American Institute of Mathematical Sciences

Advanced
2012, 9(4): 699-736. doi: 10.3934/mbe.2012.9.699

A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

H. Thomas Banks 1, , W. Clayton Thompson 2, , Cristina Peligero 3, , Sandra Giest 3, , Jordi Argilaguet 3, and  Andreas Meyerhans 3,

1. 

Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212
2. 

Center for Research in Scientific Computation, and Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, United States
3. 

ICREA Infection Biology Lab, Department of Experimental and Health Sciences, Univ. Pompeu Fabra, 08003 Barcelona, Spain, Spain, Spain, Spain

Received  February 2012 Revised  July 2012 Published  October 2012

Some key features of a mathematical description of an immune response are an estimate of the number of responding cells and the manner in which those cells divide, differentiate, and die. The intracellular dye CFSE is a powerful experimental tool for the analysis of a population of dividing cells, and numerous mathematical treatments have been aimed at using CFSE data to describe an immune response [30,31,32,37,38,42,48,49]. Recently, partial differential equation structured population models, with measured CFSE fluorescence intensity as the structure variable, have been shown to accurately fit histogram data obtained from CFSE flow cytometry experiments [18,19,52,54]. In this report, the population of cells is mathematically organized into compartments, with all cells in a single compartment having undergone the same number of divisions. A system of structured partial differential equations is derived which can be fit directly to CFSE histogram data. From such a model, cell counts (in terms of the number of divisions undergone) can be directly computed and thus key biological parameters such as population doubling time and precursor viability can be determined. Mathematical aspects of this compartmental model are discussed, and the model is fit to a data set. As in [18,19], we find temporal and division dependence in the rates of proliferation and death to be essential features of a structured population model for CFSE data. Variability in cellular autofluorescence is found to play a significant role in the data, as well. Finally, the compartmental model is compared to previous work, and statistical aspects of the experimental data are discussed.
Keywords: partial differential equations, cell division number, inverse problems., Cell proliferation, CFSE, label structured population dynamics.
Mathematics Subject Classification: Primary: 49N45, 92C37, 97M10; Secondary: 35F16, 35L4.
Citation: H. Thomas Banks, W. Clayton Thompson, Cristina Peligero, Sandra Giest, Jordi Argilaguet, Andreas Meyerhans. A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays. Mathematical Biosciences & Engineering, 2012, 9 (4) : 699-736. doi: 10.3934/mbe.2012.9.699
References:
[1]

H. T. Banks, "A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering,", CRC Press/Taylor-Francis, (2012).   Google Scholar

[2]

H. T. Banks and Kathleen Bihari, Modelling and estimating uncertainty in parameter estimation,, Inverse Problems, 17 (2001), 95.  doi: 10.1088/0266-5611/17/1/308.  Google Scholar

[3]

H. T.Banks, V. A. Bokil, S. Hu, F. C. T. Allnutt, R. Bullis, A. K. Dhar and C. L. Browdy, Shrimp biomass and viral infection for production of biological countermeasures,, CRSC-TR05-45, 3 (2006), 05.   Google Scholar

[4]

H. T. Banks, D. M. Bortz and S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics,, Math. Biosciences, 183 (2003), 63.  doi: 10.1016/S0025-5564(02)00218-3.  Google Scholar

[5]

H. T. Banks, D. M. Bortz, G. A. Pinter and L. K. Potter, Modeling and imaging techniques with potential for application in bioterrorism,, CRSC-TR03-02, FR28 (2003), 03.   Google Scholar

[6]

H. T. Banks, L. W. Botsford, F. Kappel and C. Wang, Modeling and estimation in size structured population models,, LCDS/CSS Report 87-13, (1987), 87.   Google Scholar

[7]

H. T. Banks, Frederique Charles, Marie Doumic, Karyn L. Sutton and W. Clayton Thompson, Label structured cell proliferation models,, Appl. Math. Letters, 23 (2010), 1412.  doi: 10.1016/j.aml.2010.07.009.  Google Scholar

[8]

H. T. Banks, M. Davidian, J. Samuels and K. L. Sutton, An inverse problem statistical methodology summary,, CRSC-TR08-01, (2008), 08.   Google Scholar

[9]

H. T. Banks and J. L. Davis, A comparison of approximation methods for the estimation of probability distributions on parameters,, Appl. Num. Math., 57 (2007), 753.  doi: 10.1016/j.apnum.2006.07.016.  Google Scholar

[10]

