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Measuring and interpreting neuronal correlations

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Abstract

Mounting evidence suggests that understanding how the brain encodes information and performs computations will require studying the correlations between neurons. The recent advent of recording techniques such as multielectrode arrays and two-photon imaging has made it easier to measure correlations, opening the door for detailed exploration of their properties and contributions to cortical processing. However, studies have reported discrepant findings, providing a confusing picture. Here we briefly review these studies and conduct simulations to explore the influence of several experimental and physiological factors on correlation measurements. Differences in response strength, the time window over which spikes are counted, spike sorting conventions and internal states can all markedly affect measured correlations and systematically bias estimates. Given these complicating factors, we offer guidelines for interpreting correlation data and a discussion of how best to evaluate the effect of correlations on cortical processing.

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Figure 1: Types of pair-wise neuronal correlations.
Figure 2: Measured correlations are small when responses are weak.
Figure 3: Counting spikes over short response windows can decrease measured correlations.
Figure 4: Measured correlations grow slowly with the number of units that contribute to multiunit activity.
Figure 5: Spike sorting errors can reduce the strength of measured correlations.
Figure 6: Differences in mean rates duration predict much of the variability in rSC measurements across studies.

Change history

  • 07 November 2011

    In the version of this article initially published, the firing rate and mean correlation value given in Table 1 for ref. 26 were incorrect. The correct values are 3.4 Hz and 0.18, respectively. This change affects the corresponding data point in Figure 6 and a value derived from this figure that was stated in the figure legend and main text, which should read "differences in mean rate can account for 33% of the across-study variance in reported values of rSC." The errors have been corrected in the PDF and HTML versions of this article.

References

  1. Tolhurst, D.J., Movshon, J.A. & Dean, A.F. The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vision Res. 23, 775–785 (1983).

    CAS  Article  PubMed  Google Scholar 

  2. 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).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. Abbott, L.F. & Dayan, P. The effect of correlated variability on the accuracy of a population code. Neural Comput. 11, 91–101 (1999).

    CAS  PubMed  Google Scholar 

  4. Averbeck, B.B., Latham, P.E. & Pouget, A. Neural correlations, population coding and computation. Nat. Rev. Neurosci. 7, 358–366 (2006).

    CAS  PubMed  Google Scholar 

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

    CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  PubMed  Google Scholar 

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

    CAS  PubMed  PubMed Central  Google Scholar 

  8. Mitchell, J.F., Sundberg, K.A. & Reynolds, J.H. Spatial attention decorrelates intrinsic activity fluctuations in macaque area V4. Neuron 63, 879–888 (2009).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  9. Aertsen, A.M., Gerstein, G.L., Habib, M.K. & Palm, G. Dynamics of neuronal firing correlation: modulation of “effective connectivity”. J. Neurophysiol. 61, 900–917 (1989).

    CAS  PubMed  Google Scholar 

  10. Ahissar, E. et al. Dependence of cortical plasticity on correlated activity of single neurons and on behavioral context. Science 257, 1412–1415 (1992).

    CAS  PubMed  Google Scholar 

  11. Espinosa, I.E. & Gerstein, G.L. Cortical auditory neuron interactions during presentation of 3-tone sequences: effective connectivity. Brain Res. 450, 39–50 (1988).

    CAS  PubMed  Google Scholar 

  12. Kohn, A. & Smith, M.A. Stimulus dependence of neuronal correlation in primary visual cortex of the macaque. J. Neurosci. 25, 3661–3673 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  13. Gutnisky, D.A. & Dragoi, V. Adaptive coding of visual information in neural populations. Nature 452, 220–224 (2008).

    CAS  PubMed  Google Scholar 

  14. Komiyama, T. et al. Learning-related fine-scale specificity imaged in motor cortex circuits of behaving mice. Nature 464, 1182–1186 (2010).

    CAS  PubMed  Google Scholar 

  15. Cohen, M.R. & Newsome, W.T. Context-dependent changes in functional circuitry in visual area MT. Neuron 60, 162–173 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. Poulet, J.F. & Petersen, C.C. Internal brain state regulates membrane potential synchrony in barrel cortex of behaving mice. Nature 454, 881–885 (2008).

