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Partitioning neuronal variability

Nature Neuroscience volume 17, pages 858–865 (2014)Cite this article

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Abstract

Responses of sensory neurons differ across repeated measurements. This variability is usually treated as stochasticity arising within neurons or neural circuits. However, some portion of the variability arises from fluctuations in excitability due to factors that are not purely sensory, such as arousal, attention and adaptation. To isolate these fluctuations, we developed a model in which spikes are generated by a Poisson process whose rate is the product of a drive that is sensory in origin and a gain summarizing stimulus-independent modulatory influences on excitability. This model provides an accurate account of response distributions of visual neurons in macaque lateral geniculate nucleus and cortical areas V1, V2 and MT, revealing that variability originates in large part from excitability fluctuations that are correlated over time and between neurons, and that increase in strength along the visual pathway. The model provides a parsimonious explanation for observed systematic dependencies of response variability and covariability on firing rate.

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Figure 1: The modulated Poisson model accounts for spike count variability.
Figure 2: Comparison of neural response variability for cells in different visual areas.
Figure 3: Response correlation analysis for three example pairs of simultaneously recorded V1 neurons.
Figure 4: Model-based decomposition of measured spike-count correlations into gain and point-process correlations.
Figure 5: Gain fluctuations are correlated over time.
Figure 6: Analysis of spike-count variance for a population of MT neurons recorded in awake, behaving macaques18,22.

References

  1. Mainen, Z.F. & Sejnowski, T.J. Reliability of spike timing in neocortical neurons. Science 268, 1503–1506 (1995).

    Article  CAS  PubMed  Google Scholar 

  2. Allen, C. & Stevens, C.F. An evaluation of causes for unreliability of synaptic transmission. Proc. Natl. Acad. Sci. USA 91, 10380–10383 (1994).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Softky, W.R. & Koch, C. The highly irregular firing of cortical cells is inconsistent with temporal integration of small EPSPs. J. Neurosci. 13, 334–350 (1993).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Stevens, C.F. & Zador, A. When is an integrate-and-fire neuron like a Poisson neuron? in Advances in Neural Information Processing Systems Vol. 8 (eds. Mozer, M., Touretzky, D.S. & Hasselmo, M.) 103–109 (MIT Press, 1996).

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. van Vreeswijk, C. & Sompolinsky, H. Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724–1726 (1996).

    Article  CAS  PubMed  Google Scholar 

  7. Vogels, T.P. & Abbott, L.F. Signal propagation in networks of integrate-and-fire neurons. J. Neurosci. 25, 10786–10795 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  8. Tomko, G.J. & Crapper, D.R. Neuronal variability: non-stationary responses to identical visual stimuli. Brain Res. 79, 405–418 (1974).

    Article  CAS  PubMed  Google Scholar 

  9. Tolhurst, D.J., Movshon, J.A. & Thompson, I.D. The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast. Exp. Brain Res. 41, 414–419 (1981).

    CAS  PubMed  Google Scholar 

  10. Kato, H.K., Chu, M.W., Isaacson, J.S. & Komiyama, T. Dynamic sensory representations in the olfactory bulb: modulation by wakefulness and experience. Neuron 76, 962–975 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Luck, S.J., Chelazzi, L., Hillyard, S.A. & Desimone, R. Neural mechanisms of spatial selective attention in areas V1, V2, and V4 of macaque visual cortex. J. Neurophysiol. 77, 24–42 (1997).

    Article  CAS  PubMed  Google Scholar 

  12. Benucci, A., Saleem, A.B. & Carandini, M. Adaptation maintains population homeostasis in primary visual cortex. Nat. Neurosci. 16, 724–729 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Ecker, A.S. et al. State dependence of noise correlations in macaque primary visual cortex. Neuron 82, 235–248 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Churchland, A.K. et al. Variance as a signature of neural computations during decision-making. Neuron 69, 818–831 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  15. Cohen, M.R. & Kohn, A. Measuring and interpreting neuronal correlations. Nat. Neurosci. 14, 811–819 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Brody, C.D. Correlations without synchrony. Neural Comput. 11, 1537–1551 (1999).

