Directed binding

We propose a novel physical mechanism to describe the mode of processive propagation of twoheaded kinesin motor proteins along microtubule (MT) filaments. Binding and unbinding of the kinesin heads to and from the MT filament play a crucial role in producing movement. The chemical energy of adenosine triphosphate hydrolysis is used in large part for the unbinding process of kinesin from the MT filament. Importantly, in our model, the binding of each head is to be directionally oriented to the MT filament. Therefore, we treat the two motor domains (heads) as extended objects that are connected with each other by a neck region that contains the kinesin dimerization domain. The head domains recognize tubulin binding sites by feeling the two-dimensional periodic potential from the MT surface and are also subjected to thermal noise. Using experimentally determined results regarding physical parameters of the walk, we develop a simple mathematical and mechanical model in which directed binding of the heads to tubulin results in a directed twist of the molecule, probably in the neck linker region, away from its relaxed state. Unbinding of the head from the filament relaxes the twist and defines the propagation direction. We showed that there must be at least two torsional springs (one for every head) involved that can store elastic energy. Consequently, in our model, it is the internal structure both of the relaxed and tensed-up state and the transition mode between them that define the walking direction of kinesin. We present calculations based on the model that are in good quantitative agreement with experimental observations for kinesin.