Über das optische Auflösungsvermögen der Facettenaugen von Limulus

Summary The resolving power of the human eye and the apposition eye in insects is discussed on the basis of Fraunhofer's diffraction theory. It is then shown that diffraction does not play an important role in the Limulus facet eye. In spite of this the visual fields of neighboured ommatidia overlap strongly as Waterman has shown. A mathematical relation which describes the process of imaging the optical surroundings onto the generator potentials of the excentric cells of the receptors is presented. This relation takes into account the overlap of the visual fields and the logarithmic relation between light intensity and generator potential (MacNichol, Fuortes). On the basis of Hartline and Ratliff's reports on lateral inhibition in the Limulus eye it is shown that this process corrects the overlap and therefore increases the resolving power of the eye. The functional mechanism of lateral inhibition is in principle able to create an image of the optical surroundings in the optic nerve. It therefore can compensate for the dioptric apparatus in front of the receptor mosaic. The correction process in the Limulus eye is studied quantitatively and other cases of principle interest are investigated by means of an analog computer. The results are discussed and other inhibitory processes in the visual and auditory system etc. are mentioned.     

Vergleich zweier Modelle für laterale Inhibition

Summary Two semi-linear models for lateral inhibition are discussed. The interaction between receptor units is assumed to be linear, as demonstrated by Hartline and Ratliff in the eye of the horseshoe crab Limulus polyphemus. Yet a model of such an inhibitory system must be nonlinear, since the output values correspond to nerve activities, which cannot be negativ. Models with forward inhibition were used often to describe contrast phenomena in the human nervous system. However, in order to simulate the input-output relation in systems similar to the eye of Limulus, a model with backward inhibition must be constructed. Two important properties of backward inhibition not shared by forward inhibition are: (1) Inhibition in a receptor unit has an influence upon its excitation, as well as upon its ability to inhibit other units (Disinhibition). (2) The range of interaction between sensory units is not necessarily the same as the range of direct cross connections. It is shown in this paper, that also forward inhibition may possess these two properties, provided that it is repeated on subsequent levels. Some properties of systems with backward and forward inhibition are studied and compared in models consisting of three units. The input-output relation for large systems with backward inhibition was calculated under special assumptions concerning the inhibitory coefficients. If the inhibitory coefficients in a system with backward inhibition decrease like a power series, as a function of the distance between receptor units, only neighboring receptors have an effect upon each other. That is, in an equivalent system with forward inhibition the inhibitory interaction is confined to neighbouring receptors. Conversely, when backward inhibition exists only between neighbouring receptors, the inhibitory coefficients in an equivalent system with forward inhibition are described, as a function of the distance between the receptor units, by a power series with alternating sign.     

动态神经元的网络模型 Ⅱ.计算机仿真

在动态神经元的网络模型的基础上,在计算机上进行了仿真。结果表明,我们的单元模型能再现感受器的适应性、兴奋后抑制、相位锁定和位置编码。由五十个这样的单元构成的侧抑制网络能再现鲎复眼侧抑制网络的瞬态特性,而在达到稳态时则表现出马赫带现象。仿真结果还预测侧抑制网络对运动目标特别敏感。模型有关神经元处理信息的内部机制和外部特性与生物神经元的一致性,以及由此构成的侧抑制网络与鲎复眼侧抑制网络性质的一致性,都提示此模型有希望成为一种更接近于生物神经网络的模型。     

The simulation of multi-neurone networks: Modelling of the lateral inhibition of the eye and the generation of respiratory rhythm

We describe a model of a single neurone, and a method of interconnecting such neurone models suitable for multi-neurone network simulations on a digital computer. Two simulations are described; the lateral inhibition in the eye of the Limulus and the generation of respiratory rhythm in the brain stem of the cat.     

Consequences of delayed lateral inhibition in the retina of Limulus. I. Elementary theory of spatially uniform fields.

Although the magnitude of lateral inhibition in the retina of the compound eye of Limulus polyphemus depends strongly on the distance between ommatidia, the delay time τ between the response of one ommatidium and the consequent inhibition of another is independent of the distance between them and is approximately 0·1 sec (cf., e.g., Ratliff, Knight, Dodge &; Hartline,1973). We have recently shown (Coleman &; Renninger, 1974) that under appropriate circumstances the response r of such a retina to a temporally constant and spatially uniform excitation of amount e should be a succession of “bursts” and “rest periods”, each of duration τ, so that r, although spatially uniform, is a periodic function of time with period 2τ and mean value $\text{1}\text{2}\text{ϵ}$. Further, the periodic function r can have a fine structure in which there is repeated information about the duration and sequence, but not the amplitude, of any short pulses which occurred immediately (i.e. within a time interval of length τ) before the onset of steady uniform excitation. We derive here implications of several plausible general hypotheses about the functional form of lateral inhibition. We show that, under those of the considered hypotheses which are expected to hold for Limulus in strong light, periodic bursting behavior for r is stable and is rapidly approached if the excitation is held steady and uniform.     

