A division-dependent compartmental model with cyton and intracellular label dynamics

International Journal of Pure and Applied Mathematics

Volumn 77, Issue 1, 2012, Pages 119-147

  Banks, H T ^a   Thompson, W Clayton ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Cell division number; Cell proliferation; CFSE; Cyton models; Inverse problems; Label structured population dynamics; Partial differential equations

Indexed keywords

EID: 84861386338     PISSN: 13118080     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. H.T. Banks, M. Davidian, J. Samuels, and K.L. Sutton, An inverse problem statistical methodology summary, CRSC-TR08-01, North Carolina State University, January 2008; Chapter 11 in Mathematical and Statistical Estimation Approaches in Epidemiology, G. Chowell, et al., eds., Berlin Heidelberg New York, 2009, pp. 249-302.
2. H.T. Banks and B.G. Fitzpatrick, Inverse problems for distributed systems: statistical tests and ANOVA, LCDS/CSS Report 88-16, Brown University, July 1988; Proc. International Symposium on Math. Approaches to Envir. and Ecol. Problems, Springer Lecture Notes in Biomath., 81 (1989), 262-273.
3. H.T. Banks, Zackary R. Kenz, and W. Clayton Thompson, A review of selected techniques in inverse problem nonparametric probability distribution estimation, to appear.
4. H.T. Banks, Karyn L. Sutton, W. Clayton Thompson, G. Bocharov, Marie Doumic, Tim Schenkel, Jordi Argilaguet, Sandra Giest, Cristina Peligero, and Andreas Meyerhans, A new model for the estimation of cell proliferation dynamics using CFSE data, CRSC-TR11-05, North Carolina State University, Revised July 2011; J. Immunological Methods, 373 (2011), 143-160; DOI:10.1016/j.jim.2011.08. 014.
5. H.T. Banks, Karyn L. Sutton, W. Clayton Thompson, Gennady Bocharov, Dirk Roose, Tim Schenkel, and Andreas Meyerhans, Estimation of cell proliferation dynamics using CFSE data, CRSC-TR09-17, North Carolina State University, August 2009; Bull. Math. Biol., 70 (2011), 116-150.
6. H.T. Banks and W. Clayton Thompson, Mathematical models of dividing cell populations: Application to CFSE data, CRSC-TR12-10, N. C. State University, Raleigh, NC, April, 2012; J. Math. Modeling of Natural Phenomena, submitted.
7. H.T. Banks, W. Clayton Thompson, Cristina Peligero, Sandra Giest, Jordi Argilaguet, and Andreas Meyerhans, A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays, CRSC-TR12-03, North Carolina State University, January 2012; Math Biosci. Eng., submitted.
8. H.T. Banks and H.T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes, CRC Press, Boca Raton London New York, 2009.
9. G. Bell and E. Anderson, Cell growth and division I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures, Biophysical Journal, 7 (1967), 329-351.
10. K.P. Burnham and D.R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd Edition), Springer, New York, 2002.
11. R. Callard and P.D. Hodgkin, Modeling T- and B-cell growth and differentiation, Immunological Reviews, 216 (2007), 119-129. (Pubitemid 46426518)
12. R.J. Carroll and D. Ruppert, Transformation and Weighting in Regression, Chapman Hall, London, 2000.
13. M. Davidian and D.M. Giltinan, Nonlinear Models for Repeated Measurement Data, Chapman and Hall, London, 2000.
14. R.J. DeBoer, V.V. Ganusov, D. Milutinovic, P.D. Hodgkin, and A.S. Perelson, Estimating lymphocyte division and death rates from CFSE data, Bull. Math. Biol., 68 (2006), 1011-1031. (Pubitemid 44195536)
15. R.J. DeBoer and Alan S. Perelson, Estimating division and death rates from CFSE data, J. Comp. and Appl. Mathematics, 184 (2005), 140-164. (Pubitemid 41100717)
16. E.K. Deenick, A.V. Gett, and P.D. Hodgkin, Stochastic model of T cell proliferation: a calculus revealing IL-2 regulation of precursor frequencies, cell cycle time, and survival, J. Immunology, 170 (2003), 4963-4972. (Pubitemid 36554725)
17. V.V. Ganusov, S.S. Pilyugin, R.J. De Boer, K. Murali-Krishna, R. Ahmed, and R. Antia, Quantifying cell turnover using CFSE data, J. Immunological Methods, 298 (2005), 183-200. (Pubitemid 40545104)
18. A.V. Gett and P.D. Hodgkin, A cellular calculus for signal integration by T cells, Nature Immunology, 1 (2000), 239-244.
19. J. Hasenauer, D. Schittler, and F. Allgöwer, A computational model for proliferation dynamics of division- and label-structured populations, arXive.org, arXiv:1202.4923v1,22Feb,2012.
