A model of graded synaptic transmission for use in dynamic network simulations.

1. The heartbeat central pattern-generating network of the medicinal leech contains elemental neural oscillators, comprising reciprocally inhibitory pairs of segmental heart interneurons, that use graded as well as spike-mediated synaptic transmission. We are in the process of developing a general computer model of this pattern generator. Our modeling goal is to explore the interaction of membrane currents and synaptic transmission that promote oscillation in heart interneurons. As a first step toward this goal, we have developed a computer model of graded synaptic transmission between reciprocally inhibitory heart interneurons. Previously gathered voltage-clamp data of presynaptic Ca2+ currents and simultaneous postsynaptic currents and potentials (5 mM external [Ca2+]) were used as the bases of the model. 2. We assumed that presynaptic Ca2+ current was composed of distinct fast (ICaF) and slow (Icas) components because there are two distinct time courses of inactivation for this current. We fitted standard Hodgkin-Huxley equations (Eq. 1 and 2, APPENDIX) to these components using first-order activation and inactivation kinetics. 3. Graded synaptic transfer in the model is based on calculation of a dimensionless variable [P]. A portion of both IcaF and ICaS determined by a factor A contributes to [P], and a removal factor B decreases [P] (Eq. 4, APPENDIX). [P] can be roughly equated to the [Ca2+] in an unspecified volume that is effective in causing transmitter release. Transmitter release, and thus postsynaptic conductance, is related to [P]3 (Eq. 3, APPENDIX). 4. We adapted our model to voltage-clamp data gathered at physiological external [Ca2+] (2.0 mM) and tested it for shorter presynaptic voltage steps. Presynaptic Ca2+ currents and synaptic transfer were well simulated under all conditions. 5. The graded synaptic transfer model could be used in a network simulation to reproduce the oscillatory activity of a reciprocally inhibitory pair of heart interneurons. Because synaptic transmission in the model is an explicit function of presynaptic Ca2+ current, the model should prove useful to explore the interaction between membrane currents and synaptic transmission that promote and modulate oscillation in reciprocally inhibitory heart interneurons.