    CAS  Article  PubMed  Google Scholar 

  17. Vaadia, E. et al. Dynamics of neuronal interactions in monkey cortex in relation to behavioural events. Nature 373, 515–518 (1995).

    CAS  PubMed  Google Scholar 

  18. Seriès, P., Latham, P.E. & Pouget, A. Tuning curve sharpening for orientation selectivity: coding efficiency and the impact of correlations. Nat. Neurosci. 7, 1129–1135 (2004).

    PubMed  Google Scholar 

  19. Greschner, M. et al. Correlated firing among major ganglion cell types in primate retina. J. Physiol. (Lond.) 589, 75–86 (2011).

    CAS  Google Scholar 

  20. Reid, R.C. & Alonso, J.M. Specificity of monosynaptic connections from thalamus to visual cortex. Nature 378, 281–284 (1995).

    CAS  PubMed  Google Scholar 

  21. Alonso, J.M. & Martinez, L.M. Functional connectivity between simple cells and complex cells in cat striate cortex. Nat. Neurosci. 1, 395–403 (1998).

    CAS  PubMed  Google Scholar 

  22. Bair, W., Zohary, E. & Newsome, W.T. Correlated firing in macaque visual area MT: time scales and relationship to behavior. J. Neurosci. 21, 1676–1697 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. Reich, D.S., Mechler, F. & Victor, J.D. Independent and redundant information in nearby cortical neurons. Science 294, 2566–2568 (2001).

    CAS  PubMed  Google Scholar 

  24. Constantinidis, C. & Goldman-Rakic, P.S. Correlated discharges among putative pyramidal neurons and interneurons in the primate prefrontal cortex. J. Neurophysiol. 88, 3487–3497 (2002).

    PubMed  Google Scholar 

  25. Lee, D., Port, N.L., Kruse, W. & Georgopoulos, A.P. Variability and correlated noise in the discharge of neurons in motor and parietal areas of the primate cortex. J. Neurosci. 18, 1161–1170 (1998).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  PubMed  PubMed Central  Google Scholar 

  27. Averbeck, B.B. & Lee, D. Neural noise and movement-related codes in the macaque supplementary motor area. J. Neurosci. 23, 7630–7641 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    CAS  PubMed  Google Scholar 

  29. Huang, X. & Lisberger, S.G. Noise correlations in cortical area MT and their potential impact on trial-by-trial variation in the direction and speed of smooth-pursuit eye movements. J. Neurophysiol. 101, 3012–3030 (2009).

    PubMed  PubMed Central  Google Scholar 

  30. Jermakowicz, W.J., Chen, X., Khaytin, I., Bonds, A.B. & Casagrande, V.A. Relationship between spontaneous and evoked spike-time correlations in primate visual cortex. J. Neurophysiol. 101, 2279–2289 (2009).

    PubMed  PubMed Central  Google Scholar 

  31. Rasch, M.J., Schuch, K., Logothetis, N.K. & Maass, W. Statistical comparison of spike responses to natural stimuli in monkey area V1 with simulated responses of a detailed laminar network model for a patch of V1. J. Neurophysiol. 105, 757–778 (2011).

    PubMed  Google Scholar 

  32. Zhang, M. & Alloway, K.D. Stimulus-induced intercolumnar synchronization of neuronal activity in rat barrel cortex: a laminar analysis. J. Neurophysiol. 92, 1464–1478 (2004).

    PubMed  Google Scholar 

  33. Renart, A. et al. The asynchronous state in cortical circuits. Science 327, 587–590 (2010).

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  34. 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).

    CAS  PubMed  Google Scholar 

  35. Lampl, I., Reichova, I. & Ferster, D. Synchronous membrane potential fluctuations in neurons of the cat visual cortex. Neuron 22, 361–374 (1999).

