Geometry shapes cytoplasmic Cdk1 waves that drive cortical dynamics
Cell division in large embryos is coordinated by spatial waves of Cyclin B-Cdk1 activity that spread through the cytoplasm and drive cortical contractility. However, it remains unclear how cell size and nuclear enrichment of Cyclin B-Cdk1 shape these waves, and how the cytoplasmic signal is transmitted to the cortex. Here we couple established reaction-diffusion models of Cyclin B-Cdk1 signaling and the excitable Rho-actin cortex to ask how cell geometry and elevated nuclear Cyclin B-Cdk1 concentration shape cytoplasmic wave propagation in spherical cells. We find that cytoplasmic waves consist of two distinct parts: an activation front that propagates in a manner consistent with trigger-wave behavior, and a wave back controlled by concentration gradients in the cell cycle oscillator. Because these parts are generated by different mechanisms, they can move at different speeds or even in opposite directions, depending on nuclear size and effective cell size. This yields a simple geometric explanation for why surface contraction waves propagate in opposite directions in starfish oocytes and Xenopus embryos, without invoking system-specific cortical mechanisms. Coupling the Cdk1 signal to the cortex further shows how cytoplasmic waveforms regulate Rho-actin dynamics through inhibition of the Rho GEF Ect2. Together, these results provide a mechanistic framework linking localized nuclear activation, cytoplasmic Cdk1 waves, and cortical responses in large embryonic cells.