Computational Modeling of Coupled Interactions of Fluid Membranes with Embedded Filaments

TL;DR

This paper introduces a computational model for studying the complex interactions between fluid membranes and embedded semiflexible filaments, relevant to biological systems like cytoskeletal networks and cell fission, addressing unique computational challenges.

Contribution

It presents a novel continuum mechanics-based formulation for membrane-filament interactions, combining Helfrich-Canham energy for membranes and Cosserat continuum for filaments, with validation and biological applications.

Findings

Validated the computational model against known benchmarks.

Demonstrated the model's application to biological membrane-filament systems.

Identified unique computational challenges and addressed them.

Abstract

In this work, we present a computational formulation based on continuum mechanics to study the interaction of fluid membranes embedded with semiflexible filaments. This is motivated by systems in membrane biology, such as cytoskeletal networks and protein filaments aiding the cell fission process. We model the membrane as a fluid shell via the Helfrich-Canham energy and the filament as a one-dimensional Cosserat continuum. We assume the filament to be tethered to the surface of the membrane in a way that it is allowed to float on the surface freely. The novel filament-membrane coupling, which is anticipated to yield interesting physics, also gives rise to unique computational challenges, which we address in this work. We present validation results and apply the formulation to certain problems inspired by cellular biology.