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Spatio-temporal correlations and visual signalling in a complete neuronal population

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Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies1,2,3, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses4,5. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding6. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.

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Figure 1: Multi-neuron encoding model and fitted parameters.
Figure 2: Analysis of response correlations.
Figure 3: Spike-train prediction comparison.
Figure 4: Decoding performance comparison.

Change history

  • 19 September 2008

    In the online-only extended Methods, two equations were corrected on 19 September 2008. Please see the erratum at the end of the PDF for details.


  1. Mastronarde, D. N. Correlated firing of retinal ganglion cells. Trends Neurosci. 12, 75–80 (1989)

    Article  CAS  Google Scholar 

  2. Meister, M., Lagnado, L. & Baylor, D. A. Concerted signaling by retinal ganglion cells. Science 270, 1207–1210 (1995)

    Article  ADS  CAS  Google Scholar 

  3. Shadlen, M. & Newsome, W. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J. Neurosci. 18, 3870–3896 (1998)

    Article  CAS  Google Scholar 

  4. Truccolo, W., Eden, U. T., Fellows, M. R., Donoghue, J. P. & Brown, E. N. A point process framework for relating neural spiking activity to spiking history, neural ensemble and extrinsic covariate effects. J. Neurophysiol. 93, 1074–1089 (2004)

    Article  Google Scholar 

  5. Paninski, L. Maximum likelihood estimation of cascade point-process neural encoding models. Network Comp. Neural Syst. 15, 243–262 (2004)

    Article  ADS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. Dan, Y., Alonso, J. M., Usrey, W. M. & Reid, R. C. Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus. Nature Neurosci. 1, 501–507 (1998)

    Article  CAS  Google Scholar 

  8. Panzeri, S., Golledge, H., Zheng, F., Tovee, M. P. & Young, M. J. Objective assessment of the functional role of spike train correlations using information measures. Vis. Cogn. 8, 531–547 (2001)

    Article  Google Scholar 

  9. Nirenberg, S., Carcieri, S., Jacobs, A. & Latham, P. Retinal ganglion cells act largely as independent encoders. Nature 411, 698–701 (2001)

    Article  ADS  CAS  Google Scholar 

  10. Schneidman, E., Bialek, W. & Berry, M. J. Synergy, redundancy, and independence in population codes. J. Neurosci. 21, 11539–11553 (2003)

    Article  Google Scholar 

  11. Nirenberg, S. & Latham, P. E. Decoding neuronal spike trains: how important are correlations? Proc. Natl Acad. Sci. USA 100, 7348–7353 (2003)

    Article  ADS  CAS  Google Scholar 

  12. Averbeck, B. B. & Lee, D. Coding and transmission of information by neural ensembles. Trends Neurosci. 27, 225–230 (2004)

    Article  CAS  Google Scholar 

  13. Latham, P. & Nirenberg, S. Synergy, redundancy, and independence in population codes, revisited. J. Neurosci. 25, 5195–5206 (2005)

    Article  CAS  Google Scholar 

  14. Schneidman, E., Berry, M., Segev, R. & Bialek, W. Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440, 1007–1012 (2006)

    Article  ADS  CAS  Google Scholar 

  15. Shlens, J. et al. The structure of multi-neuron firing patterns in primate retina. J. Neurosci. 26, 8254–8266 (2006)

    Article  CAS  Google Scholar 

  16. Plesser, H. & Gerstner, W. Noise in integrate-and-fire neurons: From stochastic input to escape rates. Neural Comput. 12, 367–384 (2000)

    Article  CAS  Google Scholar 

  17. Simoncelli, E. P., Paninski, L., Pillow, J. & Schwartz, O. in The Cognitive Neurosciences 3rd edn (ed. Gazzaniga, M.) 327–338 (MIT, 2004)

    Google Scholar 

  18. Frechette, E. S. et al. Fidelity of the ensemble code for visual motion in primate retina. J. Neurophysiol. 94, 119–135 (2005)

    Article  CAS  Google Scholar 

  19. Okatan, M., Wilson, M. & Brown, E. Analyzing functional connectivity using a network likelihood model of ensemble neural spiking activity. Neural Comput. 17, 1927–1961 (2005)

    Article  Google Scholar 

  20. Rigat, F., de Gunst, M. & van Pelt, J. Bayesian modelling and analysis of spatio-temporal neuronal networks. Bayes. Anal. 1, 733–764 (2006)

    Article  MathSciNet  Google Scholar 

  21. DeVries, S. H. Correlated firing in rabbit retinal ganglion cells. J. Neurophysiol. 81, 908–920 (1999)

    Article  CAS  Google Scholar 

  22. Pillow, J. W., Paninski, L., Uzzell, V. J., Simoncelli, E. P. & Chichilnisky, E. J. Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model. J. Neurosci. 25, 11003–11013 (2005)

    Article  CAS  Google Scholar 

  23. Shapley, R. M. & Victor, J. D. The effect of contrast on the transfer properties of cat retinal ganglion cells. J. Physiol. 285, 275–298 (1978)

    Article  CAS  Google Scholar 

  24. Harris, K., Csicsvari, J., Hirase, H., Dragoi, G. & Buzsaki, G. Organization of cell assemblies in the hippocampus. Nature 424, 552–556 (2003)

    Article  ADS  CAS  Google Scholar 

  25. Paninski, L., Fellows, M., Shoham, S., Hatsopoulos, N. & Donoghue, J. Superlinear population encoding of dynamic hand trajectory in primary motor cortex. J. Neurosci. 24, 8551–8561 (2004)

    Article  CAS  Google Scholar 

  26. Litke, A. M. et al. What does the eye tell the brain? Development of a system for the large scale recording of retinal output activity. IEEE Trans. Nucl. Sci. 51, 1434–1440 (2004)

    Article  ADS  Google Scholar 

  27. Watanabe, M. & Rodieck, R. W. Parasol and midget ganglion cells of the primate retina. J. Comp. Neurol. 289, 434–454 (1989)

    Article  CAS  Google Scholar 

  28. Segev, R., Goodhouse, J., Puchalla, J. & Berry, M. J. Recording spikes from a large fraction of the ganglion cells in a retinal patch. Nature Neurosci. 7, 1155–1162 (2004)

    Article  Google Scholar 

  29. Pillow, J. W. & Latham, P. in Advances in Neural Information Processing Systems 20 (eds Platt, J. C., Koller, D., Singer Y. & Roweis S.) 1161–1168 (MIT, 2008)

    Google Scholar 

  30. Meister, M. & Berry, M. J. The neural code of the retina. Neuron 22, 435–450 (1999)

    Article  CAS  Google Scholar 

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We thank M. Bethge, C. Brody, D. Butts, P. Latham, M. Lengyel, S. Nirenberg and R. Sussman for comments and discussions; G. Field, M. Greschner, J. Gauthier and C. Hulse for experimental assistance; M. I. Grivich, D. Petrusca, W. Dabrowski, A. Grillo, P. Grybos, P. Hottowy and S. Kachiguine for technical development; H. Fox, M. Taffe, E. Callaway and K. Osborn for providing access to retinas; and S. Barry for machining. Funding was provided a Royal Society USA/Canada Research Fellowship (J.W.P.); NSF IGERT DGE-03345 (J.S.); NEI grant EY018003 (E.J.C., L.P. and E.P.S.); Gatsby Foundation Pilot Grant (L.P.); Burroughs Wellcome Fund Career Award at the Scientific Interface (A.S.); US National Science Foundation grant PHY-0417175 (A.M.L.); McKnight Foundation (A.M.L. and E.J.C.); and HHMI (J.W.P., L.P. and E.P.S.).

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Correspondence to Jonathan W. Pillow.

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Pillow, J., Shlens, J., Paninski, L. et al. Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454, 995–999 (2008).

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