Modelling bacterial chemotaxis for indirectly binding attractants.

In bacterial chemotaxis, chemoattractant molecules may bind either directly or indirectly with receptors within the cell periplasmic space. The indirect binding mechanism, which involves an intermediate periplasmic binding protein, has been reported to increase sensitivity to dilute attractant concentrations as well as range of response. Current mathematical models for bacterial chemotaxis at the population scale do not appear to take the periplasmic binding protein (BP) concentration or the indirect binding mechanics into account. We formulate an indirect binding extension to the existing Rivero equation for chemotactic velocity based on fundamental reversible enzyme kinetics. The formulated indirect binding expression accounts for the periplasmic BP concentration and the dissociation constants for binding between attractant and periplasmic BP, as well as between BP and chemoreceptor. We validate the indirect-binding model using capillary assay simulations of the chemotactic responses of E. coli to the indirectly-binding attractants maltose and AI-2. The predicted response agrees well with experimental data from a number of maltose capillary assay studies conducted in previous literature. The model is also able to achieve good agreement with AI-2 capillary assay data of one study out of two tested. The chemotactic response of E. coli towards AI-2 appears to be of higher complexity due to reports of variable periplasmic BP concentration as well as the low concentration of periplasmic BP relative to the total receptor concentration. Our current model is thus suitable for indirect binding chemotactic response systems with constant periplasmic BP concentration that is significantly larger than the total receptor concentration, such as the response of E. coli towards maltose. Further considerations may be taken into account to model the chemotactic response towards AI-2 with greater accuracy.