A dynamic model for receptor‐mediated specific adhesion of bacteria under uniform shear flow

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Abstract
A dynamic mathematical model is proposed to describe bacterial cell adhesion in viscous shear flow that is mediated by specific receptor: ligand binding. Bacterial cells are assumed here to be ideal spheres covered uniformly with spring‐like receptors. The model describes the specific binding between receptor molecules on the cell and ligands associated with the target surface. Accounting for the processes of attachment, detachment, and growth of attached bacteria, a set of non‐linear ordinary differential equations (ODEs) is derived that governs the net accumulation of cell numbers per surface area (S) of ligand‐coated surface, cell numbers (X) and growth‐limiting substrate concentration (S) per volume of solution passing over the target substratum. The non‐linear ODEs are numerically solved by using the fourth‐order Runge‐Kutta algorithm. Results of numerical simulations reveal that various stages of bacterial attachment are pertinent at different stages of biofilm development. The recommendation of a proper time duration for experimental adhesion research is possible, based on model solutions. A sensitivity analysis is carried out and the results indicate that bacterial deposition is dominated by the attachment and detachment rate constants rather than by ligand density or shear rate. Specific adhesion of a defined mixed culture is also simulated with an expanded version of the basic model.