Equations representing a phenomenological model for chemotactic movement of bacteria in the standard capillary assay are analyzed using a similarity transform. The form of the transformed equations leads to a regrouping of system parameters that effectively reduces the number of independent variables and yields a straight forward solution. This solution can be represented on a single, time-independent plot for a given combination of bacteria and chemoattractant. This plot greatly simplifies the reduction of experimental results in terms of the model parameters μ and x: the random motility coefficient and the chemotaxis coefficient.
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Staffeld et al. (1987) studied this question.