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Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model

Fig 1

Power-law dynamics of individual Hodgkin-Huxley gating variables.

(A) The response of the individual gating variables (n, m, and h) using the analytical (solid) and numerical (dotted) solutions to an identical voltage command (30 mV for n, -55 mV for m, -70 mV for h) with different values of the fraction order derivative (η). (B) The long term response of the individual gates (, x = m,n or h) for all the voltages and values of η for the analytical and numerical solutions. The arrow points to the inflection point of the sigmoidal curve. For some numerical solutions were unstable. (C) For the n and h gates we fitted a dual exponential process to the temporal response to voltage commands for all values of η resulting in a fast and slow time constant (, x = m, n, or h). We fitted a single time constant to the m gate.

doi: https://doi.org/10.1371/journal.pcbi.1004776.g001