Retinal tissue thickness is reduced in diabetic peripheral neuropathy

Aim Retinal tissue integrity in relation to diabetic neuropathy is not known. The aim of this study was to investigate retinal tissue thickness in relation to diabetic peripheral neuropathy (DPN) with and without diabetic retinopathy (DR). Methods Full retinal thickness at the parafoveal and perifoveal macula and neuro-retinal thickness around the optic nerve head (ONH) and at the macula was examined using spectral domain optical coherence tomography. The eye on the hand-dominant side of 85 individuals with type 1 diabetes and 66 individuals with type 2 diabetes, with or without DR and DPN, were compared to the eyes (n=45) of age-matched non-diabetic controls. Diabetic neuropathy was defined as Neuropathy Disability Score (NDS) ≥3 on a scale of 0-10. A general linear model was used to examine the relationship between diabetic neuropathy and foveal, parafoveal and perifoveal retinal thickness and neuro-retinal thickness, in relation to DR status, age, gender, HbA1c levels and duration of diabetes. A p-value of <0.05 was considered statistically significant. Results Perifoveal retinal thickness is reduced with increasing severity of neuropathy, especially in the inferior hemisphere (p=0.004); this effect was not related to age (p=0.088). For every unit increase in NDS score, the inferior perifoveal retinal thickness reduced by 1.64 μm. Neuro-retinal thickness around the ONH decreased with increasing severity of neuropathy (p<0.014 for average and hemisphere thicknesses); for every unit increase in NDS, neuro-retinal thickness around the ONH reduced by 1.23 μm. Retinal thickness in the parafovea was increased in the absence of DR (p<0.017 for average and hemisphere thicknesses). Neuro-retinal thickness at the macula was inversely related to age alone (p<0.001). All retinal parameters, except the inferior perifovea, reduced with advancing age (p<0.007 for all). Conclusions Diabetic neuropathy is associated with changes in full retinal thickness and neuro-retinal layers. This may represent a second threat to vision integrity, in addition to the better-characterised retinopathy. This study provides new knowledge about the anatomical aspects of the retinal tissue in relation to neuropathy and retinopathy.

Temporal characteristics of melanopsin inputs to the human pupil light reflex

Rods, cones and melanopsin containing intrinsically photosensitive retinal ganglion cells (ipRGCs) operate in concert to regulate pupil diameter. The temporal properties of intrinsic ipRGC signalling are distinct to those of rods and cones, including longer latencies and sustained signalling after light offset. We examined whether the melanopsin mediated post-illumination pupil response (PIPR) and pupil constriction were dependent upon the inter-stimulus interval (ISI) between successive light pulses and the temporal frequency of sinusoidal light stimuli. Melanopsin excitation was altered by variation of stimulus wavelength (464 nm and 638 nm lights) and irradiance (11.4 and 15.2 log photons cm(-2) s(-1)). We found that 6s PIPR amplitude was independent of ISI and temporal frequency for all melanopsin excitation levels, indicating complete summation. In contrast to the PIPR, the maximum pupil constriction increased with increasing ISI with high and low melanopsin excitation, but time to minimum diameter was slower with high melanopsin excitation only. This melanopsin response to briefly presented pulses (16 and 100 ms) slows the temporal response of the maximum pupil constriction. We also demonstrate that high melanopsin excitation attenuates the phasic peak-trough pupil amplitude compared to conditions with low melanopsin excitation, indicating an interaction between inner and outer retinal inputs to the pupil light reflex. We infer that outer retina summation is important for rapidly controlling pupil diameter in response to short timescale fluctuations in illumination and may occur at two potential sites, one that is presynaptic to extrinsic photoreceptor input to ipRGCs, or another within the pupil control pathway if ipRGCs have differential temporal tuning to extrinsic and intrinsic signalling.

