Abstract
We present a multi-dimensional continuum mathematical model for modeling the growth of a symbiotic biofilm system. We take a dual-species namely, the Streptococcus–Veillonella sp. biofilm system as an example for numerical investigations. The presented model describes both the cooperation and competition between these species of bacteria. The coupled partial differential equations are solved by using an integrative finite element numerical strategy. Numerical examples are carried out for studying the evolution and distribution of the bio-components. The results demonstrate that the presented model is capable of describing the symbiotic behavior of the biofilm system. However, homogenized numerical solutions are observed locally. To study the homogenization behavior of the model, numerical investigations regarding on how random initial biomass distribution influences the homogenization process are carried out. We found that a smaller correlation length of the initial biomass distribution leads to faster homogenization of the solution globally, however, shows more fluctuated biomass profiles along the biofilm thickness direction. More realistic scenarios with bacteria in patches are also investigated numerically in this study.
Highlights
More than 90% of microbes live in biofilms which can be defined as “assemblages of bacterial cells attached to a surface and enclosed in an adhesive matrix secreted by the cells” (Madigan 2012)
The reaction model presented in this paper can be applied with discrete element based models, we present our model within the framework of continuum biofilm models which are fully described by partial differential equations (Alpkvist and Klapper 2007; Cogan 2004; Duddu et al 2009; Eberl et al 2001; Klapper and Dockery 2002; Lindley et al 2012; Wanner and Gujer 1986; Zhang et al 2008b)
We develop a mathematical model for the symbiotic S. gordonii– Veillonella biofilm system under the hypothesis that the lactic acid has a negative influence on the growth of S. gordonii and the symbiotic biofilm system studied in this paper is essentially a mutualistic ecological system
Summary
More than 90% of microbes live in biofilms which can be defined as “assemblages of bacterial cells attached to a surface and enclosed in an adhesive matrix secreted by the cells” (Madigan 2012). A biofilm in natura is usually found as a multi-component, multi-species, heterotopic matter with multi-phase properties. Competition and cooperation among species of bacteria are normally involved in multi-species biofilm systems (Yang et al 2011). A biological system is symbiotic when cooperation happens between two different organisms. Mathematical and numerical modeling is a powerful tool for understanding both the physical and bio-chemical processes during the formation and development of the biofilms. Many modeling strategies and models have been developed for describing biofilm processes. Mathematical modeling of symbiotic biofilm systems has not been well studied. Modeling a symbiotic biofilm system naturally requires the consideration of a multi-species biofilm problem which is usually challenging, especially for multi-dimensional scenarios
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