Quantification of Spike-LFP Synchronization



To uncover more details on rhythmic neuronal synchronization, an increasingly interesting method is to relate spiking activity of individual neurons and local filed potentials (LFPs) of neural ensembles. Spike field coherence (SFC) is widely used to measure the synchronization between spike trains and LFPs. However, it is not suited to analyze the relationship between bursty spike trains and LFPs, particularly in high frequency band. To address this issue, a method, referred to as weighted spike field coherence (WSFC), is introduced in this chapter, which uses multiple copies of the first spike in every burst to calculate the coherence. In the calculation, the number of copies is equal to the spike count per burst. Moreover, many experiments have compared the strength of the association between spikes and rhythms present in LFP recordings. Most existing measures are dependent upon the total number of spikes, which renders comparison of spike-LFP synchronization across experimental contexts difficult. We introduce a robust procedure for quantifying spike-LFP synchronization which performs reliably for limited samples of data. The measure is referred to as spike-triggered correlation matrix synchronization (SCMS), which takes LFP segments centered on each spike as multichannel signals and calculates the index of spike-LFP synchronization by constructing a correlation matrix.


Spike train Local field potential Burst Phase locking Synchronization Correlation matrix 


  1. Asai Y, Villa AE. Reconstruction of underlying nonlinear deterministic dynamics embedded in noisy spike trains. J Biol Phys. 2008;34:325–40.CrossRefPubMedPubMedCentralGoogle Scholar
  2. Batschelet E. Circular statistics in biology. London: Academic; 1981.Google Scholar
  3. Bauer M, Oostenveld R, Peeters M, Fries P. Tactile spatial attention enhances gamma-band activity in somatosensory cortex and reduces low-frequency activity in parieto-occipital areas. J Neurosci. 2006;26:490–501.CrossRefPubMedGoogle Scholar
  4. Berens P, Keliris GA, Ecker AS, Logothetis NK, Tolias AS. Comparing the feature selectivity of the gamma-band of the local field potential and the underlying spiking activity in primate visual cortex. Front Syst Neurosci. 2008;2:2.CrossRefPubMedPubMedCentralGoogle Scholar
  5. Bokil H, Andrews P, Kulkarni JE, Mehta S, Mitra PP. Chronux: a platform for analyzing neural signals. J Neurosci Methods. 2010;192:146–51.CrossRefPubMedPubMedCentralGoogle Scholar
  6. Buzsaki G, Wang XJ. Mechanisms of gamma oscillations. Annu Rev Neurosci. 2012;35:203–25.CrossRefPubMedPubMedCentralGoogle Scholar
  7. Buzsaki G, Anastassiou CA, Koch C. The origin of extracellular fields and currents – EEG, ECoG, LFP and spikes. Nat Rev Neurosci. 2012;13:407–20.CrossRefPubMedPubMedCentralGoogle Scholar
  8. Chalk M, Herrero JL, Gieselmann MA, Delicato LS, Gotthardt S, Thiele A. Attention reduces stimulus-driven gamma frequency oscillations and spike field coherence in V1. Neuron. 2010;66:114–25.CrossRefPubMedPubMedCentralGoogle Scholar
  9. Claverol-Tinture E, Cabestany J, Rosell X. Multisite recording of extracellular potentials produced by microchannel-confined neurons in-vitro. IEEE Trans Biomed Eng. 2007;54:331–5.CrossRefPubMedGoogle Scholar
  10. Cocatre-Zilgien JH, Delcomyn F. Identification of bursts in spike trains. J Neurosci Methods. 1992;41:19–30.CrossRefPubMedGoogle Scholar
  11. Colgin LL, Denninger T, Fyhn M, Hafting T, Bonnevie T, Jensen O, Moser MB, Moser EI. Frequency of gamma oscillations routes flow of information in the hippocampus. Nature. 2009;462:353–7.CrossRefPubMedGoogle Scholar
