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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.
MSC:
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
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[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]
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