A dynamic model of a two-synapse feedback loop in the vertebrate retina

The theoretical properties of synapses such as those in the retina which operate on graded potentials are developed using work on tetrodotoxin-treated synapses as a basis. A linearized model of a two-synapse negative feedback loop analogous to the bipolaramacrine feedback loop in the retina possesses a frequency response which developes an increasingly prominent resonance peak at higher input levels and under some circumstances shows instability. Psychophysical studies have shown that the visual system also exhibits this behaviour suggestive of progressive underdamping in a harmonic oscillator. Evidence in favor of the hypothesis that resonance originates in the loop is presented, the conclusions being that the loop functions to tune the retina to a range of temporal frequencies.Symbol Table V millivolts depolarisation relative to resting membrane potential - V _n , V _out pre-synaptic, post-synaptic depolarisation respectively - V _e , V _i reversal potential or e.m.f. of post-synaptic battery of excitatory, inhibitory synapses respectively - V _out (max) maximal post-synaptic depolarisation defined by Eq.(10c) - V ₀ input depolarisation for feedback loop - depolarisation potential normalised with respect to V _out(max) - I milliamperes of depolarising current - I _s post-synaptic membrane current - I _c cable current - I ₀ input depolarising current for feedback loop - I _max maximal physiological value for I ₀ =V _e ·G ₀ - i depolarising current normalised with respect to I_max - e reversal potential normalised with respect to V _e - r _i specific resistivity of internal medium - R _m membrane resistance - C _m membrane capacitance - cable space constant = R _m /2R _i - g ₀ characteristic cable conductance = 2/R _m ·R _i - G conductance of post-synaptic membrane - G _s maximal post-synaptic membrane conductance - g fraction of receptors occupied by transmitter = G/G _s - r the ratio G _s/G ₀ - membrane time constant = R _m·C_m - ₁ time constant of transmitter release in response to presynaptic depolarisation [Eq. (6)] - ₂ time constant of decay of g [Eq. (7a)] - _{2 2}·[1+k·exp(b·v _in)]^–1 - k equilibrium constant for transmitter-receptor interaction [Eq. (7a)] - b constant determining increase in rate of transmitter release with pre-synaptic depolarisation [Eq. (6)] - c concentration of transmitter in synaptic cleft normalised with respect to resting concentration - H _jk (s) linearised transfer function for synaptic transmission from neurone j to neurone k - G(s) H₁₂(s) - H(s) -H₂₁(s) - F(s) linearised closed-loop transfer function - _x 2 times spatial frequency of counterphase grating pattern - the ratio (1+s)/(_x)₂ - a the product (1+r)·k - d density of bipolars per unit area     

A model for the mechanisms of sensitivity control in the submammalian vertebrate retina

A model is proposed for the mechanisms of sensitivity control at the outer and inner plexiform layers in the submammalian vertebrate retina on the basis of Werblin's results and other physiological results. The model is especially based on the following suggestions: The signal that acts to shift the bipolar curves is probably carried by horizontal cell processes extending from the surround to the center of the receptive field. Furthermore, amacrine cells carry a lateral antagonistic signal across the inner plexiform layer that affects the response properties of ganglion cells. The simulations of the model were made and the results of the ones considerably coincided with the experimental results of Werblin.     

An analogue model of the luminosity-channel in the vertebrate cone retina

A model of the vertebrate cone retina was tested with physiological stimuli. Results confirm previous findings that, except for photoreceptors, the spatial and temporal properties of simulated retinal elements conform to a linear system. The model is consistent with known physiological correlates. Tonic units detect intensity when the light spot is within the center field, while phasic units detect movement across borders of contrast. There is a dynamic balance between the tonic and phasic channels: the tonic channel is favored by a center field input voltage, while the phasic channel is favored by a surround field input voltage to bipolar cells. The ON discharge of the phasic ganglion cell is developed by the excitatory center field input to the depolarizing-center bipolar cell, which has the shortest delay, while the OFF discharge is the result of the excitatory surround field input voltage to the hyperpolarizing-center bipolar cell, which has the longest delay.     

