Passive electrical cable properties and synaptic excitation of tiger salamander retinal ganglion cells

Directional excitatory input to direction-selective ganglion cells in the rabbit retina

Directional responses in retinal ganglion cells are generated in large part by direction-selective release of γ-aminobutyric acid from starburst amacrine cells onto direction-selective ganglion cells (DSGCs). The excitatory inputs to DSGCs are also widely reported to be direction-selective, however, recent evidence suggests that glutamate release from bipolar cells is not directional, and directional excitation seen in patch-clamp analyses may be an artifact resulting from incomplete voltage control. Here, we test this voltage-clamp-artifact hypothesis in recordings from 62 ON-OFF DSGCs in the rabbit retina. The strength of the directional excitatory signal varies considerably across the sample of cells, but is not correlated with the strength of directional inhibition, as required for a voltage-clamp artifact. These results implicate additional mechanisms in generating directional excitatory inputs to DSGCs.

Modelling extracellular electrical stimulation: part 4. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

OBJECTIVE

The objective of this paper is to present a concrete application of the cellular composite model for calculating the membrane potential, described in an accompanying paper.

APPROACH

A composite model that is used to determine the membrane potential for both longitudinal and transverse modes of stimulation is demonstrated.

MAIN RESULTS

Two extreme limits of the model, near-field and far-field for an electrode close to or distant from a neuron, respectively, are derived in this paper. Results for typical neural tissue are compared using the composite, near-field and far-field models as well as the standard isotropic volume conductor model. The self-consistency of the composite model, its spatial profile response and the extracellular potential time behaviour are presented. The magnitudes of the longitudinal and transverse components for different values of electrode-neurite separations are compared.

SIGNIFICANCE

The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Divergence of visual channels in the inner retina

Bipolar cells form parallel channels that carry visual signals from the outer to the inner retina. Each type of bipolar cell is thought to carry a distinct visual message to select types of amacrine cells and ganglion cells. However, the number of ganglion cell types exceeds that of the bipolar cells providing their input, suggesting that bipolar cell signals diversify on transmission to ganglion cells. We explored in the salamander retina how signals from individual bipolar cells feed into multiple ganglion cells and found that each bipolar cell was able to evoke distinct responses among ganglion cells, differing in kinetics, adaptation and rectification properties. This signal divergence resulted primarily from interactions with amacrine cells that allowed each bipolar cell to send distinct signals to its target ganglion cells. Our findings indicate that individual bipolar cell-ganglion cell connections have distinct transfer functions. This expands the number of visual channels in the inner retina and enhances the computational power and feature selectivity of early visual processing.

Retinal parallel processors: more than 100 independent microcircuits operate within a single interneuron

Most neurons are highly polarized cells with branched dendrites that receive and integrate synaptic inputs and extensive axons that deliver action potential output to distant targets. By contrast, amacrine cells, a diverse class of inhibitory interneurons in the inner retina, collect input and distribute output within the same neuritic network. The extent to which most amacrine cells integrate synaptic information and distribute their output is poorly understood. Here, we show that single A17 amacrine cells provide reciprocal feedback inhibition to presynaptic bipolar cells via hundreds of independent microcircuits operating in parallel. The A17 uses specialized morphological features, biophysical properties, and synaptic mechanisms to isolate feedback microcircuits and maximize its capacity to handle many independent processes. This example of a neuron employing distributed parallel processing rather than spatial integration provides insights into how unconventional neuronal morphology and physiology can maximize network function while minimizing wiring cost.

Mechanism underlying rebound excitation in retinal ganglion cells

Retinal ganglion cells (RGCs) display the phenomenon of rebound excitation, which is observed as rebound sodium action potential firing initiated at the termination of a sustained hyperpolarization below the resting membrane potential (RMP). Rebound impulse firing, in contrast to corresponding firing elicited from rest, displayed a lower net voltage threshold, shorter latency and was invariably observed as a phasic burst-like doublet of spikes. The preceding hyperpolarization leads to the recruitment of a Tetrodotoxin-insensitive depolarizing voltage overshoot, termed as the net depolarizing overshoot (NDO). Based on pharmacological sensitivities, we provide evidence that the NDO is composed of two independent but interacting components, including (1) a regenerative low threshold calcium spike (LTCS) and (2) a non-regenerative overshoot (NRO). Using voltage and current clamp recordings, we demonstrate that amphibian RGCs possess the hyperpolarization activated mixed cation channels/current, Ih, and low voltage activated (LVA) calcium channels, which underlie the generation of the NRO and LTCS respectively. At the RMP, the Ih channels are closed and the LVA calcium channels are inactivated. A hyperpolarization of sufficient magnitude and duration activates Ih and removes the inactivation of the LVA calcium channels. On termination of the hyperpolarizing influence, Ih adds an immediate depolarizing influence that boosts the generation of the LTCS. The concerted action of both conductances results in a larger amplitude and shorter latency NDO than either mechanism could achieve on its own. The NDO boosts the generation of conventional sodium spikes which are triggered on its upstroke and crest, thus eliciting rebound excitation.

