Efficient multiscale simulation of circadian rhythms using automated phase macromodelling techniques.

Circadian rhythm mechanisms involve multi-scale interactions between endogenous DNA-transcription oscillators. We present the application of efficient, numerically well-conditioned algorithms for abstracting (potentially large) systems of differential equation models of circadian oscillators into compact, accurate phase-only macromodels. We apply and validate our auto-extracted phase macromodelling technique on mammalian and Drosophila circadian systems, obtaining speedups of 9 - 13x over conventional time-course simulation, with insignificant loss of accuracy, for single oscillators being synchronized by day/night light variations. Further, we apply the macromodels to simulate a system of 400 coupled circadian oscillators, achieving speedups of 240x and accurately reproducing synchronization and locking phenomena amongst the oscillators. We also present the use of parameterized phase macromodels for these circadian systems, and elucidate insights into circadian timing effects directly provided by our auto-extracted macromodels.