Serotonin: A transmitter candidate in the vertebrate retina

It has been established by a combination of high performance liquid chromatographic and immunohistochemical methods that serotonin occurs in amacrine cell bodies and terminals situated in the inner plexiform layer of the frog retina, where enzymes for the synthesis of the same amine are also present. Potassium stimulation causes a release of previously accumulated radioactive serotonin by the retina. These findings support the opinion that serotonin is a retinal transmitter.     

Subsurface cisterns in the vertebrate retina

Structures identified as subsurface cisterns (SSC's) were found in retinal neurons and their processes in the Western grey squirrel, the California and 13-line ground squirrels, the South African clawed toad, and the domestic cat. The SSC's are located in amacrine, bipolar, and ganglion cells; they are connected with the rough endoplasmic reticulum and are associated with specific membrane specializations. SSC's were not seen in the Müller cells, an observation which agrees with earlier reports that these organelles do not exist in glial cells.     

GABAC receptors in the vertebrate retina

In the central nervous system (CNS), the inhibitory transmitter GABA interacts with three subtypes of GABA receptors, type A, type B, and type C. Historically, GABA receptors have been classified as either the inotropic GABA_A receptors or the metabotropic GABA_B receptors. Over the past 10 yr, studies have shown that a third class, called the GABA_C receptor, also exists. GABA_C receptors are found primarily in the vertebrate retina and to some extent in other parts of the CNS. Although GABA_A and GABA_C receptors both gate chloride channels, they are pharmacologically, molecularly, and functionally distinct. The ρ subunit of the GABA_C receptor, which has about 35% amino acid homology to GABA_A receptor subunits, was cloned from the retina and, when expressed inXenopus oocytes, has properties similar to retinal GABA_C receptors. There are probably distinct roles for GABA_C receptors in the retina, because they are found on only a subset of neurons, whereas GABA_A receptors are ubiquitous. This article reviews recent electrophysiological and molecular studies that have characterized the unique properties of GABA_C receptors and describes the roles that these receptors may play in visual information processing in the retina.     

A dynamic model of the receptive field of L-cells in the carp retina

A dynamic model of the receptive field of L2-cells in the carp retina is developed by using our experimental results on the basis of physiological and morphological evidences. Linear spatial summation is assumed in the model for the interactions among L2-cells. Linear forward and feedback loops are also assumed for the interactions between L2-cells and cones. The model has dynamic properties similar to the ones of the receptive field of L2-cells: L2-cells respond faster as the size of a light spot is enlarged and the L2-cells nearer to the center of the light spot respond faster. It is suggested that the faster responding properties of L2-cells are due to the feedback action.     

Response analysis of vertebrate retina

In a recent work (Ouztöreli, 1980) a mathematical model for studying the neural activities in a vertebrate retina has been investigated, where the basic network contains five interconnected neurons: a receptor cell, a bipolar cell, a horizontal cell, an amacrine cell, and a retinal ganglion cell. More recently, in (Ouztöreli and O'Mara, 1980) the basic network has been extended to a larger network containing twelve neurons. In both of these works, the performances of the basic and extended models were discussed under different structural and processing conditions with constant inputs by using the results of one of our earlier work (Ouztöreli, 1979). In the present paper we investigate by simulations the responses of the basic retinal network to piecewise constant and periodic inputs. The step and frequency responses of the extended retinal network will be discussed in a forthcoming paper.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 through the University of alberta     

The vertebrate retina: a model for neuronal polarization in vivo

The vertebrate retina develops rapidly from a proliferative neuroepithelium into a highly ordered laminated structure, with five distinct neuronal cell types. Like all neurons, these cells need to polarize in appropriate orientations order integrate their neuritic connections efficiently into functional networks. Its relative simplicity, amenability to in vivo imaging and experimental manipulation, as well as the opportunity to study varied cell types within a single tissue, make the retina a powerful model to uncover how neurons polarize in vivo. Here we review the progress that has been made thus far in understanding how the different retinal neurons transform from neuroepithelial cells into mature neurons, and how the orientation of polarization may be specified by a combination of pre-established intrinsic cellular polarity set up within neuroepithelial cells, and extrinsic cues acting upon these differentiating neurons.     

