Skip navigation


A Model of Graded Synaptic Transmission for Use in Dynamic Network Simulations

69: 1225-1235, 1993

E. De Schutter, J.D. Angstadt, R.L. Calabrese


  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 (I CaF ) and slow (I CaS) 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 I CaF and I CaS 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.

Related publications

Calabrese R.L. and De Schutter E.: Motor pattern generating networks in invertebrates: modeling our way toward understanding. Trends in Neurosciences 15: 439-445 (1992).

Full Paper-pdf