Skip to main content
  • Poster presentation
  • Open access
  • Published:

The ball and stick neuron model accounts both for microscopic and macroscopic power laws

Ever since Hans Berger recorded the first human electroencephalogram (EEG) in 1924 [1] its features have been under extensive study, especially since many of them are directly related to disease and to states of consciousness. In the last decades, the underlying background spectra (the power spectral density, PSD) of the EEG have also attracted great attention. The PSD is often well fit by a 1/fα power law, with α typically in the range from 1 to 2 [2, 3].

Linking features seen in global recordings, such as the EEG, to features in the underlying local activity, such as single neuron activity, is still a major challenge within the field of neuroscience. Power laws are, however, recorded both at the macroscopic level, e.g., for the EEG or the MEG, and at the level of single neurons. The PSD of the sub-threshold soma potential has been shown to exhibit a 1/fα power law, but with a larger power α than for the EEG. For the sub-threshold soma potential α is typically ranging from 2 to 3 [48]. As for the EEG, this power law seems to be very robust; it has been observed in single neuron recordings across several species and brain regions, and also in cell cultures [48].

Here, we present analytical solutions to the ball and stick neuron model with input currents spread homogeneously throughout the dendritic stick. Expressions for the PSD of the soma potential and the PSD of the single neuron contribution to the EEG are derived and shown to follow 1/fα power laws with values of α in agreement with experiments. The scale-free background spectra of the EEG may therefore originate from stochastic processes within the neuronal membrane, rather than relying on complicated network dynamics or self-critical states.

References

  1. Berger H: Über das Elektrenkephalogramm des Menschen. European Archives of Psychiatry and Clinical Neuroscience. 1929, 87: 527-570.

    Google Scholar 

  2. Buzsáki G: Rythms of the brain. 2006, Oxford University Press

    Chapter  Google Scholar 

  3. Freeman WJ, Holmes MD, Burke BC, Vanhatalo S: Spatial spectra of scalp EEG and EMG from awake humans. Clin Neurophysiol. 2003, 114 (6): 1053-1068. 10.1016/S1388-2457(03)00045-2.

    Article  PubMed  Google Scholar 

  4. Diba K, Lester HA, Koch C: Intrinsic noise in cultured hippocampal neurons: experiment and modeling. J Neurosci. 2004, 24 (43): 9723-9733. 10.1523/JNEUROSCI.1721-04.2004.

    Article  CAS  PubMed  Google Scholar 

  5. Rudolph M, Pelletier JG, Paré D, Destexhe A: Characterization of synaptic conductances and integrative properties during electrically induced EEG-activated states in neocortical neurons in vivo. J Neurophysiol. 2005, 94 (4): 2805-2821. 10.1152/jn.01313.2004.

    Article  PubMed  Google Scholar 

  6. Jacobson GA, Diba K, Yaron-Jakoubovitch A, Oz Y, Koch C, Segev I, Yarom Y: Subthreshold voltage noise of rat neocortical pyramidal neurones. J Physiol. 2005, 564 (Pt 1): 145-160. 10.1113/jphysiol.2004.080903.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  7. Yaron-Jakoubovitch A, Jacobson GA, Koch C, Segev I, Yarom Y: A paradoxical isopotentiality: a spatially uniform noise spectrum in neocortical pyramidal cells. Front Cell Neurosci. 2008, 2: 3-10.3389/neuro.03.003.2008.

    Article  PubMed Central  PubMed  Google Scholar 

  8. Bédard C, Destexhe A: A modified cable formalism for modeling neuronal membranes at high frequencies. Biophys J. 2008, 94 (4): 1133-1143. 10.1529/biophysj.107.113571.

    Article  PubMed Central  PubMed  Google Scholar 

Download references

Acknowledgements

This project was supported by the Research Council of Norway (eVITA [eNEURO], Notur).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Klas H Pettersen.

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 (http://creativecommons.org/licenses/by/2.0), 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

Pettersen, K.H., Lindén, H., Tetzlaff, T. et al. The ball and stick neuron model accounts both for microscopic and macroscopic power laws. BMC Neurosci 12 (Suppl 1), P91 (2011). https://doi.org/10.1186/1471-2202-12-S1-P91

Download citation

  • Published:

  • DOI: https://doi.org/10.1186/1471-2202-12-S1-P91

Keywords