Goodwin-Griffith genetic oscillator model.

<p>The transcription factor (TF) gene A is transcribed and translated into the TF protein product that in turn is converted to the active end-product. The end-product (or its oligomer as in case of <i>lacI</i> repressor negative-feedback-only system that was constructed in reference <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0104328#pone.0104328-Stricker1" target="_blank">[25]</a>) is the key molecule that locates the respective <i>cis</i>-regulatory elements associated with the promoter of TF gene A through a combination of one-dimensional (1D) and three-dimensional (3D) routes as that of typical site-specific DNA-protein interactions. Here either monomers of the end-product directly assemble at the corresponding regulatory elements in a combinatorial manner (I) or the fully-formed complex of <i>n_a</i>-mer binds with the respective regulatory sites (II). Assembly of combinatorial TF molecules results in the looping of DNA segment that is present in between the promoter and <i>cis</i>-regulatory elements. ARPC is the assembled repressor-promoter complex that in turn results in down-regulation. Our analysis shows that out of these two competing pathways, the pathway I is the most probable one since it takes shortest time. The corresponding set of differential equations is given in <b>Eqs (4–5)</b>. This system is well characterized by parameters of Group I, II and III. Group I consists of parameters whereas Group II consists of equilibrium parameters and Group III consists of ordinary type perturbation parameters . Most of the earlier studies assumed zero values to Group II parameters apart from assuming zero for that controls the promoter state dynamics. Blue colored spheres are the dimers of <i>lac</i> repressor. Here a.a denotes amino acids and n.a denotes nucleotides.