Modelling intrinsic electrophysiological properties of ON and OFF retinal ganglion cells

Electrophysiological Analysis of Retinal Organoid Development Using 3D Microelectrodes of Liquid Metals

Despite of the substantial potential of human-derived retinal organoids, the degeneration of retinal ganglion cells (RGCs) during maturation limits their utility in assessing the functionality of later-born retinal cell subtypes. Additionally, conventional analyses primarily rely on fluorescent emissions, which limits the detection of actual cell functionality while risking damage to the 3D cytoarchitecture of organoids. Here, an electrophysiological analysis is presented to monitor RGC development in early to mid-stage retinal organoids, and compare distinct features with fully-mature mouse retina. This approach utilizes high-resolution 3D printing of liquid-metal microelectrodes, enabling precise targeting of specific inner retinal layers within organoids. The adaptable distribution and softness of these microelectrodes facilitate the spatiotemporal recording of inner retinal signals. This study not only demonstrates the functional properties of RGCs in retinal organoid development but also provides insights into their synaptic connectivity, reminiscent of fetal native retinas. Further comparison with fully-mature mouse retina in vivo verifies the organoid features, highlighting the potential of early-stage retinal organoids in biomedical research.

Nanoparticle-based optical interfaces for retinal neuromodulation: a review

Degeneration of photoreceptors in the retina is a leading cause of blindness, but commonly leaves the retinal ganglion cells (RGCs) and/or bipolar cells extant. Consequently, these cells are an attractive target for the invasive electrical implants colloquially known as "bionic eyes." However, after more than two decades of concerted effort, interfaces based on conventional electrical stimulation approaches have delivered limited efficacy, primarily due to the current spread in retinal tissue, which precludes high-acuity vision. The ideal prosthetic solution would be less invasive, provide single-cell resolution and an ability to differentiate between different cell types. Nanoparticle-mediated approaches can address some of these requirements, with particular attention being directed at light-sensitive nanoparticles that can be accessed via the intrinsic optics of the eye. Here we survey the available known nanoparticle-based optical transduction mechanisms that can be exploited for neuromodulation. We review the rapid progress in the field, together with outstanding challenges that must be addressed to translate these techniques to clinical practice. In particular, successful translation will likely require efficient delivery of nanoparticles to stable and precisely defined locations in the retinal tissues. Therefore, we also emphasize the current literature relating to the pharmacokinetics of nanoparticles in the eye. While considerable challenges remain to be overcome, progress to date shows great potential for nanoparticle-based interfaces to revolutionize the field of visual prostheses.

Glutamate transporter contribution to retinal ganglion cell vulnerability in a rat model of multiple sclerosis

Glial glutamate transporters actively participate in neurotransmission and have a fundamental role in determining the ambient glutamate concentration in the extracellular space. Their expression is dynamically regulated in many diseases, including experimental autoimmune encephalomyelitis (EAE), a model of multiple sclerosis. In EAE, a downregulation has been reported which may render neurons more susceptible to glutamate excitotoxicity. In this study, we have investigated the expression of GLAST (EAAT1) and GLT-1 (EAAT2) in the retina of Brown Norway rats following induction of myelin oligodendrocyte glycoprotein (MOG)-EAE, which results in retinal ganglion cell (RGC) degeneration and dysfunction. In addition, we tested whether AAV-mediated overexpression of GLAST in the retina can protect RGCs from degeneration. To address the impact of glutamate transporter modulation on RGCs, we performed whole-cell recordings and measured tonic NMDA receptor-mediated currents in the absence and presence of a glutamate-uptake blocker. We report that αOFF-RGCs show larger tonic glutamate-induced currents than αON-RGCs, in line with their greater vulnerability under neuroinflammatory conditions. We further show that increased AAV-mediated expression of GLAST in the retina does indeed protect RGCs from degeneration during the inflammatory disease. Collectively, our study highlights the neuroprotective role of glutamate transporters in the EAE retina and provides a characterization of tonic glutamate-currents of αRGCs. The larger effects of increased extracellular glutamate concentration on the αOFF-subtype may underlie its enhanced vulnerability to degeneration.

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.

Targeted Stimulation of Retinal Ganglion Cells in Epiretinal Prostheses: A Multiscale Computational Study

Retinal prostheses aim at restoring partial sight to patients that are blind due to retinal degenerative diseases by electrically stimulating the surviving healthy retinal neurons. Ideally, the electrical stimulation of the retina is intended to induce localized, focused, percepts only; however, some epiretinal implant subjects have reported seeing elongated phosphenes in a single electrode stimulation due to the axonal activation of retinal ganglion cells (RGCs). This issue can be addressed by properly devising stimulation waveforms so that the possibility of inducing axonal activation of RGCs is minimized. While strategies to devise electrical stimulation waveforms to achieve a focal RGCs response have been reported in literature, the underlying mechanisms are not well understood. This article intends to address this gap; we developed morphologically and biophysically realistic computational models of two classified RGCs: D1-bistratified and A2-monostratified. Computational results suggest that the sodium channel band (SOCB) is less sensitive to modulations in stimulation parameters than the distal axon (DA), and DA stimulus threshold is less sensitive to physiological differences among RGCs. Therefore, over a range of RGCs distal axon diameters, short-pulse symmetric biphasic waveforms can enhance the stimulation threshold difference between the SOCB and the DA. Appropriately designed waveforms can avoid axonal activation of RGCs, implying a consequential reduction of undesired strikes in the visual field.

