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Analyzing plasmid segregation: Existence and stability of the eigensolution in a non-compact case.
Discrete Contin. Dyn. Syst.-Ser. B 25, 4127-4164 (2020)
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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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
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
Volume: 25,
Issue: 11,
Pages: 4127-4164
Publisher
American Institute of Mathematical Sciences (AIMS)
Publishing Place
Po Box 2604, Springfield, Mo 65801-2604 Usa
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)