Lactoseries carbohydrate epitopes in the vertebrate retina

The distribution of N-acetyl-lactosamine (NALA), a cell-surface carbohydrate epitope of the lactoseries, has been studied in the retina of representative species of all vertebrate classes by light microscope immunohistochemistry. In only some species of different classes (fish, amphibia and mammals) was NALA expression detected, and in these animals the distribution showed profound interspecies variability. In fishes and amphibia in which NALA was present, patterns ranged from single immunopositive cells to homogeneous labelling of cell layers. In mammals, NALA was found only in retinas that are cone dominated (tree squirrel and primates). In the tree squirrel, there was a dense cellular staining of the photoreceptor cell layer; whereas in primates, the carbohydrate epitope occur red only on some photoreceptor cells. From these receptor cells, positi ve axons could be traced to the inner plexiform layer. In spite of the profound interspecies differences, NALA is not randomly expressed, as its exclusive expression in mammals with cone- dominated vision indicates. The suggestion of a functional relevance for NALA glycosylation of retinal cells is supported by the labelling pattern for HNK-1 in these species, which was different from the pattern found in rod-dominated mammalian retinas. This revised version was published online in November 2006 with corrections to the Cover Date.     

Cell death in the developing vertebrate retina

Programmed cell death occurs naturally, as a physiological process, during the embryonic development of multicellular organisms. In the retina, which belongs to the central nervous system, at least two phases of cell death have been reported to occur during development. An early phase takes place concomitant with the processes of neurogenesis, cell migration and cell differentiation. A later phase affecting mainly neurons occurs when connections are established and synapses are formed, resulting in selective elimination of inappropriate connections. This pattern of cell death in the developing retina is common among different vertebrates. However, the timing and magnitude of retinal cell death varies among species. In addition, a precise regulation of apoptosis during retinal development has been described. Factors such as neurotrophins, among many others, and electrical activity influence the survival of retinal cells during the course of development. In this paper, we present a summary of these different aspects of programmed cell death during retinal development, and examine how these differ among different species.     

Modelling and simulation of vertebrate retina

In the present work we investigate the neuronal activities in a vertebrate retina by modelling and simulations using the results of (Oguztöreli, 1979). The basic retinal network considered here consists of interconnected five neurons: a receptor cell (rod or cone), a horizontal cell, a bipolar cell, an amacrine cell, and a retinal ganglion cell. The mathematical model for the basic network is a system of nonlinear ordinary integral differential difference equations. A number of simulations describing the dynamics of the neural activities in the basic network under different conditions are presented, actual and steady-state solutions are discussed. An algorithm is proposed for the determination of the system parameters experimentally.This work was supported by the Natural Sciences and Engineering Research Council Canada under Grant NSERCA-4345 through the University of Alberta     

Ultrastructural localization of rhodopsin in the vertebrate retina

Early work by Dewey and collaborators has shown the distribution of rhodopsin in the frog retina. We have repeated these experiments on cow and mouse eyes using antibodies specific to rhodopsin alone. Bovine rhodopsin in emulphogene was purified on an hydroxyapatite column. The purity of this reagent was established by spectrophotometric criteria, by sodium dodecyl sulfate (SDS) gel electrophoresis, and by isoelectric focusing. This rhodopsin was used as an immunoadsorbent to isolate specific antibodies from the antisera of rabbits immunized with bovine rod outer segments solubilized in 2% digitonin. The antibody so prepared was shown by immunoelectrophoresis to be in the IgG class and did not cross-react with lipid extracts of bovine rod outer segments. Papain-digested univalent antibodies (Fab) coupled with peroxidase were used to label rhodopsin in formaldehyde-fixed bovine and murine retinas. In addition to the disk membranes, the plasma membrane of the outer segment, the connecting cilium, and part of the rod inner segment membrane were labeled. We observed staining on both sides of the rod outer segment plasma membrane and the disk membrane. Discrepancies were observed between results of immunolabeling experiments and observations of membrane particles seen in freeze-cleaved specimens. Our experiments indicate that the distribution of membrane particles in freeze cleaving experiments reflects the distribution of membrane proteins. Immunolabeling, on the other hand, can introduce several different types of artifact, unless controlled with extreme care.     

