Mechanisms by which cell geometry controls repetitive impulse firing in retinal ganglion cells

Dendritic impulse collisions and shifting sites of action potential initiation contract and extend the receptive field of an amacrine cell

We evaluated the contributions of somatic and dendritic impulses to the receptive field dimensions of amacrine cells in the amphibian retina. For this analysis, we used the NEURON simulation program with a multicompartmental, multichannel model of an On-Off amacrine cell with a three-dimensional structure obtained through computer tracing techniques. Simulated synaptic inputs were evenly spaced along the dendritic branches and organized into eight annuli of increasing radius. The first set of simulations activated each ring progressively to simulate an area summation experiment, while a second approach activated each annulus individually. Both sets of simulations were done with and without the presence of Na channels in the dendrites and soma. Unexpectedly, the receptive field dimensions observed in the area summation simulations was often smaller than that predicted from the summation of the annular simulations. Collisions of action potentials moving in opposite directions in the dendrites largely accounted for this contraction in receptive field size for the area summation studies. The presence of dendritic Na channels increased the size of the receptive field beyond that achieved in their absence and allowed the physiological size of the receptive field to approximate the physical dimensions of the dendritic tree. This receptive field augmentation was the result of impulse generating ability in the dendrites which enhanced the signal observed at the soma. These simulations provide a plausible mechanistic explanation for physiological recordings from amacrine cells that show similar phenomena.

Narrow and wide field amacrine cells fire action potentials in response to depolarization and light stimulation

Action potentials in amacrine cells are important for lateral propagation of signals across the inner retina, but it is unclear how many subclasses of amacrine cells contain voltage-gated sodium channels or can fire action potentials. This study investigated the ability of amacrine cells with narrow (< 200 μm) and wide (> 200 μm) dendritic fields to fire action potentials in response to depolarizing current injections and light stimulation. The pattern of action potentials evoked by current injections revealed two distinct classes of amacrine cells; those that responded with a single action potential (single-spiking cells) and those that responded with repetitive action potentials (repetitive-spiking cells). Repetitive-spiking cells differed from single-spiking cells in several regards: Repetitive-spiking cells were more often wide field cells, while single-spiking cells were more often narrow field cells. Repetitive-spiking cells had larger action potential amplitudes, larger peak voltage-gated NaV currents lower action potential thresholds, and needed less current to induce action potentials. However, there was no difference in the input resistance, holding current or time constant of these two classes of cells. The intrinsic capacity to fire action potentials was mirrored in responses to light stimulation; single-spiking amacrine cells infrequently fired action potentials to light steps, while repetitive-spiking amacrine cells frequently fired numerous action potentials. These results indicate that there are two physiologically distinct classes of amacrine cells based on the intrinsic capacity to fire action potentials.

Action Potential Initiation and Propagation in CA3 Pyramidal Axons

Thin, unmyelinated axons densely populate the mammalian hippocampus and cortex. However, the location and dynamics of spike initiation in thin axons remain unclear. We investigated basic properties of spike initiation and propagation in CA3 neurons of juvenile rat hippocampus. Sodium channel alpha subunit distribution and local applications of tetrodotoxin demonstrate that the site of first threshold crossing in CA3 neurons is ∼35 μm distal to the soma, somewhat more proximal than our previous estimates. This discrepancy can be explained by the finding, obtained with simultaneous whole cell somatic and extracellular axonal recordings, that a zone of axon stretching to ∼100 μm distal to the soma reaches a maximum rate of depolarization nearly synchronously by the influx of sodium from the high-density channels. Models of the proximal axon incorporating observed distributions of sodium channel staining recapitulated salient features of somatic and axonal spike waveforms, including the predicted initiation zone, characteristic spike latencies, and conduction velocity. The preferred initiation zone was unaltered by stimulus strength or repetitive spiking, but repetitive spiking increased threshold and significantly slowed initial segment recruitment time and conduction velocity. Our work defines the dynamics of initiation and propagation in hippocampal principal cell axons and may help reconcile recent controversies over initiation site in other axons.

