Inferring cell size control mechanisms through stochastic hybrid modeling

Recent studies combining cell size dynamics measurements with mathematical modeling have uncovered how living cells regulate their division rates to buffer statistical size fluctuations around a target setpoint. Building on a previous work, we propose a framework motivated by stochastic hybrid systems (SHS), where cell size grows according to an arbitrary ordinary differential equation, and division occurs probabilistically at a size-dependent rate. We propose different forms of division rates that capture the distribution of added size from cell birth to division and implement size control via an adder (division occurs when the added size reaches a prescribed threshold), sizer (division occurs when cell size reaches a prescribed threshold) or intermediate adder-sizer models. The proposed division rates are corroborated with data from exponentially-growing bacterial cells. We further show how solving the underlying Chapman-Kolmogorov equation for the SHS provides a transient solution for the cell size distribution and its statistical moments, offering predictions that can be tested via time-lapse tracking of single-cell growth. In summary, this contribution provides novel theoretical tools for characterizing cell size homeostasis mechanisms in diverse proliferating cell types that provide experimentally testable predictions and can be generalized to model clonal expansion of cells.