ABSTRACT
Eukaryotic cells undergo shape changes during their division and growth. This involves flow of material both in the cell membrane and in the cytoskeletal layer beneath the membrane. Such flows result in redistribution of phospholipid at the cell surface and actomyosin in the cortex. Here we focus on the growth of the intercellular surface during cell division in a Caenorhabditis elegans embryo. The growth of this surface leads to the formation of a double-layer of separating membranes between the two daughter cells. The division plane typically has a circular periphery and the growth starts from the periphery as a membrane invagination, which grows radially inward like the shutter of a camera. The growth is typically not concentric, in the sense that the closing internal ring is located off-center. Cytoskeletal proteins anillin and septin have been found to be responsible for initiating and maintaining the asymmetry of ring closure but the role of possible asymmetry in the material flow into the growing membrane has not been investigated yet. Motivated by experimental evidence of such flow asymmetry, here we explore the patterns of internal ring closure in the growing membrane in response to asymmetric boundary fluxes. We highlight the importance of the flow asymmetry by showing that many of the asymmetric growth patterns observed experimentally can be reproduced by our model, which incorporates the viscous nature of the membrane and contractility of the associated cortex.
