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     

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     

An inverse problem in neural processing

Any neural network aimed at the coding sensory events must contain computational properties which generally allow the organism to reconstruct the input signals with some degree of accuracy-else the association between stimulus and response would, at best, be uncertain. In this paper we investigate the problem of reconstructing external input signals to neural networks when the activity profiles of only some of its member cells are known. The evolution and activities of such cells are defined by an earlier formulation of one of us (Ouztöreli 1979) and, here, we restrict our application to local curcuits within the vertebrate retina. Solutions to this inverse coding problem are presented for specific network equations and examplified with 1, 3, and 5 neuron cases.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 to M.N.O. and grant A-4395 to T.M.C. through the University of Alberta     

Relationship between stimulus and intensity characteristics of a sensory receptor

In this work a bridge is built between a neural model studied in a series of papers (cf. Ouztöreli 1979; Ouztöreli et al. 1987) and certain experimental laws of psychophysics and neurophysiology (Hartline 1942; Fechner 1860; Stevens 1961).This project was patially supported by Grant A4345 from the Natural Sciences and Engineering Research Council of Canada     

Mathematical analysis of optimal multichannel filtering for nerve signals

This paper extends recent analyses (Roberts and Hartline, 1975; Ouztöreli and Stein, 1977) of optimal linear filters for separating neural signals from more than one electrode site. Roberts and Hartline's result, using a matched filter criterion, represents one of a class of optimal filters with different, but symmetrical, output waveforms derived by Ouztöreli and Stein (1977). Another narrow bandwidth filter of this class will give the optimal results according to an energy criterion, but may be less useful in practical situations.This work was partially supported by the Medical Research Council of Canada (Grant MRC-MT3307), the Technical Research Council of Denmark (Grant 516-6703 E406) and the National Research Council of Canada (Grant NRC A-4345)     

Activity analysis of neural networks

In a series of articles (Leung et al., 1973, 1974; Ogztöreli, 1972, 1975, 1978, 1979; Stein et al., 1974) we have investigated some of the physiologically significant properties of a general neural model. In these papers the nature of the oscillations occuring in the model has been briefly analyzed by omitting the effects of the discrete time-lags in the interaction of neurons, although these time-lags were incoporated in the general model. In the present work we investigate the effects of the time-lags on the oscillations which are intrinsic to the neural model, depending on the structural parameters such as external inputs, interaction coefficients, self-inhibition, self-excitation and selfadaptation coefficients. The numerical solution of the neural model, the computation of the steady-state solutions and the natural modes of the oscillations around the steady-state solutions are described.This work was partly supported by the Natural Sciences and Engineering Research Council of Canada under Grant NRC-A-4345 through the University of Alberta     

Control mechanisms of a neural network

In this paper we consider some classical control theoretic properties of a nonlinear neural network proposed by Ouztöreli (1979) to represent the activities of constiuent neurones in terms of the input signals and coupling (associative) properties. By breaking the network into linear and nonlinear components we have been able to localize the nonlinearities in the individual neural response latencies through the system.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada by Grant NSERC-A 4345 to M.N.O. and Grant NSERC-A 2568 to T.M.C. through the University of Alberta     

Analysis of a model for antagonistic muscles

In the present work a linear model for a pair of antogonistic muscles is analysed. Each constituent muscle in this model is identical to ones considered previously (Stein and Ouztöreli, 1976). Analytical properties of the antagonistic muscles and dynamics of the system are described and some numerical results are discussed. The natural modes of the system are determined by a fourth order polynomial, which most commonly has one pair of conjugate complex roots and two negative real roots. The filtering of neural inputs through the active state properties of the muscle increases the order of the system to fifth order for these inputs.This work was partly supported by the National Scientific and Engineering Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MT-3307 through the University of Alberta     

A new transgenic reporter line reveals expression of protocadherin 9 at a cellular level within the zebrafish central nervous system

