Major G, Evans J D, Jack J J
University Laboratory of Physiology, Oxford, United Kingdom.
Biophys J. 1993 Jul;65(1):450-68. doi: 10.1016/S0006-3495(93)81038-5.
Analytical solutions are derived for arbitrarily branching passive neurone models with a soma and somatic shunt, for synaptic inputs and somatic voltage commands, for both perfect and imperfect somatic voltage clamp. The solutions are infinite exponential series. Perfect clamp decouples different dendritic trees at the soma: each exponential component exists only in one tree; its time constant is independent of stimulating and recording position within the tree; its amplitude is the product of a factor constant over that entire tree and factors dependent on stimulating and recording positions. Imperfect clamp to zero is mathematically equivalent to voltage recording with a shunt. As the series resistance increases, different dendritic trees become more strongly coupled. A number of interesting response symmetries are evident. The solutions reveal parameter dependencies, including an insensitivity of the early parts of the responses to specific membrane resistivity and somatic shunt, and an approximately linear dependence of the slower time constants on series resistance, for small series resistances. The solutions are illustrated using a "cartoon" representation of a CA1 pyramidal cell and a two-cylinder + soma model.
针对具有胞体和胞体分流的任意分支被动神经元模型，推导了分析解，适用于突触输入和胞体电压指令，适用于完美和不完美的胞体电压钳制。这些解是无穷指数级数。完美钳制在胞体处解耦不同的树突分支：每个指数成分仅存在于一个树突分支中；其时间常数与树突分支内的刺激和记录位置无关；其幅度是整个树突分支上的一个常数因子与依赖于刺激和记录位置的因子的乘积。不完美钳制到零在数学上等同于用分流器进行电压记录。随着串联电阻增加，不同的树突分支耦合更强。有许多有趣的响应对称性很明显。这些解揭示了参数依赖性，包括响应早期部分对特定膜电阻率和胞体分流的不敏感性，以及对于小串联电阻，较慢时间常数对串联电阻的近似线性依赖性。使用CA1锥体细胞的“卡通”表示和双圆柱体 + 胞体模型对这些解进行了说明。
