  The transcription factors, such as activators and repressors, can interact
with the promoter of gene either in a competitive or non-competitive way. In
this paper, we construct a stochastic model with non-competitive
transcriptional regulatory architecture and develop an analytical theory that
re-establishes the experimental results with an improved data fitting. The
analytical expressions in the theory allow us to study the nature of the system
corresponding to any of its parameters, and hence enable us to find out the
factors that govern the regulation of gene expression for that architecture. We
notice that, along with transcriptional reinitiation and repressors, there are
other parameters that can control the noisiness of this network. We also
observe that, the Fano factor (at mRNA level) varies from sub-Poissonian regime
to superPoissonian regime. In addition to the aforementioned properties, we
observe some anomalous characteristics of the Fano factor (at mRNA level) and
that of the variance of protein at lower activator concentrations in presence
of repressor molecules. This model is useful to understand the architecture of
interactions which may buffer the stochasticity inherent to gene transcription.
