Employing Artificial Neural Networks to Identify Reaction Coordinates and Pathways for Self-Assembly

Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook

Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Besides discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.

Divergence among Local Structure, Dynamics, and Nucleation Outcome in Heterogeneous Nucleation of Close-Packed Crystals

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

Toward a structural identification of metastable molecular conformations

Interpreting high-dimensional data from molecular dynamics simulations is a persistent challenge. In this paper, we show that for a small peptide, deca-alanine, metastable states can be identified through a neural net based on structural information alone. While processing molecular dynamics data, dimensionality reduction is a necessary step that projects high-dimensional data onto a low-dimensional representation that, ideally, captures the conformational changes in the underlying data. Conventional methods make use of the temporal information contained in trajectories generated through integrating the equations of motion, which forgoes more efficient sampling schemes. We demonstrate that EncoderMap, an autoencoder architecture with an additional distance metric, can find a suitable low-dimensional representation to identify long-lived molecular conformations using exclusively structural information. For deca-alanine, which exhibits several helix-forming pathways, we show that this approach allows us to combine simulations with different biasing forces and yields representations comparable in quality to other established methods. Our results contribute to computational strategies for the rapid automatic exploration of the configuration space of peptides and proteins.

An exploration of machine learning models for the determination of reaction coordinates associated with conformational transitions

Determining collective variables (CVs) for conformational transitions is crucial to understanding their dynamics and targeting them in enhanced sampling simulations. Often, CVs are proposed based on intuition or prior knowledge of a system. However, the problem of systematically determining a proper reaction coordinate (RC) for a specific process in terms of a set of putative CVs can be achieved using committor analysis (CA). Identifying essential degrees of freedom that govern such transitions using CA remains elusive because of the high dimensionality of the conformational space. Various schemes exist to leverage the power of machine learning (ML) to extract an RC from CA. Here, we extend these studies and compare the ability of 17 different ML schemes to identify accurate RCs associated with conformational transitions. We tested these methods on an alanine dipeptide in vacuum and on a sarcosine dipeptoid in an implicit solvent. Our comparison revealed that the light gradient boosting machine method outperforms other methods. In order to extract key features from the models, we employed Shapley Additive exPlanations analysis and compared its interpretation with the "feature importance" approach. For the alanine dipeptide, our methodology identifies ϕ and θ dihedrals as essential degrees of freedom in the C7ax to C7eq transition. For the sarcosine dipeptoid system, the dihedrals ψ and ω are the most important for the cisαD to transαD transition. We further argue that analysis of the full dynamical pathway, and not just endpoint states, is essential for identifying key degrees of freedom governing transitions.