Activity patterns with silent states in a heterogeneous network of gap-junction coupled Huber-Braun model neurons

A mathematical model of a network of nearest neighbor gap-junction coupled neurons has been used to examine the impact of neuronal heterogeneity on the networks’ activity during increasing coupling strength. Heterogeneity has been introduced by Huber-Braun model neurons with randomization of the temperature as a scaling factor. This leads to neurons of an enormous diversity of impulse pattern, including burst discharges, chaotic activity, and two different types of tonic firing—all of them experimentally observed in the peripheral as well as central nervous system. When the network is composed of all these types of neurons, randomly selected, a particular phenomenon can be observed. At a certain coupling strength, the network goes into a completely silent state. Examination of voltage traces and inter-spike intervals of individual neurons suggests that all neurons, irrespective of their original pattern, go through a well-known bifurcation scenario, resembling those of single neurons especially on external current injection. All the originally spontaneously firing neurons can achieve constant membrane potentials at which all intrinsic and gap-junction currents are balanced. With limited diversity, i.e., taking out neurons of specific patterns from the lower and upper temperature range, spontaneous firing can be reinstalled with further increasing coupling strength, especially when the tonic firing regimes are missing. Reinstalled firing develops from slowly increasing subthreshold oscillations leading to tonic firing activity with already fairly well synchronized action potentials, while the subthreshold potentials can still be significantly different. Full in phase synchronization is not achieved. Additional studies are needed elucidating the underlying mechanisms and the conditions under which such particular transitions can appear.