Aging is driven by damage accumulation leading to a decline in function over time. In single-cell systems, in addition to this damage accumulation within individuals, asymmetric damage partitioning at cell division can play a crucial role in shaping demographic aging patterns. Despite experimental single-cell studies that provide quantitative data at the molecular and demographic levels, the integration of a complementary theory explaining how cellular damage production and asymmetric partitioning propagate and influence demographic patterns is still lacking. Here, we present a generic and flexible damage model using a stochastic differential equation approach that incorporates stochastic damage accumulation and asymmetric damage partitioning during cell divisions. We formulate an analytical approximation linking cellular and damage parameters to demographic aging patterns along mother cell lineages. Interestingly, the lifespan of cells follows an inverse Gaussian distribution, whose underlying properties derive from cellular and damage parameters. We demonstrate how stochasticity (noise) in damage production, asymmetry in damage partitioning, and division frequency shape lifespan distribution. Confronting the model with various empirical E. coli mother machine data reveals nonexponential scaling in mortality rates, a scaling that cannot be captured by classical Gompertz-Makeham models. Our findings provide a deeper understanding of how fundamental processes contribute to cellular damage dynamics and generate demographic patterns. Our damage model's generic nature offers a valuable framework for investigating aging in diverse biological systems.
