Detecting Discontinuities in the Topology of Alzheimers gene Co-expression

TL;DR

This paper applies topological data analysis and the Mapper algorithm to identify disruptions in gene co-expression networks associated with Alzheimer's disease, revealing disease-specific topological features in high-dimensional transcriptomic data.

Contribution

It introduces a novel topological framework using TDA and Mapper to detect localized topological disruptions in gene expression data between healthy and AD brains.

Findings

Discontinuity hotspots correlate with disease states

Topological features differ significantly between healthy and AD tissues

Gene Ontology analysis reveals disease-relevant biological processes

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.