Toward a Stochastic Formulation of Microbial Growth in Relation to Bioreactor Performances: Case Study of an E. coli Fed-Batch Process

Abstract

A stochastic microbial growth model has been elaborated in the case of the culture of E. coli in fed-batch and scale-down reactors. This model is based on the stochastic determination of the generation time of the microbial cells. The determination of generation time is determined by choosing the appropriate value on a log-normal distribution. The appropriateness of such distribution is discussed and growth curves are obtained that show good agreement compared with the experimental results. The mean and the standard deviation of the log-normal distribution can be considered to be constant during the batch phase of the culture, but they vary when the fed-batch mode is started. It has been shown that the parameters related to the log-normal distribution are submitted to an exponential evolution. The aim of this study is to explore the bioreactor hydrodynamic effect on microbial growth. Thus, in a second time, the stochastic growth model has been reinforced by data coming from a previous stochastic bioreactor mixing model (1). The connection of these hydrodynamic data with the actual stochastic growth model has allowed us to explain the scale-down effect associated with the glucose concentration fluctuations. It is important to point out that the scale-down effect is induced differently according to the feeding strategy involved in the fed-batch experiments.