Developmental plasticity of NMDA receptor function in the retina and the influence of light

Despite the early expression of NMDA receptors (NMDARs) in the retina, not much is known about their regulation and involvement in plasticity processes during retinal development and synapse formation. Here we report that NMDAR function in the inner retina is developmentally regulated and controlled by ambient light condition. A prominent down-regulation after eye opening of NMDAR function was observed in rat retinal ganglion cells (RGCs), which was prevented by dark rearing the animals for 1 month but was again induced by subsequent light exposure. As shown by molecular analysis of single RGCs, alterations in the subunit composition of NMDAR did not account for the light-dependent regulation of NMDAR function. Immunocytochemistry showed no differences in the NMDAR protein expression pattern between normal and dark-reared animals. In conclusion, our data clearly demonstrate that NMDAR function is modulated during periods of retinal plasticity independent of structural alterations in its subunit composition and thus different from mechanisms observed in higher visual centers.

Spike generator limits efficiency of information transfer in a retinal ganglion cell

The quality of the signal a retinal ganglion cell transmits to the brain is important for preception because it sets the minimum detectable stimulus. The ganglion cell converts graded potentials into a spike train with a selective filter but in the process adds noise. To explore how efficiently information is transferred to spikes, we measured contrast detection threshold and increment threshold from graded potential and spike responses of brisk-transient ganglion cells. Intracellular responses to a spot flashed over the receptive field center of the cell were recorded in an intact mammalian retina maintained in vitro at 37 degrees C. Thresholds were measured in a single-interval forced-choice procedure with an ideal observer. The graded potential gave a detection threshold of 1.5% contrast, whereas spikes gave 3.8%. The graded potential also gave increment thresholds approximately twofold lower and carried approximately 60% more gray levels. Increment threshold "dipped" below the detection threshold at a low contrast (<5%) but increased rapidly at higher contrasts. The magnitude of the "dipper" for both graded potential and spikes could be predicted from a threshold nonlinearity in the responses. Depolarization of the cell by current injection reduced the detection threshold for spikes but also reduced the range of contrasts they can transmit. This suggests that contrast sensitivity and dynamic range are related in an essential trade-off.

Developmental maturation of passive electrical properties in retinal ganglion cells of rainbow trout

We investigated the electrotonic and anatomical features of the dendritic arbor in developing retinal ganglion cells (RGCs). Cell anatomy was studied by filling individual cells with fluorescent, membrane-bound dyes and using computer-assisted image reconstruction. Electrotonic properties were characterized through an analysis of charging membrane currents measured with tight-seal electrodes in the whole-cell mode. We studied developing RGCs in the peripheral growth zone (PGZ) of a fish retina. The PGZ presents a developmental time-line ranging from pluripotent, proliferating cells at the extreme edge, to mature, fully developed retina more centrally. In the PGZ, RGCs mature through three histologically distinct zones (in developmental sequence): bulge, transition and mature zones. In the most peripheral three-quarters of the bulge zone, cells have rounded somas, lack dendritic extensions and some are coupled so that membrane-bound dyes traverse from one cell to its immediate neighbours. In the more central quarter of the bulge, cells' dendrites are few, short and of limited branching. In the transition zone dendritic arbors becomes progressively more expansive and branched and we present a morphometric analysis of these changes. Regardless of the size and branching pattern of the developing RGC dendritic arbor, the ratio of the diameters of parent and progeny dendrites at any branching nodes is well described by Rall's 3/2 power law. Given this anatomical feature, the RGC passive electrical properties are well described by an equivalent electrical circuit consisting of an isopotential cell body in parallel with a single equivalent cylinder of finite length. We measured the values of the electrical parameters that define this equivalent circuit in bulge, transition and mature RGCs. As RGCs develop the electrical properties of their dendritic arbor change in an orderly and tightly regulated manner, not randomly. Electrically, dendritic arbors develop along either of two distinct modes, but only these modes: isoelectrotonic and isometric. In isoelectrotonic growth, electrotonic properties are constant regardless of the absolute dimensions of the dendritic arbor or its branching geometry. These cells maintain unvarying relative synaptic efficacy independently of the size or pattern of their dendritic arbor. In isometric growth, in contrast, electronic properties change, but the ratio of the changing electrotonic length to electrotonic diameter is constant. In these cells relative synaptic efficacy decreases linearly as dendrites extend.

