title: Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.
abstract: We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. 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.
authors.affiliation: UTSA Neurosciences Institute, The University of Texas at San Antonio, San Antonio, Texas, United States of America.
authors.forename: Wondimu
authors.initials: W
authors.lastname: Teka
authors.affiliation: Biomedical Engineering Program, The University of Texas at San Antonio, San Antonio, Texas, United States of America.
authors.forename: David
authors.initials: D
authors.lastname: Stockton
authors.affiliation: UTSA Neurosciences Institute, The University of Texas at San Antonio, San Antonio, Texas, United States of America.
authors.forename: Fidel
authors.initials: F
authors.lastname: Santamaria
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D002462:Cell Membrane / Q000502:physiology*; D003198:Computer Simulation; D004553:Electric Conductivity; D006801:Humans; D015640:Ion Channel Gating / Q000502:physiology*; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D015221:Potassium Channels / Q000502:physiology*; D015222:Sodium Channels / Q000502:physiology*
chemical_list: D015221:Potassium Channels; D015222:Sodium Channels