Cell cycle analysis, an experimental tool used to quantify the fraction of cells in different phases of the cell cycle, is accomplished by measuring cellular DNA content: cells with one copy of the genome are in the G0 or G1 phases, cells with two copies of the genome are in the G2 or M phases, and cells with between one and two copies of the genome are in the S-phase. While the principles of cell cycle analysis are straightforward, in practice, measurement variability makes it difficult to obtain accurate estimates of the cell cycle phase fractions from data. There is a general consensus that such data should be analyzed by fitting them to a mixture of three probability distributions one each for (i) the combined G0/G1 phases, (ii) the S-phase, and (iii) the combined G2/M phases (Watson, 1992). While it is widely accepted that the DNA content of the G0/G1 and G2/M populations should be normally distributed, it remains unclear what the S-phase distribution should be (Watson, 1992). As the S-phase corresponds to the period of time when a cell is replicating its DNA, the probability of observing an S-phase cell with a particular DNA content is intimately related to the dynamics of DNA synthesis.

In the current work, we develop a first-principles, ordinary differential equation model for the dynamics of eukaryotic DNA synthesis, based on mechanisms of DNA replication that have been well-established over the past 50 years. The model is subsequently used to propose S-phase DNA content distributions. Using previously known replication fork rates and inter-replication origin distance distributions, our model is capable of describing the DNA synthesis dynamics in the fission yeast S. Pombe, the budding yeast S. Cerevisiae, the large frog eggs Xenopus oocytes, and the model mammalian cell line Chinese Hamster Ovary (CHO) cells. It has long been debated how Xenopus oocytes can replicate their large genome (6000 Mbp) in the observed short DNA synthesis phase (~20 min.) given the seemingly random placement of replication origins—a paradox that has been termed the “random replication problem”. Our modeling results suggest that this random replication problem is solved in Xenopus oocytes by having (1) a short mean distance between potential replication origins, and (2) an extremely large number of replication units (foci) that all fire at least ~7.5 minutes before the scheduled end of the S-phase.

Our dynamic model shows that the S-phase DNA content distributions for a population of asynchronously cycling cells have a concave-up shape, with peaks at one and two copies of the genome. This concave-up distribution shape prescribed by our model is notable in that it is the exact opposite of all but one of the previously proposed S-phase distributions, all of which have a concave-down shape. The only exception is the empirically-based S-phase distribution model of Dean and Jett (1974), developed solely on the basis of goodness-of-fit to data, which indeed has a concave-down shape. Our results therefore provide a theoretical justification for this earlier purely empirical result and strongly suggest that fitting concave-down S-phase distributions to data from asynchronously cycling cell populations is inappropriate.

References

Watson JV. Flow Cytometry Data Analysis: Basic Concepts and Statistics. Cambridge University Press, 1992.

Dean PN and Jett JH. Mathematical analysis of DNA distributions derived from flow microfluorometry. J Cell Biol 60, 523-527 (1974).