Advertisement

Synaptic Channels

  • G. Bard Ermentrout
  • David H. Terman
Chapter
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 35)

Abstract

So far, we have restricted our modeling and analysis efforts to single neurons. To begin to develop networks and the theoretical background for networks, we need to introduce an additional class of membrane channels. We have already looked at voltage- and ion-gated channels. However, there are many other channels on the surface of nerve cells which respond to various substances. Among the most important of these, at least in computational neuroscience, are synaptic channels.

Keywords

Transmitter Release Postsynaptic Neuron Synaptic Depression Synaptic Conductance Postsynaptic Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 12.
    M. Beierlein, J. R. Gibson, and B. W. Connors. Two dynamically distinct inhibitory networks in layer 4 of the neocortex. J. Neurophysiol., 90:2987–3000, 2003.CrossRefGoogle Scholar
  2. 14.
    R. Bertram. Differential filtering of two presynaptic depression mechanisms. Neural Comput., 13:69–85, 2001.MATHCrossRefGoogle Scholar
  3. 36.
    M. A. Castro-Alamancos. Properties of primary sensory (lemniscal) synapses in the ventrobasal thalamus and the relay of high-frequency sensory inputs. J. Neurophysiol., 87:946–953, 2002.Google Scholar
  4. 53.
    P. Dayan and L. F. Abbott. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. Computational Neuroscience. MIT, Cambridge, MA, 2001.MATHGoogle Scholar
  5. 61.
    A. Destexhe, D. Contreras, T. J. Sejnowski, and M. Steriade. A model of spindle rhythmicity in the isolated thalamic reticular nucleus. J. Neurophysiol., 72:803–818, 1994.Google Scholar
  6. 100.
    W. Gerstner, J. L. van Hemmen, and J. Cowan. What matters in neuronal locking? Neural Comput., 8:1653–1676, 1996.CrossRefGoogle Scholar
  7. 111.
    J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York, 1983.MATHGoogle Scholar
  8. 136.
    E. M. Izhikevich. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Computational Neuroscience, MIT, Cambridge, MA, 2007.Google Scholar
  9. 179.
    B. Lindner. Interspike interval statistics of neurons driven by colored noise. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 69:022901, 2004.CrossRefGoogle Scholar
  10. 187.
    G. Mackie and R. W. Meech. Separate sodium and calcium spikes in the same axon. Nature, 313:791–793, 1985.CrossRefGoogle Scholar
  11. 271.
    S. F. Traynelis and F. Jaramillo. Getting the most out of noise in the central nervous system. Trends Neurosci., 21:137–145, 1998.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dept. MathematicsUniversity of PittsburghPittsburghUSA
  2. 2.Dept. MathematicsOhio State UniversityColumbusUSA

Personalised recommendations