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

Inference of Electrical Stimulation Sensitivity from Recorded Activity of Primate Retinal Ganglion Cells

High-fidelity electronic implants can in principle restore the function of neural circuits by precisely activating neurons via extracellular stimulation. However, direct characterization of the individual electrical sensitivity of a large population of target neurons, to precisely control their activity, can be difficult or impossible. A potential solution is to leverage biophysical principles to infer sensitivity to electrical stimulation from features of spontaneous electrical activity, which can be recorded relatively easily. Here, this approach is developed and its potential value for vision restoration is tested quantitatively using large-scale multielectrode stimulation and recording from retinal ganglion cells (RGCs) of male and female macaque monkeys ex vivo Electrodes recording larger spikes from a given cell exhibited lower stimulation thresholds across cell types, retinas, and eccentricities, with systematic and distinct trends for somas and axons. Thresholds for somatic stimulation increased with distance from the axon initial segment. The dependence of spike probability on injected current was inversely related to threshold, and was substantially steeper for axonal than somatic compartments, which could be identified by their recorded electrical signatures. Dendritic stimulation was largely ineffective for eliciting spikes. These trends were quantitatively reproduced with biophysical simulations. Results from human RGCs were broadly similar. The inference of stimulation sensitivity from recorded electrical features was tested in a data-driven simulation of visual reconstruction, revealing that the approach could significantly improve the function of future high-fidelity retinal implants.SIGNIFICANCE STATEMENT This study demonstrates that individual in situ primate retinal ganglion cells of different types respond to artificially generated, external electrical fields in a systematic manner, in accordance with theoretical predictions, that allows for prediction of electrical stimulus sensitivity from recorded spontaneous activity. It also provides evidence that such an approach could be immensely helpful in the calibration of clinical retinal implants.

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.

Retinal ganglion cell desensitization is mitigated by varying parameter constant excitation pulse trains

Retinal prostheses partially restore vision in patients blinded by retinitis pigmentosa (RP) and age-related macular degeneration (AMD). One issue that limits the effectiveness of retinal stimulation is the desensitization of the retina response to repeated pulses. Rapid fading of percepts is reported in clinical studies. We studied the retinal output evoked by fixed pulse trains vs. pulse trains that have variable parameters pulse-to-pulse. We used the current clamp to record RGC spiking in the isolated mouse retina. Trains of biphasic current pulses at different frequencies and amplitudes were applied. The main results we report are: (1) RGC desensitization was induced by increasing stimulus frequency, but was unrelated to stimulus amplitude. Desensitization persisted when the 20 Hz stimulation pulses were applied to the retinal ganglion cells at 65 μA, 85 μA, and 105 μA. Subsequent pulses in the train evoked fewer spikes. There was no obvious desensitization when 2 Hz stimulation pulse trains were applied. (2) Blocking inhibitory GABA_A receptor increased spontaneous activity but did not reduce desensitization. (3) Pulse trains with constant charge or excitation (based on strength-duration curves) but varying pulse width, amplitude, and shape increased the number of evoked spikes/pulse throughout the pulse train. This suggests that retinal desensitization can be partially overcome by introducing variability into each pulse.

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.

Differences in spike generation instead of synaptic inputs determine the feature selectivity of two retinal cell types

Retinal ganglion cells (RGCs) are the spiking projection neurons of the eye that encode different features of the visual environment. The circuits providing synaptic input to different RGC types to drive feature selectivity have been studied extensively, but there has been less research aimed at understanding the intrinsic properties and how they impact feature selectivity. We introduce an RGC type in the mouse, the Bursty Suppressed-by-Contrast (bSbC) RGC, and compared it to the OFF sustained alpha (OFFsA). Differences in their contrast response functions arose from differences not in synaptic inputs but in their intrinsic properties. Spike generation was the key intrinsic property behind this functional difference; the bSbC RGC undergoes depolarization block while the OFFsA RGC maintains a high spike rate. Our results demonstrate that differences in intrinsic properties allow these two RGC types to detect and relay distinct features of an identical visual stimulus to the brain.

