Journal of Computational Neuroscience

, Volume 38, Issue 3, pp 589–600 | Cite as

Interspike interval correlation in a stochastic exponential integrate-and-fire model with subthreshold and spike-triggered adaptation

  • LieJune Shiau
  • Tilo Schwalger
  • Benjamin Lindner


We study the spike statistics of an adaptive exponential integrate-and-fire neuron stimulated by white Gaussian current noise. We derive analytical approximations for the coefficient of variation and the serial correlation coefficient of the interspike interval assuming that the neuron operates in the mean-driven tonic firing regime and that the stochastic input is weak. Our result for the serial correlation coefficient has the form of a geometric sequence and is confirmed by the comparison to numerical simulations. The theory predicts various patterns of interval correlations (positive or negative at lag one, monotonically decreasing or oscillating) depending on the strength of the spike-triggered and subthreshold components of the adaptation current. In particular, for pure subthreshold adaptation we find strong positive ISI correlations that are usually ascribed to positive correlations in the input current. Our results i) provide an alternative explanation for interspike-interval correlations observed in vivo, ii) may be useful in fitting point neuron models to experimental data, and iii) may be instrumental in exploring the role of adaptation currents for signal detection and signal transmission in single neurons.


Stochastic activity Models of spiking neuron Models of spike-frequency adaptation Integrate-and-fire model Interspike-interval correlations 



LS would like to thank the hospitality of Bernstein Center for Computational Neuroscience (BCCN) Berlin. LS was supported in part by the BCCN Berlin and by the National Science Foundation (DMS-1226282). TS and BL were supported by the Bundesministerium für Bildung und Forschung (FKZ:01GQ1001A). TS was supported by the European Research Council (Grant Agreement no. 268689, MultiRules).

Conflict of interests

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • LieJune Shiau
    • 1
  • Tilo Schwalger
    • 2
  • Benjamin Lindner
    • 3
    • 4
  1. 1.Department of MathematicsUniversity of HoustonHoustonUSA
  2. 2.Brain Mind InstituteÉcole Polytechnique Féderale de Lausanne (EPFL) Station 15LausanneSwitzerland
  3. 3.Bernstein Center for Computational Neuroscience BerlinBerlinGermany
  4. 4.Department of PhysicsHumboldt University BerlinBerlinGermany

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