The influence of hyperpolarization-activated cation current on conduction delay and failure of action potentials along axon related to abnormal functions

Conduction delay and failure behaviors of action potentials with a high frequency along nerve fiber are related to the abnormal functions. For instance, upregulation of a hyperpolarization-activated cation current (I_h) is identified to reduce the conduction delay to recover the temporal encoding, and downregulation of the I_h current to enhance the conduction failure rate to ease the pain sensation, with the dynamic mechanisms remaining unclear. In the present paper, the dynamic mechanism is obtained in a chain network model with coupling strength (g_c) and action potentials induced by periodic stimulations with a period (T_s). At first, as the action potentials exhibit a high frequency corresponding to a short T_s and the network has a small g_c, i.e., a short and unrecovered afterpotential and a small coupling current, the conduction delay is reproduced. The conduction failure is reproduced for T_s shorter and g_c smaller than those of the conduction delay, presenting a direct relationship between the two behaviors. Then, the conduction delay and failure are explained with the response time and current threshold of an action potential evoked from the unrecovered afterpotential. The prolonged response time for short T_s and small g_c presents the cause for the conduction delay, and the enhanced threshold for shorter T_s and smaller g_c presents the cause for the conduction failure. Furthermore, reduction of the delay and enhancement of the failure rate respectively induced by upregulation and downregulation of the I_h current are reproduced and explained. The positive I_h current induces Hopf bifurcation advanced and resting membrane potential elevated. Then, upregulation and downregulation of the I_h current induce the afterpotential elevated to shorten the response time and reduced to enhance the threshold, respectively. The results present nonlinear dynamics for the non-faithful conduction behaviors and dynamical mechanism for the modulation effect of the I_h current on the conduction delay and failure related to encoding and pain.