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Stadler, E.* ; Müller, J.

Analyzing plasmid segregation: Existence and stability of the eigensolution in a non-compact case.

Discrete Contin. Dyn. Syst.-Ser. B 25, 4127-4164 (2020)
Verlagsversion DOI
: Postprint online verfügbar 11/2021
We study the distribution of autonomously replicating genetic elements, so-called plasmids, in a bacterial population. When a bacterium divides, the plasmids are segregated between the two daughter cells. We analyze a model for a bacterial population structured by their plasmid content. The model contains reproduction of both plasmids and bacteria, death of bacteria, and the distribution of plasmids at cell division. The model equation is a growth-fragmentation-death equation with an integral term containing a singular kernel. As we are interested in the long-term distribution of the plasmids, we consider the associated eigenproblem. Due to the singularity of the integral kernel, we do not have compactness. Thus, standard approaches to show the existence of an eigensolution like the Theorem of Krein-Rutman cannot be applied. We show the existence of an eigensolution using a fixed point theorem and the Laplace transform. The long-term dynamics of the model is analyzed using the Generalized Relative Entropy method.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Plasmid Dynamics ; Growth-fragmentation-death Equation ; Eigenproblem ; Non-compactness ; Generalized Relative Entropy; Multicopy Plasmids; Bacterial Plasmids; Population; Protein
ISSN (print) / ISBN 1531-3492
e-ISSN 1553-524X
Quellenangaben Band: 25, Heft: 11, Seiten: 4127-4164 Artikelnummer: , Supplement: ,
Verlag American Institute of Mathematical Sciences (AIMS)
Verlagsort Po Box 2604, Springfield, Mo 65801-2604 Usa
Begutachtungsstatus Peer reviewed