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 previous work, we propose a framework based on 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, implementing size control via three models: Adder (division occurs when the added size reaches a prescribed threshold); Sizer (division occurs when the cell reaches a prescribed size) or Adder-Sizer mixture 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 transient solutions for the cell size distribution and its statistical moments, which can be further tested through experimental tracking of cell size over time. In summary, this contribution provides novel theoretical tools for characterizing cell size homeostasis mechanisms in diverse proliferating cell types, offering experimentally testable predictions and a framework that can be generalized to model clonal expansion of cells.