Spiral wave death, breakup induced by ion channel poisoning on regular Hodgkin–Huxley neuronal networks

Abstract

The electric activities of neurons are often affected by ion channel poisoning, in particularly, interrupting normal transduction of signals within the brain. This may be due to changes in conductance and the number of active channels. Tetraethylammonium, for example, is known to cause ion channel poisoning of potassium channels, while tetrodotoxin has similar detrimental effects on sodium channels. The occurrence of spiral waves in neuronal systems was observed frequently in the past, and it was argued that these waves of excitation may play an important role by the propagation of electric signals across the quiescent regions of the brain. In this work, the parameters xk and xNa determine the ratio, with regards to the total number of ion channels, of active potassium and sodium channels, respectively, and they are taken to be representative also for the degree of channel poisoning. In the numerical studies, a well developed stable rotating spiral wave is used as the initial state to be controlled by the ion channel poisoning. We show that, under noise-free conditions, spiral waves are terminated whenever xk and xNa are set lower than a given threshold. However, breakup of spiral wave occurs if the intensity of the channel noise increases. In order to quantify these observations, we use a simple but robust synchronization measure, which captures succinctly the transition from spiral waves to homogeneous neuronal activity and/or broken turbulent state. The critical thresholds can be inferred from the abrupt changes occurring in the corresponding dependencies of synchronization versus the xk and xNa ratios. Furthermore, the sampled membrane potentials of a single neuron are recorded to detect the periodical spiral wave in a feasible way and the results could be dependent of the position of node (or site) to be monitored. Notably, small synchronization factors can be tightly associated to states where the formation of spiral waves is robust to channel poisoning and weak channel noise.