Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division

Journal of Mathematical Biology

Volumn 69, Issue 6-7, 2014, Pages 1547-1583

  Luzyanina, Tatyana ^a   Cupovic, Jovana ^b   Ludewig, Burkhard ^b   Bocharov, Gennady ^c  

^a INSTITUTE OF MATHEMATICAL PROBLEMS OF BIOLOGY   (Russian Federation)

^b CANTONAL HOSPITAL ST GALLEN   (Switzerland)

^c INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

Asymmetric cell division; Delay hyperbolic PDE model; Division and label structured cell population dynamics; Inverse problem

Indexed keywords

EID: 84889825590     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-013-0741-z     Document Type: Article

References (63)

1. Akbarian V, Wang W, Audet J (2012) Measurement of generation-dependent proliferation rates and death rates during mouse erythroid progenitor cell differentiation. Cytometry A 81(5):382–389
2. Andrew SM, Baker CTH, Bocharov GA (2007) Rival approaches to mathematical modelling in immunology. J Comput Appl Math 205:669–686
3. Baker CTH, Bocharov GA, Paul CAH, Rihan FA (2005) Computational modelling with functional differential equations: identification, selection and sensitivity. Appl Numer Math 53:107–129
4. Banks HT, Thompson WC (2012) Mathematical models of dividing cell populations: application to CFSE data. Math Model Nat Phenom 7(5):24–52
5. Banks HT, Sutton KL, Thompson WC, Bocharov G, Roose D, Schenkel T, Meyerhans A (2011a) Estimation of cell proliferation dynamics using CFSE data. Bull Math Biol 70:116–150
6. Banks HT, Sutton KL, Thompson WC, Bocharov G, Doumic M, Schenkel T, Argilaguet J, Giest S, Peligero C, Meyerhans A (2011b) A new model for the estimation of cell proliferation dynamics using CFSE data. J Immunol Methods 373:143–160
7. Banks HT, Thompson WC, Peligero C, Giest S, Argilaguet J, Meyerhans A (2012) A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assay. CRSC-TR12-03, North Carolina State University
8. Banks HT, Kapraun DF, Thompson WC, Peligero C, Argilaguet J, Meyerhans A (2013a) A novel statistical analysis and interpretation of flow cytometry data. J Biol Dyn 7(1):96–132
9. Banks HT, Choi A, Huffman T, Nardini J, Poag L, Thompson WC (2013b) Quantifying CFSE label decay in flow cytometry data. Appl Math Lett 26(5):571–577
10. Bergmann CC, Lane TE, Stohlman SA (2006) Coronavirus infection of the central nervous system: host-virus stand-off. Nat Rev Microbiol 4(2):121–132
11. Bernard S, Pujo-Menjouet L, Mackey MC (2003) Analysis of cell kinetics using a cell division marker: mathematical modeling of experimental data. Biophys J 84(5):3414–3424
12. Burnham KP, Anderson DR (2002) Model selection and multimodel inference–a practical information-theoretic approach, 2nd edn. Springer, New York
13. Chang JT, Palanivel VR, Kinjyo I, Schambach F, Intlekofer AM, Banerjee A, Longworth SA, Vinup KE, Mrass P, Oliaro J, Killeen N, Orange JS, Russell SM, Weninger W, Reiner SL (2007) Asymmetric T lymphocyte division in the initiation of adaptive immune responses. Science 315(5819):1687–1691
14. Ciocca ML, Barnett BE, Burkhardt JK, Chang JT, Reiner SL (2012) Cutting edge: asymmetric memory T cell division in response to rechallenge. J Immunol 188(9):4145–4148
15. De Boer RJ, Perelson AS (2005) Estimating division and death rates from CFSE data. J Comput Appl Math 184:140–164
16. De Boer RJ, Perelson AS (2013) Quantifying T lymphocyte turnover. J Theor Biol 327:45–87
17. De Boer RJ, Oprea M, Antia R, Murali-Krishna K, Ahmed R, Perelson AS (2001) Recruitment times, proliferation, and apoptosis rates during the $$\text( CD8 )^+$$CD8+ T-cell response to lymphocytic choriomeningitis virus. J Virol 75(22):10663–10669
18. Fernandes RL, Nierychlo M, Lundin L, Pedersen AE, Puentes Tellez PE, Dutta A, Carlquist M, Bolic A, Schpper D, Brunetti AC, Helmark S, Heins AL, Jensen AD, Nopens I, Rottwitt K, Szita N, van Elsas JD, Nielsen PH, Martinussen J, Srensen SJ, Lantz AE, Gernaey KV (2011) Experimental methods and modeling techniques for description of cell population heterogeneity. Biotechnol Adv 29(6):575–599
19. Ganusov VV, Pilyugin SS, de Boer RJ, Murali-Krishna K, Ahmed R, Antia R (2005) Quantifying cell turnover using CFSE data. J Immunol Methods 298(1–2):183–200
20. Gershenfeld N (2002) The nature of mathematical modelling. Cambridge University Press, Cambridge
21. Gyllenberg M (1986) The size and scar distributions of the yeast Saccharomyces cerevisiae. J Math Biol 24:81–101
22. Hadamard J (1932) Le probléme de Cauchy et les équations aux dérivées partielles linéaires hyperboliques. Hermann, Paris
23. Hasenauer J, Schittler D, Allgöwer F (2012a) A computational model for proliferation dynamics of division- and label-structured populations. arXiv:1202.4923v1[q-bio.PE]
24. Hasenauer J, Schittler D, Allgöwer F (2012b) Analysis and simulation of division- and label-structured population models: a new tool to analyze proliferation assays. Bull Math Biol 74(11):2692–2732
25. Hawkins ED, Turner ML, Dowling MR, van Gend C, Hodgkin PD (2007) A model of immune regulation as a consequence of randomized lymphocyte division and death times. Proc Natl Acad Sci USA 104(12):5032–5037
26. Kendall DG (1948) On the role of variable generation time in the development of a stochastic birth process. Biometrika 35:316–330
27. Knuth, KH (2006) Optimal data-based binning for histograms. arXiv:physics/0605197 [physics.data-an]
28. Ko KH, Odell R, Nordon RE (2007) Analysis of cell differentiation by division tracking cytometry. Cytometry A 71(10):773–782
29. Kosarev EL, Pantos E (1983) Optimal smoothing of ‘noisy’ data by fast Fourier transform. J Phys E Sci Instrum 16:537–543
30. Lee HY, Hawkins E, Zand MS, Mosmann T, Wu H, Hodgkin PD, Perelson AS (2009) Interpreting CFSE obtained division histories of B cells in vitro with Smith–Martin and cyton type models. Bull Math Biol 71(7):1649–1670
31. Ludewig B, Krebs P, Junt T, Metters H, Ford NJ, Anderson RM, Bocharov G (2004) Determining control parameters for dendritic cell-cytotoxic T lymphocyte interaction. Eur J Immunol 34:2407–2418
32. Luzyanina T, Mrusek S, Edwards JT, Roose D, Ehl S, Bocharov G (2007a) Computational analysis of CFSE proliferation assay. J Math Biol 54(1):57–89
33. Luzyanina T, Roose D, Schenkel T, Sester M, Ehl S, Meyerhans A, Bocharov G (2007b) Numerical modelling of label-structured cell population growth using CFSE distribution data. Theor Biol Med Model 24:4–26
34. 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(5):581–603
35. Lyons AB (2000) Analysing cell division in vivo and in vitro using flow cytometric measurement of CFSE dye dilution. J Immunol Methods 243(1–2):147–154
36. Lyons AB, Parish CR (1994) Determination of lymphocyte division by flow cytometry. J Immunol Methods 171(1):131–137
37. Mackey MC, Rudnicki R (1994) Global stability in a delayed partial differential equation describing cellular replication. J Math Biol 33:89–109
38. Mantzaris NV (2006) Stochastic and deterministic simulations of heterogeneous cell population dynamics. J Theor Biol 241(3):690–706
39. Mantzaris NV (2007) From single-cell genetic architecture to cell population dynamics: quantitatively decomposing the effects of different population heterogeneity sources for a genetic network with positive feedback architecture. Biophys J 92(12):4271–4288
