The influence of different retinal subcircuits on the nonlinearity of ganglion cell behavior

Simulating the impact of photoreceptor loss and inner retinal network changes on electrical activity of the retina

Objective.A major reason for poor visual outcomes provided by existing retinal prostheses is the limited knowledge of the impact of photoreceptor loss on retinal remodelling and its subsequent impact on neural responses to electrical stimulation. Computational network models of the neural retina assist in the understanding of normal retinal function but can be also useful for investigating diseased retinal responses to electrical stimulation.Approach.We developed and validated a biophysically detailed discrete neuronal network model of the retina in the software package NEURON. The model includes rod and cone photoreceptors, ON and OFF bipolar cell pathways, amacrine and horizontal cells and finally, ON and OFF retinal ganglion cells with detailed network connectivity and neural intrinsic properties. By accurately controlling the network parameters, we simulated the impact of varying levels of degeneration on retinal electrical function.Main results.Our model was able to reproduce characteristic monophasic and biphasic oscillatory patterns seen in ON and OFF neurons during retinal degeneration (RD). Oscillatory activity occurred at 3 Hz with partial photoreceptor loss and at 6 Hz when all photoreceptor input to the retina was removed. Oscillations were found to gradually weaken, then disappear when synapses and gap junctions were destroyed in the inner retina. Without requiring any changes to intrinsic cellular properties of individual inner retinal neurons, our results suggest that changes in connectivity alone were sufficient to give rise to neural oscillations during photoreceptor degeneration, and significant network connectivity destruction in the inner retina terminated the oscillations.Significance.Our results provide a platform for further understanding physiological retinal changes with progressive photoreceptor and inner RD. Furthermore, our model can be used to guide future stimulation strategies for retinal prostheses to benefit patients at different stages of disease progression, particularly in the early and mid-stages of RD.

A Neuronal Network Model of the Primate Visual System: Color Mechanisms in the Retina, LGN and V1

Color plays a key role in human vision but the neural machinery that underlies the transformation from stimulus to perception is not well understood. Here, we implemented a two-dimensional network model of the first stages in the primate parvocellular pathway (retina, lateral geniculate nucleus and layer 4C[Formula: see text] in V1) consisting of conductance-based point neurons. Model parameters were tuned based on physiological and anatomical data from the primate foveal and parafoveal vision, the most relevant visual field areas for color vision. We exhaustively benchmarked the model against well-established chromatic and achromatic visual stimuli, showing spatial and temporal responses of the model to disk- and ring-shaped light flashes, spatially uniform squares and sine-wave gratings of varying spatial frequency. The spatiotemporal patterns of parvocellular cells and cortical cells are consistent with their classification into chromatically single-opponent and double-opponent groups, and nonopponent cells selective for luminance stimuli. The model was implemented in the widely used neural simulation tool NEST and released as open source software. The aim of our modeling is to provide a biologically realistic framework within which a broad range of neuronal interactions can be examined at several different levels, with a focus on understanding how color information is processed.

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.

Retinal Lateral Inhibition Provides the Biological Basis of Long-Range Spatial Induction

Retinal lateral inhibition is one of the conventional efficient coding mechanisms in the visual system that is produced by interneurons that pool signals over a neighborhood of presynaptic feedforward cells and send inhibitory signals back to them. Thus, the receptive-field (RF) of a retinal ganglion cell has a center-surround receptive-field (RF) profile that is classically represented as a difference-of-Gaussian (DOG) adequate for efficient spatial contrast coding. The DOG RF profile has been attributed to produce the psychophysical phenomena of brightness induction, in which the perceived brightness of an object is affected by that of its vicinity, either shifting away from it (brightness contrast) or becoming more similar to it (brightness assimilation) depending on the size of the surfaces surrounding the object. While brightness contrast can be modeled using a DOG with a narrow surround, brightness assimilation requires a wide suppressive surround. Early retinal studies determined that the suppressive surround of a retinal ganglion cell is narrow (< 100–300 μm; ‘classic RF’), which led researchers to postulate that brightness assimilation must originate at some post-retinal, possibly cortical, stage where long-range interactions are feasible. However, more recent studies have reported that the retinal interneurons also exhibit a spatially wide component (> 500–1000 μm). In the current study, we examine the effect of this wide interneuron RF component in two biophysical retinal models and show that for both of the retinal models it explains the long-range effect evidenced in simultaneous brightness induction phenomena and that the spatial extent of this long-range effect of the retinal model responses matches that of perceptual data. These results suggest that the retinal lateral inhibition mechanism alone can regulate local as well as long-range spatial induction through the narrow and wide RF components of retinal interneurons, arguing against the existing view that spatial induction is operated by two separate local vs. long-range mechanisms.