H. T. Banks, J. L. Davis, S. L. Ernstberger, S. Hu, E. Artimovich, A. K. Dhar and C. L. Browdy, A comparison of probabilistic and stochastic formulations in modeling growth uncertainty and variability,, CRSC-TR08-03, 3 (2009), 08.   Google Scholar

[11]

H. T. Banks and B. G. Fitzpatrick, Inverse problems for distributed systems: statistical tests and ANOVA,, LCDS/CSS Report 88-16, 81 (1989), 88.   Google Scholar

[12]

H. T. Banks and B. F. Fitzpatrick, Estimation of growth rate distributions in size-structured population models,, CAMS Tech. Rep. 90-2, 49 (1991), 90.   Google Scholar

[13]

H. T. Banks and N. L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters,, CRSC-TR04-01, 18 (2005), 04.   Google Scholar

[14]

H. T. Banks and N. L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters,, CRSC-TR05-29, 64 (2006), 05.   Google Scholar

[15]

H. T. Banks and K. Kunisch, "Estimation Techniques for Distributed Parameter Systems,", Birkhauser, (1989).   Google Scholar

[16]

H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue,, CRSC-TR04-03, 3 (2005), 04.   Google Scholar

[17]

H. T. Banks and L. K. Potter, Probabilistic methods for addressing uncertainty and variability in biological models: Application to a toxicokinetic model,, CRSC-TR02-27, 192 (2004), 02.   Google Scholar

[18]

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, 373 (2011), 11.  doi: 10.1016/j.jim.2011.08.014.  Google Scholar

[19]

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, 70 (2011), 09.  doi: 10.1007/s11538-010-9524-5.  Google Scholar

[20]

H. T. Banks, W. C. Thompson, C. Peligero, S. Giest, J. Argilaguet and A. Meyerhans, A compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays,, Technical Report CRSC-TR12-03, (2012), 12.   Google Scholar

[21]

H. T. Banks and H. T. Tran, "Mathematical and Experimental Modeling of Physical and Biological Processes,", CRC Press, (2009).   Google Scholar

[22]

H. T. Banks, B. G. Fitzpatrick, Laura K. Potter and Yue Zhang, Estimation of probability distributions for individual parameters using aggregate population observations,, CRSC-TR98-06, (1998), 98.   Google Scholar

[23]

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.   Google Scholar

[24]

K. P. Burnham and D. R. Anderson, "Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach,", (2nd Edition), (2002).   Google Scholar

[25]

Nigel J. Burroughs and P. Anton van der Merwe, Stochasticity and spatial heterogeneity in T-cell activation,, Immunological Reviews, 216 (2007), 69.   Google Scholar

[26]

R. Callard and P. D. Hodgkin, Modeling T- and B-cell growth and differentiation,, Immunological Reviews, 216 (2007), 119.   Google Scholar

[27]

Robin E. Callard, Jaroslav Stark and Andrew J. Yates, Fratricide: a mechanism for T memory-cell homeostasis,, Trends in Immunology, 24 (2003), 370.  doi: 10.1016/S1471-4906(03)00164-9.  Google Scholar

[28]

R. J. Carroll and D. Ruppert, "Transformation and Weighting in Regression,", Chapman Hall, (2000).   Google Scholar

[29]

M. Davidian and D. M. Giltinan, "Nonlinear Models for Repeated Measurement Data,", Chapman and Hall, (2000).   Google Scholar

[30]

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.  doi: 10.1007/s11538-006-9094-8.  Google Scholar

[31]

R. J. DeBoer and Alan S. Perelson, Estimating division and death rates from CFSE data,, J. Comp. and Appl. Mathematics, 184 (2005), 140.  doi: 10.1016/j.cam.2004.08.020.  Google Scholar

[32]

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.   Google Scholar

[33]

Mark R Dowling, Dejan Milutinovic and Philip D Hodgkin, Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?,, J. R. Soc. Interface, 2 (2005), 517.   Google Scholar

[34]

K. Duffy and V. Subramanian, On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics,, J. Math. Biol., 59 (2009), 255.  doi: 10.1007/s00285-008-0231-x.  Google Scholar

[35]

D. A. Fulcher and S. W. J. Wong, Carboxyfluorescein diacetate succinimidyl ester-based assays for assessment of T cell function in the diagnostic laboratory,, Immunology and Cell Biology, 77 (1999), 559.  doi: 10.1046/j.1440-1711.1999.00870.x.  Google Scholar

[36]

