Estimation of cell proliferation dynamics using CFSE data

Bulletin of Mathematical Biology

Volumn 73, Issue 1, 2011, Pages 116-150

  Banks, H T ^a   Sutton, Karyn L ^a   Thompson, W Clayton ^a   Bocharov, Gennady ^b   Roose, Dirk ^c   Schenkel, Tim ^d   Meyerhans, Andreas ^e  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^c UNIVERSITY OF LEUVEN   (Belgium)

^d SAARLAND UNIVERSITY   (Germany)

^e UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Cell proliferation; CFSE; Inverse problems; Label structured population dynamics; Partial differential equations

Indexed keywords

EID: 79151477438     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9524-5     Document Type: Article

References (52)

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Banks, H. T., Kunsich, K., 1989. Estimation Techniques for Distributed Parameter Systems. Birkhauser, Boston.
7. 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.
8. 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.
9. 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.
10. Banks, H. T., Tran, H. T., 2009. Mathematical and Experimental Modeling of Physical and Biological Processes. CRC Press, Boca Raton.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. Carroll, R. J., Ruppert, D., 2000. Transformation and Weighting in Regression. Chapman & Hall, London.
22. 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.
23. Davidian, M., Giltinan, D. M., 1995. Nonlinear Models for Repeated Measurement Data. Chapman & Hall, London.
24. 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.
25. Fung, Y. C., 1993. Biomechanics: Mechanical Properties of Living Tissue. Springer, Berlin.
26. Fung, Y. C., 1994. A First Course in Continuum Mechanics. Prentice Hall, Englewood Cliffs.
27. 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.
28. 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.
29. Gett, A. V., Hodgkin, P. D., 2000. A cellular calculus for signal integration by T cells. Nat. Immunol. 1, 239-244.
30. Gyllenberg, M., Webb, G. F., 1990. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol. 28, 671-694.
31. 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.
32. 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.
33. 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.
34. Komarova, N. L., 2006. Stochastic modeling of drug resistance in cancer. J. Theor. Biol. 239, 351-366.
35. 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.
36. 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.
37. 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.
38. 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.
39. 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.
40. 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.
41. Lyons, A. B., 1999. Divided we stand: tracking cell proliferation with carboxyfluorescein diacetate succinimidyl ester. Immunol. Cell Biol. 77, 509-515.
42. 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.
43. Lyons, A. B., Parish, C. R., 1994. Determination of lymphocyte division by flow cytometry. J. Immunol. Methods 171, 131-137.
44. Marsden, J. E., Hughes, T. J. R., 1994. Mathematical Foundations of Elasticity. Dover, Mineola.
45. Matera, G., Lupi, M., Ubezio, P., 2004. Heterogeneous cell response to topotecan in a CFSE-based proliferative test. Cytometry A 62, 118-128.
46. Ogden, R. W., 1984. Non-Linear Elastic Deformations. Dover, Mineola.
47. 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.
48. Seber, G. A. F., Wild, C. J., 2003. Nonlinear Regression. Wiley, Hoboken.
49. Shampine, L. F., 2005. Solving hyperbolic PDEs in MATLAB. Appl. Numer. Anal. Comput. Math. 2, 346-358.
50. Sinko, J., Streifer, W., 1967. A new model for age-size structure of a population. Ecology 48, 910-918.
51. Smith, J. A., Martin, L., 1973. Do cells cycle? Proc. Natl. Acad. Sci. USA 70, 1263-1267.
52. Wikipedia, 2010. http://en. wikipedia. org/wiki/Fluorescence_spectroscopy.