Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-18T21:56:17.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Light adaptation in the turtle retina: embedding a parametric family of linear models in a single nonlinear model

Published online by Cambridge University Press:  02 June 2009

Daniel Tranchina  and
Charles S. Peskin
Daniel Tranchina
Affiliation:
Department of Biology, Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York
Charles S. Peskin
Affiliation:
Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York
Get access Rights & Permissions [Opens in a new window]

Abstract

A method for constructing nonlinear models for light adaptation in the retina is introduced. The components of the models are linear filters and static (instantaneous) nonlinear elements configured in a feedback arrangement. The signals in the models are combined through algebraic addition or multiplication. We apply the method to model light adaptation measured in turtle horizontal cells. Given a particular wiring diagram for the components, the functional forms of the static nonlinearities and frequency responses of the linear filters are determined by constraining the model to give temporal frequency responses (linear regime behavior) consistent with a family of linear feedback models which has been shown to provide a good description of adaptation in these cells. Two particular models, quite different in structure, are presented. Each model responds to perturbations around a mean light level as a feedback circuit in which the gain (strength) of feedback is adjusted to be proportional to the mean light level, but neither model has a separate pathway for measuring the mean light level. Thus, each of these nonlinear models embeds an entire family of linear models parametric in mean light level. Harmonic distortion in the responses of these models to sinusoidal input is found to be qualitatively consistent with physiological data. An alternative class of nonlinear models in which feedback gain is set by a separate slow pathway which tracks the mean light level is ruled out on the basis of its incorrect steady-state input-output behavior. The methods presented can be used to develop specific physical models for light adaptation based on the chemical kinetics of phototransduction or on nonlinear neural feedback. The relevance of the nonlinear models and construction techniques to modeling phototransduction is discussed.

