Hybrid Systems Analysis of the Control of Burst Duration by Low-Voltage-Activated Calcium Current in Leech Heart Interneurons

Abstract

The leech heartbeat CPG is paced by the alternating bursting of pairs of mutually inhibitory heart interneurons that form elemental half-center oscillators. We explore the control of burst duration in heart interneurons using a hybrid system, where a living, pharmacologically isolated, heart interneuron is connected with artificial synapses to a model heart interneuron running in real-time, by focusing on a low-voltage-activated (LVA) calcium current I_CaS. The transition from silence to bursting in this half-center oscillator occurs when the spike frequency of the bursting interneuron declines to a critical level, f_Final, at which the inhibited interneuron escapes owing to a build-up of the hyperpolarization-activated cation current, I_h. We varied I_CaSinactivation time constant either in the living heart interneuron or in the model heart interneuron. In both cases, varying I_CaSinactivation time constant did not affect f_Finalof either interneuron, but in the varied interneuron, the time constant of decline of spike frequency during bursts to f_Finaland thus the burst duration varied directly and nearly linearly with I_CaSinactivation time constant. Bursts of the opposite, nonvaried interneuron did not change. We show also that control of burst duration by I_CaSinactivation does not require synaptic interaction by reconstituting autonomous bursting in synaptically isolated living interneurons with injected I_CaS. Therefore inactivation of LVA calcium current is critically important for setting burst duration and thus period in a heart interneuron half-center oscillator and is potentially a general intrinsic mechanism for regulating burst duration in neurons.