Vitaly V. Ganusov, Dejan Milutinovi and Rob J. De Boer, IL-2 regulates expansion of CD4+ T cell populations by affecting cell death: Insights from modeling CFSE data,, J. Immunology, 179 (2007), 950.   Google Scholar

[37]

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.  doi: 10.1016/j.jim.2005.01.011.  Google Scholar

[38]

A. V. Gett and P. D. Hodgkin, A cellular calculus for signal integration by T cells,, Nature Immunology, 1 (2000), 239.   Google Scholar

[39]

M. Kot, "Elements of Mathematical Ecology,", Cambridge University Press, (2001).   Google Scholar

[40]

M. Gyllenberg and G. F. Webb, A nonlinear structured population model of tumor growth with quiescence,, J. Math. Biol., 28 (1990), 671.  doi: 10.1007/BF00160231.  Google Scholar

[41]

J. Hasenauer, D. Schittler, and F. Allgöwer, A computational model for proliferation dynamics of division- and label-structured populations,, , (2012).   Google Scholar

[42]

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.   Google Scholar

[43]

E. D. Hawkins, J. F. Markham, L. P. McGuinness and P. D. Hodgkin, A single-cell pedigree analysis of alternative stochastic lymphocyte fates,, Proc. Natl. Acad. Sci., 106 (2009), 13457.  doi: 10.1073/pnas.0905629106.  Google Scholar

[44]

Mirja Hommel and Philip D. Hodgkin, TCR affinity promotes CD8+ T-cell expansion by regulating survival,, J. Immunology, 179 (2007), 2250.   Google Scholar

[45]

O. Hyrien and M. S. Zand, A mixture model with dependent observations for the analysis of CFSE-labeling experiments,, J. American Statistical Association, 103 (2008), 222.  doi: 10.1198/016214507000000194.  Google Scholar

[46]

O. Hyrien, R. Chen and M. S. Zand, An age-dependent branching process model for the analysis of CFSE-labeling experiments,, Biology Direct, 5 (2010).   Google Scholar

[47]

D. E. Kirschner, S. T. Chang, T. W. Riggs, N. Perry and J. J. Linderman, Toward a multiscale model of antigen presentation in immunity,, Immunological Reviews, 216 (2007), 93.   Google Scholar

[48]

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.  doi: 10.1007/s11538-009-9418-6.  Google Scholar

[49]

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.  doi: 10.1007/s11538-007-9239-4.  Google Scholar

[50]

K. Leon, J. Faro and J. Carneiro, A general mathematical framework to model generation structure in a population of asynchronously dividing cells,, J. Theoretical Biology, 229 (2004), 455.  doi: 10.1016/j.jtbi.2004.04.011.  Google Scholar

[51]

Y. Louzoun, The evolution of mathematical immunology,, Immunological Reviews, 216 (2007), 9.   Google Scholar

[52]

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.  doi: 10.1007/s00285-008-0244-5.  Google Scholar

[53]

T. Luzyanina, M. Mrusek, J. T. Edwards, D. Roose, S. Ehl and G. Bocharov, Computational analysis of CFSE proliferation assay,, J. Math. Biol., 54 (2007), 57.  doi: 10.1007/s00285-006-0046-6.  Google Scholar

[54]

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).   Google Scholar

[55]

A. B. Lyons and C. R. Parish, Determination of lymphocyte division by flow cytometry,, J. Immunol. Methods, 171 (1994), 131.  doi: 10.1016/0022-1759(94)90236-4.  Google Scholar

[56]

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.  doi: 10.1016/S0091-679X(01)63021-8.  Google Scholar

[57]

G. Matera, M. Lupi and P. Ubezio, Heterogeneous cell response to topotecan in a CFSE-based proliferative test,, Cytometry A, 62 (2004), 118.  doi: 10.1002/cyto.a.20097.  Google Scholar

[58]

J. A. Metz and O. Diekmann, "The Dynamics of Physiologically Structured Populations,", Springer Lecture Notes in Biomathematics, 68 (1986).   Google Scholar

[59]

H. Miao, X. Jin, A. Perelson and H. Wu, Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data,, Bull. Math. Biol., 74 (2012), 300.  doi: 10.1007/s11538-011-9668-y.  Google Scholar

[60]

Robert E. Nordon, Kap-Hyoun Ko, Ross Odell and Timm Schroeder, Multi-type branching models to describe cell differentiation programs,, J. Theoretical Biology, 277 (2011), 7.  doi: 10.1016/j.jtbi.2011.02.006.  Google Scholar

