Polarization of regulatory inputs reveals structural constraints in reconstructed pathway-associated regulatory networks

Abstract

Activating and inhibitory interactions jointly shape cellular regulation, yet it remains unclear whether their allocation among individual targets exhibits systematic organization beyond basic structural constraints. Here we introduce antagonistic--cooperative polarization, a target-wise principle in which the sign of each regulatory interaction is determined by the class of its target. This formulation yields a node-separable graph polarization index and decomposes departures from perfect polarization exactly into localized conflicts at targets receiving both activating and inhibitory inputs. We applied the framework to 98 pathway-associated regulatory subnetworks reconstructed from a unified signed regulatory network. Target-wise sign consistency was generally high, but the key evidence for non-random organization came from constrained null models: mixed-input targets were depleted relative to both global sign shuffling and degree-preserving directed rewiring, with depletion increasing systematically with pathway size. This association was robust to rewiring-mobility and pathway-overlap analyses, and indegree-stratified analysis identified the clearest statistically supported depletion among targets receiving exactly two signed inputs. Mixed-input organization was pathway-specific but recurrent across genes; recurrent mixed-input targets remained enriched for Cancer Gene Census genes after accounting for pathway opportunity. Mixed-input occurrences were also preferentially associated with signed feedback motifs, particularly negative feedback, whereas downstream reach was not increased. Together, these results reveal a prevalent polarized backbone punctuated by localized sites of opposing regulation whose abundance departs from expectations under complementary null models controlling for network topology, sign composition, degree structure, and source-specific regulatory output.