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

Cell polarization and cytokinesis are fundamental processes in organismal development. In theCaenorhabditis elegansmodel system, both processes are partially driven by a local inhibition of contractility at the cell poles. Polarization is triggered by centrosome-directed, local inhibition of cortical contractility at what becomes the posterior pole, while cytokinesis occurs when spindle elongation-dependent astral relaxation combines with centralspindlin-induced accumulation of myosin at the cell equator. During both processes, Aurora A (AIR-1) kinase 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. While 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 construct 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 ofC. 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 a persistent AIR-1 cue during polarization. In the minimal model, the rapid turnover of ECT-2 causes a quasi-steady response to changes in the AIR-1 signal, and transient asymmetries are not self-sustaining. After tuning the model for polarization, we demonstrate that it can accurately predict ECT-2 accumulation during cytokinesis, suggesting a quantitative similarity between the two processes.