A study of nerve impulse generation in ganglion cells of the tiger salamander retina is carried out through a combination of experimental and analytic approaches, including computer simulations based on a single-compartment model. Whole cell recordings from ganglion cells were obtained using a superfused retina-eyecup preparation and studied with pharmacological and electrophysiological techniques, including phase plot analysis. Experimental efforts were guided by computer simulation studies of an excitability model consisting of five voltage- or ion-gated channels, which were identified from earlier voltage-clamp data. The ion channels include sodium, calcium, and three types of potassium channels, namely the A type (IK,A), Ca-activated potassium (IK,Ca), and the delayed rectifier (IK). A leakage channel was included to preserve input resistance continuity between model and experiment. Ion channel densities of Na and Ca currents (INa and ICa) for the single-compartment model were independently determined from phase plot analysis. The IK and IK,A current densities were determined from the measured width of impulses. The IK,Ca was modeled to respond to Ca influx, and a variable-rate Ca-sequestering mechanism was implemented to remove cytoplasmic calcium. Impulse frequency increases when either ICa or IK,Ca is eliminated from the model or blocked pharmacologically in whole cell recording experiments. Faithful simulations of experimental data show that the ionic currents may be grouped into small (IK,Ca, leakage, and stimulus), and large (INa, IK, IA, ICa) on the basis of their peak magnitudes throughout the impulse train. This division of the currents is reflected in their function of controlling the interspike interval (small currents) and impulse generation (large currents). Although the single-compartmental model is qualitatively successful in simulating impulse frequency behavior and its controlling mechanisms, limitations were found that specifically suggest the need to include morphological details. The spike train analysis points to a role for electrotonic currents in the control of the duration of the interspike intervals, which can be compensated by prolonged activation of gK,Ca in the single-compartment model. A detailed, multicompartmental model of the ganglion cell is presented in the companion paper.

Models for generating repetitive impulse activity were developed based on multicompartmental representations of ganglion cell morphology in the amphibian retina. Each model includes five nonlinear ion channels and one linear (leakage) channel. Compartmental distribution of ion channel type and density was designed to simulate whole cell recording experiments carried out in the intact retina-eyecup preparation. Correspondence between the model and physiology emphasized channel-specific details in the impulse waveform, based on phase plot analysis, frequency versus current (F/I) properties, and interspike trajectories for current injected into the soma, as well as the ability to conduct impulses in both orthodromic and antidromic directions. Two general types of model are developed, including equivalent cylinder representations and more realistic compartmentalizations of dendritic morphology. These multicompartmental models include representations for dendritic trees, soma, axon hillock, a thin axonal segment, and axon distal to thin segment. A large number of compartments (

Trains of action potentials of rat and cat retinal ganglion cells (RGCs) were recorded intracellularly across a temperature range of 7-37 degrees C. Phase plots of the experimental impulse trains were precision fit using multicompartment simulations of anatomically reconstructed rat and cat RGCs. Action potential excitation was simulated with a "Five-channel model" [Na, K(delayed rectifier), Ca, K(A), and K(Ca-activated) channels] and the nonspace-clamped condition of the whole cell recording was exploited to determine the channels' distribution on the dendrites, soma, and proximal axon. At each temperature, optimal phase-plot fits for RGCs occurred with the same unique channel distribution. The "waveform" of the electrotonic current was found to be temperature dependent, which reflected the shape changes in the experimental action potentials and confirmed the channel distributions. The distributions are cell-type specific and adequate for soma and dendritic excitation with a safety margin. The highest Na-channel density was found on an axonal segment some 50-130 microm distal to the soma, as determined from the temperature-dependent "initial segment-somadendritic (IS-SD) break." The voltage dependence of the gating rate constants remains invariant between 7 and 23 degrees C and between 30 and 37 degrees C, but undergoes a transition between 23 and 30 degrees C. Both gating-kinetic and ion-permeability Q10s remain virtually constant between 23 and 37 degrees C (kinetic Q10s = 1.9-1.95; permeability Q10s = 1.49-1.64). The Q10s systematically increase for T <23 degrees C (kinetic Q10 = 8 at T = 8 degrees C). The Na channels were consistently "sleepy" (non-Arrhenius) for T <8 degrees C, with a loss of spiking for T <7 degrees C.

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Nerve impulse entrainment and other excitation and passive phenomena are analyzed for a morphologically diverse and exhaustive data set (n = 57) of realistic (3-dimensional computer traced) soma-dendritic tree structures of ganglion cells in the tiger salamander (Ambystoma tigrinum) retina. The neurons, including axon and an anatomically specialized thin axonal segment that is observed in every ganglion cell, were supplied with five voltage- or ligand-gated ion channels (plus leakage), which were distributed in accordance with those found in a recent study that employed an equivalent dendritic cylinder. A wide variety of impulse-entrainment responses was observed, including regular low-frequency firing, impulse doublets, and more complex patterns involving impulse propagation failures (or aborted spikes) within the encoder region, all of which have been observed experimentally. The impulse-frequency response curves of the cells fell into three groups called FAST, MEDIUM, and SLOW in approximate proportion as seen experimentally. In addition to these, a new group was found among the traced cells that exhibited an impulse-frequency response twice that of the FAST category. The total amount of soma-dendritic surface area exhibited by a given cell is decisive in determining its electrophysiological classification. On the other hand, we found only a weak correlation between the electrophysiological group and the morphological classification of a given cell, which is based on the complexity of dendritic branching and the physical reach or "receptive field" area of the cell. Dendritic morphology determines discharge patterns to dendritic (synaptic) stimulation. Orthodromic impulses can be initiated on the axon hillock, the thin axonal segment, the soma, or even the proximal axon beyond the thin segment, depending on stimulus magnitude, soma-dendritic membrane area, channel distribution, and state within the repetitive impulse cycle. Although a sufficiently high dendritic Na-channel density can lead to dendritic impulse initiation, this does not occur with our "standard" channel densities and is not seen experimentally. Even so, impulses initiated elsewhere do invade all except very thin dendritic processes. Impulse-encoding irregularities increase when channel conductances are reduced in the encoder region, and the F/I properties of the cells are a strong function of the calcium- and Ca-activated K-channel densities. Use of equivalent dendritic cylinders requires more soma-dendritic surface area than real dendritic trees, and the source of the discrepancy is discussed.