A novel approach in bacterial growth modeling : E.coli exposed to silver nanoparticles

There are many growth and inactivation models in the literature which are purely empirical and do not poster a mechanistic insight [1, 2]. Here, we present a novel, intuitive and mathematically relatively simple model for bacterial growth and inactivation. The proposed model well describes E. coli batch culture growth curves obtained for different inoculum sizes and different initial nutrients concentration. The model is, furthermore, expanded in order to fit and explain growth curves obtained for E. coli treated with different concentrations of laser produced silver nanoparticles. The model is described by three nonlinear mutually dependent di erential equations that give time evolution of bacterial, nutrients and nanoparticle concentrations. These equations are of general nature and can be used to predict growth of different bacteria in batch culture since the equations do not include a parameter that is characteristic for E. coli. As our model can be linked to the logistic model, it is possible that the equations could be applicable to any single species growth. [1] M. Peleg and M. G. Corradini, Crit. Rev. Food Sci. Nutr. 51, 917 (2011) [2] K. D. Dolan and D. K. Mishra, Annu. Rev. Food Sci. Technol. 4, 401 (2013)