The Post-Illumination Pupil Response (PIPR)

Purpose The post-illumination pupil response (PIPR) has been quantified using four metrics, but the spectral sensitivity of only one is known; here we determine the other three. To optimize the human PIPR measurement, we determine the protocol producing the largest PIPR, the duration of the PIPR, and the metric(s) with the lowest coefficient of variation. Methods The consensual pupil light reflex (PLR) was measured with a Maxwellian view pupillometer. - Experiment 1: Spectral sensitivity of four PIPR metrics [plateau, 6 s, area under curve (AUC) early and late recovery] was determined from a criterion PIPR to a 1s pulse and fitted with Vitamin A1 nomogram (λmax = 482nm). - Experiment 2: The PLR was measured as a function of three stimulus durations (1s, 10s, 30s), five irradiances spanning low to high melanopsin excitation levels (retinal irradiance: 9.8 to 14.8 log quanta.cm-2.s-1), and two wavelengths, one with high (465nm) and one with low (637nm) melanopsin excitation. Intra and inter-individual coefficients of variation (CV) were calculated. Results The melanopsin (opn4) photopigment nomogram adequately describes the spectral sensitivity of all four PIPR metrics. The PIPR amplitude was largest with 1s short wavelength pulses (≥ 12.8 log quanta.cm-2.s-1). The plateau and 6s PIPR showed the least intra and inter-individual CV (≤ 0.2). The maximum duration of the sustained PIPR was 83.0±48.0s (mean±SD) for 1s pulses and 180.1±106.2s for 30s pulses (465nm; 14.8 log quanta.cm-2.s-1). Conclusions All current PIPR metrics provide a direct measure of the intrinsic melanopsin photoresponse. To measure progressive changes in melanopsin function in disease, we recommend that the PIPR be measured using short duration pulses (e.g., ≤ 1s) with high melanopsin excitation and analyzed with plateau and/or 6s metrics. Our PIPR duration data provide a baseline for the selection of inter-stimulus intervals between consecutive pupil testing sequences.

Melanopsin mediated post-illumination pupil response in early age-related macular degeneration

Purpose To determine whether melanopsin expressing intrinsically photosensitive Retinal Ganglion Cell (ipRGC) inputs to the pupil light reflex (PLR) are affected in early age-related macular degeneration (AMD). Methods The PLR was measured in 40 participants (20 early AMD and 20 age-matched controls) using a custom-built Maxwellian-view pupillometer. Sinusoidal stimuli (0.5 Hz, 11.9 s duration, 35.6° diameter) were presented to the study eye and the consensual pupil response was measured for stimuli with high melanopsin excitation (464nm; blue) and with low melanopsin excitation (638 nm; red) that biased activation to the outer retina. Two melanopsin PLR metrics were quantified: the Phase Amplitude Percentage (PAP) during the sinusoidal stimulus presentation and the Post-Illumination Pupil Response (PIPR). The PLR during stimulus presentation was analyzed using latency to constriction, transient pupil response and maximum pupil constriction metrics. Diagnostic accuracy was evaluated using receiver operating characteristic (ROC) curves. Results The blue PIPR was significantly less sustained in the early AMD group (p<0.001). The red PIPR was not significantly different between groups (p>0.05). The PAP and blue stimulus constriction amplitude were significantly lower in the early AMD group (p < 0.05). There was no significant difference between groups in the latency or transient amplitude for both stimuli (p>0.05). ROC analysis showed excellent diagnostic accuracy for the blue PIPR metrics (AUC>0.9). Conclusions This is the initial report that the melanopsin controlled PIPR is dysfunctional in early AMD. The non-invasive, objective measurement of the ipRGC controlled PIPR has excellent diagnostic accuracy for early AMD.