20. E.D. Hawkins, Mirja Hommel, M.L Turner, Francis Battye, J Markham and P.D Hodgkin, Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data, Nature Protocols, 2 (2007), 2057-2067. (Pubitemid 351565843)
21. E.D. Hawkins, M.L. Turner, M.R. Dowling, C. van Gend, and P.D. Hodgkin, A model of immune regulation as a consequence of randomized lymphocyte division and death times, Proc. Natl. Acad. Sci., 104 (2007), 5032-5037. (Pubitemid 47186171)
22. H.Y. Lee, E.D. Hawkins, M.S. Zand, T. Mosmann, H. Wu, P.D. Hodgkin, and A.S. Perelson, Interpreting CFSE obtained division histories of B cells in vitro with Smith-Martin and Cyton type models, Bull. Math. Biol., 71 (2009), 1649-1670.
23. H.Y. Lee and A.S. Perelson, Modeling T cell proliferation and death in vitro based on labeling data: generalizations of the Smith-Martin cell cycle model, Bull. Math. Biol., 70 (2008), 21-44.
24. T. Luzyanina, D. Roose, and G. Bocharov, Distributed parameter identification for a label-structured cell population dynamics model using CFSE histogram time-series data, J. Math. Biol., 59 (2009), 581-603.
25. T. Luzyanina, D. Roose, T. Schenkel, M. Sester, S. Ehl, A. Meyerhans, and G. Bocharov, Numerical modelling of label-structured cell population growth using CFSE distribution data, Theoretical Biology and Medical Modelling, 4 (2007), Published Online.
26. A. B. Lyons, Divided we stand: tracking cell proliferation with carboxyfluorescein diacetate succinimidyl ester, Immunology and Cell Biology, 77 (1999), 509-515.
27. A. B. Lyons, J. Hasbold and P.D. Hodgkin, Flow cytometric analysis of cell division history using diluation of carboxyfluorescein diacetate succinimidyl ester, a stably integrated fluorescent probe, Methods in Cell Biology, 63 (2001), 375-398.
28. A. B. Lyons and K. V. Doherty, Flow cytometric analysis of cell division by dye dilution, Current Protocols in Cytometry, (2004), 9.11.1-9.11.10.
29. A.B. Lyons and C.R. Parish, Determination of lymphocyte division by flow cytometry, J. Immunol. Methods, 171 (1994), 131-137. (Pubitemid 24140219)
30. G. Matera, M. Lupi and P. Ubezio, Heterogeneous cell response to topotecan in a CFSE-based proliferative test, Cytometry A, 62 (2004), 118-128. (Pubitemid 39579242)
31. J.A. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, Springer Lecture Notes in Biomathematics 68, Heidelberg, 1986.
32. H. Miao, X. Jin, A. Perelson and H. Wu, Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data, Bull. Math. Biol., 74 (2012), 300-326; DOI 10.1007/s11538-011-9668-y.
33. C. Parish, Fluorescent dyes for lymphocyte migration and proliferation studies, Immunology and Cell Biol., 77 (1999), 499-508.
34. B.J.C. Quah and C.R. Parish, New and improved methods for measuring lymphocyte proliferation in vitro and in vivo using CFSE-like fluorescent dyes, J. Immunological Methods, (2012), to appear.
35. B. Quah, H. Warren, and C. Parish, Monitoring lymphocyte proliferation in vitro and in vivo with the intracellular fluorescent dye carboxyfluorescein diacetate succinimidyl ester, Nature Protocols, 2 (2007), 2049-2056. (Pubitemid 351565842)
36. D. Schittler, J. Hasenauer, and F. Allgöwer, A generalized model for cell proliferation: Integrating division numbers and label dynamics, Proc. Eighth International Workshop on Computational Systems Biology (WCSB 2011), June 2011, Zurich, Switzerland, p. 165-168.
37. G.A. Seber and C.J. Wild, Nonlinear Regression, Wiley, Hoboken, 2003.
38. J.A. Smith and L. Martin, Do cells cycle?, Proc. Natl. Acad. Sci., 70 (1973), 1263-1267.
39. W. Clayton Thompson, Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays, Ph.D. Dissertation, Dept. of Mathematics, North Carolina State University, Raleigh, December, 2011.
40. P.K. Wallace, J.D. Tario, Jr., J.L. Fisher, S.S. Wallace, M.S. Ernstoff, and K.A. Muirhead, Tracking antigen-driven responses by flow cytometry: monitoring proliferation by dye dilution, Cytometry A, 73 (2008), 1019-1034.
41. Hilary S. Warren, Using carboxyfluorescein diacetate succinimidyl ester to monitor human NK cell division: Analysis of the effect of activating and inhibitory class I MHC receptors, Immunology and Cell Biology, 77 (1999), 544-551.
42. J.M. Witkowski, Advanced application of CFSE for cellular tracking, Current Protocols in Cytometry, (2008), 9.25.1-9.25.8.