The defect effects on the signal transport of an excitable soft cable

Abstract

How a local perturbation affects a propagating wave traveling in a homogeneous medium is a general physics question widely investigated in condensed materials. Intuitively, one might expect that a perturbation would suppress the transport ability of the medium if it is quasi one dimensional. This is generically true as defects and impurities influence numerous non-excitable systems such as carbon nanotubes, nanowires and DNA double helixes. However, if the system is excitable, such as a neuron, a defect may generate a highly non-trivial dynamical behavior. In this paper, using the Hodgkin-Huxley model, we explored this diversity generated by locally non-uniform ion channel densities caused by toxins, diseases, environmental disorders or artificial manipulations. These channel density defects could induce several exotic behaviors, in contrast with the normal destructive role of defects in solid-state physics. They may behave as an electric signal generator exhibiting spontaneous or stimulated emissions, as well as trap, reflect, rectify, delay or extinguish propagating signals or be switched to different functions by a signal. Nonlinear analysis and phase diagrams were used to quantify this dynamical complexity. The results may contribute to research on signal manipulation in biotechnology, neuronal diseases and damages, channel distribution-related cell functions and defect dynamics in general excitable mathematical models.