-
Previous Article
Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat
- MBE Home
- This Issue
- Next Article
A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays
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 |
References:
[1] |
H. T. Banks, "A Functional Analysis Framework for Modeling, Estimation and Control in Science and Engineering," CRC Press/Taylor-Francis, Boca Raton London New York, 2012. |
[2] |
H. T. Banks and Kathleen Bihari, Modelling and estimating uncertainty in parameter estimation, Inverse Problems, 17 (2001), 95-111.
doi: 10.1088/0266-5611/17/1/308. |
[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, North Carolina State University, December 2005; Mathematical Biosciences and Engineering, 3 (2006), 635-660. |
[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), 63-91.
doi: 10.1016/S0025-5564(02)00218-3. |
[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, North Carolina State University, January 2003; Chapter 6 in Bioterrorism: Mathematical Modeling Applications in Homeland Security, (eds. H. T. Banks and C. Castillo-Chavez), Frontiers in Applied Math, FR28, SIAM, Philadelphia, PA, 2003, 129-154. |
[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, Brown University, March 1987; Proc. 2nd Course on Math. Ecology, (Trieste, December 8-12, 1986) World Scientific Press, Singapore, 1988, 521-541. |
[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), 1412-1415.
doi: 10.1016/j.aml.2010.07.009. |
[8] |
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" (eds. G. Chowell, et al.), Berlin Heidelberg New York, 2009, 249-302. |
[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), 753-777.
doi: 10.1016/j.apnum.2006.07.016. |
[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, North Carolina State University, February 2008; Journal of Biological Dynamics, 3 (2009), 130-148. |
[11] |
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. |
[12] |
H. T. Banks and B. F. Fitzpatrick, Estimation of growth rate distributions in size-structured population models, CAMS Tech. Rep. 90-2, Univ. of Southern California, January 1990; Quart. Appl. Math., 49 (1991), 215-235. |
[13] |
H. T. Banks and N. L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters, CRSC-TR04-01, North Carolina State University, January 2004; Applied Math. Letters, 18 (2005), 423-430. |
[14] |
H. T. Banks and N. L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters, CRSC-TR05-29, North Carolina State University, August 2005; Quarterly of Applied Mathematics, 64 (2006), 749-795. |
[15] |
H. T. Banks and K. Kunisch, "Estimation Techniques for Distributed Parameter Systems," Birkhauser, Boston, 1989. |
[16] |
H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue, CRSC-TR04-03, North Carolina State University, January 2004; SIAM J. Multiscale Modeling and Simulation, 3 (2005), 395-412. |
[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, North Carolina State University, September 2002; Math. Biosci., 192 (2004), 193-225. |
[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, North Carolina State University, Revised July 2011; J. Immunological Methods, 373 (2011), 143-160.
doi: 10.1016/j.jim.2011.08.014. |
[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, North Carolina State University, August 2009; Bull. Math. Biol., 70 (2011), 116-150.
doi: 10.1007/s11538-010-9524-5. |
[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, North Carolina State University, January 2012. |
[21] |
H. T. Banks and H. T. Tran, "Mathematical and Experimental Modeling of Physical and Biological Processes," CRC Press, Boca Raton London New York, 2009. |
[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, North Carolina State University, January 1998; Stochastic Analysis, Control, Optimization and Applications, (eds. W. McEneaney, G. Yin and Q. Zhang), Birkhäuser, (1998), 353-371. |
[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), 329-351. |
[24] |
K. P. Burnham and D. R. Anderson, "Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach," (2nd Edition), Springer, New York, 2002. |
[25] |
Nigel J. Burroughs and P. Anton van der Merwe, Stochasticity and spatial heterogeneity in T-cell activation, Immunological Reviews, 216 (2007), 69-80. |
[26] |
R. Callard and P. D. Hodgkin, Modeling T- and B-cell growth and differentiation, Immunological Reviews, 216 (2007), 119-129. |
[27] |
Robin E. Callard, Jaroslav Stark and Andrew J. Yates, Fratricide: a mechanism for T memory-cell homeostasis, Trends in Immunology, 24 (2003), 370-375.
