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The relationship between nernst equilibrium variability and the multifractality of interspike intervals in the hippocampus

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Abstract

Spatiotemporal patterns of action potentials are considered to be closely related to information processing in the brain. Auto-generating neurons contributing to these processing tasks are known to cause multifractal behavior in the inter-spike intervals of the output action potentials. In this paper we define a novel relationship between this multifractality and the adaptive Nernst equilibrium in hippocampal neurons. Using this relationship we are able to differentiate between various drugs at varying dosages. Conventional methods limit their ability to account for cellular charge depletion by not including these adaptive Nernst equilibria. Our results provide a new theoretical approach for measuring the effects which drugs have on single-cell dynamics.

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References

  • Aslanidi, O., & Mornev, O. (1999). Soliton-like regimes and excitation pulse reflection (echo) in homogeneous cardiac purkinje fibers: results of numerical simulations. Journal of Biological Physics, 25, 149–164.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Barabasi, A., & Vicsek, T. (1991). Multifractality of self-affine fractals. Physical Review A, 44, 2730–2733.

    Article  CAS  Google Scholar 

  • Chamberland, S., & Topolnik, L. (2012). Inhibitory control of hippocampal inhibitory neurons. Frontiers in Neuroscience, 6(165).

  • Commins, S., Gigg, J., Anderson, M., & O’Mara, S. (1998). The projection from hippocampal ca1 to the subiculum sustains long-term potentiation. Neuroreport, 9, 847–50.

    Article  CAS  PubMed  Google Scholar 

  • Cressman, J., Ullah, G., Ziburkus, J., Schiff, S., & Barreto, E. (2009). The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: i. single neuron dynamics. Journal of Computational Neuroscience, 26(2), 159–170.

    Article  PubMed  PubMed Central  Google Scholar 

  • Cressman, J., Ullah, G., Ziburkus, J., Schiff, S., & Barreto, E. (2011). Erratum to: the influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. single neuron dynamics. Journal of Computational Neuroscience, 30, 781.

    Article  Google Scholar 

  • Ermentrout, B. (1996). Type 1 membranes, phase resetting curves, and synchrony. Neural Computation, 8, 979–1001.

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout, B., Pascal, M., & Gutkin, B. (2001). The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Computation, 13, 1285– 1310.

    Article  CAS  PubMed  Google Scholar 

  • Fadda, P., Robinson, L., Fratta, W., Pertwee, R.G., & Riedel, G. (2004). Differential effects of thc- or cbd-rich cannabis extracts on working memory in rats. Journal of Neuropharmacology, 47, 1170–1179.

    Article  CAS  PubMed  Google Scholar 

  • Fetterhoff, D., Opris, I., Simpson, S.L., Deadwyler, S.A., Hampson, R.E., & Kraft, R.A. (2014). Multifractal analysis of information processing in hippocampal neural ensembles during working memory under thc administration. Journal of Neuroscience Methods, 1, 1–18.

    Google Scholar 

  • Forrest, M.D. (2014). Intracellular calcium dynamics permit a purkinje neuron model to perform toggle and gain computations upon its inputs. Frontiers in Computational Neuroscience, 8, 86.

    Article  PubMed  PubMed Central  Google Scholar 

  • Hodgkin, A. (1948). The local electric changes associated with repetitive action in a non-medullated axon. Journal of Physiology, 107, 165–181.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hodgkin, A.L., & Huxley, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500–544.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hoppensteadt, F., & Izhikevich, E. (1997). Weakly connected neural networks. New York: Springer.

    Book  Google Scholar 

  • Ihlen, E.A.F. (2012). Introduction to multifractal detrended fluctuation analysis in matlab. Frontiers in Physiology, 3, 1–18.

    Article  Google Scholar 

  • Izhikevich, E.M. (2010). Dynamical systems in neuroscience: the geometry of excitability and bursting. Cambridge: The MIT Press.

    Google Scholar 

  • Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Bunde, A., Havlin, S., & Stanley, E.H. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica A, 316(141).

  • Kobayashi, R., & Kitano, K. (2016). Impact of slow k + currents on spike generation can be described by an adaptive threshold model. Journal of Computational Neuroscience, 40, 347–362.

    Article  PubMed  PubMed Central  Google Scholar 

  • Koch, C., & Segev, I. (1989). Methods in neuronal modelling: from synapses to networks. Cambridge: The MIT Press.

    Google Scholar 

  • Krinskii, V.I., & Kokoz, Y.M. (1973). Analysis of equations of excitable membranes - i. reduction of the hodgkin-huxley equations to a second order system. Biofizika, 18, 506–511.

    CAS  PubMed  Google Scholar 

  • Meier, S.R., Lancaster, J.L., & Starobin, J.M. (2015). Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium. PLoS ONE, 10, e0122401.

    Article  PubMed  PubMed Central  Google Scholar 

  • Noori, H. (2011). The impact of the glial spatial buffering on the k + nernst potential. Cognitive Neurodynamics, 5, 285–291.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Pinsky, P.F., & Rinzel, J. (1994). Intrinsic and network rhythmogenesis in a reduced traub model for ca3 neurons. Journal of Computational Neuroscience, 1, 39–60.

    Article  CAS  PubMed  Google Scholar 

  • Pinsky, P.F., & Rinzel, J. (1995). Erratum to: intrinsic and network rhythmogenesis in a reduced traub model for ca3 neurons. Journal of Computational Neuroscience, 2, 275.

    Article  Google Scholar 

  • Qian, B., & Rasheed, K. (2004). Hurst exponent and financial market predictability. In Financial engineering and applications (FEA 2004), Proceedings of the IASTED international conference (pp. 203–204).

  • Schwalger, T., & Lindner, B. (2013). Patterns of interval correlations in neural oscillators with adaptation. Frontiers in Computational Neuroscience, 7(164).

  • Scoville, W., & Milner, B. (1957). Loss of recent memory after bilateral hippocampal lesions. Journal of Neurology Neurosurgery and Psychiatry, 20, 11–21.

    Article  CAS  Google Scholar 

  • Traub, R.D., Wong, R.K.S., Miles, R., & Michelson, H. (1991). A model of a ca3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. Journal of Neurophysiology, 66, 635–650.

    CAS  PubMed  Google Scholar 

  • van Vreeswijk, C., & Hansel, D. (2001). Patterns of synchrony in neural networks with spike adaptation. Neural Computational, 5, 959–992.

    Article  Google Scholar 

  • Williams, R., & Herrup, K. (1988). The control of neuron number. Annual Review Neuroscience, 11, 423–453.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY, 11794, USA

    Stephen R. Meier

  2. Department of Physics, Roanoke College, Salem, VA, 24153, USA

    Jarrett L. Lancaster

  3. Department of Biology II, Ludwig Maximilian University of Munich, Munich, Germany

    Dustin Fetterhoff

  4. Department of Biomedical Engineering, Wake Forest School of Medicine, Winston-Salem, NC, 27109, USA

    Robert A. Kraft

  5. Department of Physiology & Pharmacology, Wake Forest School of Medicine, Winston-Salem, NC, 27109, USA

    Robert E. Hampson

  6. Department of Nanoscience, The University of North Carolina, Greensboro, NC, 27401, USA

    Joseph M. Starobin

Authors
  1. Stephen R. Meier
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  2. Jarrett L. Lancaster
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  3. Dustin Fetterhoff
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  4. Robert A. Kraft
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  5. Robert E. Hampson
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  6. Joseph M. Starobin
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Correspondence to Stephen R. Meier.

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Action Editor: Frances K. Skinner

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Meier, S.R., Lancaster, J.L., Fetterhoff, D. et al. The relationship between nernst equilibrium variability and the multifractality of interspike intervals in the hippocampus. J Comput Neurosci 42, 167–175 (2017). https://doi.org/10.1007/s10827-016-0633-5

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  • DOI: https://doi.org/10.1007/s10827-016-0633-5

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