A Multi-Skilled Mathematical Model of Bacterial Attachment in Initiation of Biofilms

The initial step of biofilm formation is bacteria attachment to biotic or abiotic surfaces and other bacteria through intra or interspecies interactions. Adhesion can be influenced by physicochemical conditions of the environment, such as iron. There is no available mathematical model of bacterial attachment giving realistic initiation rather than random adhesion. We describe a simple stochastic attachment model, from the simplest case in two dimensions with one bacterial species attaching on a homogeneous flat surface to more complex situations, with either several bacterial species, inhomogeneous or non-flat surfaces, or in three dimensions. The model depends on attachment probabilities (on the surface, laterally, or vertically on bacteria). Effects of each of these parameters were analyzed. This mathematical model is then applied to experimental oral microcolonies of Porphyromonas gingivalis, Streptococcus gordonii, and Treponema denticola, either as mono-, two, or three species, under different iron concentrations. The model allows to characterize the adhesion of three bacterial species and explore the effect of iron on attachment. This model appears as a powerful tool for initial attachment analysis of bacterial species. It will enable further modeling of biofilm formation in later steps with biofilm initialization more relevant to real-life subgingival biofilms.