Models of electrical activity, calcium concentration, and synaptic plasticity in Aplysia neurons

Abstract

Mathematical models of two Aplysia neurons simulate salient features of the electrical and chemical activity of these neurons. First, the endogenous burster R15 was modeled as a Hodgkin-Huxley (HH) type membrane equivalent circuit coupled to a fluid compartment model. The model simulates available data on potential and bulk $Ca\sp{2+}$ concentration waveforms, as well as transitions between bursting, beating, and silent modes and the effects of certain modulatory agents. A reduced two-variable nullcline analysis provided valuable insights into the activity of the full model. Second, a HH type model of a sensory neuron was coupled with a concentric shell model of radial variation in $Ca\sp{2+}$ concentration to simulate basal data on action potential shape and excitability. The effect of serotonin (5HT) on these variables was also simulated. Finally, the coupling between the sensory neuron and a follower motor neuron was modeled, including mobilization and release of transmitter, and the response of the postsynaptic membrane. The model simulated the postsynaptic excitatory potential (EPSP) waveforms and maximum amplitudes under normal, depressed, and facilitated conditions.