Performance evaluation of circadian clocks fluctuated by intrinsic noise

Using the linear noise approximation, we approach to the problem of evaluation and prediction of behavior of autonomous oscillatory genetic networks fluctuated by intrinsic noise. In this approach, the state covariance of the networks represents all the information concerning the fluctuation by intrinsic noise, and further, when the genetic network is an autonomous oscillatory system, the state covariance obeys a periodic Lyapunov differential equation that has generally unbounded solutions. Based on the analysis of stability and periodicity properties of the solution to the periodic Lyapunov differential equation, we propose two measures for evaluating intrinsic noise. Circadian clock is a typical example of autonoumous oscillatory genetic networks. Focusing on the simple core model (Gonze and Goldbeter, 2006) for circadian clocks and using the proposed measures, we evaluate robust performances concerning periodicity and amplitude of oscillations in the model fluctuated by intrinsic noise by changing system parameters.