    Article  CAS  PubMed  Google Scholar 

  17. Ecker, A.S. et al. Decorrelated neuronal firing in cortical microcircuits. Science 327, 584–587 (2010).

    Article  CAS  PubMed  Google Scholar 

  18. Zohary, E., Shadlen, M.N. & Newsome, W.T. Correlated neuronal discharge rate and its implications for psychophysical performance. Nature 370, 140–143 (1994).

    Article  CAS  PubMed  Google Scholar 

  19. Smith, M.A. & Kohn, A. Spatial and temporal scales of neuronal correlation in primary visual cortex. J. Neurosci. 28, 12591–12603 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Graf, A.B.A., Kohn, A., Jazayeri, M. & Movshon, J.A. Decoding the activity of neuronal populations in macaque primary visual cortex. Nat. Neurosci. 14, 239–245 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Pillow, J.W., Shlens, J., Chichilnisky, E.J. & Simoncelli, E.P. A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings. PLoS ONE 8, e62123 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Britten, K.H., Shadlen, M.N., Newsome, W.T. & Movshon, J.A. The analysis of visual motion: a comparison of neuronal and psychophysical performance. J. Neurosci. 12, 4745–4765 (1992).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Sherman, S.M. & Guillery, R.W. On the actions that one nerve cell can have on another: distinguishing “drivers” from “modulators”. Proc. Natl. Acad. Sci. USA 95, 7121–7126 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Kuffler, S.W., Fitzhugh, R. & Barlow, H.B. Maintained activity in the cat's retina in light and darkness. J. Gen. Physiol. 40, 683–702 (1957).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Grossman, R.G. & Viernstein, L.J. Discharge patterns of neurons in cochlear nucleus. Science 134, 99–101 (1961).

    Article  CAS  PubMed  Google Scholar 

  26. Siebert, W.M. Frequency discrimination in auditory system—place or periodicity mechanisms? Proc. IEEE 58, 723–730 (1970).

    Article  Google Scholar 

  27. Geisler, W.S. & Albrecht, D.G. Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty. Vision Res. 35, 2723–2730 (1995).

    Article  CAS  PubMed  Google Scholar 

  28. Churchland, M.M. et al. Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat. Neurosci. 13, 369–378 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Gur, M., Beylin, A. & Snodderly, D.M. Response variability in primary visual cortex (V1) of alert monkey. J. Neurosci. 17, 2914–2920 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Gershon, E.D., Wiener, M.C., Latham, P.E. & Richmond, B.J. Coding strategies in monkey V1 and inferior temporal cortices. J. Neurophysiol. 79, 1135–1144 (1998).

    Article  CAS  PubMed  Google Scholar 

  31. Oram, M.W., Wiener, M.C., Lestienne, R. & Richmond, B.J. The stochastic nature of precisely timed spike patterns in visual system neural responses. J. Neurophysiol. 81, 3021–3033 (1999).

    Article  CAS  PubMed  Google Scholar 

  32. Barbieri, R., Quirk, M.C., Frank, L.M., Wilson, M.A. & Brown, E.N. Construction and analysis of non-Poisson stimulus-response models of neural spike train activity. J. Neurosci. Methods 105, 25–37 (2001).

    Article  CAS  PubMed  Google Scholar 

  33. Kara, P., Reinagel, P. & Reid, R.C. Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron 27, 635–646 (2000).

    Article  CAS  PubMed  Google Scholar 

  34. Amarasingham, A., Chen, T.-L., Geman, S., Harrison, M. & Sheinberg, D. Spike count reliability and the Poisson hypothesis. J. Neurosci. 26, 801–809 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. 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 (2005).