Differential signalling and glutamate receptor compositions in the OFF bipolar cell types in the mouse retina

KEY POINTS

Using whole-cell clamp methods, we characterized the temporal coding in each type of OFF bipolar cell. We found that type 2 and 3a cells are transient, type 1 and 4 cells are sustained, and type 3b cells are intermediate. The light-evoked excitatory postsynaptic potentials in some types were rectified, suggesting that they provide inputs to the non-linear ganglion cells. Visual signalling from the photoreceptors was mediated exclusively through the kainate receptors in the transient OFF bipolar cells, whereas both kainate and AMPA receptors contributed in the other cells. This study demonstrates, for the first time, that parallel visual encoding starts at the OFF bipolar cells in a type-specific manner.

ABSTRACT

The retina is the entrance to the visual system, which receives various kinds of image signals and forms multiple encoding pathways. The second-order retinal neurons, the bipolar cells, are thought to initiate multiple neural streams by encoding various visual signals in different types of cells. However, the functions of each bipolar cell type have not been fully understood. We investigated whether OFF bipolar cells encode visual signals in a type-dependent manner. We recorded the changes in the bipolar cell voltage in response to two input functions: step and sinusoidal light stimuli. Type 1 and 4 OFF bipolar cells were sustained cells and responded to sinusoidal stimuli over a broad range of frequencies. Type 2 and 3a cells were transient and exhibited band-pass filtering. Type 3b cells were in the middle of these two groups. The distinct temporal responses might be attributed to different types of glutamate receptors. We examined the AMPA and kainate glutamate receptor composition in each bipolar cell type. The light responses in the transient OFF bipolar cells were exclusively mediated by kainate receptors. Although the kainate receptors mediated the light responses in the sustained cells, the AMPA receptors also mediated a portion of the responses in sustained cells. Furthermore, we found that some types of cells were rectified more than other types. Taken together, we found that the OFF bipolar cells encode diverse temporal image signals in a type-dependent manner, confirming that each type of OFF bipolar cell initiates diverse temporal visual processing in parallel.

Real-time emulator for reproducing graded potentials in vertebrate retina

In most parts of the retina, neuronal circuits process visual signals represented by slowly changing membrane potentials, or so-called graded potentials. A feasible approach to speculate about the functional roles of retinal neuronal circuits is to reproduce the graded potentials of retinal neurons in response to natural scenes. In this study, we developed a simulation platform for reproducing graded potentials with the following features: real-time reproduction of retinal neural activities in response to natural scenes, a configurable model structure, and compact hardware. The spatio-temporal properties of neurons were emulated efficiently by a mixed analog-digital architecture that consisted of analog resistive networks and a field-programmable gate array. The neural activities on sustained and transient pathways were emulated from 128 × 128 inputs at 200 frames per second.

Responses of recurrent nets of asymmetric ON and OFF cells

A neural field model of ON and OFF cells with all-to-all inhibitory feedback is investigated. External spatiotemporal stimuli drive the ON and OFF cells with, respectively, direct and inverted polarity. The dynamic differences between networks built of ON and OFF cells ("ON/OFF") and those having only ON cells ("ON/ON") are described for the general case where ON and OFF cells can have different spontaneous firing rates; this asymmetric case is generic. Neural responses to nonhomogeneous static and time-periodic inputs are analyzed in regimes close to and away from self-oscillation. Static stimuli can cause oscillatory behavior for certain asymmetry levels. Time-periodic stimuli expose dynamical differences between ON/OFF and ON/ON nets. Outside the stimulated region, we show that ON/OFF nets exhibit frequency doubling, while ON/ON nets cannot. On the other hand, ON/ON networks show antiphase responses between stimulated and unstimulated regions, an effect that does not rely on specific receptive field circuitry. An analysis of the resonance properties of both net types reveals that ON/OFF nets exhibit larger response amplitude. Numerical simulations of the neural field models agree with theoretical predictions for localized static and time-periodic forcing. This is also the case for simulations of a network of noisy integrate-and-fire neurons. We finally discuss the application of the model to the electrosensory system and to frequency-doubling effects in retina.

Motion processing with wide-field neurons in the retino-tecto-rotundal pathway

The retino-tecto-rotundal pathway is the main visual pathway in non-mammalian vertebrates and has been found to be highly involved in visual processing. Despite the extensive receptive fields of tectal and rotundal wide-field neurons, pattern discrimination tasks suggest a system with high spatial resolution. In this paper, we address the problem of how global processing performed by motion-sensitive wide-field neurons can be brought into agreement with the concept of a local analysis of visual stimuli. As a solution to this problem, we propose a firing-rate model of the retino-tecto-rotundal pathway which describes how spatiotemporal information can be organized and retained by tectal and rotundal wide-field neurons while processing Fourier-based motion in absence of periodic receptive-field structures. The model incorporates anatomical and electrophysiological experimental data on tectal and rotundal neurons, and the basic response characteristics of tectal and rotundal neurons to moving stimuli are captured by the model cells. We show that local velocity estimates may be derived from rotundal-cell responses via superposition in a subsequent processing step. Experimentally testable predictions which are both specific and characteristic to the model are provided. Thus, a conclusive explanation can be given of how the retino-tecto-rotundal pathway enables the animal to detect and localize moving objects or to estimate its self-motion parameters.

