Impulse encoding across the dendritic morphologies of retinal ganglion cells

Modeling extracellular stimulation of retinal ganglion cells: theoretical and practical aspects

Objective.Retinal prostheses use electric current to activate inner retinal neurons, providing artificial vision for blind people. Epiretinal stimulation primarily targets retinal ganglion cells (RGCs), which can be modeled with cable equations. Computational models provide a tool to investigate the mechanisms of retinal activation, and improve stimulation paradigms. However, documentation of RGC model structure and parameters is limited, and model implementation can influence model predictions.Approach.We created a functional guide for building a mammalian RGC multi-compartment cable model and applying extracellular stimuli. Next, we investigated how the neuron's three-dimensional shape will influence model predictions. Finally, we tested several strategies to maximize computational efficiency.Main results.We conducted sensitivity analyses to examine how dendrite representation, axon trajectory, and axon diameter influence membrane dynamics and corresponding activation thresholds. We optimized the spatial and temporal discretization of our multi-compartment cable model. We also implemented several simplified threshold prediction theories based on activating function, but these did not match the prediction accuracy achieved by the cable equations.Significance.Through this work, we provide practical guidance for modeling the extracellular stimulation of RGCs to produce reliable and meaningful predictions. Robust computational models lay the groundwork for improving the performance of retinal prostheses.

A varying-radius cable equation for the modelling of impulse propagation in excitable fibres

In this study, we present a varying-radius cable equation for nerve fibres taking into account the varying diameter along the neuronal segments. Finite element neuronal models utilising the classical (fixed-radius) and varying-radius cable formulations were compared using simple and realistic morphologies under intra- and extracellular electrical stimulation protocols. We found that the use of the classical cable equation to model intracellular neural electrical stimulation exhibited an error of 17% in a passive resistive cable model with abrupt change in radius from 1 to 2 μm, when compared to the known analytical solution and varying-radius cable formulation. This error was observed to increase substantially using more realistic neuron morphologies and branching structures. In the case of extracellular stimulation however, the difference between the classical and varying-radius formulations was less pronounced, but we expect this difference will increase under more complex stimulation paradigms such as high-frequency stimulation. We conclude that for computational neuroscience applications, it is essential to use the varying-radius cable equation for accurate prediction of neuronal responses under electrical stimulation.

Morphological Factors that Underlie Neural Sensitivity to Stimulation in the Retina

Retinal prostheses are a promising therapeutic intervention for patients afflicted by outer retinal degenerative diseases like retinitis pigmentosa and age-related macular degeneration. While significant advances in the development of retinal implants have been made, the quality of vision elicited by these devices remains largely sub-optimal. The variability in the responses produced by retinal devices is most likely due to the differences between the natural cell type-specific signaling that occur in the healthy retina vs. the non-specific activation of multiple cell types arising from artificial stimulation. In order to replicate these natural signaling patterns, stimulation strategies must be capable of preferentially activating specific RGC types. To design more selective stimulation strategies, a better understanding of the morphological factors that underlie the sensitivity to prosthetic stimulation must be developed. This review will focus on the role that different anatomical components play in driving the direct activation of RGCs by extracellular stimulation. Briefly, it will (1) characterize the variability in morphological properties of α-RGCs, (2) detail the influence of morphology on the direct activation of RGCs by electric stimulation, and (3) describe some of the potential biophysical mechanisms that could explain differences in activation thresholds and electrically evoked responses between RGC types.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na⁺ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na⁺ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

Biophysical basis of the linear electrical receptive fields of retinal ganglion cells

Responses of retinal ganglion cells to direct electrical stimulation have been shown experimentally to be well described by linear-nonlinear models. These models rely on the simplifying assumption that retinal ganglion cell responses to stimulation with an array of electrodes are driven by a simple linear weighted sum of stimulus current amplitudes from each electrode, known as the 'electrical receptive field'.

OBJECTIVE

This paper aims to demonstrate the biophysical basis of the linear-nonlinear model and the electrical receptive field to facilitate the development of improved stimulation strategies for retinal implants.

