IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v50y2013icp13-31.html
   My bibliography  Save this article

Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses

Author

Listed:
  • Cofré, Rodrigo
  • Cessac, Bruno

Abstract

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based integrate-and-fire neural network, driven by Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or generalized linear models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.

Suggested Citation

  • Cofré, Rodrigo & Cessac, Bruno, 2013. "Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 13-31.
    • Handle: RePEc:eee:chsofr:v:50:y:2013:i:c:p:13-31
    DOI: 10.1016/j.chaos.2012.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077913000027
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2012.12.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Elad Schneidman & Michael J. Berry & Ronen Segev & William Bialek, 2006. "Weak pairwise correlations imply strongly correlated network states in a neural population," Nature, Nature, vol. 440(7087), pages 1007-1012, April.
    2. Mario Galarreta & Shaul Hestrin, 1999. "A network of fast-spiking cells in the neocortex connected by electrical synapses," Nature, Nature, vol. 402(6757), pages 72-75, November.
    3. Yasser Roudi & Sheila Nirenberg & Peter E Latham, 2009. "Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-18, May.
    4. Daniele Linaro & Marco Storace & Michele Giugliano, 2011. "Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation," PLOS Computational Biology, Public Library of Science, vol. 7(3), pages 1-17, March.
    5. Tilo Schwalger & Karin Fisch & Jan Benda & Benjamin Lindner, 2010. "How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations," PLOS Computational Biology, Public Library of Science, vol. 6(12), pages 1-25, December.
    6. Ifije E. Ohiorhenuan & Ferenc Mechler & Keith P. Purpura & Anita M. Schmid & Qin Hu & Jonathan D. Victor, 2010. "Sparse coding and high-order correlations in fine-scale cortical networks," Nature, Nature, vol. 466(7306), pages 617-621, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. D’Onofrio, Giuseppe & Lansky, Petr & Tamborrino, Massimiliano, 2019. "Inhibition enhances the coherence in the Jacobi neuronal model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 108-113.
    2. Ma, Xiaowen & Xu, Ying, 2022. "Taming the hybrid synapse under energy balance between neurons," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hideaki Shimazaki & Shun-ichi Amari & Emery N Brown & Sonja Grün, 2012. "State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data," PLOS Computational Biology, Public Library of Science, vol. 8(3), pages 1-27, March.
    2. Montani, Fernando & Phoka, Elena & Portesi, Mariela & Schultz, Simon R., 2013. "Statistical modelling of higher-order correlations in pools of neural activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3066-3086.
    3. Einat Granot-Atedgi & Gašper Tkačik & Ronen Segev & Elad Schneidman, 2013. "Stimulus-dependent Maximum Entropy Models of Neural Population Codes," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-14, March.
    4. Arno Onken & Valentin Dragoi & Klaus Obermayer, 2012. "A Maximum Entropy Test for Evaluating Higher-Order Correlations in Spike Counts," PLOS Computational Biology, Public Library of Science, vol. 8(6), pages 1-12, June.
    5. Montangie, Lisandro & Montani, Fernando, 2015. "Quantifying higher-order correlations in a neuronal pool," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 388-400.
    6. Christian Donner & Klaus Obermayer & Hideaki Shimazaki, 2017. "Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations," PLOS Computational Biology, Public Library of Science, vol. 13(1), pages 1-27, January.
    7. Urs Köster & Jascha Sohl-Dickstein & Charles M Gray & Bruno A Olshausen, 2014. "Modeling Higher-Order Correlations within Cortical Microcolumns," PLOS Computational Biology, Public Library of Science, vol. 10(7), pages 1-12, July.
    8. Porta Mana, PierGianLuca & Rostami, Vahid & Torre, Emiliano & Roudi, Yasser, 2018. "Maximum-entropy and representative samples of neuronal activity: a dilemma," OSF Preprints uz29n, Center for Open Science.
    9. Dimitri Yatsenko & Krešimir Josić & Alexander S Ecker & Emmanouil Froudarakis & R James Cotton & Andreas S Tolias, 2015. "Improved Estimation and Interpretation of Correlations in Neural Circuits," PLOS Computational Biology, Public Library of Science, vol. 11(3), pages 1-28, March.
    10. Montangie, Lisandro & Montani, Fernando, 2017. "Higher-order correlations in common input shapes the output spiking activity of a neural population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 845-861.
    11. Jan Humplik & Gašper Tkačik, 2017. "Probabilistic models for neural populations that naturally capture global coupling and criticality," PLOS Computational Biology, Public Library of Science, vol. 13(9), pages 1-26, September.
    12. Emili Balaguer-Ballester & Christopher C Lapish & Jeremy K Seamans & Daniel Durstewitz, 2011. "Attracting Dynamics of Frontal Cortex Ensembles during Memory-Guided Decision-Making," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-19, May.
    13. Seif Eldawlatly & Karim G Oweiss, 2011. "Millisecond-Timescale Local Network Coding in the Rat Primary Somatosensory Cortex," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-14, June.
    14. Benjamin Dunn & Maria Mørreaunet & Yasser Roudi, 2015. "Correlations and Functional Connections in a Population of Grid Cells," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-21, February.
    15. Xi, Ning & Muneepeerakul, Rachata & Azaele, Sandro & Wang, Yougui, 2014. "Maximum entropy model for business cycle synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 189-194.
    16. Gašper Tkačik & Olivier Marre & Dario Amodei & Elad Schneidman & William Bialek & Michael J Berry II, 2014. "Searching for Collective Behavior in a Large Network of Sensory Neurons," PLOS Computational Biology, Public Library of Science, vol. 10(1), pages 1-23, January.
    17. Stojan Jovanović & Stefan Rotter, 2016. "Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 12(6), pages 1-28, June.
    18. Lipovetsky, Stan, 2018. "Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling," Journal of choice modelling, Elsevier, vol. 27(C), pages 62-73.
    19. Mark L Ioffe & Michael J Berry II, 2017. "The structured ‘low temperature’ phase of the retinal population code," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
    20. Yasser Roudi & Sheila Nirenberg & Peter E Latham, 2009. "Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-18, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:50:y:2013:i:c:p:13-31. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.