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Analysis of Parallel Spike Trains pp 129–156Cite as

Spike Metrics

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

Abstract

Important questions in neuroscience, such as how neural activity represents the sensory world, can be framed in terms of the extent to which spike trains differ from one another. Since spike trains can be considered to be sequences of stereotyped events, it is natural to focus on ways to quantify differences between event sequences, known as spike-train metrics. We begin by defining several families of these metrics, including metrics based on spike times, on interspike intervals, and on vector-space embedding. We show how these metrics can be applied to single-neuron and multineuronal data and then describe algorithms that calculate these metrics efficiently. Finally, we discuss analytical procedures based on these metrics, including methods for quantifying variability among spike trains, for constructing perceptual spaces, for calculating information-theoretic quantities, and for identifying candidate features of neural codes.

An invited chapter for “Analysis of Parallel Spike Trains” (S. Rotter and S. Grün, eds.)

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References

  • Abbott LF (2000) Integrating with action potentials. Neuron 26:3–4

    Article  CAS  PubMed  Google Scholar 

  • Abeles M (1982) Role of the cortical neuron: integrator or coincidence detector?. Isr J Med Sci 18:83–92

    CAS  PubMed  Google Scholar 

  • Abeles M, Prut Y (1996) Spatio-temporal firing patterns in the frontal cortex of behaving monkeys. J Physiol Paris 90:249–250

    Article  CAS  PubMed  Google Scholar 

  • Aronov D (2003) Fast algorithm for the metric-space analysis of simultaneous responses of multiple single neurons. J Neurosci Methods 124:175–179

    Article  PubMed  Google Scholar 

  • Aronov D, Victor JD (2004) Non-Euclidean properties of spike train metric spaces. Phys Rev E Stat Nonlin Soft Matter Phys 69:061905

    Article  PubMed  Google Scholar 

  • Aronov D, Reich DS, Mechler F, Victor JD (2003) Neural coding of spatial phase in V1 of the macaque monkey. J Neurophysiol 89:3304–3327

    Article  PubMed  Google Scholar 

  • Banerjee A, Series P, Pouget A (2008) Dynamical constraints on using precise spike timing to compute in recurrent cortical networks. Neural Comput 20:974–993

    Article  PubMed  Google Scholar 

  • Carlton AG (1969) On the bias of information estimates. Psychol Bull 71:108–109

    Article  Google Scholar 

  • Chichilnisky EJ, Rieke F (2005) Detection sensitivity and temporal resolution of visual signals near absolute threshold in the salamander retina. J Neurosci 25:318–330

    Article  CAS  PubMed  Google Scholar 

  • Coifman RR, Lafon S, Lee AB, Maggioni M, Nadler B, Warner F, Zucker SW (2005) Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc Natl Acad Sci USA 102:7426–7431

    Article  CAS  PubMed  Google Scholar 

  • Cover TM, Thomas JA (1991) Elements of information theory, Schilling DL (ed). Wiley, New York

    Chapter  Google Scholar 

  • Dan Y, Poo MM (2004) Spike timing-dependent plasticity of neural circuits. Neuron 44:23–30

    Article  CAS  PubMed  Google Scholar 

  • Di Lorenzo PM, Victor JD (2003) Taste response variability and temporal coding in the nucleus of the solitary tract of the rat. J Neurophysiol 90:1418–1431

    Article  PubMed  Google Scholar 

  • Di Lorenzo PM, Victor JD (2007) Neural coding mechanisms for flow rate in taste-responsive cells in the nucleus of the solitary tract of the rat. J Neurophysiol 97:1857–1861

    Article  PubMed  Google Scholar 

  • Di Lorenzo PM, Chen J-Y, Victor JD (2009) Quality time: representation of a multidimensional sensory domain through temporal coding. J Neurosci 29(29):9227–9238

    Article  PubMed  Google Scholar 

  • Dubbs AJ, Seiler BA, Magnasco MO (2009) A fast Lp spike alignment metric. arXiv:0907.3137v2

  • Egger V, Feldmeyer D, Sakmann B (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. Nat Neurosci 2:1098–1105

    Article  CAS  PubMed  Google Scholar 

  • Erickson RP (1984) Ohrwall, Henning and von Skramlik; the foundations of the four primary positions in taste. Neurosci Biobehav Rev 8:105–127

    Article  CAS  PubMed  Google Scholar 

  • Furukawa S, Middlebrooks JC (2002) Cortical representation of auditory space: information-bearing features of spike patterns. J Neurophysiol 87:1749–1762

    PubMed  Google Scholar 

  • Gaal SA (1964) Point set topology. Academic Press, New York

    Google Scholar 

  • Goldberg DH, Victor JD, Gardner EP, Gardner D (2009) Spike train analysis toolkit: enabling wider application of information-theoretic techniques to neurophysiology. Neuroinformatics 7(3):165–178

    Article  PubMed  Google Scholar 

  • Grewe J, Kretzberg J, Warzecha AK, Egelhaaf M (2003) Impact of photon noise on the reliability of a motion-sensitive neuron in the fly’s visual system. J Neurosci 23:10776–10783

    CAS  PubMed  Google Scholar 

  • Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulus representation. Nature 376:33–36

    Article  CAS  PubMed  Google Scholar 

  • Houghton C. (2009) Studying spike trains using a van Rossum metric with a synapse-like filter. J Computat Neurosci 26:149–155

    Article  Google Scholar 

  • Houghton C, Sen K (2008) A new multineuron spike train metric. Neural Comput 20(6) 1495–1511

    Article  PubMed  Google Scholar 

  • Jacobs AL, Fridman G, Douglas RM, Alam NM, Latham PE, Prusky GT, Nirenberg S (2009) Ruling out and ruling in neural codes. Proc Natl Acad Sci USA 106:5936–5941

    Article  CAS  PubMed  Google Scholar 

  • Keat J, Reinagel P, Reid RC, Meister M (2001) Predicting every spike: a model for the responses of visual neurons. Neuron 30:803–817

    Article  CAS  PubMed  Google Scholar 

  • Kreiman G, Krahe R, Metzner W, Koch C, Gabbiani F (2000) Robustness and variability of neuronal coding by amplitude-sensitive afferents in the weakly electric fish eigenmannia. J Neurophysiol 84:189–204

    CAS  PubMed  Google Scholar 

  • Kruskal JB, Wish M (1978) Multidimensional scaling. Sage, Beverly Hills

    Google Scholar 

  • Kuba H, Yamada R, Fukui I, Ohmori H (2005) Tonotopic specialization of auditory coincidence detection in nucleus laminaris of the chick. J Neurosci 25:1924–1934

    Article  CAS  PubMed  Google Scholar 

  • Lim D, Capranica RR (1994) Measurement of temporal regularity of spike train responses in auditory nerve fibers of the green treefrog. J Neurosci Methods 52:203–213

    Article  CAS  PubMed  Google Scholar 

  • Machens C, Prinz P, Stemmler M, Ronacher B, Herz A (2001) Discrimination of behaviorally relevant signals by auditory receptor neurons. Neurocomputing 38:263–268

    Article  Google Scholar 

  • MacLeod K, Backer A, Laurent G (1998) Who reads temporal information contained across synchronized and oscillatory spike trains?. Nature 395:693–698

    Article  CAS  PubMed  Google Scholar 

  • Maloney LT, Yang JN (2003) Maximum likelihood difference scaling. J Vision 3:5. doi:10.1167/3.8.5

    Article  Google Scholar 

  • Markram H, Lubke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213–215

    Article  CAS  PubMed  Google Scholar 

  • Mechler F, Victor JD, Purpura KP, Shapley R (1998) Robust temporal coding of contrast by V1 neurons for transient but not for steady-state stimuli. J Neurosci 18:6583–6598

    CAS  PubMed  Google Scholar 

  • Middlebrooks JC, Clock AE, Xu L, Green DM (1994) A panoramic code for sound location by cortical neurons. Science 264:842–844

    Article  CAS  PubMed  Google Scholar 

  • Miller GA (1955) Note on the bias on information estimates. Information Theory in Psychology: Problems and Methods II-B:95–100

    Google Scholar 

  • Needleman SB, Wunsch CD (1970) A general method applicable to the search for similarities in the amino acid sequence of two proteins. J Mol Biol 48:443–453

    Article  CAS  PubMed  Google Scholar 

  • Nelken I (2009) Personal communication

    Google Scholar 

  • Nemenman I, Bialek W, de Ruyter van Steveninck R (2004) Entropy and information in neural spike trains: progress on the sampling problem. Phys Rev E Stat Nonlin Soft Matter Phys 69:056111

    Article  PubMed  Google Scholar 

  • Paninski L (2003) Estimation of entropy and mutual information. Neural Comput 15:1191

    Article  Google Scholar 

  • Reich D, Mechler F, Victor J (2000) Temporal coding of contrast in primary visual cortex: when, what, and why?. J Neurophysiol 85:1039–1050

    Google Scholar 

  • Reinagel P, Reid RC (2002) Precise firing events are conserved across neurons. J Neurosci 22:6837–6841

    CAS  PubMed  Google Scholar 

  • Richmond BJ, Optican LM (1987) Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. II. Quantification of response waveform. J Neurophysiol 57:147–161

    CAS  PubMed  Google Scholar 

  • Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W (1997) Spikes: exploring the neural code. MIT Press, Cambridge

    Google Scholar 

  • Samonds JM, Bonds AB (2004) From another angle: differences in cortical coding between fine and coarse discrimination of orientation. J Neurophysiol 91:1193–1202

    Article  PubMed  Google Scholar 

  • Samonds JM, Allison JD, Brown HA, Bonds AB (2003) Cooperation between area 17 neuron pairs enhances fine discrimination of orientation. J Neurosci 23:2416–2425

    CAS  PubMed  Google Scholar 

  • Schreiber S, Fellous JM, Tiesinga P, Sejnowski TJ (2004) Influence of ionic conductances on spike timing reliability of cortical neurons for suprathreshold rhythmic inputs. J Neurophysiol 91:194–205

    Article  PubMed  Google Scholar 

  • Segundo JP, Perkel DH (1969) The nerve cell as an analyzer of spike trains. In: Brazier MAB (ed) The interneuron. University of California Press, Berkeley, pp 349–390

    Google Scholar 

  • Sellers P (1974) On the theory and computation of evolutionary distances. SIAM J Appl Math 26:787–793

    Article  Google Scholar 

  • Sen K, Jorge-Rivera JC, Marder E, Abbott LF (1996) Decoding synapses. J Neurosci 16:6307–6318

    CAS  PubMed  Google Scholar 

  • Shannon CE, Weaver W (1949) The mathematical theory of communication. University of Illinois Press, Urbana

    Google Scholar 

  • Singh G, Memoli F, Ishkhanov T, Sapiro G, Carlsson G, Ringach DL (2008) Topological analysis of population activity in visual cortex. J Vision 8:1–18

    Article  Google Scholar 

  • Slepian D (1976) On bandwidth. Proc IEEE 64:292–300

    Article  Google Scholar 

  • Softky WR, Koch C (1993) The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J Neurosci 13:334–350

    CAS  PubMed  Google Scholar 

  • Stopfer M, Bhagavan S, Smith BH, Laurent G (1997) Impaired odour discrimination on desynchronization of odour-encoding neural assemblies. Nature 390:70–74

    Article  CAS  PubMed  Google Scholar 

  • Tenenbaum JB, de Silva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323

    Article  CAS  PubMed  Google Scholar 

  • Tiesinga PHE (2004) Chaos-induced modulation of reliability boosts output firing rate in downstream cortical areas. Phys Rev E Stat Nonlin Soft Matter Phys 69:031912

    Article  CAS  PubMed  Google Scholar 

  • Treves A, Panzeri S (1995) The upward bias in measures of information derived from limited data samples. Neural Comput 7:399–407

    Article  Google Scholar 

  • Tversky A (1977) Features of similarity. Psychol Rev 84:327–352

    Article  Google Scholar 

  • Tversky A, Gati I (1982) Similarity, separability, and the triangle inequality. Psychol Rev 89:123–154

    Article  CAS  PubMed  Google Scholar 

  • van Rossum MC (2001) A novel spike distance. Neural Comput 13:751–763

    Article  PubMed  Google Scholar 

  • Victor JD (2000) Asymptotic bias in information estimates and the exponential (Bell) polynomials. Neural Comput 12:2797–2804

    Article  CAS  PubMed  Google Scholar 

  • Victor JD (2002) Binless strategies for estimation of information from neural data. Phys Rev E 66:51903

    Article  Google Scholar 

  • Victor JD (2006) Approaches to information-theoretic analysis of neural activity. Biological Theory 1:302–316

    Article  PubMed  Google Scholar 

  • Victor JD, Purpura KP (1996) Nature and precision of temporal coding in visual cortex: a metric-space analysis. J Neurophysiol 76:1310–1326

    CAS  PubMed  Google Scholar 

  • Victor JD, Purpura KP (1997) Metric-space analysis of spike trains: theory, algorithms and application. Network 8:127–164

    Article  Google Scholar 

  • Victor JD, Goldberg DH, Gardner D (2007) Dynamic programming algorithms for comparing multineuronal spike trains via cost-based metrics and alignments. J Neurosci Methods 161:351–360

    Article  PubMed  Google Scholar 

  • Wu L, Gotman J (1998) Segmentation and classification of EEG during epileptic seizures. Electroencephalogr Clin Neurophysiol 106:344–356

    Article  CAS  PubMed  Google Scholar 

  • Wuerger SM, Maloney LT, Krauskopf J (1995) Proximity judgments in color space: tests of a Euclidean color geometry. Vision Res 35:827–835

    Article  CAS  PubMed  Google Scholar 

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Authors and Affiliations

  1. Division of Systems Neurology and Neuroscience, Department of Neurology and Neuroscience, Weill Cornell Medical College, 1300 York Avenue, New York, NY, 10065, USA

    Jonathan D. Victor & Keith P. Purpura

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  1. Jonathan D. Victor
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  2. Keith P. Purpura
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Correspondence to Jonathan D. Victor .

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Editors and Affiliations

  1. Computational Neuroscience Group, RIKEN Brain Science Institute, Hirosawa 2-1, Saitama, 351-0198, Japan

    Sonja Grün

  2. Bernstein-Zentrum für Computational Neur, Neuroscience, Universität Freiburg, Hansastrasse 9A 9a, Freiburg, 79104, Germany

    Stefan Rotter

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Victor, J.D., Purpura, K.P. (2010). Spike Metrics. In: Grün, S., Rotter, S. (eds) Analysis of Parallel Spike Trains. Springer Series in Computational Neuroscience, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5675-0_7

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