Effect of age and refractive error on the melanopsin mediated Post-Illumination Pupil Response (PIPR)

Melanopsin containing intrinsically photosensitive Retinal Ganglion cells (ipRGCs) mediate the pupil light reflex (PLR) during light onset and at light offset (the post-illumination pupil response, PIPR). Recent evidence shows that the PLR and PIPR can provide non-invasive, objective markers of age-related retinal and optic nerve disease, however there is no consensus on the effects of healthy ageing or refractive error on the ipRGC mediated pupil function. Here we isolated melanopsin contributions to the pupil control pathway in 59 human participants with no ocular pathology across a range of ages and refractive errors. We show that there is no effect of age or refractive error on ipRGC inputs to the human pupil control pathway. The stability of the ipRGC mediated pupil response across the human lifespan provides a functional correlate of their robustness observed during ageing in rodent models.

GABAAα1 and GABAAρ1 subunits are expressed in cultured human RPE cells and GABAA receptor agents modify the intracellular calcium concentration.

Purpose: Gamma-aminobutyric acid A (GABAA) receptors (GABAARs), which are ionotropic receptors involving chloride channels, have been identified in various neural (e.g., mouse retinal ganglion cells) and nonneural cells (e.g., mouse lens epithelial cells) regulating the intracellular calcium concentration ([Ca(2+)]i). GABAAR β-subunit protein has been isolated in the cultured human and rat RPE, and GABAAα1 and GABAAρ1 mRNAs and proteins are present in the chick RPE. The purpose of this study was to investigate the expression of GABAAα1 and GABAAρ1, two important subunits in forming functional GABAARs, in the cultured human RPE, and further to explore whether altering receptor activation modifies [Ca(2+)]i. Methods: Human RPE cells were separately cultured from five donor eye cups. Real-time PCR, western blots, and immunofluorescence were used to test for GABAAα1 and GABAAρ1 mRNAs and proteins. The effects of the GABAAR agonist muscimol, antagonist picrotoxin, or the specific GABAAρ antagonist 1,2,5,6-tetrahydropyridin-4-yl) methylphosphinic acid (TPMPA) on [Ca(2+)]i in cultured human RPE were demonstrated using Fluo3-AM. Results: Both GABAAα1 and GABAAρ1 mRNAs and proteins were identified in cultured human RPE cells; antibody staining was mainly localized to the cell membrane and was also present in the cytoplasm but not in the nucleus. Muscimol (100 μM) caused a transient increase of the [Ca(2+)]i in RPE cells regardless of whether Ca(2+) was added to the buffer. Muscimol-induced increases in the [Ca(2+)]i were inhibited by pretreatment with picrotoxin (300 μM) or TPMPA (500 μM). Conclusions: GABAAα1 and GABAAρ1 are expressed in cultured human RPE cells, and GABAA agents can modify [Ca(2+)]i.

Molecular genetics of primary open angle glaucoma and exfoliation syndrome

Glaucoma is the second leading cause of blindness worldwide. It is a group of optic neuropathies, characterized by progressive optic nerve degeneration, excavation of the optic disc due to apoptosis of retinal ganglion cells and corresponding visual field defects. Open angle glaucoma (OAG) is a subtype of glaucoma, classified according to the age of onset into juvenile and adult- forms with a cut-off point of 40 years of age. The prevalence of OAG is 1-2% of the population over 40 years and increases with age. During the last decade several candidate loci and three candidate genes, myocilin (MYOC), optineurin (OPTN) and WD40-repeat 36 (WDR36), for OAG have been identified. Exfoliation syndrome (XFS), age, elevated intraocular pressure and genetic predisposition are known risk factors for OAG. XFS is characterized by accumulation of grayish scales of fibrillogranular extracellular material in the anterior segment of the eye. XFS is overall the most common identifiable cause of glaucoma (exfoliation glaucoma, XFG). In the past year, three single nucleotide polymorphisms (SNPs) on the lysyl oxidase like 1 (LOXL1) gene have been associated with XFS and XFG in several populations. This thesis describes the first molecular genetic studies of OAG and XFS/XFG in the Finnish population. The role of the MYOC and OPTN genes and fourteen candidate loci was investigated in eight Finnish glaucoma families. Both candidate genes and loci were excluded in families, further confirming the heterogeneous nature of OAG. To investigate the genetic basis of glaucoma in a large Finnish family with juvenile and adult onset OAG, we analysed the MYOC gene in family members. Glaucoma associated mutation (Thr377Met) was identified in the MYOC gene segregating with the disease in the family. This finding has great significance for the family and encourages investigating the MYOC gene also in other Finnish OAG families. In order to identify the genetic susceptibility loci for XFS, we carried out a genome-wide scan in the extended Finnish XFS family. This scan produced promising candidate locus on chromosomal region 18q12.1-21.33 and several additional putative susceptibility loci for XFS. This locus on chromosome 18 provides a solid starting point for the fine-scale mapping studies, which are needed to identify variants conferring susceptibility to XFS in the region. A case-control and family-based association study and family-based linkage study was performed to evaluate whether SNPs in the LOXL1 gene contain a risk for XFS, XFG or POAG in the Finnish patients. A significant association between the LOXL1 gene SNPs and XFS and XFG was confirmed in the Finnish population. However, no association was detected with POAG. Probably also other genetic and environmental factors are involved in the pathogenesis of XFS and XFG.

