Unitary Event Analysis

Part of the Springer Series in Computational Neuroscience book series (NEUROSCI, volume 7)


It has been proposed that cortical neurons organize dynamically into functional groups (“cell assemblies”) by the temporal structure of their joint spiking activity. The Unitary Events analysis method detects conspicuous patterns of coincident spike activity among simultaneously recorded single neurons. The statistical significance of a pattern is evaluated by comparing the number of occurrences to the number expected on the basis of the firing rates of the neurons. Key elements of the method are the proper formulation of the null hypothesis and the derivation of the corresponding count distribution of coincidences used in the significance test. Performing the analysis in a sliding window manner results in a time-resolved measure of significant spike synchrony. In this chapter we review the basic components of UE analysis and explore its dependencies on parameters like the allowed temporal imprecision and features of the data like firing rate and coincidence rate. Violations of the assumptions of stationarity of the firing rate within the analysis window and Poisson statistics can be tolerated to a reasonable degree without inducing false positives. We conclude that the UE method is robust already in its basic form. Still, it is preferable to use coincidence distributions for the significance test that are well adapted to particular features of the data. The chapter presents practical advice and solutions based on surrogates.


Spike Train Analysis Window Surrogate Data Spike Count Coincidence Count 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Abeles M (1982) Role of cortical neuron: integrator or coincidence detector?. Israel J Med Sci 18:83–92 PubMedGoogle Scholar
  2. Abeles M (1991) Corticonics: neural circuits of the cerebral cortex. Cambridge University Press, Cambridge Google Scholar
  3. Abeles M, Gat I (2001) Detecting precise firing sequences in experimental data. J Neurosci Methods 107(1–2), 141–154 CrossRefPubMedGoogle Scholar
  4. Aertsen A, Gerstein G, Habib M, Palm G (1989) Dynamics of neuronal firing correlation: modulation of “effective connectivity”. J Neurophysiol 61(5), 900–917 PubMedGoogle Scholar
  5. Baker S, Lemon R (2000) Precise spatiotemporal repeating patterns in monkey primary and supplementary motor areas occur at chance levels. J Neurophysiol 84(4):1770–1780 PubMedGoogle Scholar
  6. Barlow HB (1972) Single units and sensation: a neuron doctrine for perceptual psychology?. Perception 1:371–394 CrossRefPubMedGoogle Scholar
  7. Ben-Shaul Y, Bergman H, Ritov Y, Abeles M (2001) Trial to trial variability in either stimulus or action causes apparent correlation and synchrony in neuronal activity. J Neurosci Methods 111(2):99–110 CrossRefPubMedGoogle Scholar
  8. Bernander Ö, Koch C, Usher M (1994) The effect of synchronized inputs at the single neuron level. Neural Comput 6:622–641 CrossRefGoogle Scholar
  9. Brody CD (1999a) Correlations without synchrony. Neural Comput 11:1537–1551 CrossRefPubMedGoogle Scholar
  10. Brody CD (1999b) Disambiguating different covariation types. Neural Comput 11:1527–1535 CrossRefPubMedGoogle Scholar
  11. Brown E, Barbieri R, Ventura V, Kass R, Frank L (2002) The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput 14:325–346 CrossRefPubMedGoogle Scholar
  12. Czanner G, Grün S, Iyengar S (2005) Theory of the snowflake plot and its relations to higher-order analysis methods. Neural Comput 17(7):1456–1479 CrossRefPubMedGoogle Scholar
  13. Denker M, Riehle A, Diesmann M, Grün S (in press) Estimating the contribution of assembly activity to cortical dynamics from spike and population measures. J Comput Neurosci. doi: 10.1007/s10827-010-0241-8
  14. Diesmann M, Gewaltig MO, Aertsen A (1999) Stable propagation of synchronous spiking in cortical neural networks. Nature 402(6761):529–533 CrossRefPubMedGoogle Scholar
  15. Gerstein G, Aertsen A (1985) Representation of cooperative firing activity among simultaneously recorded neurons. J Neurophysiol 54:1513–1528 PubMedGoogle Scholar
  16. Gerstein G, Perkel D, Dayhoff J (1985) Cooperative firing activity in simultaneously recorded populations of neurons: detection and measurement. J Neurosci 5:881–889 PubMedGoogle Scholar
  17. Gerstein G, Bedenbaugh P, Aertsen A (1989) Neuronal assemblies. IEEE Trans Biomed Eng 36(1):4–14 CrossRefPubMedGoogle Scholar
  18. Goedeke S, Diesmann M (2008) The mechanism of synchronization in feed-forward neuronal networks. New J Phys 10:015007. doi: 10.1088/1367-2630/10/1/015007 CrossRefGoogle Scholar
