Intrinsic noise, gene regulation and steady-state statistics in a two-gene network

The intrinsic noise in a two-gene network model is analysed. The technique of the Fokker-Planck approximation is used to investigate the statistics of noise when the system state is near a stable equilibrium. This is called also the steady-state statistics. The relative size of noise is measured by the Fano factor that is defined as the ratio of the variance to the mean. Our main result shows that in general, the noise control in a two-gene network might be a very complicated process, but for the repressor-repressor system that is a very important case in investigating the genetic switch, the relative size of noise, i.e. the Fano factor, must be bigger than one for both the repressor proteins.