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Periodic forcing of nonlinear oscillators leads to a large number of dynamicbehaviors. The coupling of the cell-cycle to the circadian clock provides abiological realization of such forcing. Using high throughput single-cellmicroscopy, we have studied the correlations between cell cycle duration indiscrete lineages of several different organisms including those with knowncoupling to a circadian clock and those without known coupling to a circadianclock. Correlations between cell cycles duration in discrete lineages observedin the organisms with a circadian clock cannot be explained by a simplestatistical model but are consistent with predictions of a biologicallyplausible two dimensional nonlinear map. Surprisingly, the nonlinear map isequivalent to a classic nonlinear map called the fattened Arnold map. The modelpredicts that circadian coupling may increase cell to cell variability in aclonal population of cells. In agreement with this prediction, deletion of thecircadian clock reduces variability. Our results show that simple correlationscan identify systems under periodic forcing and that studies of nonlinearcoupling of biological oscillators provide insight into basic cellularprocesses of growth.

Correlations of single-cell division times with and without periodic forcing