Run-and-tumble motion is a movement pattern exhibited by certain bacteria and other microscopic agents. It consists of an alternating sequence of "runs" and "tumbles": during a run, the agent propels itself in a fixed (or slowly varying) direction, and during a tumble, it remains stationary while it reorients itself in preparation for the next run. The tumbling is erratic or "random" in the sense of a stochastic process—that is, the new direction is sampled from a probability density function, which may depend on the organism's local environment (e.g., chemical gradients). The duration of a run is usually random in the same sense. An example is wild-type E. coli in a dilute aqueous medium, for which the run duration is exponentially distributed with a mean of about 1 second. Run-and-tumble motion forms the basis of certain mathematical models of self-propelled particles, in which case the particles themselves may be called run-and-tumble particles.
Description Many bacteria swim, propelled by rotation of the flagella outside the cell body. In contrast to protist flagella, bacterial flagella are rotors and—irrespective of species and type of flagellation—they have only two modes of operation: clockwise or counterclockwise rotation. Bacterial swimming is used in bacterial taxis (mediated by specific receptors and signal transduction pathways) for the bacterium to move in a directed manner along gradients and reach more favorable conditions for life. The direction of flagellar rotation is controlled by the type of molecules detected by the receptors on the surface of the cell: in the presence of an attractant gradient, the rate of smooth swimming increases, while the presence of a repellent gradient increases the rate of tumbling.
Biological examples Run-and-tumble motion is found in many peritrichous bacteria, including E. coli, Salmonella typhimurium, and Bacillus subtilis. It has also been observed in the alga Chlamydomonas reinhardtii and the cyanobacterium Synechocystis.
Directed motility (taxis) Genetically diverse groups of microorganisms rely upon directed motility (taxis), such as chemotaxis or phototaxis, to optimally navigate through complex environments or colonise host tissues. In the model organisms Escherichia coli and Salmonella, bacteria swim in a random pattern produced by alternating counterclockwise (CCW) and clockwise (CW) flagellar rotation. Chemoreceptors detect attractants or repellents and stimulate responses through a signalling cascade that controls the direction of the flagellar motor. This can result in a chemotaxis, where attractant gradients extend the length of time flagellar motors rotate CCW, resulting in more smooth swimming in a favourable direction, while repellents cause an increase of CW rotations, resulting in more tumbling and changes in direction. The cyanobacterium Synechocystis uses run-and-tumbling in a manner which can result in phototaxis.
Escherichia coli An archetype of bacterial swimming is represented by the well-studied model organism Escherichia coli. With its peritrichous flagellation, E. coli performs a run-and-tumble swimming pattern, as shown in the diagrams below. Counterclockwise rotation of the flagellar motors leads to flagellar bundle formation that pushes the cell in a forward run, parallel to the long axis of the cell. Clockwise rotation disassembles the bundle and the cell rotates randomly (tumbling). After the tumbling event, straight swimming is recovered in a new direction. That is, counterclockwise rotation results in steady motion and clockwise rotation in tumbling; counterclockwise rotation in a given direction is maintained longer in the presence of molecules of interest (like sugars or aminoacids).
In a uniform medium, run-and-tumble trajectories appear as a sequence of nearly straight segments interspersed by erratic reorientation events, during which the bacterium remains stationary. The straight segments correspond to the runs, and the reorientation events correspond to the tumbles. Because they exist at low Reynolds number, bacteria starting at rest quickly reach a fixed terminal velocity, so the runs can be approximated as constant velocity motion. The deviation of real-world runs from straight lines is usually attributed to rotational diffusion, which causes small fluctuations in the orientation over the course of a run. In contrast with the more gradual effect of rotational diffusion, the change in orientation (turn angle) during a tumble is large; for an isolated E. Coli in a uniform aqueous medium, the mean turn angle is about 70 degrees, with a relatively broad distribution. In more complex environments, the tumbling distribution and run duration may depend on the agent's local environment, which allows for goal-oriented navigation (taxis). For example, a tumbling distribution that depends on a chemical gradient can guide bacteria toward a food source or away from a repellant, a behavior referred to as chemotaxis. Tumbles are typically faster than runs: tumbling events of E. Coli last about 0.1 seconds, compared to ~ 1 second for a run.
Synechocystis
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