APPROACH

We compare the linear-nonlinear model of subretinal electrical stimulation with a multi-layered, biophysical, volume conductor model of retinal stimulation.

MAIN RESULTS

Our results show that the linear electrical receptive field of the linear-nonlinear model matches the transmembrane currents induced by electrodes (the activating function) at the site of the high-density sodium channel band with only minor discrepancies. The discrepancies are mostly eliminated by including axial current flow originating from adjacent cell compartments. Furthermore, for cells where a single linear electrical receptive field is insufficient, we show that cell responses are likely driven by multiple sites of action potential initiation with multiple distinct receptive fields, each of which can be accurately described by the activating function.

SIGNIFICANCE

This result establishes that the biophysical basis of the electrical receptive field of the linear-nonlinear model is the superposition of transmembrane currents induced by different electrodes at and near the site of action potential initiation. Together with existing experimental support for linear-nonlinear models of electrical stimulation, this provides a firm basis for using this much simplified model to generate more optimal stimulation patterns for retinal implants.

Impact of Electrode Position on the Elicitation of Sodium Spikes in Retinal Bipolar Cells

Bipolar cells of the magnocellular pathway in the primate retina can generate action potentials because they have an axonal segment with high sodium channel density, comparable to the sodium channel band in retinal ganglion cells or pyramidal cells. The similarity between the non-human primate and the human retina is of interest for the research on retinal implants for the blind, and especially, the conditions to elicit sodium spikes in bipolar cells using extracellular stimulation. A comparison of excitation characteristics of three model neurons, a bipolar cell, a retinal ganglion cell, and a cortical pyramidal cell, demonstrates the similarities and differences regarding stimulation with microelectrodes. Moving a microelectrode parallel to the axon of a neuron commonly allows to generate spikes for every position - and this rule holds both for cathodic and anodic pulses. However, for the simulated bipolar cell anodic pulses cannot generate sodium spikes directly. Further, there is only a small region for electrode placing where extracellular cathodic stimulation causes direct spike initiation in the sodium channel band. For all other positions, a sodium spike can only be generated by antidromic current flow originating from strongly depolarized terminals.

Virtual electrode design for increasing spatial resolution in retinal prosthesis

Retinal prostheses systems are currently used to restore partial vision to patients blinded by degenerative diseases by electrically stimulating surviving retinal cells. To obtain likely maximum resolution, electrode size is minimised, allowing for a large quantity on an array and localised stimulation regions. Besides the small size leading to fabrication difficulties and higher electrochemical charge density, there are challenges associated with the number of drivers needed for a large electrode count as well as the strategies to deliver sufficient power to these drivers wirelessly. In hopes to increase electrode resolution while avoiding these issues, the authors propose a new 'virtual electrode' design to increase locations of likely stimulation. Passive metallisation strategically placed between disk electrodes, combined with alternating surrounding stimuli, channel current into a location between electrodes, producing a virtual stimulation site. A computational study was conducted to optimise the passive metal element geometry, quantify the expected current density output, and simulate retinal ganglion cell activity due to virtual electrode stimulation. Results show that this procedure leads to array geometry that focuses injected current and achieves retinal ganglion cell stimulation in a region beneath the 'virtual electrode,' creating an alternate stimulation site without additional drivers.

A general homeostatic principle following lesion induced dendritic remodeling

INTRODUCTION

Neuronal death and subsequent denervation of target areas are hallmarks of many neurological disorders. Denervated neurons lose part of their dendritic tree, and are considered "atrophic", i.e. pathologically altered and damaged. The functional consequences of this phenomenon are poorly understood.

RESULTS

Using computational modelling of 3D-reconstructed granule cells we show that denervation-induced dendritic atrophy also subserves homeostatic functions: By shortening their dendritic tree, granule cells compensate for the loss of inputs by a precise adjustment of excitability. As a consequence, surviving afferents are able to activate the cells, thereby allowing information to flow again through the denervated area. In addition, action potentials backpropagating from the soma to the synapses are enhanced specifically in reorganized portions of the dendritic arbor, resulting in their increased synaptic plasticity. These two observations generalize to any given dendritic tree undergoing structural changes.

