A numerical bifurcation analysis of circadian rhythms in pacemaker neurons

Abstract

In this study, we analyze a known minimal but biologically realistic mathematical model from system biology in order to gain more understanding of how circadian oscillations are simulated using a coupled delay differential equation model. We analyze biochemically and biophysically detailed mathematical model of gene transcription and protein synthesis which has been previously presented in the biological literature. The model has an ability of generating circadian clock rhythms to generate self-sustained or damped oscillation behavior of a Suprachiasmatic nucleus (SCN) Pacemaker Neuron under biophysically meaning parameter sets. The model takes the form of coupled DDE (delay differential equation) with time varying mRNA and protein abundances. We will also rescale time variable of coupled DDE system reducing into coupled ODE system which is different from current model.