The wiring of neuronal networks is far from understood. One outstanding question is how neurons of different types link up to form subnetworks within the greater context. Cadherins have been suggested to create an inclusion code where interconnected neurons express the same subtypes. Here, we have used a CRISPR/Cas9 knock-in approach to generate a transgenic zebrafish reporter line for protocadherin 9 (pcdh9), which is predominantly expressed within the central nervous system. Expression of eGFP was detected in subsets of neurons in the cerebellum, retina and spinal cord, in both larvae and juveniles. A closer characterization of the spinal locomotor network revealed that a portion of distinct classes of both excitatory and inhibitory interneurons, as well as motor neurons, expressed pcdh9. This transgenic line could thus be used to test the cadherin network hypothesis, through electrophysiological characterization of eGFP positive cells, to show if these are synaptically connected and form a discrete network within the spinal cord.     

Cut-loading: A Useful Tool for Examining the Extent of Gap Junction Tracer Coupling Between Retinal Neurons

In addition to chemical synaptic transmission, neurons that are connected by gap junctions can also communicate rapidly via electrical synaptic transmission. Increasing evidence indicates that gap junctions not only permit electrical current flow and synchronous activity between interconnected or coupled cells, but that the strength or effectiveness of electrical communication between coupled cells can be modulated to a great extent^1,2. In addition, the large internal diameter (~1.2 nm) of many gap junction channels permits not only electric current flow, but also the diffusion of intracellular signaling molecules and small metabolites between interconnected cells, so that gap junctions may also mediate metabolic and chemical communication. The strength of gap junctional communication between neurons and its modulation by neurotransmitters and other factors can be studied by simultaneously electrically recording from coupled cells and by determining the extent of diffusion of tracer molecules, which are gap junction permeable, but not membrane permeable, following iontophoretic injection into single cells. However, these procedures can be extremely difficult to perform on neurons with small somata in intact neural tissue.Numerous studies on electrical synapses and the modulation of electrical communication have been conducted in the vertebrate retina, since each of the five retinal neuron types is electrically connected by gap junctions^3,4. Increasing evidence has shown that the circadian (24-hour) clock in the retina and changes in light stimulation regulate gap junction coupling^3-8. For example, recent work has demonstrated that the retinal circadian clock decreases gap junction coupling between rod and cone photoreceptor cells during the day by increasing dopamine D2 receptor activation, and dramatically increases rod-cone coupling at night by reducing D2 receptor activation^7,8. However, not only are these studies extremely difficult to perform on neurons with small somata in intact neural retinal tissue, but it can be difficult to adequately control the illumination conditions during the electrophysiological study of single retinal neurons to avoid light-induced changes in gap junction conductance.Here, we present a straightforward method of determining the extent of gap junction tracer coupling between retinal neurons under different illumination conditions and at different times of the day and night. This cut-loading technique is a modification of scrape loading^9-12, which is based on dye loading and diffusion through open gap junction channels. Scrape loading works well in cultured cells, but not in thick slices such as intact retinas. The cut-loading technique has been used to study photoreceptor coupling in intact fish and mammalian retinas^{7, 8,13}, and can be used to study coupling between other retinal neurons, as described here.     

Computer modeling of mechanisms of the information processing in the olfactory bulb. I. Model of the structure-functional organizations of neuronal elements in the olfactory bulb and receptor epithelium

A computer model of the olfactory bulb was constructed. The paper describes: 1) the general architecture of a model neuron network that reflects the neurophysiological experimental and theoretical data on the structural and functional organization of the peripheral part of the olfactory system, the olfactory bulb with inputs from olfactory receptor neurons; 2) the organization of each of three levels of the model: receptors, olfactory glomeruli, and basic neurons; and 3) a scenario of the computer model work. In some aspects, in particular, in the principle of information presentation, the treatment of the role of basic neurons (mitral and tufted cells), and their interrelations in modules, the model favorably differs from the available olfactory bulb models. The model is basic and provides further refinement of the architecture, an increase in the number of modules, and the modeling of the learning process.     

