Predicting n:1 locking in pulse coupled two-neuron networks using phase resetting theory

Abstract

Background Harmonic locking has been observed between breathing and heart beat rhythms, in hippocampal slices between interneurons firing at gamma and pyramidal neurons firing at beta frequencies with missed gamma beats and in model networks between theta and gamma rhythms. Existence and stability criteria for harmonic locking modes were derived for two reciprocally pulse coupled oscillators based on their first and second order phase resetting curves (PRCs). These methods were then tested using two reciprocally inhibitory Wang and Buzsaki model neurons. Methods PRCs were generated in an open loop configuration and applied to the analysis of the circuit under the assumption that after each perturbation the trajectory returns near its limit cycle and that the synaptic inputs received in the closed loop circuit remain similar to those used to generate the PRCs [1]. Figure 1A shows how an assumed firing pattern can be used to produce a map, which can then be linearized for a stability analysis. The dots indicate a variable number of spikes in the faster neuron 1. The periodicity criteria in this case are ts1 [n] = tr2 [n], ts21 [n] = tr11 [n], ts22 [n] = tr12 [n] with the intervals defined as shown in the figure. The periodicity criteria can be rewritten in from Seventeenth Annual Computational Neuroscience Meeting: CNS*2008 Portland, OR, USA. 19–24 July 2008