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Hasenauer, J. ; Schittler, D.* ; Allgöwer, F.*

Analysis and simulation of division- and label-structured population models. A new tool to analyze proliferation assays.

Bull. Math. Biol. 74, 2692-2732 (2012)
DOI PMC
Open Access Green möglich sobald Postprint bei der ZB eingereicht worden ist.
In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models only consider the size of the overall populations, others take division numbers and labeling of the cells into account. In this work, we present a modeling and computational framework for proliferating cell populations undergoing symmetric cell division, which incorporates both the discrete division number and continuous label dynamics. Thus, it allows for the consideration of division number-dependent parameters as well as the direct comparison of the model prediction with labeling experiments, e.g., performed with Carboxyfluorescein succinimidyl ester (CFSE), and can be shown to be a generalization of most existing models used to describe these data. We prove that under mild assumptions the resulting system of coupled partial differential equations (PDEs) can be decomposed into a system of ordinary differential equations (ODEs) and a set of decoupled PDEs, which drastically reduces the computational effort for simulating the model. Furthermore, the PDEs are solved analytically and the ODE system is truncated, which allows for the prediction of the label distribution of complex systems using a low-dimensional system of ODEs. In addition to modeling the label dynamics, we link the label-induced fluorescence to the measure fluorescence which includes autofluorescence. Furthermore, we provide an analytical approximation for the resulting numerically challenging convolution integral. This is illustrated by modeling and simulating a proliferating population with division number-dependent proliferation rate.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Age-structured Population Model ; Cfse ; Division-structured Population Model ; Label-structured Population Model ; Proliferation Assay ; Systems Of Pdes
ISSN (print) / ISBN 0092-8240
e-ISSN 1522-9602
Zeitschrift Bulletin of Mathematical Biology
Quellenangaben Band: 74, Heft: 11, Seiten: 2692-2732 Artikelnummer: , Supplement: ,
Verlag Springer
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Bioinformatics and Systems Biology (IBIS)