Mathematical Models of Bacterial Chemotaxis

Abstract

Many bacterial species exhibit chemotactic behavior, the ability to bias their otherwise random motion in the direction toward increasing concentrations of nutrients (referred to as attractants) or away from increasing concentrations of metabolites or compounds toxic to the bacteria, which may be indicators of unfavorable conditions (referred to as repellents). Chemotaxis can provide a competitive advantage for bacteria because in their natural habitats they are continually exposed to changing environmental conditions, and their survival depends on their capacity to respond favorably to adverse circumstances. Because their small size (1 to 2 μn) and simple structure limits their ability to modify their surroundings, they respond either by migration to a more desirable location or by adaptation of their internal metabolic processes (Macnab 1980). Actaptation occurs naturally through genetic modification, but is relatively slow. Chemotactic bacteria can clearly respond much more quickly by moving to a more favorable environment. Chemotaxis has many practical applications and is known to play important roles in nitrogen fixation in plants, the pathogenesis of disease, and the bioremediation of contaminated aquifers. This last case is of particular interest in our research group because it has been shown that bacteria are capable of degrading many toxic organic materials—including halogenated hydrocarbons via anaerobic degradation (Bouwer 1992; Harvey 1991)—and additionally respond chemotactically to these compounds. We are pursuing a long-range research program aimed at understanding the role of bacterial motility and chemotaxis in in situ bioremediation processes. The objectives are to quantitatively measure bacterial migration at the macroscopic level (both in the presence and absence of one or more attractant and/or repellent species), understand the basis for the macroscopic behavior by measuring and analyzing the motion of individual bacteria, develop mathematical models for bacterial migration based on microscopic and macroscopic level information, and use the model to predict bacterial migration in natural processes, with particular emphasis on in situ bioremedia- tion processes.