STRUCTURED MATHEMATICAL MODELS FOR DYNAMICS OF MICROBIAL GROWTH: FIRST ORDER AND DISCRETE TIME DELAYS

摘要

Kinetic models for microbial growth are usually derived from pseudo steady-state assumptions. Dynamic conditions in the environment of the microorganisms may lead to complex responses within the metabolism of the organisms. Observing the macroscopic variables like biomass or substrate concentration, the effect of changes of metabolism within the cells results in transient behavior, which can be summarized under the term "biological inertia". This work shows two different modeling approaches for this effect, introducing a growth governing intracellular concentration, which changes after a time delay according to environmental changes. These delays are modeled by a first order and a discrete time delay respectively. Parameter estimation fom experimental data and model discrimination shows, that the discrete time delay is more suited for data representation. This is related to the concept of "maturation" of intracellular compounds, between induction of intracellular processes and the resulting activity often a discrete time delay is observed.