Abstract

Changes in the maintained discharge of retinal ganglion cells have been modeled by addition of noise to a rate-setting signal, whereas the responses of cortical cells have been reported to indicate a nonlinear relationship between noise and signal. To determine whether this represents a difference between retinal cells and cortical cells, the variance of light-evoked responses of ganglion cells in the retinas of goldfish was compared with the magnitude of the responses. Variance increased for higher firing rates. These results are discussed in terms of mechanisms by which light-evoked signals might interact with the variability of maintained discharges.

© 1988 Optical Society of America

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References

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  1. M. W. Levine, “Variability in the maintained discharges of retinal ganglion cells,” J. Opt. Soc. Am. A 4, 2308–2320 (1987).
    [CrossRef]
  2. J. G. Robson, J. B. Troy, “The nature of the noise in cat retinal ganglion cells,” J. Opt. Soc. Am. A 4, 2301–2307 (1987).
    [CrossRef] [PubMed]
  3. D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981);A. F. Dean, “The variability of discharge of simple cells in the cat striate cortex,” Exp. Brain Res. 44, 437–440 (1981);D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
    [CrossRef] [PubMed]
  4. D. J. Tolhurst, “Sources of noise in cortical neurons,” submitted to J. Opt. Soc. Am. A.
  5. M. W. Levine, J. M. Shefner, “Variability in ganglion cell firing patterns: implications for separate ‘on’ and ‘off’ processes,” Vision Res. 17, 765–776 (1977).
    [CrossRef]
  6. J. M. Shefner, M. W. Levine, “A comparison of properties of goldfish retinal ganglion cells as a function of lighting conditions during dissection,” Vision Res. 19, 83–89 (1979).
    [CrossRef] [PubMed]
  7. K. S. Ginsburg, J. A. Johnsen, M. W. Levine, “Common noise in the firing of neighbouring ganglion cells in goldfish retina,” J. Physiol. 351, 433–450 (1984).
    [PubMed]
  8. J. M. Shefner, M. W. Levine, “An analysis of receptor inputs to and spatial distribution of ganglion cell on and off processes,” Vision Res. 19, 647–653 (1979).
    [CrossRef] [PubMed]
  9. M. W. Levine, J. M. Shefner, “X-like and not X-like cells in goldfish retina,” Vision Res. 19, 95–97 (1979).
    [CrossRef] [PubMed]
  10. B. W. van Dijk, J. L. Ringo, “The variation in the light responses of carp retinal ganglion cells is independent of response amplitude,” Vision Res. 27, 493–497 (1987).
    [CrossRef] [PubMed]
  11. H. B. Barlow, W. R. Levick, M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vision Res. Suppl. 3, 87–101 (1971).
    [CrossRef]
  12. B. E. A. Saleh, M. C. Teich, “Multiplication and refractoriness in the cat’s retinal-ganglion-cell discharge at low light levels,” Biol. Cybern. 52, 101–107 (1985).
    [CrossRef]
  13. M. W. Levine, J. M. Shefner, “The effects of photic stimulation upon the variability of the interspike intervals in goldfish ganglion cells,” Vision Res. 17, 793–797 (1977).
    [CrossRef] [PubMed]
  14. M. W. Levine, J. M. Shefner, “A model for the variability of interspike intervals during sustained firing of a retinal neuron,” Biophys J. 19, 241–252 (1977).
    [CrossRef] [PubMed]
  15. G. Gestri, “Pulse frequency modulation in neural systems. A random model,” Biophys. J. 11, 98–109 (1971).
    [CrossRef] [PubMed]
  16. M. W. Levine, J. M. Shefner, “Independence of ‘on’ and ‘off’ responses of retinal ganglion cells,” Science 190, 1215–1217 (1975).
    [CrossRef] [PubMed]

1987 (3)

1985 (1)

B. E. A. Saleh, M. C. Teich, “Multiplication and refractoriness in the cat’s retinal-ganglion-cell discharge at low light levels,” Biol. Cybern. 52, 101–107 (1985).
[CrossRef]

1984 (1)

