Encoding functions of neuronal ion channels in a circuit-based approach

In this article, an ion channel diversion (ICD) method is proposed to control the channel current of a neuron model derived from the FitzHugh-Nagumo (FHN) neural circuit. A diversion element (DE) such as capacitor and inductor is intervened into the branch circuit of the FHN circuit, and the channel current across inductor for the inductive ion channel is shunted to the DE for energy regulation and current shunting. That is, a sub-branch circuit is used to shunt current from the inductor of the neural circuit, and a hybrid ion channel is built. Changes in the parameter for the DE (new capacitor or inductor) will modify the shunted current in the sub-branch circuit, and the channel current along inductive channel is changed to regulate the membrane potentials of the neuron. The circuit equations, equivalent theoretical models and Hamilton energy functions are obtained for theoretical analysis, and moderate noise intensity can induce coherence resonance (CR) and stochastic resonance (SR) supporting a maximal value for in this curve vs. noise intensity. Furthermore, a parameter observer is designed to identify the unknown parameter in the theoretical model for further adaptive control in the electrical activities. An adaptive control strategy based on energy regulation is proposed, and the neuron can achieve periodic firing, cluster firing, and chaotic firing by setting a reasonable energy threshold ε. The results show that the working state and energy distribution of ion channels can significantly affect the firing patterns and attractor morphology of neurons. The interference in ion channels and shunting current from one branch circuit of neural circuit are effective to control the neural activities in single neuron and collective behaviors in neural networks. The physical significance of this control strategy is that energy control (energy shunting or energy injection) is suitable to modify the energy level and firing modes in the neurons, and then the effect of electromagnetic stimuli on nervous system can be understood from physical aspect.