A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Escherichia coli chemotaxis to competing stimuli in a microfluidic device with a constant gradient

In natural systems bacteria are exposed to many chemical stimulants; some attract chemotactic bacteria as they promote survival, while others repel bacteria because they inhibit survival. When faced with a mixture of chemoeffectors, it is not obvious which direction the population will migrate. Predicting this direction requires an understanding of how bacteria process information about their surroundings. We used a multiscale mathematical model to relate molecular level details of their two-component signaling system to the probability that an individual cell changes its swimming direction to the chemotactic velocity of a bacterial population. We used a microfluidic device designed to maintain a constant chemical gradient to compare model predictions to experimental observations. We obtained parameter values for the multiscale model of Escherichia coli chemotaxis to individual stimuli, α-methylaspartate and nickel ion, separately. Then without any additional fitting parameters, we predicted bacteria response to chemoeffector mixtures. Migration of E. coli toward α-methylaspartate was modulated by adding increasing concentrations of nickel ion. Thus, the migration direction was controlled by the relative concentrations of competing chemoeffectors in a predictable way. This study demonstrated the utility of a multiscale model to predict the migration direction of bacteria in the presence of competing chemoeffectors. This article is protected by copyright. All rights reserved.

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).