A phosphatase of undefined function is common to the photoreceptive microvilli of several arthropod species

Summary It has previously been demonstrated, using an ultracytochemical technique, that the photoreceptive microvilli of crab retinae contain a magnesium-dependent phosphatase that hydrolyses the artificial substrate 4-nitrophenylphosphate. Whilst many phosphatases hydrolyse 4-nitrophenylphosphate, the properties of the microvillar enzyme indicated that it is not a conventional acid or alkaline phosphatase. Using the same technique, it is now shown that a similar activity resides in the rhabdomeric microvilli of both the lateral compound eye and the ventral photoreceptors of Limulus polyphemus as well as in the compound eyes of the freshwater crayfish Cherax destructor and the fly Lucilia cuprina. Control cytochemical procedures performed on crayfish and fly showed that in these species too the activity is magnesium-dependent and is not due to a Na⁺/K⁺ ATPase.     

Informationsverarbeitung in homogenen Netzen von Neuronenmodellen

Summary The interconnection structures of the peripheral part of the nervous system, which are considered here, are two-dimensional homogeneous networks with time and space dependent inputs and outputs. The principles of connection under consideration comprise lateral inhibition and facilitation. The transfer functions of those linear networks as well as the stability problem are investigated on a digital computer using different system parameters. A closed form solution is given for an infinitely large element density which describes the network properties. In this case an inhibition system acts as high pass filter on the spatial frequencies of the input, whereas a facilitation network acts as low pass filter. The properties of the networks and the transformations in case of moving patterns are analysed using the methods of systems theory.

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Auszug aus einer Dissertation an der Fakultät für Maschinenwesen der Technischen Universität Hannover, Institut für Theoretische Elektrotechnik (Prof. Dr.-Ing. habil. H. Tischner).

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Herrn Prof. Dr.-Ing. habil. H. Tischner danke ich für die Anregung zu dieser Arbeit und seine ständige Unterstützung. Mein Dank gilt ferner der Firma Brown, Boveri & Cie. AG, Mannheim, für die finanzielle Förderung. Den Mitarbeitern im Institut für Schwingungsforschung, insbesondere Herrn Direktor Dr.-Ing. A. Schief bin ich für wertvolle Diskussionen verpflichtet.     

Anatomical circuitry of lateral inhibition in the eye of the horseshoe crab, Limulus polyphemus

Lengthy uninterrupted series of sections of the neural plexus in the compound eye of the horseshoe crab, Limulus polyphemus, have been used to reconstruct all the arborizations and their synaptic interconnections in a neuropil knot. This one microglomerulus contains the axons of 19 retinular cells, which pass by without contacts; 13 efferent fibres with 44 synapses to and from eccentric cell collaterals; and arborizations from 54 eccentric cells with 577 synapses. Eccentric cell axons are devoid of synaptic input. Their collaterals ramify in synaptic knots and subserve both pre- and postsynaptic functions simultaneously. Arborizations near the axon of origin have a highly branched pattern (up to 20 bifurcations), a high synaptic input: output ratio (up to about 9:1), and high synaptic density (a maximum of 12 per micrometre of neurite length). The opposite extreme is represented by sparsely branched eccentric cell collaterals distant from their axons of origin with very little synaptic input and sparse output. Spatially graded lateral inhibition is the apparent outcome of a radially decreasing distribution of inhibitory synapses on the arborizations of eccentric cell collaterals combined with possible decremental signal transmission in the plexus. The synaptic analysis has a bearing on most physiological aspects of lateral inhibition that have been studied in the Limulus eye. Implied in the results is the suggestion that synapse formation is an intrinsic property of the presynaptic element, but that the connectivity is governed by the electrical activity of target neurons.     

