  Intracellular fluctuations, mainly triggered by gene expression, are an
inevitable phenomenon observed in living cells. It influences generation of
phenotypic diversity in genetically identical cells. Such variation of cellular
components is beneficial in some contexts but detrimental in others. To
quantify the fluctuations in a gene product, we undertake an analytical scheme
for studying few naturally abundant linear as well as branched chain network
motifs. We solve the Langevin equations associated with each motif under the
purview of linear noise approximation and quantify Fano factor and mutual
information. Both quantifiable expressions exclusively depend on the relaxation
time (decay rate constant) and steady state population of the network
components. We investigate the effect of relaxation time constraints on Fano
factor and mutual information to indentify a time scale domain where a network
can recognize the fluctuations associated with the input signal more reliably.
We also show how input population affects both quantities. We extend our
calculation to long chain linear motif and show that with increasing chain
length, the Fano factor value increases but the mutual information processing
capability decreases. In this type of motif, the intermediate components are
shown to act as a noise filter that tune up input fluctuations and maintain
optimum fluctuations in the output. For branched chain motifs, both quantities
vary within a large scale due to their network architecture and facilitate
survival of living system in diverse environmental conditions.
