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Mutual information density of stochastic integrate-and-fire models

The coherence function of integrate-and-fire neurons shows low-pass properties in the most diverse firing regimes [1]. While the coherence function provides a good approximation to the full information transfer properties in the case of a weak input, for a strong input non-linear encoding could play an important role. The complete information transfer is quantified by Shannon's mutual information rate [2] which has been estimated in certain biological model systems [3]. In general, the exact analytical calculation of the mutual information rate is unfeasible and even the numerical estimation is demanding [4].

Numerical calculation of the mutual information rate is now a commonly adopted practice, but it does not indicate what aspects of the stimulus are best represented by the neuronal response. We developed a numerical procedure to directly calculate a frequency-selective version of the mutual information rate. This can be used to study how different frequency components of a Gaussian stimulus are encoded in neural models without invoking a weak-signal paradigm.


  1. Vilela RD, Lindner B: A comparative study of different integrate fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation. Phys Rev E. 2009, 80: 031909-

    Article  Google Scholar 

  2. Shannon C: A Mathematical Theory of Communication. The Bell System Technical Journal. 1948, 27: 379-423. 623-656

    Article  Google Scholar 

  3. Strong SP, Koberle R, de Ruyter van Steveninck R, Bialek W: Entropy and Information in Neural Spike Trains. Phys Rev Lett. 1998, 80 (1): 197-200. 10.1103/PhysRevLett.80.197.

    Article  CAS  Google Scholar 

  4. Panzeri S, Senatore R, Montemurro MA, Petersen RS: Correcting for the sampling bias problem in spike train information measures. J Neurophysiol. 2007, 98 (3): 1064-1072. 10.1152/jn.00559.2007.

    Article  PubMed  Google Scholar 

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This work was funded by the BMBF (FKZ: 01GQ1001A).

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Correspondence to Davide Bernardi.

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bernardi, D., Lindner, B. Mutual information density of stochastic integrate-and-fire models. BMC Neurosci 14 (Suppl 1), P245 (2013).

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