Applying a Gaussian networking theory to model motor-driven transport along cytoskeletal filaments

TL;DR

This work extends a dynamical Gaussian networking framework to model active motor-driven transport along cytoskeletal filament networks using a Martin-Siggia-Rose representation of Langevin dynamics. A dedicated networking functional enforces periodic motor attachment to filament binding sites, enabling a collective description via RPA and a saddle-point treatment that yields a networked functional and a diffusion-like correlation function. For homogeneous networks the formalism produces a diffusion coefficient $D$ and a motor hopping speed governed by the binding-site density, while it accommodates non-homogeneous networks through fluctuations in binding-site density and corresponding quenched or annealed averaging. The approach offers a flexible, field-theoretic pathway to study directed diffusion on branched cytoskeletal architectures and to extend the model with additional physical effects and network variability.

Abstract

This paper builds on a recently introduced dynamical networking framework, applying it to model motor-driven transport along cytoskeletal filament networks. Within this approach, the networking functional describes the periodic binding and unbinding of motors to available filament sites,whilst accounting for all possible pairing, enabling a field-theoretic treatment of constrained motion in complex networks. In this application, the dynamical networking theory is introduced into a Martin-Siggia-Rose representation of the Langevin dynamics describing the motion of a motor protein and its cargo. Results are presented in a collective description of motors on a network, for two different scenarios, namely homogeneous and non-homogeneous networks. A diffusion coefficient is presented for homogeneous networks, whilst it is shown that various possibilities remain for disordered averaging over network densities for non-homogeneous networks.

Figures (3)

• Figure 1: Schematic diagram of generic motor proteins (red) transporting cargoes (blue) on the branched filaments (green) of the cytoskeleton within a cell. A portion of the cell membrane is shown in orange.
• Figure 2: Schematic diagram depicting the coupling of a cargo with position $R(t)$ to a motor protein with position $x(t)$.
• Figure 3: A diagram illustrating one of the possible pairings counted in the networking functional through the use of the fields $\Phi$ and $\Phi^*$. The configuration in the diagram depicts the motor protein (red) with position x(t) attaching to the binding site at position $r_1$.