Density fields for branching, stiff networks in rigid confining regions

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.

arXiv comment15 pages, revised

References in corpus (10)

• Spontaneous Circulation of Confined Active Suspensions
• Hard-body models of bulk liquid crystals
• Semiflexible Polymer Confined in Closed Spaces
• Shapes of Semiflexible Polymers in Confined Spaces
• Anisotropic Random Networks of Semiflexible Polymers
• Spatial Organization of the Cytoskeleton enhances Cargo Delivery to Specific Target Areas on the Plasma Membrane of Spherical Cells
• Crossover from a Kosterlitz-Thouless to a discontinuous phase transition in two-dimensional liquid crystals
• Entropic competition in polymeric systems under geometrical confinement
• Stiff polymer in monomer ensemble
• Mean Field and the Single Homopolymer