M1-Type, but Not M4-Type, Melanopsin Ganglion Cells Are Physiologically Tuned to the Central Circadian Clock

Proper circadian photoentrainment is crucial for the survival of many organisms. In mammals, intrinsically photosensitive retinal ganglion cells (ipRGCs) can use the photopigment melanopsin to sense light independently from rod and cone photoreceptors and send this information to many brain nuclei such as the suprachiasmatic nucleus (SCN), the site of the central circadian pacemaker. Here, we measure ionic currents and develop mathematical models of the electrical activity of two types of ipRGCs: M1, which projects to the SCN, and M4, which does not. We illustrate how their ionic properties differ, mainly how ionic currents generate lower spike rates and depolarization block in M1 ipRGCs. Both M1 and M4 cells have large geometries and project to higher visual centers of the brain via the optic nerve. Using a partial differential equation model, we show how axons of M1 and M4 cells faithfully convey information from the soma to the synapse even when the signal at the soma is attenuated due to depolarization block. Finally, we consider an ionic model of circadian photoentrainment from ipRGCs synapsing on SCN neurons and show how the properties of M1 ipRGCs are tuned to create accurate transmission of visual signals from the retina to the central pacemaker, whereas M4 ipRGCs would not evoke nearly as efficient a postsynaptic response. This work shows how ipRGCs and SCN neurons' electrical activities are tuned to allow for accurate circadian photoentrainment.

Color and cellular selectivity of retinal ganglion cell subtypes through frequency modulation of electrical stimulation

Epiretinal prostheses aim at electrically stimulating the inner most surviving retinal cells-retinal ganglion cells (RGCs)-to restore partial sight to the blind. Recent tests in patients with epiretinal implants have revealed that electrical stimulation of the retina results in the percept of color of the elicited phosphenes, which depends on the frequency of stimulation. This paper presents computational results that are predictive of this finding and further support our understanding of the mechanisms of color encoding in electrical stimulation of retina, which could prove pivotal for the design of advanced retinal prosthetics that elicit both percept and color. This provides, for the first time, a directly applicable "amplitude-frequency" stimulation strategy to "encode color" in future retinal prosthetics through a predictive computational tool to selectively target small bistratified cells, which have been shown to contribute to "blue-yellow" color opponency in the retinal circuitry. The presented results are validated with experimental data reported in the literature and correlated with findings in blind patients with a retinal prosthetic implant collected by our group.

Responsiveness of Retinal Ganglion Cells Through Frequency Modulation of Electrical Stimulation: A Computational Modeling Study

Electrical stimulation of surviving retinal neurons has proven effective in restoring sight to totally blind patients affected by retinal degenerative diseases. Morphological and biophysical differences among retinal ganglion cells (RGCs) are important factors affecting their response to epiretinal electrical stimulation. Although detailed models of ON and OFF RGCs have already been investigated, here we developed morphologically and biophysically realistic computational models of two classified RGCs, D1-bistratified and A2-monostratified, and analyzed their response to alternations in stimulation frequency (up to 200 Hz). Results show that the D1-bistratified cell is more responsive to high frequency stimulation compared to the A2-monostratified cell. This differential RGCs response suggests a potential avenue for selective activation, and in turn different encoded percept of RGCs.

Computational challenges and opportunities for a bi-directional artificial retina

A future artificial retina that can restore high acuity vision in blind people will rely on the capability to both read (observe) and write (control) the spiking activity of neurons using an adaptive, bi-directional and high-resolution device. Although current research is focused on overcoming the technical challenges of building and implanting such a device, exploiting its capabilities to achieve more acute visual perception will also require substantial computational advances. Using high-density large-scale recording and stimulation in the primate retina with an ex vivo multi-electrode array lab prototype, we frame several of the major computational problems, and describe current progress and future opportunities in solving them. First, we identify cell types and locations from spontaneous activity in the blind retina, and then efficiently estimate their visual response properties by using a low-dimensional manifold of inter-retina variability learned from a large experimental dataset. Second, we estimate retinal responses to a large collection of relevant electrical stimuli by passing current patterns through an electrode array, spike sorting the resulting recordings and using the results to develop a model of evoked responses. Third, we reproduce the desired responses for a given visual target by temporally dithering a diverse collection of electrical stimuli within the integration time of the visual system. Together, these novel approaches may substantially enhance artificial vision in a next-generation device.

