The excitable grammar: action potentials of heart and brain as two implementations of one dynamical language

Abstract

Action potentials in cardiac muscle and in neurons obey the same membrane equations. We treat the action potential as a physical object and ask what a single dynamical framework predicts when its parameters are swept across the range evolution has explored. Three legs support the claim. (1) Population of models: 852 virtual cells built from twelve published excitable models by log-normal conductance perturbation at 25% variability put 97.8% of their between-cell variance into four descriptor dimensions [family-level bootstrap CI 97.5-99.9%]; a descriptor-permutation null puts only 69.5 +/- 0.6% there, so the collapse is not an artefact of the descriptor choice, though the choice partly fixes the number. (2) Real data: 2,336 Allen Cell Types neurons projected onto the model manifold occupy a region adjacent to, but distinct from, the model islands. Direct measurement of the spread to 200% conductance variability (sublinear scaling) shows that conductance noise alone cannot supply the missing variance at any feasible CV. (3) Mechanistic anchoring: an explicit sarcoplasmic-reticulum calcium loop reproduces calcium-driven alternans in a heart-failure-like regime and matches published human restitution kinetics and their hERG-block prolongation (ratio 2.20 model vs 1.94 human). Topological charge is exactly conserved in the neural medium at every tracking setting; in the turbulent cardiac regime the ledger is dominated by boundary outflow. On open data, the drug-risk coordinate ranks the twelve CiPA training drugs consistently with expert-panel torsade risk (AUC 0.91, p = 0.013) - an internal-consistency check on real pharmacology, not a blinded test. Every claim is bounded where it is made: the framework survives only in the parts its data support.

Keywords