Mathematical Analysis of the Escherichia coli Chemotaxis Signalling Pathway

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

A mathematical model for Escherichia coli chemotaxis to competing stimuli

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 σ , stimuli sensitivity coefficient γ , and repellent sensitivity coefficient κ ) were determined by fitting the model with experimental results for individual stimuli. Interestingly, our model naturally identifies NiCl₂ as a repellent for κ > 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.

Rhizobial Chemoattractants, the Taste and Preferences of Legume Symbionts

The development of host-microbe interactions between legumes and their cognate rhizobia requires localization of the bacteria to productive sites of initiation on the plant roots. This end is achieved by the motility apparatus that propels the bacterium and the chemotaxis system that guides it. Motility and chemotaxis aid rhizobia in their competitiveness for space, resources, and nodulation opportunities. Here, we examine studies on chemotaxis of three major model rhizobia, namely Sinorhizobium meliloti, Rhizobium leguminosarum, and Bradyrhizobium japonicum, cataloging their range of attractant molecules and correlating this in the context of root and seed exudate compositions. Current research areas will be summarized, gaps in knowledge discussed, and future directions described.