Topological Invariance of Network Fragility Under Pharmacological Perturbation in Alzheimer's Disease: A Structural Coherence Analysis with Drug Combination Prediction

We present the first application of structural coherence analysis to Alzheimer's disease (AD) signalling networks, combining Topostability (graph-theoretic fragility analysis) and GraphCoherence (omics modulated coherence landscapes) to characterize the topological vulnerability of the AD signalling network and evaluate pharmacological interventions. A 30-node, 51-edge signaling network was constructed from published protein–protein interaction data, centred on the TrkB/FRS2/BDNF neuroprotective axis and the Aβ/tau/neuroinflammatory pathogenic cascade. Topostability analysis revealed a Fragility Index (FI) of 32%, with 19 always-fragile edges (tri(e) = 0) representing structural single points of failure independent of coupling strength. Human differential expression data from three independent AD cohorts (ROSMAP, MSBB, Mathys 2019) was injected as an omics signal, and GraphCoherence differential analysis was performed for five pharmacological conditions: CBD alone, Lithium alone, Baricitinib alone, CBD+Lithium, and CBD+Baricitinib. 

The central finding is a topological invariance theorem: the 19 always-fragile edges remain structurally fragile under all pharmacological perturbations tested. No expression-level intervention can change the topological classification of an always-fragile edge. However, pharmacological perturbations differ in their coherence trajectories: CBD+Lithium produces a maximum ΔCI of −13 percentage points relative to AD baseline across the full coupling range, while CBD+Baricitinib produces ΔCI = −10 but with a paradoxical positive ΔCI at low coupling due to disruption of microglial coherence. Topological remediation experiments — adding edges via molecular glues and scaffold proteins — rescued 3 of 19 always-fragile edges (GSK3β↔tau, AKT↔GSK3β, TrkB↔calpain) and reduced FI from 32% to 27%, while demonstrating that poorly-triangulated node additions can paradoxically increase fragility. These results establish a structural framework for precision AD therapeutics and identify the patient 
transcriptomic profile as the determinant of optimal drug combination.