Conditions for noise reduction and stable encoding of spatial structure by cortical neural networks

Cortical circuits have been proposed to encode information by forming stable spatially structured attractors. Experimentally in the primary somatosensory cortex of the monkey, temporally invariant stimuli lead to spatially structured activity patterns. The purpose of this work is to study a recurrent cortical neural network model with lateral inhibition and examine what effect additive random noise has on the networks' ability to form stable spatially structured representations of the stimulus pattern. We show numerically that this network performs edge enhancement and forms statistically stationary, spatially structured responses when the lateral inhibition is of moderate strength. We then derive analytical conditions on the connectivity matrix that ensure stochasticly stable encoding of the stimulus spatial structure by the network. For stimuli whose strength falls in the near linear region of the sigmoid, we are able to give explicit conditions on the eigenvalues of the connection matrix. Finally, we prove that a network with a connection matrix, where the total excitation and inhibition impinging upon a neural unit are nearly balanced, will yield stable spatial attractor responses. Received: 16 October 1998 / Accepted in revised form: 25 November 1999     

Die Verarbeitung stationärer optischer Nachrichten im Komplexauge von Limulus

Summary The functional properties of the processing of visual information by the complex eye of Limulus was studied. The spatial distribution of activity that results in the optic nerve when the Limulus eye is exposed to a stationary optical pattern depends upon the transfer characteristics of two subsystems: the dioptric apparatus and the nervous interactions comprising the lateral inhibition system. — The transfer characteristic of the dioptric apparatus is determined by the sensitivity distribution function of single ommatidia. This distribution was measured and found to be approximately of Gauss-function type. The sensitivity falls off to 1/e at a distance of one ommatidium; thus the visual fields of adjacent ommatidia strongly overlap. As a consequence of the overlap, amplitudes of the spatial Fourier components, of which the brightness distribution of the optical surround is made up, are more and more reduced with increasing frequency in the intensity distribution on the receptor mosaic. The amplitude of the spatial frequency 1/=0,25 ( in units of interommatidial distance) is reduced to half of the maximum value, which is attained at zero frequency. It is shown that the amplitude frequency characteristic of the sensitivity distribution function has no zeros, which means that no loss of optical information results from overlap of visual fields. Thus the resolving power of the dioptric apparatus is limited only by the number of receptors per unit area. — The transfer characteristic of the lateral inhibition system in the Limulus eye depends on the distribution of the inhibitory coefficients around the individual receptors. This distribution function was determined from excitatory responses in the optic nerve elicited by a spatial light intensity step function on the receptor mosaic. It is found that this distribution is also Gaussian in form, but decays to 1/e at a distance of eight to nine ommatidia along the major axis of the eye. The average value of the inhibitory coefficients between adjacent ommatidia was found to be 0,025. The amplitude frequency response of the inhibitory system is constant for high spatial frequencies down to 1/=0,1 while amplitudes of lower frequency sinusoids are reduced down to nearly half of the maximum value at frequency zero. The amplitude frequency characteristic of the inhibitory system ensures a one to one correspondence between the intensity distribution on the receptor mosaic and the excitation distribution in the optic nerve. The overall transfer characteristic of the eye is derived from the transfer characteristics of the dioptric apparatus and the inhibitory system. This characteristic is of bandpass type with a maximum amplitude response at a frequency of 1/=0,07. The overall transfer characteristic was independently confirmed in a separate experiment. The nature of the overall transfer characteristic shows that the inhibitory system does not exactly correct for the overlap of the visual fields of single ommatidia, which in principal the system could do if the distributions of inhibitory coefficients and ommatidia sensitivity were equal. The overall transfer characteristic of the Limulus eye garantees a one to one correspondence between patterns in the optical surround and excitation distributions in the optic nerve. — The average values of the inhibitory coefficients derived from these experiments are at least a factor ten smaller than those determined directly by other investigators. Possible explanations of this discrepency are discussed. — In a separate chapter the overall transfer characteristic for eyes submerged in water is described. It was found that this characteristic does not differ from that determined in air for the eye region which was investigated in the experiments. This result is explained by two properties of the eye which are dependent on the refractive index of the surround medium and whose influences cancel each other: the visual fields of ommatidia are reduced under water, while the divergence angles between the optical axes of adjacent ommatidia also diminish.

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This research was supported in part by the United States Air Force under Grant No. AF-EOAR-62-41 and monitored by the European Office, Office of Aerospace Research.     

Electrophysiological basis for the spatial dependence of the inhibitory coupling in the Limulus retina

A technique for measuring, with total optical isolation, the inhibition between two individual receptor units in the Limulus lateral eye is described. The extracellular responses of pairs of units were recorded, using light piping microelectrodes. The inhibitory coupling between two units was found to be nonlinear and describable by a simple hyperbolic equation written in terms of saturation rate (S), half saturation (H), and threshold (ft). By plotting reciprocal frequencies, the data could be linearized and compared for different pairs of units. The magnitude of inhibition (in terms of S and H) was found to decrease monotonically as the anatomical distance between receptors increased. An electrical model of the inhibitory system was developed which accounts for many of the properties of the observed inhibitory interactions. Using the equations from the model and the experimental data, it is shown that the "electrical distances" (which are computed in terms of space constants lambda) of the inhibitory synapses from the impulse-generating region of the test unit are directly related to the anatomical distance between receptors. It is also shown that "synaptic strength" is relatively constant with separation. The electrical distances of the inhibitory synapses range from about 0.1lambda to 0.25lambda for adjacent units to greater than 0.5lambda for units seven to nine receptors away. It is concluded that the nonlinear character of the inhibitory coupling is attributable to synaptic effects, and that the decrease of inhibition with distance between receptors is caused primarily by an increase in the electrical distance of the inhibitory synapses from the test unit.     

The Additivity of Contrast in the Human Eye

Using the method of binocular brightness matching, simultaneous brightness contrast effects were measured on two observers. The effects of a given pattern were invariably smaller than the summation of the effects of the pattern's components. This failure of additivity was valid both for patterns with isolated components as well as for those with components exactly contiguous with one another. This failure was more pronounced the farther the inducing patterns were from the test patch. These findings are interpreted as indicating that in the human (just as in the Limulus) eye, the amount of inhibition exerted by a given region on its neighbors depends upon the inhibition exerted against it as well as its excitation state.     

Tipping the Balance: Robustness of Tip Cell Selection,Migration and Fusion in Angiogenesis

Vascular abnormalities contribute to many diseases such as cancer and diabetic retinopathy. In angiogenesis new blood vessels, headed by a migrating tip cell, sprout from pre-existing vessels in response to signals, e.g., vascular endothelial growth factor (VEGF). Tip cells meet and fuse (anastomosis) to form blood-flow supporting loops. Tip cell selection is achieved by Dll4-Notch mediated lateral inhibition resulting, under normal conditions, in an interleaved arrangement of tip and non-migrating stalk cells. Previously, we showed that the increased VEGF levels found in many diseases can cause the delayed negative feedback of lateral inhibition to produce abnormal oscillations of tip/stalk cell fates. Here we describe the development and implementation of a novel physics-based hierarchical agent model, tightly coupled to in vivo data, to explore the system dynamics as perpetual lateral inhibition combines with tip cell migration and fusion. We explore the tipping point between normal and abnormal sprouting as VEGF increases. A novel filopodia-adhesion driven migration mechanism is presented and validated against in vivo data. Due to the unique feature of ongoing lateral inhibition, ‘stabilised’ tip/stalk cell patterns show sensitivity to the formation of new cell-cell junctions during fusion: we predict cell fates can reverse. The fusing tip cells become inhibited and neighbouring stalk cells flip fate, recursively providing new tip cells. Junction size emerges as a key factor in establishing a stable tip/stalk pattern. Cell-cell junctions elongate as tip cells migrate, which is shown to provide positive feedback to lateral inhibition, causing it to be more susceptible to pathological oscillations. Importantly, down-regulation of the migratory pathway alone is shown to be sufficient to rescue the sprouting system from oscillation and restore stability. Thus we suggest the use of migration inhibitors as therapeutic agents for vascular normalisation in cancer.     

Effect of thiol redox state modulators on oxidative stress and sclerotial differentiation of the phytopathogenic fungus <Emphasis Type="Italic">Rhizoctonia solani</Emphasis>

This study showed that sclerotial differentiation in the filamentous phytopathogenic fungus Rhizoctonia solani is directly related to oxidative stress and thiol redox state (TRS). Sclerotial differentiation is modulated by the availability of non-cytotoxic −SH groups as was shown by the inhibition of sclerorial differentiation by the TRS modulator N-acetyl cysteine (AcCSH), and not necessarily with those of the TRS reduced components glutathione (GSH) and its precursor cysteine (CSH) as indicated by the GSH-biosynthesis inducer and inhibitor l-2–oxo-thiazolidine-4-carboxylate and l-buthionine-S,R-sulfoximine, respectively. Moreover, inhibition of sclerotial differentiation was accompanied by decrease of the high oxidative stress indicators, lipid peroxidation and DNA damage in the mycelial substrate where sclerotia initials are formed, which suggests that this phenomenon is related to oxidative stress as it is predicted by our theory on sclerotial differentiation.     

