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Motile bacteria move by either swimming, using flagella, or glide over surfaces. The mechanism by which bacteria such as a cyanobacterium called Oscillatorium, just glide over surfaces is not known.
Using flagella to move is the most common form of motility in bacteria. Flagella can be much longer than the bacterial cell itself. Some bacteria just have one, thin 'whip-like' structure as a flagellum. However, some bacteria have clusters of flagella which can rotate together to move the bacterium forward. These clusters of flagella act a bit like a propeller does on a boat.
Many bacteria have pili on their surface. They can use pili to bind to receptors and when they retract they pull the bacterium forward. Salmonella typhimurium bacteria, which can cause nasty food poisoning, use pili in this way to move along human cells until they 'find' a suitable place to 'hook' into the human cell surface.
Despite not having a brain or nervous system bacteria can still respond to stimuli, such as chemicals. They often move in response to chemical stimuli. This is called chemotaxis. They 'track down' chemicals, such as nutrients, quite randomly.
Bacteria not only seek out food, but they also seek out the company of other bacteria. They must be able to detect other bacteria in order to do so. Bacteria that form clusters together often produce what is called a biofilm on a surface.