Hyrien Ollivier, Mayer-Pröschel Margot, Noble Mark, Yakovlev Andrei
Department of Biostatistics and Computational Biology, University of Rochester, 601 Elmwood Avenue, Rochester, NY 14642, USA.
Math Biosci. 2005 Feb;193(2):255-74. doi: 10.1016/j.mbs.2004.07.003. Epub 2005 Jan 22.
This paper presents a new method to analyze clonal data on oligodendrocyte development in cell culture. The process of oligodendrocyte generation from precursor cells is modelled as a multi-type Bellman-Harris branching process as suggested in an earlier paper [K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Proschel, M. Noble, An alternative stochastic model of generation of oligodendrocytes in cell culture, J. Math. Biol. 43 (2001) 22]. This model has been extended to allow for death of oligodendrocytes as well as a dissimilar distribution of the first mitotic cycle duration as compared to the subsequent cycles of precursor cells, which lengths are assumed to be independent and identically distributed random variables. Since the time-span of oligodendrocytes is not directly observable in clonal data, plausible parametric assumptions are invoked to make estimation problems tractable. In particular, the time to cell death follows a two-parameter gamma distribution, while the lapse of time between the event of cell death and the event of cell disintegration is assumed to be exponentially distributed. A simulated pseudo maximum likelihood method for estimation of model parameters has been developed using simulation-based approximations of the expected numbers and variance-covariance matrices for different types of cells. Finite sample properties of the estimation procedure are studied by computer simulations. The proposed method is illustrated with an analysis of the clonal development of O-2A progenitor cells isolated from the rat optic nerve and the corpus callosum.
本文提出了一种分析细胞培养中少突胶质细胞发育克隆数据的新方法。如早期一篇论文[K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Proschel, M. Noble,《细胞培养中少突胶质细胞生成的另一种随机模型》，《数学生物学杂志》43 (2001) 22]所建议的，将从前体细胞生成少突胶质细胞的过程建模为多类型贝尔曼 - 哈里斯分支过程。该模型已得到扩展，以考虑少突胶质细胞的死亡以及与前体细胞后续周期相比第一个有丝分裂周期持续时间的不同分布，假定后续周期的长度是独立同分布的随机变量。由于在克隆数据中少突胶质细胞的时间跨度不可直接观测，因此采用合理的参数假设以使估计问题易于处理。具体而言，细胞死亡时间服从双参数伽马分布，而假定细胞死亡事件与细胞解体事件之间的时间间隔服从指数分布。利用不同类型细胞预期数量和方差 - 协方差矩阵的基于模拟的近似值，开发了一种用于估计模型参数的模拟伪最大似然方法。通过计算机模拟研究了估计程序的有限样本性质。通过对从大鼠视神经和胼胝体分离的O - 2A祖细胞的克隆发育分析来说明所提出的方法。
