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A model for repetitive firing in neurons

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Abstract

This paper describes a model for the generation of repetitive firing patterns in single neurons to be used as a module in large-scale network simulation studies. The model is based on the combination of extended versions of Hill's model for accomodation and of Kernell's model for adaptation. Both digital computer and electronic circuit realizations of the model are presented. The model is shown to produce strength-duration curves for accomodation which are compatible with available data from real neurons. Both “high ceiling” and “low ceiling” cell types can be matched by adjusting parameters in the model. An equation relating steady-state firing rate to amplitude of applied steady current is presented which includes the accumulation of potassium conductance changes with repetitive firing. The occurence of phasic and tonic responses to step stimulation is mapped in the parameter space of the model. Several representative response patterns to irregular inputs are presented.

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Abbreviations

E:

Transmembrane potential

θ:

Firing threshold

gK :

Excess of potassium conductance above resting level

S:

Flag for model output spikes

Ek :

Membrane equilibrium potential for potassium

Eex :

Membrane equilibrium potential for process at excitatory synapse

Ein :

Membrane equilibrium potential for process at inhibitory synapse

SC:

Activating current applied to triggering patch from any source other than local excitatory or inhibitory synapses (e.g., externally applied electrodes, on dendritic synaptic input)

GE:

Conductance change at excitatory synapse

GI:

Conductance change at inhibitory synapse

c:

Coefficient of sensitivity of accommodation mechanism

λ:

Time constant fo threshold changes

b:

Coefficient of adaptation

τ:

Time constant of potassium conductance changes

t:

Time

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This work has been supported by National Science Foundation Grant GB-33687 to R.J. MacGregor. We express appreciation to Dr. S. K. Sharpless of the Psychology Department of the University of Colorado for critical commentary in the development of this model.

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MacGregor, R.J., Oliver, R.M. A model for repetitive firing in neurons. Kybernetik 16, 53–64 (1974). https://doi.org/10.1007/BF00270295

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  • DOI: https://doi.org/10.1007/BF00270295

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