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In the limit of very high loads approaching stall, or very low ATP concentrations, dwell intervals for kinesin are distributed exponentially because the stepping rate is dominated by a single rate-determining transition in the biochemical cycle (1-3). Under the conditions of the current work (4 pN rearward load and 2 mM ATP), the dwell interval distributions are expected to deviate slightly from pure exponentials (2, 3).
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0345799422
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The limp factor, L, is a statistic derived from each individual record. The ratio of fast to slow phase lifetimes is an ensemble statistic derived from the combined data for many such records. The average limp factor therefore provides an alternative measure of the overall stepping asymmetry. Its expectation value is not identical to the global lifetime ratio because of the effect of finite run lengths.
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0346430521
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The simulations contained runs with numbers of steps chosen to match closely those in our experiments (18).
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0346430523
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For example, one such molecule generated 21 runs in all, 13 of which included more than eight dwell, intervals, and were therefore scored (18). This molecule accounted for three of the nine outliers with L > 6, and the average limp factor for the molecule was 4.7.
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One quantity that varies systematically with the length of the construct in our experiments is the angle, θ, between the microtubute axis and the kinesin stalk, which experiences a force on its distal end acting through the center of the attached bead (fig. S2). This force has both rearward and upward components, and Howard and colleagues (13) have shown that the speed of kinesin movement can be affected by changes in the upward force. For the constructs used here, we estimate that θ ranges from 45° to 63° (tabte S1), which corresponds to a 26% maximal variation in upward loading, seemingly too small to account for a threefold change in limp factor. Moreover, small changes in loading would not be expected a priori to affect the two heads differentially.
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For example, an asymmetric effect on the characteristic step times for limping constructs could be explained in the misregistration model by assuming that for correctly dimerized molecules, the rates of stepping are not normally limited by the rates at which heads can locate new binding sites. In the case of misregistration, however, the head with the shorter tether takes additional time to reach its new site, thereby slowing its rate of advance to such an extent that it becomes rate-determining for the slow phase. Correspondingly, the head with the longer tether takes less time to advance, but because this is not the limiting factor, there is no significant variation in the fast phase. A similar explanation could be invoked to explain asymmetry in the winding model. A high energetic penalty for overwinding could cause the slow step to become rate-determining, whereas the low penalty for underwinding could have little effect on the fast phase, during which other unidentified transitions would govern the stepping rate.
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Manly, B.F.J.1
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0347060720
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note
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This study was initiated by C.L.A. but subsequently carried out with equal contributions from A.N.F and C.L.A. in the laboratory of S.M.B. We thank J. Gelles, W. Hancock, and S. Rosenfeld for generously providing expression plasmids and kinesin protein, and C. Spiess for assistance with protein expression. B. Weis, P. Harbury, D. Donoho, M. Filler, K. Slon, and members of our laboratory provided helpful advice and discussions. C.L.A. is supported by the Cancer Research Fund of the Damon Runyon-Walter Winchell Foundation (Fellowship DRG-1649). A.N.F. is supported by a Predoctoral Fellowship from the NSF. This work was supported by a grant from the National Institute of General Medical Sciences to S.M.B.
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