doi: 10.1016/S1471-4906(03)00164-9. |
[28] |
R. J. Carroll and D. Ruppert, "Transformation and Weighting in Regression," Chapman Hall, London, 2000. |
[29] |
M. Davidian and D. M. Giltinan, "Nonlinear Models for Repeated Measurement Data," Chapman and Hall, London, 2000. |
[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), 1011-1031.
doi: 10.1007/s11538-006-9094-8. |
[31] |
R. J. DeBoer and Alan S. Perelson, Estimating division and death rates from CFSE data, J. Comp. and Appl. Mathematics, 184 (2005), 140-164.
doi: 10.1016/j.cam.2004.08.020. |
[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), 4963-4972. |
[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), 517-526. |
[34] |
K. Duffy and V. Subramanian, On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics, J. Math. Biol., 59 (2009), 255-285.
doi: 10.1007/s00285-008-0231-x. |
[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), 559-564.
doi: 10.1046/j.1440-1711.1999.00870.x. |
[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), 950-957. |
[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), 183-200.
doi: 10.1016/j.jim.2005.01.011. |
[38] |
A. V. Gett and P. D. Hodgkin, A cellular calculus for signal integration by T cells, Nature Immunology, 1 (2000), 239-244. |
[39] |
M. Kot, "Elements of Mathematical Ecology," Cambridge University Press, Cambridge, UK, 2001. |
[40] |
M. Gyllenberg and G. F. Webb, A nonlinear structured population model of tumor growth with quiescence, J. Math. Biol., 28 (1990), 671-694.
doi: 10.1007/BF00160231. |
[41] |
J. Hasenauer, D. Schittler, and F. Allgöwer, A computational model for proliferation dynamics of division- and label-structured populations, arXiv:1202.4923v1, 22 Feb, 2012. |
[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), 2057-2067. |
[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), 13457-13462.
doi: 10.1073/pnas.0905629106. |
[44] |
Mirja Hommel and Philip D. Hodgkin, TCR affinity promotes CD8+ T-cell expansion by regulating survival, J. Immunology, 179 (2007), 2250-2260. |
[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), 222-239.
doi: 10.1198/016214507000000194. |
[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), Published Online. |
[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), 93-118. |
[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), 1649-1670.
doi: 10.1007/s11538-009-9418-6. |
[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), 21-44.
doi: 10.1007/s11538-007-9239-4. |
[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), 455-476.
doi: 10.1016/j.jtbi.2004.04.011. |
[51] |
Y. Louzoun, The evolution of mathematical immunology, Immunological Reviews, 216 (2007), 9-20. |
[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), 581-603.
doi: 10.1007/s00285-008-0244-5. |
[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), 57-89.
doi: 10.1007/s00285-006-0046-6. |
[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), Published Online. |
[55] |
A. B. Lyons and C. R. Parish, Determination of lymphocyte division by flow cytometry, J. Immunol. Methods, 171 (1994), 131-137.
doi: 10.1016/0022-1759(94)90236-4. |
[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), 375-398.
doi: 10.1016/S0091-679X(01)63021-8. |
[57] |
G. Matera, M. Lupi and P. Ubezio, Heterogeneous cell response to topotecan in a CFSE-based proliferative test, Cytometry A, 62 (2004), 118-128.
doi: 10.1002/cyto.a.20097. |
[58] |
J. A. Metz and O. Diekmann, "The Dynamics of Physiologically Structured Populations," Springer Lecture Notes in Biomathematics, 68, 1986. |
[59] |
H. Miao, X. Jin, A. Perelson and H. Wu, Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data, Bull. Math. Biol., 74 (2012), 300-326.
doi: 10.1007/s11538-011-9668-y. |
[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), 7-18.
doi: 10.1016/j.jtbi.2011.02.006. |
[61] |
R. E. Nordon, M. Nakamura, C. Ramirez and R. Odell, Analysis of growth kinetics by division tracking, Immunology and Cell Biology, 77 (1999), 523-529.
doi: 10.1046/j.1440-1711.1999.00869.x. |
[62] |
C. Parish, Fluorescent dyes for lymphocyte migration and proliferation studies, Immunology and Cell Biol., 77 (1999), 499-508.
doi: 10.1046/j.1440-1711.1999.00877.x. |
[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), 275-283.
doi: 10.1016/S0022-5193(03)00245-5. |
[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), 2049-2056. |
[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), 925-931. |
[66] |
G. A. Sever and C. J. Wild, "Nonlinear Regression," Wiley, Hoboken, NJ, 2003. |
[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), June 2001, Zurich, Switzerland, 165-168 |
[68] |
J. Sinko and W. Streifer, A new model for age-size structure of a population, Ecology, 48 (1967), 910-918.
doi: 10.2307/1934533. |
[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), 861-892.
doi: 10.1007/s00285-007-0142-2. |
[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), 640-656.
doi: 10.1128/MCB.00882-09. |
[71] |
W. Clayton Thompson, "Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays," Ph.D. Dissertation, North Carolina State University, December, 2011. |
[72] |
B. Tummers, DataThief III. 2006. (http://datathief.org/) |
[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), 374-382. |
[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), 47-53. |
[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), 1019-1034. |
[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), 443-449.
doi: 10.1016/j.jtbi.2010.02.019. |
[77] |
J. M. Witkowski, Advanced application of CFSE for cellular tracking, Current Protocols in Cytometry, (2008), 9.25.1-9.25.8. |
[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), Published Online. |
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, Boca Raton London New York, 2012. |
[2] |
H. T. Banks and Kathleen Bihari, Modelling and estimating uncertainty in parameter estimation, Inverse Problems, 17 (2001), 95-111.
doi: 10.1088/0266-5611/17/1/308. |
[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, North Carolina State University, December 2005; Mathematical Biosciences and Engineering, 3 (2006), 635-660. |
[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), 63-91.
doi: 10.1016/S0025-5564(02)00218-3. |
[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, North Carolina State University, January 2003; Chapter 6 in Bioterrorism: Mathematical Modeling Applications in Homeland Security, (eds. H. T. Banks and C. Castillo-Chavez), Frontiers in Applied Math, FR28, SIAM, Philadelphia, PA, 2003, 129-154. |
[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, Brown University, March 1987; Proc. 2nd Course on Math. Ecology, (Trieste, December 8-12, 1986) World Scientific Press, Singapore, 1988, 521-541. |
[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), 1412-1415.
doi: 10.1016/j.aml.2010.07.009. |
[8] |
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" (eds. G. Chowell, et al.), Berlin Heidelberg New York, 2009, 249-302. |
[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), 753-777.
doi: 10.1016/j.apnum.2006.07.016. |
[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, North Carolina State University, February 2008; Journal of Biological Dynamics, 3 (2009), 130-148. |
[11] |
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. |
[12] |
H. T. Banks and B. F. Fitzpatrick, Estimation of growth rate distributions in size-structured population models, CAMS Tech. Rep. 90-2, Univ. of Southern California, January 1990; Quart. Appl. Math., 49 (1991), 215-235. |
[13] |
H. T. Banks and N. L. Gibson, Well-posedness in Maxwell systems with distributions of polarization relaxation parameters, CRSC-TR04-01, North Carolina State University, January 2004; Applied Math. Letters, 18 (2005), 423-430. |
[14] |
H. T. Banks and N. L. Gibson, Electromagnetic inverse problems involving distributions of dielectric mechanisms and parameters, CRSC-TR05-29, North Carolina State University, August 2005; Quarterly of Applied Mathematics, 64 (2006), 749-795. |
[15] |
H. T. Banks and K. Kunisch, "Estimation Techniques for Distributed Parameter Systems," Birkhauser, Boston, 1989. |
[16] |
H. T. Banks and G. A. Pinter, A probabilistic multiscale approach to hysteresis in shear wave propagation in biotissue, CRSC-TR04-03, North Carolina State University, January 2004; SIAM J. Multiscale Modeling and Simulation, 3 (2005), 395-412. |
[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, North Carolina State University, September 2002; Math. Biosci., 192 (2004), 193-225. |
[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, North Carolina State University, Revised July 2011; J. Immunological Methods, 373 (2011), 143-160.
doi: 10.1016/j.jim.2011.08.014. |
[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, North Carolina State University, August 2009; Bull. Math. Biol., 70 (2011), 116-150.