  12. Courtemanche R, Pellerin JP, Lamarre Y. Local field potential oscillations in primate cerebellar cortex: modulation during active and passive expectancy. J Neurophysiol. 2002;88:771–82.PubMedGoogle Scholar
  13. Csicsvari J, Jamieson B, Wise KD, Buzsaki G. Mechanisms of gamma oscillations in the hippocampus of the behaving rat. Neuron. 2003;37:311–22.CrossRefPubMedGoogle Scholar
  14. Delorme A, Makeig S. EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods. 2004;134:9–21.CrossRefPubMedGoogle Scholar
  15. Eggermont JJ, Smith GM. Synchrony between single-unit activity and local field potentials in relation to periodicity coding in primary auditory cortex. J Neurophysiol. 1995;73:227–45.PubMedGoogle Scholar
  16. Fell J, Klaver P, Lehnertz K, Grunwald T, Schaller C, Elger CE, Fernandez G. Human memory formation is accompanied by rhinal-hippocampal coupling and decoupling. Nat Neurosci. 2001;4:1259–64.CrossRefPubMedGoogle Scholar
  17. Fries P, Roelfsema PR, Engel AK, Konig P, Singer W. Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry. Proc Natl Acad Sci U S A. 1997;94:12699–704.CrossRefPubMedPubMedCentralGoogle Scholar
  18. Fries P, Reynolds JH, Rorie AE, Desimone R. Modulation of oscillatory neuronal synchronization by selective visual attention. Science. 2001;291:1560–3.CrossRefPubMedGoogle Scholar
  19. Fries P, Schroder JH, Roelfsema PR, Singer W, Engel AK. Oscillatory neuronal synchronization in primary visual cortex as a correlate of stimulus selection. J Neurosci. 2002;22:3739–54.PubMedGoogle Scholar
  20. Galashan FO, Rempel HC, Meyer A, Gruber-Dujardin E, Kreiter AK, Wegener D. A new type of recording chamber with an easy-to-exchange microdrive array for chronic recordings in macaque monkeys. J Neurophysiol. 2011;105:3092–105.CrossRefPubMedGoogle Scholar
  21. Grasse DW, Moxon KA. Correcting the bias of spike field coherence estimators due to a finite number of spikes. J Neurophysiol. 2010;104:548–58.CrossRefPubMedGoogle Scholar
  22. Hagan MA, Dean HL, Pesaran B. Spike-field activity in parietal area LIP during coordinated reach and saccade movements. J Neurophysiol. 2012;107:1275–90.CrossRefPubMedGoogle Scholar
  23. Harris KD, Hirase H, Leinekugel X, Henze DA, Buzsáki G. Temporal interaction between single spikes and complex spike bursts in hippocampal pyramidal cells. Neuron. 2001;32:141–9.CrossRefPubMedGoogle Scholar
  24. Harris KD, Henze DA, Hirase H, Leinekugel X, Dragoi G, Czurko A, Buzsaki G. Spike train dynamics predicts theta-related phase precession in hippocampal pyramidal cells. Nature. 2002;417:738–41.CrossRefPubMedGoogle Scholar
  25. Howard MW, Rizzuto DS, Caplan JB, Madsen JR, Lisman J, Aschenbrenner-Scheibe R, Schulze-Bonhage A, Kahana MJ. Gamma oscillations correlate with working memory load in humans. Cereb Cortex. 2003;13:1369–74.CrossRefPubMedGoogle Scholar
  26. Hubel DH, Wiesel TN. Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J Physiol. 1962;160:106–54.CrossRefPubMedPubMedCentralGoogle Scholar
  27. Hubel DH, Wiesel TN. Receptive fields and functional architecture of monkey striate cortex. J Physiol. 1968;195:215–43.CrossRefPubMedPubMedCentralGoogle Scholar
  28. Issa EB, Wang X. Altered neural responses to sounds in primate primary auditory cortex during slow-wave sleep. J Neurosci. 2011;31:2965–73.CrossRefPubMedPubMedCentralGoogle Scholar
  29. Jarvis MR, Mitra PP. Sampling properties of the spectrum and coherency of sequences of action potentials. Neural Comput. 2001;13:717–49.CrossRefPubMedGoogle Scholar
  30. Kepecs A, Lisman J. Information encoding and computation with spikes and bursts. Network. 2003;14:103–18.CrossRefPubMedGoogle Scholar
  31. Le Van Quyen M, Bragin A, Staba R, Crepon B, Wilson CL, Engel Jr J. Cell type-specific firing during ripple oscillations in the hippocampal formation of humans. J Neurosci. 2008;28:6104–10.CrossRefGoogle Scholar
