Mathematical model for the growth of P. aeruginosa and four mutator strains in sub-MIC concentration of Ciprofloxacin

P. aeruginosa causes very critical and complicated infections, for which treatment is strongly dependent on successful antibiotic treatment. Therefore the evolution of antibiotic resistant P. aeruginosa does have serious consequences. Cystic fibrosis (CF) is characterized by the chronic P. aeruginosa lung infection. Intensive antibiotic treatment has improved the survival and clinical condition of CF patients, but development of resistance to antibiotics makes these infections difficult to treat efficiently. Ciprofloxacin is commonly used in the early and aggressive treatment. A hypothesis is that the presence of antibiotic results in selection of mutators in the lungs of CF patients, as these bacteria has a higher fitness under the presence of antibiotics. The goal of this study is to model the growth of P. aeruginosa and four different mutator strains (PAO1 mutT, mutY, mutM and mutM-mutY mutants) when growing under sub-MIC Ciprofloxacin concentration (0.1 μg/ml), in order to describe the growth pattern under the presence of antibiotic. Data available for the modelling process is bioscreen measurements of the bacterial content as a function of time for each bacteria strain growing in LB media with and without the presence of Ciprofloxacin. The growth of the bacteria strains is modelled with a continuous-discrete time stochastic state space model consisting of a continuous time state equation expressed as a system of stochastic differential equations and a discrete time measurement equation. The model parameters are estimated from data using a Maximum Likelihood approach. We introduce a new expression for multiple substrate dependent growth in LB media, which is identified by a method first introducing the growth as a random walk in the model. From the bioscreen measurement we found a change in the growth pattern under the presence of Ciprofloxacin. In most cases the presence of Ciprofloxacin resulted in a longer lag phase, a period of growth followed by a transition phase and then a second period of growth. We have developed a new mathematical model using a multi substrate approach, which will be able to describe this change in growth as a function of the Ciprofloxacin concentration. Following the determination of the growth pattern we wish to continue this study by modelling a competition experiment between PA01 and each of the four mutator strains. The goal is to determine whether the mutator strain has an advantage in an environment with sub-MIC concentrate of Ciprofloxacin.