  We study a synthetic system of motile Escherichia coli bacteria encapsulated
inside giant lipid vesicles. Forces exerted by the bacteria on the inner side
of the membrane are sufficient to extrude membrane tubes filled with one or
several bacteria. We show that a physical coupling between the membrane tube
and the flagella of the enclosed cells transforms the tube into an effective
helical flagellum propelling the vesicle. We develop a simple theoretical model
to estimate the propulsive force from the speed of the vesicles, and
demonstrate the good efficiency of this coupling mechanism. Together, these
results point to design principles for conferring motility to synthetic cells.
