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Molecular dynamics simulations offer detailed insights into atomic motions but face timescale limitations. Enhanced sampling methods have addressed these challenges but even with machine learning, they often rely on pre-selected expert-based features. In this work, we present the Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph neural networks and the State Predictive Information Bottleneck to automatically learn low-dimensional representations directly from atomic coordinates. Tested on three benchmark systems, our approach predicts essential structural, thermodynamic and kinetic information for slow processes, demonstrating robustness across diverse systems. The method shows promise for complex systems, enabling effective enhanced sampling without requiring pre-defined reaction coordinates or input features.

The recent surge in Generative Artificial Intelligence (AI) has introduced exciting possibilities for computational chemistry. Generative AI methods have made significant progress in sampling molecular structures across chemical species, developing force fields, and speeding up simulations. This Perspective offers a structured overview, beginning with the fundamental theoretical concepts in both Generative AI and computational chemistry. It then covers widely used Generative AI methods, including autoencoders, generative adversarial networks, reinforcement learning, flow models and language models, and highlights their selected applications in diverse areas including force field development, and protein/RNA structure prediction. A key focus is on the challenges these methods face before they become truly predictive, particularly in predicting emergent chemical phenomena. We believe that the ultimate goal of a simulation method or theory is to predict phenomena not seen before, and that Generative AI should be subject to these same standards before it is deemed useful for chemistry. We suggest that to overcome these challenges, future AI models need to integrate core chemical principles, especially from statistical mechanics.

The weighted ensemble (WE) method stands out as a widely used segment-based sampling technique renowned for its rigorous treatment of kinetics. The WE framework typically involves initially mapping the configuration space onto a low-dimensional collective variable (CV) space and then partitioning it into bins. The efficacy of WE simulations heavily depends on the selection of CVs and binning schemes. The recently proposed State Predictive Information Bottleneck (SPIB) method has emerged as a promising tool for automatically constructing CVs from data and guiding enhanced sampling through an iterative manner. In this work, we advance this data-driven pipeline by incorporating prior expert knowledge. Our hybrid approach combines SPIB-learned CVs to enhance sampling in explored regions with expert-based CVs to guide exploration in regions of interest, synergizing the strengths of both methods. Through benchmarking on alanine dipeptide and chignoin systems, we demonstrate that our hybrid approach effectively guides WE simulations to sample states of interest, and reduces run-to-run variances. Moreover, our integration of the SPIB model also enhances the analysis and interpretation of WE simulation data by effectively identifying metastable states and pathways, and offering direct visualization of dynamics.

We investigate crystal nucleation in supersaturated colloid suspensions using enhanced molecular dynamics simulations augmented with machine learning techniques. The simulations reveal that crystallization in the model colloidal system studied here, with particles interacting through a repulsive screened Coulomb Yukawa potential, proceeds from vapor to dense liquid droplet to crystalline phases across multiple high barriers. Employing a one-dimensional reaction coordinate derived from the State Predictive Information Bottleneck framework, our simulations capture backand-forth phase transitions across multiple barriers effectively in biased metadynamics simulations. We obtain relative free energy differences between different phases and also quantify the roles of different molecular level features in driving the phase changes.

Small molecule drug design hinges on obtaining co-crystallized ligand-protein structures. Despite AlphaFold2's strides in protein native structure prediction, its focus on apo structures overlooks ligands and associated holo structures. Moreover, designing selective drugs often benefits from the targeting of diverse metastable conformations. Therefore, direct application of AlphaFold2 models in virtual screening and drug discovery remains tentative. Here, we demonstrate an AlphaFold2 based framework combined with all-atom enhanced sampling molecular dynamics and induced fit docking, named AF2RAVE-Glide, to conduct computational model based small molecule binding of metastable protein kinase conformations, initiated from protein sequences. We demonstrate the AF2RAVE-Glide workflow on three different protein kinases and their type I and II inhibitors, with special emphasis on binding of known type II kinase inhibitors which target the metastable classical DFG-out state. These states are not easy to sample from AlphaFold2. Here we demonstrate how with AF2RAVE these metastable conformations can be sampled for different kinases with high enough accuracy to enable subsequent docking of known type II kinase inhibitors with more than 50% success rates across docking calculations. We believe the protocol should be deployable for other kinases and more proteins generally., Comment: added revised version and DOI link to eLife version

