2023, 19, 4355-4363).

Graph Attention Site Prediction (GrASP): Identifying Druggable Binding Sites Using Graph Neural Networks with Attention.

Identifying and discovering druggable protein binding sites is an important early step in computer-aided drug discovery, but it remains a difficult task where most campaigns rely on a priori knowledge of binding sites from experiments. Here, we present a binding site prediction method called Graph Attention Site Prediction (GrASP) and re-evaluate assumptions in nearly every step in the site prediction workflow from data set preparation to model evaluation. GrASP is able to achieve state-of-the-art performance at recovering binding sites in PDB structures while maintaining a high degree of precision which will minimize wasted computation in downstream tasks such as docking and free energy perturbation.

Molecular recognition of methylated amino acids and peptides by Pillar[6]MaxQ.

We report the molecular recognition properties of Pillar[n]MaxQ (P[n]MQ) toward a series of (methylated) amino acids, amino acid amides, and post-translationally modified peptides by a combination of 1H NMR, isothermal titration calorimetry, indicator displacement assays, and molecular dynamics simulations. We find that P6MQ is a potent receptor for N-methylated amino acid side chains. P6MQ recognized the H3K4Me3 peptide with Kd = 16 nM in phosphate buffered saline.

Protein Flexibility and Dissociation Pathway Differentiation Can Explain Onset of Resistance Mutations in Kinases.

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.

State predictive information bottleneck.

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.

Understanding the role of predictive time delay and biased propagator in RAVE.

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.

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics.

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.

Kinetics of Ligand-Protein Dissociation from All-Atom Simulations: Are We There Yet?

Large parallel gains in the development of both computational resources and sampling methods have now made it possible to simulate dissociation events in ligand-protein complexes with all-atom resolution. Such encouraging progress, together with the inherent spatiotemporal resolution associated with molecular simulations, has left their use for investigating dissociation processes brimming with potential, both in rational drug design, where it can be an invaluable tool for determining the mechanistic driving forces behind dissociation rate constants, and in force-field development, where it can provide a catalog of transient molecular structures with which to refine force fields. Although much progress has been made in making force fields more accurate, reducing their error for transient structures along a transition path could yet prove to be a critical development helping to make kinetic predictions much more accurate. In what follows, we will provide a state-of-the-art compilation of the enhanced sampling methods based on molecular dynamics (MD) simulations used to investigate the kinetics and mechanisms of ligand-protein dissociation processes. Due to the time scales of such processes being slower than what is accessible using straightforward MD simulations, several ingenious schemes are being devised at a rapid rate to overcome this obstacle. Here we provide an up-to-date compendium of such methods and their achievements and shortcomings in extracting mechanistic insight into ligand-protein dissociation. We conclude with a critical and provocative appraisal attempting to answer the title of this Perspective.

Reaction coordinates and rate constants for liquid droplet nucleation: Quantifying the interplay between driving force and memory.

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.

Spectral gap optimization of order parameters for sampling complex molecular systems.

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.

Reweighted autoencoded variational Bayes for enhanced sampling (RAVE).

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.

Frequency adaptive metadynamics for the calculation of rare-event kinetics.

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.

Multi-dimensional spectral gap optimization of order parameters (SGOOP) through conditional probability factorization.

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.

Role of water and steric constraints in the kinetics of cavity-ligand unbinding.

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.

Kinetics of protein-ligand unbinding: Predicting pathways, rates, and rate-limiting steps.

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 k off is computed from the mean residence time of the ligand. Using our previously computed binding affinity we also obtain the binding rate k on. Both rates are in agreement with reported experimental values. We uncover the complex pathways of unbinding trajectories and describe the critical rate-limiting 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.

Unbinding Kinetics of a p38 MAP Kinase Type II Inhibitor from Metadynamics Simulations.

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.