Vectorial loading of processive motor proteins: implementing a landscape picture

Individual processive molecular motors, of which conventional kinesin is the most studied quantitatively, move along polar molecular tracks and, by exerting a force F = (Fx,Fy,Fz) on a tether, drag cellular cargoes, in vivo, or spherical beads, in vitro, taking up to hundreds of nanometre-scale steps. From observations of velocities and the dispersion of displacements with time, under measured forces and controlled fuel supply (typically ATP), one may hope to obtain insight into the molecular motions undergone in the individual steps. In the simplest situation, the load force F may be regarded as a scalar resisting force, Fx<0, acting parallel to the track: however, experiments, originally by Gittes et al (1996 Biophys. J. 70 418), have imposed perpendicular (or vertical) loads, Fz>0, while more recently Block and co-workers (2002 Biophys. J. 83 491, 2003 Proc. Natl Acad. Sci. USA 100 2351) and Carter and Cross (2005 Nature 435 308) have studied assisting (or reverse) loads, Fx>0, and also sideways (or transverse) loads . We extend previous mechanochemical kinetic models by explicitly implementing a free-energy landscape picture in order to allow for the full vectorial nature of the force F transmitted by the tether. The load-dependence of the various forward and reverse transition rates is embodied in load distribution vectors, and , which relate to substeps of the motor, and in next order, in compliance matrices and . The approach is applied specifically to discuss the experiments of Howard and co-workers (1996 Biophys. J. 70 418) in which the buckling of partially clamped microtubules was measured under the action of bound kinesin molecules which induced determined perpendicular loads. But in the normal single-bead assay it also proves imperative to allow for Fz>0: the appropriate analysis for kinesin, suggesting that the motor ‘crouches’ on binding ATP prior to stepping, is sketched. It yields an expression for the velocity, V (Fx,Fz;[ATP]), needed to address the buckling experiments.