A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and de-labelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU+ cells are expected to divide into BrdU+ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU+ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU+ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virus-infected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU+ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations.

[1]  Douglas A. Hosack,et al.  Induction of prolonged survival of CD4+ T lymphocytes by intermittent IL-2 therapy in HIV-infected patients. , 2005, The Journal of clinical investigation.

[2]  Alan S. Perelson,et al.  Quantification of Cell Turnover Kinetics Using 5-Bromo-2′-deoxyuridine1 , 2000, The Journal of Immunology.

[3]  J. Sprent,et al.  Lifespan of γ/δ T Cells , 1998, The Journal of experimental medicine.

[4]  Alan S. Perelson,et al.  Increased Turnover of T Lymphocytes in HIV-1 Infection and Its Reduction by Antiretroviral Therapy , 2001, The Journal of experimental medicine.

[5]  Becca Asquith,et al.  Measurement and modeling of human T cell kinetics. , 2003, European journal of immunology.

[6]  Ollivier Hyrien,et al.  An age-dependent branching process model for the analysis of CFSE-labeling experiments , 2010, Biology Direct.

[7]  Ronald B. Herberman,et al.  T Cell Turnover in SIV Infection , 1999 .

[8]  J. Harty,et al.  Division-linked generation of death-intermediates regulates the numerical stability of memory CD8 T cells , 2012, Proceedings of the National Academy of Sciences.

[9]  Julia A. Metcalf,et al.  Naïve T-Cell Dynamics in Human Immunodeficiency Virus Type 1 Infection: Effects of Highly Active Antiretroviral Therapy Provide Insights into the Mechanisms of Naïve T-Cell Depletion , 2006, Journal of Virology.

[10]  Z. Grossman,et al.  The Journal of Experimental Medicine , 2000 .

[11]  V. Maino,et al.  Insufficient Production and Tissue Delivery of CD4+Memory T Cells in Rapidly Progressive Simian Immunodeficiency Virus Infection , 2004, The Journal of experimental medicine.

[12]  R. D. de Boer,et al.  IL-2 Regulates Expansion of CD4+ T Cell Populations by Affecting Cell Death: Insights from Modeling CFSE Data1 , 2007, The Journal of Immunology.

[13]  R. Ahmed,et al.  The rescaling method for quantifying the turnover of cell populations. , 2003, Journal of theoretical biology.

[14]  Ingo Röder,et al.  Stem Cell Proliferation and Quiescence—Two Sides of the Same Coin , 2009, PLoS Comput. Biol..

[15]  J. Guardiola,et al.  Kinetics of In Vivo Proliferation and Death of Memory and Naive CD8 T Cells: Parameter Estimation Based on 5-Bromo-2′-Deoxyuridine Incorporation in Spleen, Lymph Nodes, and Bone Marrow 1 , 2008, The Journal of Immunology.

[16]  R. Lempicki,et al.  Impact of HIV-1 infection and highly active antiretroviral therapy on the kinetics of CD4+ and CD8+ T cell turnover in HIV-infected patients. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[17]  A S Perelson,et al.  Rapid turnover of T lymphocytes in SIV-infected rhesus macaques. , 1998, Science.

[18]  Richard A. Lempicki,et al.  Identification of Dynamically Distinct Subpopulations of T Lymphocytes That Are Differentially Affected by HIV , 2001, The Journal of experimental medicine.

[19]  A. Yates,et al.  Mathematical Modeling Reveals the Biological Program Regulating Lymphopenia-Induced Proliferation1 , 2008, The Journal of Immunology.

[20]  Shenghui He,et al.  Haematopoietic stem cells do not asymmetrically segregate chromosomes or retain BrdU , 2007, Nature.

[21]  Becca Asquith,et al.  Lymphocyte kinetics: the interpretation of labelling data. , 2002, Trends in immunology.

[22]  R. Lempicki,et al.  Differential effects of HIV viral load and CD4 count on proliferation of naive and memory CD4 and CD8 T lymphocytes. , 2011, Blood.

[23]  A. Burny,et al.  Increased cell proliferation, but not reduced cell death, induces lymphocytosis in bovine leukemia virus-infected sheep , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Karyn L. Sutton,et al.  A new model for the estimation of cell proliferation dynamics using CFSE data. , 2011, Journal of immunological methods.

[25]  Alan S. Perelson,et al.  Estimating Lymphocyte Division and Death Rates from CFSE Data , 2006, Bulletin of mathematical biology.

[26]  Alan S. Perelson,et al.  Turnover Rates of B Cells, T Cells, and NK Cells in Simian Immunodeficiency Virus-Infected and Uninfected Rhesus Macaques1 , 2003, The Journal of Immunology.

[27]  Alan S. Perelson,et al.  Estimating average cellular turnover from 5–bromo–2'–deoxyuridine (BrdU) measurements , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[28]  Hulin Wu,et al.  Evaluation of Multitype Mathematical Models for CFSE-Labeling Experiment Data , 2012, Bulletin of mathematical biology.

[29]  D. Roose,et al.  Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data , 2009, Journal of mathematical biology.

[30]  J. Sprent,et al.  Turnover of Naive-and Memory-phenotype T Cells , 1994 .

[31]  Rustom Antia,et al.  Quantifying cell turnover using CFSE data. , 2005, Journal of immunological methods.

[32]  Rob J. De Boer,et al.  Explicit Kinetic Heterogeneity: Mathematical Models for Interpretation of Deuterium Labeling of Heterogeneous Cell Populations , 2009, PLoS Comput. Biol..

[33]  John F Markham,et al.  Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data , 2007, Nature Protocols.

[34]  Ruy M Ribeiro,et al.  Modelling deuterium labelling of lymphocytes with temporal and/or kinetic heterogeneity , 2012, Journal of The Royal Society Interface.