A mathematical model for Escherichia coli chemotaxis to competing stimuli

Abstract

Chemotactic bacteria sense and respond to temporal and spatial gradients of chemical cues in their surroundings. This phenomenon plays a critical role in many microbial processes such as groundwater bioremediation, microbially enhanced oil recovery, nitrogen fixation in legumes, and pathogenesis of the disease. Chemical heterogeneity in these natural systems may produce numerous competing signals from various directions. Predicting the migration behavior of bacterial populations under such conditions is necessary for designing effective treatment schemes. In this study, experimental studies and mathematical models are reported for the chemotactic response of Escherichia coli to a combination of attractant (α-methylaspartate) and repellent (NiCl₂ ), which bind to the same transmembrane receptor complex. The model describes the binding of chemoeffectors and phosphorylation of the kinase in the signal transduction mechanism. Chemotactic parameters of E. coli (signaling efficiency $\sigma$ , stimuli sensitivity coefficient $\gamma$ , and repellent sensitivity coefficient $\kappa$ ) were determined by fitting the model with experimental results for individual stimuli. Interestingly, our model naturally identifies NiCl₂ as a repellent for $\kappa >1$ . The model is capable of describing quantitatively the response to the individual attractant and repellent, and correctly predicts the change in direction of bacterial population migration for competing stimuli with a twofold increase in repellent concentration.

Keywords: bacteria motility; chemotactic response; microfluidic device; multiple stimuli; signal transduction mechanism.