Together with the electrical synapse from the primary afferent onto the granular cell, excitatory, fast ionotropic glutamate receptors and their associated ion channels constitute the total known set of excitatory inputs onto granular cells of the medial ELL in Gnathonemus petersii (Han, Grant and Bell, 2000). Pharmacological manipulations revealed both AMPA and NMDA mediated EPSP components, although the precise relative contribution of each of these receptors to the total relevant EPSP seen in the granular cell is unknown. Accordingly, the relative contribution of these receptors was allowed to vary in the model. Constraints on amplitude, rise-time, and decay-time were taken from intracellular recordings of these EPSPs after they had traveled in a retrograde manner into the axon of an innervating primary afferent (Bell, 1989).

Chemical EPSP shapes were implemented both from an eariler model of turtle cerebellar granule cell AMPA and NMDA synapses (Gabbiani, Midtgaard, and Knopfeel, 1994), and as artificial synapse functions contained in the NEURON simulation package. In both cases, free parameters included maximal inward depolarizing conductance (g_bar), rise time constant (t _rise), and decay time constant (t _decay). Reversal potential for these conductances was set to 0mV (Gabbiani et al., 1994). The Ca²⁺ conductance and voltage dependent Mg²⁺ block of NMDA receptors were not included in the model, since this local Ca²⁺ conductance was found not to play a major role in rat cerebellar granule cell bursting (D’Angelo et al., 2001) and NMDA receptors in rat cerebellar granule cells show little or no voltage dependent Mg²⁺ block membrane voltages more positive than —60mV (D’Angelo et al., 1997). The following equation describes the Na⁺ conductance of both AMPA and NMDA receptors used in this model:

gGlutR(t) = g_bar(GlutR) (e^{(-t/t decay)} — e^{(-t/t rise)}), (8)

where g_bar is the maximum conductance associated with the receptor, and the following two terms describe the time course of this conductance. Since the relative contributions of AMPA and NMDA mediated EPSPs to the total ELL granular cell chemical EPSP is unknown, both components were modeled as a lump conductance. Values for t _rise and t _decay ranged between experimentally reported levels, reported in Gabbiani et al. (1994), of 0.09ms:1.5ms (AMPA) and 3ms:40ms (NMDA). EPSPs driven by juxtalobar input to ELL granular cells, as measured intracellularly in primary afferents by Bell (1989), are fit well using a t _rise negligibly above 0ms and a t _decay of around 3ms. However, it is thought that the gap junction between ELL granular cells and their innervating primary afferent acts as a high-pass filter (Bell, personal communication). This would suggest that the actual EPSP, as it appears in the ELL granular cell, has components with longer t _decay constants and possibly larger amplitudes than are evident from primary afferent recordings. For this reason, t _decay and gbar for the mixed AMPA/NMDA synapse were allowed to vary above 3ms and a conductance producing a maximum depolarization of ~+5mV (Bell, 1989), respectively.

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