Fig 1.
Depiction of a hypothetical GRN architecture.
(A) Schematic of a simple GRN in which A and B cooperatively activate B, C activates A and itself, and B represses C in a manner that can override the self-activation of C. (B) The network topology table represents the direct activating, inhibiting, and null connections by 1, -1, and 0, respectively. (C) The protein coordination parameters are assigned to each gene in the genome and qualitatively describe the coordination between each gene’s regulatory TFs. ‘ActivatorNmer’ decides whether the activators of a gene work independently (0) or cooperatively (1); ‘RepressorNmer’ decides whether the repressors of a gene work independently (0) or cooperatively (1). f0 determines the basal expression level of a gene and whether its activators or repressors outcompete the other.
Table 1.
Parameter table for the GRN dynamic system.
Fig 2.
Demonstration of the combinatorial Hill functions (A and B), and the regulation function (C and D) under the regulation of an activator and a repressor.
In the top two panels (A and B), two combinatorial Hill functions are plotted; in (A) two activators work independently to activate a target gene, while in (B), two repressors work synergistically. In the bottom two panels (C and D), the dependence of the regulatory function on the activating and repressing combinatorial Hill functions is plotted for two example cases. In (C),
achieves the basal transcription rate fraction of 0.5 when there is a lack of both activator and repressor, or when both are present. Activation (resp. inhibition) occurs when the activator (resp. repressor) is abundant, and the repressor (resp. activator) is scarce. In (D), The Hill coefficient, k, determines the steepness of the regulation function; The basal expression level, f0, controls the position of the middle plane and can slide between 0 and 1. The threshold T decides the TF abundance that will trigger the activation or repression.
Fig 3.
A flowchart illustrating the step-by-step processes of our iterative computational and experimental strategy to infer GRNs and predict novel attractors.
Fig 4.
(A) Five GRN architectures were arbitrarily generated as references in the in silico test. They have 5–9 genes and at least 9 different fixed-point attractors and no oscillations. The pointed and blunt arrows represent activating and repressing regulatory interactions, respectively. (B) GRN dynamics when initiated near a fixed-point attractor of a reference GRN. The consensus GRN was inferred by the attractors of the 5-gene in silico reference GRN. The initial states were obtained by the attractor position plus a uniform distributed random variable by Eq K in S1 Text. The perturbation power was set to 0.1. The dynamics showed similarly good agreement in other reference GRNs. (C) Positive correlation between Anet similarity (Hamming distance on the horizontal axis) and attractor profiles similarity (attractor distance on the vertical axis). Each column in the box plot contains 1000 random mutated from the
consisting of 5 genes. Similar strong correlation has been observed in all other reference GRNs (see Fig C in S1 Text). (D) in silico attractors prediction result summary. Two attractors considered matched have an attractor distance less than 0.16 (a cutoff below which a simple null model has a less than 5% chance of producing matched attractors; see Table C in S1 Text). Overall, the single-knockout reference GRNs produced 384 fixed-point attractors and the single-knockout inferred GRNs produced 385. Of these attractors, 273 were matched. No attractors were matched in a random GRN.
Fig 5.
The in silico test comparison result in F1 score (upper panel), AUROC (middle panel), and AUPRC (bottom panel).
The F1 scores are calculated using a threshold cutoff of 0.5 for all models. Best performances are marked by asterisks for symmetric and asymmetric methods.
Fig 6.
(A) The schematic diagram of the S. cerevisiae synthetic circuit. Solid lines represent direct transcriptional regulation and dotted lines indicate indirect transcriptional regulation mediated by a protein-level activation or inhibition of a transcription factor. Edges accurately inferred by EA are labeled in green, otherwise in black. Gal80 protein can inhibit SWI5 transcription by preventing Gal4-mediated activation of target genes in the absence of galactose. Modified from the original paper [56]. (B) The schematic diagram of the inferred circuit. Additional inferred edges that are not present in the original design but are supported by previously published literature are labeled in orange. Inferred inhibitory edges indicated in red represent putative mechanisms for indirect repression of SWI5 by Gal80, but are not supported by known mechanisms of Gal80 function as discussed in the text.
Table 2.
Experimental evidence for regulatory associations in the synthetic circuit.
Table 3.
C. albicans strains transcriptional profiles prediction results.