Net growth rate of continuum heterogeneous biofilms with inhibition kinetics

Abstract

Biofilm systems can be modeled using a variety of analytical and numerical approaches, usually by making simplifying assumptions regarding biofilm heterogeneity and activity as well as effective diffusivity. Inhibition kinetics, albeit common in experimental systems, are rarely considered and analytical approaches are either lacking or consider effective diffusivity of the substrate and the biofilm density to remain constant. To address this obvious knowledge gap an analytical procedure to estimate the effectiveness factor (dimensionless substrate mass flux at the biofilm-fluid interface) was developed for a continuum heterogeneous biofilm with multiple limiting-substrate Monod kinetics to different types of inhibition kinetics. The simple perturbation technique, previously validated to quantify biofilm activity, was applied to systems where either the substrate or the inhibitor is the limiting component, and cases where the inhibitor is a reaction product or the substrate also acts as the inhibitor. Explicit analytical equations are presented for the effectiveness factor estimation and, therefore, the calculation of biomass growth rate or limiting substrate/inhibitor consumption rate, for a given biofilm thickness. The robustness of the new biofilm model was tested using kinetic parameters experimentally determined for the growth of Pseudomonas putida CCRC 14365 on phenol. Several additional cases have been analyzed, including examples where the effectiveness factor can reach values greater than unity, characteristic of systems with inhibition kinetics. Criteria to establish when the effectiveness factor can reach values greater than unity in each of the cases studied are also presented.

Biofilm growth: Investigating inhibition

A method to model and assess the effect of interactions and processes that inhibit biofilm growth closes a gap in understanding. Biofilm growth is often inhibited by chemicals used or produced by microorganisms, or by other components and characteristics of the surroundings. This has been a neglected aspect of the procedures used to analyze and predict biofilm behavior. Stefan Wuertz at Nanyang Technological University in Singapore, with colleagues in Singapore and Argentina, mathematically modeled these often-overlooked inhibitory effects. They tested the accuracy of their procedure on complex biofilms under a variety of growing conditions. The insights gained into growth inhibition should help with the design of bioreactors, including those used to degrade pollutants. The method should be widely applicable to all types of biofilms, ranging from laboratory to industrial scale applications.