A Three-Dimensional Microelectrode Array to Generate Virtual Electrodes for Epiretinal Prosthesis Based on a Modeling Study

Despite many advances in the development of retinal prostheses, clinical reports show that current retinal prosthesis subjects can only perceive prosthetic vision with poor visual acuity. A possible approach for improving visual acuity is to produce virtual electrodes (VEs) through electric field modulation. Generating controllable and localized VEs is a crucial factor in effectively improving the perceptive resolution of the retinal prostheses. In this paper, we aimed to design a microelectrode array (MEA) that can produce converged and controllable VEs by current steering stimulation strategies. Through computational modeling, we designed a three-dimensional concentric ring–disc MEA and evaluated its performance with different stimulation strategies. Our simulation results showed that electrode–retina distance (ERD) and inter-electrode distance (IED) can dramatically affect the distribution of electric field. Also the converged VEs could be produced when the parameters of the three-dimensional MEA were appropriately set. VE sites can be controlled by manipulating the proportion of current on each adjacent electrode in a current steering group (CSG). In addition, spatial localization of electrical stimulation can be greatly improved under quasi-monopolar (QMP) stimulation. This study may provide support for future application of VEs in epiretinal prosthesis for potentially increasing the visual acuity of prosthetic vision.

Voltage- and calcium-gated ion channels of neurons in the vertebrate retina

In this review, we summarize studies investigating the types and distribution of voltage- and calcium-gated ion channels in the different classes of retinal neurons: rods, cones, horizontal cells, bipolar cells, amacrine cells, interplexiform cells, and ganglion cells. We discuss differences among cell subtypes within these major cell classes, as well as differences among species, and consider how different ion channels shape the responses of different neurons. For example, even though second-order bipolar and horizontal cells do not typically generate fast sodium-dependent action potentials, many of these cells nevertheless possess fast sodium currents that can enhance their kinetic response capabilities. Ca2+ channel activity can also shape response kinetics as well as regulating synaptic release. The L-type Ca2+ channel subtype, CaV1.4, expressed in photoreceptor cells exhibits specific properties matching the particular needs of these cells such as limited inactivation which allows sustained channel activity and maintained synaptic release in darkness. The particular properties of K+ and Cl- channels in different retinal neurons shape resting membrane potentials, response kinetics and spiking behavior. A remaining challenge is to characterize the specific distributions of ion channels in the more than 100 individual cell types that have been identified in the retina and to describe how these particular ion channels sculpt neuronal responses to assist in the processing of visual information by the retina.

Mediating Retinal Ganglion Cell Spike Rates Using High-Frequency Electrical Stimulation

Recent retinal studies have directed more attention to sophisticated stimulation strategies based on high-frequency (>1.0 kHz) electrical stimulation (HFS). In these studies, each retinal ganglion cell (RGC) type demonstrated a characteristic stimulus-strength-dependent response to HFS, offering the intriguing possibility of focally targeting retinal neurons to provide useful visual information by retinal prosthetics. Ionic mechanisms are known to affect the responses of electrogenic cells during electrical stimulation. However, how these mechanisms affect RGC responses is not well understood at present, particularly when applying HFS. Here, we investigate this issue via an in silico model of the RGC. We calibrate and validate the model using an in vitro retinal preparation. An RGC model based on accurate biophysics and realistic representation of cell morphology, was used to investigate how RGCs respond to HFS. The model was able to closely replicate the stimulus-strength-dependent suppression of RGC action potentials observed experimentally. Our results suggest that spike inhibition during HFS is due to local membrane hyperpolarization caused by outward membrane currents near the stimulus electrode. In addition, the extent of HFS-induced inhibition can be largely altered by the intrinsic properties of the inward sodium current. Finally, stimulus-strength-dependent suppression can be modulated by a wide range of stimulation frequencies, under generalized electrode placement conditions. In vitro experiments verified the computational modeling data. This modeling and experimental approach can be extended to further our understanding on the effects of novel stimulus strategies by simulating RGC stimulus-response profiles over a wider range of stimulation frequencies and electrode locations than have previously been explored.

Electrical receptive fields of retinal ganglion cells: Influence of presynaptic neurons

