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Estimation of Cell Proliferation Dynamics Using CFSE Data

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Abstract

Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57–89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1–26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences.

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References

  • Banks, H.T., Davis, J.L., 2007. A comparison of approximation methods for the estimation of probability distributions on parameters. Appl. Numer. Math. 57, 753–777.

    Article  MATH  MathSciNet  Google Scholar 

  • Banks, H.T., Fitzpatrick, B.G., 1989. Inverse problems for distributed systems: statistical tests and ANOVA. In: Proc. International Symposium on Math. Approaches to Envir. and Ecol. Problems, Springer Lecture Note in Biomath., vol. 81, pp. 262–273. Springer, Berlin. LCDS/CCS Rep. 88-16, July, 1988, Brown University.

    Google Scholar 

  • Banks, H.T., Fitzpatrick, B.G., 1990. Statistical methods for model comparison in parameter estimation problems for distributed systems. J. Math. Biol. 28, 501–527. CAMS Tech. Rep. 89-4, September, 1989, University of Southern California.

    Article  MATH  MathSciNet  Google Scholar 

  • Banks, H.T., Fitzpatrick, B.G., 1991. Estimation of growth rate distributions in size-structured population models. Quart. Appl. Math. 49, 215–235. CAMS Tech. Rep. 90-2, January, 1990, University of Southern California.

    MATH  MathSciNet  Google Scholar 

  • Banks, H.T., Iles, D.W., 1987. On compactness of admissible parameter sets: convergence and stability in inverse problems for distributed parameter systems. In: Proc. Conf. on Control Systems Governed by PDE’s, February, 1986, Gainesville, FL. Springer Lecture Notes in Control & Inf. Science, vol. 97, pp. 130–142. Springer, Berlin. ICASE Report #86-38, NASA Langley Res. Ctr., Hampton VA 1986.

    Google Scholar 

  • Banks, H.T., Kunsich, K., 1989. Estimation Techniques for Distributed Parameter Systems. Birkhauser, Boston.

    MATH  Google Scholar 

  • Banks, H.T., Lybeck, N., 1996. Modeling methodology for elastomer dynamics. In: Systems and Control in the 21st Century, pp. 37–50. Birkhauser, Boston. CRSC-TR96-29, NCSU, September, 1996.

    Google Scholar 

  • Banks, H.T., Pedersen, M., 2009. Well-posedness of inverse problems for systems with time dependent parameters. Arab. J. Sci. Eng. Math. 1, 39–58. CRSC-TR08-10, August, 2008.

    MATH  Google Scholar 

  • Banks, H.T., Samuels, J.R., 2009. Detection of cardiac occlusions using viscoelastic wave propagation. Adv. Appl. Math. Mech. 1, 1–28. CRSC-TR08-23, December, 2008.

    MathSciNet  Google Scholar 

  • Banks, H.T., Tran, H.T., 2009. Mathematical and Experimental Modeling of Physical and Biological Processes. CRC Press, Boca Raton.

    MATH  Google Scholar 

  • Banks, H.T., Botsford, L.W., Kappel, F., Wang, C., 1988. Modeling and estimation in size structured population models. LCDC-CSS Report 87-13, Brown University; Proceedings 2nd Course on Mathematical Ecology (Trieste, December 8–12, 1986) World Press, Singapore, pp. 521–541.

  • Banks, H.T., Smith, R.C., Wang, Y., 1996. Smart Material Structures: Modeling, Estimation and Control. Masson Series on Research in Applied Math. Masson/Wiley, Paris/New York.

    MATH  Google Scholar 

  • Banks, H.T., Bortz, D.M., Holte, S.E., 2003. Incorporation of variability into the modeling of viral delays in HIV infection dynamics. Math. Biosci. 183, 63–91.

    Article  MATH  MathSciNet  Google Scholar 

  • Banks, H.T., Davidian, M., Samuels, Jr., J.R., Sutton, Karyn L., 2009. An inverse problem statistical methodology summary. In: Chowell, G., Hyman, M., Hengartner, N., Bettencourt, L.M.A., Castillo-Chavez, C. (Eds.), Statistical Estimation Approaches in Epidemiology, pp. 249–302. Springer, Berlin. CRSC-TR08-01, January, 2008.

    Chapter  Google Scholar 

  • Banks, H.T., Holm, K., Robbins, D., 2010. Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping. Arab. J. Sci. Eng. Math., submitted. CRSC-TR09-13, June, 2009; Revised August, 2009.

  • Bell, G., Anderson, E., 1967. Cell growth and division I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures. Biophys. J. 7, 329–351.

