Brownian motion in a phase-separated biopolymer network

Abstract

We present a computational model for studying anomalous diffusion in a phase-separated biopolymer network composed of a rigid gel-forming component and a non-gelling solution component. Using κ-carrageenan (KC) and λ-carrageenan (LC) as model components, a bicontinuous network is generated by numerically solving the Cahn−Hilliard equation via a semi-implicit Fourier pseudo-spectral method. The particles' Brownian motion is governed by the Itô-form overdamped Langevin equation with a spatially heterogeneous diffusivity field D(r), where gel- and solution-phase diffusivities differ by a factor of ≈37. Ensemble MSD shows higher anomalous exponents for sol-phase particles and a lag time dependent MSD ratio that converges as both ensembles sample the full heterogeneity. Sliding-window radius of gyration R_g(t) distributions are bimodal for gel-phase particles. Van Hove distributions confirm heterogeneous, non-Gaussian diffusion in both phases.