Implantable retinal stimulators activate surviving neurons to restore a sense of vision in people who have lost their photoreceptors through degenerative diseases. Complex spatial and temporal interactions occur in the retina during multi-electrode stimulation. Due to these complexities, most existing implants activate only a few electrodes at a time, limiting the repertoire of available stimulation patterns. Measuring the spatiotemporal interactions between electrodes and retinal cells, and incorporating them into a model may lead to improved stimulation algorithms that exploit the interactions. Here, we present a computational model that accurately predicts both the spatial and temporal nonlinear interactions of multi-electrode stimulation of rat retinal ganglion cells (RGCs). The model was verified using in vitro recordings of ON, OFF, and ON-OFF RGCs in response to subretinal multi-electrode stimulation with biphasic pulses at three stimulation frequencies (10, 20, 30 Hz). The model gives an estimate of each cell’s spatiotemporal electrical receptive fields (ERFs); i.e., the pattern of stimulation leading to excitation or suppression in the neuron. All cells had excitatory ERFs and many also had suppressive sub-regions of their ERFs. We show that the nonlinearities in observed responses arise largely from activation of presynaptic interneurons. When synaptic transmission was blocked, the number of sub-regions of the ERF was reduced, usually to a single excitatory ERF. This suggests that direct cell activation can be modeled accurately by a one-dimensional model with linear interactions between electrodes, whereas indirect stimulation due to summated presynaptic responses is nonlinear.

Implantable neural stimulation devices are being widely used and clinically tested for the restoration of lost function (e.g. cochlear implants) and the treatment of neurological disorders. Smart devices that can combine sensing and stimulation will dramatically improve future patient outcomes. To this end, mathematical models that can accurately predict neural responses to electrical stimulation will be critical for the development of smart stimulation devices. Here, we demonstrate a model that predicts neural responses to simultaneous stimulation across multiple electrodes in the retina. We show that the activation of presynaptic neurons leads to nonlinearities in the responses of postsynaptic retinal ganglion cells. The model is accurate and is applicable to a wide range of neural stimulation devices.

Modeling electrical stimulation of retinal ganglion cell with optimizing additive noises for reducing threshold and energy consumption

BACKGROUND

Epiretinal prosthesis is one device for the treatment of blindness, which target retinal ganglion cells (RGCs) by electrodes on retinal surface. The stimulating current of epiretinal prosthesis is an important factor that influences the safety threshold and visual perception. Stochastic resonance (SR) can be used to enhance the detection and transmission of subthreshold stimuli in neurons. Here, it was assumed that SR was a potential way to improve the performance of epiretinal prosthesis. The effect of noises on the response of RGCs to electrical stimulation and the energy of stimulating current was studied based on a RGC model.

METHODS

The RGC was modeled as a multi-compartment model consisting of dendrites and its branches, soma and axon. To evoke SR, a subthreshold signal, a series of bipolar rectangular pulse sequences, plus stochastic biphasic pulse sequences as noises, were used as a stimulus to the model. The SR-type behavior in the model was characterized by a "power norm" measure. To decrease energy consumption of the stimulation waveform, the stochastic biphasic pulse sequences were only added to the cathode and anode phase of the subthreshold pulse and the noise parameters were optimized by using a genetic algorithm (GA).

RESULTS

When certain intensity of noise is added to the subthreshold signal, RGC model can fire. With the noise's RMS amplitudes increased, more spikes were elicited and the curve of power norm presents the inverted U-like graph. The larger pulse width of stochastic biphasic pulse sequences resulted in higher power norm. The energy consumption and charges of the single bipolar rectangular pulse without noise in threshold level are 468.18 pJ, 15.30 nC, and after adding optimized parameters's noise to the subthreshold signal, they became 314.8174 pJ, 11.9281 nC and were reduced by 32.8 and 22.0%, respectively.

CONCLUSIONS

The SR exists in the RGC model and can enhance the representation of RGC model to the subthreshold signal. Adding the stochastic biphasic pulse sequences to the cathode and anode phase of the subthreshold signal helps to reduce stimulation threshold, energy consumption and charge of RGC stimulation. These may be helpful for improving the performance of epiretinal prosthesis.

Single-compartment models of retinal ganglion cells with different electrophysiologies

There are more than 15 different types of retinal ganglion cells (RGCs) in the mammalian retina. To model responses of RGCs to electrical stimulation, we use single-compartment Hodgkin-Huxley-type models and run simulations in the Neuron environment. We use our recently published in vitro data of different morphological cell types to constrain the model, and study the effects of electrophysiology on the cell responses separately from the effects of morphology. We find simple models that can match the spike patterns of different types of RGCs. These models, with different input-output properties, may be used in a network to study retinal network dynamics and interactions.

The impact of inhibitory mechanisms in the inner retina on spatial tuning of RGCs

Spatial tuning properties of retinal ganglion cells (RGCs) are sharpened by lateral inhibition originating at both the outer and inner plexiform layers. Lateral inhibition in the retina contributes to local contrast enhancement and sharpens edges. In this study, we used dynamic clamp recordings to examine the contribution of inner plexiform inhibition, originating from spiking amacrine cells, to the spatial tuning of RGCs. This was achieved by injecting currents generated from physiologically recorded excitatory and inhibitory stimulus-evoked conductances, into different types of primate and mouse RGCs. We determined the effects of injections of size-dependent conductances in which presynaptic inhibition and/or direct inhibition onto RGCs were partly removed by blocking the activity of spiking amacrine cells. We found that inhibition originating from spiking amacrine cells onto bipolar cell terminals and onto RGCs, work together to sharpen the spatial tuning of RGCs. Furthermore, direct inhibition is crucial for preventing spike generation at stimulus offset. These results reveal how inhibitory mechanisms in the inner plexiform layer contribute to determining size tuning and provide specificity to stimulus polarity.

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.

Selective activation of ON and OFF retinal ganglion cells to high-frequency electrical stimulation: a computational modeling study

In this study, ON and OFF retinal ganglion cell (RGC) models based on accurate biophysics and realistic representations of cell morphologies were used to understand how these cells selectively respond to high-frequency electrical stimulation (HFS). With optimized model parameters and the incorporation of detailed cell morphologies, these two models were able to closely replicate experimental ON and OFF RGC responses to epiretinal electrical stimulation. This modeling approach can be used to design electrical stimulus profiles capable of cell-specific activation, and is broadly applicable for the development of sophisticated stimulation strategies for visual prostheses.

Properties of a Glutamatergic Synapse Controlling Information Output from Retinal Bipolar Cells

One general categorization of retinal ganglion cells is to segregate them into tonically or phasically responding neurons, each conveying discrete aspects of the visual scene. Although best identified in the output signals of the retina, this distinction is initiated at the first synapse: between photoreceptors and the dendrites of bipolar cells. In this study we found that the output synapses of bipolar cells also contribute to separate these pathways. Both transient and sustained ganglion cells can produce maintained spike activity, but bipolar cell glutamate release exhibits a divergence that corresponds to the response characteristics of the ganglion cells. Comparing light intensity coding in the sustained and transient ON pathways revealed that they shared the intensity spectrum. The transient pathway had greater sensitivity but smaller dynamic range, and switched from intensity coding to event detection at light levels where sustained pathway sensitivity began to rise. The distinctive properties of the sustained pathway depended upon inhibition and shifted toward those of the transient pathway in the absence of inhibition. The transient system was comparatively unaffected by the loss of inhibition and this was due to the concomitant activation of perisynaptic NMDA receptors. Overall, the properties of bipolar cell dendritic and axon terminals both contribute to the formation of key aspects of the sustained/transient dichotomy normally associated with ganglion cells.

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.

Dendritic morphology predicts pattern recognition performance in multi-compartmental model neurons with and without active conductances

In this paper we examine how a neuron’s dendritic morphology can affect its pattern recognition performance. We use two different algorithms to systematically explore the space of dendritic morphologies: an algorithm that generates all possible dendritic trees with 22 terminal points, and one that creates representative samples of trees with 128 terminal points. Based on these trees, we construct multi-compartmental models. To assess the performance of the resulting neuronal models, we quantify their ability to discriminate learnt and novel input patterns. We find that the dendritic morphology does have a considerable effect on pattern recognition performance and that the neuronal performance is inversely correlated with the mean depth of the dendritic tree. The results also reveal that the asymmetry index of the dendritic tree does not correlate with the performance for the full range of tree morphologies. The performance of neurons with dendritic tapering is best predicted by the mean and variance of the electrotonic distance of their synapses to the soma. All relationships found for passive neuron models also hold, even in more accentuated form, for neurons with active membranes.

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.

Multicompartment retinal ganglion cells response to high frequency bi-phasic pulse train stimulation: Simulation results

Retinal ganglion cells (RGCs) are the sole output neurons of the retina that carry information about a visual scene to the brain. By stimulating RGCs with electrical stimulation, it is possible to elicit a sensation of light for people with macular degeneration or retinitis pigmentosa. To investigate the responses of RGCs to high frequency bi-phasic pulse train stimulation, we use previously constrained models of multi-compartment OFF RGCs. The morphologies of mouse RGCs are taken from the Chalupa set of the NeuroMorpho database. The cell models are divided into compartments representing the dendrites, soma and axon that vary between the cells. A total of 132 cells are simulated in the NEURON environment. Results show that the cell morphology plays an important role in the response characteristics of the cell to high frequency bi-phasic pulse train stimulation.

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.

Mechanisms of electrical stimulation with neural prostheses

Individual electric and geometric characteristics of neural substructures can have surprising effects on artificially controlled neural signaling. A rule of thumb approved for the stimulation of long peripheral axons may not hold when the central nervous system is involved. This is demonstrated here with a comparison of results from the electrically stimulated cochlea, retina, and spinal cord. A generalized form of the activating function together with accurate modeling of the neural membrane dynamics are the tools to analyze the excitation mechanisms initiated by neural prostheses. Analysis is sometimes possible with a linear theory, in other cases, simulation of internal calcium concentration or ion channel current fluctuations is needed to see irregularities in spike trains. Spike initiation site can easily change within a single target neuron under constant stimulation conditions of a cochlear implant. Poor myelinization in the soma region of the human cochlear neurons causes firing characteristics different from any animal data. Retinal ganglion cells also generate propagating spikes within the dendritic tree. Bipolar cells in the retina are expected to respond with neurotransmitter release before a spike is generated in the ganglion cell, even when they are far away from the electrode. Epidural stimulation of the lumbar spinal cord predominantly stimulates large sensory axons in the dorsal roots which induce muscle reflex responses. Analysis with the generalized activating function, computer simulations of the nonlinear neural membrane behavior together with experimental and clinical data analysis enlighten our understanding of artificial firing patterns influenced by neural prostheses.

Intrinsic physiological properties of the five types of mouse ganglion-cell photoreceptors

In the mammalian retina, some ganglion cells express the photopigment melanopsin and function as photoreceptors. Five morphological types of these intrinsically photosensitive retinal ganglion cells (ipRGCs), M1-M5, have been identified in mice. Whereas M1 specializes in non-image-forming visual functions and drives such behaviors as the pupillary light reflex and circadian photoentrainment, the other types appear to contribute to image-forming as well as non-image-forming vision. Recent work has begun to reveal physiological diversity among some of the ipRGC types, including differences in photosensitivity, firing rate, and membrane resistance. To gain further insights into these neurons' functional differences, we conducted a comprehensive survey of the electrophysiological properties of all five morphological types. Compared with the other types, M1 had the highest membrane resistance, longest membrane time constant, lowest spike frequencies, widest action potentials, most positive spike thresholds, smallest hyperpolarization-activated inwardly-rectifying current-induced "sagging" responses to hyperpolarizing currents, and the largest effects of voltage-gated K(+) currents on membrane potentials. M4 and M5 were at the other end of the spectrum for most of these measures, while M2 and M3 tended to be in the middle of this spectrum. Additionally, M1 and M2 cells generated more diverse voltage-gated Ca(2+) currents than M3-M5. In conclusion, M1 cells are significantly different from all other ipRGCs in most respects, possibly reflecting the unique physiological requirements of non-image-forming vision. Furthermore, the non-M1 ipRGCs are electrophysiologically heterogeneous, implicating these cells' diverse functional roles in both non-image-forming vision and pattern vision.

Directional summation in non-direction selective retinal ganglion cells

Retinal ganglion cells receive inputs from multiple bipolar cells which must be integrated before a decision to fire is made. Theoretical studies have provided clues about how this integration is accomplished but have not directly determined the rules regulating summation of closely timed inputs along single or multiple dendrites. Here we have examined dendritic summation of multiple inputs along On ganglion cell dendrites in whole mount rat retina. We activated inputs at targeted locations by uncaging glutamate sequentially to generate apparent motion along On ganglion cell dendrites in whole mount retina. Summation was directional and dependent13 on input sequence. Input moving away from the soma (centrifugal) resulted in supralinear summation, while activation sequences moving toward the soma (centripetal) were linear. Enhanced summation for centrifugal activation was robust as it was also observed in cultured retinal ganglion cells. This directional summation was dependent on hyperpolarization activated cyclic nucleotide-gated (HCN) channels as blockade with ZD7288 eliminated directionality. A computational model confirms that activation of HCN channels can override a preference for centripetal summation expected from cell anatomy. This type of direction selectivity could play a role in coding movement similar to the axial selectivity seen in locust ganglion cells which detect looming stimuli. More generally, these results suggest that non-directional retinal ganglion cells can discriminate between input sequences independent of the retina network.

