Pilyugin Sergei S, Ganusov Vitaly V, Murali-Krishna Kaja, Ahmed Rafi, Antia Rustom
Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA.
J Theor Biol. 2003 Nov 21;225(2):275-83. doi: 10.1016/s0022-5193(03)00245-5.
The dynamic nature of immune responses requires the development of appropriate experimental and theoretical tools to quantitatively estimate the division and death rates which determine the turnover of immune cells. A number of papers have used experimental data from BrdU and D-glucose labels together with a simple random birth-death model to quantify the turnover of immune cells focusing on HIV/SIV infections [Mohri et al. 279 (1998) 1223-1227, Hellerstein et al. 5 (1999) 83-89, Bonhoeffer et al. 164 (2000) 5049-5054, Mohri et al. 87 (2001) 1277-1287]. We show how uncertainties in the assumptions of the random birth-death model may lead to substantial errors in the parameters estimated. We then show how more accurate estimates can be obtained from the more recent CFSE data which allow to track the number of divisions each cell has undergone. Specifically, we: (i) describe a general stage-structured model of cell division where the probabilities of division and death are functions of time since the previous division; (ii) develop a rescaling method to identify invariant parameters (i.e. the ones that are independent of the specific functions describing division and death); (iii) show how these invariant parameters can be estimated, and (iv) illustrate this technique by applying it to CFSE data taken from the literature.
免疫反应的动态特性需要开发适当的实验和理论工具，以定量估计决定免疫细胞更新的分裂和死亡率。许多论文使用了来自BrdU和D-葡萄糖标记的实验数据，结合简单的随机生死模型，来量化免疫细胞的更新，重点是HIV/SIV感染[Mohri等人，《自然》279(1998)1223 - 1227；Hellerstein等人，《美国国家科学院院刊》5(1999)83 - 89；Bonhoeffer等人，《细胞》164(2000)5049 - 5054；Mohri等人，《实验医学杂志》87(2001)1277 - 1287]。我们展示了随机生死模型假设中的不确定性如何导致估计参数出现重大误差。然后我们展示了如何从更新的CFSE数据中获得更准确的估计，这些数据能够追踪每个细胞经历的分裂次数。具体来说，我们：(i)描述了一个细胞分裂的一般阶段结构模型，其中分裂和死亡的概率是自上次分裂以来时间的函数；(ii)开发了一种重新缩放方法来识别不变参数（即与描述分裂和死亡的特定函数无关的参数）；(iii)展示了如何估计这些不变参数，以及(iv)通过将其应用于从文献中获取的CFSE数据来说明该技术。
