Geometric dynamics of anchored filamentous networks subject to viscous flow

Abstract

The Endoplasmic Reticulum (ER) is an organelle that can form a complex dynamic network of filaments embedded in the viscous flowing cytoplasm of plant cells, anchored to points in the cell membrane. We consider an idealised dynamical model of the ER network as constant tension filaments subject to viscous forces from cytoplasmic flow. We show that simple configurations lead to the creation of a filamentous network that is analogous to 2D foams, but with different physical mechanisms. We consider a fixed set of anchor points and propose an adaptive algorithm to track the network in the presence of the flow. We find that minimal (Steiner) networks joining these anchor points can support filamentous network of varying geometries with and without an imposed flow. We demonstrate that after any flow has ceased, the filamentous network can retain memory of previous flow direction and intensity.