ANALYSIS OF BACTERIAL MIGRATION .1. NUMERICAL-SOLUTION OF BALANCE EQUATION

Chemotaxis describes the ability of motile bacteria to bias their moti on in the direction of increasing gradients of chemicals, usually ener gy sources, known as attractants. In experimental studies of the migra tion of chemotactic bacteria, 1-D phenomenological cell balance equati ons (Rivero et al., 1989) have been used to quantitatively analyze exp erimental observations (Ford et al., 1991; Ford and Lauffenburger, 199 1), While attractive for their simplicity and the ease of solution, th ey are limited in the strict mathematical sense to the situation in wh ich individual bacteria are confined to motion in one dimension and re spond to attractant gradients in one dimension only. Recently, Ford an d Cummings (1992) reduced the general 3-D cell balance equation of Alt (1980) to obtain an equation describing the migration of a bacterial population in response to a 1-D attractant gradient. Solutions of this equation for single gradients of attractants are compared to those of 1-D balance equations, results from cellular dynamics simulations (Fr ymier et al., 1993), and experimental data from our laboratory for E. coli responding to alpha-methylaspartate. We also investigate two aspe cts of the experimentally derived expression for the tumbling probabil ity: the effect of different models for the down-gradient swimming beh avior of the bacteria and the validity of ignoring the temporal deriva tive of the attractant concentration.