FIG. 7.

Automaticity regimes in heterogeneous cell pairs with ephaptic and gap junction coupling. (a) Gap junction coupling strength $g_{gap}$ has negligible influence on the regimes for which automaticity occurs. Black dotted lines are the reference point for the Hopf bifurcation (HB) for the minimal $f_{K1}$ for automaticity for identical cells and $g_{gap}=0$ (cleft volume $vcl=0.38\mu {\text{m}}^3$). Note that the asterisk in the left region of “both quiescent” indicates that for $g_{gap}=0$ and small $f_{K1}^{(2)}$, cell-1 triggers APs and cell-2 has sub-threshold oscillations [recall Fig. 6(c)]. However, this only occurs when $g_{gap}=0$; for $g_{gap}>0$, both cells are quiescent in that region. (b) Similar plot as (a) for various cleft volumes $vcl$—the boundary for automaticity shifts but varying $g_{gap}$ does not significantly change regimes for automaticity. The black dotted lines denoting the HB point are shorter to avoid clutter. (c) Detailed two-parameter bifurcation diagrams, fixing cell-1’s $f_{K1}$ ( $f_{K1}^{(1)}$), with cleft volume on the vertical axis and cell-2’s $f_{K1}$ ( $f_{K1}^{(2)}$) on horizontal. As in (a) and (b), gap junction coupling does not alter the boundary for which both cells are triggering APs. The near vertical line for $g_{gap}=0$ (blue dotted) for small $f_{K1}^{(2)}$ is indicative of the dynamics described in Fig. 6(c). (d) The blue curves (no gap junction) in (c) are shown on a single axis, related to Fig. 3(f) (black).