Phase field model for viscous inclusions in anisotropic networks

TL;DR

This paper presents a theoretical phase field model combining liquid crystal theory and elasticity to explain the influence of anisotropic actin networks on lipid domain growth, aligning with experimental observations.

Contribution

It introduces a novel model incorporating actin filament anisotropy and elastic effects to simulate lipid domain ripening in membrane-actin systems.

Findings

Simulates lipid domain growth slowing due to actin elasticity

Reproduces experimental lipid domain coarsening behavior

Shows domain growth scales as t^α with α<1/4 in actin networks

Abstract

The growth of viscous two-dimensional lipid domains in contact with a viscoelastic actin network was recently shown to exhibit unusual lipid domain ripening due to the geometry and anisotropy of the actin network [Arnold & Takatori. Langmuir. 40, 26570-26578 (2024)]. In this work, we interpret previous experimental results on lipid membrane-actin composites with a theoretical model that combines the Cahn-Hilliard and Landau-de Gennes liquid crystal theory. In our model, we incorporate fiber-like characteristics of actin filaments and bundles through a nematic order parameter, and elastic anisotropy through cubic nematic gradients. Numerical simulations qualitatively agree with experimental observations, by reproducing the competition between the thermodynamic forces that coarsen lipid domains versus the elastic forces generated by the surrounding actin network that resist domain coarsening. We observe a decrease in the growth of domain sizes, finding $R(t) \sim t^{\alpha}$ with $\alpha < 1/4$ for different actin network stiffnesses, in sharp contrast to the $\sim t^{1/3}$ scaling for diffusive growth of domains in the absence of the actin network. Our findings may serve as a foundation for future developments in modeling elastic ripening in complex systems.