Normal and rebound impulse firing in retinal ganglion cells

Given that the action potential output of retinal ganglion cells (RGCs) determines the nature of the visual information that is transmitted from the retina, an understanding of their intrinsic impulse firing characteristics is critical for an appreciation of the overall processing of visual information. Recordings from RGCs within an isolated whole-mount retina preparation showed that their normal impulse firing from the resting membrane potential (RMP) was linearly correlated in its frequency with the stimulus intensity. In addition to describing the relationship between the magnitude of the current injection and the resulting impulse frequency (F/I relationship), we have characterized the properties of individual action potentials when they are elicited from the RMP. In contrast, hyperpolarizing below the RMP revealed that RGCs displayed a time dependent anomalous rectification, manifested by the appearance of a depolarizing sag in their voltage response. When an adequate period of hyperpolarization was terminated, a fast phasic period of “rebound excitation” was observed, characterized by a brief phasic burst of impulse activity. When compared to equivalent action potential firing evoked by depolarizing from the RMP, rebound spiking was associated with a lower threshold and shorter latency for impulse activation as well as a prominent, phasic, burst-like doublet, or triplet of impulses. The rebound action potential had a more positive voltage overshoot and displayed a higher peak rate of rise in its upstroke than those correspondingly generated by depolarizing current pulses from the RMP. Blocking sodium spikes with TTX confirmed that the preceding hyperpolarization led to the recruitment and subsequent generation of a transient depolarizing voltage overshoot, which we have termed the net depolarizing overshoot (NDO). We propose that the NDO boosts the generation of sodium spikes by triggering rebound spikes on its upstroke and crest, thus accounting for the observed voltage dependent change in the firing pattern of RGCs.

Low-voltage activated calcium currents in ganglion cells of the tiger salamander retina: Experiment and simulation

We examined the functional properties of a low-voltage-activated (LVA) calcium current in ganglion cells of the neotenous tiger salamander (Ambystoma tigrinum) retina. Our analysis was based on whole-cell recordings from acutely dissociated ganglion cell bodies identified by retrograde dye injections. Using a continuously perfused cell preparation, the LVA current was isolated with the use of potassium channel blocking agents added to the bathing medium and the pipette solution, while tetrodotoxin was added to the bathing medium to block Na+channels. Approximately 70% of ganglion cells had an easily identified LVA current. The LVA current activated at membrane potentials more positive than −90 mV, and inactivated rapidly. It was relatively insensitive to nickel (IC50 > 500 μM) and amiloride (IC50 > 750 μM). Voltage- and current-clamp studies allowed us to generate a model of this current using the NEURON simulation program. Studies were also carried out to measure the LVA Ca2+current in ganglion cells with dendrites to confirm that it had a significant dendritic representation. Physiological mechanisms that may depend on LVA Ca2+currents are discussed with an emphasis on the role that dendrites play in ganglion cell function.

Form and Function of on-off Amacrine Cells in the Amphibian Retina

on-off amacrine cells were studied with whole cell recording techniques and intracellular staining methods using intact retina-eyecup preparations of the tiger salamander ( Ambystoma tigrinum) and the mudpuppy ( Necturus maculosus). Morphological characterization of these cells included three-dimensional reconstruction methods based on serial optical sections obtained with a confocal microscope. Some cells had their detailed morphology digitized with a computer-assisted tracing system and converted to compartmental models for computer simulations. The dendrites of on-off amacrine cells have spines and numerous varicosities. Physiological recordings confirmed that on-off amacrine cells generate both large- and small-amplitude impulses attributed, respectively, to somatic and dendritic generation sites. Using a multichannel model for impulse generation, computer simulations were carried out to evaluate how impulses are likely to propagate throughout these structures. We conclude that the on-off amacrine cell is organized with multifocal dendritic impulse generating sites and that both dendritic and somatic impulse activity contribute to the functional repertoire of these interneurons: locally generated dendritic impulses can provide regional activation, while somatic impulse activity results in rapid activation of the entire dendritic tree.

Voltage-gated sodium channels improve contrast sensitivity of a retinal ganglion cell

Voltage-gated channels in a retinal ganglion cell are necessary for spike generation. However, they also add noise to the graded potential and spike train of the ganglion cell, which may degrade its contrast sensitivity, and they may also amplify the graded potential signal. We studied the effect of blocking Na+ channels in a ganglion cell on its signal and noise amplitudes and its contrast sensitivity. A spot was flashed at 1-4 Hz over the receptive field center of a brisk transient ganglion cell in an intact mammalian retina maintained in vitro. We measured signal and noise amplitudes from its intracellularly recorded graded potential light response and measured its contrast detection thresholds with an "ideal observer." When Na+ channels in the ganglion cell were blocked with intracellular lidocaine N-ethyl bromide (QX-314), the signal-to-noise ratio (SNR) decreased (p < 0.05) at all tested contrasts (2-100%). Likewise, bath application of tetrodotoxin (TTX) reduced the SNR and contrast sensitivity but only at lower contrasts (< or = 50%), whereas at higher contrasts, it increased the SNR and sensitivity. The opposite effect of TTX at high contrasts suggested involvement of an inhibitory surround mechanism in the inner retina. To test this hypothesis, we blocked glycinergic and GABAergic inputs with strychnine and picrotoxin and found that TTX in this case had the same effect as QX-314: a reduction in the SNR at all contrasts. Noise analysis suggested that blocking Na+ channels with QX-314 or TTX attenuates the amplitude of quantal synaptic voltages. These results demonstrate that Na+ channels in a ganglion cell amplify the synaptic voltage, enhancing the SNR and contrast sensitivity.

