Unveiling interatomic distances influencing the reaction coordinates in alanine dipeptide isomerization: An explainable deep learning approach.

The present work shows that the free energy landscape associated with alanine dipeptide isomerization can be effectively represented by specific interatomic distances without explicit reference to dihedral angles. Conventionally, two stable states of alanine dipeptide in vacuum, i.e., C7eq (ß-sheet structure) and C7ax (left handed α-helix structure), have been primarily characterized using the main chain dihedral angles, φ (C-N-Cα-C) and ψ (N-Cα-C-N). However, our recent deep learning combined with the "Explainable AI" (XAI) framework has shown that the transition state can be adequately captured by a free energy landscape using φ and θ (O-C-N-Cα) [Kikutsuji et al., J. Chem. Phys. 156, 154108 (2022)]. In the perspective of extending these insights to other collective variables, a more detailed characterization of the transition state is required. In this work, we employ interatomic distances and bond angles as input variables for deep learning rather than the conventional and more elaborate dihedral angles. Our approach utilizes deep learning to investigate whether changes in the main chain dihedral angle can be expressed in terms of interatomic distances and bond angles. Furthermore, by incorporating XAI into our predictive analysis, we quantified the importance of each input variable and succeeded in clarifying the specific interatomic distance that affects the transition state. The results indicate that constructing a free energy landscape based on the identified interatomic distance can clearly distinguish between the two stable states and provide a comprehensive explanation for the energy barrier crossing.

Revealing the hidden dynamics of confined water in acrylate polymers: Insights from hydrogen-bond lifetime analysis.

Polymers contain functional groups that participate in hydrogen bond (H-bond) with water molecules, establishing a robust H-bond network that influences bulk properties. This study utilized molecular dynamics (MD) simulations to examine the H-bonding dynamics of water molecules confined within three poly(meth)acrylates: poly(2-methoxyethyl acrylate) (PMEA), poly(2-hydroxyethyl methacrylate) (PHEMA), and poly(1-methoxymethyl acrylate) (PMC1A). Results showed that H-bonding dynamics significantly slowed as the water content decreased. Additionally, the diffusion of water molecules and its correlation with H-bond breakage were analyzed. Our findings suggest that when the H-bonds between water molecules and the methoxy oxygen of PMEA are disrupted, those water molecules persist in close proximity and do not diffuse on a picosecond time scale. In contrast, the water molecules H-bonded with the hydroxy oxygen of PHEMA and the methoxy oxygen of PMC1A diffuse concomitantly with the breakage of H-bonds. These results provide an in-depth understanding of the impact of polymer functional groups on H-bonding dynamics.

Explaining reaction coordinates of alanine dipeptide isomerization obtained from deep neural networks using Explainable Artificial Intelligence (XAI).

A method for obtaining appropriate reaction coordinates is required to identify transition states distinguishing the product and reactant in complex molecular systems. Recently, abundant research has been devoted to obtaining reaction coordinates using artificial neural networks from deep learning literature, where many collective variables are typically utilized in the input layer. However, it is difficult to explain the details of which collective variables contribute to the predicted reaction coordinates owing to the complexity of the nonlinear functions in deep neural networks. To overcome this limitation, we used Explainable Artificial Intelligence (XAI) methods of the Local Interpretable Model-agnostic Explanation (LIME) and the game theory-based framework known as Shapley Additive exPlanations (SHAP). We demonstrated that XAI enables us to obtain the degree of contribution of each collective variable to reaction coordinates that is determined by nonlinear regressions with deep learning for the committor of the alanine dipeptide isomerization in vacuum. In particular, both LIME and SHAP provide important features to the predicted reaction coordinates, which are characterized by appropriate dihedral angles consistent with those previously reported from the committor test analysis. The present study offers an AI-aided framework to explain the appropriate reaction coordinates, which acquires considerable significance when the number of degrees of freedom increases.

Breakdown of the Stokes-Einstein relation in supercooled liquids: A cage-jump perspective.

