The cell cycle is canonically described as a series of four consecutive phases: G1, S, G2, and M. In single cells, the duration of each phase varies, but the quantitative laws that govern phase durations are not well understood. Using time‐lapse microscopy, we found that each phase duration follows an Erlang distribution and is statistically independent from other phases. We challenged this observation by perturbing phase durations through oncogene activation, inhibition of DNA synthesis, reduced temperature, and DNA damage. Despite large changes in durations in cell populations, phase durations remained uncoupled in individual cells. These results suggested that the independence of phase durations may arise from a large number of molecular factors that each exerts a minor influence on the rate of cell cycle progression. We tested this model by experimentally forcing phase coupling through inhibition of cyclin‐dependent kinase 2 ( CDK 2) or overexpression of cyclin D. Our work provides an explanation for the historical observation that phase durations are both inherited and independent and suggests how cell cycle progression may be altered in disease states.

The cell cycle is canonically described as a series of 4 phases: G1 (gap phase 1), S (DNA synthesis), G2 (gap phase 2), and M (mitosis). Various models have been proposed to describe the durations of each phase, including a two-state model with fixed S-G2-M duration and random G1 duration 1,2 ; a "stretched" model in which phase durations are proportional 3 ; and an inheritance model in which sister cells show correlated phase durations 2,4 . A fundamental challenge is to understand the quantitative laws that govern cell-cycle progression and to reconcile the evidence supporting these different models. Here, we used time-lapse fluorescence microscopy to quantify the durations of G1, S, G2, and M phases for thousands of individual cells from three human cell lines. We found no evidence of correlation between any pair of phase durations. Instead, each phase followed an Erlang distribution with a characteristic rate and number of steps. These observations suggest that each cell cycle phase is memoryless with respect to previous phase durations. We challenged this model by perturbing the durations of specific phases through oncogene activation, inhibition of DNA synthesis, reduced temperature, and DNA damage. Phase durations remained uncoupled in individual cells despite large changes in durations in cell populations. To explain this behavior, we propose a mathematical model in which the independence of cell-cycle phase durations arises from a large number of molecular factors that each exerts a minor influence on the rate of cell-cycle progression. The model predicts that it is possible to force correlations between phases by making large perturbations to a single factor that contributes to more than one phase duration, which we confirmed experimentally by inhibiting cyclindependent kinase 2 (CDK2). We further report that phases can show coupling under certain dysfunctional states such as in a transformed cell line with defective cell cycle checkpoints. This quantitative model of cell cycle progression explains the paradoxical observation that phase durations are both inherited and independent and suggests how cell cycle progression may be altered in disease states.The discovery that DNA synthesis occurs during a well-defined period of time between cell divisions 5 led to the development of the canonical four-stage cell cycle model comprising G1, S, G2, and M phases. It has long been known that the durations of these phases can vary considerably across cell types 6 . For example, stem cells and immune cells have relatively brief G1 durations compared to somatic cells 7-9 . Phase durations can also change under certain environmental stresses such as starvation, which lengthens G1 10 , or DNA damage, which prolongs G1 and G2 11,12 . Furthermore, examination of individual cells has revealed that phase durations vary even among clonal cells under similar environmental conditions 6 . These apparently stochastic differences in cell-cycle durations were originally attributed exclusively to the G1 phase 13 . However, more ...