A Quantum-Stochastic Rotary Gear Model of the GABA-A Receptor–Benzodiazepine–Chloride Ionophore Complex: Allosteric Coupling, Epicycloid Phase Space, and Testable Predictions from a Turbine Analogy

The GABAA receptor–benzodiazepine (BZ)–chloride ionophore complex is a pentameric ligand-gated ion channel whose allosteric pharmacology has been extensively characterised yet incompletely modelled in geometric, thermodynamic, and quantum mechanical terms. Existing Markov state models treat allosteric modulators as scalar rate multipliers without capturing the directionality or coupling geometry of conformational change. We propose the Quantum-Stochastic Rotary Gear Model (QSRGM), which models the five subunits as coupled gear elements analogous to the F₀F₁-ATP synthase rotary turbine. Each allosteric binding site modifies a gear’s radius, angular velocity, or rotational direction. The γ subunit is modelled with structural eccentricity — consistent with cryo-EM data — mechanistically explaining BZ eccentric-gear modulation and α isoform selectivity. Chloride conductance traces an epicycloid phase portrait whose curve topology constitutes a pharmacological fingerprint. We further propose that spontaneous sub-threshold channel openings arise in part from quantum mechanical tunneling across the hydrophobic energy barrier of the leucine-9’ (L9’) gate. London dispersion forces in the L9’ pocket are proposed to provide quantum shielding analogous to the Orch OR mechanism. Four independent biological precedents support warm-protein quantum effects: quantum coherence in photosynthesis; proton tunneling in enzymatic catalysis producing non-Arrhenius kinetics; vibrational tunneling in olfactory transduction; and the radical-pair quantum magnetoreception mechanism enabling bar-tailed godwits (Limosa lapponica baueri) to navigate 11,000 km across the Pacific non-stop — the most compelling precedent, confirmed at molecular level and under positive evolutionary selection. The model generates five experimentally testable predictions accessible with standard electrophysiology equipment, including upward deviation from the classical Arrhenius line at low temperature as the primary tunneling signature, inverse agonist-specific closed-state kinetics, α-subtype phase portrait divergence, BZ–barbiturate synergy index >2.0, and epicycloid fingerprinting of novel modulators. An interactive simulation of QSRGM is added here.