Demographic Consequences of Damage Dynamics in Single-Cell Ageing

Ageing 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 ageing patterns. Despite empirical single-cell studies providing quantitative data at the molecular and demographic level, a comprehensive theory of 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 at cell divisions. We formulate an analytical approximation linking cellular and damage parameters to demographic ageing patterns. 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 to various empirical E . coli data reveals non-exponential scaling in mortality rates, a scaling that cannot be captured by classical Gompertz-Makeham models. Our findings provide a deep 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 ageing in diverse biological systems. Significance Asymmetries and randomness in cellular events play important roles in establishing the diversity at evolutionary and demographic scales. Looking at single-cells, ageing processes are influenced by stochastic damage accumulation and asymmetric damage partitioning at cell divisions. Utilising stochastic differential equations, we develop a cellular damage model that encapsulate both noisy damage accumulation within cells and asymmetric damage partitioning among cells when they divide. In doing so we bridge molecular stochastic processes, demographic fates of individuals, and population level demographic distributions. Our model aligns with empirical data from E . coli single-cell studies and advances our understanding compared to traditional demographic models. The generic and adaptable nature of our model paves the way for broader applications in ageing research across biological systems, highlighting the influences of stochasticity and asymmetry on cellular biology. ### Competing Interest Statement The authors have declared no competing interest.