  Recently, several studies have investigated the transcription process
associated to specific genetic regulatory networks. In this work, we present a
stochastic approach for analyzing the dynamics and effect of negative feedback
loops (FBL) on the transcriptional noise. First, our analysis allows us to
identify a bimodal activity depending of the strength of self-repression
coupling D. In the strong coupling region D>>1, the variance of the
transcriptional noise is found to be reduced a 28 % more than described
earlier. Secondly, the contribution of the noise effect to the abundance of
regulating protein becomes manifest when the coefficient of variation is
computed. In the strong coupling region, this coefficient is found to be
independent of all parameters and in fair agreement with the experimentally
observed values. Finally, our analysis reveals that the regulating protein is
significantly induced by the intrinsic and external noise in the strong
coupling region. In short, it indicates that the existence of inherent noise in
FBL makes it possible to produce a basal amount of proteins even though the
repression level D is very strong.