Electrical stimulation of mammalian retinal ganglion cells with multielectrode arrays

Existing epiretinal implants for the blind are designed to electrically stimulate large groups of surviving retinal neurons using a small number of electrodes with diameters of several hundred micrometers. To increase the spatial resolution of artificial sight, electrodes much smaller than those currently in use are desirable. In this study, we stimulated and recorded ganglion cells in isolated pieces of rat, guinea pig, and monkey retina. We used microfabricated hexagonal arrays of 61 platinum disk electrodes with diameters between 6 and 25 microm, spaced 60 microm apart. Charge-balanced current pulses evoked one or two spikes at latencies as short as 0.2 ms, and typically only one or a few recorded ganglion cells were stimulated. Application of several synaptic blockers did not abolish the evoked responses, implying direct activation of ganglion cells. Threshold charge densities were typically <0.1 mC/cm2 for a pulse duration of 100 micros, corresponding to charge thresholds of <100 pC. Stimulation remained effective after several hours and at high frequencies. To show that closely spaced electrodes can elicit independent ganglion cell responses, we used the multielectrode array to stimulate several nearby ganglion cells simultaneously. From these data, we conclude that electrical stimulation of mammalian retina with small-diameter electrode arrays is achievable and can provide high temporal and spatial precision at low charge densities. We review previous epiretinal stimulation studies and discuss our results in the context of 32 other publications, comparing threshold parameters and safety limits.

Polarized distribution of ion channels within microdomains of the axon initial segment

Voltage-gated sodium (Na(v)) channels accumulate at the axon initial segment (IS), where their high density supports spike initiation. Maintenance of this high density of Na(v) channels involves a macromolecular complex that includes the cytoskeletal linker protein ankyrin-G, the only protein known to bind Na(v) channels and localize them at the IS. We found previously that Na(v)1.6 is the predominant Na(v) channel isoform at IS of adult rodent retinal ganglion cells. However, here we report that Na(v)1.6 immunostaining is consistently reduced or absent in short regions of the IS proximal to the soma, although both ankyrin-G and pan-Na(v) antibodies stain this region. We show that this proximal IS subregion is a unique axonal microdomain, containing an accumulation of Na(v)1.1 channels that are spatially segregated from the Na(v)1.6 channels of the distal IS. Additionally, we find that axonal K(v)1.2 potassium channels are present within the distal IS, but are also excluded from the Na(v)1.1-enriched proximal IS microdomain. Because ankyrin-G was prominent in both proximal and distal subcompartments of the IS, where it colocalized with either Na(v)1.1 or Na(v)1.6, respectively, mechanisms other than association with ankyrin-G must mediate differential targeting of Na(v) channel subtypes to achieve the spatial precision observed within the IS. This precise arrangement of ion channels within the axon initial segment is likely an important determinant of the firing properties of ganglion cells and other mammalian neurons.

Direction-selective dendritic action potentials in rabbit retina

Dendritic spikes that propagate toward the soma are well documented, but their physiological role remains uncertain. Our in vitro patch-clamp recordings and two-photon calcium imaging show that direction-selective retinal ganglion cells (DSGCs) utilize orthograde dendritic spikes during physiological activity. DSGCs signal the direction of image motion. Excitatory subthreshold postsynaptic potentials are observed in DSGCs for motion in all directions and provide a weakly tuned directional signal. However, spikes are generated over only a narrow range of motion angles, indicating that spike generation greatly enhances directional tuning. Our results indicate that spikes are initiated at multiple sites within the dendritic arbors of DSGCs and that each dendritic spike initiates a somatic spike. We propose that dendritic spike failure, produced by local inhibitory inputs, might be a critical factor that enhances directional tuning of somatic spikes.