The effects of multiple reflex pathways on the oscillations in neuro-muscular systems

Summary A model of mammalian neuro-muscular systems described previously (Ouztöreli and Stein, 1975) has been extended to include multiple reflex pathways, as have been shown to exist in primates, including man (Milner-Brown et al., 1975). A number of general mathematical properties of the extended system are described. In the final section, using computer solutions, it is shown that the presence of multiple reflex pathways can effectively reduce the tendency for oscillation which will exist if high reflex gain were concentrated in a single pathway. High loop gain is desirable for good control in any negative feedback system, so the presence of multiple reflex pathways could improve reflex control, while limiting the magnitude of tremor or other unwanted oscillations in neuromuscular systems.This work was partly supported by the National Research Council of Canada (Grant NRC-A4345) and by the Medical Research Council of Canada (Grant MRC-MA 3307) through the University of Alberta.     

Neural stem cell properties of Müller glia in the mammalian retina: regulation by Notch and Wnt signaling

The retina in adult mammals, unlike those in lower vertebrates such as fish and amphibians, is not known to support neurogenesis. However, when injured, the adult mammalian retina displays neurogenic changes, raising the possibility that neurogenic potential may be evolutionarily conserved and could be exploited for regenerative therapy. Here, we show that Müller cells, when retrospectively enriched from the normal retina, like their radial glial counterparts in the central nervous system (CNS), display cardinal features of neural stem cells (NSCs), i.e., they self-renew and generate all three basic cell types of the CNS. In addition, they possess the potential to generate retinal neurons, both in vitro and in vivo. We also provide direct evidence, by transplanting prospectively enriched injury-activated Müller cells into normal eye, that Müller cells have neurogenic potential and can generate retinal neurons, confirming a hypothesis, first proposed in lower vertebrates. This potential is likely due to the NSC nature of Müller cells that remains dormant under the constraint of non-neurogenic environment of the adult normal retina. Additionally, we demonstrate that the mechanism of activating the dormant stem cell properties in Müller cells involves Wnt and Notch pathways. Together, these results identify Müller cells as latent NSCs in the mammalian retina and hence, may serve as a potential target for cellular manipulation for treating retinal degeneration.     

Horizontal cells of the carp retina: Golgi impregnation and Procion-Yellow injection

Summary Application of two methods for the selective staining of neurons, Golgi impregnation and intracellular marking with Procion Yellow, has revealed the anatomical arrangements of the horizontal cells in the carp retina. There are two basic horizontal-cell types, those with axons and these without. The former can be subdivided into three groups on the basis of the pattern of branching of the dendrites. These three structural groups are also functionally distinct, as shown by the electrical recordings made during Procion-Yellow injection. The axons of these three types of cell project into the proximal part of the inner nuclear layer, where they expand to form morphologically indistinguishable terminals. Fine horizontal processes leave the surfaces of these axon terminals. The functional behavior of a terminal resembles that of the associated soma. The horizontal cells lacking axons vary in morphological appearance, but they are similar functionally.This work was supported by the Deutsche Forschungsgemeinschaft     

Stability of the steady-state size distribution in a model of cell growth and division

The approach to steady-state size distribution is studied for a growing population of cells. The model incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase.This work was supported by the National Science Foundation under Grant No. MCS 8300559This work was supported by the National Science Foundation under Grant No. MCS 8301104     

The mechanism of pattern formation in the developing drosophila retina

The biological patterning of the drosophila retina in vivo has striking resemblance to liquid bubbles, in which the surface mechanics due to N-cadherin within a sub-group of retina cells can be mimicked by surface tension. In this work, the aggregating patterns were reasonably simplified into 2D clusters consisting of 2—6 identical bubbles confined within a shrinking boundary. By using a hybrid fluid dy-namics model proposed for liquid foams, the aggregating process of 2―6 retina cells was studied. Assuming the minimal perimeter for patterning cells to be the condition of stability patterns, the stable converged patterns we simulated in this work are the same as the experimental observations. More importantly, a new pattern of 6 cells was obtained which was found physically more stable than the other two reported by Hayashi and Carthew[1]. Aggregating perimeters of cells, i.e. the surface energy, showed a good linear fit with the cell numbers.     