Hemoglobin senses body temperature

When aspirating human red blood cells (RBCs) into 1.3 mum pipettes (DeltaP = -2.3 kPa), a transition from blocking the pipette below a critical temperature T(c) = 36.3 +/- 0.3 degrees C to passing it above the T(c) occurred (micropipette passage transition). With a 1.1 mum pipette no passage was seen which enabled RBC volume measurements also above T(c). With increasing temperature RBCs lost volume significantly faster below than above a T(c) = 36.4 +/- 0.7 (volume transition). Colloid osmotic pressure (COP) measurements of RBCs in autologous plasma (25 degrees C < or = T < or = 39.5 degrees C) showed a T (c) at 37.1 +/- 0.2 degrees C above which the COP rapidly decreased (COP transition). In NMR T(1)-relaxation time measurements, the T(1) of RBCs in autologous plasma changed from a linear (r = 0.99) increment below T(c) = 37 +/- 1 degrees C at a rate of 0.023 s/K into zero slope above T(c) (RBC T(1) transition).

IN CONCLUSION

An amorphous hemoglobin-water gel formed in the spherical trail, the residual partial sphere of the aspirated RBC. At T(c), a sudden fluidization of the gel occurs. All changes mentioned above happen at a distinct T(c) close to body temperature. The T(c) is moved +0.8 degrees C to higher temperatures when a D(2)O buffer is used. We suggest a mechanism similar to a "glass transition" or a "colloidal phase transition". At T(c), the stabilizing Hb bound water molecules reach a threshold number enabling a partial Hb unfolding. Thus, Hb senses body temperature which must be inscribed in the primary structure of hemoglobin and possibly other proteins.

Virtual Retina: a biological retina model and simulator, with contrast gain control

We propose a new retina simulation software, called Virtual Retina, which transforms a video into spike trains. Our goal is twofold: Allow large scale simulations (up to 100,000 neurons) in reasonable processing times and keep a strong biological plausibility, taking into account implementation constraints. The underlying model includes a linear model of filtering in the Outer Plexiform Layer, a shunting feedback at the level of bipolar cells accounting for rapid contrast gain control, and a spike generation process modeling ganglion cells. We prove the pertinence of our software by reproducing several experimental measurements from single ganglion cells such as cat X and Y cells. This software will be an evolutionary tool for neuroscientists that need realistic large-scale input spike trains in subsequent treatments, and for educational purposes.

A numerical study of red-green colour opponent properties in the primate retina

It remains an important question whether neural function is mediated entirely by its tailored circuitry. A persistent debate in retinal colour vision is whether the centre and the surround of a ganglion cell receptive field receive dominant inputs either from L or M cones in an antagonistic manner (the selective wiring model) or mixed inputs (the mixed wiring model). Despite many anatomical, physiological and psychophysical experiments, a decisive conclusion has not been reached. An in-depth examination of what the pure mixed wiring mechanisms predicts is therefore important. These two models make different predictions both for the fovea and for the peripheral retina. Recently, a dynamic cellular model of the primate fovea was developed [Momiji et al. (2006) Vis. Res., 46, 365-381]. Unlike earlier models, it explicitly incorporates spatial non-uniformities, such as the random arrangement of L and M cones. Here, a related model is developed for the peripheral retina by incorporating anatomically reasonable degrees of convergence between cones, bipolar cells and ganglion cells. These two models, in which selective wiring mechanisms are absent, are applied to describe both foveal and peripheral colour vision. In numerical simulations, peripheral ganglion cells are less colour sensitive than foveal counterparts, but none-the-less display comparative sensitivities. Furthermore, peripheral colour sensitivity increases with temporal frequency, relative to foveal sensitivity. These results are congruent with recent physiological experiments.

