A quantitative circuit motif analysis

We have recently developed a new approach for gene circuit motif analysis³⁰, which allows identifying reoccurring two-node circuit motifs and patterns of motif coupling from the ranking of 60,212 non-redundant four-node gene circuits by a certain dynamical feature. In this approach, we numerate all possible non-redundant four-node gene circuits, and, for each circuit, we generate the steady-state gene expression profiles for an ensemble of 10,000 mathematical models with the random circuit perturbation (RACIPE) method^33,34 (see section “RACIPE simulations” and SI Text 1 for details). Based on a user-defined scoring function computed from the simulated gene expression data (see section “Defining network multiplicity and flexibility” for the two scores defined in this study), we can rank all the four-node circuits and identify two-node circuit motifs enriched in the top-ranking circuits. A similar enrichment analysis can also be applied to evaluate the co-occurrence of two circuit motifs. Our approach has several advantages over some existing methods. First, to ensure a robust statistical analysis, the circuit motif analysis utilizes extensive simulation data from all non-redundant four-node gene circuits. Second, the ensemble-based circuit simulations allow us to quantify circuits’ dynamical behavior not specific to a special set of kinetic parameters. A scoring function defined in this way enables us to rank gene circuits robustly and efficiently. Third, from the analysis of all four-node gene circuits, we can evaluate the enrichment of small circuit motifs and their coupling. Note that we limit our analysis to four-node gene circuits without any signaling node, i.e., a node without another regulator, as a circuit with signaling nodes could usually be reduced to a gene circuit of a smaller size. Therefore, the circuit motifs we would explore here could be complimentary but also distinct from the most significant circuit motifs identified in the previous studies². In this study, we applied this enrichment analysis to identify small circuit motifs contributing to a functional regulatory system.