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Mathematically modeling complex transport phenomena at the molecular levelcan be a powerful tool for identifying transport mechanisms and predictingmacroscopic properties. We use two different stochastic time series models,parameterized from long molecular dynamics (MD) simulation trajectories of across-linked HII phase lyotropic liquid crystal (LLC) membrane, in order topredict solute mean squared displacements (MSDs) and solute flux, and thussolute selectivity, in macroscopic length pores. First, using anomalousdiffusion theory, we show how solute dynamics can be modeled as a fractionaldiffusion process subordinate to a continuous time random walk. From the MDsimulations, we parameterize the distribution of dwell times, hop lengthsbetween dwells and correlation between hops. We explore two variations of theanomalous diffusion modeling approach. The first applies a single set ofparameters to the solute displacements and the second applies two sets ofparameters based on the solute's radial distance from the closest pore center.Next, we generalize Markov state models, treating the configurational states ofthe system as a Markov process where each state has distinct transportproperties. For each state and transition between states, we parameterize thedistribution and temporal correlation structure of positional fluctuations as ameans of characterization and to allow us to predict solute MSDs. Qualitativedifferences between MD and Markov state dependent model-generated trajectoriesmay limit its usefulness. Finally, we demonstrate how one can use these modelsto estimate flux of a solute across a macroscopic-length pore and, based onthose quantities, the membrane's selectivity towards each solute. This workhelps to connect microscopic chemically-dependent solute motions that do notfollow simple diffusive behavior with macroscopic membrane performance.

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