Biological Cybernetics

, Volume 59, Issue 1, pp 1–11 | Cite as

On the significance of correlations among neuronal spike trains

  • G. Palm
  • A. M. H. J. Aertsen
  • G. L. Gerstein


We consider several measures for the correlation of firing activity among different neurons, based on coincidence counts obtained from simultaneously recorded spike trains. We obtain explicit formulae for the probability distributions of these measures. This allows an exact, quantitative assessment of significance levels, and thus a comparison of data obtained in different experimental paradigms. In particular it is possible to compare stimulus-locked, and therefore time dependent correlations for different stimuli and also for different times relative to stimulus onset. This allows to separate purely stimulus-induced correlation from intrinsic interneuronal correlation. It further allows investigation of the dynamic characteristics of the interneuronal correlation. For the display of significance levels or the corresponding probabilities we propose a logarithmic measure, called “surprise”.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abeles M (1982) Local cortical circuits. Studies of brain function, vol 6. Springer, Berlin Heidelberg New YorkGoogle Scholar
  2. Aertsen AMHJ, Gerstein GL (1985) Evaluation of neuronal connectivity: sensitivity of cross correlation. Brain Res 340:341–354Google Scholar
  3. Aertsen A, Bonhoeffer T, Krüger J (1987) Coherent activity in neuronal populations: analysis and interpretation. In: Caianiello ER (ed) Physics of cognitive processes. World Scientific Publishing, Singapore, pp 1–34Google Scholar
  4. Aertsen AMHJ, Gerstein GL, Habib M, Palm G et al. (1988) Dynamics of neuronal firing correlation: modulation of “effective connectivity” (submitted for publication)Google Scholar
  5. Billingsley P (1965) Ergodic theory and information. Wiley, New YorkGoogle Scholar
  6. Boltzmann L (1887) Über die mechanischen Analogien des zweiten Hauptsatzes der Thermodynamik. J Reine Angew Math 100:201–212Google Scholar
  7. Boogaard H van den, Hesselmans G, Johannesma P (1986) System identification based on point processes and correlation densities. I. The nonrefractory neuron model. Math Biosci 80:143–171Google Scholar
  8. Gerstein G (1987) Information flow and state in cortical neural networks: interpreting multi-neuron experiments. In: Seelen W von, Shaw G, Leinhos U (eds) Organization of neural networks: structures and models. VCH Verlagsgesellschaft, Weinheim, pp 53–75Google Scholar
  9. Gerstein GL, Perkel DH (1969) Simultaneously recorded trains of action potentials: analysis and functional interpretation. Science 164:828–830Google Scholar
  10. Gerstein GL, Perkel DH (1972) Mutual temporal relationships among neuronal spike trains. Biophys J 12:453–473Google Scholar
  11. Gerstein G, Bloom M, Espinosa I, Evanczuk S, Turner M (1983) Design of a laboratory for multi-neuron studies. IEEE Trans SMC-13:668–676Google Scholar
  12. Gerstein GL, Aertsen AMHJ et al. (1988) Neuronal assemblies as observed in multi-neuron experiments: dynamic organization depending on stimulus (in preparation)Google Scholar
  13. Glaser EM, Ruchkin DS (1976) Principles of neurobiological signal analysis. Academic Press, New YorkGoogle Scholar
  14. Grinvald A (1985) Real-time optical mapping of neuronal activity: from single growth cones to the intact mammalian brain. Ann Rev Neurosci 8:263–305Google Scholar
  15. Habib MK, Sen PK (1985) Non-stationary stochastic pointprocess models in neurophysiology with applications to learning. In: Sen PK (ed) Biostatistics: statistics in biomedical, public health and environmental sciences. Elsevier/North-Holland, Amsterdam, pp 481–509Google Scholar
  16. Krüger J (1982) A 12-fold microelectrode for recording from vertically aligned cortical neurons. J Neurosci Methods 6:347–350Google Scholar
  17. Krüger J (1983) Simultaneous individual recordings from many cerebral neurons: techniques and results. Rev Physiol Biochem Pharmacol 98:177–233Google Scholar
  18. Kuznetsov PI, Stratonovich RL (1956) A note on the mathematical theory of correlated random points. Izv Akad Nauk SSSR Ser Math 20:167–178; also in: Kuznetsov PI, Stratonovich RL, Tikhonov VI (eds) (1965) Nonlinear transformations of stochastic processes. Pergamon Press, New York, pp 101–115Google Scholar
  19. Legéndy CR (1975) Three principles of brain function and structure. Int J Neurosci 6:237–254Google Scholar
  20. Legéndy CR, Salcman M (1985) Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons. J Neurophys 53:926–939Google Scholar
  21. Palm G (1981) Evidence, information, and surprise. Biol Cybern 42:57–68Google Scholar
  22. Palm G (1988) Information theory. MIT Press, Cambridge, Mass (in press)Google Scholar
  23. Perkel DH, Gerstein GL, Moore GP (1967) Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J 7:419–440Google Scholar
  24. Perkel DH, Gerstein GL, Smith MS, Tatton WG (1975) Nerveimpulse patterns: a quantitative display technique for three neurons. Brain Res 100:271–296Google Scholar
  25. Shannon C (1948) A mathematical theory of communication. Bell Syst Techn J 27:379–423, 623–656Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • G. Palm
    • 1
  • A. M. H. J. Aertsen
    • 1
  • G. L. Gerstein
    • 2
  1. 1.Max-Planck-Institut für Biologische KybernetikTübingenFederal Republic of Germany
  2. 2.Department of PhysiologyUniversity of PennsylvaniaPhiladelphiaUSA

Personalised recommendations