  We study the noise characteristics of stochastic oscillations in protein
number dynamics of simple genetic oscillatory systems. Using the
three-component negative feedback transcription regulatory system called the
repressilator as a prototypical example, we quantify the degree of fluctuations
in oscillation periods and amplitudes, as well as the noise propagation along
the regulatory cascade in the stable oscillation regime via dynamic Monte Carlo
simulations. For the single protein-species level, the fluctuation in the
oscillation amplitudes is found to be larger than that of the oscillation
periods, the distributions of which are reasonably described by the Weibull
distribution and the Gaussian tail, respectively. Correlations between
successive periods and between successive amplitudes, respectively, are
measured to assess the noise propagation properties, which are found to decay
faster for the amplitude than for the period. The local fluctuation property is
also studied.
