Hodgkin–Huxley model with fractional gating (Teka et al. 2016)

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We use fractional order derivatives to model the kinetic dynamics of the gate variables for the potassium and sodium conductances of the Hodgkin-Huxley model. Our results show that power-law dynamics of the different gate variables result in a wide range of action potential shapes and spiking patterns, even in the case where the model was stimulated with constant current. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.
1 . Teka W, Stockton D, Santamaria F (2016) Power-law dynamics of membrane conductances increase spiking diversity in a Hodgkin-Huxley model PLoS Comput Biol 12(3):e1004776
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Model Information (Click on a link to find other models with that property)
Model Type: Channel/Receptor;
Brain Region(s)/Organism:
Cell Type(s): Hodgkin-Huxley neuron; Wide dynamic range neuron; Abstract integrate-and-fire fractional leaky neuron; Abstract single compartment conductance based cell;
Channel(s): I K; I K,leak; I Sodium;
Gap Junctions:
Transmitter(s): Ions;
Simulation Environment: MATLAB; MATLAB (web link to model);
Model Concept(s): Action Potential Initiation; Bursting; Ion Channel Kinetics; Action Potentials; Spike Frequency Adaptation;
Search NeuronDB for information about:  I K; I K,leak; I Sodium; Ions;
Simulation of power-law dynamic gate variables in the Hodgkin-Huxley
model using fractional order derivatives.
Teka W, Stockton D, Santamaria F. "Power-law dynamics of membrane
conductances increase spiking diversity in a Hdgkin-Huxley model" PLoS
Computational Biology, in press, 2016.
If you use this software please reference our paper. 
This package have several matlab codes and functions. The main codes just to do simulations 
of figures are: Tekaetal2016_SingleGates.m and Tekaetal2016_SingleAP.m.
 In the file Tekaetal2016_SingleGates.m, there are  6 sections that compute the simulations and
analyze the results for Figures 1 and 2 of our paper. Section 1-3 simulate voltage clamp on the individual gates having 
power-law dynamcis. They correspond to figure 1 in the paper.Section 4-6 analyze the data produced by section 1-3.
 In the file Tekaetal2016_SingleAP.m,  sections 7-9 generate a few action potentials. 
Sections 10-12 analyze these data which corresponds to Figure 2. 
The other figures were generate by running sections 7-9 for very long
periods of time. They require super-computer resources and multiple days
of simulation time. You can request the data files.