Poznański R R
Department of Mathematics, Monash University, Clayton, Victoria, Australia.
IMA J Math Appl Med Biol. 1988;5(2):113-45. doi: 10.1093/imammb/5.2.113.
An exponentially tapering equivalent cylinder model is employed in order to approximate the loss of the dendritic trunk parameter observed from anatomical data on apical and basilar dendrites of CA1 and CA3 hippocampal pyramidal neurons. This model allows dendritic trees with a relative paucity of branching to be treated. In particular, terminal branches are not required to end at the same electrotonic distance. The Laplace transform method is used to obtain analytic expressions for the Green's function corresponding to an instantaneous pulse of current injected at a single point along a tapering equivalent cylinder with sealed ends. The time course of the voltage in response to an arbitrary input is computed using the Green's function in a convolution integral. Examples of current input considered are (1) an infinitesimally brief (Dirac delta function) pulse and (2) a step pulse. It is demonstrated that inputs located on a tapering equivalent cylinder are more effective at the soma than identically placed inputs on a nontapering equivalent cylinder. Asymptotic solutions are derived to enable the voltage response behaviour over both relatively short and long time periods to be analysed. Semilogarithmic plots of these solutions provide a basis for estimating the membrane time constant tau m from experimental transients. Transient voltage decrement from a clamped soma reveals that tapering tends to reduce the error associated with inadequate voltage clamping of the dendritic membrane. A formula is derived which shows that tapering tends to increase the estimate of the electrotonic length parameter L.
采用指数渐缩等效圆柱体模型，以近似从CA1和CA3海马锥体神经元顶树突和基底树突的解剖数据中观察到的树突干参数的损失。该模型允许处理分支相对较少的树突树。特别地，终端分支不需要在相同的电紧张距离处结束。使用拉普拉斯变换方法来获得对应于沿具有密封端的渐缩等效圆柱体上的单个点注入的电流瞬时脉冲的格林函数的解析表达式。使用卷积积分中的格林函数来计算响应于任意输入的电压的时间进程。所考虑的电流输入示例为：(1) 无限短暂（狄拉克δ函数）脉冲和(2) 阶跃脉冲。结果表明，位于渐缩等效圆柱体上的输入在胞体处比位于非渐缩等效圆柱体上相同位置的输入更有效。推导渐近解以分析相对短和长时间段内的电压响应行为。这些解的半对数图为从实验瞬变中估计膜时间常数τm提供了基础。来自钳制胞体的瞬态电压衰减表明，渐缩倾向于减少与树突膜电压钳制不足相关的误差。推导了一个公式，该公式表明渐缩倾向于增加电紧张长度参数L的估计值。
