Fig. 4: A resource-aware mathematical modeling framework.

a General framework for transforming molecular interaction network models. Existing models of molecular interaction networks can be transformed to include shared limiting resources by substituting k_i, the reaction rate of a resource-limited production, with k^eff_i. Shown above an exemplary resource-limited production are the detailed interactions between the substrate and the shared resource. b Limited shared resources reproduce non-monotonous dose response in open-loop and incoherent feedforward circuit topologies. On the left, a graphical representation of a model for both the open-loop (OLP) and incoherent feedforward (IFF) topologies from Lillacci et al.²⁴. Transcriptional activation is modeled by a Hill-type function. The solid arrows denote reactions assumed to follow the law of mass action. The model incorporates resources as introduced in panel a. These reactions are depicted as double-headed arrows. The model was fit to data obtained by transiently transfecting HEK293T cells with increasing amounts of plasmid encoding tTA-Cerulean. The data and the fit are shown on the right. c Limited shared resources reproduce non-monotonous dose-response in feedback and hybrid circuit topologies. The model shown on the left is the same as in panel b with an additional negative feedback from miR-FF4 to tTA-mRNA. These topologies correspond to the feedback (FBK) and hybrid (HYB) topologies from Lillacci et al.²⁴ The activation of gene expression by tTA-Cerulean is modeled by a Hill-type function as shown in the center. Reactions with double-headed arrows denote resource-limited production reactions as introduced in panel a. Solid arrows are assumed to follow the law of mass action. The model was fit to experimental data obtained from transient transfections with increasing amounts of plasmid encoding tTA-Cerulean. A description of the models can be found in Supplementary Note 4 and the parameter values obtained by fitting are summarized in Supplementary Table 7. Data were obtained 48 h after transfection and are plotted as mean ± SE. SE standard error. N = 3 biological replicates. Source data are provided as a Source Data file.