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 affect cortical contractility. However, it is still unclear how cell size and localized activation near the nucleus shape these waves, and how the cytoplasmic signal is transmitted to the cortex. Here, we develop a reaction-diffusion model of Cyclin B-Cdk1 signaling in spherical cells with localized nuclear activation. We find that cytoplasmic waves have two distinct parts: an activation front that travels as a trigger wave, and a wave back that is controlled by inhibitory gradients in the cell cycle oscillator. Because these two parts are generated by different mechanisms, they can move at different speeds or even in opposite directions. This gives rise to different wave behaviors depending on nuclear size, nuclear position, and effective cell size. We then couple the Cdk1 signal to a cortical excitable network and show how cytoplasmic waveforms can regulate Rho-actin reactivation through inhibition of the RhoGEF Ect2. In this model, cortical patterns emerge mainly as downstream responses to cytoplasmic signaling, rather than as self-organized cortical waves. Overall, our results provide a mechanistic framework linking localized nuclear activation, cytoplasmic cell cycle waves, and cortical responses in large embryonic cells.