**4. Conclusion**

Until now, it has been mainly proposed that the cell membrane and neurons are modeled by an RC circuit. However, from the fact that many neurons in various regions of the brain have band pass properties, a neuron should be modeled by an RLC circuit. In this chapter, an equivalent RLC circuit was developed for a neuron model with *h* and *NaP* channels, and it was clarified that the subthreshold resonance property of this neuron model comes from inductive properties of *h* and *NaP* channels, especially, *h* channel. Furthermore, by incorporating the Hodgkin-Huxley dynamics into this neuron model, we showed the relation between the subthreshold resonance oscillation and the generation of action potentials. By computer simulations, it was shown that the amplitude of an AC input and a DC bias current input strongly play a role in the generation of action potentials, coupled with AC input frequencies.

It is presumed that the subthreshold resonance phenomena may relate closely to various practical neuron activities and behaviors in our brain, such as the sensitivity to external noises in sensory system. So, it is very important and interesting to study firing patterns of a neuron or properties of burst oscillations by using computer simulations, in order to clarify the mechanisms of higher information processing in the brain.

Needless to say, mutual collaboration of experimental research and modeling research is of large significance, in order to create more sophisticated models based on the most recent findings from experiments, and in order to develop new experimental methods to verify the facts suggested from simulation results.
