Eur. Phys. J. E (2019) 42: 23
https://doi.org/10.1140/epje/i2019-11784-0

Regular Article

Density fields for branching, stiff networks in rigid confining regions

¹ Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch, South Africa
² National Institute for Theoretical Physics, Stellenbosch, South Africa

^* e-mail: somialo.azote@aims-senegal.org

Received: 23 October 2018
Accepted: 23 January 2019
Published online: 22 February 2019

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.