IJPAM: Volume 77, No. 1 (2012)


H.T. Banks$^1$, W. Clayton Thompson$^2$
$^1$Center for Research in Scientific Computation
Center for Quantitative Sciences in Biomedicine
N.C. State University
Raleigh, NC, USA
$^2$ICREA Infection Biology Lab
Department of Experimental and Health Sciences
Universitat Pompeu Fabra
Barcelona, SPAIN

Abstract. Intracellular dyes such as carboxyfluorescein succinimidyl ester (CFSE) have become an important tool for the flow cytometric analysis of a proliferating population of cells. The quantitative analysis of flow cytometry data involves two components. First, the generation structure (cell counts in terms of the number of divisions undergone) of the population must be related to a description of the manner in which cells divide and die. To this end, the cyton model [#!Callard2007!#,#!Hawkins2007b!#,#!Hawkins2007!#], which relates generation structure directly to probability distributions over times to divide and die, is both experimentally accurate and intuitive. Second, the manner in which the intracellular dye is processed by growing, dividing, and dying cells must be related to the measured fluorescence profiles of the population of cells. Several models of label-structured populations [#!CellProlif2!#,#!CellProlif!#,#!CellProlif3!#,#!Hasenauer2012!#,#!Luzyanina2009!#,#!TBMM!#,#!Schittler2011!#] have been used to accurately describe these fluorescence profiles. Here, we rely upon the compartmental formulations [#!CellProlif3!#,#!Hasenauer2012!#,#!Schittler2011!#,#!WCT!#] along with the recent computational framework of [#!Hasenauer2012!#,#!Schittler2011!#] to combine these two components to derive a new single model. This new model is capable of simultaneously describing generation dynamics and label structure dynamics in a proliferating population of cells in an extremely fast computational model. The new model is shown to be at least as accurate as those of previous efforts, while also providing a more biologically intuitive analysis of the behavior of the population of cells.

Received: May 8, 2012

AMS Subject Classification:

Key Words and Phrases: cell proliferation, cell division number, CFSE, label structured population dynamics, cyton models, partial differential equations, inverse problems

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 77
Issue: 1