    CAS  PubMed  Google Scholar 

  36. Okun, M. & Lampl, I. Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities. Nat. Neurosci. 11, 535–537 (2008).

    CAS  PubMed  Google Scholar 

  37. Kazama, H. & Wilson, R.I. Origins of correlated activity in an olfactory circuit. Nat. Neurosci. 12, 1136–1144 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

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

    PubMed  Google Scholar 

  39. Carandini, M. Amplification of trial-to-trial response variability by neurons in visual cortex. PLoS Biol. 2, e264 (2004).

    PubMed  PubMed Central  Google Scholar 

  40. Mazurek, M.E. & Shadlen, M.N. Limits to the temporal fidelity of cortical spike rate signals. Nat. Neurosci. 5, 463–471 (2002).

    CAS  PubMed  Google Scholar 

  41. Bedenbaugh, P. & Gerstein, G.L. Multiunit normalized cross correlation differs from the average single-unit normalized correlation. Neural Comput. 9, 1265–1275 (1997).

    CAS  PubMed  Google Scholar 

  42. Rosenbaum, R.J., Trousdale, J. & Josic, K. Pooling and correlated neural activity. Front. Comput. Neurosci. 4, 9 (2010).

    PubMed  PubMed Central  Google Scholar 

  43. Müller, H.J. & Rabbitt, P.M. Reflexive and voluntary orienting of visual attention: time course of activation and resistance to interruption. J. Exp. Psychol. Hum. Percept. Perform. 15, 315–330 (1989).

    PubMed  Google Scholar 

  44. Cheal, M. & Lyon, D.R. Central and peripheral precuing of forced-choice discrimination. Q. J. Exp. Psychol. A 43, 859–880 (1991).

    CAS  PubMed  Google Scholar 

  45. Müller, M.M., Teder-Salejarvi, W. & Hillyard, S.A. The time course of cortical facilitation during cued shifts of spatial attention. Nat. Neurosci. 1, 631–634 (1998).

    PubMed  Google Scholar 

  46. Kröse, B.J. & Julesz, B. The control and speed of shifts of attention. Vision Res. 29, 1607–1619 (1989).

    PubMed  Google Scholar 

  47. Nakayama, K. & Mackeben, M. Sustained and transient components of focal visual attention. Vision Res. 29, 1631–1647 (1989).

    CAS  PubMed  Google Scholar 

  48. Bisley, J.W. & Goldberg, M.E. Neuronal activity in the lateral intraparietal area and spatial attention. Science 299, 81–86 (2003).

    CAS  PubMed  Google Scholar 

  49. Herrington, T.M. & Assad, J.A. Neural activity in the middle temporal area and lateral intraparietal area during endogenously cued shifts of attention. J. Neurosci. 29, 14160–14176 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. Bair, W. & O'Keefe, L.P. The influence of fixational eye movements on the response of neurons in area MT of the macaque. Vis. Neurosci. 15, 779–786 (1998).

    CAS  PubMed  Google Scholar 

  51. Berens, P., Keliris, G.A., Ecker, A.S., Logothetis, N.K. & Tolias, A.S. Feature selectivity of the gamma-band of the local field potential in primate primary visual cortex. Front. Neurosci. 2, 199–207 (2008).

    PubMed  PubMed Central  Google Scholar 

  52. Amari, S. Measure of correlation orthogonal to change in firing rate. Neural Comput. 21, 960–972 (2009).

    PubMed  Google Scholar 

  53. Britten, K.H., Newsome, W.T., Shadlen, M.N., Celebrini, S. & Movshon, J.A. A relationship between behavioral choice and the visual responses of neurons in macaque MT. Vis. Neurosci. 13, 87–100 (1996).

    CAS  PubMed  Google Scholar 

  54. Nienborg, H. & Cumming, B. Correlations between the activity of sensory neurons and behavior: how much do they tell us about a neuron's causality? Curr. Opin. Neurobiol. 20, 376–381 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  55. Parker, A.J. & Newsome, W.T. Sense and the single neuron: probing the physiology of perception. Annu. Rev. Neurosci. 21, 227–277 (1998).

