zbMATH — the first resource for mathematics

A novel statistical analysis and interpretation of flow cytometry data. (English) Zbl 1447.92115
Summary: A recently developed class of models incorporating the cyton model of population generation structure into a conservation-based model of intracellular label dynamics is reviewed. Statistical aspects of the data collection process are quantified and incorporated into a parameter estimation scheme. This scheme is then applied to experimental data for PHA-stimulated CD4+T and CD8+T cells collected from two healthy donors. This novel mathematical and statistical framework is shown to form the basis for accurate, meaningful analysis of cellular behaviour for a population of cells labelled with the dye carboxyfluorescein succinimidyl ester and stimulated to divide.
92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] J.E. Aubin, Autoflouresecence of viable cultured mammalian cells, J. Histochem. Cytochem. 27 (1979), pp. 36-43. doi: 10.1177/27.1.220325[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[2] H.T. Banks and B.G. Fitzpatrick, Inverse Problems for Distributed Systems: Statistical Tests and ANOVA, Proceedings of the International Symposium on Mathematical Approaches to Environmental and Ecological Problems, Springer Lecture Notes in Biomath, Vol. 81, Springer-Verlag, Berlin, 1989, pp. 262-273. LCDS/CSS Report 88-16, Brown University, July 1988. [Google Scholar]
[3] H.T. Banks and W.C. Thompson, A division-dependent compartmental model with cyton and intracellular label dynamics, Int. J. Pure Appl. Math. 77 (2012), pp. 119-147. CRSC-TR12-12, North Carolina State University, May 2012. [Google Scholar] · Zbl 1247.92007
[4] H.T. Banks and W.C. Thompson, Mathematical models of dividing cell populations: Application to CFSE data, J. Math. Model. Nat. Phenom. 7 (2012), pp. 24-52. CRSC-TR12-10, North Carolina State University, April 2012. doi: 10.1051/mmnp/20127504[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1260.76047
[5] H.T. Banks and W.C. Thompson, Least squares estimation of probability measures in the Prohorov metric framework, Center for Research in Scientific Computation Tech Rep, CRSC-TR12-21, North Carolina State University, Raleigh, NC, November, 2012. [Google Scholar]
[6] H.T. Banks and H.T. Tran, Mathematical and Experimental Modeling of Physical and Biological Processes, CRC Press, Boca Raton, FL, 2009. [Crossref], [Google Scholar] · Zbl 1402.00037
[7] H.T. Banks, M. Davidian, J. Samuels, and K.L. Sutton, An inverse problem statistical methodology summary, Chapter 11 inMathematical and Statistical Estimation Approaches in Epidemiology, G. Chowell, M. Hyman, L. M. A. Bettencourt, and C. Castillo-Chavez, eds., Springer, Berlin, 2009, pp. 249-302. CRSC-TR08-01, North Carolina State University, January 2008. [Crossref], [Google Scholar] · Zbl 1345.92006
[8] H.T. Banks, K. Holm, and F. Kappel, Comparison of optimal design methods in inverse problems, Inv. Prob. 27 (2011), p. 075002. doi: 10.1088/0266-5611/27/7/075002[Crossref], [Google Scholar] · Zbl 1271.62169
[9] H.T. Banks, Z.R. Kenz, and W.C. Thompson, An extension of RSS-based model comparison tests for weighted least squares, Int. J. Pure Appl. Math. 79 (2012), pp. 155-183. CRSC-TR12-18, North Carolina State University, August 2012. [Google Scholar] · Zbl 1402.62025
[10] H.T. Banks, Z.R. Kenz, and W.C. Thompson, A review of selected techniques in inverse problem nonparametric probability distribution estimation, J. Inv. Ill-posed Problems 20 (2012), pp. 429-460. Special issue on the occasion of the 80th anniversary of the birthday of M.M. Lavrentiev. [Crossref], [Web of Science ®], [Google Scholar] · Zbl 1279.34018
[11] H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, M. Doumic, T. Schenkel, J. Argilaguet, S. Giest, C. Peligero, and A. Meyerhans, A new model for the estimation of cell proliferation dynamics using CFSE data, J. Immunol. Methods 373 (2011), pp. 143-160. doi:10.1016/j.jim.2011.08.014. CRSC-TR11-05, North Carolina State University, Revised July 2011. doi: 10.1016/j.jim.2011.08.014[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[12] H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, D. Roose, T. Schenkel, and A. Meyerhans, Estimation of cell proliferation dynamics using CFSE data, Bull. Math. Biol. 70 (2011), pp. 116-150. CRSC-TR09-17, North Carolina State University, August 2009. doi: 10.1007/s11538-010-9524-5[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1209.92012
