Hodgkin-Huxley with dynamic ion concentrations (Hubel and Dahlem, 2014)

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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. This model includes slow dynamics in an extended HH framework that simulates time-dependent ion concentrations, pumps, and buffers. Fluxes across the neuronal membrane change intra- and extracellular ion concentrations, whereby the latter can also change through contact to reservoirs in the surroundings. The dynamics on three distinct slow times scales is determined by the cell volume-to-surface-area ratio and the membrane permeability (seconds), the buffer time constants (tens of seconds), and the slower backward buffering (minutes to hours). The modulatory dynamics and the newly emerging excitable dynamics corresponds to pathological conditions observed in epileptiform burst activity, and spreading depression in migraine aura and stroke, respectively.
1 . Hübel N, Dahlem MA (2014) Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs. PLoS Comput Biol 10:e1003941 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s): I Na,t; I K; I K,leak; Na/K pump; I Cl, leak; I Na, leak;
Gap Junctions:
Simulation Environment: XPP;
Model Concept(s): Homeostasis; Spreading depression;
Search NeuronDB for information about:  I Na,t; I K; I K,leak; Na/K pump; I Cl, leak; I Na, leak;
This is the README for the code for the article

N. Hubel and M. A. Dahlem: "Dynamics from seconds to hours in
Hodgkin-Huxley model with time-dependent ion concentrations and buffer
reservoirs" PLoS Comp Biol (2014)

email: niklas.huebel@gmail.com
Oct. 7, 2014

This model requires XPP which is freely available from:

Notes on the supplied two XPP simulation files:


This code computes time series like in Fig. 5. SD is triggered either
by current stimulation (dynamics of variable "stim") or by pump
interruption (dynamics of pump coefficient "z"). Two regulation
schemes for potassium are implemented: glial buffering and diffusive
coupling to the vascular system (with a switch parameter "s", see
below). For diffusive coupling with elevated "k_bath" values the time
series of Fig. 7 can be simulated.


To compute the fixed point continuation of Fig. 2 run xppaut with this
file. To reach the exact fixed point use (I)nitial and (G)o
first. Then use (F)ile + (A)UTO to open the AUTO interface. (R)un +
(S)teady state will start the forward continuation. Then change the
(N)umerics parameter DS from 0.2 to -0.2, (G)rab (+ 'Enter') the
starting point of the forward continuation curve, and (R)un again.
(Remark: The Hopf line of Fig. 4 can only be obtained by changing this
code so that also "cli" is a parameter.)

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