Phase field model for viscous inclusions in anisotropic 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. <i>Langmuir</i>. <b>40</b>, 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 <i>versus</i> the elastic forces generated by the surrounding actin network that resist domain coarsening. We observe a decrease in the growth of domain sizes, finding <i>R</i>(<i>t</i>) ∼ <i>t</i>^<i>α</i> with <i>α</i> < 1/4 for different actin network stiffnesses, in sharp contrast to the ∼<i>t</i>^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.