Modulation of a Single Neuron Has State-Dependent Actions on Circuit Dynamics

When does neuromodulation of a single neuron influence the output of the entire network? We constructed a five-cell circuit in which a neuron is at the center of the circuit and the remaining neurons form two distinct oscillatory subnetworks. All neurons were modeled as modified Morris-Lecar models with a hyperpolarization-activated conductance ( ) in addition to calcium ( ), potassium ( ), and leak conductances. We determined the effects of varying , , and on the frequency, amplitude, and duty cycle of a single neuron oscillator. The frequency of the single neuron was highest when the and conductances were high and was moderate whereas, in the traditional Morris-Lecar model, the highest frequencies occur when both and are high. We randomly sampled parameter space to find 143 hub oscillators with nearly identical frequencies but with disparate maximal conductance, duty cycles, and burst amplitudes, and then embedded each of these hub neurons into networks with different sets of synaptic parameters. For one set of network parameters, circuit behavior was virtually identical regardless of the underlying conductances of the hub neuron. For a different set of network parameters, circuit behavior varied with the maximal conductances of the hub neuron. This demonstrates that neuromodulation of a single target neuron may dramatically alter the performance of an entire network when the network is in one state, but have almost no effect when the circuit is in a different state.