[13] H.T. Banks, W.C. Thompson, C. Peligero, S. Giest, J. Argilaguet, and A. Meyerhans, A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays, Math. Biosci. Eng. 9 (2012), pp. 699-736. CRSC-TR12-03, North Carolina State University, January 2012. doi: 10.3934/mbe.2012.9.699[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1259.92017
[14] G. Bell and E. Anderson, Cell growth and division I. A mathematical model with applications to cell volume distributions in mammalian suspension cultures, Biophys. J. 7 (1967), pp. 329-351. doi: 10.1016/S0006-3495(67)86592-5[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[15] F. Billy, J. Clairambault, F. Delaunay, C. Feillet, and N. Robert, Age-structured cell population model to study the influence of growth factors on cell cycle dynamics, Math. Biosci. Eng. 10 (2013), pp. 1-17. doi: 10.3934/mbe.2013.10.1[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1259.92018
[16] K.P. Burnham and D.R. Anderson, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed., Springer, New York, 2002. [Crossref], [Google Scholar] · Zbl 1005.62007
[17] N.J. Burroughs and P.A. van der Merwe, Stochasticity and spatial heterogeneity in T-cell activation, Immunol. Rev. 216 (2007), pp. 69-80. [PubMed], [Web of Science ®], [Google Scholar]
[18] A. Choi, T. Huffman, J. Nardini, L. Poag, W.C. Thompson, and H.T. Banks, Quantifying CFSE label decay in flow cytometry data, Appl. Math. Lett. 26 (2013), pp. 571-577. doi:10.1016/j.aml.2012.12.010. CRSC-TR12-20, North Carolina State University, December 2012. doi: 10.1016/j.aml.2012.12.010[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1257.92019
[19] M. Davidian and D.M. Giltinan, Nonlinear Models for Repeated Measurement Data, Chapman & Hall, London, 2000. [Google Scholar]
[20] 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), pp. 1011-1031. doi: 10.1007/s11538-006-9094-8[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1334.92112
[21] M.R. Dowling, D. Milutinovic, and P.D. Hodgkin, Modelling cell lifespan and proliferation: Is likelihood to die or to divide independent of age? J. R. Soc. Interface 2 (2005), pp. 517-526. doi: 10.1098/rsif.2005.0069[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[22] K. Duffy and V. Subramanian, On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics, J. Math. Biol. 59 (2009), pp. 255-285. doi: 10.1007/s00285-008-0231-x[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1311.92061
[23] W. Feller, An Introduction to Probability Theory and its Applications, Vol. I, Wiley, New York, 1971. [Google Scholar] · Zbl 0219.60003
[24] A.R. Gallant, Nonlinear Statistical Models, Wiley, New York, 1987. [Crossref], [Google Scholar] · Zbl 0611.62071
[25] A.V. Gett and P.D. Hodgkin, A cellular calculus for signal integration by T cells, Nat. Immunol. 1 (2000), pp. 239-244. doi: 10.1038/79782[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[26] S. Goh, H.W. Kwon, M.Y. Choi, and J.Y. Fortin, Emergence of skew distributions in controlled growth processes, Phys. Rev. E 82 (2010), p. 061 115. doi: 10.1103/PhysRevE.82.061115[Crossref], [Google Scholar]
[27] J. Hasenauer, D. Schittler, and F. Allgöwer, Analysis and simulation of division- and label-structured population models: a new tool to analyze proliferation assays, Bull. Math. Biol. 74 (2012), pp. 2692-2732. [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1362.92062
[28] E.D. Hawkins, M. Hommel, M.L Turner, F. Battye, J. Markham, and P.D Hodgkin, Measuring lymphocyte proliferation, survival and differentiation using CFSE time-series data, Nat. Protoc. 2 (2007), pp. 2057-2067. doi: 10.1038/nprot.2007.297[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[29] 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), pp. 5032-5037. doi: 10.1073/pnas.0700026104[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[30] 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), pp. 13457-13462. doi: 10.1073/pnas.0905629106[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[31] O. Hyrien and M.S. Zand, A mixture model with dependent observations for the analysis of CFSE-labeling experiments, J. Amer. Statist. Assoc. 103 (2008), pp. 222-239. doi: 10.1198/016214507000000194[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 05564482
[32] O. Hyrien, R. Chen, and M.S. Zand, An age-dependent branching process model for the analysis of CFSE-labeling experiments, Biol. Direct 5 (2010), Published Online. doi:10.1186/1745-6150-5-41 [Google Scholar]
[33] S.N. Lahiri, A. Chatterjee, and T. Maiti, Normal approximation to the hypergeometric distribution in nonstandard cases and a sub-Gaussian Berry-Esseen theorem, J. Statist. Plann. Inference 137 (2007), pp. 3570-3590. doi: 10.1016/j.jspi.2007.03.033[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1123.60014
[34] 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), pp. 581-603. doi: 10.1007/s00285-008-0244-5[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1231.92027
[35] 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, Theor. Biol. Medical Model. 4 (2007), published online. doi:10.1186/1742-4682-4-26 [PubMed], [Web of Science ®], [Google Scholar]
[36] A.B. Lyons and C.R. Parish, Determination of lymphocyte division by flow cytometry, J. Immunol. Methods 171 (1994), pp. 131-137. doi: 10.1016/0022-1759(94)90236-4[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[37] 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 Cell Biol. 63 (2001), pp. 375-398. [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[38] H. Miao, X. Jin, A. Perelson, and H. Wu, Evaluation of multitype mathemathematical models for CFSE-labeling experimental data, Bull. Math. Biol. 74 (2012), pp. 300-326. doi:10.1007/s11538-011-9668-y doi: 10.1007/s11538-011-9668-y[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1317.92028
[39] R.E. Nordon, K.-H. Ko, R. Odell, and T. Schroeder, Multi-type branching models to describe cell differentiation programs, J. Theor. Biol. 277 (2011), pp. 7-18. doi: 10.1016/j.jtbi.2011.02.006[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1405.92081
[40] 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. Immunol. Methods 379 (2012), pp. 1-14. doi: 10.1016/j.jim.2012.02.012[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[41] B. Quah, H. Warren, and C. Parish, Monitoring lymphocyte proliferation in vitro and in vivo with the intracellular fluorescent dye carboxyfluorescein diacetate succinimidyl ester, Nat. Protoc. 2 (2007), pp. 2049-2056. doi: 10.1038/nprot.2007.296[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[42] D. Schittler, J. Hasenauer, and F. Allgöwer, A generalized model for cell proliferation: Integrating division numbers and label dynamics, Proceedings of the Eighth International Workshop on Computational Systems Biology (WCSB 2011), Zurich, Switzerland, June 2011, pp. 165-168. [Google Scholar]
[43] G.A.F. Seber and A.J. Lee, Linear Regression Analysis, Wiley, Hoboken, NJ, 2003. [Crossref], [Google Scholar] · Zbl 1029.62059
[44] G.A. Seber and C.J. Wild, Nonlinear Regression, Wiley, Hoboken, NJ, 2003. [Google Scholar] · Zbl 0721.62062
[45] 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), pp. 861-892. doi: 10.1007/s00285-007-0142-2[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1206.92013
[46] D.T. Terrano, M. Upreti, and T.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), pp. 640-656. doi: 10.1128/MCB.00882-09[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[47] W.C. 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. [Google Scholar]
[48] M.L. Turner, E.D. Hawkins, and P.D. Hodgkin, Quantitative regulation of B cell division destiny by signal strength, J. Immunol. 181 (2008), pp. 374-382. [PubMed], [Web of Science ®], [Google Scholar]
[49] P.K. Wallace, J.D. TarioJr., 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, Cytom. A 73 (2008), pp. 1019-1034. doi: 10.1002/cyto.a.20619[Crossref], [PubMed], [Web of Science ®], [Google Scholar]
[50] C. Wellard, J. Markham, E.D. Hawkins, and P.D. Hodgkin, The effect of correlations on the population dynamics of lymphocytes, J. Theor. Biol. 264 (2010), pp. 443-449. doi: 10.1016/j.jtbi.2010.02.019[Crossref], [PubMed], [Web of Science ®], [Google Scholar] · Zbl 1406.92164
[51] J.M. Witkowski, Advanced application of CFSE for cellular tracking, Curr. Protoc. Cytom. 44 (2008), pp. 9.25.1-9.25.8. [Google Scholar]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.