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

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(CaS) inactivation time constant either in the living heart interneuron or in the model heart interneuron. In both cases, varying I(CaS) inactivation time constant did not affect f(Final) of either interneuron, but in the varied interneuron, the time constant of decline of spike frequency during bursts to f(Final) and thus the burst duration varied directly and nearly linearly with I(CaS) inactivation time constant. Bursts of the opposite, nonvaried interneuron did not change. We show also that control of burst duration by I(CaS) inactivation 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.