Persistent homology of blood gene co-expression networks reveals reduced cycle structure in autism spectrum disorder: a multi-cohort analysis.

Autism spectrum disorder (ASD) exhibits substantial molecular heterogeneity that challenges traditional gene-centric analyses. We applied persistent homology of the graph 1-skeleton to characterize co-expression cycle structure in mutual information-based gene networks in ASD. Using transcriptomic data from brain tissue and peripheral blood, we constructed MI networks from the 500 most variable genes, computed Betti-1 numbers across 30 filtration steps, and assessed significance via 10,000-permutation testing. We note that this approach computes first homology on the 1-skeleton, not the full flag/clique complex; this distinction is made explicit throughout. ASD peripheral blood networks exhibited nominally significant topological reorganization relative to neurotypical controls, with a 20.4% reduction in the area under the Betti-1 curve. After excluding 44 redundant SNORD115-family probes to address microarray probe-redundancy concerns, the finding strengthened substantially to [Formula: see text], which we consider the primary result. This indicates that regulatory cycle structure accumulates less readily in ASD blood co-expression networks across the full filtration range. Brain cortex networks showed no significant topological differences; however, a post-hoc power analysis indicates the brain cohort has only ∼ 36% power to detect the blood-magnitude effect, so this null result should not be interpreted as evidence of preserved brain topology or tissue specificity. After SNORD115 probe exclusion, ASD hub genes form a ribosomal protein gene cluster consistent with translational dysregulation in ASD. To validate the blood finding, we applied the identical TDA pipeline to two independent blood transcriptome datasets: GSE42133 and GSE25507. Both independent cohorts exhibited the same ASD < control direction. Stouffer meta-analysis combining the z-scores from all three blood datasets, demonstrating robust directional replication of the reduced-cycle-structure signal across independent cohorts (spanning two Affymetrix platforms, Human Gene 1.0 ST and U133 Plus 2.0). These findings demonstrate that graph-filtration cycle-rank analysis detects reduced co-expression cycle structure in ASD peripheral blood, independently replicated across three blood transcriptome cohorts. The Stouffer meta-analysis substantially exceeds conventional significance thresholds and supports the potential utility of topological biomarkers in neurodevelopmental disorders.