Analysis of bacterial migration: II. Studies with multiple attractant gradients

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Abstract
Many motile bacteria exhibit chemotaxis, the ability to bias their random motion to ward or away from increasing concentrations of chemical substances which benefit or inhibit their survival, respectively. Since bacteria encounter numerous chemical concentration gradients simulatneously in natural surroundings, it is necessary to know quantitatively how a bacterial population responds in the presence of more than one chemical stimulus to develop predictive mathematical models describing bacterial migration in natural systems. This work evaluates three hypothetical models describing the integration of chemical signals from multiple stimuli: high sensitivity, maximum signal, and simple additivity. An expression for the tumbling probability for individual stimuli (Brown and Berg, 1974) is modified according to the proposed models and incorporated into the cell balance equation for a 1‐D attractant gradient (Ford and Cummings, 1992). Random motility and chemotactic sensitivity coefficients, required input parameters for the model, are measured for single stimulus responses. Theoretical predictions with the three signal integration models are compared to the net chemotactic response of Escherichia coli to co‐ and antidirectional gradients of D‐fucose and α‐methylaspartate in the stopped‐flow diffusion chamber assay. Results eliminate the high‐sensitivity model and favor the simple additivity over the maximum signal. None of the simple models, however, accurately predict the observed behavior, suggesting a more complex model with more steps in the signal processing mechanism is required to predict responses to multiple stimuli.

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