Theoretical Biology, Utrecht University, Utrecht, The Netherlands.
PLoS Comput Biol. 2010 Feb 5;6(2):e1000666. doi: 10.1371/journal.pcbi.1000666.
Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three most common models, which are based on quite different biological assumptions, actually predict mathematically identical labeling curves with one parameter for the exponential up and down slope, and one parameter defining the maximum labeling level. By extending these previous models, we here propose a novel approach for the analysis of data from deuterium labeling experiments. We construct a model of "kinetic heterogeneity" in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a novel way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length.
在不同条件下估算淋巴细胞的分裂和死亡率对于定量理解免疫系统至关重要。氘（以氘代葡萄糖或重水的形式）可用于测量体内淋巴细胞的增殖和死亡速率。从标记和去标记曲线推断这些速率一直是一个有争议的问题，不同的研究小组提出了不同的数学模型来解决这个问题。我们表明，三种最常见的模型，它们基于相当不同的生物学假设，实际上预测了数学上相同的标记曲线，其中一个参数用于指数上升和下降斜率，另一个参数定义了最大标记水平。通过扩展这些先前的模型，我们在这里提出了一种分析氘标记实验数据的新方法。我们构建了一个“动力学异质性”模型，其中总细胞群体由具有不同细胞周转率的许多亚群组成。在这个模型中，对于给定的周转率分布，可以计算出标记 DNA 积累和丢失的预测分数。我们的模型再现了几个先前的实验观察结果，例如标记期长度与标记停止后标记 DNA 丢失速度之间的负相关。我们通过将新的显式动力学异质性模型应用于人工生成的数据集来证明其可靠性，并通过拟合实验数据来说明其有用性。与先前的模型相比，显式动力学异质性模型 1）提供了一种解释标记数据的新方法；2）允许在去标记过程中标记细胞的非指数损失；3）可用于描述具有可变标记长度的数据。
