Estimating division and death rates from CFSE data
Estimating division and death rates from CFSE data
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DOI：
10.1016/j.cam.2004.08.020
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发表时间：
2005-12-01
影响因子：
2.4
通讯作者：
Perelson, AS
中科院分区：
文献类型：
--
作者：
De Boer, RJ;Perelson, AS
分裂跟踪染料，羧基荧光素二醋酸酯琥珀酰亚胺酯(CFSE)是目前最有信息量的标记技术，用于表征免疫系统中细胞的分裂历史。Gett和Hodgkin(NAT.免疫系统。1(2000)239-244)提出了用与每个分裂相关的2倍扩张来归一化使用数据，并论证了归一化数据的平均值随着时间t线性增加，斜率反映了分裂速率p。我们发展了一些关于刺激后静止细胞克隆扩张的数学模型，并在这些模型的背景下证明了该方法在什么条件下是有效的。我们比较了时间t的细胞在使用分布上的三个平均值：平均值，u(T)，正态分布的平均值，u(2)(T)，以及不包括未分割的细胞的正态分布的平均值，(u(2))在帽(T)上。在最简单的模型中，处理具有恒定分裂和死亡率的均匀细胞总体的模型中，各个分裂数上的细胞的归一化频率分布是泊松分布，平均值u(2)(T)=pt，其中p是分裂速率。因此，在数据中这些分布看起来是高斯的这一事实不足以确定小区被招募到第一分区的时间具有高斯变化，因为对于大的pt，泊松分布接近高斯分布。排除未分割单元会使数据分析复杂化，因为(Mu(2))Over Cap(T)不等于pt，并且仅在初始瞬变后才接近斜率p。在静止单元的第一次分割比后续分割花费更长时间的模型中，所有三种均值在接近渐近区域之前都有初始瞬变，这是预期的Mu(T)=2pt和Mu 2(T)=(Mu(2))Over Cap(T)=pt。这样的瞬变明显使数据分析变得复杂。在相同的初始瞬变时间后，归一化细胞数趋于以e(-dt)的速率减少，其中d是死亡率。Gett和Hodgkin获得的CFSE数据与含有细胞增殖和死亡的一阶项的常微分方程(ODE)模型的非线性参数拟合效果较差。对于细胞周期的确定性阶段，具有显式时间延迟的Smith-Martin模型的表现要好得多。然而，从对ODE的分析中获得的见解被证明是有用的，正如我们所展示的那样，通过模拟模型生成虚拟使用数据，其中细胞周期时间从不同的分布中提取，然后计算各种平均分裂数。(C)2005 Elsevier B.V.保留所有权利。
The division tracking dye, carboxyfluorescin diacetate succinimidyl ester (CFSE) is currently the most informative labeling technique for characterizing the division history of cells in the immune system. Gett and Hodgkin (Nat. Immunol. 1 (2000) 239-244) have proposed to normalize USE data by the 2-fold expansion that is associated with each division, and have argued that the mean of the normalized data increases linearly with time, t, with a slope reflecting the division rate p. We develop a number of mathematical models for the clonal expansion of quiescent cells after stimulation and show, within the context of these models, under which conditions this approach is valid. We compare three means of the distribution of cells over the USE profile at time t: the mean, mu(t), the mean of the normalized distribution, mu(2) (t), and the mean of the normalized distribution excluding nondivided cells, (mu(2)) over cap (t).In the simplest models, which deal with homogeneous populations of cells with constant division and death rates, the normalized frequency distribution of the cells over the respective division numbers is a Poisson distribution with mean mu(2) (t) = pt, where p is the division rate. The fact that in the data these distributions seem Gaussian is therefore insufficient to establish that the times at which cells are recruited into the first division have a Gaussian variation because the Poisson distribution approaches the Gaussian distribution for large pt. Excluding nondivided cells complicates the data analysis because (mu(2)) over cap (t) not equal pt, and only approaches a slope p after an initial transient.In models where the first division of the quiescent cells takes longer than later divisions, all three means have an initial transient before they approach an asymptotic regime, which is the expected mu(t) = 2pt and mu 2 (t) = (mu(2)) over cap (t) = pt. Such a transient markedly complicates the data analysis. After the same initial transients, the normalized cell numbers tend to decrease at a rate e(-dt), where d is the death rate.Nonlinear parameter fitting of CFSE data obtained from Gett and Hodgkin to ordinary differential equation (ODE) models with first-order terms for cell proliferation and death gave poor fits to the data. The Smith-Martin model with an explicit time delay for the deterministic phase of the cell cycle performed much better. Nevertheless, the insights gained from analysis of the ODEs proved useful as we showed by generating virtual USE data with a simulation model, where cell cycle times were drawn from various distributions, and then computing the various mean division numbers. (c) 2005 Elsevier B.V. All rights reserved.