Rallian "equivalent" cylinders reconsidered: comparisons with literal compartments

In Rall's "equivalent" cylinder morphological-to-electrical transformation, neuronal arborizations are reduced to single unbranched core-conductors. The conventional assumption that such an "equivalent" reconstructs the electrical properties of the fibers it represents was tested directly; electrical properties and responses of "equivalent" cylinders were compared with those of their literal branch constituents for fibers with a single symmetrical bifurcation. The numerical solution methods were validated independently by their accurate reconstruction of the responses of an analog circuit configured with compartmental architecture to solve the cable equation for passive fibers with a symmetrical bifurcation. In passive fibers, "equivalent" cylinders misestimated the spatial distribution of voltage amplitudes and steady-state input resistance, partly due to the lack of axial current bifurcation. In active fibers with a single propagating action potential, the spatial distributions of point-to-point conduction velocity values (measured in meters/second) for a literal branch point differed significantly from those of their "equivalent" cylinders. "Equivalent" cylinders also underestimated the diameter-dependent delay in propagation through the branch point and branches, due to the larger "equivalent" diameter. Corrections to the "equivalent" cylinder did not reconcile differences between "equivalent" and literal models. However, "equivalent" and literal branch fibers had the same (a) steady-state resistance "looking into" an isolated symmetrical branch point and (b) geometry-independent point-to-point propagation velocity when measured in space constants per millisecond except within +/-1 space constant from the geometrical inhomogeneity. In summary, Rall's "equivalent" cylinders did not accurately reconstruct all passive or active electrophysiological properties and responses of their literal compartments. For the modeling of individual neurons, the requirement of single-branch resolution is discussed.

A computational model of the ribbon synapse

A model of the ribbon synapse was developed to replicate both pre- and postsynaptic functions of this glutamatergic juncture. The presynaptic portion of the model is rich in anatomical and physiological detail and includes multiple release sites for each ribbon based on anatomical studies of presynaptic terminals, presynaptic voltage at the terminal, the activation of voltage-gated calcium channels and a calcium-dependent release mechanism whose rate varies as a function of the calcium concentration that is monitored at two different sites which control both an ultrafast, docked pool of vesicles and a release ready pool of tethered vesicles. The postsynaptic portion of the program models diffusion of glutamate and the physiological properties of glutamatergic neurotransmission in target cells. We demonstrate the behavior of the model using the retinal bipolar cell to ganglion cell ribbon synapse. The model was constrained by the anatomy of salamander bipolar terminals based on the ultrastructure of these synapses and presynaptic contacts were placed onto realistic ganglion cell morphology activated by a range of ribbon synapses (46-138). These inputs could excite the cell in a manner consistent with physiological observations. This model is a comprehensive, first-generation attempt to assemble our present understanding of the ribbon synapse into a domain that permits testing our understanding of this important structure. We believe that with minor modifications of this model, it can be fine tuned for other ribbon synapses.

Neurons with radial basis like rate functions

Artificial neural networks constructed with "locally tuned processing units" and more generally referred to as "radial basis function networks" have been proposed by a number of workers. In this communication, I submit a conjecture, based on indirect experimental and direct computational evidence of the Hodgkin-Huxley model, that there may be biological neurons in nervous systems for which the rate function is locally tuned. If proved to be valid, this conjecture may simplify neurodynamic models of some functions of nervous systems.

Estimating action potential thresholds from neuronal time-series: new metrics and evaluation of methodologies

The estimation of action potential thresholds is a subjective process, which we quantified by surveying experienced electrophysiologists via a software application that allowed them to select action potential thresholds from several presented neuronal time series. Independent of this survey, we derived two nonparametric techniques for automating the detection of an action potential threshold from the time-series of intracellular recordings. Both methods start with a phase-space representation of the action potential (dV/dt versus V). Method I detects the maximum slope in the phase space, while Method II detects the maximum second derivative in the phase space. These two methods, as well as five additional methods in the literature, were tested on three data sets representing a variety of action potential shapes, the same three datasets that were used in the electrophysiologist survey. The database of user responses was used to provide an external benchmark against which to statistically evaluate all seven methods. Method II, as well as the curvature-based Methods VI and VII, provided the best results tracking both absolute and relative changes in threshold versus the other nonparametric methods (peak of second and third time derivatives). The one parametric method evaluated, detection of threshold crossing of the first temporal derivative, performed comparably to these methods, provided that an appropriate threshold was chosen. We conclude that Methods II, VI, and VII were the best methods evaluated due to their performance across a wide range of action potential shapes and the fact that they are nonparametric. Our user database of responses may be useful to other investigators interested in developing additional methods in that it quantifies what has often been a subjective estimate.

