Abstract
The signature of neuronal assemblies is the higher-order correlation structure of the spiking activity of the participating neurons. Due to the rapid progress in recording technology the massively parallel data required to search for such signatures are now becoming available. However, existing statistical analysis tools are severely limited by the combinatorial explosion in the number of spike patterns to be considered. Therefore, population measaures need to be constructed reducing the number of tests and the recording time required, potentially for the price of being able to answer only a restricted set of questions.
Here we investigate the population histogram of the time course of neuronal activity as the simplest example. The amplitude distribution of this histogram is called the complexity distribution. Independent of neuron identity it describes the probability to observe a particular number of synchronous spikes.
On the basis of two models we illustrate that in the presence of higher-order correlations already the complexity distribution exhibits characteristic deviations from expectation. The distribution reflects the presence of correlation of a given order in the data near the corresponding complexity. However, depending on the details of the model also the regime of low complexities may be perturbed.
In conclusion we propose that, for certain research questions, new statistical tools can overcome the problems caused by the combinatorial explosion in massively parallel recordings by evaluating features of the complexity distribution.
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Abeles, M., Bergman, H., Margalit, E., Vaadia, E.: Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J. Neurophysiol. 70(4), 1629–1638 (1993)
Abeles, M., Gerstein, G.L.: Detecting spatiotemporal firing patterns among simultaneously recorded single neurons. J. Neurophysiol. 60(3), 909–924 (1988)
Aertsen, A.M.H.J., Gerstein, G.L., Habib, M.K., Palm, G.: Dynamics of neuronal firing correlation: Modulation of ‘effective connectivity’. J. Neurophysiol. 61(5), 900–917 (1989)
Brown, E.N., Kaas, R.E., Mitra, P.P.: Multiple neural spike train data analysis: state-of-the-art and future challenges. Nat. Neurosci. 7(5), 456–461 (2004)
Csicsvari, J., Henze, D.A., Jamieson, B., Harris, K.D., Sirota, A., Barth, P., Wise, K.D., Buzsaki, G.: Massively parallel recording of unit and local field potentials with silicon-based electrodes. J. Neurophysiol. 90, 1314–1323 (2003)
Dayhoff, J.E., Gerstein, G.L.: Favored patterns in spike trains. I. detection. J. Neurophysiol. 49(6), 1334–1348 (1983)
Diesmann, M., Gewaltig, M.-O., Aertsen, A.: Stable propagation of synchronous spiking in cortical neural networks. Nature 402(6761), 529–533 (1999)
Ehm, W., Staude, B., Rotter, S.: Decomposition of neuronal assembly activity via empirical de-poissonization. Electron. J. Statist. 1, 473–495 (2007)
Gerstein, G.L., Perkel, D.H., Dayhoff, J.E.: Cooperative firing activity in simultaneously recorded populations of neurons: Detection and measurement. J. Neurosci. 5(4), 881–889 (1985)
Grün, S.: Data driven significance estimation for precise spike correlation (invited review). J. Neurophysiol. (submitted 2008)
Grün, S., Abeles, M., Diesmann, M.: The impact of higher-order correlations on coincidence distributions of massively parallel data. In: Proc. 5th Meeting German Neuroscience Society, pp. 650–651 (2003)
Grün, S., Diesmann, M., Aertsen, A.: ‘Unitary Events’ in multiple single-neuron spiking activity. I. Detection and significance. Neural Comput. 14(1), 43–80 (2002a)
Grün, S., Diesmann, M., Aertsen, A.: Unitary Events in multiple single-neuron spiking activity. II. Non-Stationary data. Neural Comput. 14(1), 81–119 (2002b)
Grün, S., Diesmann, M., Grammont, F., Riehle, A., Aertsen, A.: Detecting unitary events without discretization of time. J. Neurosci. Methods 94(1), 67–79 (1999)
