Random Motility of Swimming Bacteria: Single Cells Compared to Cell Populations z b J Bret R. Phillips and John A. Quinn zyxw FED Dept. of Chemical Engineering, University of Pennsylvania, Philadelphia, PA 19104 Howard Goldfine Dept. of Microbiology, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 zy DC The motility of a population of swimming bacteria can be characterized by a random motility coefficient, zyxwv NMLK p, the operational equivalent of a diffusion coefficient at the macroscopic level and in the absence of interacting chemical gradients. At the microscopic level, random motility is related to the single-cell parameters: speed, tumbling probability, and index of directional persistence (related to the angle a cell’s path assumes following a change in direction). Various mathematical models have been proposed for relating the macroscopic random motility coefficient to these microscopic single-cell parameters. In separate experiments, we have measured motility at both the cell-population and single-cell levels for Escherichia coli. The agreement of these results shows that the macroscopic transport behavior of a population of motile bacteria can be predicted from straightforward microscopic observations on single cells. Introduction A characteristic feature of many motile microorganisms is their zigzag movement which may be represented approxi- mately as a sequence of straight line steps interrupted by turns (Hall, 1977). The swimming motion of the bacterium zyxwvu A Esche- richiu coli illustrates this behavior. E. coli swim in a series of smooth straight paths called “runs” which are terminated by a rapid turning maneuver called a “tumble.” This gives the cell a nearly random reorientation from which to begin the next run (Berg and Brown, 1972). This run and tumble random motility behavior can best be approximated as a three-dimen- sional random walk. In the presence of a spatial or temporal gradient of an attractant (sugars and amino acids), a bacterium swimming up the gradient will suppress its tumbling response. This results in a longer run in the direction of the higher attractant concentration (Brown and Berg, 1974; Macnab and Koshland, 1972; Lovely et al., 1974; Tsang et al., 1973); the opposite response, that is, a longer run in the direction of lower concentration is displayed in the presence of a repellent (pH extremes and aliphatic alcohols). This behavior, termed chemoklinokinesis, enables an individual bacterium to control Correspondence concerning this article should be addressed zyxwvutsrqp to J . A. Quinn. Current addresi of B. R. Phillips: Merck & Co.. Inc.. Danville. PA. its tumbling frequency, and results in a biased or directed random walk towards attractants and away from repelle At the macroscopic cell-population level, this net migration termed chemotaxis. This behavior is illustrated in Figure 1. The bacterium E. coli is a peritrichously (uniformly) flag- ellated, rod-shaped organism approximately 2 pm long and I pm in diameter. E. coli has on average eight flagellar filaments, each 25-10 pm long and 20 nm in diameter (O’Brien an Bennett, 1972). Motility is generated by a reversible rotary motor located at the base of each flagellar filament (Berg and Anderson, 1973; Silverman and Simon, 1974). When rota in the counterclockwise direction (as viewed from the d end), the flagella form a coordinated bundle which propels the cell, resulting in the run type behavior discussed above. A clockwise rotation of the flagellum results in a disruption the coordinated bundle which causes the cell to move chao ically or tumble (Larsen et al., 1974; Macnab and Ornston 1977). Due to the random-walk behavior of individual ce the dispersion of a population of cells in an isotropic medium can be described in terms of a random motility coefficient, z p, the operational equivalent of a diffusion coefficient. For a single cell, motility can be further interpreted in terms of its speed, zyxwv s, tumbling frequency (or the reciprocal mean run length 334 February 1994 Vol. 40, No. 2 AIChE Journal