Co-expression transition network model: a framework for differential co-expression and clustering

Differential co-expression networks provide a powerful framework to highlight changes in gene–gene interactions between biological conditions, going beyond the analysis of individual gene activity. However, their interpretability is often limited to binary (considering only whether changes are significant) or, signed representations (positive/negative edge to consider also if the change is in favour of one specific condition), which may introduce inconsistencies in edge interpretation. To overcome these limitations, we developed a Co-Expression Transition Network Model (CTNM) extending signed network theory by modelling transitions in correlation structure that can occur when a pathological condition is compared to a control one. Edges are classified into four types: appearance (0+) and disappearance (+0) of positive correlation, and appearance (0-) and disappearance (-0) of negative correlation). The framework was applied to publicly available transcriptomic data from glioblastoma patients and healthy controls. The analysis of the obtained CTNM showed that large cliques contain only 0+ or +0 edges, never both, suggesting cooperative but mutually exclusive behaviour, while 0− and −0 transitions act antagonistically, not appearing in these dense structures. Based on these observations, we developed a clustering strategy based on modularity optimization, generalizing its definition to account for the four transition types. Each cluster is assigned a dominant cooperative transition (0+ or +0) and optimization maximizes intra-cluster coherence while favouring inter-cluster antagonism. The resulting structure revealed 3 functional clusters, two deactivating (immune system and neurological pathways) and one activating (extracellular organization, cell death pathways) with emerging connections toward the others.