Slow Na+ inactivation and variance adaptation in salamander retinal ganglion cells

The retina adapts to the temporal contrast of the light inputs. One component of contrast adaptation is intrinsic to retinal ganglion cells: temporal contrast affects the variance of the synaptic inputs to ganglion cells, which alters the gain of spike generation. Here we show that slow Na+ inactivation is sufficient to produce the observed variance adaptation. Slow inactivation caused the Na+ current available for spike generation to depend on the past history of activity, both action potentials and subthreshold voltage variations. Recovery from slow inactivation required several hundred milliseconds. Increased current variance caused the threshold for spike generation to increase, presumably because of the decrease in available Na+ current. Simulations indicated that slow Na+ inactivation could account for the observed decrease in excitability. This suggests a simple picture of how ganglion cells contribute to contrast adaptation: (1) increasing contrast causes an increase in input current variance that raises the spike rate, and (2) the increased spike rate reduces the available Na+ current through slow inactivation, which feeds back to reduce excitability. Cells throughout the nervous system face similar problems of accommodating a large range of input signals; furthermore, the Na+ currents of many cells exhibit slow inactivation. Thus, adaptation mediated by feedback modulation of the Na+ current through slow inactivation could serve as a general mechanism to control excitability in spiking neurons.

Temporal contrast adaptation in the input and output signals of salamander retinal ganglion cells

We investigated how the light-evoked input and output signals of salamander retinal ganglion cells adapt to changes in temporal contrast, i.e., changes in the depth of the temporal fluctuations in the light intensity about the mean. Increasing the temporal contrast sped the kinetics and reduced the sensitivity of both the light-evoked input currents measured at the ganglion cell soma and the output spike trains of the cell. The decline in sensitivity of the input currents after an increase in contrast had two distinct kinetic components with fast (<2 sec) and slow (>10 sec) time constants. The recovery of sensitivity after a decrease in contrast was dominated by a single component with an intermediate (4-18 sec) time constant. Contrast adaptation differed for on and off cells, with both the kinetics and amplitude of the light-evoked currents of off cells adapting more strongly than those of on cells. Contrast adaptation in the input currents of a ganglion cell, however, was unable to account for the extent of adaptation in the output spike trains of the cell, indicating that mechanisms intrinsic to the ganglion cell contributed. Indeed, when fluctuating currents were injected into a ganglion cell, the sensitivity of spike generation decreased with increased current variance. Pharmacological experiments indicated that adaptation of spike generation to the current variance was attributable to properties of tetrodotoxin-sensitive Na(+) channels.

Developmental switch in excitability, Ca(2+) and K(+) currents of retinal ganglion cells and their dendritic structure

In the retina of teleost fish, continuous neuronal development occurs at the margin, in the peripheral growth zone (PGZ). We prepared tissue slices from the retina of rainbow trout that include the PGZ and that comprise a time line of retinal development, in which cells at progressive stages of differentiation are present side by side. We studied the changes in dendritic structure and voltage-dependent Ca(2+), Na(+), and K(+) currents that occur as ganglion cells mature. The youngest ganglion cells form a distinct bulge. Cells in the bulge have spare and short dendritic trees. Only half express Ca(2+) currents and then only high-voltage-activated currents with slow inactivation (HVAslow). Bulge cells are rarely electrically excitable. They express a mixture of rapidly inactivating and noninactivating K(+) currents (IKA and IKdr). The ganglion cells next organize into a transition zone, consisting of a layered structure two to three nuclei thick, before forming the single layered structure characteristic of the mature retina. In the transition zone, the dendritic arbor is elaborately branched and extends over multiple laminae in the inner plexiform layer, without apparent stratification. The arbor of the mature cells is stratified, and the span of the dendritic arbor is well over five times the cell body's diameter. The electrical properties of cells in the transition and mature zones differ significantly from those in the bulge cells. Correlated with the more elaborate dendritic structures are the expression of both rapidly inactivating HVA (HVAfast) and of low-voltage-activated (LVA) Ca(2+) currents and of a high density of Na(+) currents that renders the cells electrically excitable. The older ganglion cells also express a slowly activating K(+) current (IKsa).

