Figure 5.

Cooperativity in a two-compartment ML model. (A) Panels a-f represent different compartment connectivity patterns (curved arrows) and site of stimulation (jagged arrow). A single evoked spike in the neuroma is sufficient to evoke AD in the neuroma (a, b). A unidirectional soma→neuroma connection allows a spike evoked in the soma to trigger AD in the neuroma, but that single evoked spike is insufficient to evoke AD in the soma (c). However, a unidirectional neuroma→soma connection allows phase 1 AD (originating in the neuroma) to relay spikes to the soma, eventually triggering phase 2 AD in the soma (d). If the connection is bidirectional, phase 2 AD spikes will propagate to the neuroma after phase 1 AD ends (e,f). Spike marked with a star in d is propagated to the soma because the unidirectional connectivity allows one last spike to be initiated in the neuroma; with bidirectional connectivity, the spike initiated earlier in the soma propagates to the neuroma and replaces the locally initiated spike. This illustrates how the sites compete to control spike initiation. (B) Bifurcation diagrams onto which the sample response from panel Ae is projected in order to illustrate the basis for initiation and termination of phase 1 and 2 AD. Bifurcation diagrams for the neuroma (left) and soma (right) were produced by converting intracellular sodium concentration [Na⁺]_i to a parameter whose value was systematically varied. Phase 1 AD starts when the evoked spike causes z, which controls activation of g_NaP, to cross and remain above a threshold represented by the central dashed curve. Once threshold is crossed, the system converges on the stable limit cycle that represents the AD attractor state. Unlike phase 1 AD, which is initiated by a single evoked spike, phase 2 AD requires three triggering spike (i.e. the initial evoked spike plus at two spikes from phase 1 AD). In the neuroma, [Na⁺]_i continues to increase, eventually forcing the system beyond the upper border of the stable limit cycle, at which point phase 1 AD stops. In contrast, [Na⁺]_i does not continue to increase in the soma, thus allowing the system to remain within the borders of the stable limit cycle, meaning phase 2 AD can continue indefinitely under these conditions.