40. Mantzaris NV, Liou J, Daoutidis P, Srienc F (1999) Numerical solution of a mass structured cell population balance model in an environment of changing substrate concentration. J Biotechnol 71:157–174
41. Matera G, Lupi M, Ubezio P (2004) Heterogeneous cell response to topotecan in a CFSE-based proliferation test. Cytometry A 62(2):118–128
42. McKendrick AG (1925) Applications of mathematics to medical problems. Proc Edinb Math Soc 44:98–130
43. Metzger P (2012) A unified growth model for division-, age- and label-structured cell populations. University of Stuttgart, Stuttgart, Germany, Diploma Thesis
44. Metzger P, Hasenauer J, Allgöwer F (2012) Modeling and analysis of division-, age-, and label-structured cell populations. In: Proceedings of the 9th workshop on computational systems biology (WCSB), vol 9, Ulm, Germany
45. Miao H, Jin X, Perelson AS, Wu H (2012) Evaluation of multitype mathematical models for CFSE-labeling experiment data. Bull Math Biol 74(2):300–326
46. Monod J (1949) The growth of bacterial cultures. Ann Rev Microbiol 3:371–394
47. Nordon RE, Nakamura M, Ramirez C, Odell R (1999) Analysis of growth kinetics by division tracking. Immunol Cell Biol 77(6):523–529
48. Nordon RE, Ko KH, Odell R, Schroeder T (2011) Multi-type branching models to describe cell differentiation programs. J Theor Biol 277(1):7–18
49. Pagliara D, Savoldo B (2012) Cytotoxic T lymphocytes for the treatment of viral infections and posttransplant lymphoproliferative disorders in transplant recipients. Curr Opin Infect Dis 25(4):431–437
50. Pilyugin SS, Ganusov VV, Murali-Krishna K, Ahmed R, Antia R (2003) The rescaling method for quantifying the turnover of cell populations. J Theor Biol 225(2):275–83
51. Quah BJ, Parish CR (2012) New and improved methods for measuring lymphocyte proliferation in vitro and in vivo using CFSE-like fluorescent dyes. J Immunol Methods 379(1–2):1–14
52. Roederer M (2011) Interpretation of cellular proliferation data: avoid the panglossian. Cytometry A 79(2):95–101
53. Schittler D, Hasenauer J, Allgöwer F (2011) A generalized model for cellproliferation: Integrating division numbers and label dynamics. In: Proceedings of the eight international workshop on computationalsystems biology (WCSB, 2011), Zurich, Switzerland, pp 165–168
54. Scott DW (1979) On optimal and data-based histograms. Biometrika 66(3):605–610
55. Sennerstam R (1988) Partition of protein (mass) to sister cell pairs at mitosis: a re-evaluation. J Cell Sci 90(2):301–306
56. Smith JA, Martin L (1973) Do cells cycle? Proc Natl Acad Sci USA 70(4):1263–1267
57. Sturges HA (1926) The choice of a class interval. J Am Stat Assoc 21(153):65–66
58. Taylor CC (1987) Akaike’s information criterion and the histogram. Biometrika 74(3):636–639
59. Thompson WC (2011) Partial differential equation modelling of flow cytometry data from CFSE-based proliferation assays. PhD Dissertation. Department of Mathematics, North Carolina State University, Raleigh
60. Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Winston & Sons, Washington, DC
61. Venzon DJ, Moolgavkar SH (1988) A method for computing profile-likelihood-based confidence intervals. Appl Stat 37(1):87–94
62. Wallace PK, Tario JD Jr, Fisher JL, Wallace SS, Ernstoff MS, Muirhead KA (2008) Tracking antigen-driven responses by flow cytometry: monitoring proliferation by dye dilution. Cytometry A 73(11):1019–1034
63. Wand MP (1997) Data-based choice of histograms bin width. Am Stat 51(1):59–64