Motility is a capacity for movement (or movement-potential) caused by consumption of energy by an organism in response to a gradient. The spontaneous movement of a cell relies on a flagellum, a propulsion mechanism in the form of a hollow, rigid cylinder composed of the protein flagellin.

Fig. 1 Longitudonal section through a flagellal area. In the cell apex is the basal body that is the anchoring site for a flagella. Basal bodies originate from and have a substructure similar to that of centrioles, with nine peripheral microtubule triplets (see structure at bottom center of image). The two inner microtubules of each triplet in a basal body become the two outer doublets in the flagella. This image also shows the transition region, with its fibers of the stellate structure. The top of the image shows the flagella passing through the cell wall. [ source ]

Motility denotes potential rather than actual movement. In bacterial motility this includes rotation, tumbling, gliding . The “motors” for some of these forms of motility are not well understood by biologists.

Fig. 2 Motile Chromatium cells: short, Gram-negative rods, ~1 µm in diameter and 3-4 µm long. Watch for the tumbles as the cells change direction.
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In a network representation of a city as a set of nodes with movement-potential, the concept of motility adds a notion of stochastic uncertainty at a low scale, capturing the capacity for agents to use additional energy to express their own agency through their movement trails, and at a larger scale the role of gradients as drivers of movement.

Motile space can then be defined as space with a capacity for through-movement.