  19. Grammont F, Riehle A (1999) Precise spike synchronization in monkey motor cortex involved in preparation for movement. Experimental Brain Res 128:118–122 CrossRefGoogle Scholar
  20. Grammont F, Riehle A (2003) Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time. Biol Cybernet 88(5):360–373 CrossRefGoogle Scholar
  21. Grün S (2009) Data-driven significance estimation of precise spike correlation. J Neurophysiol 101(3):1126–1140 (invited review) CrossRefPubMedGoogle Scholar
  22. Grün S, Diesmann M, Grammont F, Riehle A, Aertsen A (1999) Detecting unitary events without discretization of time. J Neurosci Methods 94(1):67–79 CrossRefPubMedGoogle Scholar
  23. Grün S, Diesmann M, Aertsen A (2002a) ‘Unitary Events’ in multiple single-neuron spiking activity. I. Detection and significance. Neural Comput 14(1):43–80 CrossRefPubMedGoogle Scholar
  24. Grün S, Diesmann M, Aertsen A (2002b) ‘Unitary Events’ in multiple single-neuron spiking activity. II. Non-stationary data. Neural Comput 14(1):81–119 CrossRefPubMedGoogle Scholar
  25. Grün S, Riehle A, Diesmann M (2003) Effect of cross-trial nonstationarity on joint-spike events. Biol Cybernet 88(5):335–351 CrossRefGoogle Scholar
  26. Gütig R, Aertsen A, Rotter S (2002) Significance of coincident spikes: count-based versus rate-based statistics. Neural Comput 14:121–153 CrossRefPubMedGoogle Scholar
  27. Harris K (2005) Neural signatures of cell assembly organization. Nature Neurosci Rev 5(6):339–407 Google Scholar
  28. Harrison M, Geman S (2009) A rate and history-preserving resampling algorithm for neural spike trains. Neural Comput 21(5):1244–1258 CrossRefPubMedGoogle Scholar
  29. Hebb DO (1949) The organization of behavior: a neuropsychological theory. Wiley, New York Google Scholar
  30. Ito H (2007) Bootstrap significance test of synchronous spike events – a case study of oscillatory spike trains. Statistical Med 26:3976–3996 CrossRefGoogle Scholar
  31. Ito J, Maldonado P, Singer W, Grün S (submitted) Saccade-related LFP modulations support synchrony of visually elicited spikes Google Scholar
  32. Johnson DH (1996) Point process models of single-neuron discharges. J Comput Neurosci 3(4):275–299 CrossRefPubMedGoogle Scholar
  33. Kass R, Ventura V (2006) Spike count correlation increases with length of time interval in the presence of trial-to-trial variation. Neural Comput 18(11):2583–2591 CrossRefPubMedGoogle Scholar
  34. Kilavik B, Roux S, Ponce-Alvarez A, Confais J, Grün S, Riehle A (2009) Long-term modifications in motor cortical dynamics induced by intensive practice. J Neurosci 29(40):12653–12663 CrossRefPubMedGoogle Scholar
  35. Kumar A, Rotter S, Aertsen A (2008) Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model. J Neurosci 28:5268–5280 CrossRefPubMedGoogle Scholar
  36. Louis S, Gerstein GL, Grün S, Diesmann M (in press) Surrogate spike train generation through dithering in operational time. Front Comput Neurosci Google Scholar
  37. Maldonado P, Babul C, Singer W, Rodriguez E, Berger D, Grün S (2008) Synchronization of neuronal responses in primary visual cortex of monkeys viewing natural images. J Neurophysiol 100:1523–1532 CrossRefPubMedGoogle Scholar
  38. Marsalek P, Koch C, Maunsel J (1997) On the relationship between synaptic input and spike output jitter in individual neurons. Proc Natl Acad Sci 94:735–740 CrossRefPubMedGoogle Scholar
  39. Nawrot M, Aertsen A, Rotter S (1999) Single-trial estimation of neuronal firing rates: from single-neuron spike trains to population activity. J Neurosci Methods 94:81–92 CrossRefPubMedGoogle Scholar
  40. Nawrot M, Aertsen A, Rotter S (2003) Elimination of response latency variability in neuronal spike trains. Biol Cybernet 88:321–334 CrossRefGoogle Scholar
  41. Nawrot M, Boucsein C, Rodriguez-Molina V, Aertsen A, Grün S, Rotter S (2007) Serial interval statistics of spontaneous activity in cortical neurons in vivo and in vitro. Neurocomputing 70:1717–1722 CrossRefGoogle Scholar
  42. Nawrot M, Boucsein C, Rodriguez Molina V, Riehle A, Aertsen A, Rotter S (2008a) Measurement of variability dynamics in cortical spike trains. J Neurosci Methods 169:374–390 CrossRefPubMedGoogle Scholar
  43. Nawrot M, Farkhooi F, Grün S (2008b) Significance of coincident spiking considering inter-spike interval variability and serial interval correlation. In: Frontiers in computational neuroscience. Conference abstract: Bernstein symposium 2008. doi: 10.3389/conf.neuro.10.2008.01.017
  44. Palm G (1981) Evidence, information and surprise. Biol Cybernet 42:57–68 CrossRefGoogle Scholar