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.

Bistability in Hodgkin-Huxley-type equations

We study how initial conditions of the Hodgkin-Huxley model affect the dynamics of simulated neurons. We systematically vary the amplitudes of depolarization currents in order to bring neuron dynamics to stable equilibrium. Our results demonstrate that simulated neurons can have spontaneous spiking or a silent state, depending on the initial conditions. We propose the methodology to study the circumstances under which Purkinje cells transit between hyperpolarized quiescent state (down state) and a depolarized spiking state (up state). We show that results derived using the Hodgkin-Huxley methodology should be carefully analyzed before suggesting a direct relevance to neuroprosthetic implants.

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.

Formulation and Implementation of Nonlinear Integral Equations to Model Neural Dynamics Within the Vertebrate Retina

Existing computational models of the retina often compromise between the biophysical accuracy and a hardware-adaptable methodology of implementation. When compared to the current modes of vision restoration, algorithmic models often contain a greater correlation between stimuli and the affected neural network, but lack physical hardware practicality. Thus, if the present processing methods are adapted to complement very-large-scale circuit design techniques, it is anticipated that it will engender a more feasible approach to the physical construction of the artificial retina. The computational model presented in this research serves to provide a fast and accurate predictive model of the retina, a deeper understanding of neural responses to visual stimulation, and an architecture that can realistically be transformed into a hardware device. Traditionally, implicit (or semi-implicit) ordinary differential equations (OES) have been used for optimal speed and accuracy. We present a novel approach that requires the effective integration of different dynamical time scales within a unified framework of neural responses, where the rod, cone, amacrine, bipolar, and ganglion cells correspond to the implemented pathways. Furthermore, we show that adopting numerical integration can both accelerate retinal pathway simulations by more than 50% when compared with traditional ODE solvers in some cases, and prove to be a more realizable solution for the hardware implementation of predictive retinal models.

Bond graph modelling of chemoelectrical energy transduction

Energy‐based bond graph modelling of biomolecular systems is extended to include chemoelectrical transduction thus enabling integrated thermodynamically compliant modelling of chemoelectrical systems in general and excitable membranes in particular. Our general approach is illustrated by recreating a well‐known model of an excitable membrane. This model is used to investigate the energy consumed during a membrane action potential thus contributing to the current debate on the trade‐off between the speed of an action potential event and energy consumption. The influx of Na+ is often taken as a proxy for energy consumption; in contrast, this study presents an energy‐based model of action potentials. As the energy‐based approach avoids the assumptions underlying the proxy approach it can be directly used to compute energy consumption in both healthy and diseased neurons. These results are illustrated by comparing the energy consumption of healthy and degenerative retinal ganglion cells using both simulated and in vitro data.

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.

On the computation of a retina resistivity profile for applications in multi-scale modeling of electrical stimulation and absorption

This study proposes a methodology for computationally estimating resistive properties of tissue in multi-scale computational models, used for studying the interaction of electromagnetic fields with neural tissue, with applications to both dosimetry and neuroprosthetics. Traditionally, models at bulk tissue- and cellular-level scales are solved independently, linking resulting voltage from existing resistive tissue-scale models as extracellular sources to cellular models. This allows for solving the effects that external electric fields have on cellular activity. There are two major limitations to this approach: first, the resistive properties of the tissue need to be chosen, of which there are contradicting measurements in literature; second, the measurements of resistivity themselves may be inaccurate, leading to the mentioned contradicting results found across different studies. Our proposed methodology allows for constructing computed resistivity profiles using knowledge of only the neural morphology within the multi-scale model, resulting in a practical implementation of the effective medium theory; this bypasses concerns regarding the choice of resistive properties and accuracy of measurement setups. A multi-scale model of retina is constructed with an external electrode to serve as a test bench for analyzing existing and resulting resistivity profiles, and validation is presented through the reconstruction of a published resistivity profile of retina tissue. Results include a computed resistivity profile of retina tissue for use with a retina multi-scale model used to analyze effects of external electric fields on neural activity.

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.

Cell-specific modeling of retinal ganglion cell electrical activity

Variations in ionic channel expression and anatomical properties can influence how different retinal ganglion cell (RGC) types process synaptic information. Computational modeling approaches allow us to precisely control these biophysical and physical properties and isolate their effects in shaping RGC firing patterns. In this study, three models based on realistic representations of RGC morphologies were used to simulate the contribution of spatial structure of neurons and membrane ion channel properties to RGC electrical activity. In all simulations, the RGC models shared common ionic channel kinetics, differing only in their regional ionic channel distributions and cell morphology.