CONCLUSIONS

Structural homeostatic plasticity, i.e. homeostatic dendritic remodeling, is operating in long-term denervated neurons to achieve functional homeostasis.

Electrical activity of ON and OFF retinal ganglion cells: a modelling study

OBJECTIVE

Retinal ganglion cells (RGCs) demonstrate a large range of variation in their ionic channel properties and morphologies. Cell-specific properties are responsible for the unique way RGCs process synaptic inputs, as well as artificial electrical signals such as that from a visual prosthesis. A cell-specific computational modelling approach allows us to examine the functional significance of regional membrane channel expression and cell morphology.

APPROACH

In this study, an existing RGC ionic model was extended by including a hyperpolarization activated non-selective cationic current as well as a T-type calcium current identified in recent experimental findings. Biophysically-defined model parameters were simultaneously optimized against multiple experimental recordings from ON and OFF RGCs.

MAIN RESULTS

With well-defined cell-specific model parameters and the incorporation of detailed cell morphologies, these models were able to closely reconstruct and predict ON and OFF RGC response properties recorded experimentally.

SIGNIFICANCE

The resulting models were used to study the contribution of different ion channel properties and spatial structure of neurons to RGC activation. The techniques of this study are generally applicable to other excitable cell models, increasing the utility of theoretical models in accurately predicting the response of real biological neurons.

Effects of different three-dimensional electrodes on epiretinal electrical stimulation by modeling analysis

BACKGROUND

Epiretinal prostheses have been greatly successful in helping restore the vision of patients blinded by retinal degenerative diseases. The design of stimulating electrodes plays a crucial role in the performance of epiretinal prostheses. The objective of this study was to investigate, through computational modeling analysis, the effects on the excitation of retinal ganglion cells (RGCs) when different three-dimensional (3-D) electrodes were placed in the epiretinal space.

METHODS

3-D finite element models of retinal electrical stimulation were created in COMSOL using a platinum microelectrode, a vitreous body, multi-layered retinal tissue, and retinal pigment epithelium (RPE). Disk and non-planar electrodes with different 3-D structures were used in the epiretinal electrical stimulation. In addition, a multi-RGC model including ionic mechanisms was constructed in NEURON to study the excitability of RGCs in response to epiretinal electrical stimulation by different types of electrodes. Threshold current, threshold charge density, and the activated RGC area were the three key factors used to evaluate the stimulating electrode's performance.

RESULTS

As the electrode-retina distance increased, both threshold current and threshold charge density showed an approximately linear relationship. Increasing the disk electrode's diameter resulted in an increase in threshold current and a decrease in threshold charge density. Non-planar electrodes evoked different activation responses in RGCs than the disk electrode. Concave electrodes produced superior stimulation localization and electrode safety while convex electrodes performed relatively poorly.

CONCLUSIONS

Investigation of epiretinal electrical stimulation using different 3-D electrodes would further the optimization of electrode design and help improve the performance of epiretinal prostheses. The combination of finite element analysis in COMSOL and NEURON software provides an efficient way to evaluate the influences of various 3-D electrodes on epiretinal electrical stimulation. Non-planar electrodes had larger threshold currents than disk electrodes. Of the five types of electrodes, concave hemispherical electrodes may be the ideal option, considering their superior stimulation localization and electrode safety.

Influence of active dendrites on firing patterns in a retinal ganglion cell model

Active regional conductances and inhomogeneous distribution of membrane ionic channels in dendrites influence the integration of synaptic inputs in cortical neurons. How these properties shape the response properties of retinal ganglion cells (RGC) in the mammalian retina has remained largely unexplored. In this study, we used a morphologically-realistic RGC computational model to study how active dendritic properties contribute to neural behaviors. Our simulations suggest that the dendritic distribution of voltage-gated ionic channels strongly influences RGC firing patterns, indicating their important contribution to neuronal function.

ViSAPy: a Python tool for biophysics-based generation of virtual spiking activity for evaluation of spike-sorting algorithms

BACKGROUND

New, silicon-based multielectrodes comprising hundreds or more electrode contacts offer the possibility to record spike trains from thousands of neurons simultaneously. This potential cannot be realized unless accurate, reliable automated methods for spike sorting are developed, in turn requiring benchmarking data sets with known ground-truth spike times.

NEW METHOD

We here present a general simulation tool for computing benchmarking data for evaluation of spike-sorting algorithms entitled ViSAPy (Virtual Spiking Activity in Python). The tool is based on a well-established biophysical forward-modeling scheme and is implemented as a Python package built on top of the neuronal simulator NEURON and the Python tool LFPy.

RESULTS

ViSAPy allows for arbitrary combinations of multicompartmental neuron models and geometries of recording multielectrodes. Three example benchmarking data sets are generated, i.e., tetrode and polytrode data mimicking in vivo cortical recordings and microelectrode array (MEA) recordings of in vitro activity in salamander retinas. The synthesized example benchmarking data mimics salient features of typical experimental recordings, for example, spike waveforms depending on interspike interval.

COMPARISON WITH EXISTING METHODS

ViSAPy goes beyond existing methods as it includes biologically realistic model noise, synaptic activation by recurrent spiking networks, finite-sized electrode contacts, and allows for inhomogeneous electrical conductivities. ViSAPy is optimized to allow for generation of long time series of benchmarking data, spanning minutes of biological time, by parallel execution on multi-core computers.

CONCLUSION

ViSAPy is an open-ended tool as it can be generalized to produce benchmarking data or arbitrary recording-electrode geometries and with various levels of complexity.

Ionic channel changes in glaucomatous retinal ganglion cells: multicompartment modeling

This research takes a step towards discovering underlying ionic channel changes in the glaucomatous ganglion cells. Glaucoma is characterized by a gradual death of retinal ganglion cells. In this paper, we propose a hypothesis that the ionic channel concentrations change during the progression of glaucoma. We use computer simulation of a multi-compartment morphologically correct model of a mouse retinal ganglion cell to verify our hypothesis. Using published experimental data, we alter the morphology of healthy ganglion cells to replicate glaucomatous cells. Our results suggest that in glaucomatous cell, the sodium channel concentration decreases in the soma by 30% and by 60% in the dendrites, calcium channel concentration decreases by 10% in all compartments, and leak channel concentration increases by 40% in the soma and by 100% in the dendrites.

Influence of the sodium channel band on retinal ganglion cell excitation during electric stimulation--a modeling study

Electric stimulation using retinal implants allows blind people to re-experience a rudimentary kind of vision. The elicited percepts or so called 'phosphenes' are highly inconstant and therefore do not restore vision properly. The better knowledge of how retinal neurons, especially retinal ganglion cells, respond to electric stimulation will help to develop more sophisticated stimulation strategies. Special anatomic and physiologic properties like a band of highly dense sodium channels in retinal ganglion cells may help to achieve a focal activation of target cells and as a result better restoration of vision. A portion of retinal ganglion cell axons, about 40μm from the soma and between 25 and 40μm in length, shows a specific biophysical property. Electrode locations close to a band of highly dense sodium channels which were identified immunochemically show lowest thresholds during electric stimulation. The (modeled) thresholds for this kind of structure result in lowest thresholds as well. The influence on the location where action potentials are generated within the axon is far reaching. When a stimulating electrode is positioned far outside the actual band region the site of spike initiation still remains within the sodium channel band. These findings suggest to further examine the key mechanisms of activation for retinal ganglion cells because focal activation without influencing passing axons of neurons located far away can improve the outcome of electric stimulation and therefore the development of retinal implants.

Ionic mechanisms underlying tonic and phasic firing behaviors in retinal ganglion cells: a model study

In the retina, the firing behaviors that ganglion cells exhibit when exposed to light stimuli are very important due to the significant roles they play in encoding the visual information. However, the detailed mechanisms, especially the intrinsic properties that generate and modulate these firing behaviors is not completely clear yet. In this study, 2 typical firing behaviors—i.e., tonic and phasic activities, which are widely observed in retinal ganglion cells (RGCs)—are investigated. A modified computational model was developed to explore the possible ionic mechanisms that underlie the generation of these 2 firing patterns. Computational results indicate that the generation of tonic and phasic activities may be attributed to the collective actions of 2 kinds of adaptation currents, i.e., an inactivating sodium current and a delayed-rectifier potassium current. The concentration of magnesium ions has crucial but differential effects in the modulation of tonic and phasic firings, when the model neuron is driven by N-methyl-D-aspartate (NMDA) -type synaptic input instead of constant current injections. The proposed model has robust features that account for the ionic mechanisms underlying the tonic and phasic firing behaviors, and it may also be used as a good candidate for modeling some other firing patterns in RGCs.

Retinal ganglion cells electrophysiology: the effect of cell morphology on impulse waveform

There are 16 morphologically defined classes of rats retinal ganglion cells (RGCs). Using computer simulation of a realistic anatomically correct A1 mouse RGC, we investigate the effect of the cell's morphology on its impulse waveform, using the first-, and second-order time derivatives as well as the phase plot features. Using whole cell patch clamp recordings, we recorded the impulse waveform for each of the rat RGCs types. While we found some clear differences in many features of the impulse waveforms for A2 and B2 cells compared to other cell classes, many cell types did not show clear differences.

The effect of morphology upon electrophysiological responses of retinal ganglion cells: simulation results

Retinal ganglion cells (RGCs) display differences in their morphology and intrinsic electrophysiology. The goal of this study is to characterize the ionic currents that explain the behavior of ON and OFF RGCs and to explore if all morphological types of RGCs exhibit the phenomena described in electrophysiological data. We extend our previous single compartment cell models of ON and OFF RGCs to more biophysically realistic multicompartment cell models and investigate the effect of cell morphology on intrinsic electrophysiological properties. The membrane dynamics are described using the Hodgkin - Huxley type formalism. A subset of published patch-clamp data from isolated intact mouse retina is used to constrain the model and another subset is used to validate the model. Two hundred morphologically distinct ON and OFF RGCs are simulated with various densities of ionic currents in different morphological neuron compartments. Our model predicts that the differences between ON and OFF cells are explained by the presence of the low voltage activated calcium current in OFF cells and absence of such in ON cells. Our study shows through simulation that particular morphological types of RGCs are capable of exhibiting the full range of phenomena described in recent experiments. Comparisons of outputs from different cells indicate that the RGC morphologies that best describe recent experimental results are ones that have a larger ratio of soma to total surface area.

Coding and decoding with dendrites

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.

Model-based analysis of multiple electrode array stimulation for epiretinal visual prostheses

OBJECTIVE

Epiretinal stimulation, which uses an array of electrodes implanted on the inner retinal surface to relay a representation of the visual scene to the neuronal elements of the retina, has seen considerable success. The objective of the present study was to quantify the effects of multi-electrode stimulation on the patterns of neural excitation in a computational model of epiretinal stimulation.

APPROACH

A computational model of retinal ganglion cells was modified to represent the morphology of human retinal ganglion cells and validated against published experimental data. The ganglion cell model was then combined with a model of an axon of the nerve fiber layer to produce a population model of the inner retina. The response of the population of model neurons to epiretinal stimulation with a multi-electrode array was quantified across a range of electrode geometries using a novel means to quantify the model response-the minimum radius circle bounding the activated model neurons as a proxy for the evoked phosphene.

MAIN RESULTS

Multi-electrode stimulation created unique phosphenes, uch that the number of potential phosphenes can far exceed the number of electrode contacts.

SIGNIFICANCE

The ability to exploit the spatial and temporal interactions of stimulation may be critical to improvements in the performance of epiretinal prostheses.

Responses of retinal ganglion cells to extracellular electrical stimulation, from single cell to population: model-based analysis

Retinal ganglion cells (RGCs), which survive in large numbers following neurodegenerative diseases, could be stimulated with extracellular electric pulses to elicit artificial percepts. How do the RGCs respond to electrical stimulation at the sub-cellular level under different stimulus configurations, and how does this influence the whole-cell response? At the population level, why have experiments yielded conflicting evidence regarding the extent of passing axon activation? We addressed these questions through simulations of morphologically and biophysically detailed computational RGC models on high performance computing clusters. We conducted the analyses on both large-field RGCs and small-field midget RGCs. The latter neurons are unique to primates. We found that at the single cell level the electric potential gradient in conjunction with neuronal element excitability, rather than the electrode center location per se, determined the response threshold and latency. In addition, stimulus positioning strongly influenced the location of RGC response initiation and subsequent activity propagation through the cellular structure. These findings were robust with respect to inhomogeneous tissue resistivity perpendicular to the electrode plane. At the population level, RGC cellular structures gave rise to low threshold hotspots, which limited axonal and multi-cell activation with threshold stimuli. Finally, due to variations in neuronal element excitability over space, following supra-threshold stimulation some locations favored localized activation of multiple cells, while others favored axonal activation of cells over extended space.

Dynamic range of vertebrate retina ganglion cells: importance of active dendrites and coupling by electrical synapses

The vertebrate retina has a very high dynamic range. This is due to the concerted action of its diverse cell types. Ganglion cells, which are the output cells of the retina, have to preserve this high dynamic range to convey it to higher brain areas. Experimental evidence shows that the firing response of ganglion cells is strongly correlated with their total dendritic area and only weakly correlated with their dendritic branching complexity. On the other hand, theoretical studies with simple neuron models claim that active and large dendritic trees enhance the dynamic range of single neurons. Theoretical models also claim that electrical coupling between ganglion cells via gap junctions enhances their collective dynamic range. In this work we use morphologically reconstructed multi-compartmental ganglion cell models to perform two studies. In the first study we investigate the relationship between single ganglion cell dynamic range and number of dendritic branches/total dendritic area for both active and passive dendrites. Our results support the claim that large and active dendrites enhance the dynamic range of a single ganglion cell and show that total dendritic area has stronger correlation with dynamic range than with number of dendritic branches. In the second study we investigate the dynamic range of a square array of ganglion cells with passive or active dendritic trees coupled with each other via dendrodendritic gap junctions. Our results suggest that electrical coupling between active dendritic trees enhances the dynamic range of the ganglion cell array in comparison with both the uncoupled case and the coupled case with cells with passive dendrites. The results from our detailed computational modeling studies suggest that the key properties of the ganglion cells that endow them with a large dynamic range are large and active dendritic trees and electrical coupling via gap junctions.

Intrinsic physiological properties of rat retinal ganglion cells with a comparative analysis

Mammalian retina contains 15–20 different retinal ganglion cell (RGC) types, each of which is responsible for encoding different aspects of the visual scene. The encoding is defined by a combination of RGC synaptic inputs, the neurotransmitter systems used, and their intrinsic physiological properties. Each cell's intrinsic properties are defined by its morphology and membrane characteristics, including the complement and localization of the ion channels expressed. In this study, we examined the hypothesis that the intrinsic properties of individual RGC types are conserved among mammalian species. To do so, we measured the intrinsic properties of 16 morphologically defined rat RGC types and compared these data with cat RGC types. Our data demonstrate that in the rat different morphologically defined RGC types have distinct patterns of intrinsic properties. Variation in these properties across cell types was comparable to that found for cat RGC types. When presumed morphological homologs in rat and cat retina were compared directly, some RGC types had very similar properties. The rat A2 cell exhibited patterns of intrinsic properties nearly identical to the cat alpha cell. In contrast, rat D2 cells (ON-OFF directionally selective) had a very different pattern of intrinsic properties than the cat iota cell. Our data suggest that the intrinsic properties of RGCs with similar morphology and suspected visual function may be subject to variation due to the behavioral needs of the species.

The interplay between branching and pruning on neuronal target search during developmental growth: functional role and implications

Regenerative strategies that facilitate the regrowth and reconnection of neurons are some of the most promising methods in spinal cord injury research. An essential part of these strategies is an increased understanding of the mechanisms by which growing neurites seek out and synapse with viable targets. In this paper, we use computational and theoretical tools to examine the targeting efficiency of growing neurites subject to limited resources, such as maximum total neural tree length. We find that in order to efficiently reach a particular target, growing neurites must achieve balance between pruning and branching: rapidly growing neurites that do not prune will exhaust their resources, and frequently pruning neurites will fail to explore space effectively. We also find that the optimal branching/pruning balance must shift as the target distance changes: different strategies are called for to reach nearby vs. distant targets. This suggests the existence of a currently unidentified higher-level regulatory factor to control arborization dynamics. We propose that these findings may be useful in future therapies seeking to improve targeting rates through manipulation of arborization behaviors.

The sodium channel band shapes the response to electric stimulation in retinal ganglion cells

To improve the quality of prosthetic vision, it is desirable to understand how targeted retinal neurons respond to stimulation. Unfortunately, the factors that shape the response of a single neuron to stimulation are not well understood. A dense band of voltage-gated sodium channels within the proximal axon of retinal ganglion cells is the site most sensitive to electric stimulation, suggesting that band properties are likely to influence the response to stimulation. Here, we examined how three band properties influence sensitivity using a morphologically realistic ganglion cell model in NEURON. Longer bands were more sensitive to short-duration pulses than shorter bands and increasing the distance between band and soma also increased sensitivity. Simulations using the known limits of band length and location resulted in a sensitivity difference of approximately 2. Additional simulations tested how changes to sodium channel conductance within the band influenced threshold and found that the sensitivity difference increased to a factor of nearly 3. This is close to the factor of 5 difference measured in physiological studies suggesting that band properties contribute significantly to the sensitivity differences found between different types of retinal neurons.

Dendritic spikes amplify the synaptic signal to enhance detection of motion in a simulation of the direction-selective ganglion cell

The On-Off direction-selective ganglion cell (DSGC) in mammalian retinas responds most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree, which are thought to propagate to the soma with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas somatic PSPs (postsynaptic potentials) are only weakly directional, indicating that spike generation includes marked enhancement of the directional signal. We used a realistic computational model based on anatomical and physiological measurements to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate electrotonic regions, each summing its local excitatory and inhibitory synaptic inputs to initiate spikes. Within each local region the local spike threshold nonlinearly amplifies the preferred response over the null response on the basis of PSP amplitude. Using inhibitory conductances previously measured in DSGCs, the simulation results showed that inhibition is only sufficient to prevent spike initiation and cannot affect spike propagation. Therefore, inhibition will only act locally within the dendritic arbor. We identified the role of three mechanisms that generate directional selectivity (DS) in the local dendritic regions. First, a mechanism for DS intrinsic to the dendritic structure of the DSGC enhances DS on the null side of the cell's dendritic tree and weakens it on the preferred side. Second, spatially offset postsynaptic inhibition generates robust DS in the isolated dendritic tips but weak DS near the soma. Third, presynaptic DS is apparently necessary because it is more robust across the dendritic tree. The pre- and postsynaptic mechanisms together can overcome the local intrinsic DS. These local dendritic mechanisms can perform independent nonlinear computations to make a decision, and there could be analogous mechanisms within cortical circuitry.

The On-Off direction-selective ganglion cell (DSGC) found in mammalian retinas generates a directional signal, responding most strongly to a stimulus moving in a specific direction. The DSGC initiates spikes in its dendritic tree which are thought to propagate to the soma and brain with high probability. Both dendritic and somatic spikes in the DSGC display strong directional tuning, whereas postsynaptic potentials (PSPs) recorded in the soma are only weakly directional, indicating that postsynaptic spike generation markedly enhances the directional signal. We constructed a realistic computational model to determine the source of the enhancement. Our results indicate that the DSGC dendritic tree is partitioned into separate computational regions. Within each region, the local spike threshold produces nonlinear amplification of the preferred response over the null response on the basis of PSP amplitude. The simulation results showed that inhibition acts locally within the dendritic arbor and will not stop dendritic spikes from propagating. We identified the role of three mechanisms that generate direction selectivity in the local dendritic regions, which suggests the origin of the previously described “non-direction-selective region,” and also suggests that the known DS in the synaptic inputs is apparently necessary for robust DS across the dendritic tree.

Impact of dendritic size and dendritic topology on burst firing in pyramidal cells

Neurons display a wide range of intrinsic firing patterns. A particularly relevant pattern for neuronal signaling and synaptic plasticity is burst firing, the generation of clusters of action potentials with short interspike intervals. Besides ion-channel composition, dendritic morphology appears to be an important factor modulating firing pattern. However, the underlying mechanisms are poorly understood, and the impact of morphology on burst firing remains insufficiently known. Dendritic morphology is not fixed but can undergo significant changes in many pathological conditions. Using computational models of neocortical pyramidal cells, we here show that not only the total length of the apical dendrite but also the topological structure of its branching pattern markedly influences inter- and intraburst spike intervals and even determines whether or not a cell exhibits burst firing. We found that there is only a range of dendritic sizes that supports burst firing, and that this range is modulated by dendritic topology. Either reducing or enlarging the dendritic tree, or merely modifying its topological structure without changing total dendritic length, can transform a cell's firing pattern from bursting to tonic firing. Interestingly, the results are largely independent of whether the cells are stimulated by current injection at the soma or by synapses distributed over the dendritic tree. By means of a novel measure called mean electrotonic path length, we show that the influence of dendritic morphology on burst firing is attributable to the effect both dendritic size and dendritic topology have, not on somatic input conductance, but on the average spatial extent of the dendritic tree and the spatiotemporal dynamics of the dendritic membrane potential. Our results suggest that alterations in size or topology of pyramidal cell morphology, such as observed in Alzheimer's disease, mental retardation, epilepsy, and chronic stress, could change neuronal burst firing and thus ultimately affect information processing and cognition.

Mechanisms and distribution of ion channels in retinal ganglion cells: using temperature as an independent variable

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.

Axonal sodium-channel bands shape the response to electric stimulation in retinal ganglion cells

Electric stimulation of the retina reliably elicits light percepts in patients blinded by outer retinal diseases. However, individual percepts are highly variable and do not readily assemble into more complex visual images. As a result, the quality of visual information conveyed to patients has been quite limited. To develop more effective stimulation methods that will lead to improved psychophysical outcomes, we are studying how retinal neurons respond to electric stimulation. The situation in the retina is analogous to other neural prosthetic applications in which a better understanding of the underlying neural response may lead to improved clinical outcomes. Here, we determined which element in retinal ganglion cells has the lowest threshold for initiating action potentials. Previous studies suggest multiple possibilities, although all were within the soma/proximal axon region. To determine the actual site, we measured thresholds in a dense two-dimensional grid around the soma/proximal axon region of rabbit ganglion cells in the flat mount preparation. In directionally selective (DS) ganglion cells, the lowest thresholds were found along a small section of the axon, about 40 microm from the soma. Immunochemical staining revealed a dense band of voltage-gated sodium channels centered at the same location, suggesting that thresholds are lowest when the stimulating electrode is closest to the sodium-channel band. The size and location of the low-threshold region was consistent within DS cells, but varied for other ganglion cell types. Analogously, the length and location of sodium channel bands also varied by cell type. Consistent with the differences in band properties, we found that the absolute (lowest) thresholds were also different for different cell types. Taken together, our results suggest that the sodium-channel band is the site that is most responsive to electric stimulation and that differences in the bands underlie the threshold differences we observed.

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.

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.

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.

An integrated approach to classifying neuronal phenotypes

Characterizing the functional phenotypes of neurons is essential for understanding how genotypes can be related to the neural basis of behaviour. Traditional classifications of neurons by single features (such as morphology or firing behaviour) are increasingly inadequate for reflecting functional phenotypes, as they do not integrate functions across different neuronal types. Here, we describe a set of rules for identifying and predicting functional phenotypes that combine morphology, intrinsic ion channel species and their distributions in dendrites, and functional properties. This more comprehensive neuronal classification should be an improvement on traditional classifications for relating genotype to functional phenotype.

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.

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.

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.

NEURON: a tool for neuroscientists

NEURON is a simulation environment for models of individual neurons and networks of neurons that are closely linked to experimental data. NEURON provides tools for conveniently constructing, exercising, and managing models, so that special expertise in numerical methods or programming is not required for its productive use. This article describes two tools that address the problem of how to achieve computational efficiency and accuracy.

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.