Sivan Pearl Mizrahi,
& Nathalie Q. Balaban
Heterogeneity amongst populations of cells is a fundamental observation in cell biology. One example of this is cell cycle duration, which can be thought of as being determined stochastically, perhaps by inheritance of mitochondrial content at mitosis. According to this intuition, mathematical models can be constructed to describe the expected correlation between mothers, daughters and cousin cell cycle periods, such as the bifurcating autoregression model. This model predicts that the correlation between cousins is less than that between a mother and daughter cell.
However, time series which appear stochastic in nature can sometimes be derived from underlying deterministic, chaotic, behaviour. The authors set out to determine whether cell cycle distributions are indeed stochastic, or deterministically chaotic. Using Fucci markers, the authors generated lymphoblasts which fluoresced red at G1 phase, yellow at S phase, green at G2 and no fluorescence during mitosis. Using single-cell microscopy, they found that the cell cycle period between cousins had a greater Spearman's correlation (0.63) than between mothers and daughters (0.04). In other words, this is the reverse of what is to be expected from the bifurcating autoregression model, which they label as the 'cousin-mother inequality'.
The authors go on to suggest that the cousin-mother inequality is evidence for deterministic inheritance. They use the Grassberger-Procaccia algorithm on the cell cycle periods, to examine whether the data is stochastic in nature, or in fact deterministic chaos. This returns a quantity called the 'correlation dimension', which is thought to be low for deterministic systems and high for stochastic ones (although see here for subtleties associated with this). They find a small correlation dimension (~3) for the cell cycle period data (whereas random noise is >10), and use this to conclude that cell cycle times are deterministic. They suggest a dynamical model (containing 6 parameters) to explain their data: the 'kicked cell cycle' model. This states that cell-cycle
duration is drawn from a deterministic circadian clock oscillator (see Fig. 3D).
It remains to be seen whether there exist alternative stochastic models to the bifurcating autoregression model, which can explain the heterogeneity in cell cycle times. For instance, can the inheritance of mitochondrial content at cell division also recover the correlation between cousins?