WHY STRENGTHENING GAP JUNCTIONS MAY HINDER ACTION POTENTIAL PROPAGATION

The paper’s Theorems 3.1–3.2 characterize persistent propagation via the same geometric criterion used by the model: (i) existence of a positive fixed point requires gk ≤ F′(vE), and (ii) persistence holds iff the straight line of slope g(k+1) through (v+,F(v+)) lies nowhere above the critical segment; for large g this yields kprop(g)=F′(vE)/g, while for g near gmin the boundary is given by a tangency condition, and kprop has an interior maximum. These facts are stated and argued geometrically in the paper and are reproduced—slightly more formally—by the model’s δ(g,k) ≤ 0 criterion and continuity/uniqueness arguments. Aside from minor, nonessential issues (an unnecessary restriction vT<1/2 and a shaky proof of ϕ(vu)≤vu), the model aligns with and supports the paper’s results. Theorem 3.1 and Theorem 3.2 in the paper assert exactly these claims, including the large-g formula and the existence of an optimal g, matching the model’s conclusions .