  32. Lee H, Simpson GV, Logothetis NK, Rainer G. Phase locking of single neuron activity to theta oscillations during working memory in monkey extrastriate visual cortex. Neuron. 2005;45:147–56.CrossRefPubMedGoogle Scholar
  33. Lewandowski BC, Schmidt M. Short bouts of vocalization induce long-lasting fast gamma oscillations in a sensorimotor nucleus. J Neurosci. 2011;31:13936–48.CrossRefPubMedPubMedCentralGoogle Scholar
  34. Li X, Cui D, Jiruska P, Fox JE, Yao X, Jefferys JG. Synchronization measurement of multiple neuronal populations. J Neurophysiol. 2007;98:3341–8.CrossRefPubMedGoogle Scholar
  35. Lisman JE. Bursts as a unit of neural information: making unreliable synapses reliable. Trends Neurosci. 1997;20:38–43.CrossRefPubMedGoogle Scholar
  36. Mizuseki K, Sirota A, Pastalkova E, Buzsaki G. Theta oscillations provide temporal windows for local circuit computation in the entorhinal-hippocampal loop. Neuron. 2009;64:267–80.CrossRefPubMedPubMedCentralGoogle Scholar
  37. Mizuseki K, Diba K, Pastalkova E, Buzsaki G. Hippocampal CA1 pyramidal cells form functionally distinct sublayers. Nat Neurosci. 2011;14:1174–81.CrossRefPubMedPubMedCentralGoogle Scholar
  38. Mizuseki K, Royer S, Diba K, Buzsaki G. Activity dynamics and behavioral correlates of CA3 and CA1 hippocampal pyramidal neurons. Hippocampus. 2012;22:1659–80.CrossRefPubMedPubMedCentralGoogle Scholar
  39. Muzzio IA, Levita L, Kulkarni J, Monaco J, Kentros C, Stead M, Abbott LF, Kandel ER. Attention enhances the retrieval and stability of visuospatial and olfactory representations in the dorsal hippocampus. PLoS Biol. 2009;7:e1000140.CrossRefPubMedPubMedCentralGoogle Scholar
  40. Palm G. Evidence, information, and surprise. Biol Cybern. 1981;42:57–68.CrossRefPubMedGoogle Scholar
  41. Perelman Y, Ginosar R. An integrated system for multichannel neuronal recording with spike/LFP separation, integrated A/D conversion and threshold detection. IEEE Trans Biomed Eng. 2007;54:130–7.CrossRefPubMedGoogle Scholar
  42. Pesaran B, Pezaris J, Sahani M, Mitra P, Andersen R. Temporal structure in neuronal activity during working memory in macaque parietal cortex. Nat Neurosci. 2002;5:805–11.CrossRefPubMedGoogle Scholar
  43. Pienkowski M, Eggermont JJ. Sound frequency representation in primary auditory cortex is level tolerant for moderately loud, complex sounds. J Neurophysiol. 2011;106:1016–27.CrossRefPubMedGoogle Scholar
  44. Priebe NJ, Ferster D. Mechanisms of neuronal computation in mammalian visual cortex. Neuron. 2012;75:194–208.CrossRefPubMedPubMedCentralGoogle Scholar
  45. Quiroga RQ, Nadasdy Z, Ben-Shaul Y. Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering. Neural Comput. 2004;16:1661–87.CrossRefPubMedGoogle Scholar
  46. Rasch MJ, Gretton A, Murayama Y, Maass W, Logothetis NK. Inferring spike trains from local field potentials. J Neurophysiol. 2008;99:1461–76.CrossRefPubMedGoogle Scholar
  47. Ray S. Challenges in the quantification and interpretation of spike-LFP relationships. Curr Opin Neurobiol. 2014;31C:111–18.Google Scholar
  48. Ray S, Maunsell JH. Differences in gamma frequencies across visual cortex restrict their possible use in computation. Neuron. 2010;67:885–96.CrossRefPubMedPubMedCentralGoogle Scholar
  49. Reimann MW, Anastassiou CA, Perin R, Hill SL, Markram H, Koch C. A biophysically detailed model of neocortical local field potentials predicts the critical role of active membrane currents. Neuron. 2013;79:375–90.CrossRefPubMedPubMedCentralGoogle Scholar
  50. Ringach DL, Hawken MJ, Shapley R. Dynamics of orientation tuning in macaque primary visual cortex. Nature. 1997;387:281–4.CrossRefPubMedGoogle Scholar