Molecular genetics of Usher syndrome -inherited deafness and blindness

Usher syndrome (USH) is an inherited blindness and deafness disorder with variable vestibular dysfunction. The syndrome is divided into three subtypes according to the progression and severity of clinical symptoms. The gene mutated in Usher syndrome type 3 (USH3), clarin 1 (CLRN1), was identified in Finland in 2001 and two mutations were identified in Finnish patients at that time. Prior to this thesis study, the two CLRN1 gene mutations were the only USH mutations identified in Finnish USH patients. To further clarify the Finnish USH mutation spectrum, all nine USH genes were studied. Seven mutations were identified: one was a previously known mutation in CLRN1, four were novel mutations in myosin VIIa (MYO7A) and two were a novel and a previously known mutation in usherin (USH2A). Another aim of this thesis research was to further study the structure and function of the CLRN1 gene, and to clarify the effects of mutations on protein function. The search for new splice variants resulted in the identification of eight novel splice variants in addition to the three splice variants that were already known prior to this study. Studies of the possible promoter regions for these splice variants showed the most active region included the 1000 bases upstream of the translation start site in the first exon of the main three exon splice variant. The 232 aa CLRN1 protein encoded by the main (three-exon) splice variant was transported to the plasma membrane when expressed in cultured cells. Western blot studies suggested that CLRN1 forms dimers and multimers. The CLRN1 mutant proteins studied were retained in the endoplasmic reticulum (ER) and some of the USH3 mutations caused CLRN1 to be unstable. During this study, two novel CLRN1 sequence alterations were identified and their pathogenicity was studied with cell culture protein expression. Previous studies with mice had shown that Clrn1 is expressed in mouse cochlear hair cells and spiral ganglion cells, but the expression profile in mouse retina remained unknown. The Clrn1 knockout mice display cochlear cell disruption/death, but do not have a retinal phenotype. The zebrafish, Danio rerio, clrn1 was found to be expressed in hair cells associated with hearing and balance. Clrn1 expression was also found in the inner nuclear layer (INL), photoreceptor layer and retinal pigment epithelium layer (RPE) of the zebrafish retina. When Clrn1 production was knocked down with injected morpholino oligonucleotides (MO) targeting Clrn1 translation or correct splicing, the zebrafish larvae showed symptoms similar to USH3 patients. These larvae had balance/hearing problems and reduced response to visual stimuli. The knowledge this thesis research has provided about the mutations in USH genes and the Finnish USH mutation spectrum are important in USH patient diagnostics. The extended information about the structure and function of CLRN1 is a step further in exploring USH3 pathogenesis caused by mutated CLRN1 as well as a step in finding a cure for the disease.

