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Motor proteins are key players in intracellular transport processes and biological motion. Theoretical modeling of these systems has been achieved by the use of step processes on one-dimensional lattices. After a comprehensive introduction to the total asymmetric exclusion process and some analytical tools, we will give a review on different lines of research attracted to the aspects of this systems. We will focus on the generic properties of a coupling between the exclusion process and Langmuir bulk kinetics that induce topological changes in the phase diagram and multi-phase coexistence.

From Intracellular Traffic to a Novel Class of Driven Lattice Gas Models