Oscillation in cell cycle times in Drosophila abdomen modeled as cell phase synchronization

Analysis of tissue growth in the Drosophila abdomen has revealed that the cell cycle times are correlated in space and time. One manifestation of such correlations is through the average rate of cell division in the Histoblast nests which has been observed to oscillate with a period of roughly four hours, before decaying after 28 hAPF. As a simple explanation for such oscillations, we propose that neighbouring cells have synchronous cycles. We develop a model of the cell cycle where each cell is a phase oscillator evolving from a phase of 0 to 2π between birth and division. We then study phase synchronization for a growing and dividing population of cells on a two-dimensional lattice using a variant of the standard Kuramoto model with nearest neighbour coupling and a Gaussian noise term. Our results show that, unlike the two-dimensional Kuramoto model, this model exhibits a continuous phase transition with a true synchronous phase for high values of the coupling constant. Further, the temporal evolution of the correlation of cell phases indeed shows decaying oscillatory behaviour.