GATA Factors Regulate Inner Ear Development and Midbrain Neurogenesis

The zinc-finger transcription factors GATA2 and GATA3 in vertebrates belong to the six-member family that are essential regulators in the development of various organs. The aim of this study was to gain new information of the roles of GATA2 and GATA3 in inner ear morphogenesis and of the function of GATA2 in neuronal fate specification in the midbrain using genetically modified mouse and chicken embryos as models. A century ago the stepwise process of inner ear epithelial morphogenesis was described, but the molecular players regulating the cellular differentiation of the otic epithelium are still not fully resolved. This study provided novel data on GATA factor roles in several developmental processes during otic development. The expression analysis in chicken suggested that GATA2 and GATA3 possess redundant roles during otic cup and vesicle formation, but complementary cell-type specific functions during vestibular and cochlear morphogenesis. The comparative analysis between mouse and chicken Gata2 and Gata3 expression revealed many conserved aspects, especially during later stages of inner ear development, while the expression was more divergent at early stages. Namely, expression of both Gata genes was initiated earlier in chicken than mouse otic epithelium relative to the morphogenetic stages. Likewise, important differences concerning Gata3 expression in the otic cup epithelium were detected between mouse and chicken, suggesting that distinct molecular mechanisms regulate otic vesicle closure in different vertebrate species. Temporally distinct Gata2 and Gata3 expression was also found during otic ganglion formation in mouse and chicken. Targeted inactivation of Gata3 in mouse embryos caused aberrant morphology of the otic vesicle that in severe cases was disrupted into two parts, a dorsal and a ventral vesicle. Detailed analyses of Gata3 mutant embryos unveiled a crucial role for GATA3 in the initial inner ear morphogenetic event, the invagination of the otic placode. A large-scale comparative expression analysis suggested that GATA3 could control cell adhesion and motility in otic epithelium, which could be important for early morphogenesis. GATA3 was also identified as the first factor to directly regulate Fgf10 expression in the otic epithelium and could thus influence the development of the semicircular ducts. Despite the serious problems in the early inner ear development, the otic sensory fate establishment and some vestibular hair cell differentiation was observable in pharmacologically rescued Gata3-/- embryos. Cochlear sensory differentiation was, however, completely blocked so that no auditory hair cells were detected. In contrast to the early morphogenetic phenotype in Gata3-/- mutants, conditional inactivation of Gata2 in mouse embryos resulted in a relatively late growth defect of the three semicircular ducts. GATA2 was required for the proliferation of the vestibular nonsensory epithelium to support growing of the three ducts. Concurrently, with the role in epithelial semicircular ducts, GATA2 was also required for the mesenchymal cell clearance from the vestibular perilymphatic region between the membranous labyrinth and bony capsule. The gamma-aminobutyric acid-secreting (GABAergic) neurons in the midbrain are clinically relevant since they contribute to fear, anxiety, and addiction regulation. The molecular mechanisms regulating the GABAergic neuronal development, however, are largely unknown. Using tissue-specific mutagenesis in mice, GATA2 was characterized as a critical determinant of the GABAergic neuronal fate in the midbrain. In Gata2-deficient mouse midbrain, GABAergic neurons were not produced, instead the Gata2-mutant cells acquired a glutamatergic neuronal phenotype. Gain-of-function experiments in chicken also revealed that GATA2 was sufficient to induce GABAergic differentiation in the midbrain.

l-pGlu-(2-propyl)-l-His-l-ProNH2 attenuates 4-aminopyridine-induced epileptiform activity and sodium current: a possible action of new thyrotropin-releasing hormone analog for its anticonvulsant potential

