Loss of phaselocking in nonweakly coupled inhibi

Authors: Myongkeun Oh Victor Matveev

Publish Date: 2008/08/09

Volume: 26, Issue: 2, Pages: 303-

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Abstract

Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks it is known that strong coupling can destabilize phaselocked firing Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of typeI Morris–Lecar model oscillators which is characterized by a perioddoubling cascade and leads to modelocked states with alternation in the firing order of the two cells as reported recently by Maran and Canavier J Comput Nerosci 2008 for a network of WangBuzsáki model neurons Although alternatingorder firing has been previously reported as a nearsynchronous state we show that the stable phase difference between the spikes of the two Morris–Lecar cells can constitute as much as 70 of the unperturbed oscillation period Further we examine the generality of this phenomenon for a class of typeI oscillators that are close to their excitation thresholds and provide an intuitive geometric description of such “leapfrog” dynamics In the Morris–Lecar model network the alternation in the firing order arises under the condition of fast closing of K +  channels at hyperpolarized potentials which leads to slow dynamics of membrane potential upon synaptic inhibition allowing the presynaptic cell to advance past the postsynaptic cell in each cycle of the oscillation Further we show that nonzero synaptic decay time is crucial for the existence of leapfrog firing in networks of phase oscillators However we demonstrate that leapfrog spiking can also be obtained in pulsecoupled inhibitory networks of onedimensional oscillators with a multibranched phase domain for instance in a network of quadratic integrateandfire model cells Finally for the case of a homogeneous network we establish quantitative conditions on the phase resetting properties of each cell necessary for stable alternatingorder spiking complementing the analysis of Goel and Ermentrout Physica D 163191–216 2002 of the orderpreserving phase transition map

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