Journal of Computational Neuroscience

, Volume 30, Issue 3, pp 543–553 | Cite as

Spatial and temporal correlations of spike trains in frog retinal ganglion cells

  • Wen-Zhong Liu
  • Wei Jing
  • Hao Li
  • Hai-Qing Gong
  • Pei-Ji LiangEmail author


For a neuron, firing activity can be in synchrony with that of others, which results in spatial correlation; on the other hand, spike events within each individual spike train may also correlate with each other, which results in temporal correlation. In order to investigate the relationship between these two phenomena, population neurons’ activities of frog retinal ganglion cells in response to binary pseudo-random checker-board flickering were recorded via a multi-electrode recording system. The spatial correlation index (SCI) and temporal correlation index (TCI) were calculated for the investigated neurons. Statistical results showed that, for a single neuron, the SCI and TCI values were highly related—a neuron with a high SCI value generally had a high TCI value, and these two indices were both associated with burst activities in spike train of the investigated neuron. These results may suggest that spatial and temporal correlations of single neuron’s spiking activities could be mutually modulated; and that burst activities could play a role in the modulation. We also applied models to test the contribution of spatial and temporal correlations for visual information processing. We show that a model considering spatial and temporal correlations could predict spikes more accurately than a model does not include any correlation.


Ganglion cell Spatial correlation Temporal correlation Multi-electrode recording Burst activities 





retinal ganglion cell


multi-electrode array


spatial correlation index


Spike-triggered averaged


temporal correlation index


lateral geniculate nucleus



The authors would like to thank Mr. Xin-Wei Gong for helpful discussions. This work was supported by the grants from the State Key Basic Research and Development Plan (No.2005CB724301) and National Foundation of Natural Science of China (No.30670519).