[61]

R. E. Nordon, M. Nakamura, C. Ramirez and R. Odell, Analysis of growth kinetics by division tracking,, Immunology and Cell Biology, 77 (1999), 523.  doi: 10.1046/j.1440-1711.1999.00869.x.  Google Scholar

[62]

C. Parish, Fluorescent dyes for lymphocyte migration and proliferation studies,, Immunology and Cell Biol., 77 (1999), 499.  doi: 10.1046/j.1440-1711.1999.00877.x.  Google Scholar

[63]

Sergei S. Pilyugin, Vitaly V. Ganusov, Kaja Murali-Krishnac, Rafi Ahmed and Rustom Antia, The rescaling method for quantifying the turnover of cell populations,, J. Theoretical Biology, 225 (2003), 275.  doi: 10.1016/S0022-5193(03)00245-5.  Google Scholar

[64]

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.   Google Scholar

[65]

P. Revy, M. Sospedra, B. Barbour and A. Trautmann, Functional antigen-independent synapses formed between T cells and dendritic cells,, Nature Immunology, 2 (2001), 925.   Google Scholar

[66]

G. A. Sever and C. J. Wild, "Nonlinear Regression,", Wiley, (2003).   Google Scholar

[67]

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), (2011), 165.   Google Scholar

[68]

J. Sinko and W. Streifer, A new model for age-size structure of a population,, Ecology, 48 (1967), 910.  doi: 10.2307/1934533.  Google Scholar

[69]

V. G. Subramanian, K. R. Duffy, M. L. Turner and P. D. Hodgkin, Determining the expected variability of immune responses using the cyton model,, J. Math. Biol., 56 (2008), 861.  doi: 10.1007/s00285-007-0142-2.  Google Scholar

[70]

David T. Terrano, Meenakshi Upreti and Timothy C. Chambers, Cyclin-dependent kinase 1-mediated $Bcl-x_L$/Bcl-2 phosphorylation acts as a functional link coupling mitotic arrest and apoptosis,, Mol. Cell. Biol., 30 (2010), 640.  doi: 10.1128/MCB.00882-09.  Google Scholar

[71]

W. Clayton Thompson, "Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays,", Ph.D. Dissertation, (2011).   Google Scholar

[72]

B. Tummers, DataThief III., 2006. (, ().   Google Scholar

[73]

M. L. Turner, E. D. Hawkins and P. D. Hodgkin, Quantitative regulation of B cell division destiny by signal strength,, J. Immunology, 181 (2008), 374.   Google Scholar

[74]

H. Veiga-Fernandez, U. Walter, C. Bourgeois, A. McLean and B. Rocha, Response of naive and memory CD8+ T cells to antigen stimulation in vivo,, Nature Immunology, 1 (2000), 47.   Google Scholar

[75]

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.   Google Scholar

[76]

C. Wellard, J. Markham, E. D. Hawkins and P. D. Hodgkin, The effect of correlations on the population dynamics of lymphocytes,, J. Theoretical Biology, 264 (2010), 443.  doi: 10.1016/j.jtbi.2010.02.019.  Google Scholar

[77]

J. M. Witkowski, Advanced application of CFSE for cellular tracking,, Current Protocols in Cytometry, (2008), 1.   Google Scholar

[78]

A. Yates, C. Chan, J. Strid, S. Moon, R. Callard, A. J. T. George and J. Stark, Reconstruction of cell population dynamics using CFSE,, BMC Bioinformatics, 8 (2007).   Google Scholar

show all references

References:
[1]

H. T. Banks, "A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering,", CRC Press/Taylor-Francis, (2012).   Google Scholar

[2]

H. T. Banks and Kathleen Bihari, Modelling and estimating uncertainty in parameter estimation,, Inverse Problems, 17 (2001), 95.  doi: 10.1088/0266-5611/17/1/308.  Google Scholar

[3]

H. T.Banks, V. A. Bokil, S. Hu, F. C. T. Allnutt, R. Bullis, A. K. Dhar and C. L. Browdy, Shrimp biomass and viral infection for production of biological countermeasures,, CRSC-TR05-45, 3 (2006), 05.   Google Scholar

[4]

H. T. Banks, D. M. Bortz and S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics,, Math. Biosciences, 183 (2003), 63.  doi: 10.1016/S0025-5564(02)00218-3.  Google Scholar

[5]

