Capturing Subdiffusive Solute Dynamics and Predicting Selectivity in Nanoscale Pores with Time Series Modeling.

Area of Science:

• Computational chemistry and physics
• Materials science
• Chemical engineering

Background:

• Molecular simulations generate large datasets that require sophisticated models for extracting meaningful physical insights.
• Understanding solute transport in complex media like liquid crystal membranes is crucial for predicting macroscopic properties.
• Previous work identified subdiffusive solute transport in a lyotropic liquid crystal membrane, characterized by hopping and entrapment.

Purpose of the Study:

• To develop and apply novel stochastic time series models for predicting long-time-scale behavior and macroscopic properties from molecular dynamics (MD) simulations.
• To parameterize models based on MD data to generate realistic trajectory realizations for predicting solute mean-squared displacements (MSDs), flux, and selectivity.
• To generalize existing modeling approaches for complex diffusion phenomena in various molecular systems.

Main Methods:

• Anomalous diffusion theory: Modeled solute dynamics as a fractional diffusion process within a continuous time random walk framework, parameterizing dwell times, hop lengths, and hop correlations.
• Two variations of anomalous diffusion modeling were explored: single-parameter set and two-parameter set based on radial distance from pore centers.
• Generalized Markov state models: Treated system configurations as Markov processes with distinct transport properties, parameterizing positional fluctuations and temporal correlations.

Main Results:

• Both stochastic models successfully reproduced mean-squared displacements (MSDs) calculated from molecular dynamics (MD) simulations.
• The models enabled the estimation of solute flux across macroscopic pores and the calculation of membrane selectivity for different solutes.
• Qualitative differences between MD and Markov state-dependent model trajectories were observed, potentially impacting their applicability in specific cases.

Conclusions:

• Parameterized stochastic models effectively bridge the gap between microscopic solute motions and long-time-scale macroscopic behavior in complex systems.
• The developed approaches offer a generalizable framework for analyzing and predicting transport properties in molecular systems exhibiting non-Fickian diffusion.
• This work provides a pathway to connect detailed molecular dynamics with observable transport phenomena, enhancing the predictive power of simulations.