Rate of quantal excitation to a retinal ganglion cell evoked by sensory input

To determine the rate and statistics of light-evoked transmitter release from bipolar synapses, intracellular recordings were made from ON-alpha ganglion cells in the periphery of the intact, superfused, cat retina. Sodium channels were blocked with tetrodotoxin to prevent action potentials. A light bar covering the receptive field center excited the bipolar cells that contact the alpha cell and evoked a transient then a sustained depolarization. The sustained depolarization was quantified as change in mean voltage (Deltav), and the increase in voltage noise that accompanied it was quantified as change in voltage variance (Deltasigma(2)). As light intensity increased, Deltav and Deltasigma(2) both increased, but their ratio held constant. This behavior is consistent with Poisson arrival of transmitter quanta at the ganglion cell. The response component attributable to glutamate quanta from bipolar synapses was isolated by application of 6-cyano-7-nitroquinoxaline (CNQX). As CNQX concentration increased, the signal/noise ratio of this response component (Deltav(CNQX)/Deltasigma(CNQX)) held constant. This is also consistent with Poisson arrival and justified the application of fluctuation analysis. Two different methods of fluctuation analysis applied to Deltav(CNQX) and Deltasigma(CNQX) produced similar results, leading to an estimate that a just-maximal sustained response was caused by approximately 3,700 quanta s(-1). The transient response was caused by a rate that was no more than 10-fold greater. Because the ON-alpha cell at this retinal locus has approximately 2,200 bipolar synapses, one synapse released approximately 1.7 quanta s(-1) for the sustained response and no more than 17 quanta s(-1) for the transient. Consequently, within the ganglion cell's integration interval, here calculated to be approximately 16 ms, a bipolar synapse rarely releases more than one quantum. Thus for just-maximal sustained and transient depolarizations, the conductance modulated by a single bipolar cell synapse is limited to the quantal conductance ( approximately 100 pS at its peak). This helps preserve linear summation of quanta. The Deltav/Deltasigma(2) ratio remained constant even as the ganglion cell's response saturated, which suggested that even at the peak of sensory input, summation remains linear, and that saturation occurs before the bipolar synapse.

Passive normalization of synaptic integration influenced by dendritic architecture

We examined how biophysical properties and neuronal morphology affect the propagation of individual postsynaptic potentials (PSPs) from synaptic inputs to the soma. This analysis is based on evidence that individual synaptic activations do not reduce local driving force significantly in most central neurons, so each synapse acts approximately as a current source. Therefore the spread of PSPs throughout a dendritic tree can be described in terms of transfer impedance (Z(c)), which reflects how a current applied at one location affects membrane potential at other locations. We addressed this topic through four lines of study and uncovered new implications of neuronal morphology for synaptic integration. First, Z(c) was considered in terms of two-port theory and contrasted with dendrosomatic voltage transfer. Second, equivalent cylinder models were used to compare the spatial profiles of Z(c) and dendrosomatic voltage transfer. These simulations showed that Z(c) is less affected by dendritic location than voltage transfer is. Third, compartmental models based on morphological reconstructions of five different neuron types were used to calculate Z(c), input impedance (Z(N)), and voltage transfer throughout the dendritic tree. For all neurons, there was no significant variation of Z(c) with location within higher-order dendrites. Furthermore, Z(c) was relatively independent of synaptic location throughout the entire cell in three of the five neuron types (CA3 interneurons, CA3 pyramidal neurons, and dentate granule cells). This was quite unlike Z(N), which increased with distance from the soma and was responsible for a parallel decrease of voltage transfer. Fourth, simulations of fast excitatory PSPs (EPSPs) were consistent with the analysis of Z(c); peak EPSP amplitude varied <20% in the same three neuron types, a phenomenon that we call "passive synaptic normalization" to underscore the fact that it does not require active currents. We conclude that the presence of a long primary dendrite, as in CA1 or neocortical pyramidal cells, favors substantial location-dependent variability of somatic PSP amplitude. In neurons that lack long primary dendrites, however, PSP amplitude at the soma will be much less dependent on synaptic location.