Feedback stimulation strategy: control of retinal ganglion cells activation

It is possible to cause a sensation of light in patients who have lost photoreceptors due to degenerative eye diseases by targeting surviving neurons with electrical stimulation by means of visual prosthetic devices. All stimulation strategies in currently used visual prostheses are open-loop, that is, the stimulation parameters do not depend on the level of activation of neurons surrounding stimulating electrodes. In this paper, we investigate a closed-loop stimulation strategy using computer simulations of previously constrained models of ON and OFF retinal ganglion cells. Using a proportional-integral-type controller we show that it is possible to control activation level of both types of retinal ganglion cells. We also demonstrate that the controller tuned for a particular combination of synaptic currents continues to work during retina degeneration when excitatory currents are reduced by 20%.

The unique characteristics of ON and OFF retinal ganglion cells: a modeling study

Retinal ganglion cells (RGCs) demonstrate a large range of variation in their ionic channel properties and morphologies. These cell-specific properties are responsible for the unique way they process synaptic inputs. A cell-specific modeling approach allows us to examine the functional significance of regional membrane channel expression and cell morphology. ON and OFF RGC models based on accurate biophysics and realistic representation of morphologies were used to study the contribution of different ion channel properties and spatial structure of neurons to RGC electrical activity. Using this approach, morphologically-complex retinal neurons such as amacrine cells or RGCs can be modelled and their interactions and processing can be better understood.

Differential responses to high-frequency electrical stimulation in ON and OFF retinal ganglion cells

OBJECTIVE

The field of retinal prosthetics for artificial vision has advanced considerably in recent years, however clinical outcomes remain inconsistent. The performance of retinal prostheses is likely limited by the inability of electrical stimuli to preferentially activate different types of retinal ganglion cell (RGC).

APPROACH

Here we examine the response of rabbit RGCs to high-frequency stimulation, using biphasic pulses applied at 2000 pulses per second. Responses were recorded using cell-attached patch clamp methods, and stimulation was applied epiretinally via a small cone electrode.

MAIN RESULTS

When prolonged stimulus trains were applied to OFF-brisk transient (BT) RGCs, the cells exhibited a non-monotonic relationship between response strength and stimulus amplitude; this response pattern was different from those elicited previously by other electrical stimuli. When the amplitude of the stimulus was modulated transiently from a non-zero baseline amplitude, ON-BT and OFF-BT cells exhibited different activity patterns: ON cells showed an increase in activity while OFF cells exhibited a decrease in activity. Using a different envelope to modulate the amplitude of the stimulus, we observed the opposite effect: ON cells exhibited a decrease in activity while OFF cells show an increase in activity.

SIGNIFICANCE

As ON and OFF RGCs often exhibit opposing activity patterns in response to light stimulation, this work suggests that high-frequency electrical stimulation of RGCs may be able to elicit responses that are more physiological than traditional pulsatile stimuli. Additionally, the prospect of an electrical stimulus capable of cell-type specific selective activation has broad applications throughout the fields of neural stimulation and neuroprostheses.

Minimisation of required charge for desired neuronal spike rate

Retinal implants restore limited visual perception to blind implantees by electrical stimulation of surviving neurons. We consider the efficacy of two electrical stimulation parameters, frequency of stimulation and interphase gap between cathodic and anodic phases, on the required charge to reach a desired neuronal spike rate. Using a Hodgkin-Huxley model of a neuron, we find the most efficient means of achieving a desired spike rate for neurons by electrical stimulation is to use a stimulation frequency identical to the desired spike rate, as well as a long interphase gap.

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.

Modeling normal and rebound excitation in mammalian retinal ganglion cells

In this study, we used a novel missing currents technique to extend an existing conductance-based ionic current model of retinal ganglion cells (RGCs). The revised model reproduced a variety of biological behaviors. In particular, the model contains a hyperpolarization activated current (I(h)). This model can effectively simulate the mechanisms underlying both normal and rebound action potentials. The technique used in this study is generally applicable to other excitable cell models, reducing the gap between theoretical models and real biological neurons.

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.

Simulating electrical stimulation of degenerative retinal ganglion cells with bi-phasic pulse trains

The aim of this work was to investigate how retinal ganglion cells (RGCs) respond to repetitive electrical stimulation in degenerative retina. The response of modeled ON and OFF cells was examined to bi-phasic pulse train stimulation of varying frequencies. Previously developed models of RGCs were extended to include an experimentally observable balance of excitatory and inhibitory currents in degenerative retina. The phenomena of fading and dark phosphenes with retinal implants were investigated. A hypothesis for a mechanism contributing to these phenomena was formulated.