K. S. Ginsburg, J. A. Johnsen, M. W. Levine, “Common noise in the firing of neighbouring ganglion cells in goldfish retina,” J. Physiol. 351, 433–450 (1984).
[PubMed]

1981 (1)

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981);A. F. Dean, “The variability of discharge of simple cells in the cat striate cortex,” Exp. Brain Res. 44, 437–440 (1981);D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

1979 (3)

J. M. Shefner, M. W. Levine, “An analysis of receptor inputs to and spatial distribution of ganglion cell on and off processes,” Vision Res. 19, 647–653 (1979).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “X-like and not X-like cells in goldfish retina,” Vision Res. 19, 95–97 (1979).
[CrossRef] [PubMed]

J. M. Shefner, M. W. Levine, “A comparison of properties of goldfish retinal ganglion cells as a function of lighting conditions during dissection,” Vision Res. 19, 83–89 (1979).
[CrossRef] [PubMed]

1977 (3)

M. W. Levine, J. M. Shefner, “Variability in ganglion cell firing patterns: implications for separate ‘on’ and ‘off’ processes,” Vision Res. 17, 765–776 (1977).
[CrossRef]

M. W. Levine, J. M. Shefner, “The effects of photic stimulation upon the variability of the interspike intervals in goldfish ganglion cells,” Vision Res. 17, 793–797 (1977).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “A model for the variability of interspike intervals during sustained firing of a retinal neuron,” Biophys J. 19, 241–252 (1977).
[CrossRef] [PubMed]

1975 (1)

M. W. Levine, J. M. Shefner, “Independence of ‘on’ and ‘off’ responses of retinal ganglion cells,” Science 190, 1215–1217 (1975).
[CrossRef] [PubMed]

1971 (2)

H. B. Barlow, W. R. Levick, M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vision Res. Suppl. 3, 87–101 (1971).
[CrossRef]

G. Gestri, “Pulse frequency modulation in neural systems. A random model,” Biophys. J. 11, 98–109 (1971).
[CrossRef] [PubMed]

Barlow, H. B.

H. B. Barlow, W. R. Levick, M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vision Res. Suppl. 3, 87–101 (1971).
[CrossRef]

Gestri, G.

G. Gestri, “Pulse frequency modulation in neural systems. A random model,” Biophys. J. 11, 98–109 (1971).
[CrossRef] [PubMed]

Ginsburg, K. S.

K. S. Ginsburg, J. A. Johnsen, M. W. Levine, “Common noise in the firing of neighbouring ganglion cells in goldfish retina,” J. Physiol. 351, 433–450 (1984).
[PubMed]

Johnsen, J. A.

K. S. Ginsburg, J. A. Johnsen, M. W. Levine, “Common noise in the firing of neighbouring ganglion cells in goldfish retina,” J. Physiol. 351, 433–450 (1984).
[PubMed]

Levick, W. R.

H. B. Barlow, W. R. Levick, M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vision Res. Suppl. 3, 87–101 (1971).
[CrossRef]

Levine, M. W.

M. W. Levine, “Variability in the maintained discharges of retinal ganglion cells,” J. Opt. Soc. Am. A 4, 2308–2320 (1987).
[CrossRef]

K. S. Ginsburg, J. A. Johnsen, M. W. Levine, “Common noise in the firing of neighbouring ganglion cells in goldfish retina,” J. Physiol. 351, 433–450 (1984).
[PubMed]

J. M. Shefner, M. W. Levine, “A comparison of properties of goldfish retinal ganglion cells as a function of lighting conditions during dissection,” Vision Res. 19, 83–89 (1979).
[CrossRef] [PubMed]

J. M. Shefner, M. W. Levine, “An analysis of receptor inputs to and spatial distribution of ganglion cell on and off processes,” Vision Res. 19, 647–653 (1979).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “X-like and not X-like cells in goldfish retina,” Vision Res. 19, 95–97 (1979).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “The effects of photic stimulation upon the variability of the interspike intervals in goldfish ganglion cells,” Vision Res. 17, 793–797 (1977).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “A model for the variability of interspike intervals during sustained firing of a retinal neuron,” Biophys J. 19, 241–252 (1977).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “Variability in ganglion cell firing patterns: implications for separate ‘on’ and ‘off’ processes,” Vision Res. 17, 765–776 (1977).
[CrossRef]

M. W. Levine, J. M. Shefner, “Independence of ‘on’ and ‘off’ responses of retinal ganglion cells,” Science 190, 1215–1217 (1975).
[CrossRef] [PubMed]

Movshon, J. A.

