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On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics

Duffy, Ken R. and Subramanian, Vijay G. (2009) On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics. Journal of Mathematical Biology, 59 (2). pp. 255-285. ISSN 1432-1416

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Abstract

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. (PNAS, 2007, 104, 5032{5037) 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., 2008, 56:6, 861{892), 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 for publication) report on cine 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-ordivision 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.

Item Type: Article
Keywords: Transient cell population dynamics; Expected variability; Continuous time branching processes; Time-dependent offspring distributions; Correlated collaterally consanguineous cells; Lymphocytes; Hamilton Institute.
Subjects: Science & Engineering > Biology
Science & Engineering > Hamilton Institute
Science & Engineering > Mathematics
Item ID: 1650
Identification Number: 10.1007/s00285-008-0231-x
Depositing User: Hamilton Editor
Date Deposited: 09 Nov 2009 16:13
Journal or Publication Title: Journal of Mathematical Biology
Publisher: Springer
Refereed: No
URI:

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