A mathematical model of mormyrid ELL granular cell electroresponsiveness was constructed using the NEURON simulator (Hines and Carnevale, 1997). Due to the electrotonically compact structure of this cell type, a single compartment model (soma) was built with uniform ionic and input conductances. Ionic conductances for Na⁺, K⁺, Ca2⁺, a nonspecific cation leak, and a GABA_A leak current were borrowed from D’Angelo’s model of rat cerebellar granule cells (D’Angelo et al., 2001). Synaptic inputs were modeled by direct current injection for electrical synapses, and by biologically realistic values of maximum conductance, rise time, decay time, and reversal potential for NMDA, AMPA, and GABA_A mediated currents.

Simulation of neuronal electrical properties was accomplished by solving a set of differential equations describing membrane voltage, intracellular Ca²⁺ concentration, and ion channel gating dynamics. Resting potential of the cell membrane was set to –65mV, and voltage changes were determined by the following equation:

where V is membrane potential, t is time, C_m is membrane capacitance, g_i is ionic conductance, V_i is reversal potential, and i(inj) is injected current. Membrane conductances were represented using Hodgkin-Huxley-like models (Hodgkin and Huxley, 1952) of the type:

where G_max is the maximum ionic conductance, x_i and y_i are state variables (probabilities ranging from 0 to 1) for a gating particle, and z_i is the number of such gating particles in ionic channel i. The variables x and y were related to the first-order rate constants a and b by the equations:

x = a _x / (a _x + b _x), y = a _y / (a _y + b _y) (3)

t _x = 1 / (a _x + b _x), t _y = 1 / (a _y + b _y) (4)

where a and b are functions of voltage. The equations used to parameterize a and b and the state variables x,t _x, y, and t _y for different ionic channels (D’Angelo et al., 2001) are shown in Table 1. The state kinetic variables were:

d x/d t = (x_°-x) / t _x (5)

d y/d t = (y_°-y) / t _y (6)

The model included AMPA, NMDA, and GABA_A synaptic conductances, and an electrical synapse modeled with NEURON’s built-in I_clamp point process. A leakage current (D’Angelo et al., 2001), and voltage-dependent Na⁺, Ca2⁺, and K⁺ conductances were also included (D’Angelo et al., 2001; see Table 1).

All ionic currents included in the model were previously shown to be present in mature rat cerebellar granule cells (D’Angelo et al., 1997). These currents were used in the absence of experimentally verified ionic conductances in the granular cells of mormyrid ELL, with the assumption of homology between these two groups of granule-type cells. Gating kinetics, taken from D’Angelo et al. (2001), were previously adjusted to account for differences between experimental temperature and simulated temperature (T_sim=30o C).

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