A mathematical framework for understanding the timing of cell decisions: from developmental tempo to molecular mechanisms of gene regulation

Cells make decisions across developmental biology, immunology, and synthetic biology. Yet, while the timing of these decisions can be as important as their outcome, mathematical models often focus primarily on stable cell states. In this talk, I will present a mathematical framework based on orbital equivalence to identify molecular mechanisms that can control the speed of cellular decisions while preserving their underlying dynamics. I will first address developmental tempo, where embryos from different species execute remarkably similar genetic programmes at different speeds. I will then turn to gene regulatory networks, showing how critical slowing down and transient dynamics can regulate decision times, and how analysing different network topologies can reveal design principles for controlling dynamical speed in synthetic and natural systems.