Dynamic responses of electrically coupled systems

An identified pair of electrically coupled neurons in the buccal ganglion of the freshwater snail Helisoma trivolvis is an experimentally accessible model of electrical synaptic transmission. In this investigation, electrical synaptic transmission is characterized using sinusoidal frequency (Bode) responses computed by Laplace transforms and responses to brief stimuli. The frequency response of the injected neuron shows a 20-dB/decade attenuation and a phase shift from 0 degree at low frequencies to -90 degrees at high frequencies. The response of a coupled cell shows a 40-dB/decade attenuation and a phase shift from 0 degrees at low frequencies to -180 degrees at high frequencies. A simple mathematical model of electrical synaptic transmission is described that displays each of these crucial features of the measured frequency responses. Methods are described to estimate the frequency responses of coupled systems based on presynaptic measurements. The responses of the coupled system to brief pulses of current were computed using the principle of superposition. The electrical properties of coupled systems impose a minimum delay in reaching a peak in all postsynaptic responses. The delays in the postsynaptic responses to brief stimuli are related to the electrical and anatomical parameters of coupled networks.