An integrate-and-fire model to generate spike trains with long-range dependence

Area of Science:

• Computational Neuroscience
• Statistical Physics

Background:

• Long-range dependence (LRD) is observed in natural phenomena and neuronal spiking activity.
• LRD is often attributed to non-Markovian processes.

Purpose of the Study:

• Investigate if Markovian integrate-and-fire (IF) models can exhibit apparent LRD.
• Compare Markovian models with a non-Markovian IF model featuring fractional noise.
• Develop and apply a methodology for assessing the stationarity of interspike intervals (ISIs).

Main Methods:

• Simulated a Markovian IF model with a noisy slow adaptation term.
• Introduced a non-Markovian IF model with fractional noise.
• Analyzed spike train correlations for LRD.
• Developed and applied a stationarity evaluation methodology for ISIs.

Main Results:

• The Markovian IF model with adaptation generated ISIs that appeared to have LRD but lacked it asymptotically.
• The non-Markovian IF model with fractional noise demonstrated genuine LRD in spike train correlations.
• Stationarity analysis revealed that apparent LRD in Markovian models can arise from non-stationarities.

Conclusions:

• Purely Markovian IF models, even with adaptation, do not exhibit true LRD.
• Fractional noise is a viable mechanism for generating LRD in neuronal firing.
• Proper stationarity assessment is crucial for accurately identifying LRD in neuronal data.