Reduction of conductance-based neuron models

@article{Kepler2004ReductionOC,
  title={Reduction of conductance-based neuron models},
  author={Thomas B. Kepler and L. F. Abbott and Eve Marder},
  journal={Biological Cybernetics},
  year={2004},
  volume={66},
  pages={381-387}
}
We present a scheme for systematically reducing the number of differential equations required for biophysically realistic neuron models. The techniques are general, are designed to be applicable to a large set of such models and retain in the reduced system as high a degree of fidelity to the original system as possible. As examples, we provide reductions of the Hodgkin-Huxley system and the A-current model of Connor et al. (1977). 
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References

SHOWING 1-10 OF 21 REFERENCES
Model neurons: From Hodgkin-Huxley to hopfield
A new technique is used to reduce the classic Hodgkin-Huxley model to a two-dimensional neuronal model which retains the essential features of the full description. The resulting equations areExpand
Excitation dynamics: insights from simplified membrane models.
  • J. Rinzel
  • Chemistry, Medicine
  • Federation proceedings
  • 1985
TLDR
This work describes a two-variable simplification of the Hodgkin-Huxley (HH) model, which exhibits many membrane phenomena and reproduces, with good agreement, many HH responses. Expand
The assembly of ionic currents in a thalamic neuron I. The three-dimensional model
  • R. M. Rose, J. Hindmarsh
  • Materials Science, Medicine
  • Proceedings of the Royal Society of London. B. Biological Sciences
  • 1989
TLDR
This paper reports the results of making a similar sequence of modifications to a more elaborate six-dimensional model of repetitive firing which is based on the Hodgkin–Huxley equations. Expand
Impulses and Physiological States in Theoretical Models of Nerve Membrane.
TLDR
Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle, which qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. Expand
A model of the nerve impulse using two first-order differential equations
TLDR
The second-order Fitzhugh equations are generalized, and the form of the functions in the new equations based on voltage-clamp data obtained from a snail neurone are based on, providing a model which predicts the linearity of the frequency–current relationship and may be useful for studying detailed interactions in networks containing small numbers of neurones. Expand
A quantitative description of membrane current and its application to conduction and excitation in nerve
This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkinet al., 1952,J. Physiol.116, 424–448; Hodgkin andExpand
Mathematical model of an identified stomatogastric ganglion neuron.
TLDR
The model and biological neurons show similar action-potential shapes, durations, steady-state current-voltage (I-V) curves, and respond to injected current in a comparable way. Expand
Neural networks and physical systems with emergent collective computational abilities
TLDR
A model of a system having a large number of simple equivalent components, based on aspects of neurobiology but readily adapted to integrated circuits, produces a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. Expand
Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons.
The Hodgkin-Huxley equations for space-clamped squid axon (18 degrees C) have been modified to approximate voltage clamp data from repetitive-firing crustacean walking leg axons and activity inExpand
Contribution of individual ionic currents to activity of a model stomatogastric ganglion neuron.
TLDR
The behavior of the mathematical model for the lateral pyloric (LP) neuron of the crustacean stomatogastric ganglion (STG) developed in the previous paper was further studied and iA appears to regulate action-potential frequency as well as postinhibitory rebound activity. Expand
...
1
2
3
...