The mechanics clarifying counterclockwise rotation in most IVF eggs in mice

The N-flagella problem: elastohydrodynamic motility transition of multi-flagellated bacteria

Peritrichous bacteria such as Escherichia coli swim in viscous fluids by forming a helical bundle of flagellar filaments. The filaments are spatially distributed around the cell body to which they are connected via a flexible hook. To understand how the swimming direction of the cell is determined, we theoretically investigate the elastohydrodynamic motility problem of a multi-flagellated bacterium. Specifically, we consider a spherical cell body with a number N of flagella which are initially symmetrically arranged in a plane in order to provide an equilibrium state. We solve the linear stability problem analytically and find that at most six modes can be unstable and that these correspond to the degrees of freedom for the rigid-body motion of the cell body. Although there exists a rotation-dominated mode that generates negligible locomotion, we show that for the typical morphological parameters of bacteria the most unstable mode results in linear swimming in one direction accompanied by rotation around the same axis, as observed experimentally.

Biophysics in oviduct: Planar cell polarity, cilia, epithelial fold and tube morphogenesis, egg dynamics

Organs and tissues in multi-cellular organisms exhibit various morphologies. Tubular organs have multi-scale morphological features which are closely related to their functions. Here we discuss morphogenesis and the mechanical functions of the vertebrate oviduct in the female reproductive tract, also known as the fallopian tube. The oviduct functions to convey eggs from the ovary to the uterus. In the luminal side of the oviduct, the epithelium forms multiple folds (or ridges) well-aligned along the longitudinal direction of the tube. In the epithelial cells, cilia are formed orienting toward the downstream of the oviduct. The cilia and the folds are supposed to be involved in egg transportation. Planar cell polarity (PCP) is developed in the epithelium, and the disruption of the Celsr1 gene, a PCP related-gene, causes randomization of both cilia and fold orientations, discontinuity of the tube, inefficient egg transportation, and infertility. In this review article, we briefly introduce various biophysical and biomechanical issues in the oviduct, including physical mechanisms of formation of PCP and organized cilia orientation, epithelial cell shape regulation, fold pattern formation generated by mechanical buckling, tubulogenesis, and egg transportation regulated by fluid flow. We also mention about possible roles of the oviducts in egg shape formation and embryogenesis, sinuous patterns of tubes, and fold and tube patterns observed in other tubular organs such as the gut, airways, etc.