Groupe de travail Bio-MathsModeling and Analysis of Vertical Gene Transfer of Plasmids
Thursday 22 November 2018 15:30 - Tours - Salle à préciser
Plasmids are autonomously replicating genetic elements in bacteria. At cell division, plasmids are distributed among the two daughter cells. This gene transfer from one generation to the next is called vertical gene transfer. We study the dynamics of a bacterial population carrying plasmids and are in particular interested in the long-time distribution of plasmids. Starting with a model for a bacterial population structured by the discrete number of plasmids, we proceed to the continuum limit in order to derive a continuous model. The model incorporates plasmid reproduction, division and death of bacteria, and distribution of plasmids at cell division. We consider also a second continuous model that includes an assumption about plasmid segregation at low plasmid numbers. Both models are hyperbolic integro-differential equations, transport equations, and a so-called growth-fragmentation-death models. As we are interested in the long-time distribution of plasmids we study the associated eigenproblem and show existence of eigensolutions for both models. The stability of this solution is studied by analyzing the spectrum of the integro-differential operator given by the respective eigenproblems. The eigenfunctions are numerically constructed and thereby visualized.