doi: 10.1007/s11538-010-9524-5. |
[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, North Carolina State University, January 2012. |
[21] |
H. T. Banks and H. T. Tran, "Mathematical and Experimental Modeling of Physical and Biological Processes," CRC Press, Boca Raton London New York, 2009. |
[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, North Carolina State University, January 1998; Stochastic Analysis, Control, Optimization and Applications, (eds. W. McEneaney, G. Yin and Q. Zhang), Birkhäuser, (1998), 353-371. |
[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), 329-351. |
[24] |
K. P. Burnham and D. R. Anderson, "Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach," (2nd Edition), Springer, New York, 2002. |
[25] |
Nigel J. Burroughs and P. Anton van der Merwe, Stochasticity and spatial heterogeneity in T-cell activation, Immunological Reviews, 216 (2007), 69-80. |
[26] |
R. Callard and P. D. Hodgkin, Modeling T- and B-cell growth and differentiation, Immunological Reviews, 216 (2007), 119-129. |
[27] |
Robin E. Callard, Jaroslav Stark and Andrew J. Yates, Fratricide: a mechanism for T memory-cell homeostasis, Trends in Immunology, 24 (2003), 370-375.
doi: 10.1016/S1471-4906(03)00164-9. |
[28] |
R. J. Carroll and D. Ruppert, "Transformation and Weighting in Regression," Chapman Hall, London, 2000. |
[29] |
M. Davidian and D. M. Giltinan, "Nonlinear Models for Repeated Measurement Data," Chapman and Hall, London, 2000. |
[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), 1011-1031.
doi: 10.1007/s11538-006-9094-8. |
[31] |
R. J. DeBoer and Alan S. Perelson, Estimating division and death rates from CFSE data, J. Comp. and Appl. Mathematics, 184 (2005), 140-164.
doi: 10.1016/j.cam.2004.08.020. |
[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), 4963-4972. |
[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), 517-526. |
[34] |
K. Duffy and V. Subramanian, On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics, J. Math. Biol., 59 (2009), 255-285.
doi: 10.1007/s00285-008-0231-x. |
[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), 559-564.
doi: 10.1046/j.1440-1711.1999.00870.x. |
[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), 950-957. |
[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), 183-200.
doi: 10.1016/j.jim.2005.01.011. |
[38] |
A. V. Gett and P. D. Hodgkin, A cellular calculus for signal integration by T cells, Nature Immunology, 1 (2000), 239-244. |
[39] |
M. Kot, "Elements of Mathematical Ecology," Cambridge University Press, Cambridge, UK, 2001. |
[40] |
M. Gyllenberg and G. F. Webb, A nonlinear structured population model of tumor growth with quiescence, J. Math. Biol., 28 (1990), 671-694.
doi: 10.1007/BF00160231. |
[41] |
J. Hasenauer, D. Schittler, and F. Allgöwer, A computational model for proliferation dynamics of division- and label-structured populations, arXiv:1202.4923v1, 22 Feb, 2012. |
[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), 2057-2067. |
[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), 13457-13462.
doi: 10.1073/pnas.0905629106. |
[44] |
Mirja Hommel and Philip D. Hodgkin, TCR affinity promotes CD8+ T-cell expansion by regulating survival, J. Immunology, 179 (2007), 2250-2260. |
[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), 222-239.
doi: 10.1198/016214507000000194. |
[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), Published Online. |
[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), 93-118. |
[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), 1649-1670.
doi: 10.1007/s11538-009-9418-6. |
[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), 21-44.
doi: 10.1007/s11538-007-9239-4. |
[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), 455-476.
doi: 10.1016/j.jtbi.2004.04.011. |
[51] |
Y. Louzoun, The evolution of mathematical immunology, Immunological Reviews, 216 (2007), 9-20. |
[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), 581-603.
doi: 10.1007/s00285-008-0244-5. |
[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), 57-89.
doi: 10.1007/s00285-006-0046-6. |
[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), Published Online. |
[55] |
A. B. Lyons and C. R. Parish, Determination of lymphocyte division by flow cytometry, J. Immunol. Methods, 171 (1994), 131-137.
