Junior Applied Mathematics Seminar

Cell proliferation has been widely studied across experimental systems and mathematical modelling frameworks, from early embryonic development to regenerating tissues. A characteristic feature of early embryonic development is that initially synchronous cell populations progressively lose synchrony after a species-specific number of divisions. Here, we use an age-dependent branching process to determine how variability in cell-cycle duration controls the persistence of synchrony. We derive analytical expressions for the mean and variance of cell number and show how they identify the underlying generation-time distribution. For gamma-distributed generation times, this establishes a direct relationship between cell-cycle variability and the number of synchronous divisions. We use these results to infer generation-time statistics from population-level cell counts and investigate how systematic changes in cell-cycle duration can bias inference under a stationary model. Our results provide a quantitative framework linking the precision of individual cell-cycle clocks to observable population-level dynamics.