  The generation and conduction of action potentials represents a fundamental
means of communication in the nervous system, and is a metabolically expensive
process. In this paper, we investigate the energy efficiency of neural systems
in a process of transfer pulse signals with action potentials. By computer
simulation of a stochastic version of Hodgkin-Huxley model with detailed
description of ion channel random gating, and analytically solve a bistable
neuron model that mimic the action potential generation with a particle
crossing the barrier of a double well, we find optimal number of ion channels
that maximize energy efficiency for a neuron. We also investigate the energy
efficiency of neuron population in which input pulse signals are represented
with synchronized spikes and read out with a downstream coincidence detector
neuron. We find an optimal combination of the number of neurons in neuron
population and the number of ion channels in each neuron that maximize the
energy efficiency. The energy efficiency depends on the characters of the input
signals, e.g., the pulse strength and the inter-pulse intervals. We argue that
trade-off between reliability of signal transmission and energy cost may
influence the size of the neural systems if energy use is constrained.