H. T. Banks, D. M. Bortz, G. A. Pinter and L. K. Potter, Modeling and imaging techniques with potential for application in bioterrorism,, CRSC-TR03-02, FR28 (2003), 03.   Google Scholar

[6]

H. T. Banks, L. W. Botsford, F. Kappel and C. Wang, Modeling and estimation in size structured population models,, LCDS/CSS Report 87-13, (1987), 87.   Google Scholar

[7]

H. T. Banks, Frederique Charles, Marie Doumic, Karyn L. Sutton and W. Clayton Thompson, Label structured cell proliferation models,, Appl. Math. Letters, 23 (2010), 1412.  doi: 10.1016/j.aml.2010.07.009.  Google Scholar

[8]

H. T. Banks, M. Davidian, J. Samuels and K. L. Sutton, An inverse problem statistical methodology summary,, CRSC-TR08-01, (2008), 08.   Google Scholar

[9]

H. T. Banks and J. L. Davis, A comparison of approximation methods for the estimation of probability distributions on parameters,, Appl. Num. Math., 57 (2007), 753.  doi: 10.1016/j.apnum.2006.07.016.  Google Scholar

[10]

H. T. Banks, J. L. Davis, S. L. Ernstberger, S. Hu, E. Artimovich, A. K. Dhar and C. L. Browdy, A comparison of probabilistic and stochastic formulations in modeling growth uncertainty and variability,, CRSC-TR08-03, 3 (2009), 08.   Google Scholar

[11]

H. T. Banks and B. G. Fitzpatrick, Inverse problems for distributed systems: statistical tests and ANOVA,, LCDS/CSS Report 88-16, 81 (1989), 88.   Google Scholar

[12]

H. T. Banks and B. F. Fitzpatrick, Estimation of growth rate distributions in size-structured population models,, CAMS Tech. Rep. 90-2, 49 (1991), 90.   Google Scholar

[13]

H. T. Banks and N. L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters,, CRSC-TR04-01, 18 (2005), 04.   Google Scholar

[14]

H. T. Banks and N. L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters,, CRSC-TR05-29, 64 (2006), 05.   Google Scholar

[15]

H. T. Banks and K. Kunisch, "Estimation Techniques for Distributed Parameter Systems,", Birkhauser, (1989).   Google Scholar

[16]

H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue,, CRSC-TR04-03, 3 (2005), 04.   Google Scholar

[17]

H. T. Banks and L. K. Potter, Probabilistic methods for addressing uncertainty and variability in biological models: Application to a toxicokinetic model,, CRSC-TR02-27, 192 (2004), 02.   Google Scholar

[18]

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, 373 (2011), 11.  doi: 10.1016/j.jim.2011.08.014.  Google Scholar

[19]

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, 70 (2011), 09.  doi: 10.1007/s11538-010-9524-5.  Google Scholar

[20]

H. T. Banks, W. C. Thompson, C. Peligero, S. Giest, J. Argilaguet and A. Meyerhans, A compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays,, Technical Report CRSC-TR12-03, (2012), 12.   Google Scholar

[21]

H. T. Banks and H. T. Tran, "Mathematical and Experimental Modeling of Physical and Biological Processes,", CRC Press, (2009).   Google Scholar

[22]

H. T. Banks, B. G. Fitzpatrick, Laura K. Potter and Yue Zhang, Estimation of probability distributions for individual parameters using aggregate population observations,, CRSC-TR98-06, (1998), 98.   Google Scholar

[23]

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.   Google Scholar

[24]

K. P. Burnham and D. R. Anderson, "Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach,", (2nd Edition), (2002).   Google Scholar

[25]

Nigel J. Burroughs and P. Anton van der Merwe, Stochasticity and spatial heterogeneity in T-cell activation,, Immunological Reviews, 216 (2007), 69.   Google Scholar

[26]

R. Callard and P. D. Hodgkin, Modeling T- and B-cell growth and differentiation,, Immunological Reviews, 216 (2007), 119.   Google Scholar

[27]

Robin E. Callard, Jaroslav Stark and Andrew J. Yates, Fratricide: a mechanism for T memory-cell homeostasis,, Trends in Immunology, 24 (2003), 370.  doi: 10.1016/S1471-4906(03)00164-9.  Google Scholar

[28]

R. J. Carroll and D. Ruppert, "Transformation and Weighting in Regression,", Chapman Hall, (2000).   Google Scholar

[29]

M. Davidian and D. M. Giltinan, "Nonlinear Models for Repeated Measurement Data,", Chapman and Hall, (2000).   Google Scholar

