Stochastic Mechanochemistry for Processive Motor Proteins: Kinesin Crouches before Sprinting.

Experiments by Block and coworkers (2003) applied assisting, resisting, and sideways loads {\boldmath $F$}$=(F_{x},F_{y},F_ {z})$ to single-molecules of kinesin as they moved along a microtubule (MT) taking steps of size $d\simeq 8.2$ nm. The velocity, $V_{x}$, and the randomness were observed as functions of {\boldmath $F$} and [ATP]. To uncover substeps and intermediate motions from such data, we have extended a discrete-state stochastic model, previously applied to kinesin$^ {1}$ and myosin V,$^{2}$ to allow for the {\em vectorial} loading of processive motors by invoking a {\em three}- dimensional ``energy landscape'' with a potential $\Phi(\mbox {\boldmath $F$})$.$^{3}$ The size of the attached bead and the resulting angle of the motor's tether relative to the track play a crucial role. The analysis for kinesin then indicates that on binding ATP (and, possibly, catalysing hydrolysis, etc.) the motor `crouches,' i.e., the point of attachment of the tether moves {\em downwards} (toward the MT) by 0.5-0.8 nm but {\em forwards} by only 0.1-0.2 nm, before completing a rapid swing of close to 8 nm. Unlike the scalar, $F_{x}$-only, analysis,$^{1}$ this is consistent with the observations of Higuchi and coworkers. Furthermore, assisting ({\em i.e.}, forward) loads are opposed since the `upwards' component, $F_{z} $, is enhanced by $\sim$2 pN which {\em reduces} the velocity.\\ 1. M.\ E.\ Fisher and A.\ B.\ Kolomeisky, PNAS USA {\bf 98}, 7748 (2001).\\ 2. A.\ B.\ Kolomeisky and M.\ E.\ Fisher, Biophys.\ J.\ {\bf 84}, 1642 (2003).\\ 3. M.\ E.\ Fisher and Y.\ C.\ Kim, Biophys.\ J.\ {\bf 86}, 527a, 2738-Plat.\ (2004).