Hierarchical organization in sparse gene regulatory networks shapes structural coherence and emergent regulatory coordination

Abstract

A fundamental challenge in systems biology is understanding how regulatory coordination is maintained within extremely sparse gene regulatory networks (GRNs). While traditional unsigned network metrics can quantify the overall magnitude of influence a specific node or edge exerts over the network, they cannot predict the functional direction and consistency of these regulatory changes. To address this gap, we introduce the coherence matrix. This topology-based framework for signed, directed GRNs computes a strictly bounded, interpretable measure of directional regulatory coordination between gene pairs. Using synthetic network ensembles, we demonstrate that architectures with low intrinsic structural coherence suffer severe density-driven scaling penalties. Such structures cannot scale without requiring biologically unrealistic edge densities. Applying this framework to six whole-organism GRNs reveals how biological topologies overcome these limitations. Whole-organism GRNs exhibit lower overall coherence and more fragmented structures than expected, avoiding rigid global co-regulation to maximize regulatory degrees of freedom. Furthermore, these systems resolve the scaling penalties of complex, low-coherence architectures by restricting dense regulatory crosstalk to a compact intermediate core. Modeling synthetic hierarchical networks confirms that this architecture, a compact core within a globally feed-forward scaffold, neutralizes scaling penalties by minimizing nodes requiring dense connectivity. This allows GRNs to efficiently route decisions despite extreme sparsity. Finally, validation with transcriptomic data confirms that coherence matrix accurately predicts empirical co-regulation directionality. By moving beyond unsigned connectivity, the structural coherence framework provides a quantitative tool to map how the intrinsic behavior of localized interactions scales into macroscopic, system-wide coordination.