Fractal ion-channel behavior generates fractal firing patterns in neuronal models

Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a population of ion channels with either fractal or Markov gating characteristics. Fractal gating characteristics changed the form of the interspike interval histogram (ISIH) and also induced fractal behavior in the firing rate. For the HH model, the K⁺ conductance was represented as a collection of ion channels with either quasifractal or Markov gating properties. Fractal gating induced fractal-rate behavior without changing the ISIH. We conclude that fractal ion-channel gating activity is sufficient to account for fractal-rate firing behavior.