Mathematical Models of Bacterial Chemotaxis

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 of diverse plants across a range of environments. Aerotaxis, or the ability to navigate oxygen gradients is one of the strongest behavioral responses in A. brasilense. The aerotaxis response of A. brasilense is characterized by high precision with motile cells able to detect narrow regions in a gradient where the oxygen concentration is low enough (below 1%) to support their microaerobic lifestyle. We develop a model for aerotaxis band formation that captures most critical features of aerotaxis in A. brasilense. Remarkably, this model recapitulates experimental observations that were not captured in previous modeling efforts and further permits parameter values, which are difficult to obtain in experiments.Single-particle tracking (SPT) has become an important method to study a number of well-characterized phenotypes including chemotaxis and cell migration. SPT methods extract the individual particle trajectories from time-lapse frames and provide useful information about both individual particle and collective behavior of particles. A large number of trajectories have to be analyzed to ensure that any inferences drawn from the observations are statistically representative of the particles. We develop an automated tracking software for free-swimming bacteria to track a large number of bacteria and analyze the resulting trajectories.Biochemical pathways of chemotaxis in A. brasilense still remain elusive. This allows mathematical modeling to make testable predictions with biologically probable hypotheses about the biochemical mechanisms. The regulation of chemotaxis is achieved by a network of interaction proteins constituting a signal transduction pathway. It has been recently found that A. brasilense cells have multiple (Che) systems whereas the model organism Escherichia coli possesses one chemotaxis system. We present a novel mathematical model to help determine the plausible network connectivity of chemotaxis pathways in A. brasilense by first developing four biologically plausible models and then invalidating all competing models, but one, which represents wild-type and all mutants data well.