Vectorial loading of processive motor proteins: implementing a landscape picture

Abstract

Individual processive molecular motors, of which conventional kinesin is the moststudied quantitatively, move along polar molecular tracks and, by exerting a forceF = (Fx,Fy,Fz) on a tether, drag cellular cargoes, in vivo, or spherical beads, in vitro, takingup to hundreds of nanometre-scale steps. From observations of velocities andthe dispersion of displacements with time, under measured forces and controlledfuel supply (typically ATP), one may hope to obtain insight into the molecularmotions undergone in the individual steps. In the simplest situation, the load forceF may be regarded as ascalar 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. USA100 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 afree-energy landscape picture in order to allow for the full vectorial nature of the forceF transmitted by the tether. The load-dependence of the various forward and reversetransition 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 wasmeasured under the action of bound kinesin molecules which induced determinedperpendicular loads. But in the normal single-bead assay it also proves imperative to allow forFz>0: the appropriate analysis for kinesin, suggesting that the motor ‘crouches’ onbinding ATP prior to stepping, is sketched. It yields an expression for the velocity,V (Fx,Fz;[ATP]), needed to address the buckling experiments.