General anesthesia has revolutionized healthcare over the past 200 years and continues to show advancements. However, many phenomena induced by general anesthetics including paradoxical excitation are still poorly understood. Voltage-gated sodium channels (Na V ) were believed to be one of the proteins targeted during general anesthesia. Based on electrophysiological measurements before and after propofol treatments of different concentrations, we mathematically modified the Hodgkin-Huxley sodium channel formulations and constructed a thalamocortical model to investigate the potential roles of Na V . The ion channels of individual neurons were modeled using the Hodgkin-Huxley type equations. The enhancement of propofol-induced GABAa current was simulated by increasing the maximal conductance and the time-constant of decay. Electroencephalogram (EEG) was evaluated as the post-synaptic potential from pyramidal (PY) cells. We found that a left shift in activation of Na V was induced primarily by a low concentration of propofol (0.3-10 μM), while a left shift in inactivation of Na V was induced by an increasing concentration (0.3-30 μM). Mathematical simulation indicated that a left shift of Na V activation produced a Hopf bifurcation, leading to cell oscillations. Left shift of Na V activation around a value of 5.5 mV in the thalamocortical models suppressed normal bursting of thalamocortical (TC) cells by triggering its chaotic oscillations. This led to irregular spiking of PY cells and an increased frequency in EEG readings. This observation suggests a mechanism leading to paradoxical excitation during general anesthesia. While a left shift in inactivation led to light hyperpolarization in individual cells, it inhibited the activity of the thalamocortical model after a certain depth of anesthesia. This finding implies that high doses of propofol inhibit the network partly by accelerating Na V toward inactivation. Additionally, this result explains why the application of sodium channel blockers decreases the requirement for general anesthetics. Our study provides an insight into the roles that Na V plays in the mechanism of general anesthesia. Since the activation and inactivation of Na V are structurally independent, it should be possible to avoid side effects by state-dependent binding to the Na V to achieve precision medicine in the future.
Keywords: Hodgkin–Huxley model; Hopf bifurcation; paradoxical excitation; propofol; thalamocortical model; voltage-gated sodium channels.
Copyright © 2020 Xiao, Chen and Yu.