Characterization of spontaneous excitatory synaptic currents in newt retinal bipolar cells

The kinetics of glutamate concentration in the synaptic cleft is an important determinant of synaptic function. To elucidate peak concentration of glutamate released from a single vesicle in the cleft, spontaneous excitatory postsynaptic currents (sEPSCs) in Off-bipolar cells from the sliced newt retina were analyzed using whole-cell patch clamp recording and the computer simulation. The sEPSCs were blocked by an AMPA/kainate (KA) antagonist, 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), and prolonged by cyclothiazide. However, an N-methyl-D-aspartate (NMDA) antagonist, D-2-amino-5-phosphonopentanoic acid (D-AP5), was ineffective. These suggest that sEPSCs in Off-bipolar cells are mediated exclusively by AMPA/KA receptors. sEPSCs simulated by a detailed kinetic model of AMPA receptor best approximated the data, when peak glutamate concentration was 10 microM. Therefore, it was concluded that peak concentration of glutamate released from a single vesicle would be elevated to approximately 10 microM at the newt Off-bipolar dendrite.

Mechanisms of concerted firing among retinal ganglion cells

Nearby retinal ganglion cells often fire action potentials in near synchrony. We have investigated the circuit mechanisms that underlie these correlations by recording simultaneously from many ganglion cells in the salamander retina. During spontaneous activity in darkness, three types of correlations were distinguished: broad (firing synchrony within 40-100 ms), medium (10-50 ms), and narrow (<1 ms). When chemical synaptic transmission was blocked, the broad correlations disappeared, but the medium and narrow correlations persisted. Further analysis of the strength and time course of synchronous firing suggests that nearby ganglion cells share inputs from photoreceptors conveyed through interneurons via chemical synapses (broad correlations), share excitation from amacrine cells via electrical junctions (medium), and excite each other via electrical junctions (narrow). It appears that the firing patterns in the optic nerve are strongly shaped by electrical coupling in the inner retina.

Estimating the contributions of NMDA and non-NMDA currents to EPSPs in retinal ganglion cells

Whole-cell recordings were obtained from retinal ganglion cells of the tiger salamander (Ambystoma tigrinum) in a superfused slice preparation to evaluate contributions of NMDA (N-methyl-D-aspartate) and KA/AMPA (kainate/alpha-amino-3-hydroxy-5-methyl-4-isoxalone propionic acid) receptors to excitatory postsynaptic potentials (EPSPs) of retinal ganglion cells. Synaptic activation of retinal ganglion cells was achieved through the use of a brief pressure pulse of hyperosmotic Ringer (Ringer + sucrose) delivered through a microelectrode visually placed in the inner plexiform layer while whole-cell recordings were obtained from adjacent cells in the ganglion cell layer. Separation of NMDA and KA/AMPA excitatory postsynaptic currents (EPSCs) was achieved through the application of the antagonists NBQX and D-AP7, while inhibitory currents were blocked by strychnine and picrotoxin. Simple addition of the two independent EPSCs showed, most often, that the sum of the KA/AMPA and NMDA currents was less than the control response, but in some cases the sum of the two currents exceeded the magnitude of the control response. Neither result was consistent with expectations based on voltage-clamp principles and the assumption that the two currents were independent; for this reason, we considered the possibility of nonlinear interactions between KA/AMPA and NMDA receptors. Computer simulations were carried out to evaluate the summation experiments. We used both an equivalent cylinder model and a more realistic, compartmental model of a ganglion cell constrained by a passive leakage conductance, a linear KA/AMPA synaptic current, and a nonlinear NMDA current based on the well-known, voltage-sensitive Mg2+ block. Computer simulation studies suggest that the hypo- and hyper-summation of NMDA and KA/AMPA currents, observed physiologically, can be accounted for by a failure to adequately space clamp the neuron. Clamp failure leads to enhanced NMDA currents as the ion channels are relieved of the Mg2+ block; their contribution is thus exaggerated depending on the magnitude of the conductance change and the spatial location of the synaptic input.