Mechanisms of very fast oscillations in networks of axons coupled by gap junctions

Because electrical coupling among the neurons of the brain is much faster than chemical synaptic coupling, it is natural to hypothesize that gap junctions may play a crucial role in mechanisms underlying very fast oscillations (VFOs), i.e., oscillations at more than 80 Hz. There is now a substantial body of experimental and modeling literature supporting this hypothesis. A series of modeling papers, starting with work by Roger Traub and collaborators, have suggested that VFOs may arise from expanding waves propagating through an "axonal plexus", a large random network of electrically coupled axons. Traub et al. also proposed a cellular automaton (CA) model to study the mechanisms of VFOs in the axonal plexus. In this model, the expanding waves take the appearance of topologically circular "target patterns". Random external stimuli initiate each wave. We therefore call this kind of VFO "externally driven". Using a computational model, we show that an axonal plexus can also exhibit a second, distinctly different kind of VFO in a wide parameter range. These VFOs arise from activity propagating around cycles in the network. Once triggered, they persist without any source of excitation. With idealized, regular connectivity, they take the appearance of spiral waves. We call these VFOs "re-entrant". The behavior of the axonal plexus depends on the reliability with which action potentials propagate from one axon to the next, which, in turn, depends on the somatic membrane potential V (s) and the gap junction conductance g (gj). To study these dependencies, we impose a fixed value of V (s), then study the effects of varying V (s) and g (gj). Not surprisingly, propagation becomes more reliable with rising V (s) and g (gj). Externally driven VFOs occur when V (s) and g (gj) are so high that propagation never fails. For lower V (s) or g (gj), propagation is nearly reliable, but fails in rare circumstances. Surprisingly, the parameter regime where this occurs is fairly large. Even a single propagation failure can trigger re-entrant VFOs in this regime. Lowering V (s) and g (gj) further, one finds a third parameter regime in which propagation is unreliable, and no VFOs arise. We analyze these three parameter regimes by means of computations using model networks adapted from Traub et al., as well as much smaller model networks.