    Article  PubMed  Google Scholar 

  36. 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 

  37. Pillow, J.W. & Scott, J.G. Fully Bayesian inference for neural models with negative-binomial spiking. in Advances in Neural Information Processing Systems Vol. 25 (eds. Bartlett, P., Pereira, F.C.N., Burges, C.J.C., Bottou, L. & Weinberger, K.Q.) 1907–1915 (MIT Press, 2012).

  38. Wiener, M.C. & Richmond, B.J. Decoding spike trains instant by instant using order statistics and the mixture-of-Poissons model. J. Neurosci. 23, 2394–2406 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Cohen, M.R. & Maunsell, J.H.R. Attention improves performance primarily by reducing interneuronal correlations. Nat. Neurosci. 12, 1594–1600 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Dorn, J.D. & Ringach, D.L. Estimating membrane voltage correlations from extracellular spike trains. J. Neurophysiol. 89, 2271–2278 (2003).

    Article  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  42. Vidne, M. et al. Modeling the impact of common noise inputs on the network activity of retinal ganglion cells. J. Comput. Neurosci. 33, 97–121 (2012).

    Article  PubMed  Google Scholar 

  43. Goris, R.L.T., Putzeys, T., Wagemans, J. & Wichmann, F.A. A neural population model for visual pattern detection. Psychol. Rev. 120, 472–496 (2013).

    Article  PubMed  Google Scholar 

  44. van den Berg, R., Shin, H., Chou, W.-C., George, R. & Ma, W.J. Variability in encoding precision accounts for visual short-term memory limitations. Proc. Natl. Acad. Sci. USA 109, 8780–8785 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Cavanaugh, J.R., Bair, W. & Movshon, J.A. Nature and interaction of signals from the receptive field center and surround in macaque V1 neurons. J. Neurophysiol. 88, 2530–2546 (2002).

    Article  PubMed  Google Scholar 

  46. Smith, M.A., Majaj, N.J. & Movshon, J.A. Dynamics of motion signaling by neurons in macaque area MT. Nat. Neurosci. 8, 220–228 (2005).

    Article  CAS  PubMed  Google Scholar 

  47. Cox, D.R. Some statistical methods connected with series of events. J. R. Stat. Soc. Ser. A 17, 129–164 (1955).

    Google Scholar 

  48. Greenwood, M. & Yule, G.U. An inquiry into the nature of frequency distributions of multiple happenings, with particular reference to the occurrence of multiple attacks of disease or repeated accidents. J. R. Stat. Soc. A. 83, 255–279 (1920).

    Article  Google Scholar 

  49. Polson, N.G., Scott, J.G. & Windle, J. Bayesian inference for logistic models using Polya-gamma latent variables. J. Am. Stat. Assoc. 108, 1339–1349 (2013).

    Article  CAS  Google Scholar 

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Acknowledgements

We are grateful to R. Kumbhani and N. Rabinowitz for discussions and to members of the Movshon laboratory for sharing their data. This work was supported by US National Institutes of Health grants EY04440, EY022428, the Howard Hughes Medical Institute and postdoctoral fellowships from the Fund for Scientific Research of Flanders and the Belgian American Educational Foundation awarded to R.L.T.G.

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Authors and Affiliations

  1. Center for Neural Science, New York University, New York, New York, USA

    Robbe L T Goris, J Anthony Movshon & Eero P Simoncelli

  2. Howard Hughes Medical Institute, New York University, New York, New York, USA

    Eero P Simoncelli

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  1. Robbe L T Goris
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R.L.T.G., J.A.M. and E.P.S. designed research; R.L.T.G. analyzed data; and R.L.T.G., J.A.M. and E.P.S. wrote the paper.

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Correspondence to Eero P Simoncelli.

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Goris, R., Movshon, J. & Simoncelli, E. Partitioning neuronal variability. Nat Neurosci 17, 858–865 (2014). https://doi.org/10.1038/nn.3711

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