Mathematical modeling of dendritic growth in vitro.
Mathematical modeling of dendritic growth in vitro.
复制标题
体外树突生长的数学模型。
DOI：
10.1016/0006-8993(94)01310-e
复制
发表时间：
1995
期刊：
影响因子：
2.9
通讯作者：
Goodwin,J
中科院分区：
文献类型：
--
作者：
Uemura,E;Carriquiry,A;Kliemann,W;Goodwin,J
对培养的海马神经元的树突分枝模式进行了分析，以获得在有限的外界影响下树突生长随时间变化的数学参数。用无毒的碳菁染料(Dio)对培养的神经元进行染色，并在电镀后第1、2、3、4、6和7天对物理上相互分离的锥体状神经元进行分析。树突的几何分支模式使用一个数学模型进行分析，该模型包括Galton-Watson分支过程的随机效应，其中一个分支的分裂在统计上独立于所有其他分支的分裂，以及确定性效应的参数形式，该参数衡量形成密集模式(簇)或稀疏模式(细长树)的程度。利用包含随机效应和确定性效应的数学模型分析了枝晶的几何分枝模式。采用极大似然法对模型参数进行估计。这些数据表明，在体外，基生树突按照纯粹的随机分枝过程生长，没有明显的密集或稀疏模式，而顶端树突倾向于形成细长的树，次级分叉较少。这种趋势是量化的，它取决于神经元生长的培养条件。讨论了对枝晶生长模式的各种影响的定量评估。
The dendritic branching pattern of cultured hippocampal neurons was analyzed to obtain mathematical parameters that fit the time-dependent growth of dendrites under limited extrinsic influence. Cultured neurons were stained with a non-toxic carbocyanine dye (diO) and pyramidal-shaped neurons that were physically separated from one another were analyzed at post-plating days 1, 2, 3, 4, 6 and 7. The geometric branching pattern of the dendrites was analyzed using a mathematical model that incorporates random effects in the form of a Galton-Watson branching process where splitting of one branch is statistically independent of the splitting of all other branches, and deterministic effects in the form of a parameter that measures the extent to which dense patterns (clusters) or sparse patterns (elongated trees) are formed. The geometric branching pattern of the dendrites was analyzed using a mathematical model that incorporates random and deterministic effects. The model parameters were estimated via the method of maximum likelihood. The data suggest that in vitro basal dendrites grow according to a purely random branching process without pronounced dense or sparse patterns, while apical dendrites tend to form elongated trees with fewer secondary bifurcations. This trend is quantified, and it depends on the culture conditions in which the neurons are grown. The quantitative assessment of various influences on dendritic growth patterns are discussed.