Abstract
The aim of this work is twofold. First, we survey the techniques developed in Perthame and Zubelli (Inverse Probl 23(3):1037–1052, 2007), Doumic et al. (Inverse Probl 25, 2009) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the experimental data experimental data reported in the classical work of Kubitschek (Biophys J 9(6):792–809, 1969) concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, FL, USA). Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features.
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Acknowledgments
The authors were supported by the CNPq-INRIA agreement INVEBIO. JPZ was supported by CNPq under grants 302161/2003-1 and 474085/2003-1. JPZ is thankful to the RICAM special semester and to the International Cooperation Agreement Brazil-France. A substantial part of this work was developed during a 3-month international internship of PM at INRIA Rocquencourt during the Spring of 2008 and supported by INRIA. The authors thank very much S. Boatto (UFRJ) for facilitating this visit and for helpful discussions.
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Doumic, M., Maia, P. & Zubelli, J.P. On the Calibration of a Size-Structured Population Model from Experimental Data. Acta Biotheor 58, 405–413 (2010). https://doi.org/10.1007/s10441-010-9114-9
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DOI: https://doi.org/10.1007/s10441-010-9114-9