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.