Inherent Biological Adaptive Control of Feedback Gain of Circadian Rhythms in a Mathematical Model Stabilization of the Sustained Oscillations in a mRNA-Protein Model

Abstract

A mathematical model of cell-autonomous mammalian circadian clock is integrated into an adaptive control scheme. We analyze circadian clock rhythms with time delayed biophysically meaning parameter sets to generate self-oscillation behavior of a SCN neuron (Suprachiasmatic Nucleus Neuron). We demonstrate how an adaptive control scheme is utilized to stabilize of time varying mRNA and protein expression levels. Biological system optimizes the control parameters of coupled ODE with respect to minimizing energy metabolism or the time to satisfy the control goal. We will also investigate the robustness of inherent control mechanism to perturbations of coupled ODE system.