A dynamical systems model for the measurement of cellular senescence.

Senescent cells provide a good in vitro model to study ageing. However, cultures of `senescent' cells consist of a mix of cell subtypes (proliferative, senescent, growth-arrested and apoptotic). Determining the proportion of senescent cells is crucial for studying ageing and developing new antidegenerative therapies. Commonly used markers such as doubling population, senescence-associated beta-galactosidase, Ki-67, gamma H2AX and TUNEL assays capture diverse and overlapping cellular populations and are not purely specific to senescence. A newly developed dynamical systems model follows the transition of an initial culture to senescence tracking population doubling, and the proportion of cells in proliferating, growtharrested, apoptotic and senescent states. Our model provides a parsimonious description of transitions between these states accruing towards a predominantly senescent population. Using a genetic algorithm, these model parameters are well constrained by an in vitro human primary fibroblast dataset recording five markers at 16 time points. The computational model accurately fits to the data and translates these joint markers into the first complete description of the proportion of cells in different states over the lifetime. The high temporal resolution of the dataset demonstrates the efficacy of strategies for reconstructing the trajectory towards replicative senescence with a minimal number of experimental recordings.