Optimal Stimulus Shapes for Neuronal Excitation

An important problem in neuronal computation is to discern how features of stimuli control the timing of action potentials. One aspect of this problem is to determine how an action potential, or spike, can be elicited with the least energy cost, e.g., a minimal amount of applied current. Here we show in the Hodgkin & Huxley model of the action potential and in experiments on squid giant axons that: 1) spike generation in a neuron can be highly discriminatory for stimulus shape and 2) the optimal stimulus shape is dependent upon inputs to the neuron. We show how polarity and time course of post-synaptic currents determine which of these optimal stimulus shapes best excites the neuron. These results are obtained mathematically using the calculus of variations and experimentally using a stochastic search methodology. Our findings reveal a surprising complexity of computation at the single cell level that may be relevant for understanding optimization of signaling in neurons and neuronal networks.神经元计算领域的一项关键科学问题，是探明刺激特征如何调控动作电位的发放时序。该问题的一个研究分支，旨在探究如何以最低能量成本引发动作电位（action potential），或称锋电位（spike），例如通过施加最小幅值的注入电流。本研究基于霍奇金-赫胥黎（Hodgkin & Huxley）动作电位模型，以及鱿鱼巨轴突的实验数据，得到如下结论：其一，神经元的锋电位发放对刺激波形具备高度的辨别选择性；其二，最优刺激波形取决于神经元的输入信号。本研究阐明了突触后电流的极性与时程，如何决定哪一类最优刺激波形可最优激活神经元。上述结论通过变分法（calculus of variations）完成数学推导，并借助随机搜索方法完成实验验证。本研究结果揭示了单细胞层面计算过程的出人意料的复杂性，这一发现或有助于理解神经元及神经元网络内信号传导的优化机制。