A minimal mathematical model for polarity establishment and centralspindlin-independent cytokinesis.

Cell polarization and cytokinesis are fundamental processes in organismal development. In the Caenorhabditis elegans model system, both processes are partially driven by local inhibition of contractility at the cell poles. This inhibition comes from Aurora A kinase (AIR-1), which is activated on centrosomes and diffuses to the cortex, where it inhibits the guanine nucleotide exchange factor (GEF) ECT-2, attenuating RHO-1 activation and actomyosin-based contractility. Although these biochemical processes have been characterized experimentally, a quantitative understanding of how this circuit drives cortical dynamics in polarization and cytokinesis is still lacking. Here, we constructed a mathematical model to test whether a minimal set of well-characterized, essential elements are necessary and sufficient to explain the spatiotemporal dynamics of AIR-1, ECT-2 and myosin during polarization and cytokinesis of C. elegans. We show that robust establishment of polarity can be obtained in response to a weak AIR-1 signal and demonstrate the relevance of rapid ECT-2 exchange and persistent AIR-1 cues during polarization. The model, tuned for polarization, can also predict ECT-2 accumulation during cytokinesis, suggesting a quantitative similarity between the two processes.