    CAS  PubMed  Google Scholar 

  56. Palmer, C., Cheng, S.Y. & Seidemann, E. Linking neuronal and behavioral performance in a reaction-time visual detection task. J. Neurosci. 27, 8122–8137 (2007).

    CAS  PubMed  PubMed Central  Google Scholar 

  57. Bollimunta, A., Chen, Y., Schroeder, C.E. & Ding, M. Neuronal mechanisms of cortical alpha oscillations in awake-behaving macaques. J. Neurosci. 28, 9976–9988 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  58. Thut, G., Nietzel, A., Brandt, S.A. & Pascual-Leone, A. Alpha-band electroencephalographic activity over occipital cortex indexes visuospatial attention bias and predicts visual target detection. J. Neurosci. 26, 9494–9502 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  59. Fox, M.D., Snyder, A.Z., Vincent, J.L. & Raichle, M.E. Intrinsic fluctuations within cortical systems account for intertrial variability in human behavior. Neuron 56, 171–184 (2007).

    CAS  PubMed  Google Scholar 

  60. Grill-Spector, K., Knouf, N. & Kanwisher, N. The fusiform face area subserves face perception, not generic within-category identification. Nat. Neurosci. 7, 555–562 (2004).

    CAS  PubMed  Google Scholar 

  61. Leber, A.B. Neural predictors of within-subject fluctuations in attentional control. J. Neurosci. 30, 11458–11465 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  62. Ress, D., Backus, B.T. & Heeger, D.J. Activity in primary visual cortex predicts performance in a visual detection task. Nat. Neurosci. 3, 940–945 (2000).

    CAS  PubMed  Google Scholar 

  63. Ress, D. & Heeger, D.J. Neuronal correlates of perception in early visual cortex. Nat. Neurosci. 6, 414–420 (2003).

    CAS  PubMed  PubMed Central  Google Scholar 

  64. Sapir, A., d'Avossa, G., McAvoy, M., Shulman, G.L. & Corbetta, M. Brain signals for spatial attention predict performance in a motion discrimination task. Proc. Natl. Acad. Sci. USA 102, 17810–17815 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  65. Nienborg, H. & Cumming, B.G. Decision-related activity in sensory neurons reflects more than a neuron's causal effect. Nature 459, 89–92 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  66. Cohen, M.R. & Newsome, W.T. Estimates of the contribution of single neurons to perception depend on timescale and noise correlation. J. Neurosci. 29, 6635–6648 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  67. Cook, E.P. & Maunsell, J.H. Dynamics of neuronal responses in macaque MT and VIP during motion detection. Nat. Neurosci. 5, 985–994 (2002).

    CAS  PubMed  Google Scholar 

  68. Price, N.S. & Born, R.T. Timescales of sensory- and decision-related activity in the middle temporal and medial superior temporal areas. J. Neurosci. 30, 14036–14045 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  69. Ditterich, J., Mazurek, M.E. & Shadlen, M.N. Microstimulation of visual cortex affects the speed of perceptual decisions. Nat. Neurosci. 6, 891–898 (2003).

    CAS  PubMed  Google Scholar 

  70. Huk, A.C. & Shadlen, M.N. Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making. J. Neurosci. 25, 10420–10436 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  71. Beck, J.M. et al. Probabilistic population codes for Bayesian decision making. Neuron 60, 1142–1152 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  72. Mazurek, M.E., Roitman, J.D., Ditterich, J. & Shadlen, M.N. A role for neural integrators in perceptual decision making. Cereb. Cortex 13, 1257–1269 (2003).

    PubMed  Google Scholar 

  73. Wang, X.J. Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36, 955–968 (2002).

    CAS  PubMed  Google Scholar 

  74. Wong, K.F., Huk, A.C., Shadlen, M.N. & Wang, X.J. Neural circuit dynamics underlying accumulation of time-varying evidence during perceptual decision making. Front. Comput. Neurosci. 1, 6 (2007).

    PubMed  PubMed Central  Google Scholar 

  75. 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).

    PubMed  Google Scholar 

  76. Kass, R.E., Ventura, V. & Brown, E.N. Statistical issues in the analysis of neuronal data. J. Neurophysiol. 94, 8–25 (2005).

