Linear stability analysis for asymmetric contraction of the cytokinetic ring

The contraction of the cytokinetic ring is a crucial part of the cell-division cycle. In a previous work [1], using a continuum gel theory framework in a weak flow coupling regime, we obtained exact analytical solutions for the quasi-static dynamics of the radially symmetric ring contraction. Here, we study the stability of this process under angular perturbations. Linear stability analysis of the angular modes shows that, in the experimentally relevant regime of the parameter space, the lowest order breathing mode and most of the higher-order modes are stable, leaving a window of unstable modes in between. Furthermore as the ring shrinks in radius, this window gradually disappears, turning all modes stable. This is consistent with the experimental observation [2] that the ring, most often, is not circular at the beginning, but becomes increasingly circular as it contracts.
[1] Chatterjee, Mainak, et al. arXiv preprint arXiv:2007.13441 (2020).
[2] Maddox, A. S., et al. Developmental cell 12, 827 (2007)