[30]

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.  doi: 10.1007/s11538-006-9094-8.  Google Scholar

[31]

R. J. DeBoer and Alan S. Perelson, Estimating division and death rates from CFSE data,, J. Comp. and Appl. Mathematics, 184 (2005), 140.  doi: 10.1016/j.cam.2004.08.020.  Google Scholar

[32]

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.   Google Scholar

[33]

Mark R Dowling, Dejan Milutinovic and Philip D Hodgkin, Modelling cell lifespan and proliferation: is likelihood to die or to divide independent of age?,, J. R. Soc. Interface, 2 (2005), 517.   Google Scholar

[34]

K. Duffy and V. Subramanian, On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics,, J. Math. Biol., 59 (2009), 255.  doi: 10.1007/s00285-008-0231-x.  Google Scholar

[35]

D. A. Fulcher and S. W. J. Wong, Carboxyfluorescein diacetate succinimidyl ester-based assays for assessment of T cell function in the diagnostic laboratory,, Immunology and Cell Biology, 77 (1999), 559.  doi: 10.1046/j.1440-1711.1999.00870.x.  Google Scholar

[36]

Vitaly V. Ganusov, Dejan Milutinovi and Rob J. De Boer, IL-2 regulates expansion of CD4+ T cell populations by affecting cell death: Insights from modeling CFSE data,, J. Immunology, 179 (2007), 950.   Google Scholar

[37]

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.  doi: 10.1016/j.jim.2005.01.011.  Google Scholar

[38]

A. V. Gett and P. D. Hodgkin, A cellular calculus for signal integration by T cells,, Nature Immunology, 1 (2000), 239.   Google Scholar

[39]

M. Kot, "Elements of Mathematical Ecology,", Cambridge University Press, (2001).   Google Scholar

[40]

M. Gyllenberg and G. F. Webb, A nonlinear structured population model of tumor growth with quiescence,, J. Math. Biol., 28 (1990), 671.  doi: 10.1007/BF00160231.  Google Scholar

[41]

J. Hasenauer, D. Schittler, and F. Allgöwer, A computational model for proliferation dynamics of division- and label-structured populations,, , (2012).   Google Scholar

[42]

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.   Google Scholar

[43]

E. D. Hawkins, J. F. Markham, L. P. McGuinness and P. D. Hodgkin, A single-cell pedigree analysis of alternative stochastic lymphocyte fates,, Proc. Natl. Acad. Sci., 106 (2009), 13457.  doi: 10.1073/pnas.0905629106.  Google Scholar

[44]

Mirja Hommel and Philip D. Hodgkin, TCR affinity promotes CD8+ T-cell expansion by regulating survival,, J. Immunology, 179 (2007), 2250.   Google Scholar

[45]

O. Hyrien and M. S. Zand, A mixture model with dependent observations for the analysis of CFSE-labeling experiments,, J. American Statistical Association, 103 (2008), 222.  doi: 10.1198/016214507000000194.  Google Scholar

[46]

O. Hyrien, R. Chen and M. S. Zand, An age-dependent branching process model for the analysis of CFSE-labeling experiments,, Biology Direct, 5 (2010).   Google Scholar

[47]

D. E. Kirschner, S. T. Chang, T. W. Riggs, N. Perry and J. J. Linderman, Toward a multiscale model of antigen presentation in immunity,, Immunological Reviews, 216 (2007), 93.   Google Scholar

[48]

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.  doi: 10.1007/s11538-009-9418-6.  Google Scholar

[49]

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.  doi: 10.1007/s11538-007-9239-4.  Google Scholar

[50]

K. Leon, J. Faro and J. Carneiro, A general mathematical framework to model generation structure in a population of asynchronously dividing cells,, J. Theoretical Biology, 229 (2004), 455.  doi: 10.1016/j.jtbi.2004.04.011.  Google Scholar

[51]

Y. Louzoun, The evolution of mathematical immunology,, Immunological Reviews, 216 (2007), 9.   Google Scholar

[52]

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.  doi: 10.1007/s00285-008-0244-5.  Google Scholar

[53]

T. Luzyanina, M. Mrusek, J. T. Edwards, D. Roose, S. Ehl and G. Bocharov, Computational analysis of CFSE proliferation assay,, J. Math. Biol., 54 (2007), 57.  doi: 10.1007/s00285-006-0046-6.  Google Scholar

[54]

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).   Google Scholar

[55]