    Article  Google Scholar 

  • Bellomo, N., Preziosi, L., 2000. Modelling and mathematical problems related to tumor evolution and its integration with the immune system. Math. Comput. Model. 32, 413–452.

    Article  MATH  MathSciNet  Google Scholar 

  • Bernard, S., Pujo-Menjouet, L., Mackey, M.C., 2003. Analysis of cell kinetics using a cell division marker: Mathematical modeling of experimental data. Biophys. J. 84, 3414–3424.

    Article  Google Scholar 

  • Bird, J.J., Brown, D.R., Mullen, A.C., Moskowitz, N.H., Mahowald, M.A., Sider, J.R., Ajewski, T.F., Wang, C., Reiner, S.L., 1998. Helper T cell differentiation is controlled by the cell cycle. Immunity 9, 229–237.

    Article  Google Scholar 

  • Bonhoeffer, S., Mohri, H., Ho, D., Perleson, A.S., 2000. Quantification of cell turnover kinetics using 5-Bromo-2′-deoxyuridine. J. Immunol. 164, 5049–5054.

    Google Scholar 

  • Carroll, R.J., Ruppert, D., 2000. Transformation and Weighting in Regression. Chapman & Hall, London.

    Google Scholar 

  • Chao, D.L., Davenport, M.P., Forrest, S., Perleson, A.S., 2003. Stochastic stage-structured modeling of the adaptive immune system. In: Proceedings of the 2003 IEEE Bioinformatics Conference (CSB 2003), pp. 124–131, Albuquerque, August 11–14, 2003.

  • Davidian, M., Giltinan, D.M., 1995. Nonlinear Models for Repeated Measurement Data. Chapman & Hall, London.

    Google Scholar 

  • de Boer, R.J., Ganusov, V.V., Milutinovic, D., Hodgkin, P., Perelson, A.S., 2006. Estimating lymphocyte division and death rates from CFSE data. Bull. Math. Biol. 68, 1011–1031.

    Article  Google Scholar 

  • Fung, Y.C., 1993. Biomechanics: Mechanical Properties of Living Tissue. Springer, Berlin.

    Google Scholar 

  • Fung, Y.C., 1994. A First Course in Continuum Mechanics. Prentice Hall, Englewood Cliffs.

    Google Scholar 

  • Ganusov, V.V., Pilyugin, S.S., de Boer, R.J., Murali-Krishna, K., Ahmed, R., Anti, R., 2005. Quantifying cell turnover using CFSE data. J. Immunol. Methods 298, 183–200.

    Article  Google Scholar 

  • Gett, A.V., Hodgkin, P.D., 1998. Cell division regulates the T cell cytokine repertoire, revealing a mechanism underlying immune class regulation. Proc. Natl. Acad. Sci. USA. 95, 9488–9493.

    Article  Google Scholar 

  • Gett, A.V., Hodgkin, P.D., 2000. A cellular calculus for signal integration by T cells. Nat. Immunol. 1, 239–244.

    Article  Google Scholar 

  • Gyllenberg, M., Webb, G.F., 1990. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol. 28, 671–694.

    Article  MATH  MathSciNet  Google Scholar 

  • Hawkins, E.D., Hommel, M., Turner, M.L., Battye, F., Markham, J., Hodgkin, P.D., 2007. Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data. Nat. Protocols 2, 2057–2067.

    Article  Google Scholar 

  • Hawkins, E.D., Turner, M.L., Dowling, M.R., van Gend, C., Hodgkin, P.D., 2007. A model of immune regulation as a consequence of randomized lymphocyte division and death times. Proc. Natl. Acad. Sci. 104(12), 5032–5037.

    Article  Google Scholar 

  • Hodgkin, P.D., Go, N.F., Cupp, J.E., Howard, M., 1996. Interleukin-4 enhances anti-IgM stimulation of B cells by improving cell viability and by increasing the sensitivity of B cells to the anti-IgM signal. Cell. Immunol. 134, 14–30.

    Article  Google Scholar 

  • Komarova, N.L., 2006. Stochastic modeling of drug resistance in cancer. J. Theor. Biol. 239, 351–366.

    Article  MathSciNet  Google Scholar 

  • Komarova, N.L., Wodarz, D., 2007. Effect of cellular quiescence on the success of targeted CML therapy. In: PloS ONE, vol. 2, p. 10, e990.

  • Lee, H.Y., Hawkins, E.D., Zand, M.S., Mosmann, T., Wu, H., Hodgkin, P.D., Perelson, A.S., 2009. Interpreting CFSE obtained division histories of B cells in vitro with Smith-Martin and cyton type models. Bull. Math Biol. 71, 1649–1670.