  1. Bhattacharya, J., Edwards, J., Mamelak, A. N., & Schuman, E. M. (2005). Long-range temporal correlations in the spontaneous spiking of neurons in the hippocampal-amygdala complex of humans. Neuroscience, 131(2), 547–555.PubMedCrossRefGoogle Scholar
  2. Bloomfield, S. A., & Völgyi, B. (2009). The diverse functional roles and regulation of neuronal gap junctions in the retina. Nature Reviews. Neuroscience, 10(7), 495–506.PubMedCrossRefGoogle Scholar
  3. Brivanlou, I. H., Warland, D. K., & Meister, M. (1998). Mechanisms of concerted firing among retinal ganglion cells. Neuron, 20(3), 527–540.PubMedCrossRefGoogle Scholar
  4. Buonomano, D. V., & Maass, W. (2009). State-dependent computations: spatiotemporal processing in cortical networks. Nature Reviews. Neuroscience, 10(2), 113–125.PubMedCrossRefGoogle Scholar
  5. Cai, C. F., Zhang, Y. Y., Liu, X., Liang, P. J., & Zhang, P. M. (2008). Detecting determinism in firing activities of retinal ganglion cells during response to complex stimuli. Chinese Physics Letters, 25(5), 1595–1598.CrossRefGoogle Scholar
  6. DeVries, S. H. (1999). Correlated firing in rabbit retinal ganglion cells. Journal of Neurophysiology, 81(2), 908–920.PubMedGoogle Scholar
  7. Devries, S. H., & Baylor, D. A. (1997). Mosaic arrangement of ganglion cell receptive fields in rabbit retina. Journal of Neurophysiology, 78(4), 2048–2060.PubMedGoogle Scholar
  8. Field, G. D., & Chichilnisky, E. J. (2007). Information processing in the primate retina: circuitry and coding. Annual Review of Neuroscience, 30, 1–30.PubMedCrossRefGoogle Scholar
  9. Hosoya, T., Baccus, S. A., & Meister, M. (2005). Dynamic predictive coding by the retina. Nature, 436(7047), 71–77.PubMedCrossRefGoogle Scholar
  10. Ishikane, H., Gangi, M., Honda, S., & Tachibana, M. (2005). Synchronized retinal oscillations encode essential information for escape behavior in frogs. Nature Neuroscience, 8(8), 1087–1095.PubMedCrossRefGoogle Scholar
  11. Jing, W., Liu, W. Z., Gong, X. W., Gong, H. Q., & Liang, P. J. (2010a). Influence of GABAergic inhibition on concerted activity between the ganglion cells. NeuroReport, 21(12), 797–801.PubMedCrossRefGoogle Scholar
  12. Jing, W., Liu, W. Z., Gong, X. W., Gong, H. Q., & Liang, P. J. (2010b). Visual pattern recognition based on spatio-temporal patterns of retinal ganglion cells’ activities. Cognitive Neurodynamics, 4, 179–188.CrossRefGoogle Scholar
  13. Koch, K., McLean, J., Berry, M., Sterling, P., Balasubramanian, V., & Freed, M. A. (2004). Efficiency of information transmission by retinal ganglion cells. Current Biology, 14(17), 1523–1530.PubMedCrossRefGoogle Scholar
  14. Koch, K., McLean, J., Segev, R., Freed, M. A., Berry, M. J., Balasubramanian, V., et al. (2006). How much the eye tells the brain. Current Biology, 16(14), 1428–1434.PubMedCrossRefGoogle Scholar
  15. Lesica, N., & Stanley, G. (2004). Encoding of natural scene movies by tonic and burst spikes in the lateral geniculate nucleus. The Journal of Neuroscience, 24(47), 10731.PubMedCrossRefGoogle Scholar
  16. Lettvin, J., Maturana, H., McCulloch, W., & Pitts, W. (1959). What the frog’s eye tells the frog’s brain. Proceedings of the IRE, 47(11), 1940–1951.CrossRefGoogle Scholar
  17. Lisman, J. E. (1997). Bursts as a unit of neural information: making unreliable synapses reliable. Trends in Neurosciences, 20(1), 38–43.PubMedCrossRefGoogle Scholar
  18. Liu, X., Zhou, Y., Gong, H. Q., & Liang, P. J. (2007). Contribution of the GABAergic pathway (s) to the correlated activities of chicken retinal ganglion cells. Brain Research, 1177, 37–46.PubMedCrossRefGoogle Scholar
  19. Lowen, S. B., & Teich, M. C. (1992). Auditory-nerve action potentials form a nonrenewal point process over short as well as long time scales. Journal of the Acoustical Society of America, 92(2I), 803–806.PubMedCrossRefGoogle Scholar
  20. Meister, M., Pine, J., & Baylor, D. A. (1994). Multi-neuronal signals from the retina: acquisition and analysis. Journal of Neuroscience Methods, 51(1), 95–106.PubMedCrossRefGoogle Scholar
  21. Meister, M., Lagnado, L., & Baylor, D. A. (1995). Concerted signaling by retinal ganglion cells. Science, 270(5239), 1207.PubMedCrossRefGoogle Scholar
  22. Neuenschwander, S., & Singer, W. (1996). Long-range synchronization of oscillatory light responses in the cat retina and lateral geniculate nucleus. Nature, 379(6567), 728–733.PubMedCrossRefGoogle Scholar
  23. Oram, M., Wiener, M., Lestienne, R., & Richmond, B. (1999). Stochastic nature of precisely timed spike patterns in visual system neuronal responses. Journal of Neurophysiology, 81(6), 3021–3033.PubMedGoogle Scholar
  24. Pillow, J. W., Shlens, J., Paninski, L., Sher, A., Litke, A. M., Chichilnisky, E. J., et al. (2008). Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature, 454(7207), 995–999.PubMedCrossRefGoogle Scholar
  25. Reid, R., Victor, J., & Shapley, R. (1997). The use of m-sequences in the analysis of visual neurons: linear receptive field properties. Visual Neuroscience, 14(06), 1015–1027.PubMedCrossRefGoogle Scholar
  26. Reinagel, P., & Reid, R. C. (2000). Temporal coding of visual information in the thalamus. The Journal of Neuroscience, 20(14), 5392.PubMedGoogle Scholar
  27. Schneidman, E., Berry, M. J., II, Segev, R., & Bialek, W. (2006). Weak pairwise correlations imply strongly correlated network states in a neural population. Nature, 440(7087), 1007.PubMedCrossRefGoogle Scholar
  28. Schnitzer, M. J., & Meister, M. (2003). Multineuronal firing patterns in the signal from eye to brain. Neuron, 37(3), 499–511.PubMedCrossRefGoogle Scholar
  29. Segev, R., Goodhouse, J., Puchalla, J., & Berry Ii, M. J. (2004). Recording spikes from a large fraction of the ganglion cells in a retinal patch. Nature Neuroscience, 7(10), 1154–1161.PubMedCrossRefGoogle Scholar
  30. Shlens, J., Rieke, F., & Chichilnisky, E. J. (2008). Synchronized firing in the retina. Current Opinion in Neurobiology, 18(4), 396–402.PubMedCrossRefGoogle Scholar
  31. Snider, R., Kabara, J., Roig, B., & Bonds, A. (1998). Burst firing and modulation of functional connectivity in cat striate cortex. Journal of Neurophysiology, 80(2), 730–744.PubMedGoogle Scholar
  32. Strong, S., Koberle, R., van Steveninck, R., & Bialek, W. (1998). Entropy and information in neural spike trains. Am Phys Soc, 80, 197–200.Google Scholar
  33. Teich, M. C., Turcott, R. G., & Siegel, R. M. (1996). Temporal correlation in cat striate-cortex neural spike trains. IEEE Engineering in Medicine and Biology Magazine, 15(5), 79–87.CrossRefGoogle Scholar
  34. Teich, M. C., Heneghan, C., Lowen, S. B., Ozaki, T., & Kaplan, E. (1997). Fractal character of the neural spike train in the visual system of the cat. Journal of the Optical Society of America A, 14(3), 529–546.CrossRefGoogle Scholar
  35. Usrey, W. M., Reppas, J. B., & Reid, R. C. (1998). Paired-spike interactions and synaptic efficacy of retinal inputs to the thalamus. Nature, 395(6700), 384–387.PubMedCrossRefGoogle Scholar
  36. Zhang, P. M., Wu, J. Y., Zhou, Y., Liang, P. J., & Yuan, J. (2004). Spike sorting based on automatic template reconstruction with a partial solution to the overlapping problem. Journal of Neuroscience Methods, 135(1–2), 55–65.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Wen-Zhong Liu
    • 1
  • Wei Jing
    • 1
  • Hao Li
    • 1
  • Hai-Qing Gong
    • 1
  • Pei-Ji Liang
    • 1
    Email author
  1. 1.Department of Biomedical EngineeringShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations