Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Decorrelation and efficient coding by retinal ganglion cells

Abstract

An influential theory of visual processing asserts that retinal center-surround receptive fields remove spatial correlations in the visual world, producing ganglion cell spike trains that are less redundant than the corresponding image pixels. For bright, high-contrast images, this decorrelation would enhance coding efficiency in optic nerve fibers of limited capacity. We tested the central prediction of the theory and found that the spike trains of retinal ganglion cells were indeed decorrelated compared with the visual input. However, most of the decorrelation was accomplished not by the receptive fields, but by nonlinear processing in the retina. We found that a steep response threshold enhanced efficient coding by noisy spike trains and that the effect of this nonlinearity was near optimal in both salamander and macaque retina. These results offer an explanation for the sparseness of retinal spike trains and highlight the importance of treating the full nonlinear character of neural codes.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Decorrelation of naturalistic stimuli.
Figure 2: Nonlinearity accounts for much of decorrelation.
Figure 3: Sparseness in retinal responses.
Figure 4: Decorrelation and efficient coding in the LNP model.
Figure 5: Efficiency of stimulus coding by RGCs.

Similar content being viewed by others

References

  1. Attneave, F. Some informational aspects of visual perception. Psychol. Rev. 61, 183–193 (1954).

    Article  CAS  PubMed  Google Scholar 

  2. Barlow, H.B. Possible principles underlying the transformation of sensory messages. in Sensory Communication (ed. Rosenblith, W.A.) 217–234 (MIT Press, Cambridge, MA, 1961).

  3. Srinivasan, M.V., Laughlin, S.B. & Dubs, A. Predictive coding: a fresh view of inhibition in the retina. Proc. R. Soc. Lond. B Biol. Sci. 216, 427–459 (1982).

    Article  CAS  PubMed  Google Scholar 

  4. Atick, J.J. & Redlich, A.N. What does the retina know about natural scenes? Neural Comput. 4, 196–210 (1992).

    Article  Google Scholar 

  5. Atick, J.J. & Redlich, A.N. Convergent algorithm for sensory receptive field development. Neural Comput. 5, 45–60 (1993).

    Article  Google Scholar 

  6. Atick, J.J. & Redlich, A.N. Could information theory provide an ecological theory of sensory processing? Network 3, 213–251 (1992).

    Article  Google Scholar 

  7. van Hateren, J.H. Real and optimal neural images in early vision. Nature 360, 68–70 (1992).

    Article  CAS  PubMed  Google Scholar 

  8. van Hateren, J.H. Spatiotemporal contrast sensitivity of early vision. Vision Res. 33, 257–267 (1993).

    Article  CAS  PubMed  Google Scholar 

  9. Field, D.J. Relations between the statistics of natural images and the response properties of cortical cells. J. Opt. Soc. Am. A 4, 2379–2394 (1987).

    Article  CAS  PubMed  Google Scholar 

  10. Atick, J.J. & Redlich, A.N. Toward a theory of early visual processing. Neural Comput. 2, 308–320 (1990).

    Article  Google Scholar 

  11. Dan, Y., Atick, J.J. & Reid, R.C. Efficient coding of natural scenes in the lateral geniculate nucleus: experimental test of a computational theory. J. Neurosci. 16, 3351–3362 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  12. Puchalla, J.L., Schneidman, E., Harris, R.A. & Berry, M.J. Redundancy in the population code of the retina. Neuron 46, 493–504 (2005).

    Article  CAS  PubMed  Google Scholar 

  13. Chichilnisky, E.J. A simple white noise analysis of neuronal light responses. Network 12, 199–213 (2001).

    Article  CAS  PubMed  Google Scholar 

  14. Warland, D.K., Reinagel, P. & Meister, M. Decoding visual information from a population of retinal ganglion cells. J. Neurophysiol. 78, 2336–2350 (1997).

    Article  CAS  PubMed  Google Scholar 

  15. Segev, R., Puchalla, J. & Berry, M.J. Functional organization of ganglion cells in the salamander retina. J. Neurophysiol. 95, 2277–2292 (2006).

    Article  PubMed  Google Scholar 

  16. Enroth–Cugell, C. & Robson, J.G. Functional characteristics and diversity of cat retinal ganglion cells. Basic characteristics and quantitative description. Invest. Ophthalmol. Vis. Sci. 25, 250–267 (1984).

