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, inducing cortical flows towards the anterior. In cytokinesis, spindle elongation-dependent astral relaxation combines with centralspindlin-induced accumulation of myosin at the cell equator to set up a robust contractility gradient. During both processes, inhibition of contractility occurs through Aurora A (AIR-1) kinase, which is activated on the centrosomes and diffuses to the cortex, where it inhibits the guanine nucleotide exchange factor (GEF) ECT-2, which generates actomyosin-based contractility by activating the GTPase RHO-1. 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. The tuned model also correctly predicts previously-observed ultrasensitive ECT-2 dynamics during cytokinesis, suggesting quantitatively that the same minimal circuit operates in both processes.