A cybernetic model of bacterial chemotactic response to nutrient limitation
Abstract
One response bacteria have to their environment is chemotaxis, in which the cells respond to the gradient of stimuli. The strength of the chemotactic response to a nutrient depends upon the concentration of the nutrient at which the bacteria are cultivated. To create a more realistic model of chemotaxis, the cybernetic perspective is applied to the growth of the bacteria: the manipulation by the cells of their chemotactic sensitivity ($\delta$) is considered to be goal-seeking: maximization of an objective function. Hence, an objective function is sought that predicts the sensitivity dependence on the nutrient concentration in agreement with experimental measurements. Long-term, short-term and matching-law objectives are considered, using a modification of the chemotaxis model by Rivero et al. (1989). A confined-growth model is used for the long-term perspective, in which the total number of cells is maximized. Two first-order ODE's for the cell mass and substrate concentration are solved using orthogonal collocation on finite elements (OCFE), initially for constant $\delta$ (${\not=}\delta$(x)). Optimized long-term solutions are found with a GRG algorithm and $\delta$ a function of x. In the matching-law model, first- and second-order stationarity conditions are applied to locate the optimal $\delta$ profile. Solutions of the ODE's are very sensitive to the placement of the finite elements. Through analysis of the discretization error (resulting in improved element placement), the near-singular system is solved accurately. The long-term perspective yields a $\delta$-profile with sharp oscillations near the nutrient source and a transition to slow decay elsewhere, and is probably a numerical artifact. The short-term model is dismissed since it can not properly represent the response of the cells to a source of nutrient. The results of the matching-law model qualitatively resemble the experimental measurements. The principal conclusions are: (1) the long- and short-term objectives do not apply, as the computed $\delta$ profiles are not qualitatively similar to the experimental measurements, (2) the matching-law model predicts these measurements qualitatively, (3) the confined-growth model, with Monod or Moser growth kinetics, is unacceptable for highly-chemotactic cells, and (4) the placement of the elements in the OCFE method is crucial to compute accurate solution profiles.
Subject Area
Chemical engineering
Recommended Citation
Koster, Loretta Gail, "A cybernetic model of bacterial chemotactic response to nutrient limitation" (1991). Dissertations available from ProQuest. AAI9125695.
https://repository.upenn.edu/dissertations/AAI9125695