2014, 11(1): 27-48. doi: 10.3934/mbe.2014.11.27

Cross nearest-spike interval based method to measure synchrony dynamics

1. 

Department of Mathematics, Facultad de Informática, Campus de Elviña s/n, 15071, Universidade da Coruña, A Coruña, Spain, Spain

2. 

Interuniversity Institute for Biostatistics and statistical Bionformatics, Hasselt University and KULeuven, Hasselt, Belgium, Belgium

3. 

Neuroscience and Motor Control Group (NEUROcom), Department of Medicine, Facultad de Ciencias de la Salud, Campus de Oza s/n, 15006, Universidade da Coruña, A Coruña, Spain, Spain, Spain

Received  December 2012 Revised  June 2013 Published  September 2013

A new synchrony index for neural activity is defined in this paper. The method is able to measure synchrony dynamics in low firing rate scenarios. It is based on the computation of the time intervals between nearest spikes of two given spike trains. Generalized additive models are proposed for the synchrony profiles obtained by this method. Two hypothesis tests are proposed to assess for differences in the level of synchronization in a real data example. Bootstrap methods are used to calibrate the distribution of the tests. Also, the expected synchrony due to chance is computed analytically and by simulation to assess for actual synchronization.
Citation: Aldana M. González Montoro, Ricardo Cao, Christel Faes, Geert Molenberghs, Nelson Espinosa, Javier Cudeiro, Jorge Mariño. Cross nearest-spike interval based method to measure synchrony dynamics. Mathematical Biosciences & Engineering, 2014, 11 (1) : 27-48. doi: 10.3934/mbe.2014.11.27
References:
[1]

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C. Faes, H. Geys, G. Molenberghs, M. Aerts, C. Cadarso-Suárez, C. Acuña and M. Cano, A flexible method to measure synchrony in neuronal firing,, J. Amer. Statist. Assoc., 103 (2008), 149.  doi: 10.1198/016214507000000419.  Google Scholar

[6]

G. L. Gerstein and D. H. Perkel, Simultaneously recorded trains of action potentials: Analysis and functional interpretation,, Science, 164 (1969), 828.  doi: 10.1126/science.164.3881.828.  Google Scholar

[7]

S. Grün, "Unitary Joint-Events in Multiple-Neuron Spiking Activity: Detection, Significance, and Interpretation,", Reihe Physik, (1996).   Google Scholar

[8]

S. Grün, M. Diesmann and A. Aertsen, Unitary events in multiple single-neuron spiking activity: I. Detection and significance,, Neural Computation, 14 (2002), 43.   Google Scholar

[9]

T. J. Hastie and R. J. Tibshirani, "Generalized Additive Models,", Monographs on Statistics and Applied Probability, 43 (1990).   Google Scholar

[10]

R. E. Kass, V. Ventura and E. N. Brown, Statistical issues in the analysis of neuronal data,, Journal of Neurophysiology, 94 (2005), 8.  doi: 10.1152/jn.00648.2004.  Google Scholar

[11]

J. Mariño and J. Cudeiro, Nitric oxide-mediated cortical activation: A diffuse wake-up system,, The Journal of Neuroscince, 23 (2003), 4299.   Google Scholar

[12]

M. Nawrot, A. Aertsen and E. Rotter, Single-trial estimation of neural firing rates: From single-neuron spike trains to population activity,, Journal of Neuroscience Methods, 94 (1999), 81.   Google Scholar

[13]

R. Q. Quiroga, T. Kreuz and P. Grassberger, Event synchronization: A simple and fast method to measure synchronicity and time delay patterns,, Physical Review E (3), 66 (2002).  doi: 10.1103/PhysRevE.66.041904.  Google Scholar

[14]

M. Steriade, D. A. McCormick and T. J. Sejnowski, Thalamocortical oscillations in the sleeping and arousal brain,, Science, 262 (1993), 679.  doi: 10.1126/science.8235588.  Google Scholar

[15]

M. Steriade, Sleep oscillations and their blockage by activating systems,, Journal of Psychiatry and Neuroscience, 19 (1994), 354.   Google Scholar

[16]

M. P. Wand and M. C. Jones, "Kernel Smoothing,", Monographs on Statistics and Applied Probability, 60 (1995).   Google Scholar

[17]

S. Wood, "Generalized Additive Models. An Introduction with R,", Texts in Statistical Science Series, (2006).   Google Scholar

show all references

References:
[1]

M. Bazhenov, I. Timofeev, M. Steriade and T. Sejnowski, Model of thalamocortical slow-wave sleep oscillations and transitions to activated states,, The Journal of Neuroscience, 22 (2002), 8691.   Google Scholar

[2]

C. E. Bonferroni, Il calcolo delle assicurazioni su gruppi di teste,, Studi in Onore del Professore Salvatore Ortu Carboni, (1935), 13.   Google Scholar

[3]

E. N. Brown, R. E. Kass and P. P. Mitra, Multiple neural spike train data analysis: State-of-the-art and future challenges,, Nature Neuroscience, 7 (2004), 456.  doi: 10.1038/nn1228.  Google Scholar

[4]

R. Cao, M. Francisco-Fernández and E. J. Quinto, A random effect multiplicative heteroscedastic model for bacterial growth,, BMC Bioinformatics, 11 (2010).  doi: 10.1186/1471-2105-11-77.  Google Scholar

[5]

C. Faes, H. Geys, G. Molenberghs, M. Aerts, C. Cadarso-Suárez, C. Acuña and M. Cano, A flexible method to measure synchrony in neuronal firing,, J. Amer. Statist. Assoc., 103 (2008), 149.  doi: 10.1198/016214507000000419.  Google Scholar

[6]

G. L. Gerstein and D. H. Perkel, Simultaneously recorded trains of action potentials: Analysis and functional interpretation,, Science, 164 (1969), 828.  doi: 10.1126/science.164.3881.828.  Google Scholar

[7]

S. Grün, "Unitary Joint-Events in Multiple-Neuron Spiking Activity: Detection, Significance, and Interpretation,", Reihe Physik, (1996).   Google Scholar

[8]

S. Grün, M. Diesmann and A. Aertsen, Unitary events in multiple single-neuron spiking activity: I. Detection and significance,, Neural Computation, 14 (2002), 43.   Google Scholar

[9]

T. J. Hastie and R. J. Tibshirani, "Generalized Additive Models,", Monographs on Statistics and Applied Probability, 43 (1990).   Google Scholar

[10]

R. E. Kass, V. Ventura and E. N. Brown, Statistical issues in the analysis of neuronal data,, Journal of Neurophysiology, 94 (2005), 8.  doi: 10.1152/jn.00648.2004.  Google Scholar

[11]

J. Mariño and J. Cudeiro, Nitric oxide-mediated cortical activation: A diffuse wake-up system,, The Journal of Neuroscince, 23 (2003), 4299.   Google Scholar

[12]

M. Nawrot, A. Aertsen and E. Rotter, Single-trial estimation of neural firing rates: From single-neuron spike trains to population activity,, Journal of Neuroscience Methods, 94 (1999), 81.   Google Scholar

[13]

R. Q. Quiroga, T. Kreuz and P. Grassberger, Event synchronization: A simple and fast method to measure synchronicity and time delay patterns,, Physical Review E (3), 66 (2002).  doi: 10.1103/PhysRevE.66.041904.  Google Scholar

[14]

M. Steriade, D. A. McCormick and T. J. Sejnowski, Thalamocortical oscillations in the sleeping and arousal brain,, Science, 262 (1993), 679.  doi: 10.1126/science.8235588.  Google Scholar

[15]

M. Steriade, Sleep oscillations and their blockage by activating systems,, Journal of Psychiatry and Neuroscience, 19 (1994), 354.   Google Scholar

[16]

M. P. Wand and M. C. Jones, "Kernel Smoothing,", Monographs on Statistics and Applied Probability, 60 (1995).   Google Scholar

[17]

S. Wood, "Generalized Additive Models. An Introduction with R,", Texts in Statistical Science Series, (2006).   Google Scholar

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