Figure 1.

Schematic of model autoregulation gene circuit. The DNA binding status is indicated by Dxy, where x corresponds to the operator region (empty = 0, monomer = 1, dimer = 2), and y to the promoter region (empty = 0, RNA polymerase bound = 1). C represents the open complex of DNA-RNAp holoenzyme with the promoter sequence just cleared of RNAp and is subject to transcription elongation. Finally, M, P1 and P2 correspond to mRNA, protein monomer, and dimer, respectively. The network topologies can be grouped into two classes, monomer-only (MO) or dimer-allowed (DA) circuits. We have studied DA1 (red lines), which only allows the dimer to bind with the DNA-operator sequence, DA2 (green) with sequential binding of monomers on the DNA, and DA3 (blue), which shares protein-DNA binding kinetics with MO while allowing dimerization in the cytosol. Note that for topology DA2, we have chosen K₃₁ = K₃₀ (see text for details) We have assumed cells to be in the exponential growth phase and the number of RNAp (R) constant.