Modeling the effect of cell division on genetic oscillators

Many genetic oscillators (circadian clocks, synthetic oscillators) continue to oscillate across the cell division cycle. Since cell divisions create discontinuities in the dynamics of genetic oscillators the question about the resilience of oscillations and the factors that contribute to the robustness of the oscillations may be raised. We study here, through stochastic simulations, the effect of the cell division cycle on genetic oscillations using the Repressilator-a genetic oscillator developed in the context of synthetic biology. We consider intrinsic noise (molecular noise due to the limited number of molecules) and extrinsic noise (variability in the cell division time and in the partition of the molecules into daughter cells, cell-cell variability in kinetic parameters, etc). Our numerical simulations show that, although noisy, oscillations are quite resilient to cell division and that cell-cell heterogeneity may be the main source of variability observed experimentally. Finally, similar simulations performed with another model, the Goodwin model, show that oscillations may be entrained and synchronized by cell division. This highlights the influence of the clock architecture on the robustness of genetic oscillations. Our approach provides a general framework to study the effect of cell division on dynamical systems and several possible extensions are described.