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Estimating the division rate from indirect measurements of single cells

Marie Doumic, ,Sorbonne Université, Inria, Université Paris-Diderot, CNRS, Laboratoire Jacques-Louis Lions, 75005 Paris, France, Adélaïde Olivier, Lydia Robert, ,Laboratoire de Mathematiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France, ,Laboratoire Jean Perrin, Sorbonne Université, 75005 Paris, France
2017 Discrete and continuous dynamical systems. Series B  

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Is it possible to estimate the dependence of a growing and dividing population on a given trait in the case where this trait is not directly accessible by experimental measurements, but making use of measurements of another variable? This article adresses this general question for a very recent and popular model describing bacterial growth, the so-called incremental or adder model. In this model, the division rate depends on the increment of size between birth and division, whereas the most
more » ... ssible trait is the size itself. We prove that estimating the division rate from size measurements is possible, we state a reconstruction formula in a deterministic and then in a statistical setting, and solve numerically the problem on simulated and experimental data. Though this represents a severely ill-posed inverse problem, our numerical results prove to be satisfactory. 2010 Mathematics Subject Classification. Primary: 35R30, 92B05; Secondary: 35Q62, 62G30, 45Q05.
doi:10.3934/dcdsb.2020078 fatcat:wflaqyovrvhtbk6qcqy73f4pze
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Marie Doumic, ,Sorbonne Université, Inria, Université Paris-Diderot, CNRS, Laboratoire Jacques-Louis Lions, 75005 Paris, France, Adélaïde Olivier, Lydia Robert, ,Laboratoire de Mathematiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France, ,Laboratoire Jean Perrin, Sorbonne Université, 75005 Paris, France. "Estimating the division rate from indirect measurements of single cells." Discrete and continuous dynamical systems. Series B 22.11 (2017) 0-0