    PubMed  Google Scholar 

  77. Paninski, L. et al. A new look at state-space models for neural data. J. Comput. Neurosci. 29, 107–126 (2010).

    PubMed  Google Scholar 

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

    PubMed  Google Scholar 

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

    CAS  PubMed  PubMed Central  Google Scholar 

  80. Truccolo, W., Hochberg, L.R. & Donoghue, J.P. Collective dynamics in human and monkey sensorimotor cortex: predicting single neuron spikes. Nat. Neurosci. 13, 105–111 (2010).

    CAS  PubMed  Google Scholar 

  81. Kohn, A., Zandvakili, A. & Smith, M.A. Correlations and brain states: from electrophysiology to functional imaging. Curr. Opin. Neurobiol. 19, 434–438 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  82. Poort, J. & Roelfsema, P.R. Noise correlations have little influence on the coding of selective attention in area V1. Cereb. Cortex 19, 543–553 (2009).

    PubMed  Google Scholar 

  83. Samonds, J.M., Potetz, B.R. & Lee, T.S. Cooperative and competitive interactions facilitate stereo computations in macaque primary visual cortex. J. Neurosci. 29, 15780–15795 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  84. Erickson, C.A., Jagadeesh, B. & Desimone, R. Clustering of perirhinal neurons with similar properties following visual experience in adult monkeys. Nat. Neurosci. 3, 1143–1148 (2000).

    CAS  PubMed  Google Scholar 

  85. Averbeck, B.B. & Lee, D. Effects of noise correlations on information encoding and decoding. J. Neurophysiol. 95, 3633–3644 (2006).

    PubMed  Google Scholar 

  86. Stark, E., Globerson, A., Asher, I. & Abeles, M. Correlations between groups of premotor neurons carry information about prehension. J. Neurosci. 28, 10618–10630 (2008).

    CAS  PubMed  PubMed Central  Google Scholar 

  87. Maynard, E.M. et al. Neuronal interactions improve cortical population coding of movement direction. J. Neurosci. 19, 8083–8093 (1999).

    CAS  PubMed  PubMed Central  Google Scholar 

  88. Nevet, A., Morris, G., Saban, G., Arkadir, D. & Bergman, H. Lack of spike-count and spike-time correlations in the substantia nigra reticulata despite overlap of neural responses. J. Neurophysiol. 98, 2232–2243 (2007).

    PubMed  Google Scholar 

  89. Cohen, J.Y. et al. Cooperation and competition among frontal eye field neurons during visual target selection. J. Neurosci. 30, 3227–3238 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  90. Bichot, N.P., Thompson, K.G., Chenchal Rao, S. & Schall, J.D. Reliability of macaque frontal eye field neurons signaling saccade targets during visual search. J. Neurosci. 21, 713–725 (2001).

    CAS  PubMed  PubMed Central  Google Scholar 

  91. Barlow, H.B. & Foldiak, P. Adaptation and decorrelation in the cortex. in The Computing Neuron (eds. Durbin, R., Miall, C. & Mitchinson, G.) (Addison-Wesley, New York, 1989).

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

    CAS  PubMed  Google Scholar 

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Acknowledgements

We are grateful to P. Latham for analytical descriptions for our simulations and for the derivation of the relationship between measurement window and correlations that are not based on common spikes and to R. Coen-Cagli for the derivation relating correlation to the proportion of spikes discarded during spike sorting. We thank R. Coen-Cagli, B. Cumming, M. Histed, X. Jia, K. Josic, J. Maunsell, A. Ni, H. Nienborg, A. Pouget, O. Schwartz, S. Tanabe, and J.A. Movshon and E. Simoncelli and members of their laboratories for helpful discussions and comments on an earlier version of the manuscript. This work was supported by US National Institutes of Health grants R01 EY016774 (A.K.) and K99 EY020844-01 (M.R.C.).

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Cohen, M., Kohn, A. Measuring and interpreting neuronal correlations. Nat Neurosci 14, 811–819 (2011). https://doi.org/10.1038/nn.2842

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