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A recent burst of dynamic single-cell growth-division data makes it possibleto characterize the stochastic dynamics of cell division control in bacteria.Different modeling frameworks were used to infer specific mechanisms from suchdata, but the links between frameworks are poorly explored, with relevantconsequences for how well any particular mechanism can be supported by thedata. Here, we describe a simple and generic framework in which two commonformalisms can be used interchangeably: (i) a continuous-time division processdescribed by a hazard function and (ii) a discrete-time equation describingcell size across generations (where the unit of time is a cell cycle). In ourframework, this second process is a discrete-time Langevin equation with asimple physical analogue. By perturbative expansion around the mean initialsize (or inter-division time), we show explicitly how this framework describesa wide range of division control mechanisms, including combinations of time andsize control, as well as the constant added size mechanism recently found tocapture several aspects of the cell division behavior of different bacteria. Aswe show by analytical estimates and numerical simulation, the available dataare characterized with great precision by the first-order approximation of thisexpansion. Hence, a single dimensionless parameter defines the strength and theaction of the division control. However, this parameter may emerge from severalmechanisms, which are distinguished only by higher-order terms in ourperturbative expansion. An analytical estimate of the sample size needed todistinguish between second-order effects shows that this is larger than what isavailable in the current datasets. These results provide a unified frameworkfor future studies and clarify the relevant parameters at play in the controlof cell division.

Relevant parameters in models of cell division control