Structural fragility of the basal ganglia circuit: a Topostability analysis of dopaminergic modulation and deep brain stimulation

The basal ganglia circuit underlies voluntary motor control and is centrally implicated in Parkinson’s disease, yet its structural robustness has not been characterised using graph-theoretic fragility metrics. To our knowledge, this is the first structural fragility analysis of the basal ganglia circuit. We apply Topostability, a parameter-free topological method that derives a local bifurcation threshold — the Fragility Index (FI) — for each edge from its triangle count tri(e), focusing on structural redundancy rather than dynamical signstructure. We analysed four circuit models ranging from the canonical basal ganglia architecture to an extended Albin–DeLong model including dopaminergic projections, and a Parkinson state with STN deep brain stimulation (DBS), approximated as functional suppression of STN output pathways. Across all models, the circuit operates in a constitutively high-fragility regime (FI = 65–68), with a single structurally redundant edge: GPe↔GPi (tri = 2). Random graphs of identical size and density yield zero alwaysfragile edges, confirming that high fragility is a non-trivial architectural property. Dopaminergic projections (SNc↔Striatum, SNc↔STN) exhibit tri = 0 across all circuit variants, indicating that dopamine acts as a structurally non-redundant modulator rather than a topological backbone, consistent with its known role as a dynamic gain regulator. Simulating STN-DBS reduces FI from 68 to 55 and converts previously always-fragile STN output edges to stable or fragile states, increasing structural redundancy in the STN subgraph. We propose that DBS exerts its therapeutic effect in part through topological cycle reorganisation, disrupting structurally critical oscillatory loops. These findings suggest that basal ganglia circuits are constitutively poised near structural instability, a property that may underlie both their sensitivity to dopaminergic modulation and their susceptibility to pathological synchronisation in Parkinson’s disease.