The spatiotemporal transfer function of the Limulus lateral eye

The dynamics of the Limulus retina may be well described by the spatiotemporal transfer function, which measures the response of the eye to moving sinusoidal gratings. We consider a model for this system, which incorporates an excitatory generator potential, and self- and lateral inhibitory processes. Procedures are described which allow estimation of parameters for the model consistent with the empirical transfer function data. Transfer functions calculated from the model show good agreement with laboratory measurements, and may be used to predict accurately the response of the eye to arbitrary moving stimuli. The model allows convenient interpretation of the transfer function measurements in terms of physiological processes which underly the response of the Limulus retina.     

Growth inhibition by L-phenylalanine in Agmenellum quadruplicatum

Summary L-Phenylalanine is a potent inhibitor of growth in a marine species of blue-green bacteria, Agmenellum quadruplicatum. The growth inhibition is reversed by many amino acids when added to the culture medium simultaneously with L-phenylalanine. The most effective L-phenylalanine antagonists are L-tyrosine, L-alanine, L-leucine, L-methionine, L-tryptophan, and L-isoleucine. However, L-tyrosine is the only effective L-phenylalanine antagonist when growth is inhibited by L-phenylalanine for two or more hours prior to addition of an equimolar concentration of the compound tested as an antagonist. Various explanations that could account for inhibition of growth by L-phenylalanine are discussed. Inhibition of growth by L-phenylalanine is not a feature peculiar to the general physiology of blue-green bacteria. For example, the growth of Anacystis nidulans, a fresh water species, was not inhibited by L-phenylalanine, although a different pattern of metabolite sensitivity was found.     

Categorical and prolonged potentials are evoked when brief, intermediate-intensity flashes stimulate horseshoe crab lateral eye photoreceptors during octopamine neuromodulation.

Octopamine, a major efferent neurotransmitter in the lateral eye of the horseshoe crab (Limulus polyphemus), has previously been shown to modulate photoreceptor responses evoked by long flashes. Quantification of these data indicates that this modulation produced a genuine increase in sensitivity to light which cannot be entirely due to an increase in optical efficiency consequent on an anatomical alteration. Other previous studies demonstrated that extrinsic current can modulate Limulus lateral eye photoreceptor cells by inducing a bistable membrane potential with two distinct states. The present study was therefore undertaken to find out if octopamine could modulate visual responses by inducing prolonged and bistable polarization shifts similar to those demonstrated in several other neural systems. Intracellular microelectrodes were used to execute an electrophysiological study of the receptor potentials evoked in the lateral eye of Limulus when brief (20-ms) flashes were delivered while 50 microM octopamine perfused dark-adapted photoreceptors. The combined chemical and optical stimuli prolonged photoreceptor responses to light to the degree that they often exceeded the duration of the brief stimulus by hundreds of milliseconds. Moreover, these prolonged potentials were clearly bistable because they were categorical--either a prolongation was perceptually clear-cut and present or it was not, with no intermediate patterns being observed. During seawater control perfusions, such prolongations were absent. This appears to be the first demonstration of such categorical and prolonged potentials in a photoreceptor neuron. This finding particularly suggests that efferent-driven neuromodulation can enable the development of a persisting short-term representation of a brief stimulus, with this representation being retained at the most distal possible neural site.     

The divalent cation dependence of liver glycogen synthase phosphatase activity

Summary In a previous report it was shown that EDTA inhibition of liver glycogen synthase phosphatase activity in preparations from normal, fed rats could be increased upon glucagon or cAMP treatment. This occurred without a change in the half-maximum inhibitory concentration of EDTA. Glucose administration to animals resulted in decreased EDTA inhibition. The inhibitory action of EDTA has been further characterized by comparing its action with that of other chelators (CDTA and EGTA) and examining the effects of various divalent cations on chelator inhibition. Both CDTA and EDTA which differ structurally were inhibitory at 5 mm concentrations whereas EGTA which is structurally similar to EDTA was not inhibitory at concentrations up to 10 mm. The lack of inhibition by EGTA could be explained by its weak affinity for Mg⁺⁺ in the preparation. A comparison of CDTA and EDTA revealed that CDTA was a more potent inhibitor than EDTA (I_0.5, 0.15 mm vs 0.3 mm). Glucagon and glucose treatment of rats resulted in changes in CDTA inhibition which closely paralleled those of EDTA. A large group of divalent cations were tested but only Mg⁺⁺, Ca⁺⁺, and Mn⁺⁺ both prevented and reversed CDTA or EDTA inhibition. Fifty percent reversal using either chelator occurred at calculated free-metal ion concentrations of approximately 2 µm, 0.08 µm and 0.0004 µm, respectively. Thus, it is clear that EDTA inhibition is due to its chelation effect and is not due to a nonspecific anionic effect.