Skip to main content

Effective neuronal refractoriness dominates the statistics of superimposed spike trains

The pooled spike trains of populations of neurons are typically modeled as Poisson processes [2]. It is known, though, that the superposition of point processes is a Poisson process if and only if all components are Poisson processes [3]. However, neocortical neurons spike more regularly [1]. Partly this is because they often have a refractory period, but also because the membrane potential is hyperpolarized after each spike, as illustrated in Figure 1A. Here we analyze neuronal spike trains recorded intracellularly in vivo from rat somatosensory cortex. We match them with a Poisson process with dead-time [4], which is the simplest model of neuronal activity that incorporates refractory effects. The dead-time here models the effective refractoriness of the neuron, which can be larger than the refractory period due to channel kinetics alone. From the spike train recordings we construct independent superpositions (see Figure 1B) and compare their statistics to our analytical results for the model processes. We find that the effective refractoriness of the neurons dominates the second-order statistics of the superposition spike trains. We uncover profound statistical differences as compared to Poisson processes, which considerably affect the dynamics of the membrane potential of neurons that receive such superpositions, as we further show in numerical simulations (see also [5]).

Figure 1
figure 1

A: Membrane potential trajectories of a simulated neocortical neuron. After each spike, the potential has to charge up until spikes can be initiated by input fluctuations, leading to an effective refractoriness. Green line shows the mean subthreshold trajectory, yellow lines show mean +/- standard deviation. B: Scheme of the independent superposition of three spike trains. Adapted from [6].


  1. Maimon G, Assad JA: Beyond poisson: Increased spike-time regularity across primate parietal cortex. Neuron. 2009, 62: 426-440. 10.1016/j.neuron.2009.03.021.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  2. Brunel N: Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci. 2000, 8 (3): 183-208. 10.1023/A:1008925309027.

    Article  CAS  PubMed  Google Scholar 

  3. Lindner B: Superposition of many independent spike trains is generally not a Poisson process. Phys Rev E. 2006, 73: 022-901.

    Google Scholar 

  4. Johnson DH: Point process models of single-neuron discharges. J Comput Neurosci. 1996, 3 (4): 275-299. 10.1007/BF00161089.

    Article  CAS  PubMed  Google Scholar 

  5. Câteau H, Reyes A: Relation between single neuron and population spiking statistics and effects on network activity. Phys Rev Lett. 2006, 96: 058-101. 10.1103/PhysRevLett.96.058101.

    Article  Google Scholar 

  6. Cox DR, Smith WL: On the superposition of renewal processes. Biometrika. 1954, 41 (1/2): 91-99. 10.2307/2333008.

    Article  Google Scholar 

Download references


Partially funded by BMBF grant 01GQ0420 to BCCN Freiburg, and DFG grant to SFB 780, subproject C4.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Moritz Deger.

Rights and permissions

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.

Reprints and Permissions

About this article

Cite this article

Deger, M., Helias, M., Boucsein, C. et al. Effective neuronal refractoriness dominates the statistics of superimposed spike trains. BMC Neurosci 12 (Suppl 1), P273 (2011).

Download citation

  • Published:

  • DOI: