Likelihood-Based Identification of Cell Division Mechanisms
Cell-division control in bacteria has been studied for many years, but gaps in understanding its logic still remain. Simple candidate models of cell division control have been studied, but are assessed with heuristic analysis of single-cell data that does not provide a quantitative scale for comparison. We recast division control mechanism identification as a likelihood-based inference problem, defining an explicit metric for model comparison: among candidate mechanisms, the model with higher likelihood provides the better explanation of the data. We demonstrate that within a broad class of models, discrimination depends only on the conditional distribution of cell-cycle durations. Under mild independence assumptions, variability in growth rates and division asymmetry do not contribute to the likelihood-based comparison, effectively separating the problem of understanding growth from that of identifying division control. Applying the likelihood framework to simulations and experimentally measured long-term single-cell lineages of Escherichia coli, we find that candidate simple models are statistically identifiable in principle, but only weakly separated in practice. Sizer, adder, and related mechanisms all achieve comparable and generally high likelihoods, but no single one consistently outperforms others: their relative likelihood depends on the dataset and growth condition. In contrast, a flexible model trained directly on the data always achieves significantly higher likelihood, revealing structure not captured by any one of the simplified rules; surprisingly, it can be well fit by a low-dimensional variable combination. More broadly, this work establishes a general likelihood-based framework for identifying stochastic regulatory mechanisms and for comparing future mechanistic models on a quantitative scale.