Modeling the Geometry and Dynamics of the Endoplasmic Reticulum Network

Abstract

Abstract-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.

Plant organelle dynamics: cytoskeletal control and membrane contact sites

“…The latter will provide predictive power to determine which parts of the system provide the ultimate control over organelle dynamics. For example, models of ER network formation have provided a first principle approximation of the biophysical properties required to form a dynamic model of network formation which fits in vivo ER network dynamics (Lemarchand et al ., ; Lin et al ., , ; Griffing et al ., ).…”

Lessons from optical tweezers: quantifying organelle interactions, dynamics and modelling subcellular events

“…Mathematical modelling approaches have determined that a dynamic ER network can be computationally modelled to fit the expected ER network based on anchoring at these static nodes. Here, the ER network tends towards limiting its entire length and generates additional mobile nodes (steiner points) in order to do so [16][17][18].…”

intER‐ACTINg: The structure and dynamics of ER and actin are interlinked

“…8 The actin cytoskeleton, through the action of actin-binding proteins which physically link actin filaments to a variety of cellular constituents, 10,9 is required for cellular processes such as cell division and elongation, 11 endocytosis and vesicle trafficking 13,14,12,15 and immunity. [17][18][19]16 The structure of the ER, and the varying proportions of the structural ER subdomains (tubules and cisternae), may play a role in the normal functioning of the ER. A high abundance of cisternae has been associated with increased production of secretory proteins, based on evidence of an increased proportion of cisternae being commonly associated with cells with increased secretory demands in both plants and animals.…”