  45. Pauluis Q, Baker SN (2000) An accurate measure of the instantaneous discharge probability with application to unitary joint-event analysis. Neural Comput 12(3):647–669 CrossRefPubMedGoogle Scholar
  46. Pazienti A, Maldonado P, Diesmann M, Grün S (2008) Effectiveness of systematic spike dithering depends on the precision of cortical synchronization. Brain Res 1225:39–46 CrossRefPubMedGoogle Scholar
  47. Perkel DH, Gerstein GL, Moore GP (1967) Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J 7(4):419–440 CrossRefPubMedGoogle Scholar
  48. Perkel DH, Gerstein GL, Smith MS, Tatton WG (1975) Nerve-impulse patterns: a quantitative display technique for three neurons. Brain Res 100:271–296 CrossRefPubMedGoogle Scholar
  49. Pipa G, Grün S, van Vreeswijk C (under revision) Impact of spike-train autostructure on probability distribution of joint-spike events. Neural Comput Google Scholar
  50. Pipa G, Riehle A, Grün S (2007) Validation of task-related excess of spike coincidences based on NeuroXidence. Neurocomputing 70:2064–2068. Published online 2006: doi: 10.1016/j.neucom.2006.10.142 CrossRefGoogle Scholar
  51. Pipa G, van Vreeswijk C, Grün S (in preparation) Impact of spike-train autostructure on Unitary Events Google Scholar
  52. Pipa G, Wheeler D, Singer W, Nikolic D (2008) NeuroXidence: reliable and efficient analysis of an excess or deficiency of joint-spike events. J Comput Neurosci 25(1):64–88 CrossRefPubMedGoogle Scholar
  53. Prut Y, Vaadia E, Bergman H, Haalman I, Hamutal S, Abeles M (1998) Spatiotemporal structure of cortical activity: properties and behavioral relevance. J Neurophysiol 79(6):2857–2874 PubMedGoogle Scholar
  54. Reyes A (2003) Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nature Neurosci 6:593–599 CrossRefPubMedGoogle Scholar
  55. Richmond B (2009) Stochasticity spikes and decoding: sufficiency and utility of order statistics. Biol Cybernet 100(9):447–457 CrossRefGoogle Scholar
  56. Riehle A, Grün S, Diesmann M, Aertsen A (1997) Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278(5345):1950–1953 CrossRefPubMedGoogle Scholar
  57. Riehle A, Grammont F, Diesmann M, Grün S (2000) Dynamical changes and temporal precision of synchronized spiking activity in monkey motor cortex during movement preparation. J Physiol (Paris) 94:569–582 CrossRefGoogle Scholar
  58. Rodriguez-Molina V, Aertsen A, Heck D (2007) Spike timing and reliability in cortical pyramidal neurons: Effects of EPSC kinetics input synchronization and background noise on spike timing. PLoS ONE 2(3):e319. doi: 10.1371/journal.pone.0000319 CrossRefPubMedGoogle Scholar
  59. Roy A, Steinmetz PN, Niebur E (2000) Rate limitations of unitary event analysis. Neural Comput 12:2063–2082 CrossRefPubMedGoogle Scholar
  60. Shadlen MN, Movshon AJ (1999) Synchrony unbound: a critical evaluation of the temporal binding hypothesis. Neuron 24:67–77 CrossRefPubMedGoogle Scholar
  61. Shimazaki H, Amari S, Brown E, Grün S (2009) State-space analysis on time-varying correlations in parallel spike sequences. In: IEEE international conference on acoustics, speech, and signal processing (ICASSP), pp 3501–3504 Google Scholar
  62. Shimazaki H, Shinomoto S (2010) Kernel bandwidth optimization in spike rate estimation. J Comput Neurosci. doi: 10.1007/s10827-009-0180-4
  63. Singer W (1999) Neuronal synchrony: a versatile code for the definition of relations?. Neuron 24(1):49–65 CrossRefPubMedGoogle Scholar
  64. Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci 13(1):334–350 PubMedGoogle Scholar
  65. Vaadia E, Haalman I, Abeles M, Bergman H, Prut Y, Slovin H, Aertsen A (1995) Dynamics of neuronal interactions in monkey cortex in relation to behavioral events. Nature 373:515–518 CrossRefPubMedGoogle Scholar
  66. Ventura V, Carta R, Kass R, Gettner S, Olson C (2002) Statistical analysis of temporal evolution in single-neuron firing rates. Biostatistics 3(1):1–20 CrossRefPubMedGoogle Scholar
  67. Ventura V, Cai C, Kass R (2005) Trial-to-trial variability and its effect on time-varying dependency between two neurons. J Neurophysiol 94(4):2928–2939 CrossRefPubMedGoogle Scholar
  68. Von der Malsburg C (1981) The correlation theory of brain function. Internal report 81-2, Max-Planck-Institute for Biophysical Chemistry, Göttingen, FRG Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Laboratory for Statistical NeuroscienceRIKEN Brain Science InstituteWakoshiJapan
  2. 2.Laboratory for Computational NeurophysicsRIKEN Brain Science InstituteWakoshiJapan
  3. 3.Neurobiology and Biophysics, Institute of Biology III, Faculty of BiologyAlbert-Ludwig UniversityFreiburgGermany

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