Richardson Magnus J E, Gerstner Wulfram
Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratory of Computational Neuroscience, School of Computer and Communication Sciences and Brain Mind Institute, CH-1015 Lausanne, Switzerland.
Chaos. 2006 Jun;16(2):026106. doi: 10.1063/1.2203409.
Neurons in the central nervous system, and in the cortex in particular, are subject to a barrage of pulses from their presynaptic populations. These synaptic pulses are mediated by conductance changes and therefore lead to increases or decreases of the neuronal membrane potential with amplitudes that are dependent on the voltage: synaptic noise is multiplicative. The statistics of the membrane potential are of experimental interest because the measurement of a single subthreshold voltage can be used to probe the activity occurring across the presynaptic population. Though the interpulse interval is not always significantly smaller than the characteristic decay time of the pulses, and so the fluctuations have the nature of shot noise, the majority of results available in the literature have been calculated in the diffusion limit, which is valid for high-rate pulses. Here the effects that multiplicative conductance noise and shot noise have on the voltage fluctuations are examined. It is shown that both these aspects of synaptic drive sculpt high-order features of the subthreshold voltage distribution, such as the skew. It is further shown that the diffusion approximation can only capture the effects arising from the multiplicative conductance noise, predicting a negative voltage skew for excitatory drive. Exact results for the full dynamics are derived from a master-equation approach, predicting positively skewed distributions with long tails in voltage ranges typical for action potential generation. It is argued that, although the skew is a high-order feature of subthreshold voltage distributions, the increased probability of reaching firing threshold suggests a potential role for shot noise in shaping the neuronal transfer function.
中枢神经系统中的神经元，尤其是皮层中的神经元，会受到来自其突触前群体的一连串脉冲的影响。这些突触脉冲由电导变化介导，因此会导致神经元膜电位的增加或减少，其幅度取决于电压：突触噪声是乘性的。膜电位的统计特性具有实验意义，因为单个阈下电压的测量可用于探测突触前群体中发生的活动。尽管脉冲间隔并不总是显著小于脉冲的特征衰减时间，因此波动具有散粒噪声的性质，但文献中大多数可用结果都是在扩散极限下计算的，这对于高速率脉冲是有效的。这里研究了乘性电导噪声和散粒噪声对电压波动的影响。结果表明，突触驱动的这两个方面塑造了阈下电压分布的高阶特征，如偏度。进一步表明，扩散近似只能捕捉乘性电导噪声产生的影响，预测兴奋性驱动下的负电压偏度。完整动力学的精确结果是通过主方程方法得出的，预测在动作电位产生的典型电压范围内具有长尾的正偏态分布。有人认为，虽然偏度是阈下电压分布的高阶特征，但达到放电阈值的概率增加表明散粒噪声在塑造神经元传递函数方面可能发挥作用。
