(A) Gene regulatory network controlling the lambda phage lysis/lysogeny decision consists of the core repressor pair CI and Cro, and a number of additional regulators, such as N and CII. Cro and CI mutually repress each other, and CI also activates itself from the O
R2 operator site, which results in a structure of nested positive and negative feedback loops. The mutual regulatory effects of CI and Cro are annotated with the number of the O
R site corresponding to each particular interaction.
(B) Nullclines for CI and Cro, based on the model from Weitz and colleagues () at a multiplicity of infection MOI=2. Along the CI nullcline there is no change in CI and along the Cro nullcline there is no change in Cro. Neither CI nor Cro changes in the points where the nullclines intersect, which represent steady states. The nullclines intersect in three distinct points, indicating that there are three steady states.
(C) Potential calculated along the Cro nullcline, based on the Fokker-Planck approximation:

, where
f and
g represent CI synthesis and degradation along the Cro nullcline, respectively. Filled circles indicate stable nodes. The gray circle indicates that the middle state is a saddle (unstable along the Cro nullcline, but stable along the CI nullcline). Molecular noise will force the system to transition between the two valleys, especially in the beginning of infection when transcripts and proteins are rare and noise is high.
(D) The autoregulation of the TatA transcription factor from HIV was reconstituted by expressing both GFP and TatA from the LTR promoter, which is naturally activated by TatA. The
internal
ribosomal
entry
site (
IRES) () between the two coding regions ensures that GFP and TatA are co-translated from the same mRNA template.
(E) After being sorted based on their expression level as Off, Dim, Mid and Bright, the cells followed different relaxation patterns: Off remained Off; Dim first trifurcated into Off, Dim and Bright, and then the Dim peak gradually disappeared; Mid relaxed to Bright, and most of Bright remained Bright, with a small subpopulation relaxing to Low.
(F) Control synthetic gene circuit without feedback.
(G) After sorting, the control gene circuit had a much simpler relaxation pattern. Most cells were Low, which remained Low after sorting; while Dim cells mostly remained Dim, with a few of them relaxing to Off. These patterns were interpreted as the hallmarks of excitable dynamics.