Andrew B. Goryachev

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.

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.

We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves. A simplified linear model effectively explains the mechanisms behind the variety of phase patterns observed, providing insights into the complex interplay between a cell's internal and external environments.

In a world where computational methods are essential for research, code clarity is crucial. This poster highlights three key aspects that often are lacking and enhance readability and reproducibility, which in turn promotes scientific collaboration.

Summary: The Rho GTPases pattern the cell cortex in a variety of fundamental cell-morphogenetic processes including division, wound repair, and locomotion. It has recently become apparent that this patterning arises from the ability of the Rho GTPases to self-organize into static and migrating spots, contractile pulses, and propagating waves in cells from yeasts to mammals ¹ . These self-organizing Rho GTPase patterns have been explained by a variety of theoretical models which require multiple interacting positive and negative feedback loops. However, it is often difficult, if not impossible, to discriminate between different models simply because the available experimental data do not simultaneously capture the dynamics of multiple molecular concentrations and biomechanical variables at fine spatial and temporal resolution. Specifically, most studies typically provide either the total Rho GTPase signal or the Rho GTPase activity as reported by various sensors, but not both. Therefore, it remains largely unknown how membrane accumulation of Rho GTPases (i.e., Rho membrane enrichment) is related to Rho activity. Here we dissect the dynamics of RhoA by simultaneously imaging both total RhoA and active RhoA in the regime of acute cortical excitability ² , characterized by pronounced waves of Rho activity and F-actin polymerization ^3-5 . We find that within nascent waves, accumulation of active RhoA precedes that of total RhoA, and we exploit this finding to distinguish between two popular theoretical models previously used to explain propagating cortical Rho waves.

The Rho GTPases — RHOA, RAC1 and CDC42 — are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.