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Beschreibung:
Bacteria of certain species communicate with each other to organise group-beneficial collective behaviour such as bioluminescence or swarming motility. The cell-to-cell communication of these bacteria is based on a cell-density dependent mechanism called quorum sensing (QS). For this process different mathematical models in the form of ordinary differential equations (ODEs), partial differential equations (PDEs), and delay differential equations (DDEs) have been proposed and studied in literature. In this thesis we consider a mathematical model of QS in Pseudomonas putida IsoF ( P. putida IsoF) which was published by Buddrus-Schiemann et al. They conducted growth experiments of P. putida IsoF under steady state conditions in a chemostat and could describe their measurements by a mathematical QS model of DDEs. We discuss the motivation of this model, building on well-known mathematical models for chemostat experiments and generic QS models. Moreover, we derive a modification of the QS model which accounts for subpopulations of P. putida IsoF with different roles in the QS system. Buddrus-Schiemann et al. speculated about the existence of these subpopulations which could explain some of their surprising findings. After a short theoretical analysis of both QS models we investigate which numerical methods are suited for computing simulations of these models. We provide a general introduction to numerical DDE solvers and present DelayDiffEq.jl, an improved and rewritten DDE solver in Julia. The last part of this thesis is dedicated to the inverse problems of the QS models. We develop a suitable objective function for parameter estimation and apply regularization and global optimisation to deal with the ill-conditioning and non-convexity of the parameter estimation problem. Moreover, we determine structurally and practically non-identifiable parameters. Our parameter estimation yields slightly different parameter estimates that fit the experimental data better than the parameters published by Buddrus-Schiemann et al. ...