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The Influence of Different Retinal Subcircuits on the Nonlinearity Of The Journal of Neuroscience, October 1, 2002, 22(19):8726–8738 The Influence of Different Retinal Subcircuits on the Nonlinearity of Ganglion Cell Behavior Matthias H. Hennig,1 Klaus Funke,2 and Florentin Wo¨ rgo¨ tter1 1Institute for Neuronal Computational Intelligence and Technology, Department of Psychology, University of Stirling, Stirling, FK9 4LA, United Kingdom, and 2Institut fu¨ r Physiologie, Ruhr-Universita¨ t Bochum, D-44780 Bochum, Germany Y-type retinal ganglion cells show a pronounced, nonlinear, second harmonic response components were determined to frequency-doubling behavior in response to modulated sin- estimate the degree of nonlinearity. By means of circuit dissec- ewave gratings. This is not observed in X-type cells. The source tion, we found that a high degree of the Y-cell nonlinear behav- of this spatial nonlinear summation is still under debate. We ior arises from the spatial integration of temporal photoreceptor have designed a realistic biophysical model of the cat retina to nonlinearities. Furthermore, we found a weaker and less uni- test the influence of different retinal cell classes and subcircuits form influence of the nested amacrine circuit. Different sources on the linearity of ganglion cell responses. The intraretinal of nonlinearities interact in a multiplicative manner, and the connectivity consists of the fundamental feedforward pathway influence of the amacrine circuit is ϳ25% weaker than that of via bipolar cells, lateral horizontal cell connectivity, and two the photoreceptor. The model predicts that significant nonlineari- amacrine circuits. The wiring diagram of X- and Y-cells is ties occur already at the level of horizontal cell responses. Phar- identical apart from two aspects: (1) Y-cells have a wider re- macological inactivation of the amacrine circuit is expected to ceptive field and (2) they receive input from a nested amacrine exert a milder effect in reducing ganglion cell nonlinearity. circuit consisting of narrow- and wide-field amacrine cells. The Key words: receptive field; rectification; ganglion cell; ama- model was tested with contrast-reversed gratings. First and crine cell; cat retina; model The mammalian retina encodes visual information in several still under debate, and there is evidence that nested feedback different parallel channels (Roska and Werblin, 2001). An impor- from narrow- and wide-field amacrine cells onto bipolar cell axon tant functional classification is the distinction between linear and terminals contributes to nonlinear responses (Roska et al., 1998; nonlinear responding ganglion cells (for review, see Kaplan and Passaglia et al., 2001). However, a recent study in which parts of Benardete, 2001). Y-cells, which form the transient channel of the the retinal circuitry were inactivated pharmacologically provides retinal output, exhibit nonlinear spatial summation. X-cells are evidence that amacrine cells are less important for the generation essentially linear (Enroth-Cugell and Robson, 1966). Stimulating of nonlinear responses (Demb et al., 2001). Y-cells with contrast-reversed gratings leads to frequency- As an alternative hypothesis, it has been suggested that non- doubled responses (Enroth-Cugell and Robson, 1966; Hochstein linear ganglion cell responses could arise from the response and Shapley, 1976), and the remote stimulation of the receptive properties of photoreceptors (Gaudiano, 1992a,b). This assump- field changes the responsiveness of the center (McIlwain, 1964; tion was derived from a modeling study in which a specific Kru¨ger and Fischer, 1973). In spite of the fact that these effects push–pull circuitry along with the wide receptive field of Y-cells have been intensively studied, their origin is still unknown. was found to be the main source of nonlinear behavior. Previous studies suggested a common linear receptive field for In the current study, we have designed a detailed model of the X- and Y-cells resulting from bipolar cell input (Kuffler, 1953; vertebrate retina to examine the origin of nonlinear behavior of Rodieck and Stone, 1965). In addition, there is strong evidence ganglion cells. By quantifying the contributions of a realistically that Y-cells receive input from small nonlinear receptive field modeled photoreceptor and a nested amacrine circuit to ganglion subunits (Hochstein and Shapley, 1976; Victor, 1988). It is be- cell nonlinearities, we show that both have a distinctive influence lieved that amacrine cells form these subunits (Fisher et al., 1975; on the linearity of ganglion cell responses. Hochstein and Shapley, 1976; Frishman and Linsenmeier, 1982), We show that although amacrine cells contribute to nonlinear and several nonlinear responding amacrine cell types have been responses, a photoreceptor nonlinearity is sufficient to reproduce identified (Freed et al., 1996). The specific cell type or circuitry is frequency-doubled