Burke R E, Marks W B, Ulfhake B
Laboratory of Neural Control, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland 20892.
J Neurosci. 1992 Jun;12(6):2403-16. doi: 10.1523/JNEUROSCI.12-06-02403.1992.
Most quantitative descriptions of neuronal dendrite morphology involve tabulations of measurements and correlations among them. The present work is an attempt to extract from such data a parsimonious set of parameters that are sufficient to describe the quantitative features of individual and pooled dendrites, including their statistical variability. A relatively simple stochastic (Monte Carlo) model was devised to simulate branching dendritic trees. The necessary parameters were then derived directly from measurements of 64 completely reconstructed dendrites belonging to six gastrocnemius alpha-motoneurons, labeled by intracellular injection of HRP. Comparison of actual and simulated dendrites was used to guide the process of parameter extraction. The model included only two processes, one to generate individual branches given their starting diameters and the second to select starting diameters for the daughter branches produced at dichotomous branching points. The stochastic process for branch generation was controlled by probability functions for branching (Pbr) and for terminating (Ptrm), together with a constant rate of branch taper. All model parameters were fixed by motoneuron measurements except for branch taper rate, which was allowed to vary within limits consistent with observed taper rates in order to generate the appropriate total number of branches. The simplest model (model 1), in which Pbr and Ptrm depended only on local branch diameter, produced simulated dendrites that fit many, but not all, characteristics of actual motoneuron dendrites. Two additional properties produced significant improvements in the fit: (1) a small but significant dependence of daughter diameters on the normalized starting diameter of the parent branch, and (2) a dependence of Pbr and Ptrm on distance from the soma as well as on local branch diameter. The process of developing this model revealed unsuspected relations in the original data that suggest the existence of fundamental mechanisms for morphological control. The final model succinctly describes a large amount of data and will enable quantitative comparisons between the dendritic structures of different types of neurons, regardless of their relative sizes.
大多数对神经元树突形态的定量描述都涉及测量值的列表以及它们之间的相关性。目前的工作是尝试从这些数据中提取一组简约的参数，这些参数足以描述单个和汇总的树突的定量特征，包括它们的统计变异性。设计了一个相对简单的随机（蒙特卡罗）模型来模拟分支树突。然后直接从对64个完全重建的属于六个腓肠肌α运动神经元的树突的测量中得出必要的参数，这些树突通过细胞内注射HRP进行标记。实际树突与模拟树突的比较用于指导参数提取过程。该模型仅包括两个过程，一个是根据起始直径生成单个分支，另一个是为在二分分支点产生的子分支选择起始直径。分支生成的随机过程由分支概率函数（Pbr）和终止概率函数（Ptrm）以及恒定的分支变细率控制。除了分支变细率外，所有模型参数都由运动神经元测量确定，分支变细率被允许在与观察到的变细率一致的范围内变化，以便生成适当的分支总数。最简单的模型（模型1），其中Pbr和Ptrm仅取决于局部分支直径，产生的模拟树突符合实际运动神经元树突的许多但不是所有特征。另外两个特性在拟合方面有显著改进：（1）子直径对母分支归一化起始直径有小但显著的依赖性，以及（2）Pbr和Ptrm对距胞体的距离以及局部分支直径都有依赖性。开发这个模型的过程揭示了原始数据中意想不到的关系，这表明存在形态控制的基本机制。最终模型简洁地描述了大量数据，并将能够对不同类型神经元的树突结构进行定量比较，而不管它们的相对大小如何。
