Phase Resetting and Phase Locking in Hybrid Circuits of One Model and One Biological Neuron

Abstract

To determine why elements of central pattern generators phase lock in a particular pattern under some conditions but not others, we tested a theoretical pattern prediction method. The method is based on the tabulated open loop pulsatile interactions of bursting neurons on a cycle-by-cycle basis and was tested in closed loop hybrid circuits composed of one bursting biological neuron and one bursting model neuron coupled using the dynamic clamp. A total of 164 hybrid networks were formed by varying the synaptic conductances. The prediction of 1:1 phase locking agreed qualitatively with the experimental observations, except in three hybrid circuits in which 1:1 locking was predicted but not observed. Correct predictions sometimes required consideration of the second order phase resetting, which measures the change in the timing of the second burst after the perturbation. The method was robust to offsets between the initiation of bursting in the presynaptic neuron and the activation of the synaptic coupling with the postsynaptic neuron. The quantitative accuracy of the predictions fell within the variability (10%) in the experimentally observed intrinsic period and phase resetting curve (PRC), despite changes in the burst duration of the neurons between open and closed loop conditions.

Predictions of Phase-Locking in Excitatory Hybrid Networks: Excitation Does Not Promote Phase-Locking in Pattern-Generating Networks as Reliably as Inhibition

“…Previously, we showed that our theoretical methods predict 1:1 modes of phase-locking robustly, where 161 of 164 networks were predicted correctly (Oprisan et al 2004). In contrast to the uniform success we experienced with inhibitory circuits, a significant fraction of the hybrid circuits constructed with excitation suffered from prediction failures.…”

“…This framework was used to derive a discrete map for the time evolution of the system on a cycle-to-cycle basis. (Figure adapted from Oprisan et al 2004. ) interval of the current cycle and the effect of F2 is localized to the ts interval of the next cycle.…”

“…We used the theoretical methods of Oprisan et al (2004) to predict 1:1 phase-locking in hybrid networks from the PRCs of component neurons. This method first checks for the existence of 1:1 phaselocking using a periodicity criterion then checks that solutions are locally stable by analyzing a linearized version the system.…”

“…4A). Conduction delays are ignored here, although they can be included in the approximation as shown previously (Oprisan et al 2004;Woodman and Canavier 2008). Equilibrium stimulus phase * and stimulus (recovery) interval ts* (tr*) are defined as and ts (tr) earlier, but in the context of an ongoing 1:1 phase-locked mode rather than a single input.…”

“…To date these methods have been evaluated both in model networks (Achuthan and Canavier 2009;Canavier et al 1997Canavier et al , 1999Luo et al 2004;Maran et al 2008;Oh and Matveev 2008) and in hybrid networks coupled with inhibition (Oprisan et al 2004). Here we test the applicability of PRC-based firing time maps (Ermentrout and Chow 2002) to excitatory coupling of significant strength and duration, using a wide range of synaptic strengths (from 1 to 10,000 nS) and input durations (from 0.3 to 1.5 s).…”