PMC

(A) Some biochemical oscillators utilizing the three-component negative feedback loop motif. Positive feedback loops (in blue) are often found along with the core negative feedback loop (in orange) (B) Oscillatory motifs involving the three-component negative feedback loop (top) with all possible auxiliary positive feedback loops (in blue). The motifs encountered in biochemical oscillators are clearly recognizable. The kinetic model formulation for each motif is also listed with the term representing the positive feedback in blue. The three components of the negative feedback loop are activator , intermediate and repressor . The parameter tunes the strength of the positive feedback, with a value of representing no positive feedback. (C) Waveform of the Goodwin oscillator with equal degradation in all steps with cooperativity increased from 3 (left) to 10 (right).

Genetic architectures and corresponding transcriptional logic depicting the coupling of feedback loops. (a) PPA: a gene network depicting the additive coupling of two positive feedback loops. The transcription of gene X is controlled from two independent promoters, P₁ and P₂, both of which possess upstream operator sites for the TF X_A. Bound TF upregulates transcription from the two promoters, thereby giving rise to two positive feedback loops. (b) PPM: a gene network depicting multiplicative coupling of two positive feedback loops. The transcription of gene X is controlled from one promoter P. TF X_A regulates transcription by binding to the operator sites upstream of the promoter, thereby resulting in two positive feedback loops such as in the case of additive coupling. (c) PNA: a gene network depicting additive coupling of a positive and a negative feedback loop. The transcription of gene X is controlled from two independent promoters P₁ and P₂, both of which possess upstream operator sites for the TF X_A. Bound TF upregulates and downregulates the transcription from the promoters P₁ and P₂, respectively, thereby giving rise to positive and negative feedback loops. (d) PNM: a gene network depicting multiplicative coupling of a positive and a negative feedback loop. The transcription of gene X is controlled by one promoter P. TF X_A regulates transcription by binding to the operator sites upstream of the promoter, thereby resulting in positive and negative feedback loops similar to the case of additive coupling.

(a) Topology of a general negative feedback loop. (b) An example of negative feedback system that causes desensitization - the USP18-mediated negative feedback loop in the JAK-STAT pathway. (c) Time traces of a delayed negative feedback system in response to repetitive stimulations. Green – signal; blue – effector/output; red – inhibitor.

Loops captured in the model are shown with solid lines. The arrow labeled PF1 represents positive feedback. This feedback loop has been implicated in mediating bistable switching. The arrows labeled NF1–NF3 represent negative feedbacks. The NF1 feedback loop encompasses the positive feedback loop. The NF2 and NF3 feedback loops are placed out of the positive feedback loop. Dotted lines indicate feedbacks not included in the model.