The cytoplasm and biomembranes in biological cells contain large numbers of
proteins that cyclically change their shapes. They are molecular machines that
can function as molecular motors or carry out many other tasks in the cell. We
analyze the effects that hydrodynamic flows induced by active proteins have on
other passive molecules in solution or membranes. We show that the diffusion
constants of passive particles are enhanced substantially. Furthermore, when
gradients of active proteins are present, a chemotaxis-like drift of passive
particles takes place. In lipid bilayers, the effects are strongly nonlocal, so
that active inclusions in the membrane contribute to diffusion enhancement and
the drift. The results indicate that the transport properties of passive
particles in systems containing active proteins machines operating under
nonequilibrium conditions differ from their counterparts in systems at thermal
equilibrium
