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Intracellular fluctuations, mainly triggered by gene expression, are aninevitable phenomenon observed in living cells. It influences generation ofphenotypic diversity in genetically identical cells. Such variation of cellularcomponents is beneficial in some contexts but detrimental in others. Toquantify the fluctuations in a gene product, we undertake an analytical schemefor studying few naturally abundant linear as well as branched chain networkmotifs. We solve the Langevin equations associated with each motif under thepurview of linear noise approximation and quantify Fano factor and mutualinformation. Both quantifiable expressions exclusively depend on the relaxationtime (decay rate constant) and steady state population of the networkcomponents. We investigate the effect of relaxation time constraints on Fanofactor and mutual information to indentify a time scale domain where a networkcan recognize the fluctuations associated with the input signal more reliably.We also show how input population affects both quantities. We extend ourcalculation to long chain linear motif and show that with increasing chainlength, the Fano factor value increases but the mutual information processingcapability decreases. In this type of motif, the intermediate components areshown to act as a noise filter that tune up input fluctuations and maintainoptimum fluctuations in the output. For branched chain motifs, both quantitiesvary within a large scale due to their network architecture and facilitatesurvival of living system in diverse environmental conditions.

Role of relaxation time scale in noisy signal transduction