Spike-threshold And Energy Efficiency In Model Neurons

The nervous system of an animal is a complex system that constitutes with numerous neurons complicatedly interacting with each other. However, neurons in different brain function areas are well-organized and specialized, whose different functions are determined by their specific input-output functions. Usually, a neuron will receive and integrate many synaptic inputs to determine whether generate an output. The output signal inside a neuron is action potential, i.e. spike, an all-or-none stereo membrane potential pulse, which will be generated if a threshold voltage is exceeded. Threshold of action potential generation plays an important role in temporal integration and is a key step in neuronal signal processing, yet the threshold is not a constant and the mechanism of threshold variability is still not well understood.We first introduce the research background in chapter one. Then we present the basic biophysical knowledge of neuron and action potential in the next chapter. Several normal neuron models and the basic knowledge of dynamic system are described in chapter three.In chapter 4, we focus on the spike threshold. We propose that threshold phenomena can be classified as parameter thresholds and state thresholds. The voltage thresholds that belong to state threshold are determined by the ‘general separatrix’ in state space. We show that the separatrix generally exists in the state space of neuron models and the previously assumed threshold evolving equation versus time is naturally deduced from the separatrix. In terms of neuron dynamics, the threshold voltage variation under different stimuli is determined by crossing the separatrix at different points in state space. We suggest that the separatrix-crossing mechanism in state space is the intrinsic dynamic mechanism for threshold voltages and post-stimulus threshold parameters. The proposals are also systematically verified in several example models, three of which have analytic separatrices and one is the classic Hodgkin-Huxley model. The sepratrix-crossing framework provides a general thought of the neuronal threshold and will facilitate understanding of the nature of threshold variability.The energy efficiency of neural spike trains is investigated in chapter 5. Recent studies show that energy efficiency, which measures the amount of information processed by a neuron with per unit of energy consumption, plays an important role in the evolution of neural systems. Here we calculate the information rates and energy efficiency of the Hodgkin–Huxley neuron model at different temperatures in a noisy environment. It is found that both the information rate and energy efficiency are maximized by certain temperatures. Though the information rate and energy efficiency cannot be maximized simultaneously, the neuron holds a high information processing capacity at the temperature corresponding to the maximal energy efficiency. Our results support the idea that the energy efficiency is a selective pressure that influences the evolution of nervous systems.In the last chapter, we summarize this thesis and prospect related possible future works.