Skip to main content
SpringerLink
Log in

Analysis and Interpretation of Interval and Count Variability in Neural Spike Trains

  • Chapter
Analysis of Parallel Spike Trains

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

Abstract

Understanding the nature and origin of neural variability at the level of single neurons and neural networks is fundamental to our understanding of how neural systems can reliably process information. This chapter provides a starting point to the empirical analysis and interpretation of the variability of single neuron spike trains. In the first part, we cover a number of practical issues of measuring the inter-spike interval variability with the coefficient of variation (CV) and the trial-by-trial count variability with the Fano factor (FF), including the estimation bias for finite observations, the measurement from rate-modulated spike trains, and the time-resolved analysis of variability dynamics. In the second part, we specifically explore the effect of serial interval correlation in nonrenewal spike trains and the impact of slow fluctuations of neural activity on the relation of interval and count variability in stochastic models and in in vivo recordings from cortical neurons. Finally, we discuss how we can interpret the empirical results with respect to potential neuron-intrinsic and neuron-extrinsic sources of single neuron output variability.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ariav G, Polsky A, Schiller J (2003) Submillisecond precision of the input–output transformation function mediated by fast sodium dendritic spikes in basal dendrites of CA1 pyramidal neurons. J Neurosci 23:7750–7758

    CAS  PubMed  Google Scholar 

  • Benda J (2002) Single neuron dynamics-models linking theory and experiment. Ph.D. thesis, Humboldt Universität zu Berlin. Ph.D. Dissertation

    Google Scholar 

  • Benda J, Herz AVM (2003) A universal model for spike-frequency adaptation. Neural Comput 15(11):2523–2564. doi:10.1162/089976603322385063

    Article  PubMed  Google Scholar 

  • Brown EN, Barbieri R, Ventura V, Kaas RE, Frank LM (2002) The time-rescaling theorem and its application to neural spike train data analysis. Neural Comput 14:325–346

    Article  PubMed  Google Scholar 

  • Carandini M (2004) Amplification of trial-to-trial response variability by neurons in visual cortex. PLoS Biology 2(9):1483–1493

    Article  CAS  Google Scholar 

  • Chacron MJ, Lindner B, Longtin A (2007 Dec) Threshold fatigue and information transfer. J Comput Neurosci 23(3):301–311

    Article  PubMed  Google Scholar 

  • Chacron MJ, Longtin A, Maler L (2001) Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli. J Neurosci 21(14):5328–5343

    CAS  PubMed  Google Scholar 

  • Chacron MJ, Maler L, Bastian J (2005 May) Electroreceptor neuron dynamics shape information transmission. Nat Neurosci 8(5):673–678

    Article  CAS  PubMed  Google Scholar 

  • Churchland M, Yu B, Cunningham J, Sugrue L, Cohen M, Corrado G, Newsome W, Clark A, Hosseini P, Scott B, Bradley D, Smith M, Kohn A, Movshon J, Armstrong K, Moore T, Chang S, Snyder L, Lisberger S, Priebe N, Finn I, Ferster D, Ryu S, Santhanam G, Sahani M, Shenoy  K (2010) Stimulus onset quenches neural variability: a widespread cortical phenomenon. Nat Neurosci 13(3):369–378

    Article  CAS  PubMed  Google Scholar 

  • Churchland MM, Yu BM, Ryu SI, Santhanam G, Shenoy KV (2006) Neural variability in premotor cortex provides a signature of motor preparation. J Neurosci 26(14):3697–3712

    Article  CAS  PubMed  Google Scholar 

  • Cox DR, Lewis PAW (1966) The statistical analysis of series of events. Methuen’s monographs on applied probability and statistics. Methuen, London

    Google Scholar 

  • Davies RM, Gerstein GL, Baker SN (2006) Measurement of time-dependent changes in the irregularity of neural spiking. J Neurophysiol 96:906–918

    Article  PubMed  Google Scholar 

  • DeWeese MR, Zador AM (2004) Shared and private variability in the auditory cortex. J Neurophysiol 92:1840–1855

    Article  PubMed  Google Scholar 

  • Farkhooi F, Strube-Bloss M, Nawrot MP (2009) Serial correlation in neural spike trains: experimental evidence, stochastic modelling, and single neuron variability. Phys Rev E 79:021905

    Article  Google Scholar 

  • Grün S, Farkhooi F, Nawrot MP (2008) Significance of coincident spiking considering inter-spike interval variability and serial interval correlation. In: Frontiers comp neurosci conf abstr: neuroinformatics 2008. doi:10.3389/conf.neuro.11.2008.01.021

  • Holt GR, Softky WR, Koch C, Douglas RJ (1996) Comparison of discharge variability in vitro and in vivo in cat visual cortex neurons. J Neurophysiol 75(5):1806–1814

    CAS  PubMed  Google Scholar 

  • Knoblauch A, Palm G (2005) What is signal and what is noise in the brain? Biosystems 79:83–90

    Article  PubMed  Google Scholar 

  • Lewis CD, Gebber GL, Larsen PD, Barman SM (2001) Long-term correlations in the spike trains of medullary sympathetic neurons. J Neurophysiol 85(4):1614–1622

    CAS  PubMed  Google Scholar 

  • Lindner B, Chacron MJ, Longtin A (2005 Aug) Integrate-and-fire neurons with threshold noise: a tractable model of how interspike interval correlations affect neuronal signal transmission. Phys Rev E Stat Nonlin Soft Matter Phys 72(2 Pt 1):021911

    Article  PubMed  Google Scholar 

  • Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons. Science 268:1503–1506

    Article  CAS  PubMed  Google Scholar 

  • McFadden J (1962) On the lengths of intervals in stationary point processes. J Roy Stat Soc B 24:364–382

    Google Scholar 

  • Meier R, Egert U, Aertsen A, Nawrot MP (2008) Find – a unified framework for neural data analysis. Neural Networks 21:1085–1093. http://find.bccn.uni-freiburg.de/

    Article  PubMed  Google Scholar 

  • Middleton JW, Chacron MJ, Lindner B, Longtin A (2003 Aug) Firing statistics of a neuron model driven by long-range correlated noise. Phys Rev E Stat Nonlin Soft Matter Phys 68(2 Pt 1):021920

    Article  CAS  PubMed  Google Scholar 

  • Miura K, Okada M, Amari S (2006) Estimating spiking irregularities under changing environments. Neural Comput 18:2359–2386

    Article  PubMed  Google Scholar 

  • Muller E, Buesing L, Schemmel J, Meier K (2007) Spike-frequency adapting neural ensembles: Beyond mean adaptation and renewal theories. Neural Comput 19(11):2958–3010

    Article  PubMed  Google Scholar 

  • Nawrot M, Aertsen A, Rotter S (1999) Single-trial estimation of neuronal firing rates: from single-neuron spike trains to population activity. J Neurosci Meth 94:81–92

    Article  CAS  Google Scholar 

  • Nawrot M, Aertsen A, Rotter S (2003) Elimination of response latency variability in neuronal spike trains. Biol Cybern 5(88):321–334

    Article  Google Scholar 

  • Nawrot MP (2003) Ongoing activity in cortical networks: noise, variability and context. Ph.D. thesis, Faculty of Biology, Albert-Ludwigs-University Freiburg, Germany. URN: nbn:de:bsz:25-opus-73426. http://www.freidok.uni-freiburg.de/volltexte/7342/

  • Nawrot MP, Benda J (2006) Two methods for time-resolved inter-spike interval analysis. In: Berlin neuroforum abstr, p 62

    Google Scholar 

  • Nawrot MP, 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

    Article  Google Scholar 

  • Nawrot MP, Boucsein C, Rodriguez Molina V, Riehle A, Aertsen A, Rotter S (2008) Measurement of variability dynamics in cortical spike trains. J Neurosci Meth 169:374–390

    Article  Google Scholar 

  • Nawrot MP, Rodriguez V, Heck D, Riehle A, Aertsen A, Rotter S (2001) Trial-by-trial variability of spike trains in vivo and in vitro. Soc Neurosci Abstr 27:64.9

    Google Scholar 

  • Nawrot MP, Schnepel P, Aertsen A, Boucsein C (2009) Precisely timed signal transmission in neocortical networks with reliable intermediate-range projections. Frontiers Neural Circ 3:1. doi:103389/neurv.04.001.2009

    Google Scholar 

  • Nowak LG, Sanchez-Vives MV, McCormick DA (1997) Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cereb Cortex 7:487–501

    Article  CAS  PubMed  Google Scholar 

  • Parzen E (1962) On estimation of a probability density function and mode. Ann Math Statist 33:1065–1076

    Article  Google Scholar 

  • Ponce-Alvarez A, Kilavik B, Riehle A (2009) Comparison of local measures of spike time irregularity and relating variability to firing rate in motor cortical neurons. J Comput Neurosci. doi:10.1007/s10827-009-0158-2

    PubMed  Google Scholar 

  • Prescott SA, Sejnowski TJ (2008) Spike-rate coding and spike-time coding are affected oppositely by different adaptation mechanisms. J Neurosci 28:13649–13661

    Article  CAS  PubMed  Google Scholar 

  • Ratnam R, Nelson M (2000) Nonrenewal statistics of electrosensory afferent spike trains: implications for the detection of weak sensory signals. J Neurosci 20(17):6672–6683

    CAS  PubMed  Google Scholar 

  • Reich DS, Victor JD, Knight BW (1998) The power ratio and the interval map: Spiking models and extracellular recordings. J Neurosci 18:10090–10104

    CAS  PubMed  Google Scholar 

  • Rickert J, Riehle A, Aertsen A, Rotter S, Nawrot MP (2009) Dynamic encoding of movement direction in motor cortical neurons. J Neurosci 29:13870–13882

    Article  CAS  PubMed  Google Scholar 

  • Schwalger T, Schimansky-Geier L (2008) Interspike interval statistics of a leaky integrate-and-fire neuron driven by Gaussian noise with large correlation times. Phys Rev E Stat Nonlin Soft Matter Phys 77(3 Pt 1):031914

    Article  PubMed  Google Scholar 

  • Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. J Neurosci 18(10):3870–3896

    CAS  PubMed  Google Scholar 

  • Shimazaki H, Shinomoto S (2010) Kernel bandwidth optimization in spike rate estimation. J Comput Neurosci. doi:10.1007/s10827-009-0180-4

    PubMed  Google Scholar 

  • Shimokawa T, Shinomoto S (2009) Estimating instantaneous irregularity of neuronal firing. Neural Comput 21:1931–1951

    Article  PubMed  Google Scholar 

  • Shinomoto S, Miura K, Koyama S (2005) A measure of local variation of inter-spike intervals. Biosystems 79:67–72

    Article  PubMed  Google Scholar 

  • Shoham S, O’Connor DH, Sarkisov DV, Wang SSH (2005) Rapid neurotransmitter uncaging in spatially defined patterns. Nature Meth 2:837–843

    Article  CAS  Google Scholar 

  • Teich MC, Heneghan C, Lowen SB, Ozaki T, Kaplan E (1997) Fractal character of the neural spike train in the visual system of the cat. J Opt Soc Am A Opt Image Sci Vis 14(3):529–546

    Article  CAS  PubMed  Google Scholar 

  • Teich MC, Turcott RG, Siegel RM (1996) Temporal correlation in cat striate-cortex neural spike trains. IEEE Eng Med Biol Mag 15(5):79–87

    Article  Google Scholar 

  • Wang XJ (1998) Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J Neurophysiol 79:1549–1566

    CAS  PubMed  Google Scholar 

  • Wiener MC (2003) An adjustment of the time-rescaling method for application to short-trial spike train data. Neural Comput 15:2565–2576

    Article  PubMed  Google Scholar 

  • Zador A (1998) Impact of synaptic unreliability on the information transmitted by spiking neurons. J Neurophysiol 79:1219–1229

    CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Neuroinformatics and Theoretical Neuroscience, Institute of Biology, Freie Universität Berlin, Königin Luise Straße 1-3, 14195, Berlin, Germany

    Martin Paul Nawrot

Authors
  1. Martin Paul Nawrot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Paul Nawrot .

Editor information

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

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Nawrot, M.P. (2010). Analysis and Interpretation of Interval and Count Variability in Neural Spike Trains. 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_3

Download citation

Publish with us

Policies and ethics

Search

Navigation