Modeling the Geometry and Dynamics of the Endoplasmic Reticulum Network.

The endoplasmic reticulum (ER) is an intricate network that pervades the entire cortex of plant cells and its geometric shape undergoes drastic changes. This paper proposes a mathematical model to reconstruct geometric network dynamics by combining the node movements within the network and topological changes engendered by these nodes. The network topology in the model is determined by a modified optimization procedure from the work (Lemarchand, et al. 2014) which minimizes the total length taking into account both degree and angle constraints, beyond the conditions of connectedness and planarity. A novel feature for solving our optimization problem is the use of "lifted" angle constraints, which allows one to considerably reduce the solution runtimes. Using this optimization technique and a Langevin approach for the branching node movement, the simulated network dynamics represent the ER network dynamics observed under latrunculin B treated condition and recaptures features such as the appearance/disappearance of loops within the ER under the native condition. The proposed modeling approach allows quantitative comparison of networks between the model and experimental data based on topological changes induced by node dynamics. An increased temporal resolution of experimental data will allow a more detailed comparison of network dynamics using this modeling approach.