Model representation.

<p>(a) Multi-scale stochastic model of gene regulation of the RK2 central control operon. The population dynamic layer contains plasmid replication as an independent Poisson process and continuous host cell growth at an exponential rate with cell division when the cell doubles its initial size. After each division, only one daughter cell is tracked. The plasmid molecular dynamics layer contains protein synthesis, dimerization, cooperative binding of KorA and KorBdimers to the promoter, and repression of the operon. (b) The four models for comparison: CCO is the wild type system; CCOnoC is a system with two regulators but with no cooperativity between then regulators; CCOregB is a system with just a single dimeric regulator; CCOnoR is a system with no regulation. In order to ensure comparability, the rates of protein synthesis are tuned so that protein abundance is the same in all models (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049678#s4" target="_blank"><i>Methods</i></a>). (c) Stochastic model formulation for the CCO model: A₁, A₂, B₁, B₂– KorA and KorB monomer and dimer, respectively; D, X, Y, Z – states of the DNA strand: empty DNA, KorA-DNA, KorB-DNA, KorA-KorB-DNA complexes respectively; k_p – plasmid replication rate, k_A, k_B – maximal KorA and KorB synthesis rates, π_X, π_Y - scaling parameters for the protein synthesys, k_onP – protein dimerization rate, k_onD – protein association rate to the DNA; k_off1, k_off2, k_off3, k_off4– KorA, KorB dissociation rates, KorA for KorA-DNA complex, KorB from KorB-DNA complex, KorA from KorA-KorB-DNA complex and KorB from KorA-KorB-DNA complex, respectively. Each of the other models is derived by appropriate simplification of this model. For CCOnoC, k_off1 = k_off3 and k_off2 = k_off4; for CCOregB, the reactions between KorAdimers and DNA are removed from the model; for CCOnoR, the reactions between KorBdimers and DNA are also removed from the model.