Spatial heterogeneity of axon induces complex dynamics of enhanced conduction failure rate and irregular pattern of action potentials

Many recent experiments present a novel phenomenon in which some action potentials/spikes fail to conduct along thin axons, a phenomenon named conduction failure, differing from the common view of faithful conduction. For instance, the failure rate of spikes increases along the conduction distance, and irregular firing patterns appear in C-nerve fibers related to pathological pain. However, in the frequently used theoretical model of axons, which contains homogeneous compartments with electrical coupling, only regular firing patterns and unchanged failure rates are simulated. In the present paper, an axonal model containing compartments with heterogeneous potassium conductance is considered. First, the spatial heterogeneity induces irregular firing and an enhanced conduction failure rate of spikes at the compartments with large potassium conductance, closely matching experimental observations. Second, the regularities of the failure are analyzed. Larger heterogeneity induces more compartments with enhanced failure rates. High frequency of action potentials, weak coupling currents, and high potassium conductance induce high failure rates. Finally, the current threshold to evoke an action potential from the damping afterpotential related to Hopf bifurcation is obtained, providing explanations for conduction failure. For compartments with large potassium conductance, the membrane potential, coupling current, and total ionic current are low, resulting in a high threshold and an enhanced failure rate. The results provide explanations for the complex dynamics of conduction failure in the C-fiber and suggest measures to modulate pathological pain.