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Dynamical estimation of neuron and network properties III: network analysis using neuron spike times

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Abstract

Estimating the behavior of a network of neurons requires accurate models of the individual neurons along with accurate characterizations of the connections among them. Whereas for a single cell, measurements of the intracellular voltage are technically feasible and sufficient to characterize a useful model of its behavior, making sufficient numbers of simultaneous intracellular measurements to characterize even small networks is infeasible. This paper builds on prior work on single neurons to explore whether knowledge of the time of spiking of neurons in a network, once the nodes (neurons) have been characterized biophysically, can provide enough information to usefully constrain the functional architecture of the network: the existence of synaptic links among neurons and their strength. Using standardized voltage and synaptic gating variable waveforms associated with a spike, we demonstrate that the functional architecture of a small network of model neurons can be established.

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References

  • Abarbanel HDI (2013) Predicting the future: completing models of observed complex systems. Springer, Berlin

    Book  Google Scholar 

  • Buzsáki G (2004) Large-scale recording of neuronal ensembles. Nat Neurosci 7:446–51

    Article  PubMed  Google Scholar 

  • Destexhe A, Mainen Z, Sejnowski T (1994) Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. J Comput Neurosci 1:195–230

    Article  CAS  PubMed  Google Scholar 

  • Destexhe A, Sejnowski T (2001) Thalamocortical assemblies: how ion channels, single neurons and large-scale networks organize sleep oscillations. Oxford University Press, USA. ISBN 0198524250/0-19-852425-02001

  • Fano RM (1961) Transmission of information: a statistical theory of communication. Wiley, New York

  • Gill PE, Murray W, Saunders MA (2005) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM Rev 47(1):99–131

    Article  Google Scholar 

  • Gold C, Henze DA, Koch C (2007) Using extracellular action potential recordings to constrain compartmental models. J Comput Neurosci 23(1):39–58. doi:10.1007/s10827-006-0018-2

    Article  PubMed  Google Scholar 

  • Hamill OP, Marty A, Neher E, Sakmann B, Sigworth FJ (1981) Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflugers Archiv Eur J Physiol 391:85–100. doi:10.1007/BF00656997

    Article  CAS  Google Scholar 

  • Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109

    Article  Google Scholar 

  • Huxley AF, Hodgkin AL (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544

    Google Scholar 

  • Johnston D, Wu SMS (1995) Foundations of cellular neurophysiology. The MIT Press. ISBN: 0-262-10053-3

  • Kostuk M, Toth B, Meliza CD, Abarbanel HDI, Margoliash D (2012) Dynamical estimation of neuron and network properties II: Monte Carlo methods. Biol Cybern 106:155–167

    Article  PubMed  Google Scholar 

  • Laplace PS (1774) Memoir on the probability of causes of events. Mémoires de Mathmatique et de Physique 16 (English translation by S. M. Stigler, Statist. Sci. 1: 364378 (1986))

  • Meliza CD, Margoliash D, Kostuk M, Toth B, Abarbanel HDI (2014) Using dynamical state and parameter estimation methods in the analysis of stimulus response experiments on individual neurons in the bird song nucleus HVC. In preparation Spring

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  CAS  Google Scholar 

  • Neher E, Sakmann B, Sigworth FJ, Hamill OP, Marty A (1981) Improved patch clamp techniques for high-resolution current recording from cells and cell free membrane patches. Pflugers Archiv Eur J Physiol 39:85–100

    Google Scholar 

  • Quinn JC, Abarbanel HDI (2010) State and parameter estimation using Monte Carlo evaluation of path integrals. Q J R Meteorol Soci 136:1855–1867. doi:10.1002/qj.690

    Article  Google Scholar 

  • Smetters D, Majewska A, Yuste R (1999) Detecting action potentials in neuronal populations with calcium imaging. Methods Companion Methods Enzymol 18:215–221

    Article  CAS  Google Scholar 

  • Toth BA (2010) Python scripting for dynamical parameter estimation in IPOPT. SIAG/OPT Views-and-News 21(1):1–8

    Google Scholar 

  • Toth BA, Kostuk M, Meliza CD, Margoliash D, Abarbanel HDI (2011) Dynamical estimation of neuron and network properties I: variational methods. Biol Cybern 1–21. doi:10.1007/s00422-011-0459-1

  • Wächter A, Biegler LT (2006) On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math Program 106:25–57

    Article  Google Scholar 

  • Zinn-Justin J (2002) Quantum field theory and critical phenomena, 4th edn. Oxford University Press, Oxford

    Book  Google Scholar 

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Acknowledgments

This work was funded in part under a grant from National Science Foundation (PHY-0961153). Partial support from the NSF sponsored Center for Theoretical Biological Physics is also appreciated (PHY-0822283). Conversations with Mark Kostuk and Jingxin Ye were very helpful.

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Authors and Affiliations

  1. Department of Physics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA , 92093-0402, USA

    Chris Knowlton & Henry D. I. Abarbanel

  2. University of Chicago, Chicago, IL , 60637, USA

    C. Daniel Meliza & Daniel Margoliash

  3. Marine Physical Laboratory (Scripps Institution of Oceanography) BioCircuits Institute, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA , 92093-0374, USA

    Henry D. I. Abarbanel

Authors
  1. Chris Knowlton
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  2. C. Daniel Meliza
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  3. Daniel Margoliash
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  4. Henry D. I. Abarbanel
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Correspondence to Chris Knowlton.

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Knowlton, C., Meliza, C.D., Margoliash, D. et al. Dynamical estimation of neuron and network properties III: network analysis using neuron spike times. Biol Cybern 108, 261–273 (2014). https://doi.org/10.1007/s00422-014-0601-y

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  • DOI: https://doi.org/10.1007/s00422-014-0601-y

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