Keywords

Light adaptationNonlinear feedbackPhototransduction
Type
Research Articles
Information
Visual Neuroscience , Volume 1 , Issue 4 , July 1988 , pp. 339 - 348
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Altman, J. (1985). New visions in photoreception. Nature 313, 264–265.CrossRefGoogle Scholar
Atwell, D. (1985). Phototransduction changes focus. Nature 317, 14–15.CrossRefGoogle Scholar
Baylor, D.A. (1987). Photoreceptor signals and vision. Investigative Opthalmology and Visual Science 28, 34–49.Google ScholarPubMed
Baylor, D.A. & Hodgkin, A.L. (1974). Changes in time scale and sensitivity in turtle photoreceptors. Journal of Physiology (London) 242, 729–758.CrossRefGoogle ScholarPubMed
Baylor, D.A., Hodgkin, A.L. & Lamb, T.D. (1974). Reconstruction of the electrical responses of turtle cones to flashes and steps of light. Journal of Physiology (London) 242, 759–791.CrossRefGoogle ScholarPubMed
Baylor, D.A., Nunn, B.J. & Schnapf, J.L. (1984). The photocurrent, noise, and spectral sensitivity of rods of the monkey (Macaca fasicularis). Journal of Physiology (London) 357, 575–607.CrossRefGoogle Scholar
Baylor, D.A., Fuortes, M.G.F. & O'bryan, P.M. (1971). Receptive fields of cones in the retina of the turtle. Journal of Physiology (London) 214, 265–294.CrossRefGoogle Scholar
Bedrosian, E. & Rice, S.O. (1971). The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs. Proceedings of the IEEE 59, 1688–1707.CrossRefGoogle Scholar
Carpenter, G.A. & Grossberg, S. (1981). Adaptation and transmitter gating in vertebrate photoreceptors. Journal of Theoretical Neu-robiology 1, 1–42.Google Scholar
Chappell, R.Z., Naka, K. I. & Sakuranaga, M. (1985). Dynamics of turtle horizontal cell responses. Journal of General Physiology 86, 423–453.CrossRefGoogle Scholar
Cobbs, W.H., Barkdoll, A.E. III, & Pugh, E.N. Jr., (1985). Cyclic GMP increases photocurrent and light sensitivity of retinal cones. Nature 317, 64–66.CrossRefGoogle ScholarPubMed
Copenhagen, D.R. & Green, D.G. (1987). Spatial spread of adaptation within the cone network of turtle retina. Journal of Physiology (London) 393, 763–776.CrossRefGoogle ScholarPubMed
Daly, S.J. & Normann, R.A. (1985). Temporal information processing in cones: effects of light adaptation on temporal summation and modulation. Vision Research 25, 1197–1206.CrossRefGoogle ScholarPubMed
Hayhoe, M.M., Benimoff, N.I. & Hodd, D.C. (1987). The time course of multiplicative and subtractive adaptation processes. Vision Research 27, 1981–1986.CrossRefGoogle Scholar
Haynes, L. & Yau, K. W. (1985). Cyclic GMP-sensitive conductance in outer segment membrane of catfish cones. Nature 317, 61–63.CrossRefGoogle ScholarPubMed
Itzhaki, A. & Perlman, I. (1987). Light adaptation of red cones and LI-horizontal cells in the turtle retina: effects of the background spatial pattern. Vision Research 27, 685–696.CrossRefGoogle ScholarPubMed
Kelly, O.H. (1971). Theory of flicker and transient responses, I: Uniform fields, Journal of the Optical Society of America 61, 537–546.CrossRefGoogle ScholarPubMed
Lamb, T.D. (1986). Transduction in vertebrate photoreceptors: the roles of cyclic GMP and calcium. Trends in Neuroscience 9(5), 224–228.CrossRefGoogle Scholar
Lewin, R. (1985). Unexpected progress in photoreception. Science 221, 500–503.CrossRefGoogle Scholar
Naka, K.-I., Itoh, M.-A. & Chappell, R.L. (1987). Dynamics of turtle cones. Journal of General Physiology 89, 321–337.CrossRefGoogle ScholarPubMed
Normann, R.A. & Perlman, I. (1979 a). The effects of background illumination on the photoresponses of red and green cones. Journal of Physiology (London) 286, 491–507.CrossRefGoogle ScholarPubMed
Normann, R.A. & Perlman, I. (1979 b). Signal transmission from red cones to horizontal cells in the turtle retina. Journal of Physiology (London) 286, 509–524.CrossRefGoogle ScholarPubMed
O'bryan, P.M. (1973). Properties of the depolarizing synaptic potential evoked by peripheral illumination in cones of the turtle retina. Journal of Physiology (London) 235, 207–223.CrossRefGoogle ScholarPubMed
Pugh, E.N. & Cobbs, W.H. (1986). Visual transduction in vertebrate rods and cones: a tale of two transmitters, calcium and cyclic GMP. Vision Research 26, 1613–1643.CrossRefGoogle ScholarPubMed
Shapley, R.M. & Enroth-Cugell, C. (1984). Visual adaptation and retinal gain controls. In Progress in Retinal Research, ed. Osborne, N. & Chader, G., pp. 263–346. London, England: Pergamon Press.Google Scholar
Siminoff, R. (1985). Dynamics of the cone-horizontal cell circuit in the turtle retina. Biological Cybernetics 52, 1–14.CrossRefGoogle ScholarPubMed
Siminoff, R. (1986). Dynamics of chromatic adaptation in cones of freshwater turtle. Biological Cybernetics 53, 347–358.CrossRefGoogle ScholarPubMed
Sperling, G. & Sondhi, M.M. (1968). Model for visual luminance discrimination and flicker detection. Journal of the Optical Society of America 58, 1133–1145.CrossRefGoogle ScholarPubMed
Stieve, H., ed. (1986). The Molecular Mechanism of Photoreception. New York: Springer-Verlag.CrossRefGoogle Scholar
Stryer, L. (1986). Cyclic GMP cascade of vision. Annual Review of Neuroscience 9, 87–119.CrossRefGoogle ScholarPubMed
Tranchina, D., Gordon, J., Shapley, R. & Toyoda, J.-I. (1981). Linear information processing in the retina: a study of horizontal cell responses. Proceedings of the National Academy of Sciences (USA) 78, 6549–6542.CrossRefGoogle ScholarPubMed
Tranchina, D., Gordon, J. & Shapley, R. (1983). Spatial and temporal properties of luminosity horizontal cells in the turtle retina. Journal of General Physiology 82, 573–598.CrossRefGoogle ScholarPubMed
Tranchina, D., Gordon, J. & Shapley, R. (1984). Retinal light adaptation–evidence for a feedback mechanisms. Nature 310, 314–316.CrossRefGoogle Scholar
Victor, J.D. (1987). The dynamics of the cat retinal X cell centre. Journal of Physiology (London) 386, 219–246.CrossRefGoogle ScholarPubMed
Yau, K.W. & Nakatani, K. (1985). Light-induced reduction of cyto-plasmic free calcium in retinal rod outer segment. Nature 313, 579–582.CrossRefGoogle Scholar