L-PGlu-(2-proPyl)-L-His-L-ProNH(2) (NP-647) is a CNS active thyrotropin-releasing hormone (TRH) analog with potential application in various CNS disorders including seizures. In the present study, mechanism of action for protective effect of NP-647 was explored by studying role of NP-647 on epileptiform activity and sodium channels by using patch-clamp methods. Epileptiform activity was induced in subicular pyramidal neurons of hippocampal slice of rat by perfusing 4-aminopyridine (4-AP) containing Mg(+2)-free normal artificial cerebrospinal fluid (nACSF). Increase in mean firing frequency was observed after perfusion of 4-AP and zero Mg(+2) (2.10+/-0.47 Hz) as compared with nACSF (0.12+/-0.08 Hz). A significant decrease in mean firing frequency (0.61+/-0.22 Hz), mean frequency of epileptiform events (0.03+/-0.02 Hz vs. 0.22+/-0.05 Hz of 4-AP+0 Mg), and average number of action potentials in paroxysmal depolarization shift-burst (2.54+/-1.21 Hz vs. 8.16+/-0.88 Hz of 4-AP +0 Mg) was observed. A significant reduction in peak dV/dt (246+/-19 mV ms(-1) vs. 297 18 mV ms-1 of 4-AP+0 Mg) and increase (1.332+/-0.018 ms vs. 1.292+/-0.019 ms of 4-AP+0 Mg) in time required to reach maximum depolarization were observed indicating role of sodium channels. Concentration-dependent depression of sodium current was observed after exposure to dorsal root ganglion neurons to NP-647. NP-647 at different concentrations (1, 3, and 10 mu M) depressed sodium current (15+/-0.5%, 50+/-2.6%, and 75+/-0.7%, respectively). However, NP-647 did not show change in the peak sodium current in CNa18 cells. Results of present study demonstrated potential of NP-647 in the inhibition of epileptiform activity by inhibiting sodium channels indirectly. (C) 2011 IBRO. Published by Elsevier Ltd. All rights reserved.

Polymer optoelectronic structures for retinal prosthesis

This commentary highlights the effectiveness of optoelectronic properties of polymer semiconductors based on recent results emerging from our laboratory, where these materials are explored as artificial receptors for interfacing with the visual systems. Organic semiconductors based polymer layers in contact with physiological media exhibit interesting photophysical features, which mimic certain natural photoreceptors, including those in the retina. The availability of such optoelectronic materials opens up a gateway to utilize these structures as neuronal interfaces for stimulating retinal ganglion cells. In a recently reported work entitled ``A polymer optoelectronic interface provides visual cues to a blind retina,'' we utilized a specific configuration of a polymer semiconductor device structure to elicit neuronal activity in a blind retina upon photoexcitation. The elicited neuronal signals were found to have several features that followed the optoelectronic response of the polymer film. More importantly, the polymer-induced retinal response resembled the natural response of the retina to photoexcitation. These observations open up a promising material alternative for artificial retina applications.

A Disulfide Stabilized beta-Sandwich Defines the Structure of a New Cysteine Framework M-Superfamily Conotoxin

The structure of a new cysteine framework (-C-CC-C-C-C) ``M''-superfamily conotoxin, Mo3964, shows it to have a beta-sandwich structure that is stabilized by inter-sheet cross disulfide bonds. Mo3964 decreases outward K+ currents in rat dorsal root ganglion neurons and increases the reversal potential of the Na(V)1.2 channels. The structure of Mo3964 (PDB ID: 2MW7) is constructed from the disulfide connectivity pattern, i.e., 1-3, 2-5, and 4-6, that is hitherto undescribed for the ``M''-superfamily conotoxins. The tertiary structural fold has not been described for any of the known conus peptides. NOE (549), dihedral angle (84), and hydrogen bond (28) restraints, obtained by measurement of (h3)J(NC') scalar couplings, were used as input for structure calculation. The ensemble of structures showed a backbone root mean square deviation of 0.68 +/- 0.18 angstrom, with 87% and 13% of the backbone dihedral (phi, psi) angles lying in the most favored and additional allowed regions of the Ramachandran map. The conotoxin Mo3964 represents a new bioactive peptide fold that is stabilized by disulfide bonds and adds to the existing repertoire of scaffolds that can be used to design stable bioactive peptide molecules.