A. B. Lyons and C. R. Parish, Determination of lymphocyte division by flow cytometry,, J. Immunol. Methods, 171 (1994), 131.  doi: 10.1016/0022-1759(94)90236-4.  Google Scholar

[56]

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.  doi: 10.1016/S0091-679X(01)63021-8.  Google Scholar

[57]

G. Matera, M. Lupi and P. Ubezio, Heterogeneous cell response to topotecan in a CFSE-based proliferative test,, Cytometry A, 62 (2004), 118.  doi: 10.1002/cyto.a.20097.  Google Scholar

[58]

J. A. Metz and O. Diekmann, "The Dynamics of Physiologically Structured Populations,", Springer Lecture Notes in Biomathematics, 68 (1986).   Google Scholar

[59]

H. Miao, X. Jin, A. Perelson and H. Wu, Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data,, Bull. Math. Biol., 74 (2012), 300.  doi: 10.1007/s11538-011-9668-y.  Google Scholar

[60]

Robert E. Nordon, Kap-Hyoun Ko, Ross Odell and Timm Schroeder, Multi-type branching models to describe cell differentiation programs,, J. Theoretical Biology, 277 (2011), 7.  doi: 10.1016/j.jtbi.2011.02.006.  Google Scholar

[61]

R. E. Nordon, M. Nakamura, C. Ramirez and R. Odell, Analysis of growth kinetics by division tracking,, Immunology and Cell Biology, 77 (1999), 523.  doi: 10.1046/j.1440-1711.1999.00869.x.  Google Scholar

[62]

C. Parish, Fluorescent dyes for lymphocyte migration and proliferation studies,, Immunology and Cell Biol., 77 (1999), 499.  doi: 10.1046/j.1440-1711.1999.00877.x.  Google Scholar

[63]

Sergei S. Pilyugin, Vitaly V. Ganusov, Kaja Murali-Krishnac, Rafi Ahmed and Rustom Antia, The rescaling method for quantifying the turnover of cell populations,, J. Theoretical Biology, 225 (2003), 275.  doi: 10.1016/S0022-5193(03)00245-5.  Google Scholar

[64]

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.   Google Scholar

[65]

P. Revy, M. Sospedra, B. Barbour and A. Trautmann, Functional antigen-independent synapses formed between T cells and dendritic cells,, Nature Immunology, 2 (2001), 925.   Google Scholar

[66]

G. A. Sever and C. J. Wild, "Nonlinear Regression,", Wiley, (2003).   Google Scholar

[67]

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), (2011), 165.   Google Scholar

[68]

J. Sinko and W. Streifer, A new model for age-size structure of a population,, Ecology, 48 (1967), 910.  doi: 10.2307/1934533.  Google Scholar

[69]

V. G. Subramanian, K. R. Duffy, M. L. Turner and P. D. Hodgkin, Determining the expected variability of immune responses using the cyton model,, J. Math. Biol., 56 (2008), 861.  doi: 10.1007/s00285-007-0142-2.  Google Scholar

[70]

David T. Terrano, Meenakshi Upreti and Timothy C. Chambers, Cyclin-dependent kinase 1-mediated $Bcl-x_L$/Bcl-2 phosphorylation acts as a functional link coupling mitotic arrest and apoptosis,, Mol. Cell. Biol., 30 (2010), 640.  doi: 10.1128/MCB.00882-09.  Google Scholar

[71]

W. Clayton Thompson, "Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays,", Ph.D. Dissertation, (2011).   Google Scholar

[72]

B. Tummers, DataThief III., 2006. (, ().   Google Scholar

[73]

M. L. Turner, E. D. Hawkins and P. D. Hodgkin, Quantitative regulation of B cell division destiny by signal strength,, J. Immunology, 181 (2008), 374.   Google Scholar

[74]

H. Veiga-Fernandez, U. Walter, C. Bourgeois, A. McLean and B. Rocha, Response of naive and memory CD8+ T cells to antigen stimulation in vivo,, Nature Immunology, 1 (2000), 47.   Google Scholar

[75]

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.   Google Scholar

[76]

C. Wellard, J. Markham, E. D. Hawkins and P. D. Hodgkin, The effect of correlations on the population dynamics of lymphocytes,, J. Theoretical Biology, 264 (2010), 443.  doi: 10.1016/j.jtbi.2010.02.019.  Google Scholar

[77]

J. M. Witkowski, Advanced application of CFSE for cellular tracking,, Current Protocols in Cytometry, (2008), 1.   Google Scholar

