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Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model

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Abstract

The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative feedback processes in the HH model that regulate rhythmic spiking. The first is an outward current with an activation variable n that has an opposite influence to the excitatory inward current and therefore provides subtractive negative feedback. The other is the inactivation of an inward current with an inactivation variable h that reduces the amount of positive feedback and therefore provides divisive feedback. Rhythmic spiking can be obtained with either negative feedback process, so we ask what is gained by having two feedback processes. We also ask how the different negative feedback processes contribute to spiking. We show that having two negative feedback processes makes the HH model more robust to changes in applied currents and conductance densities than models that possess only one negative feedback variable. We also show that the contributions made by the subtractive and divisive feedback variables are not static, but depend on time scales and conductance values. In particular, they contribute differently to the dynamics in Type I versus Type II neurons.

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Acknowledgments

RB and JT were supported by NIH grant DK43200 and NSF grant DMS1220063.

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306-4510, USA

    Sevgi Şengül

  2. Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    Robert Clewley

  3. Department of Mathematics and Programs in Neuroscience and Molecular Biophysics, Florida State University, Tallahassee, FL, 32306, USA

    Richard Bertram

  4. Department of Mathematics and Department of Biological Sciences, Florida State University, Tallahassee, FL, 32306-4510, USA

    Joël Tabak

Authors
  1. Sevgi Şengül
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  2. Robert Clewley
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  3. Richard Bertram
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  4. Joël Tabak
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Correspondence to Joël Tabak.

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Action Editor: J. Rinzel

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Şengül, S., Clewley, R., Bertram, R. et al. Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model. J Comput Neurosci 37, 403–415 (2014). https://doi.org/10.1007/s10827-014-0511-y

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  • DOI: https://doi.org/10.1007/s10827-014-0511-y

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