  51. Robin K, Maurice N, Degos B, Deniau JM, Martinerie J, Pezard L. Assessment of bursting activity and interspike intervals variability: a case study for methodological comparison. J Neurosci Methods. 2009;179:142–9.CrossRefPubMedGoogle Scholar
  52. Rosenblum MG, Pikovsky AS, Kurths J. Phase synchronization of chaotic oscillators. Phys Rev Lett. 1996;76:1804–7.CrossRefPubMedGoogle Scholar
  53. Rutishauser U, Ross IB, Mamelak AN, Schuman EM. Human memory strength is predicted by theta-frequency phase-locking of single neurons. Nature. 2010;464:903–7.CrossRefPubMedGoogle Scholar
  54. Schwartz AB. Cortical neural prosthetics. Annu Rev Neurosci. 2004;27:487–507.CrossRefPubMedGoogle Scholar
  55. Senior TJ, Huxter JR, Allen K, O’Neill J, Csicsvari J. Gamma oscillatory firing reveals distinct populations of pyramidal cells in the CA1 region of the hippocampus. J Neurosci. 2008;28:2274–86.CrossRefPubMedGoogle Scholar
  56. Shapley R, Hawken M, Ringach DL. Dynamics of orientation selectivity in the primary visual cortex and the importance of cortical inhibition. Neuron. 2003;38:689–99.CrossRefPubMedGoogle Scholar
  57. Siegel M, Konig P. A functional gamma-band defined by stimulus-dependent synchronization in area 18 of awake behaving cats. J Neurosci. 2003;23:4251–60.PubMedGoogle Scholar
  58. Stafford BK, Sher A, Litke AM, Feldheim DA. Spatial-temporal patterns of retinal waves underlying activity-dependent refinement of retinofugal projections. Neuron. 2009;64:200–12.CrossRefPubMedPubMedCentralGoogle Scholar
  59. Swadlow HA, Gusev AG. The impact of ‘bursting’ thalamic impulses at a neocortical synapse. Nat Neurosci. 2001;4:402–8.CrossRefPubMedGoogle Scholar
  60. Theiler J, Eubank S, Longtin A, Galdrikian B, Doyne Farmer J. Testing for nonlinearity in time series: the method of surrogate data. Physica D Nonlinear Phenomena. 1992;58:77–94.CrossRefGoogle Scholar
  61. Tiesinga PH, Fellous JM, Salinas E, Jose JV, Sejnowski TJ. Inhibitory synchrony as a mechanism for attentional gain modulation. J Physiol Paris. 2004;98:296–314.CrossRefPubMedGoogle Scholar
  62. van Vugt MK, Schulze-Bonhage A, Litt B, Brandt A, Kahana MJ. Hippocampal gamma oscillations increase with memory load. J Neurosci. 2010;30:2694–9.CrossRefPubMedPubMedCentralGoogle Scholar
  63. van Wingerden M, Vinck M, Lankelma JV, Pennartz CM. Learning-associated gamma-band phase-locking of action-outcome selective neurons in orbitofrontal cortex. J Neurosci. 2010;30:10025–38.CrossRefPubMedGoogle Scholar
  64. Vinck M, van Wingerden M, Womelsdorf T, Fries P, Pennartz CM. The pairwise phase consistency: a bias-free measure of rhythmic neuronal synchronization. Neuroimage. 2010;51:112–22.CrossRefPubMedGoogle Scholar
  65. Wang Y, Iliescu BF, Ma J, Josic K, Dragoi V. Adaptive changes in neuronal synchronization in macaque V4. J Neurosci. 2011;31:13204–13.CrossRefPubMedPubMedCentralGoogle Scholar
  66. Xing D, Shen Y, Burns S, Yeh CI, Shapley R, Li W. Stochastic generation of gamma-band activity in primary visual cortex of awake and anesthetized monkeys. J Neurosci. 2012;32:13873–80a.CrossRefPubMedPubMedCentralGoogle Scholar
  67. Xu S, Jiang W, Poo MM, Dan Y. Activity recall in a visual cortical ensemble. Nat Neurosci. 2012;15:449–55.CrossRefPubMedPubMedCentralGoogle Scholar
  68. Zanos TP, Mineault PJ, Pack CC. Removal of spurious correlations between spikes and local field potentials. J Neurophysiol. 2011;105:474–86.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.School of Information Science and EngineeringYanshan UniversityQinhuangdaoChina
  2. 2.State Key Laboratory of Cognitive Neuroscience and Learning & IDG/McGovern Institute for Brain ResearchBeijing Normal UniversityBeijingChina
  3. 3.Center for Collaboration and Innovation in Brain and Learning SciencesBeijing Normal UniversityBeijingChina

Personalised recommendations