A statistical approach for modelling the physical process of bacterial attachment to abiotic surfaces

Abstract

A statistical approach using a polynomial linear model in combination with a probability distribution model was developed to mathematically represent the process of bacterial attachment and study its mechanism. The linear deterministic model was built based on data from experiments investigating bacterial and substratum surface physico-chemical factors as predictors of attachment. The prediction results were applied to a normal-approximated binomial distribution model to probabilistically predict attachment. The experimental protocol used mixtures of Streptococcus salivarius and Escherichia coli, and mixtures of porous poly(butyl methacrylate-co-ethyl dimethacrylate) and aluminum sec-butoxide coatings, at varying ratios, to allow bacterial attachment to substratum surfaces across a range of physico-chemical properties (including the surface hydrophobicity of bacterial cells and the substratum, the surface charge of the cells and the substratum, the substratum surface roughness and cell size). The model was tested using data from independent experiments. The model indicated that hydrophobic interaction was the most important predictor while reciprocal interactions existed between some of the factors. More importantly, the model established a range for each factor within which the resultant attachment is unpredictable. This model, however, considers bacterial cells as colloidal particles and accounts only for the essential physico-chemical attributes of the bacterial cells and substratum surfaces. It is therefore limited by a lack of consideration of biological and environmental factors. This makes the model applicable only to specific environments and potentially provides a direction to future modelling for different environments.