We established a simple assay to screen for large libraries of chemotactic mutants; a key component of this assay is the formation of a gradient of an attractant in semisolid agar plates. The aim is to select mutants that migrate toward the source of an attractant and bacterial chemotaxis is based on the presence of a concentration gradient in the range of sensitivity of the receptor. Thus, in order to correctly interpret the change in movement, the gradient formation needs to be coordinated with the plating time and position of the bacterial library with respect to the source. We thus built a model that predicts the attractant gradient at a given point in time and we used it to determine when to plate the bacteria such that they grow in an optimal gradient.
The model is based on the second Fick’s law of diffusion and, given initial concentration at the source, position and dimension of the source and diffusion coefficient of the small molecule in agar, it simulates the gradient formation over time. The solution of the second Fick’s law is given in Table 1 and the parameters are described in Fig 1. The initial condition is based on the heavy side function theta .
The general solution was evaluated for a given concentration of a small molecule c (mM), a position from the source x (mm) and an arbitrary long time t (s) [Table 2].
While diffusion coefficients are often available for compounds in water, the value needs to be adapted for diffusion in 0.3% agar. We thus implemented this conversion as shown in Table 3 .
The parameters for the conversion and the dimension of the plate are detailed in Table 4, the diffusion coefficient, the width of the stripe and the initial concentration of the source need to be set depending on the experiment.
We simulated the diffusion of aspartate and DNT, starting from a source of 10 mM with a width of 1/3 the plate. The model predicts at what time a concentration of 0.1 mM will reach the middle of the plate, and indicates it as plating time. This threshold concentration of 0.1 mM should be tuned by the user according to the experimental set up.
The accuracy of the model was validated by observing the bacterial response to the aspartate gradient. The model simulated the time from the plating of the stripe and of the bacteria, to the imaging. It can be observed that bacteria that are predicted to be plated on the lower part of the gradient, have the highest motility toward the source.
-  Lead, J. R., K. Starchev, and K. J. Wilkinson. “Diffusion Coefficients of Humic Substances in Agarose Gel and in Water.” Environmental Science and Technology 37.3 (2003): 482–487. Web.
- Pluen, Alain et al. “Diffusion of Macromolecules in Agarose Gels: Comparison of Linear and Globular Configurations.” Biophysical Journal 77.1 (1999): 542–552. Web.