The breakdown of the Stokes-Einstein relation in supercooled liquids, which is the increase in the ratio τατD between the two macroscopic times for structural relaxation and diffusion on decreasing the temperature, is commonly ascribed to dynamic heterogeneities, but a clear-cut microscopic interpretation is still lacking. Here, we tackle this issue exploiting the single-particle cage-jump framework to analyze molecular dynamics simulations of soft disk assemblies and supercooled water. We find that τατD∝⟨tp⟩⟨tc⟩, where ⟨tp⟩ and ⟨tc⟩ are the cage-jump times characterizing slow and fast particles, respectively. We further clarify that this scaling does not arise from a simple term-by-term proportionality; rather, the relations τα∝⟨tp⟩⟨ΔrJ 2⟩ and τD∝⟨tc⟩⟨ΔrJ 2⟩ effectively connect the macroscopic and microscopic timescales, with the mean square jump length ⟨ΔrJ 2⟩ shrinking on cooling. Our work provides a microscopic perspective on the Stokes-Einstein breakdown and generalizes previous results on lattice models to the case of more realistic glass-formers.

Transition pathway of hydrogen bond switching in supercooled water analyzed by the Markov state model.

In this work, we examine hydrogen-bond (H-bond) switching by employing the Markov State Model (MSM). During the H-bond switching, a water hydrogen initially H-bonded with water oxygen becomes H-bonded to a different water oxygen. MSM analysis was applied to trajectories generated from molecular dynamics simulations of the TIP4P/2005 model from a room-temperature state to a supercooled state. We defined four basis states to characterize the configuration between two water molecules: H-bonded ("H"), unbound ("U"), weakly H-bonded ("w"), and alternative H-bonded ("a") states. A 16 × 16 MSM matrix was constructed, describing the transition probability between states composed of three water molecules. The mean first-passage time of the H-bond switching was estimated by calculating the total flux from the HU to UH states. It is demonstrated that the temperature dependence of the mean first-passage time is in accordance with that of the H-bond lifetime determined from the H-bond correlation function. Furthermore, the flux for the H-bond switching is decomposed into individual pathways that are characterized by different forms of H-bond configurations of trimers. The dominant pathway of the H-bond switching is found to be a direct one without passing through such intermediate states as "w" and "a," the existence of which becomes evident in supercooled water. The pathway through "w" indicates a large reorientation of the donor molecule. In contrast, the pathway through "a" utilizes the tetrahedral H-bond network, which is revealed by the further decomposition based on the H-bond number of the acceptor molecule.

Diffusion dynamics of supercooled water modeled with the cage-jump motion and hydrogen-bond rearrangement.

The slow dynamics of glass-forming liquids is generally ascribed to the cage jump motion. In the cage jump picture, a molecule remains in a cage formed by neighboring molecules and, after a sufficiently long time, it jumps to escape from the original position by cage breaking. The clarification of the cage jump motion is therefore linked to unraveling the fundamental element of the slow dynamics. Here, we develop a cage jump model for the dynamics of supercooled water. The caged and jumping states of a water molecule are introduced with respect to the hydrogen-bond (H-bond) rearrangement process and describe the motion in supercooled states. It is then demonstrated from the molecular dynamics simulation of the TIP4P/2005 model that the characteristic length and time scales of cage jump motions provide a good description of the self-diffusion constant that is determined in turn from the long-time behavior of the mean square displacement. Our cage jump model thus enables the connection between H-bond dynamics and molecular diffusivity.

How do hydrogen bonds break in supercooled water?: Detecting pathways not going through saddle point of two-dimensional potential of mean force.

Supercooled water exhibits remarkably slow dynamics similar to the behavior observed for various glass-forming liquids. The local order of tetrahedral structures due to hydrogen-bonds (H-bonds) increases with decreasing temperature. Thus, it is important to clarify the temperature dependence of the H-bond breakage process. This was investigated here using molecular dynamics simulations of TIP4P supercooled water. The two-dimensional (2D) potential of mean force (PMF) is presented using combinations of intermolecular distance and angle between two water molecules. The saddle point of the 2D PMF suggests the presence of the transition state that distinguishes between H-bond and non H-bond states. However, we observed pathways not going through this saddle point particularly at supercooled states, which are due to translational rather than rotational motions of the molecules. We quantified the characteristic time scales of rotational and translational H-bond breakages. The time scale of the translational H-bond breakage shows a non-Arrhenius temperature dependence comparable to that of the H-bond lifetime. This time scale is relevant for the temperature dependence of the transmission coefficient based on the transition state theory. The translational H-bond breakage is also related to cage-jumps observed in glass-forming liquids, which mostly involve spatially correlated molecules. Our findings warrant further exploration of an appropriate free-energy surface or reaction coordinates beyond the geometrical variables of the water dimer to describe a possible saddle point related to collective jump motions.