responses in Y-cells. Nonlinearities from differ- ent sources interact in a multiplicative way, and the influence of the Received Feb. 26, 2002; revised July 11, 2002; accepted July 12, 2002. amacrine circuit is ϳ25% weaker than that of the photoreceptor. This work was supported by a Scottish higher education funding council research Preliminary results have been published in abstract form (Hen- development grant from the Institute for Neuronal Computational Intelligence and nig et al., 2001). Technology (M.H.H., F.W.), European Commission grant Early Cognitive Vision (M.H.H., F.W.), and the Deutsche Forschungsgemeinschaft (Sonderforschungsbe- reich 509/A2; K.F.). We thank H. Wa¨ssle for his helpful comments and Paul MATERIALS AND METHODS Dudchenko for correcting the English. Many thanks also to our two reviewers for their helpful and detailed reviews. Stimuli. As stimuli, noncolored luminance-modulated full-field flashes Correspondence should be addressed to Matthias H. Hennig, Institute for Neu- and sinewave gratings were used. Except where noted, 100% Michelson ronal Computational Intelligence and Technology, Department of Psychology, Uni- contrast was used. The sine gratings were contrast-reversed with a versity of Stirling, Stirling, FK9 4LA, UK. E-mail: [email protected]. temporal frequency of 4 Hz and a spatial frequency varying between 0.25 Copyright © 2002 Society for Neuroscience 0270-6474/02/228726-13$15.00/0 and 5.56 cycles per degree (cpd). Hennig et al. • Nonlinearities in Retinal Ganglion Cells J. Neurosci., October 1, 2002, 22(19):8726–8738 8727 Structure of the model retina. The model is mainly based on data from nonlinear relation between the stimulus intensity and the response of the the light-adapted cat retina. Model neurons are arranged on a two- photoreceptor. dimensional, regular hexagonal grid representing 4.8° by 4.8° visual angle Because the temporal shape of photocurrent and photovoltage VP of the area centralis. Details of the cell models are given below. Distance differ significantly, voltage-dependent currents are likely to shape the between two photoreceptors was chosen as 6 ␮m, assuming an estimated responses of the photoreceptors. As shown experimentally, a hyperpo- photoreceptor density of 25,000 cones/mm 2 (area centralis; Steinberg et larization-activated current has a strong impact on photovoltage (Bader al., 1973; Wa¨ssle and Boycott, 1991). This distance corresponds to a and Bertrand, 1984; Demontis et al., 1999). It was modeled by: visual angle of ϳ1.7 arcmin (Vakkur and Bishop, 1963). Optical blurring d͓H͔͑t͒ ␭ has been included by attributing a Gaussian-shaped spatial sensitivity ϭ ͩ H ͪ ⅐ ͑ Ϫ ͓ ͔͑ ͒͒ Ϫ ␦ ͓ ͔͑ ͒ ͑ ͑ ͒Ϫ ͒ 1 H t ␶ H t , (4) profile to each photoreceptor with a SD of 6 arcmin (Smith and Sterling, dt e VP t AH SH ϩ 1 H 1990). A schematic diagram of the model is shown in Figure 1A, and its ϭ connectivity is described in the legend. Our analysis focuses on On- where AH 40 mV defines the activation of the receptor at which the ϭ Ϫ1 center cells, because the corresponding literature data allows for quan- current is half-activated, and SH 10 mV gives the slope of the ␭ ϭ Ϫ1 ␦ ϭ activation function. The constants 1 msec and H␶ 0.025 titative modeling of this cell class, whereas less is known about Off-center Ϫ H cells (see Discussion). msec 1 define the rates of increase and decay of the ionic concentrations. The simulation software has been developed in Cϩϩ, and simulations Finally, the membrane potential of the photoreceptor is computed by: were performed on Intel x86/Linux systems. The Euler method was used ͑ ͒ ͓ ͔͑ ͒ ͓ ͔͑ ͒ dVP t d Ca t d H t for integration with a time step of 0.1 msec. For data analysis, Matlab C ϭ q ϩ q , (5) programs were used. P dt P dt I dt Photoreceptor. Photoreceptors are implemented in the model by means of a state-variable description, which allows inclusion of all important ϭ ␮ ϭ 6 ϭ where CP 1 F/cm is the membrane capacity and qP 10 C and qI details of the signal transduction process (for review, see McNaughton, 5 6 ϫ 10 C are constants that define the amount of unit charge transported 1990; Mu¨ller and Kaupp, 1998; Fain et al., 2001). Details like the by the ionic currents. partition of the photoreceptor into outer and inner segments as well as Neuron models and synaptic coupling. All remaining retinal neurons spatial concentration gradients of ions and proteins are not considered. were implemented according to the membrane equation for a passive The model is, therefore, similar to a previous mathematical description neural membrane (Wo¨rgo¨tter and Koch, 1991) given by: of the photocurrent after brief stimulation (Schnapf et al., 1990; Hennig and Funke, 2001). N In the outer segment of a photoreceptor, light-sensitive rhodopsin dV͑t͒ ␶ ϭ R ⅐ ͩ͸ g ͑t͒ ⅐ ͑E Ϫ V͑t͒͒ͪ ϩ V Ϫ V͑t͒, (6) molecules become activated by photons. This is followed by two sequen- dt i i rest tial stages that amplify the signal by a factor of ϳ1,000,000.
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