Regional distribution of three ultrastructural retinula types in the retina of Cataglyphis bicolor Fabr. (Formicidae,Hymenoptera)

Summary The retina of Cataglyphis bicolor was investigated by electron microscopy. Three types of structurally distinct retinulae were found and mapped throughout the compound eye: Type I is composed of four unpigmented thin cells, four larger pigmented cells as well as a basal ninth cell. Its rhabdom possesses a round cross section and four microvilli directions. This type occupies most of the dorsal two-thirds of the retina. Type II consists of two thin cells, two intermediate cells and four large cells. A basal ninth cell is also present; the rhabdom is as in type I. Type II retinulae are located in the ventral third of the retina. Type III ommatidia are unique within the Hymenoptera: there are four large pigmented cells, four thinner unpigmented cells and a basal ninth cell. The rhabdom, however, has a dumb-bell shaped cross section; two small cells lie at its opposed extremities and the remaining six cells have mutually perpendicular microvilli orientations. This type of retinula is found at the dorso-medial eye margin. Serial sectioning in this region revealed a conical shaped rhabdom without any torsion along the longitudinal axis. The rhabdomere cross section was calculated from distal and proximal thin sections. Angular statistics were applied to the microvilli directions of all three ommatidial types to determine the degree of order. A possible functional significance of the structural specializations of the different eye regions is discussed.Supported by Swiss National Science Foundation, Grant No. 3.814.72 awarded to Prof. Dr. R. Wehner. This work is part of a Ph. D. thesis. I wish to thank Prof. Dr. R. Wehner for continuous support and my colleagues Dr. P. Duelli and Dr. E. Meyer for a fruitful collaboration     

The relationship between signal response selectivity and the functional structure of complex retinal neural networks

In this paper we simulate the simultaneous responses of 45 neurones within a hypothetical retina to a variety of spatio-temporal signals. Our results demonstrate how specific convergent and divergent excitatory and inhibitory connections are sufficient to determine signal response selectivity of specific ganglion cells and so delimit the known types of center-surround receptive fields.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grant A-4345 to M.N.O. and Grant A-4395 to T.M.C. through the University of Alberta     

The organization of giant horizontal-motion-sensitive neurons and their synaptic relationships in the lateral deutocerebrum of Calliphora erythrocephala and Musca domestica

Summary Three giant horizontal-motion-sensitive (HS) neurons arise in the lobula plate. Their axons terminate ipsilaterally in the medial deutocerebrum and suboesophageal ganglion. Both Golgi impregnations and cobalt fills demonstrate that endings of the two HS cells, representing the upper and middle third of the retina, differ in shape and location from that of the HS cell subtending the lower third of the eye. This dichotomy is reflected by the terminals of a pair of centrifugal horizontal cells (CH), one of which invades lobula plate neuropil subtending the upper two-thirds of the retina. The other overlaps the dendrites of the HS cell subtending the lower one-third of the retina.The HS cells are cobalt-coupled to a variety of complexly arborizing descending neurons. In Musca domestica, gap-junction-like apposition areas have been observed between HS axon collaterals and descending neuron dendrites. The three HS cells also share conventional chemical synapses with postsynaptic elements, which include the dendritic spines of descending neurons. Unlike the giant vertical-motion-sensitive neurons of the lobula plate, whose relationships with descending neurons appear to be relatively simple, the horizontal cells end on a large number of descending neurons where they comprise one of several different populations of terminals. These descending neurons terminate within various centres of the thoracic ganglia, including neuropil supplying leg, neck, and flight muscle.