A novel physical mechanism is discussed for the processive propagation of two-headed motor proteins such as kinesin along protein filaments. Our model uses the fact that the binding of each head must be directionality oriented to the protein filament. The binding sites are realized by a 2D periodic potential due to the filament's surface. The deviation of the geometry of the kinesin from the relaxed state to the state where both motor domains are simultaneously bound to the filament results in an internal stress of the molecule. Un-binding of one of the motor domains from the filament, which is due to the release of chemical energy from ATP hydrolysis, results in a mechanical movement until the relaxed state is reached again. We develop a simple mathematical and mechanical model in which directed binding of the heads to the filament results in a directed twist away from its relaxed state of the molecule, occurring probably in the neck linker region. Un-binding of the head from the filament relaxes the twist and defines the propagation direction. We show that there must be at least one torsional spring for every head to store elastic energy. It is the internal structure both of the relaxed and tensed-up state that defines the walking direction of kinesin. Calculations based on the model are in good quantitative agreement with experimental observations.

PACS numbers: 87.16.Ka, 87.16.Nn