Complex Spike-Event Pattern of Transienton-offRetinal Ganglion Cells

on-off transient ganglion cells of the turtle retina show distinct spike-event patterns in response to abrupt intensity changes, such as during saccadic eye movements. These patterns consist of two main spike events, with the latency of each event showing a systematic dependency on stimulus contrast. Whereas the latency of the first event decreases monotonically with increasing contrast, as expected, the second event shows the shortest latency for intermediate contrasts and a longer latency for high and low contrasts. These spike-event patterns improve the discrimination of different light-intensity transitions based on ensemble responses of the on-off transient ganglion cell subpopulation. Although the discrimination results are far better than chance using either spike counts or latencies of the first spikes, they are further improved by using properties of the second spike event. The best classification results are obtained when spike rates and latencies of both events are considered in combination. Thus spike counts and temporal structure of retinal ganglion cells carry complementary information about the stimulus condition, and thus spike-event patterns could be an important aspect of retinal coding. To investigate the origin of the spike-event patterns in retinal ganglion cells, two computational models of retinal processing are compared. A linear–nonlinear model consisting of separate filters for on and off response components fails to reproduce the spike-event patterns. A more complex cascade filter model, however, accurately predicts the timing of the spike events by using a combination of gain control loop and spike rate adaptation.

The temporal structure of transient ON/OFF ganglion cell responses and its relation to intra-retinal processing

A subpopulation of transient ON/OFF ganglion cells in the turtle retina transmits changes in stimulus intensity as series of distinct spike events. The temporal structure of these event sequences depends systematically on the stimulus and thus carries information about the preceding intensity change. To study the spike events' intra-retinal origins, we performed extracellular ganglion cell recordings and simultaneous intracellular recordings from horizontal and amacrine cells. Based on these data, we developed a computational retina model, reproducing spike event patterns with realistic intensity dependence under various experimental conditions. The model's main features are negative feedback from sustained amacrine onto bipolar cells, and a two-step cascade of ganglion cell suppression via a slow and a fast transient amacrine cell. Pharmacologically blocking glycinergic transmission results in disappearance of the spike event sequence, an effect predicted by the model if a single connection, namely suppression of the fast by the slow transient amacrine cell, is weakened. We suggest that the slow transient amacrine cell is glycinergic, whereas the other types release GABA. Thus, the interplay of amacrine cell mediated inhibition is likely to induce distinct temporal structure in ganglion cell responses, forming the basis for a temporal code.

Nonlinear information processing in a model sensory system

Understanding the mechanisms by which sensory neurons encode and decode information remains an important goal in neuroscience. We quantified the performance of optimal linear and nonlinear encoding models in a well-characterized sensory system: the electric sense of weakly electric fish. We show that linear encoding models generally perform better under spatially localized stimulation than under spatially diffuse stimulation. Through pharmacological blockade of feedback input and spatial saturation of the receptive field center, we show that there is significantly less synaptic noise under spatially diffuse stimuli as compared with spatially localized stimuli. Modeling results suggest that pyramidal cells nonlinearly encode sensory information through shunting in their dendrites and clarify the influence of synaptic noise on the performance of linear encoding models. Finally, we used information theory to quantify the performance of linear decoders. While the optimal linear decoder for spatially localized stimuli could capture 60% of the information in pyramidal cell spike trains, the optimal linear decoder for spatially diffuse stimuli could only capture 40% of the information. These results show that nonlinear decoders are necessary to fully access information in pyramidal cell spike trains, and we discuss potential mechanisms by which higher-order neurons could decode this information.

Numerical study of short-term afterimages and associate properties in foveal vision

A cellular model of the primate retina has been developed. Unlike existing models, it incorporates spatial non-uniformities, such as the random arrangement of L and M cones, and the radial dilation with eccentricity. Based on a population of ganglion cell activities, colour-image representation is modelled with the luminance and the R-G opponent channels. The developed model reproduces experimentally known properties in temporal and spatial vision. Furthermore, spatio-temporally coupled properties such as transition from positive to negative phases in an afterimage, are recapped. In colour vision, the model can explain the insensitivity in our colour perception to the L/M cone ratio.

The influence of the corticothalamic projection on responses in thalamus and cortex

We review results on the in vivo properties of neurons in the dorsal lateral geniculate nucleus (dLGN) that receives its afferent input from the retina and projects to the visual cortex. In addition, the dLGN receives input from the brain stem and from a rather strong corticothalamic back-projection, which originates in layer 6 of the visual cortex. We compare the behaviour of dLGN cells during spontaneous changes of the frequency contents of the electroencephalograph (EEG) (which are mainly related to a changing brain stem influence), with those that are obtained when experimentally silencing the corticothalamic feedback. The spatial and temporal response properties of dLGN cells are compared during these two conditions, and we report that the neurons behave similarly during a synchronized EEG state and during inactive corticothalamic feedback. In both situations, dLGN cells are rather phasic and their remaining tonic activity is temporally dispersed, indicating a hyperpolarizing effect. By means of a novel method, we were able to chronically eliminate a large proportion of the corticothalamic projection neurons from the otherwise intact cortex. In this condition, we found that cortical cells also lose their EEG specific response differences but, in this instance, probably due to a facilitatory (depolarizing) plasticity reaction of the remaining network.