Design,optimization and in vivo evaluation of non-viral vectors for gene therapy. Applications in ocular disorders

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Wireless parylene-based retinal implant

The degeneration of the outer retina usually causes blindness by affecting the photoreceptor cells. However, the ganglion cells, which consist of optic nerves, on the middle and inner retina layers are often intact. The retinal implant, which can partially restore vision by electrical stimulation, soon becomes a focus for research. Although many groups worldwide have spent a lot of effort on building devices for retinal implant, current state-of-the-art technologies still lack a reliable packaging scheme for devices with desirable high-density multi-channel features. Wireless flexible retinal implants have always been the ultimate goal for retinal prosthesis. In this dissertation, the reliable packaging scheme for a wireless flexible parylene-based retinal implants has been well developed. It can not only provide stable electrical and mechanical connections to the high-density multi-channel (1000+ channels on 5 mm × 5 mm chip area) IC chips, but also survive for more than 10 years in the human body with corrosive fluids.

The device is based on a parylene-metal-parylene sandwich structure. In which, the adhesion between the parylene layers and the metals embedded in the parylene layers have been studied. Integration technology for high-density multi-channel IC chips has also been addressed and tested with dummy and real 268-channel and 1024-channel retinal IC chips. In addition, different protection schemes have been tried in application to IC chips and discrete components to gain the longest lifetime. The effectiveness has been confirmed by the accelerated and active lifetime soaking test in saline solution. Surgical mockups have also been designed and successfully implanted inside dog's and pig's eyes. Additionally, the electrodes used to stimulate the ganglion cells have been modified to lower the interface impedance and shaped to better fit the retina. Finally, all the developed technologies have been applied on the final device with a dual-metal-layer structure.

Nonlinear dynamic transfer functions for certain retinal neuronal systems

The applicability of the white-noise method to the identification of a nonlinear system is investigated. Subsequently, the method is applied to certain vertebrate retinal neuronal systems and nonlinear, dynamic transfer functions are derived which describe quantitatively the information transformations starting with the light-pattern stimulus and culminating in the ganglion response which constitutes the visually-derived input to the brain. The retina of the catfish, Ictalurus punctatus, is used for the experiments.

The Wiener formulation of the white-noise theory is shown to be impractical and difficult to apply to a physical system. A different formulation based on crosscorrelation techniques is shown to be applicable to a wide range of physical systems provided certain considerations are taken into account. These considerations include the time-invariancy of the system, an optimum choice of the white-noise input bandwidth, nonlinearities that allow a representation in terms of a small number of characterizing kernels, the memory of the system and the temporal length of the characterizing experiment. Error analysis of the kernel estimates is made taking into account various sources of error such as noise at the input and output, bandwidth of white-noise input and the truncation of the gaussian by the apparatus.

Nonlinear transfer functions are obtained, as sets of kernels, for several neuronal systems: Light → Receptors, Light → Horizontal, Horizontal → Ganglion, Light → Ganglion and Light → ERG. The derived models can predict, with reasonable accuracy, the system response to any input. Comparison of model and physical system performance showed close agreement for a great number of tests, the most stringent of which is comparison of their responses to a white-noise input. Other tests include step and sine responses and power spectra.

Many functional traits are revealed by these models. Some are: (a) the receptor and horizontal cell systems are nearly linear (small signal) with certain "small" nonlinearities, and become faster (latency-wise and frequency-response-wise) at higher intensity levels, (b) all ganglion systems are nonlinear (half-wave rectification), (c) the receptive field center to ganglion system is slower (latency-wise and frequency-response-wise) than the periphery to ganglion system, (d) the lateral (eccentric) ganglion systems are just as fast (latency and frequency response) as the concentric ones, (e) (bipolar response) = (input from receptors) - (input from horizontal cell), (f) receptive field center and periphery exert an antagonistic influence on the ganglion response, (g) implications about the origin of ERG, and many others.

An analytical solution is obtained for the spatial distribution of potential in the S-space, which fits very well experimental data. Different synaptic mechanisms of excitation for the external and internal horizontal cells are implied.