Figure 5. The inheritance matrix reveals the periodicity of hidden biological oscillators underlying the cell cycle.

(a) Schematic showing how sampling a high frequency rhythm at each cell division could result in a lower frequency oscillator being constructed. (b) Possible oscillator periods (Equation 7) indexed by $n$ for a correlation oscillation period $T_0=3\overline{\tau }$. (c) Density plot of the complex eigenvalue output from the model sampling for cyanobacteria (purple) and mouse embryonic fibroblasts (orange). (d) Posterior distributions of the correlation oscillation period ${\displaystyle T_0}$ in cyanobacteria (purple) and mouse embryonic fibroblasts (orange). (e) Posterior distributions of the oscillator period $T_{-1}$ in cyanobacteria (purple) and mouse embryonic fibroblasts (orange). Arbitrary units in (d) and (e) are used to compare histograms, the density values are not normalised in relation to each other in order to display both histograms clearly on the same plot. (f) Density plot of complex eigenvalues for human colorectal cancer. (g) Posterior distributions of the correlation oscillation period in human colorectal cancer (shaded area) and oscillator clusters corresponding to positive (cluster A, orange) and negative real parts (cluster B, blue). The bar chart shows the posterior mass of the clusters. (h) Posterior distributions of the oscillator periods $T_{-1}$ corresponding to (g). (i) Model fit and 95% credible intervals for human colorectal cancer (cf. legend of Figure 3). Red area indicates the grandmother granddaughter correlation explored in (j). (j) Posterior distribution of oscillator vs alternator clusters give grandmother correlations with opposite signs. (k) Lineage and cross-branch correlation functions of oscillator clusters A (orange) and B (blue) in human colorectal cancer. Red area indicates the great-grandmother great-granddaughter correlation explored in (l). (l) Posterior distributions of oscillator clusters A (orange) and B (blue) have great-grandmother correlations of opposite signs.