Limping Factors for Motor Proteins

Abstract

Conventional kinesin is a two-headed motor protein that walks “hand-over-hand” along microtubules, with the two heads (or motor domains) moving alternatively. In vitro single-molecule measurements by Asbury, Fehr and Block [Science 302 (2003) 2130; also Fehr et al, Biophys. J. 97 (2009) 1663] find that the stepping motion of kinesin embodies a limp, i.e., alternate steps have different mean dwell times. We report an analytical study of the statistics of the observed limping factor, L, defined as the ratio of average dwell times for the slow phase to those for the fast phase. Employing basic models we find that, owing to the finite run lengths of experimental measurements, the observed limping factor is always significantly larger than the “true” or intrinsiclimping factor, L0. Essentially, for large L0 the average observed limping factor, ,for runs of n odd steps interlaced with n even steps is at least n/(n-1) times larger than the intrinsic factor, L0. Thus, if L0 = 1.0, so that the walk is limp-free, the observed mean values for runs of 2n = 8, 10, and 12 steps would be = 2.06, 1.87, and 1.74, respectively. Moreover, the corresponding standard deviations are D Ln= 1.41, 1.04, and 0.83. To improve estimates of L0 on the basis of observed values, the analysis has been extended (a) to allow for runs of length at least 2k steps terminated stochastically by detachment from the track and (b) to utilize information, obtained experimentally or hypothesized, regarding the dwell-time distributions. Reliable estimates of intrinsic limping factors should be useful in untangling the details of asymmetric hand-over-hand stepping in processive motor proteins.