Clustering through post inhibitory rebound in synaptically coupled neurons

Post inhibitory rebound is a nonlinear phenomenon present in a variety of nerve cells. Following a period of hyper-polarization this effect allows a neuron to fire a spike or packet of spikes before returning to rest. It is an important mechanism underlying central pattern generation for heartbeat, swimming and other motor patterns in many neuronal systems. In this paper we consider how networks of neurons, which do not intrinsically oscillate, may make use of inhibitory synaptic connections to generate large scale coherent rhythms in the form of cluster states. We distinguish between two cases i) where the rebound mechanism is due to anode break excitation and ii) where rebound is due to a slow T-type calcium current. In the former case we use a geometric analysis of a McKean type model to obtain expressions for the number of clusters in terms of the speed and strength of synaptic coupling. Results are found to be in good qualitative agreement with numerical simulations of the more detailed Hodgkin-Huxley model. In the second case we consider a particular firing rate model of a neuron with a slow calcium current that admits to an exact analysis. Once again existence regions for cluster states are explicitly calculated. Both mechanisms are shown to prefer globally synchronous states for slow synapses as long as the strength of coupling is sufficiently large. With a decrease in the duration of synaptic inhibition both systems are found to break into clusters. A major difference between the two mechanisms for cluster generation is that anode break excitation can support clusters with several groups, whilst slow T-type calcium currents predominantly give rise to clusters of just two (anti-synchronous) populations.

Spatio-temporal filtering properties of a dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modeled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. In this paper we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded on a simple one-dimensional cable. In the first instance this system is shown to support saltatory waves with the same qualitative features as those observed in a model with Hodgkin-Huxley kinetics in the spine-head. Moreover, there is excellent agreement with the analytically calculated speed for a solitary saltatory pulse. Upon driving the system with time varying external input we find that the distribution of spines can play a crucial role in determining spatio-temporal filtering properties. In particular, the SDS model in response to periodic pulse train shows a positive correlation between spine density and low-pass temporal filtering that is consistent with the experimental results of Rose and Fortune [1999, Mechanisms for generating temporal filters in the electrosensory system. The Journal of Experimental Biology 202, 1281-1289]. Further, we demonstrate the robustness of observed wave properties to natural sources of noise that arise both in the cable and the spine-head, and highlight the possibility of purely noise induced waves and coherent oscillations.