On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics
On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics
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DOI：
10.1007/s00285-008-0231-x
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发表时间：
2009-08-01
影响因子：
1.9
通讯作者：
Subramanian, Vijay G.
中科院分区：
文献类型：
--
作者：
Duffy, Ken R.;Subramanian, Vijay G.
在适应性免疫反应中，淋巴细胞增殖5到25次细胞分裂，然后在数周内停止并死亡。基于广泛的流式细胞术数据，Hawkins等人（Proc Natl Acad Sci USA 104:5032-5037, 2007）引入了一种细胞水平的淋巴细胞群体动态随机模型，称为细胞模型，该模型准确地捕获了平均淋巴细胞群体大小作为时间的函数。在Subramanian等人（J Math Biol 56(6):861-892, 2008）中，我们对细胞模型进行了分支过程分析，并从体外和体内数据的参数化推断出，尽管每个细胞的命运高度可变，但免疫反应是可预测的。流式细胞术数据的一个缺点是单个细胞不能被跟踪，因此不可能调查家族树中细胞命运的依赖性。在没有这些信息的情况下，Cyton模型放弃了分支过程的一个通常假设（寿命和子代数的独立性），而采用了另一个标准分支过程假设：子代的命运是随机独立的。然而，淋巴细胞的新实验观察表明，同一家谱中的细胞命运不是随机独立的。Hawkins et al.（2008，已提交）报道了一项摄影实验，该实验记录了对有丝分裂刺激作出反应的增殖淋巴细胞系统的每个初始细胞的家谱。这些实验的数据表明，旁系近亲细胞（在一个起始细胞的家谱中属于同一代的细胞）的死亡或分裂命运具有很强的相关性，而不同代的细胞之间和不同家谱中的细胞之间几乎没有相关性。由于这一发现与细胞模型的一个假设形成对比，在本文中，我们介绍了细胞模型的三种变体，它们具有越来越高的旁系血缘相关结构水平，以纳入这些新发现的依赖性。我们研究了它们对细胞群体大小的预测预期变异性的影响。在数学上，我们得出结论，虽然引入相关结构使平均种群规模与Cyton模型保持不变，但种群规模分布的方差通常更大。生物学上，通过比较体外和体内实验确定的细胞模型参数化的模型预测，我们推断，如果旁系亲缘关系延伸到表兄弟之外，那么免疫反应就比从原始细胞模型得出的结论更难以预测。也就是说，我们之前归因于实验误差的数据中的一些可变性可能是由于细胞群体大小动态的内在可变性。
During an adaptive immune response, lymphocytes proliferate for five to twenty-five cell divisions, then stop and die over a period of weeks. Based on extensive flow cytometry data, Hawkins et al. (Proc Natl Acad Sci USA 104:5032-5037, 2007) introduced a cell-level stochastic model of lymphocyte population dynamics, called the Cyton Model, that accurately captures mean lymphocyte population size as a function of time. In Subramanian et al. (J Math Biol 56(6):861-892, 2008), we performed a branching process analysis of the Cyton Model and deduced from parameterizations for in vitro and in vivo data that the immune response is predictable despite each cell's fate being highly variable. One drawback of flow cytometry data is that individual cells cannot be tracked, so that it is not possible to investigate dependencies in the fate of cells within family trees. In the absence of this information, while the Cyton Model abandons one of the usual assumptions of branching processes (the independence of lifetime and progeny number), it adopts another of the standard branching processes hypotheses: that the fates of progeny are stochastically independent. However, new experimental observations of lymphocytes show that the fates of cells in the same family tree are not stochastically independent. Hawkins et al. (2008, submitted) report on cin, lapse photography experiments where every founding cell's family tree is recorded for a system of proliferating lymphocytes responding to a mitogenic stimulus. Data from these experiments demonstrate that the death-or-division fates of collaterally consanguineous cells (those in the same generation within a founding cell's family tree) are strongly correlated, while there is little correlation between cells of distinct generations and between cells in distinct family trees. As this finding contrasts with one of the assumptions of the Cyton Model, in this paper we introduce three variants of the Cyton Model with increasing levels of collaterally consanguineous correlation structure to incorporate these new found dependencies. We investigate their impact on the predicted expected variability of cell population size. Mathematically we conclude that while the introduction of correlation structure leaves the mean population size unchanged from the Cyton Model, the variance of the population size distribution is typically larger. Biologically, through comparison of model predictions for Cyton Model parameterizations determined by in vitro and in vivo experiments, we deduce that if collaterally consanguineous correlation extends beyond cousins, then the immune response is less predictable than would be concluded from the original Cyton Model. That is, some of the variability seen in data that we previously attributed to experimental error could be due to intrinsic variability in the cell population size dynamics.