Density fields for branching, stiff networks in rigid confining regions

TL;DR

This paper introduces a formalism to model the equilibrium distribution of stiff, branched filament networks within confined regions, relevant to cellular cytoskeleton structures like actin filaments with branching.

Contribution

It develops a grand ensemble formalism and nonlinear integral equations to compute density and polarization profiles of confined branched networks, including semi-flexible filaments.

Findings

Identifies three classes of behavior based on filament length, branching, and persistence length.

Provides a numerical method for semi-flexible filament network analysis.

Applicable to cellular cytoskeleton modeling.

Abstract

We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin filaments with branching due to the Arp2/3 complex. We develop a grand ensemble formalism that enables the computation of segment density and polarisation profiles within the confines of the cell. This is expressed in terms of the solution to nonlinear integral equations for auxiliary functions. We find three specific classes of behaviour depending on filament length, degree of branching and the ratio of persistence length to the dimensions of the geometry. Our method allows a numerical approach for semi-flexible filaments that are networked.