    Article  MATH  MathSciNet  Google Scholar 

  • León, K., Faro, J., Carneiro, J., 2004. A general mathematical framework to model generation structure in a population of asynchronously dividing cells. J. Theor. Biol. 229, 455–476.

    Article  Google Scholar 

  • Luzyanina, T., Mrusek, S., Edwards, J.T., Roose, D., Ehl, S., Bocharov, G., 2007. Computational analysis of CFSE proliferation assay. J. Math. Biol. 54, 57–89.

    Article  MATH  MathSciNet  Google Scholar 

  • Luzyanina, T., Roose, D., Schenkel, T., Sester, M., Ehl, S., Meyerhans, A., Bocharov, G., 2007. Numerical modelling of label-structured cell population growth using CFSE distribution data. Theor. Biol. Med. Model. 4, 1–26.

    Article  Google Scholar 

  • Luzyanina, T., Roose, D., Bocharov, G., 2009. Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data. J. Math. Biol. 59, 581–603.

    Article  MATH  MathSciNet  Google Scholar 

  • Lyons, A.B., 1999. Divided we stand: tracking cell proliferation with carboxyfluorescein diacetate succinimidyl ester. Immunol. Cell Biol. 77, 509–515.

    Article  Google Scholar 

  • Lyons, A.B., Doherty, K.V., 2004. Flow cytometric analysis of cell division by dye dilution. Curr. Protocols Cytom. 9.11.1–9.11.10.

  • Lyons, A.B., Parish, C.R., 1994. Determination of lymphocyte division by flow cytometry. J. Immunol. Methods 171, 131–137.

    Article  Google Scholar 

  • Marsden, J.E., Hughes, T.J.R., 1994. Mathematical Foundations of Elasticity. Dover, Mineola.

    Google Scholar 

  • Matera, G., Lupi, M., Ubezio, P., 2004. Heterogeneous cell response to topotecan in a CFSE-based proliferative test. Cytometry A 62, 118–128.

    Article  Google Scholar 

  • Ogden, R.W., 1984. Non-Linear Elastic Deformations. Dover, Mineola.

    Google Scholar 

  • Quah, B., Warren, H., Parish, C., 2007. Monitoring lymphocyte proliferation in vitro and in vivo with the intracellular fluorescent dye carboxyfluorescein diacetate succinimidyl ester. Nat. Protocols 2, 2049–2056.

    Article  Google Scholar 

  • Seber, G.A.F., Wild, C.J., 2003. Nonlinear Regression. Wiley, Hoboken.

    Google Scholar 

  • Shampine, L.F., 2005. Solving hyperbolic PDEs in MATLAB. Appl. Numer. Anal. Comput. Math. 2, 346–358.

    Article  MATH  MathSciNet  Google Scholar 

  • Sinko, J., Streifer, W., 1967. A new model for age-size structure of a population. Ecology 48, 910–918.

    Article  Google Scholar 

  • Smith, J.A., Martin, L., 1973. Do cells cycle? Proc. Natl. Acad. Sci. USA 70, 1263–1267.

    Article  Google Scholar 

  • Wikipedia, 2010. http://en.wikipedia.org/wiki/Fluorescence_spectroscopy.

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Authors and Affiliations

  1. Center for Research in Scientific Computation, Center for Quantitative Science in Biomedicine, North Carolina State University, Raleigh, NC, 27695-8212, USA

    H. T. Banks, Karyn L. Sutton & W. Clayton Thompson

  2. Institute of Numerical Mathematics, RAS, Moscow, Russia

    Gennady Bocharov

  3. Department of Computer Science, Katholieke Universiteit, Lueven, Belgium

    Dirk Roose

  4. Department of Virology, University of the Saarland, Homburg, Germany

    Tim Schenkel

  5. Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona, 08003, Spain

    Andreas Meyerhans

Authors
  1. H. T. Banks
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  2. Karyn L. Sutton
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  3. W. Clayton Thompson
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  4. Gennady Bocharov
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  5. Dirk Roose
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  6. Tim Schenkel
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  7. Andreas Meyerhans
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Correspondence to H. T. Banks.

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Banks, H.T., Sutton, K.L., Clayton Thompson, W. et al. Estimation of Cell Proliferation Dynamics Using CFSE Data. Bull. Math. Biol. 73, 116–150 (2011). https://doi.org/10.1007/s11538-010-9524-5

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  • DOI: https://doi.org/10.1007/s11538-010-9524-5

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