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.
Model Type: Channel/Receptor
Cell Type(s): Hodgkin-Huxley neuron; Wide dynamic range neuron; Abstract integrate-and-fire fractional leaky neuron; Abstract single compartment conductance based cell
Currents: I K; I K,leak; I Sodium
Model Concept(s): Action Potential Initiation; Bursting; Ion Channel Kinetics; Action Potentials; Spike Frequency Adaptation
Simulation Environment: MATLAB; MATLAB (web link to model)
Santamaria F, Teka W, Stockton D. (2016). Power-law dynamics of membrane conductances increase spiking diversity in a Hodgkin-Huxley model PLoS Comput Biol. 12(3)