Effective Electrode Configuration for Selective Stimulation With Inner Eye Prostheses

The quality of visual perception with retinal prostheses strongly depends on the local selectivity. Electrode arrays at the surface of the retina should excite exclusively cells within a local area but they are expected to co-stimulate bypassing axons originating from ganglion cells of the outer regions. Long electrodes parallel to these axons are shown to be good candidates for avoiding the co-stimulation phenomenon. Efficiency of focal excitation depends on the length and resistance of the electrodes.

Asymmetric temporal properties in the receptive field of retinal transient amacrine cells

The speed of signal conduction is a factor determining the temporal properties of individual neurons and neuronal networks. We observed very different conduction velocities within the receptive field of fast-type On-Off transient amacrine cells in carp retina cells, which are tightly coupled to each other via gap junctions. The fastest speeds were found in the dorsal area of the receptive fields, on average five times faster than those detected within the ventral area. The asymmetry was similar in the On- and Off-part of the responses, thus being independent of the pathway, pointing to the existence of a functional mechanism within the recorded cells themselves. Nonetheless, the spatial decay of the graded-voltage photoresponse within the receptive field was found to be symmetrical, with the amplitude center of the receptive field being displaced to the faster side from the minimum-latency location. A sample of the orientation of varicosity-laden polyaxons in neurobiotin-injected cells supported the model, revealing that approximately 75% of these processes were directed dorsally from the origin cells. Based on these results, we modeled the velocity asymmetry and the displacement of amplitude center by adding a contribution of an asymmetric polyaxonal inhibition to the network. Due to the asymmetry in the conduction velocity, the time delay of a light response is proposed to depend on the origin of the photostimulus movement, a potentially important mechanism underlying direction selectivity within the inner retina.

Effects of noise on the spike timing precision of retinal ganglion cells

Information in a spike train is limited by variability in the spike timing. This variability is caused by noise from several sources including synapses and membrane channels; but how deleterious each noise source is and how they affect spike train coding is unknown. Combining physiology and a multicompartment model, we studied the effect of synaptic input noise and voltage-gated channel noise on spike train reliability for a mammalian ganglion cell. For tonic stimuli, the SD of the interspike intervals increased supralinearly with increasing interspike interval. When the cell was driven by current injection, voltage-gated channel noise and background synaptic noise caused fluctuations in the interspike interval of comparable amplitude. Spikes initiated on the dendrites could cause additional spike timing fluctuations. For transient stimuli, synaptic noise was dominant and spontaneous background activity strongly increased fluctuations in spike timing but decreased the latency of the first spike.

Functional specialization of the axon initial segment by isoform-specific sodium channel targeting

Voltage-dependent sodium channels cluster at high density at axon initial segments, where propagating action potentials are thought to arise, and at nodes of Ranvier. Here, we show that the sodium channel Na(v)1.6 is precisely localized at initial segments of retinal ganglion cells (RGCs), whereas a different isoform, Na(v)1.2, is found in the neighboring unmyelinated axon. During development, initial segments first expressed Na(v)1.2, and Na(v)1.6 appeared later, approximately in parallel with the onset of repetitive RGC firing. In Shiverer mice, Na(v)1.6 localization at the initial segment was unaffected, although Na(v)1.6 expression was severely disrupted in the aberrantly myelinated optic nerve. Targeting or retention of Na(v)1.6 requires molecular interactions that normally occur only at initial segments and nodes of Ranvier. Expression at nodes but not initial segments exhibits an additional requirement for intact myelination. Because of their high density at the initial segment, Na(v)1.6 channels may be crucial in determining neuronal firing properties.

Modeling temporal behavior of postnatal cat retinal ganglion cells

During development, mammalian retinal ganglion cells (RGCs) go through marked ontogenetic changes with respect to their excitable membrane properties. Voltage-clamp studies conducted in our laboratory have shown that the amplitude, voltage-dependence and kinetics of activation and inactivation (where present) of Na(+), K(+) and Ca(2+) conductances all exhibit developmental changes during a time when the firing patterns of mammalian ganglion cells shift from being transient to being predominantly sustained in nature. In order to better understand the contribution of each conductance to the generation of spikes and spiking patterns, we have developed a model based on our experimental data. For simplicity, we have initially used experimental data obtained from postnatal ganglion cells. At this age the ontogenetic changes observed in the characteristics of the various ionic currents are complete. Utilizing the methods adopted by Hodgkin and Huxley for the giant squid axon, we have determined rate equations for the activation and inactivation properties of the I(A), I(K dr), I(Na), I(Ca L), I(Ca N), and I(leak) currents in postnatal cat RGCs. Combining these with a simplified model of the calcium-activated potassium current (I(KCa)), we have solved and analysed the resulting differential equations. While spikes and spiking patterns resembling experimental data could be obtained from a model in which [Ca(2+)i] was averaged across the whole cell, more accurate simulations were obtained when the diffusion of intracellular Ca(2+) was modeled spatially. The resulting spatial calcium gradients were more effective in gating I(KCa), and our simulations more accurately matched the recorded amplitude and shape of individual spikes as well as the frequency of maintained discharges observed in mammalian postnatal RGCs.

Calcium channel immunoreactivity in the salamander retina

This study reports the distribution of the alpha1D and alpha1E calcium channel subunits in the neotenous tiger salamander retina based on immunohistochemical techniques. Confocal and light microscopy were used to localize staining with fluorescently tagged antibodies to alpha1D and alpha1E in cross-sectional and flatmount preparations of retina. Alpha1D-immunoreactivity (alpha1D-IR) was localized to the inner and outer plexiform layers (IPL and OPL, respectively), ganglion cell layer (GCL), and optic fiber layer. Alpha1E-IR was found predominantly in the IPL, with scattered, weak representation in the OPL. Alpha1E-IR was not detected in the GCL or fiber layer. These findings suggest that different alpha1 calcium channel proteins have distinctive distributions in retina, which may reflect their unique and different roles in retinal processing and homeostasis.

Cellular and molecular features of axon collaterals and dendrites

Neural geometry is the major factor that determines connectivity and, possibly, functional output from a nervous system. Recently some of the proteins and pathways involved in specific modes of branch formation or maintenance, or both, have been described. To a variable extent, dendrites and axon collaterals can be viewed as dynamic structures subject to fine modulation that can result either in further growth or retraction. Each form of branching results from specific molecular mechanisms. Cell-internal, substrate-derived factors and functional activity, however, can often differ in their effect according to cell type and physiological context at the site of branch formation. Neural branching is not a linear process but an integrative one that takes place in a microenvironment where we have only a limited experimental access. To attain a coherent mechanism for this phenomenon, quantitative in situ data on the proteins involved and their interactions will be required.

Deactivation, recovery from inactivation, and modulation of extra-synaptic ion currents in fish retinal ganglion cells

As is shown magnificently by Heron Island's reef, the visual environment of many fishes includes various light intensities, hues and shapes that can change on large and small scales in space and time. Several articles in this issue address why fishes are sensitive to some of these properties, and how fishes and other aquatic species have acquired or fostered these sensitivities. This article discusses contributions of extrasynaptic ion currents, in a specific population of neurons, to the detection of ambient light levels, the appearance of certain visual stimuli and the disappearance of others.

A computational model of electrical stimulation of the retinal ganglion cell

Localized retinal electrical stimulation in blind volunteers results in discrete round visual percepts corresponding to the location of the stimulating electrode. The success of such an approach to provide useful vision depends on elucidating the neuronal target of surface electrical stimulation. To determine if electrodes preferentially stimulate ganglion cells directly below them or passing fibers from distant ganglion cells, we developed a compartmental model for electric field stimulation of the retinal ganglion cell (RGC). In this model a RGC is stimulated by extracellular electrical fields with active channels and realistic cell morphology derived directly from a neuronal tracing. Three membrane models were applied: a linear passive model, a Hodgkin-Huxley model with passive dendrites (HH), and a model composed of all active compartments (FCM) with five nonlinear ion channels. Idealized monopolar point and disk stimulating electrodes were positioned above the cell. For the HH and FCM models, the position of lowest cathodal threshold to propagate an action potential was over the soma. Brief (100 microseconds) cathodic stimuli were 20% (HH with disk electrode) to 73% (FCM with point-source) more effective over the soma than over the axon. In the passive model, the axon is preferentially stimulated versus the soma. Although it may be possible to electrically stimulate RGC's near their cell body at lower thresholds than at their axon, these differences are relatively small. Alternative explanations should be sought to explain the focal perceptions observed in previously reported patient trials.

Impulse encoding across the dendritic morphologies of retinal ganglion cells

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.

Impulse encoding mechanisms of ganglion cells in the tiger salamander retina

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.