    PubMed  Google Scholar 

  17. Berry, M.J. & Meister, M. Refractoriness and neural precision. J. Neurosci. 18, 2200–2211 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Burrone, J. & Lagnado, L. Synaptic depression and the kinetics of exocytosis in retinal bipolar cells. J. Neurosci. 20, 568–578 (2000).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Demb, J.B., Zaghloul, K., Haarsma, L. & Sterling, P. Bipolar cells contribute to nonlinear spatial summation in the brisk-transient (Y) ganglion cell in mammalian retina. J. Neurosci. 21, 7447–7454 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Field, G.D. & Rieke, F. Nonlinear signal transfer from mouse rods to bipolar cells and implications for visual sensitivity. Neuron 34, 773–785 (2002).

    Article  CAS  PubMed  Google Scholar 

  21. Uzzell, V.J. & Chichilnisky, E.J. Precision of spike trains in primate retinal ganglion cells. J. Neurophysiol. 92, 780–789 (2004).

    Article  CAS  PubMed  Google Scholar 

  22. Pillow, J.W. et al. Spatio-temporal correlations and visual signaling in a complete neuronal population. Nature 454, 995–999 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Chichilnisky, E.J. & Kalmar, R.S. Functional asymmetries in ON and OFF ganglion cells of primate retina. J. Neurosci. 22, 2737–2747 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Croner, L.J., Purpura, K. & Kaplan, E. Response variability in retinal ganglion cells of primates. Proc. Natl. Acad. Sci. USA 90, 8128–8130 (1993).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Schwartz, O., Pillow, J.W., Rust, N.C. & Simoncelli, E.P. Spike-triggered neural characterization. J. Vis. 6, 484–507 (2006).

    Article  PubMed  Google Scholar 

  26. Lancaster, H.O. Some properties of the bivariate normal distribution considered in the form of a contingency table. Biometrika 44, 289–292 (1957).

    Article  Google Scholar 

  27. de la Rocha, J., Doiron, B., Shea–Brown, E., Josic, K. & Reyes, A. Correlation between neural spike trains increases with firing rate. Nature 448, 802–806 (2007).

    Article  CAS  PubMed  Google Scholar 

  28. Berry, M.J., Warland, D.K. & Meister, M. The structure and precision of retinal spike trains. Proc. Natl. Acad. Sci. USA 94, 5411–5416 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Reinagel, P. How do visual neurons respond in the real world? Curr. Opin. Neurobiol. 11, 437–442 (2001).

    Article  CAS  PubMed  Google Scholar 

  30. Baccus, S.A. & Meister, M. Fast and slow contrast adaptation in retinal circuitry. Neuron 36, 909–919 (2002).

    Article  CAS  PubMed  Google Scholar 

  31. Stein, R.B. The information capacity of nerve cells using a frequency code. Biophys. J. 7, 797–826 (1967).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Shamai, S. Capacity of a pulse amplitude modulated direct detection photon channel. IEE Proc. Commun. Speech Vis. 137, 424–430 (1990).

    Article  Google Scholar 

  33. Keat, J., Reinagel, P., Reid, R.C. & Meister, M. Predicting every spike: a model for the responses of visual neurons. Neuron 30, 803–817 (2001).

    Article  CAS  PubMed  Google Scholar 

  34. Balasubramanian, V. & Berry, M.J. A test of metabolically efficient coding in the retina. Network 13, 531–552 (2002).

    Article  PubMed  Google Scholar 

  35. Hosoya, T., Baccus, S.A. & Meister, M. Dynamic predictive coding by the retina. Nature 436, 71–77 (2005).

    Article  CAS  PubMed  Google Scholar 

  36. Croner, L.J. & Kaplan, E. Receptive fields of P and M ganglion cells across the primate retina. Vision Res. 35, 7–24 (1995).

    Article  CAS  PubMed  Google Scholar 

  37. Barlow, H.B. & Levick, W.R. The mechanism of directionally selective units in rabbit′s retina. J. Physiol. (Lond.) 178, 477–504 (1965).

    Article  CAS  Google Scholar 

  38. Ölveczky, B.P., Baccus, S.A. & Meister, M. Segregation of object and background motion in the retina. Nature 423, 401–408 (2003).

    Article  PubMed  Google Scholar 

  39. Levick, W.R. Receptive fields and trigger features of ganglion cells in the visual streak of the rabbits retina. J. Physiol. (Lond.) 188, 285–307 (1967).

    Article  CAS  Google Scholar 

  40. Gollisch, T. & Meister, M. Eye smarter than scientists believed: neural computations in circuits of the retina. Neuron 65, 150–164 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Dacey, D.M. Origins of perception: retinal ganglion cell diversity and the creation of parallel visual pathways. in The Cognitive Neurosciences (ed. Gazzaniga, M.S.) 281–301 (MIT Press, Cambridge, Massachusetts, 2004).

  42. Laughlin, S.B. A simple coding procedure enhances a neuron′s information capacity. Z. Naturforsch. C 36c, 910–912 (1981).

    Article  Google Scholar 

  43. Olshausen, B.A. & Field, D.J. Sparse coding of sensory inputs. Curr. Opin. Neurobiol. 14, 481–487 (2004).

    Article  CAS  PubMed  Google Scholar 

  44. Ringach, D.L. & Malone, B.J. The operating point of the cortex: neurons as large deviation detectors. J. Neurosci. 27, 7673–7683 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. van Vreeswijk, C.A. Whence sparseness? Adv. Neural Inf. Process. Syst. 13, 189–195 (2001).

    Google Scholar 

  46. Vinje, W.E. & Gallant, J.L. Sparse coding and decorrelation in primary visual cortex during natural vision. Science 287, 1273–1276 (2000).

    Article  CAS  PubMed  Google Scholar 

  47. Wang, X.J., Liu, Y., Sanchez–Vives, M.V. & McCormick, D.A. Adaptation and temporal decorrelation by single neurons in the primary visual cortex. J. Neurophysiol. 89, 3279–3293 (2003).

    Article  PubMed  Google Scholar 

  48. Rucci, M. & Casile, A. Fixational instability and natural image statistics: implications for early visual representations. Network 16, 121–138 (2005).

    Article  PubMed  Google Scholar 

  49. Cleland, T.A. Early transformations in odor representation. Trends Neurosci. 33, 130–139 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. Wiechert, M.T., Judkewitz, B., Riecke, H. & Friedrich, R.W. Mechanisms of pattern decorrelation by recurrent neuronal circuits. Nat. Neurosci. 13, 1003–1010 (2010).

    Article  CAS  PubMed  Google Scholar 

  51. Meister, M., Pine, J. & Baylor, D.A. Multi–neuronal signals from the retina: acquisition and analysis. J. Neurosci. Methods 51, 95–106 (1994).

    Article  CAS  PubMed  Google Scholar 

  52. Segev, R., Puchalla, J. & Berry, M.J. Functional organization of ganglion cells in the salamander retina. J. Neurophysiol. 95, 2277–2292 (2006).

    Article  PubMed  Google Scholar 

  53. Himstedt, W. Prey selection in salamanders. in Analysis of Visual Behavior (eds. Ingale, D.J., Goodale, M.A. & Mansfield, R.J.W.) 47–66 (MIT Press, Cambridge, Massachusetts, 1982).

  54. Dong, D.W. & Atick, J.J. Statistics of natural time-varying images. Network 6, 345–358 (1995).

    Article  Google Scholar 

  55. Croner, L.J. & Kaplan, E. Receptive fields of P and M ganglion cells across the primate retina. Vision Res. 35, 7–24 (1995).

    Article  CAS  PubMed  Google Scholar 

  56. Chichilnisky, E.J. & Kalmar, R.S. Functional asymmetries in ON and OFF ganglion cells of primate retina. J. Neurosci. 22, 2737–2747 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  57. Berry, M.J. & Meister, M. Refractoriness and neural precision. J. Neurosci. 18, 2200–2211 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. Uzzell, V.J. & Chichilnisky, E.J. Precision of spike trains in primate retinal ganglion cells. J. Neurophysiol. 92, 780–789 (2004).

    Article  CAS  PubMed  Google Scholar 

  59. Schneidman, E., Bialek, W. & Berry, M.J. Synergy, redundancy and independence in population codes. J. Neurosci. 23, 11539–11553 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Pillow, J.W. et al. Spatio–temporal correlations and visual signaling in a complete neuronal population. Nature 454, 995–999 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

We thank the members of the Meister laboratory, M. Berry, T. Toyozumi and J.-P. Nadal for helpful advice. This work was funded by grants from the US National Institutes of Health to M.M.

Author information

Authors and Affiliations

Authors

Contributions

X.P. and M.M. designed the study. X.P. performed all of the experiments, analysis and modeling. X.P. and M.M. wrote the article.

Corresponding author

Correspondence to Markus Meister.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–3 (PDF 501 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pitkow, X., Meister, M. Decorrelation and efficient coding by retinal ganglion cells. Nat Neurosci 15, 628–635 (2012). https://doi.org/10.1038/nn.3064

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nn.3064

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing