Three Simple Models of Neurons in Rodent Brains

  • Christoph Börgers
Part of the Texts in Applied Mathematics book series (TAM, volume 66)


Hodgkin and Huxley modeled the giant axon of the squid. Since then, many similar models of neurons in mammalian brains have been proposed. In this chapter, we list three examples, which will be used throughout the book.


Potassium Current Sodium Current Leak Current Density Inhibitory Interneuron Basket Cell 
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  1. [17]
    C. Börgers and B. Walker, Toggling between gamma-frequency activity and suppression of cell assemblies, Frontiers in Computational Neuroscience, 7, doi: 10.3389/fncom.2013.00033 (2013).Google Scholar
  2. [45]
    A. Erisir, D. Lau, B. Rudy, and C. S. Leonard, Function of specific K(+) channels in sustained high-frequency firing of fast-spiking neocortical interneurons, J. Neurophysiol., 82 (1999), pp. 2476–89.Google Scholar
  3. [50]
    G. B. Ermentrout and, Fine structure of neural spiking and synchronization in the presence of conduction delay, Proc. Natl. Acad. Sci. USA, 95 (1998), pp. 1259–1264.Google Scholar
  4. [55]
    T. Freund and I. Katona, Perisomatic inhibition, Neuron, 56 (2007), pp. 33–42.CrossRefGoogle Scholar
  5. [148]
    K. M. Stiefel, B. Englitz, and T. J. Sejnowski, Origin of intrinsic irregular firing in cortical interneurons, Proc. Natl. Acad. Sci. USA, 110 (2013), pp. 7886–7891.CrossRefzbMATHGoogle Scholar
  6. [161]
    R. D. Traub and R. Miles, Neuronal Networks of the Hippocampus, Cambridge University Press, Cambridge, UK, 1991.CrossRefGoogle Scholar
  7. [174]
    X.-J. Wang and G. Buzsáki, Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model, J. Neurosci., 16 (1996), pp. 6402–6413.Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  • Christoph Börgers
    • 1
  1. 1.Department of MathematicsTufts UniversityMedfordUSA

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