Gütig, R., Aertsen, A., Rotter, S.: Analysis of higher-order neuronal interactions based on conditional inference. Biol. Cybern. 88(5), 352–359 (2003)
Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D., Yuste, R.: Synfire chains and cortical songs: temporal modules of cortical activity. Science 5670(304), 559–564 (2004)
Kohn, A., Smith, M.A.: Stimulus dependence of neuronal correlations in primary visual cortex of the Macaque. J. Neurosci. 25(14), 3661–3673 (2005)
Kuhn, A., Aertsen, A., Rotter, S.: Higher-order statistics of input ensembles and the response of simple model neurons. Neural Comput. 1(15), 67–101 (2003)
Martignon, L., von Hasseln, H., Grün, S., Aertsen, A., Palm, G.: Detecting higher-order interactions among the spiking events in a group of neurons. Biol. Cybern. 73, 69–81 (1995)
Nakahara, H., Amari, S.: Information-geometric measure for neural spikes. Neural Comput. 14, 2269–2316 (2002)
Nicolelis, M., Ghazanfar, A., Faggin, B., Votaw, S., Oliverira, L.: Reconstructing the engram: simultaneous, multisite, many single neuron recordings. Neuron 18(4), 529–537 (1997)
Nowak, L.G., Munk, M.H., Nelson, J.I., James, A., Bullier, J.: Structural basis of cortical synchronization. I. Three types of interhemispheric coupling. J. Neurophysiol. 74(6), 2379–2400 (1995)
Pazienti, A., Diesmann, M., Grün, S.: The effectiveness of systematic spike dithering depends on the precision of cortical synchronization. Brain Research 1225, 39–46 (2008)
Pipa, G., Grün, S.: Non-parametric significance estimation of joint-spike events by shuffling and resampling. Neurocomputing 52–54, 31–37 (2003)
Pipa, G., Wheeler, D., Singer, W., Nikolic, D.: Neuroxidence: Reliable and efficient analysis of an excess or deficiency of joint-spike events. J. Comput. Neurosci. 25(1), 64–88 (2008)
Prut, Y., Vaadia, E., Bergman, H., Haalman, I., Hamutal, S., Abeles, M.: Spatiotemporal structure of cortical activity: Properties and behavioral relevance. J. Neurophysiol. 79(6), 2857–2874 (1998)
Riehle, A., Grün, S., Diesmann, M., Aertsen, A.: Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278(5345), 1950–1953 (1997)
Schneider, G., Grün, S.: Analysis of higher-order correlations in multiple parallel processes. Neurocomputing 52–54, 771–777 (2003)
Schneidman, E., Berry, M.J., Segev, R., Bialek, W.: Weak pairwise correlations imply strongly correlated network states in a neural population. Nature 440, 1007–1012 (2006)
Schrader, S., Grün, S., Diesmann, M., Gerstein, G.: Detecting synfire chain activity using massively parallel spike train recording (in press, 2008)
Shlens, J., Field, G.D., Gauthier, J.L., Matthew, I.P.D., Sher, A., Litke, A.M., Chichilnisky, E.: The structure of multi-neuron firing patterns in primate retina. J. Neurosci. 26(32), 8254–8266 (2006)
Shmiel, T., Drori, R., Shmiel, O., Ben-Shaul, Y., Nadasdy, Z., Shemesh, M., Teicher, M., Abeles, M.: Temporally precise cortical firing patterns are associated with distinct action segments. J. Neurophysiol. 96(5), 2645–2652 (2006)
Staude, B., Rotter, S., Grün, S.: Detecting the existence of higher-order correlations in multiple single-unit spike trains. In: Society for Neuroscience, Volume 103.9/AAA18 of Abstract Viewer/Itinerary Planner, Washington, DC (2007)
Staude, B., Rotter, S., Grün, S.: Inferring assembly-activity from population spike trains (submitted, 2008)
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Grün, S., Abeles, M., Diesmann, M. (2008). Impact of Higher-Order Correlations on Coincidence Distributions of Massively Parallel Data. In: Marinaro, M., Scarpetta, S., Yamaguchi, Y. (eds) Dynamic Brain - from Neural Spikes to Behaviors. NN 2007. Lecture Notes in Computer Science, vol 5286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88853-6_8
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DOI: https://doi.org/10.1007/978-3-540-88853-6_8
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