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981);A. F. Dean, “The variability of discharge of simple cells in the cat striate cortex,” Exp. Brain Res. 44, 437–440 (1981);D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

Ringo, J. L.

B. W. van Dijk, J. L. Ringo, “The variation in the light responses of carp retinal ganglion cells is independent of response amplitude,” Vision Res. 27, 493–497 (1987).
[CrossRef] [PubMed]

Robson, J. G.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, “Multiplication and refractoriness in the cat’s retinal-ganglion-cell discharge at low light levels,” Biol. Cybern. 52, 101–107 (1985).
[CrossRef]

Shefner, J. M.

M. W. Levine, J. M. Shefner, “X-like and not X-like cells in goldfish retina,” Vision Res. 19, 95–97 (1979).
[CrossRef] [PubMed]

J. M. Shefner, M. W. Levine, “A comparison of properties of goldfish retinal ganglion cells as a function of lighting conditions during dissection,” Vision Res. 19, 83–89 (1979).
[CrossRef] [PubMed]

J. M. Shefner, M. W. Levine, “An analysis of receptor inputs to and spatial distribution of ganglion cell on and off processes,” Vision Res. 19, 647–653 (1979).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “The effects of photic stimulation upon the variability of the interspike intervals in goldfish ganglion cells,” Vision Res. 17, 793–797 (1977).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “A model for the variability of interspike intervals during sustained firing of a retinal neuron,” Biophys J. 19, 241–252 (1977).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “Variability in ganglion cell firing patterns: implications for separate ‘on’ and ‘off’ processes,” Vision Res. 17, 765–776 (1977).
[CrossRef]

M. W. Levine, J. M. Shefner, “Independence of ‘on’ and ‘off’ responses of retinal ganglion cells,” Science 190, 1215–1217 (1975).
[CrossRef] [PubMed]

Teich, M. C.

B. E. A. Saleh, M. C. Teich, “Multiplication and refractoriness in the cat’s retinal-ganglion-cell discharge at low light levels,” Biol. Cybern. 52, 101–107 (1985).
[CrossRef]

Thompson, I. D.

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981);A. F. Dean, “The variability of discharge of simple cells in the cat striate cortex,” Exp. Brain Res. 44, 437–440 (1981);D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

Tolhurst, D. J.

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981);A. F. Dean, “The variability of discharge of simple cells in the cat striate cortex,” Exp. Brain Res. 44, 437–440 (1981);D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

D. J. Tolhurst, “Sources of noise in cortical neurons,” submitted to J. Opt. Soc. Am. A.

Troy, J. B.

van Dijk, B. W.

B. W. van Dijk, J. L. Ringo, “The variation in the light responses of carp retinal ganglion cells is independent of response amplitude,” Vision Res. 27, 493–497 (1987).
[CrossRef] [PubMed]

Yoon, M.

H. B. Barlow, W. R. Levick, M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vision Res. Suppl. 3, 87–101 (1971).
[CrossRef]

Biol. Cybern. (1)

B. E. A. Saleh, M. C. Teich, “Multiplication and refractoriness in the cat’s retinal-ganglion-cell discharge at low light levels,” Biol. Cybern. 52, 101–107 (1985).
[CrossRef]

Biophys J. (1)

M. W. Levine, J. M. Shefner, “A model for the variability of interspike intervals during sustained firing of a retinal neuron,” Biophys J. 19, 241–252 (1977).
[CrossRef] [PubMed]

Biophys. J. (1)

