Dynamics from Seconds to Hours in Hodgkin-Huxley Model with Time-Dependent Ion Concentrations and Buffer Reservoirs

  title={Dynamics from Seconds to Hours in Hodgkin-Huxley Model with Time-Dependent Ion Concentrations and Buffer Reservoirs},
  author={Niklas H{\"u}bel and Markus A. Dahlem},
  journal={PLoS Computational Biology},
The classical Hodgkin-Huxley (HH) model neglects the time-dependence of ion concentrations in spiking dynamics. The dynamics is therefore limited to a time scale of milliseconds, which is determined by the membrane capacitance multiplied by the resistance of the ion channels, and by the gating time constants. We study slow dynamics in an extended HH framework that includes time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular… 

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  • D. DiFrancescoD. Noble
  • Biology
    Philosophical transactions of the Royal Society of London. Series B, Biological sciences
  • 1985
The model takes account of extensive developments in experimental work since the formulation of the M.N. Noble equations, and successfully account for all the properties formerly attributed to i $\_{K2}$ , as well as giving more complete descriptions of i $\_K$ and i $\-K$ .

Unification of Neuronal Spikes, Seizures, and Spreading Depression

The results demonstrate that unified frameworks for neuronal dynamics are feasible, can be achieved using existing biological structures and universal physical conservation principles, and may be of substantial importance in enabling the understanding of brain activity and in the control of pathological states.