Markov state models (MSMs) are valuable for studying dynamics of protein conformational changes via statistical analysis of molecular dynamics (MD) simulations. In MSMs, the complex configuration space is coarse-grained into conformational states, with the dynamics modeled by a series of Markovian transitions among these states at discrete lag times. Constructing the Markovian model at a specific lag time requires state defined without significant internal energy barriers, enabling internal dynamics relaxation within the lag time. This process coarse grains time and space, integrating out rapid motions within metastable states. This work introduces a continuous embedding approach for molecular conformations using the state predictive information bottleneck (SPIB), which unifies dimensionality reduction and state space partitioning via a continuous, machine learned basis set. Without explicit optimization of VAMP-based scores, SPIB demonstrates state-of-the-art performance in identifying slow dynamical processes and constructing predictive multi-resolution Markovian models. When applied to mini-proteins trajectories, SPIB showcases unique advantages compared to competing methods. It automatically adjusts the number of metastable states based on a specified minimal time resolution, eliminating the need for manual tuning. While maintaining efficacy in dynamical properties, SPIB excels in accurately distinguishing metastable states and capturing numerous well-populated macrostates. Furthermore, SPIB's ability to learn a low-dimensional continuous embedding of the underlying MSMs enhances the interpretation of dynamic pathways. Accordingly, we propose SPIB as an easy-to-implement methodology for end-to-end MSM construction., Comment: 19 pages, 7 figures

In this work we examine the nucleation from NaCl aqueous solutions within nano-confined environments, employing enhanced sampling molecular dynamics simulations integrated with machine learning-derived reaction coordinates. Through our simulations, we successfully induce phase transitions between solid, liquid, and a hydrated phase, typically observed at lower temperatures in bulk environments. Interestingly, nano-confinement serves to stabilize the solid phase and elevate melting points. Our simulations explain these findings by underscoring the significant role of water, alongside ion aggregation and subtle, anistropic dielectric behavior, in driving nucleation within nano-constrained environments. This letter thus provides a framework for sampling, analyzing and understanding nucleation processes under nano-confinement.

In this study, we present a graph neural network-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced sampling to observe state-to-state transitions and reliable thermodynamic weights. Our approach uses simple convolution and pooling methods. To verify the effectiveness of our protocol, we examined the nucleation of various allotropes and polymorphs of iron and glycine from their molten states. Our graph latent variables when biased in well-tempered metadynamics consistently show transitions between states and achieve accurate free energy calculations in agreement with experiments, both of which are indicators of dependable sampling. This underscores the strength and promise of our graph neural net variables for improved sampling. The protocol shown here should be applicable for other systems and with other sampling methods.

Ligand unbinding is mediated by the free energy change, which has intertwined contributions from both energy and entropy. It is important but not easy to quantify their individual contributions. We model hydrophobic ligand unbinding for two systems, a methane particle and a C60 fullerene, both unbinding from hydrophobic pockets in all-atom water. By using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as ligand and pocket sizes change. Irrespective of the contrasting roles of energy and entropy, we also find that for both the systems the transition from the bound to unbound states is driven primarily by solvation of the pocket and ligand, independent of ligand size. Our framework thus gives useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean., Comment: 27 pages; 5 figures

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling all-atom molecular dynamics with deep learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in the aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, while fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Our protocol proposed here enables robust nucleation analysis and phase sampling, and could offer insights into nucleation mechanisms for generic small molecules in different environments.

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 makes specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved 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 noticably 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 learnt order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations.

Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within different phases' domains of stability. Our approach is called Thermodynamic Maps, which combines statistical mechanics and molecular simulations with score-based generative models. Thermodynamic Maps enable learning the temperature dependence of arbitrary thermodynamic observables across a wide range of temperatures. We show its usefulness by calculating phase transition attributes such as melting temperature, temperature-dependent heat capacities, and critical exponents. For instance, we demonstrate the ability of thermodynamic maps to infer the ferromagnetic phase transition of the Ising model, including temperature-dependent heat capacity and critical exponents, despite never having seen samples from the transition region. In addition, we efficiently characterize the temperature-dependent conformational ensemble and compute melting curves of the two RNA systems GCAA tetraloop and HIV-TAR, which are notoriously hard to sample due to glassy-like landscapes.

Understanding nucleation from aqueous solutions is of fundamental importance in a multitude of fields, ranging from materials science to biophysics. The complex solvent-mediated interactions in aqueous solutions hamper the development of a simple physical picture elucidating the roles of different interactions in nucleation processes. In this work we make use of three complementary techniques to disentangle the role played by short and long-range interactions in solvent mediated nucleation. Specifically, the first approach we utilize is the local molecular field (LMF) theory to renormalize long-range Coulomb electrostatics. Secondly, we use well-tempered metadynamics to speed up rare events governed by short-range interactions. Thirdly, deep learning-based State Predictive Information Bottleneck approach is employed in analyzing the reaction coordinate of the nucleation processes obtained from LMF treatment coupled with well-tempered metadynamics. We find that the two-step nucleation mechanism can largely be captured by the short-range interactions, while the long-range interactions further contribute to the stability of the primary crystal state at ambient conditions. Furthermore, by analyzing the reaction coordinate obtained from combined LMF-metadynamics treatment, we discern the fluctuations on different time scales, highlighting the need for long-range interactions when accounting for metastability.

Lack of rigorous reproducibility and validation are major hurdles for scientific development across many fields. Materials science in particular encompasses a variety of experimental and theoretical approaches that require careful benchmarking. Leaderboard efforts have been developed previously to mitigate these issues. However, a comprehensive comparison and benchmarking on an integrated platform with multiple data modalities with both perfect and defect materials data is still lacking. This work introduces JARVIS-Leaderboard, an open-source and community-driven platform that facilitates benchmarking and enhances reproducibility. The platform allows users to set up benchmarks with custom tasks and enables contributions in the form of dataset, code, and meta-data submissions. We cover the following materials design categories: Artificial Intelligence (AI), Electronic Structure (ES), Force-fields (FF), Quantum Computation (QC) and Experiments (EXP). For AI, we cover several types of input data, including atomic structures, atomistic images, spectra, and text. For ES, we consider multiple ES approaches, software packages, pseudopotentials, materials, and properties, comparing results to experiment. For FF, we compare multiple approaches for material property predictions. For QC, we benchmark Hamiltonian simulations using various quantum algorithms and circuits. Finally, for experiments, we use the inter-laboratory approach to establish benchmarks. There are 1281 contributions to 274 benchmarks using 152 methods with more than 8 million data-points, and the leaderboard is continuously expanding. The JARVIS-Leaderboard is available at the website: https://pages.nist.gov/jarvis_leaderboard

Molecular dynamics (MD) enables the study of physical systems with excellent spatiotemporal resolution but suffers from severe time-scale limitations. To address this, enhanced sampling methods have been developed to improve exploration of configurational space. However, implementing these is challenging and requires domain expertise. In recent years, integration of machine learning (ML) techniques in 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 like dimensionality reduction, reinforcement learning, and flow-based methods. Finally, we discuss open problems at the exciting ML-enhanced MD interface., Comment: Submitted as invited article to Annual Review of Physical Chemistry vol 75; updated formatting issues

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., Comment: 15 pages; 1 figure

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 to 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 liquid-solid transitions of different polymorphs and from these trajectories calculate the polymorph stability relative to the dissolved liquid state. We further observe that the obtained reaction coordinates and transitions are highly non-classical., Comment: 12 pages, 7 figures

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned representation through prior probability distributions. However, such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density - a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. We show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.

The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations which dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques such as metadynamics. The resulting algorithm, which we call the "target measure Mahalanobis diffusion map" (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro-Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible., Comment: Restructured introduction, improved explanation of key algorithms and formulas (Section II.C and III.B,C). Streamlined presentation and proof of Theorem 1

In recent years, predictive machine learning methods have gained prominence in various scientific domains. However, due to their black-box nature, it is essential to establish trust in these models before accepting them as accurate. One promising strategy for assigning trust involves employing explanation techniques that elucidate the rationale behind a black-box model's predictions in a manner that humans can understand. However, assessing the degree of human interpretability of the rationale generated by such methods is a nontrivial challenge. In this work, we introduce interpretation entropy as a universal solution for assessing the degree of human interpretability associated with any linear model. Using this concept and drawing inspiration from classical thermodynamics, we present Thermodynamics-inspired Explainable Representations of AI and other black-box Paradigms (TERP), a method for generating accurate, and human-interpretable explanations for black-box predictions in a model-agnostic manner. To demonstrate the wide-ranging applicability of TERP, we successfully employ it to explain various black-box model architectures, including deep learning Autoencoders, Recurrent Neural Networks, and Convolutional Neural Networks, across diverse domains such as molecular simulations, text, and image classification., Comment: revised theory and examples

When examining dynamics occurring at non-zero temperatures, both energy and entropy must be taken into account while describing activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called the State Predictive Information Bottleneck (SPIB) to find non-linear reaction coordinates for three systems of varying complexity. The SPIB is able to predict correctly an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Finally, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy and energy/enthalpy barriers in physical systems, which can then be used for enhanced understanding and sampling of different activated mechanisms.

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections., Comment: Added results for open quantum system with dissipative photon dynamics

An effective implementation of enhanced sampling algorithms for molecular dynamics simulations requires a priori knowledge of the approximate reaction coordinate describing the relevant mechanisms in the system. Here we demonstrate how the artificial intelligence based recent State Predictive Information Bottleneck (SPIB) approach can learn such a reaction coordinate as a deep neural network even from under-sampled trajectories. We demonstrate its usefulness by achieving more than 40 magnitudes of acceleration in simulating two test-piece biophysical systems through well-tempered metadynamics performed by biasing along the SPIB learned reaction coordinate. These include left- to right- handed chirality transitions in a synthetic protein (Aib)_9, and permeation of a small, asymmetric molecule benzoic acid through a synthetic, symmetric phospholipid bilayer. In addition to significantly accelerating the dynamics and achieving back-and-forth movement between different metastable states, the SPIB based reaction coordinate gives mechanistic insight into the processes driving these two important problems.

We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long range Coulomb interactions and for a well chosen reference system with short range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool "State predictive information bottleneck" (SPIB) we show that the system with short range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long range interactions can be largely neglected for these processes because long range forces from the direct interionic Coulomb interactions are almost completely canceled ($>90\%$) by those from solvent interactions over the length scale where the transition takes place. Thus for this important monovalent ion-pair system, short range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short range models for the disassociation event. We believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long range contributions may be more important.