Progranulin regulates neurogenesis in the developing vertebrate retina

We evaluated the expression and function of the microglia‐specific growth factor, Progranulin‐a (Pgrn‐a) during developmental neurogenesis in the embryonic retina of zebrafish. At 24 hpf pgrn‐a is expressed throughout the forebrain, but by 48 hpf pgrn‐a is exclusively expressed by microglia and/or microglial precursors within the brain and retina. Knockdown of Pgrn‐a does not alter the onset of neurogenic programs or increase cell death, however, in its absence, neurogenesis is significantly delayed—retinal progenitors fail to exit the cell cycle at the appropriate developmental time and postmitotic cells do not acquire markers of terminal differentiation, and microglial precursors do not colonize the retina. Given the link between Progranulin and cell cycle regulation in peripheral tissues and transformed cells, we analyzed cell cycle kinetics among retinal progenitors following Pgrn‐a knockdown. Depleting Pgrn‐a results in a significant lengthening of the cell cycle. These data suggest that Pgrn‐a plays a dual role during nervous system development by governing the rate at which progenitors progress through the cell cycle and attracting microglial progenitors into the embryonic brain and retina. Collectively, these data show that Pgrn‐a governs neurogenesis by regulating cell cycle kinetics and the transition from proliferation to cell cycle exit and differentiation. © 2017 The Authors. Developmental Neurobiology Published by Wiley Periodicals, Inc. Develop Neurobiol 77: 1114–1129, 2017     

Phosphoinositide 3-kinase signaling in the vertebrate retina

The phosphoinositide (PI) cycle, discovered over 50 years ago by Mabel and Lowell Hokin, describes a series of biochemical reactions that occur on the inner leaflet of the plasma membrane of cells in response to receptor activation by extracellular stimuli. Studies from our laboratory have shown that the retina and rod outer segments (ROSs) have active PI metabolism. Biochemical studies revealed that the ROSs contain the enzymes necessary for phosphorylation of phosphoinositides. We showed that light stimulates various components of the PI cycle in the vertebrate ROS, including diacylglycerol kinase, PI synthetase, phosphatidylinositol phosphate kinase, phospholipase C, and phosphoinositide 3-kinase (PI3K). This article describes recent studies on the PI3K-generated PI lipid second messengers in the control and regulation of PI-binding proteins in the vertebrate retina.     

Cytoprotection by endogenous zinc in the vertebrate retina

Our recent studies have shown that endogenous zinc, co‐released with glutamate from the synaptic terminals of vertebrate retinal photoreceptors, provides a feedback mechanism that reduces calcium entry and the concomitant vesicular release of glutamate. We hypothesized that zinc feedback may serve to protect the retina from glutamate excitotoxicity, and conducted in vivo experiments on the retina of the skate (Raja erinacea) to determine the effects of removing endogenous zinc by chelation. These studies showed that removal of zinc by injecting the zinc chelator histidine results in inner retinal damage similar to that induced by the glutamate receptor agonist kainic acid. In contrast, when an equimolar quantity of zinc followed the injection of histidine, the retinal cells were unaffected. Our results are a good indication that zinc, co‐released with glutamate by photoreceptors, provides an auto‐feedback system that plays an important cytoprotective role in the retina.

     

Molecular regulation of vertebrate retina cell fate

The specification of retinal cell fate is a multistep process that begins during early development and results from the spatio‐temporal coordination of cell cycle, cell differentiation, and morphogenesis. This review focuses on recent advances in understanding the molecular mechanisms underlying the distinct steps of retinal specification. Emphasis is placed on key regulatory events that control the multipotency of retinal progenitors, the generation of cell diversity, and the establishment of the clock that determines the ordered generation of retinal cell types. These basic studies have paved the way to the latest progress on the isolation and in vitro generation of retinal stem cells, which is presented in the light of possible therapeutic applications. Birth Defects Research (Part C) 87:284–295, 2009. © 2009 Wiley‐Liss, Inc.