Modeling aerotaxis band formation in Azospirillum brasilense

Abstract

Background: Bacterial chemotaxis, the ability of motile bacteria to navigate gradients of chemicals, plays key roles in the establishment of various plant-microbe associations, including those that benefit plant growth and crop productivity. The motile soil bacterium Azospirillum brasilense colonizes the rhizosphere and promotes the growth of diverse plants across a range of environments. Aerotaxis, or the ability to navigate oxygen gradients, is a widespread behavior in bacteria. It is one of the strongest behavioral responses in A. brasilense and it is essential for successful colonization of the root surface. Oxygen is one of the limiting nutrients in the rhizosphere where density and activity of organisms are greatest. The aerotaxis response of A. brasilense is also characterized by high precision with motile cells able to detect narrow regions in a gradient where the oxygen concentration is low enough to support their microaerobic lifestyle and metabolism.

Results: Here, we present a mathematical model for aerotaxis band formation that captures most critical features of aerotaxis in A. brasilense. Remarkably, this model recapitulates experimental observations of the formation of a stable aerotactic band within 2 minutes of exposure to the air gradient that were not captured in previous modeling efforts. Using experimentally determined parameters, the mathematical model reproduced an aerotactic band at a distance from the meniscus and with a width that matched the experimental observation.

Conclusions: Including experimentally determined parameter values allowed us to validate a mathematical model for aerotactic band formation in spatial gradients that recapitulates the spatiotemporal stability of the band and its position in the gradient as well as its overall width. This validated model also allowed us to capture the range of oxygen concentrations the bacteria prefer during aerotaxis, and to estimate the effect of parameter values (e.g. oxygen consumption rate), both of which are difficult to obtain in experiments.

Keywords: Aerotaxis; Azospirillum brasilense; Band formation; Chemotaxis; Mathematical modeling.

Fig. 1

Images of aerotactic band formation of wild-type (Sp7) A. brasilense with 21% oxygen set at the meniscus. (a) At time 0 sec, when oxygen is applied at the meniscus. (b) At time 50 sec. (c) At time 100 sec. (d) At time 140 sec, by which time the band has already stabilized. Scale bar is 500 μm in all panels

Fig. 2

Aerotactic band formation predicted by the model. Top row: With parameters of Table 1. The band forms and stabilizes within a minute, and remains steady, exactly as observed in experiments. Band location and width are 406 μm and 132 μm, in excellent agreement with the experimentally measured values of 407 and 132 μm. Bottom row: With parameter values taken from Mazzag et al. [15]. The band is moving (not steady); location and width are 1517 and 185 μm at 300 s, but 1760 and 186 μm at 600 s. (a),(c): Band evolution in time: Left (blue) and Right (red) sides of the band. Note the different scales on x-axis. (b),(d): Profiles of (normalized) bacteria concentration (B) at time 50 s (blue) and 300 s (red), and of Oxygen concentration (C) at 300 s (green). Note the different scales on both axes

Fig. 3

Reversal frequency of right swimming (solid line) and left swimming (dashed line) cells, depicting formulas (3) and (4), for setting f_RL and f_LR in the model