Abstract
Intracellular polarization, where a cell specifies a spatial axis by segregation of specific factors, is a fundamental biological process. In the early embryo of the nematode worm Caenorhabditis elegans (C. elegans), polarization is often accompanied by deformations of the cortex, a highly contractile structure consisting of actin filaments cross-linked by the motor protein myosin (actomyosin). It has been suggested that the eggshell surrounding the early embryo plays a role in polarization although its function is not understood. Here we develop a mathematical model which couples a reaction-diffusion model of actomyosin dynamics with a phase field model of the cell cortex to implicitly track cell shape changes in the early C. elegans embryo. We investigate the potential rigidity effect of the geometric constraint imposed by the presence and size of the eggshell on polarization dynamics. Our model suggests that the geometric constraint of the eggshell is essential for proper polarization and the size of the eggshell also affects the dynamics of polarization. Therefore, we conclude that geometric constraint on a cell might affect the dynamics of a biochemical process.
Highlights
The geometry of a cell can have a profound influence on cell function and survival [1,2,3,4]
We wish to see if our model can produce a pseudocleavage furrow, an invagination that advects with the edge of the actomyosin cap and the interface between the anterior and posterior Par proteins
We are interested in the role of the eggshell in formation of the pseudocleavage furrow, and the interaction between the eggshell and the asymmetric distribution of actomyosin concentration observed during polarization
Summary
The geometry of a cell can have a profound influence on cell function and survival [1,2,3,4]. The developmental time frame we consider in this paper, the actomyosin cortex, a thin structure below the membrane consisting primarily of polymerized actin filaments and cross-linked by the motor protein myosin, is highly dynamic and contractile, creating small invaginations on the cell surface called ruffles [9, 11]. The cue locally relaxes the actomyosin cortex causing local loss of ruffles and initiation of cortical flow that transports the anterior Par proteins, PAR-3, PAR-6 and aPKC, towards the anterior pole. This allows the posterior Par proteins, PAR-1, PAR-2 and LGL, which are mutually antagonistic to the anterior Par proteins, to bind to the cleared area at the posterior pole [10, 12, 13]. The pseudocleavage furrow retracts and the segregated Par protein domains are held through the maintenance phase as the cell prepares for first division
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