Detecting Discontinuities in the Topology of Alzheimers gene Co-expression

Abstract

Alzheimer's disease (AD) emerges from a complex interplay of molecular, cellular, and network-level disturbances that are not easily captured by traditional reductionist frameworks. Conventional analyses of gene expression often rely on thresholded correlation networks or clustering-based module detection, approaches that may obscure nonlinear structure and higher-order organization. Here, we introduce a comparative topological framework that makes use of topological data analysis (TDA) and the Mapper algorithm to detect discontinuities - localized disruptions in the topology of gene co-expression space between healthy and AD brain tissue. Using gene expression data from 3 brain regions, we mapped how AD reshapes the global topology of gene-gene relationships. Discontinuity hotspots were identified via variability-based node scoring and subjected to Gene Ontology Biological Process enrichment analysis. This work illustrates the potential of TDA to uncover disease-relevant structure in high-dimensional transcriptomic data and motivates broader application of shape-based comparative methods in neurodegeneration research and other areas that benefit from comparative analysis.