Realistic mathematical models of single neurons are significant in assessing the contribution of specific ionic conductances to neuronal excitability. This study presents a detailed computational model of the Cerebral Giant Cells (CGCs), a pair of serotonergic neurons in the feeding network of Lymnaea stagnalis, which are critical for the expression of motor behaviour (feeding) and the formation of long-term memory.
First, we fitted a single-compartment, Hodgkin-Huxley model of the CGCs to two-electrode voltage- and current-clamp data  using a combination of linear and non-linear least-square fitting techniques. Then, we selectively blocked each ionic current to assess its role in the model, thus mimicking the application of pharmacological agents in the biological neuron.
The model replicates accurately the shape of the action potentials and the tonic firing (~0.74 Hz) of the biological neuron (Fig. 1A). A persistent sodium current INaP and a transient low-threshold calcium current ILVA keep the neuron spontaneously active (Fig. 1Bi, ii). A transient potassium current IA regulates the interspike interval, while a transient high-threshold calcium current IHVA increases the duration of each spike (Fig. 1Biii, iv). Transient sodium and delayed rectifier potassium currents are responsible for the depolarizing and repolarizing phases of the action potential, as in the classical Hodgkin-Huxley model. The available experimental data  are in agreement with these conclusions.
Figure 1. Overview of the CGCs model and the contribution of specific currents to neuronal excitability. In A, the model has been shifted to the right by 2 msec compared to the biological action potential.
The model we have developed here provides an accurate description of the CGCs at the biophysical level and it is a useful tool for studying the electrical properties of these important modulatory neurons.
This research was supported by EPSRC and BBSRC, United Kingdom