  Contraction of the cytokinetic ring during cell division leads to physical
partitioning of a eukaryotic cell into two daughter cells. This involves flows
of actin filaments and myosin motors in the growing membrane interface at the
mid-plane of the dividing cell. Assuming boundary driven alignment of the
acto-myosin filaments at the inner edge of the iterface we explore how the
resulting active stresses influence the flow. Using the continuum gel theory
framework, we obtain exact axisymmetric solutions of the dynamical equations.
These solutions are consistent with experimental observations on closure rate.
Using these solutions we perform linear stability analysis for the contracting
ring under non-axisymmetric deformations. Our analysis shows that few low wave
number modes, which are unstable during onset of the constriction, later on
become stable when the ring shrinks to smaller radii, which is a generic
feature of actomyosin ring closure. Our theory also captures how the effective
tension in the ring decreases with its radius causing significant slow down in
the contraction process at later times.