[78]

A. Yates, C. Chan, J. Strid, S. Moon, R. Callard, A. J. T. George and J. Stark, Reconstruction of cell population dynamics using CFSE,, BMC Bioinformatics, 8 (2007).   Google Scholar

[1]

Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1
[2]

Ali Ashher Zaidi, Bruce Van Brunt, Graeme Charles Wake. A model for asymmetrical cell division. Mathematical Biosciences & Engineering, 2015, 12 (3) : 491-501. doi: 10.3934/mbe.2015.12.491
[3]

Ricardo Borges, Àngel Calsina, Sílvia Cuadrado. Equilibria of a cyclin structured cell population model. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 613-627. doi: 10.3934/dcdsb.2009.11.613
[4]

Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. El-Dessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3771-3782. doi: 10.3934/dcdsb.2017189
[5]

Mostafa Adimy, Abdennasser Chekroun, Tarik-Mohamed Touaoula. Age-structured and delay differential-difference model of hematopoietic stem cell dynamics. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 2765-2791. doi: 10.3934/dcdsb.2015.20.2765
[6]

Janet Dyson, Rosanna Villella-Bressan, G.F. Webb. The steady state of a maturity structured tumor cord cell population. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 115-134. doi: 10.3934/dcdsb.2004.4.115
[7]

Qi Wang, Lifang Huang, Kunwen Wen, Jianshe Yu. The mean and noise of stochastic gene transcription with cell division. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1255-1270. doi: 10.3934/mbe.2018058
[8]

Jinliang Wang, Jiying Lang, Yuming Chen. Global dynamics of an age-structured HIV infection model incorporating latency and cell-to-cell transmission. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3721-3747. doi: 10.3934/dcdsb.2017186
[9]

Cristina Anton, Alan Yong. Stochastic dynamics and survival analysis of a cell population model with random perturbations. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1077-1098. doi: 10.3934/mbe.2018048
[10]

Tomas Alarcon, Philipp Getto, Anna Marciniak-Czochra, Maria dM Vivanco. A model for stem cell population dynamics with regulated maturation delay. Conference Publications, 2011, 2011 (Special) : 32-43. doi: 10.3934/proc.2011.2011.32
[11]

Fadia Bekkal-Brikci, Giovanna Chiorino, Khalid Boushaba. G1/S transition and cell population dynamics. Networks & Heterogeneous Media, 2009, 4 (1) : 67-90. doi: 10.3934/nhm.2009.4.67
[12]

Yangjin Kim, Soyeon Roh. A hybrid model for cell proliferation and migration in glioblastoma. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 969-1015. doi: 10.3934/dcdsb.2013.18.969
[13]

Keith E. Howard. A size structured model of cell dwarfism. Discrete & Continuous Dynamical Systems - B, 2001, 1 (4) : 471-484. doi: 10.3934/dcdsb.2001.1.471
[14]

Janet Dyson, Rosanna Villella-Bressan, G. F. Webb. The evolution of a tumor cord cell population. Communications on Pure & Applied Analysis, 2004, 3 (3) : 331-352. doi: 10.3934/cpaa.2004.3.331
[15]

Gabriella Di Blasio, Alfredo Lorenzi. Direct and inverse problems in age--structured population diffusion. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 539-563. doi: 10.3934/dcdss.2011.4.539
[16]

Mostafa Adimy, Laurent Pujo-Menjouet. Asymptotic behavior of a singular transport equation modelling cell division. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 439-456. doi: 10.3934/dcdsb.2003.3.439
[17]

Christian Engwer, Markus Knappitsch, Christina Surulescu. A multiscale model for glioma spread including cell-tissue interactions and proliferation. Mathematical Biosciences & Engineering, 2016, 13 (2) : 443-460. doi: 10.3934/mbe.2015011
[18]

Z.-R. He, M.-S. Wang, Z.-E. Ma. Optimal birth control problems for nonlinear age-structured population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 589-594. doi: 10.3934/dcdsb.2004.4.589
[19]

Shinji Nakaoka, Hisashi Inaba. Demographic modeling of transient amplifying cell population growth. Mathematical Biosciences & Engineering, 2014, 11 (2) : 363-384. doi: 10.3934/mbe.2014.11.363
[20]

A. Chauviere, L. Preziosi, T. Hillen. Modeling the motion of a cell population in the extracellular matrix. Conference Publications, 2007, 2007 (Special) : 250-259. doi: 10.3934/proc.2007.2007.250

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (17)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences