The landscape (projected onto the concentration of a specific molecule) is reshaped as the environment changes in time. The blue ball represents a cell that under the influence of a changing environment can assume three different fates at the proximal edge of the landscape (white balls at the end of the time course). Even in a constant environment, cells can transition between local minima due to random perturbations to the landscape (intrinsic molecular noise).

(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.

(A) The gene regulatory network controlling entry into competence consists of the master regulator ComK and its indirect activator, ComS. ComK activates its own expression, and ComS is downregulated during competence, which results in a structure of nested positive and negative feedback loops. Regulatory interactions mediating positive and negative feedback are shown in red and blue, respectively. Arrowheads indicate activation; blunt arrows indicate repression.
(B) Nullclines for ComK and ComS, based on the model from (). The nullclines intersect in three distinct points, indicating that there are three steady states.
(C) Potential calculated along the nullcline d[comS]/dt=0, based on the Fokker-Planck approximation: , where f and g represent comK synthesis and degradation, respectively, along the ComS nullcline. The filled circle on the left indicates a stable steady state. The gray circles in the middle and on the right indicate saddle points: the middle one is unstable along the ComS nullcline (it is sitting on a “crest“ in the potential), while the one on the right is unstable along the ComK nullcline. A small perturbation (due to molecular noise) will drive ComK expression from the stable steady state near the other two steady states, initiating transient differentiation into competence, after which the system returns to the steady state on the left.

(A) Regulatory network controlling galactose uptake. Regulatory interactions mediating positive and negative feedback are shown in red and blue, respectively, while the regulatory interaction that participates in both positive and negative feedback loops is shown in purple. Solid lines indicate transcriptional regulation; dashed lines indicate non-transcriptional regulation (for example, Gal80p binds to Gal4p and represses Gal4p activator function on GAL promoters). Arrowheads indicate activation; blunt arrows indicate repression.
(B) Gal3p synthesis (blue lines) and degradation (red line) rates as functions of Gal3p concentration, for three different galactose concentrations.
(C) Potential based on the Fokker-Planck approximation: , where f and g represent Gal3p synthesis and degradation, respectively. There is a stable steady state on the left side of the surface at all galactose concentrations. At sufficiently high galactose concentrations, an additional steady state appears (deep well on the right). As galactose concentration is slowly increased, cells can end up in either potential well (cellular decision-making). Moreover, molecular noise can move cells from one potential well to the other even in constant galactose concentration.

(A) The morphogen Bicoid regulates hunchback expression during fruit fly development, setting up the scene for subsequent patterning of the embryo.
(B) Bicoid and Hunchback concentrations along the anterior-posterior axis of the fruit fly embryo (length: ~500 µm), according to the measurements by Gregor and colleagues (). The Bicoid concentration (red color) is exponentially decreasing towards the posterior end, with a length constant of 500 µm, and is “read out” by Hunchback (green color) with a 10% relative error rate according to the average dose-response relationship Hb/Hb_max=(Bcd/Bcd_1/2)⁵/[1+(Bcd/Bcd_1/2)⁵].
(C) Gene regulatory network controlling intestinal cell-fate specification during Caenorhabditis elegans development.

(A) The Nanog-Oct4 gene regulatory network primes ESC differentiation. Regulatory interactions mediating positive and negative feedback are shown in red and blue, respectively. Regulatory interactions that participate in both positive and negative feedback loops are shown in purple. Arrowheads indicate activation; blunt arrows indicate repression.
(B) Nullclines for Nanog and Oct4, based on the model from Kalmar et al. (). The nullclines intersect only once, corresponding to a single stable steady state.
(C) Potential calculated along the nullcline d[Nanog]/dt=0, based on the Fokker-Planck approximation. The filled circle on the right indicates the only stable steady state. The gray shaded area is inaccessible since it corresponds to non-physical solutions. The system undergoes transient excursions to the left (low Nanog concentrations) under the influence of molecular noise. This will prime the ESCs for differentiation if appropriate signals are present.