G. Gestri, “Pulse frequency modulation in neural systems. A random model,” Biophys. J. 11, 98–109 (1971).
[CrossRef] [PubMed]

Exp. Brain Res. (1)

D. J. Tolhurst, J. A. Movshon, I. D. Thompson, “The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast,” Exp. Brain Res. 41, 414–419 (1981);A. F. Dean, “The variability of discharge of simple cells in the cat striate cortex,” Exp. Brain Res. 44, 437–440 (1981);D. J. Tolhurst, J. A. Movshon, A. F. Dean, “The statistical reliability of signals in single neurons in cat and monkey visual cortex,” Vision Res. 23, 775–785 (1983).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

J. Physiol. (1)

K. S. Ginsburg, J. A. Johnsen, M. W. Levine, “Common noise in the firing of neighbouring ganglion cells in goldfish retina,” J. Physiol. 351, 433–450 (1984).
[PubMed]

Science (1)

M. W. Levine, J. M. Shefner, “Independence of ‘on’ and ‘off’ responses of retinal ganglion cells,” Science 190, 1215–1217 (1975).
[CrossRef] [PubMed]

Vision Res. (6)

M. W. Levine, J. M. Shefner, “The effects of photic stimulation upon the variability of the interspike intervals in goldfish ganglion cells,” Vision Res. 17, 793–797 (1977).
[CrossRef] [PubMed]

J. M. Shefner, M. W. Levine, “An analysis of receptor inputs to and spatial distribution of ganglion cell on and off processes,” Vision Res. 19, 647–653 (1979).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “X-like and not X-like cells in goldfish retina,” Vision Res. 19, 95–97 (1979).
[CrossRef] [PubMed]

B. W. van Dijk, J. L. Ringo, “The variation in the light responses of carp retinal ganglion cells is independent of response amplitude,” Vision Res. 27, 493–497 (1987).
[CrossRef] [PubMed]

M. W. Levine, J. M. Shefner, “Variability in ganglion cell firing patterns: implications for separate ‘on’ and ‘off’ processes,” Vision Res. 17, 765–776 (1977).
[CrossRef]

J. M. Shefner, M. W. Levine, “A comparison of properties of goldfish retinal ganglion cells as a function of lighting conditions during dissection,” Vision Res. 19, 83–89 (1979).
[CrossRef] [PubMed]

Vision Res. Suppl. (1)

H. B. Barlow, W. R. Levick, M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vision Res. Suppl. 3, 87–101 (1971).
[CrossRef]

Other (1)

D. J. Tolhurst, “Sources of noise in cortical neurons,” submitted to J. Opt. Soc. Am. A.

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Figures (2)

Fig. 1
Fig. 1

Variance of the firing rate versus the mean firing rate, for maintained discharges and responses to repeated 1-sec flashes. Data were analyzed for sampling of periods of 1 sec (solid squares, fitted with solid line), 0.5 sec (solid triangles, fitted with dashed line), and 0.25 sec (stars, fitted with dotted–dashed line). Maintained discharges were taken from the second preceding the first flash in each cycle and are indicated by the arrow on the abscissa. Each represents 12 cycles of four flashes, with 0.8-mm spots and 710-nm light. (a) Cell 1/14/87A. Slopes: 1 sec, 1.13 (r = 0.90); 0.5 sec, 0.80 (r = 0.83); 0.25 sec, 0.51 (r = 0.83). (b) Cell 1/21/87E. Slopes: 1 sec, 0.60 (r = 0.86); 0.5 sec, 0.51 (r = 0.91); 0.25 sec, 0.44 (r = 0.86). Insets, average peristimulus time histograms from the data in the main graphs, averaged across all cycles for 250-msec bins. Ordinate is mean rate; tics every 25 impulses/sec. Abscissas are time in the sequence in seconds; heavy bars under the abscissas indicate presence of stimuli.

Fig. 2
Fig. 2

Histogram of measured slopes from the 30 cells with at least one correlation coefficient greater than 0.7. Results are shown for sampling periods of 1 sec (solid bars), 0.5 sec (diagonal hatching), and 0.25 sec (crosshatching).

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