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

The anterior-posterior axis of Caenorhabditis elegans embryos is determined by the position of sperm entry. The sperm-provided centrosome induces local inhibition of cortical contractility, leading to large-scale myosin flows. This process is driven by the guanine nucleotide exchange factor (GEF) ECT-2, which activates myosin through the GTPase RHO-1. Previously, we showed that in both cell polarization and cytokinesis, Aurora A (AIR-1) is activated on the centrosomes and diffuses to the cortex, where it locally inhibits ECT-2, leading to gradients in myosin concentration. These gradients in turn drive long-range flows that amplify ECT-2 asymmetries (Longhini and Glotzer, 2022). 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 of the C. elegans model organism. 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 that the same minimal circuit operates in both processes.