Kenyon G T, Puff R D, Fetz E E
Division of Neuroscience, Baylor College of Medicine, Houston, TX 77030.
Biol Cybern. 1992;67(2):133-41. doi: 10.1007/BF00201020.
We describe a general diffusion model for analyzing the efficacy of individual synaptic inputs to threshold neurons. A formal expression is obtained for the system propagator which, when given an arbitrary initial state for the cell, yields the conditional probability distribution for the state at all later times. The propagator for a cell with a finite threshold is written as a series expansion, such that each term in the series depends only on the infinite threshold propagator, which in the diffusion limit reduces to a Gaussian form. This procedure admits a graphical representation in terms of an infinite sequence of diagrams. To connect the theory to experiment, we construct an analytical expression for the primary correlation kernel (PCK) which profiles the change in the instantaneous firing rate produced by a single postsynaptic potential (PSP). Explicit solutions are obtained in the diffusion limit to first order in perturbation theory. Our approximate expression resembles the PCK obtained by computer simulation, with the accuracy depending strongly on the mode of firing. The theory is most accurate when the synaptic input drives the membrane potential to a mean level more than one standard deviation below the firing threshold, making such cells highly sensitive to synchronous synaptic input.
我们描述了一种用于分析单个突触输入对阈值神经元功效的通用扩散模型。得到了系统传播子的形式表达式，当给定细胞的任意初始状态时，该表达式可得出所有后续时刻状态的条件概率分布。具有有限阈值的细胞的传播子被写成级数展开形式，使得级数中的每一项仅取决于无限阈值传播子，在扩散极限下该传播子简化为高斯形式。此过程允许用无限序列的图进行图形表示。为了将该理论与实验联系起来，我们构建了一个用于初级相关核（PCK）的解析表达式，该表达式描绘了由单个突触后电位（PSP）产生的瞬时放电率的变化。在扩散极限下，通过微扰理论得到了一阶显式解。我们的近似表达式类似于通过计算机模拟得到的PCK，其精度强烈依赖于放电模式。当突触输入将膜电位驱动到比放电阈值低一个以上标准差的平均水平时，该理论最为准确，这使得此类细胞对同步突触输入高度敏感。
