Differential effects of conductances on the phase resetting curve of a bursting neuronal oscillator

The intrinsically oscillating neurons in the crustacean pyloric circuit have membrane conductances that influence their spontaneous activity patterns and responses to synaptic activity. The relationship between the magnitudes of these membrane conductances and the response of the oscillating neurons to synaptic input has not yet been fully or systematically explored. We examined this relationship using the phase resetting curve (PRC), which summarizes the change in the cycle period of a neuronal oscillator as a function of the input's timing within the oscillation. We first utilized a large database of single-compartment model neurons to determine the effect of individual membrane conductances on PRC shape; we found that the effects vary across conductance space, but on average, the hyperpolarization-activated and leak conductances advance the PRC. We next investigated how membrane conductances affect PRCs of the isolated pacemaker kernel in the pyloric circuit of Cancer borealis by: (1) tabulating PRCs while using dynamic clamp to artificially add varying levels of specific conductances, and (2) tabulating PRCs before and after blocking the endogenous hyperpolarization-activated current. We additionally used a previously described four-compartment model to determine how the location of the hyperpolarization-activated conductance influences that current's effect on the PRC. We report that while dynamic-clamp-injected leak current has much smaller effects on the PRC than suggested by the single-compartment model, an increase in the hyperpolarization-activated conductance both advances and reduces the noisiness of the PRC in the pacemaker kernel of the pyloric circuit in both modeling and experimental studies.