Contraction of the cytokinetic ring during cell division leads to physical
partitioning of a cell into two daughter cells. This contraction involves flows
of actin filaments and myosin motors in the growing membrane interface that
causes this separation. Within a continuum gel theory framework, we explore a
weak flow coupling approximation where the dynamics of the order parameter,
namely the degree of alignment of the acto-myosin filaments, is not
significantly affected by the flow, however the flow is influenced by the
active stresses generated by the filaments. This allows exact solution of the
dynamical equations, producing good agreement with experimental observations.
While the relevant time scale of the dynamics turns out to be the ratio of flow
viscosity and acto-myosin activity, our theory captures how the effective
tension in the ring decreases with its radius. We show how this effect
significantly slows down the contraction process at later times.
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