Predicting phase-locking in excitatory hybrid circuits
© Sieling et al; licensee BioMed Central Ltd. 2008
Published: 11 July 2008
Phase-locked activity is thought to be an underlying mechanism controlling aspects of memory, recognition, circadian rhythms, and epileptic seizures, yet no general theoretical framework has been shown to predict the existence of a simple form of phase-locked activity, phase-locking between 2 reciprocally coupled endogenously oscillating neurons. Here, we investigate a general method for predicting the behavior of coupled bursting neurons.
Previously, Oprisan, Prinz, and Canavier produced a general theoretical framework that used phase resetting theory to predict the existence, stability, and phase relations (phase-locking) of 1:1 phase-locked modes in networks consisting of 1 biological (bio) and 1 model neuron (mdl) reciprocally connected with artificial inhibitory synapses. First- and second-order phase response curves (PRCs) measured from each neuron in open loop configuration define a relationship between intervals of stimulus (ts) and recovery (tr) for each neuron, where ts is the time interval between burst onset and stimulus delivery and tr is the time interval between stimulus delivery and burst onset. When these neurons are coupled, a 1:1 phase-locked mode, that is a periodic mode of activity in a network of two neurons where each neuron fires one burst per network period, may exist if and only if these relationships are compatible, allowing the time evolution of the coupled system to be 1:1 periodic. For such cases, phase relations for the network, ts and tr, can be derived. This method is quite general, requiring few assumptions-those being that 1) the effects of a stimulus die out within one cycle period, and 2) the closed loop bursts are similar to the open loop bursts used to generate the PRCs .
Results and discussion
This article is published under license to BioMed Central Ltd.