Figure 2. Nav-CLS induced spontaneous activities of injured node: steady state with fixed E_Ion, tonic spiking, tonic subthreshold oscillations (STOs).

By setting I_maxpump, g_Naleak, and g_Kleak to zero and eliminating Eqs (11) and (12), the E_Ion are artificially maintained at fixed values. Three sets of values are considered: left column, E_Na = 50 mV, E_K = −77 mV; middle column: E_Na = 42 mV, E_K = −77 mV; right column: E_Na = 42 mV, E_K = −71 mV. For the first 3 rows, Nav-CLS have Gaussian distributions (mean±SD): (A,B,C) 1.3±0.4 mV; (D,E,F) 8±1 mV; (G,H,I) 15±1 mV. For the last rows,(J,K,L) bifurcation diagrams (solution of V_m in terms of LS) are plotted, and there, for computational tractability, single g_Na populations (i.e. f = 1, no Gaussian “smears”) are used. As labeled, the solid line, dashed line, filled dots, open dots and “HB” respectively denote: stable fixed point (i.e. resting potential (RP)), unstable fixed point, stable limit cycle (SLC, i.e., tonically firing APs), unstable limit cycle (ULC) and Hopf bifurcation point (HB). When E_Na alone changes (J to K), the bifurcation structure shows only slight changes in the amplitude of SLC and the locations of subcritical HB on both ends. When E_K changes (K to L), the HBs on both ends shift to the left (i.e. towards relatively smaller E_Na) and the previously subcritical HB (right side) becomes supercritical. Across the 3 columns, note that if the system did have pumps, interactions between the E_Ion and I_pump would continually and slowly change E_Ion thereby repeatedly evoking these activity patterns.