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

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 <i>Streptococcus salivarius</i> and <i>Escherichia coli</i>, 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.

本研究开发了一种结合多项式线性模型与概率分布模型的统计方法，用于从数学层面表征细菌附着过程并探究其作用机制。该线性确定性模型以探究细菌与基底表面理化因素作为附着预测因子的实验数据为基础构建。将预测结果代入正态近似二项分布模型，即可实现细菌附着的概率化预测。本实验方案采用了不同比例的唾液链球菌（Streptococcus salivarius）与大肠杆菌（Escherichia coli）混合菌液，以及多孔聚(甲基丙烯酸丁酯-共-二甲基丙烯酸乙酯)（poly(butyl methacrylate-co-ethyl dimethacrylate)）与仲丁醇铝涂层（aluminum sec-butoxide coatings）的混合基底，以此实现细菌在一系列理化性质各异的基底表面的附着实验，所涉及的理化参数包括细菌细胞与基底的表面疏水性、细菌细胞与基底的表面电荷、基底表面粗糙度以及细菌细胞尺寸。该模型通过独立实验获得的数据进行了验证。模型结果显示，疏水相互作用是最为关键的预测因子，且部分因素之间存在相互影响关系。更为重要的是，该模型为各影响因子划定了一个区间，在此区间内细菌附着结果将无法被精准预测。但该模型将细菌细胞视为胶体颗粒，仅考量了细菌细胞与基底表面的核心理化属性，因此因未纳入生物学与环境因素而存在局限性。这使得该模型仅适用于特定场景，同时也为未来针对不同环境的建模研究提供了研究方向。