doi: 10.1016/0022-1759(94)90236-4. |
[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), 375-398.
doi: 10.1016/S0091-679X(01)63021-8. |
[57] |
G. Matera, M. Lupi and P. Ubezio, Heterogeneous cell response to topotecan in a CFSE-based proliferative test, Cytometry A, 62 (2004), 118-128.
doi: 10.1002/cyto.a.20097. |
[58] |
J. A. Metz and O. Diekmann, "The Dynamics of Physiologically Structured Populations," Springer Lecture Notes in Biomathematics, 68, 1986. |
[59] |
H. Miao, X. Jin, A. Perelson and H. Wu, Evaluation of multitype mathemathematical modelsfor CFSE-labeling experimental data, Bull. Math. Biol., 74 (2012), 300-326.
doi: 10.1007/s11538-011-9668-y. |
[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), 7-18.
doi: 10.1016/j.jtbi.2011.02.006. |
[61] |
R. E. Nordon, M. Nakamura, C. Ramirez and R. Odell, Analysis of growth kinetics by division tracking, Immunology and Cell Biology, 77 (1999), 523-529.
doi: 10.1046/j.1440-1711.1999.00869.x. |
[62] |
C. Parish, Fluorescent dyes for lymphocyte migration and proliferation studies, Immunology and Cell Biol., 77 (1999), 499-508.
doi: 10.1046/j.1440-1711.1999.00877.x. |
[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), 275-283.
doi: 10.1016/S0022-5193(03)00245-5. |
[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), 2049-2056. |
[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), 925-931. |
[66] |
G. A. Sever and C. J. Wild, "Nonlinear Regression," Wiley, Hoboken, NJ, 2003. |
[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), June 2001, Zurich, Switzerland, 165-168 |
[68] |
J. Sinko and W. Streifer, A new model for age-size structure of a population, Ecology, 48 (1967), 910-918.
doi: 10.2307/1934533. |
[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), 861-892.
doi: 10.1007/s00285-007-0142-2. |
[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), 640-656.
doi: 10.1128/MCB.00882-09. |
[71] |
W. Clayton Thompson, "Partial Differential Equation Modeling of Flow Cytometry Data from CFSE-based Proliferation Assays," Ph.D. Dissertation, North Carolina State University, December, 2011. |
[72] |
B. Tummers, DataThief III. 2006. (http://datathief.org/) |
[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), 374-382. |
[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), 47-53. |
[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), 1019-1034. |
[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), 443-449.
doi: 10.1016/j.jtbi.2010.02.019. |
[77] |
J. M. Witkowski, Advanced application of CFSE for cellular tracking, Current Protocols in Cytometry, (2008), 9.25.1-9.25.8. |
[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), Published Online. |
[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 and 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 and 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 and 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 and 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 and Continuous Dynamical Systems - B, 2017, 22 (10) : 3721-3747. doi: 10.3934/dcdsb.2017186 |
[9] |
Yangjin Kim, Soyeon Roh. A hybrid model for cell proliferation and migration in glioblastoma. Discrete and Continuous Dynamical Systems - B, 2013, 18 (4) : 969-1015. doi: 10.3934/dcdsb.2013.18.969 |
[10] |
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 |
[11] |
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 |
[12] |
Fadia Bekkal-Brikci, Giovanna Chiorino, Khalid Boushaba. G1/S transition and cell population dynamics. Networks and Heterogeneous Media, 2009, 4 (1) : 67-90. doi: 10.3934/nhm.2009.4.67 |
[13] |
Keith E. Howard. A size structured model of cell dwarfism. Discrete and 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 and Applied Analysis, 2004, 3 (3) : 331-352. doi: 10.3934/cpaa.2004.3.331 |
[15] |
Mostafa Adimy, Laurent Pujo-Menjouet. Asymptotic behavior of a singular transport equation modelling cell division. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 439-456. doi: 10.3934/dcdsb.2003.3.439 |
[16] |
Gabriella Di Blasio, Alfredo Lorenzi. Direct and inverse problems in age--structured population diffusion. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 539-563. doi: 10.3934/dcdss.2011.4.539 |
[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 and 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
Other articles
by authors
[Back to Top]