Visual information is coded by the output of retinal ganglion cells. Through evolution retinal ganglion cells acquired unique properties that allowed them to transmit to the brain such signals as direction of movement. The quest for the cellular mechanism of the detection of movement by retinal ganglion cells has been the holy grail of research on direction selectivity. In this study we have found a mechanism that allows individual non-direction selective On retinal ganglion cells to code sequences of excitatory inputs moving either away or toward the soma. We observed that inputs moving away from the soma resulted in enhanced, supralinear EPSP summation. Evidence from computational modeling suggests that expression of a specific set of voltage-dependent channels in dendrites introduces nonlinearities that could give a ganglion cell the ability to code looming motion. We predict that in a retinal network, such a directional tuning mechanism, together with asymmetric presynaptic inhibition, could be the building block for the development of more complex detection of visual motion.

Influence of cell morphology in a computational model of ON and OFF retinal ganglion cells

We developed anatomically and biophysically detailed ionic models to understand how cell morphology contributes to the unique firing patterns of ON and OFF retinal ganglion cells (RGCs). With identical voltage-gated channel kinetics and distribution, cell morphology alone is sufficient to generate quantitatively distinct electrophysiological responses. Notably, recent experimental observations from ON and OFF RGCs can be closely reproduced by the variations in their cell morphologies alone. Our results suggest that RGC morphology in conjunction with biophysical properties and network connectivity are able to produce the diverse response repertoire of RGCs.

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.

Inducing repetitive action potential firing in neurons via synthesized photoresponsive nanoscale cellular prostheses

Recently we reported an analysis that examined the potential of synthesized photovoltaic functional abiotic nanosystems (PVFANs) to modulate membrane potential and activate action potential firing in neurons. Here we extend the analysis to delineate the requirements on the electronic energy levels and the attendant photophysical properties of the PVFANs to induce repetitive action potential under continuous light, a capability essential for the proposed potential application of PVFANs as retinal cellular prostheses to compensate for loss of photoreceptors. We find that repetitive action potential firing demands two basic characteristics in the electronic response of the PVFANs: an exponential dependence of the PVFAN excited state decay rate on the membrane potential and a three-state system such that, following photon absorption, the electron decay from the excited state to the ground state is via intermediate state(s) whose lifetime is comparable to the refractory time following an action potential.

FROM THE CLINICAL EDITOR

In this study, the potential of synthetic photovoltaic functional abiotic nanosystems (PVFANs) is examined under continuous light to modulate membrane potential and activate action potential firing in neurons with the proposed potential application of PVFANs as retinal cellular prostheses.

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.

Modelling intrinsic electrophysiological properties of ON and OFF retinal ganglion cells

ON and OFF retinal ganglion cells (RGCs) display differences in their intrinsic electrophysiology: OFF cells maintain spontaneous activity in the absence of any input, exhibit subthreshold membrane potential oscillations, rebound excitation and burst firing; ON cells require excitatory input to drive their activity and display none of the aforementioned phenomena. The goal of this study was to identify and characterize ionic currents that explain these intrinsic electrophysiological differences between ON and OFF RGCs. A mathematical model of the electrophysiological properties of ON and OFF RGCs was constructed and validated using published patch-clamp data from isolated intact mouse retina. The model incorporates three ionic currents hypothesized to play a role in generating behaviors that are different between ON and OFF RGCs. These currents are persistent Na( + ), I (NaP), hyperpolarization-activated, I (h), and low voltage activated Ca(2 + ), I (T), currents. Using computer simulations of Hodgkin-Huxley type neuron with a single compartment model we found two distinct sets of I (NaP), I (h), I (T) conductances that correspond to ON and OFF RGCs populations. Simulations indicated that special properties of I (T) explain the differences in intrinsic electrophysiology between ON and OFF RGCs examined here. The modelling shows that the maximum conductance of I (T) is higher in OFF than in ON cells, in agreement with recent experimental data.

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.

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.

How the optic nerve allocates space, energy capacity, and information

Fiber tracts should use space and energy efficiently, because both resources constrain neural computation. We found for a myelinated tract (optic nerve) that astrocytes use nearly 30% of the space and >70% of the mitochondria, establishing the significance of astrocytes for the brain's space and energy budgets. Axons are mostly thin with a skewed distribution peaking at 0.7 microm, near the lower limit set by channel noise. This distribution is matched closely by the distribution of mean firing rates measured under naturalistic conditions, suggesting that firing rate increases proportionally with axon diameter. In axons thicker than 0.7 microm, mitochondria occupy a constant fraction of axonal volume--thus, mitochondrial volumes rise as the diameter squared. These results imply a law of diminishing returns: twice the information rate requires more than twice the space and energy capacity. We conclude that the optic nerve conserves space and energy by sending most information at low rates over fine axons with small terminal arbors and sending some information at higher rates over thicker axons with larger terminal arbors but only where more bits per second are needed for a specific purpose. Thicker axons seem to be needed, not for their greater conduction velocity (nor other intrinsic electrophysiological purpose), but instead to support larger terminal arbors and more active zones that transfer information synaptically at higher rates.

A nerve model of greatly increased energy-efficiency and encoding flexibility over the Hodgkin-Huxley model

A mammalian "RGC model" (retinal ganglion cells) is distinguished from the Hodgkin-Huxley model by the virtual absence of K-current during, and the virtual absence of Na-current after, the regenerative (rising) phase of the action potential. Both Na- and K-currents remain negligible throughout the interspike interval, whose control is therefore relinquished to stimulus currents. These properties yield a highly flexible and energy-efficient nerve impulse encoder. For the Hodgkin-Huxley model, in contrast, only 15% of the Na-ions enter the axon regeneratively during the action potential (squid giant axon); a wasteful 85% enter during the falling phase. Further, early activation of K-current causes the Na- and K-currents of the action potential to dominate over stimulus currents in controlling the sub-threshold membrane potential (interspike interval). This property makes the Hodgkin-Huxley model an intractable high frequency oscillator, which cannot be converted to flexible impulse encoding. The temperature difference between the squid giant axon (6.3 degrees C) and RGCs (37 degrees C) is bridged by a Q10 analysis, which suggests that an additional molecular gating mechanism of high Q10 - which is not present in the squid - is active in RGCs.

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.

High-resolution electrical stimulation of primate retina for epiretinal implant design

The development of retinal implants for the blind depends crucially on understanding how neurons in the retina respond to electrical stimulation. This study used multielectrode arrays to stimulate ganglion cells in the peripheral macaque retina, which is very similar to the human retina. Analysis was restricted to parasol cells, which form one of the major high-resolution visual pathways in primates. Individual cells were characterized using visual stimuli, and subsequently targeted for electrical stimulation using electrodes 9-15 microm in diameter. Results were accumulated across 16 ON and 9 OFF parasol cells. At threshold, all cells responded to biphasic electrical pulses 0.05-0.1 ms in duration by firing a single spike with latency lower than 0.35 ms. The average threshold charge density was 0.050 +/- 0.005 mC/cm(2), significantly below established safety limits for platinum electrodes. ON and OFF ganglion cells were stimulated with similar efficacy. Repetitive stimulation elicited spikes within a 0.1 ms time window, indicating that the high temporal precision necessary for spike-by-spike stimulation can be achieved in primate retina. Spatial analysis of observed thresholds suggests that electrical activation occurred near the axon hillock, and that dendrites contributed little. Finally, stimulation of a single parasol cell produced little or no activation of other cells in the ON and OFF parasol cell mosaics. The low-threshold, temporally precise, and spatially specific responses hold promise for the application of high-density arrays of small electrodes in epiretinal implants.

Nav1.6 sodium channels are critical to pacemaking and fast spiking in globus pallidus neurons

Neurons in the external segment of the globus pallidus (GPe) are autonomous pacemakers that are capable of sustained fast spiking. The cellular and molecular determinants of pacemaking and fast spiking in GPe neurons are not fully understood, but voltage-dependent Na+ channels must play an important role. Electrophysiological studies of these neurons revealed that macroscopic activation and inactivation kinetics of their Na+ channels were similar to those found in neurons lacking either autonomous activity or the capacity for fast spiking. What was distinctive about GPe Na+ channels was a prominent resurgent gating mode. This mode was significantly reduced in GPe neurons lacking functional Nav1.6 channels. In these Nav1.6 null neurons, pacemaking and the capacity for fast spiking were impaired, as was the ability to follow stimulation frequencies used to treat Parkinson's disease (PD). Simulations incorporating Na+ channel models with and without prominent resurgent gating suggested that resurgence was critical to fast spiking but not to pacemaking, which appeared to be dependent on the positioning of Na+ channels in spike-initiating regions of the cell. These studies not only shed new light on the mechanisms underlying spiking in GPe neurons but also suggest that electrical stimulation therapies in PD are unlikely to functionally inactivate neurons possessing Nav1.6 Na+ channels with prominent resurgent gating.