Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation
Figure 8
Common phase plane geometries associated with different parameter changes.
(A) βw controls positioning of the w-nullcline (i.e. voltage-dependency of Islow). For βw = 0 mV, the nullclines intersect tangentially at rheobasic stimulation, which translates into an SNIC bifurcation. For βw = −13 mV, the w-nullcline crosses the V-nullcline on its middle arm, which translates into a Hopf bifurcation. For βw = −21 mV, the w-nullcline crosses the V-nullcline on its left arm, meaning spike initiation is limited to a QSC. See Figure 2B for corresponding bifurcation diagrams. Thus, spike initiating dynamics (and the resulting pattern of excitability) are directly related to phase plane geometry (i.e. how the nullclines intersect). (B) βm controls positioning of the V-nullcline (i.e., voltage-dependency of Ifast). Reducing βm had the same effect on phase plane geometry as increasing βw. The predicted consequences for excitability are confirmed on the bifurcation diagrams. Like Islow, Ifast may comprise more than one current; therefore, differences in the voltage-dependency of the net fast current may reflect the expression of different fast currents rather than variation in the voltage-dependency of any one current (see Figure 4). For (B–E), βw = −10 mV, γw = 13 mV, and all other parameters are as indicated in Methods unless otherwise stated. (C) Varying ḡfast changed the shape rather than positioning of the V-nullcline, but both had equivalent consequences for excitability. (D) Varying ḡslow also changed the shape of the V-nullcline, in a slightly different manner than ḡfast, but with the same consequences for excitability. (E) Varying γw, which controls the slope of the voltage-dependent activation curve for Islow, altered the w-nullcline, again, with predictable consequences for excitability. βw = 0 mV.