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note
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-6 torr), followed by a 20-nm layer of chromium. The remaining photoresist was stripped in acetone and the samples were immersed in buffered hydrofluoric acid for 7 min. This produced channels 1 μm deep and 30 μm wide, with "overhangs" on the walls resulting from the slow etching of SiO as compared with glass (see Fig. 1B). The remaining chromium was stripped and the samples were cleaned and stored in ethanol.
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2, MT seeds, and an oxygen scavenging system [4 mM dithiothreitol, catalase (0.2 mg/ml), glucose oxidase (0.4 mg/ml), and 50 mM glucose] was squashed firmly between slide and cover slip. The sample was sealed with paraffin and held at a constant temperature of 22°C on the microscope stage (12). Catastrophes were often observed under these conditions, and growth from the minus-end of the seeds was rare.
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2, MT seeds, and an oxygen scavenging system [4 mM dithiothreitol, catalase (0.2 mg/ml), glucose oxidase (0.4 mg/ml), and 50 mM glucose] was squashed firmly between slide and cover slip. The sample was sealed with paraffin and held at a constant temperature of 22°C on the microscope stage (12). Catastrophes were often observed under these conditions, and growth from the minus-end of the seeds was rare.
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1842295547
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note
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Samples were viewed by video-enhanced differential interference contrast (DIC) microscopy (Nikon Diaphot with Paultek charge-coupled device camera). The oil immersion objective (60×) was held at constant temperature (22°C) and the condenser was used without oil to keep the sample temperature coupled to that of the objective. Background subtraction, two-frame averaging, and contrast enhancement were performed online (Omnex, Imagen) and images were recorded on videotape. For MT tracking and shape analysis, frames were digitized (Perceptics Pixelbuffer) and stored on a Macintosh computer.
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1842374899
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M. Dogterom and B. Yurke, data not shown
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M. Dogterom and B. Yurke, data not shown.
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22
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1842339157
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note
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L was taken as the length L of the MT. The results for four MTs were rejected, two because of a bad fit and two because they were curved before encountering the wall and appeared to grow twice as fast after encountering the wall. Before contact with the wall, the ends of freely growing MTs were tracked by eye with a computer mouse, and the MT length was determined as the distance between the MT end and the position of the seed. Not all MT ends that approached the wall were caught underneath the overhang on the wall; some of the MTs that were caught stopped growing because they were too short to buckle under their polymerization force (none of these MTs were followed any further).
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The changes in MT length and the applied forces were extracted for each 2-s time interval from data such as shown in Fig. 3A (total of 24 MTs, 1292 intervals). The results were binned according to force, and within each force interval the corresponding MT length changes were averaged to give the average growth velocity and its standard error. The uncertainty in the estimate of the average growth velocity is attributable to measurement errors and to variability in the growth velocity [F. Verde, M. Dogterom, E. Stelzer, E. Karsenti, S. Leibler, J. Cell Biol. 118, 1097 (1992)]. The velocity at zero force was calculated from data taken before contact with the wall (total of 23 MTs, 2309 intervals). To address the concern that we might be overestimating the velocity at high force (because MTs that stall do not buckle and cannot be analyzed), we checked our video recordings for stalling MTs. We found only one that was within the length range (and therefore the force range) of the other MTs we analyzed, so we assume that we are not seriously overestimating the velocities.
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2 (mean ± SD). Errors in this number could arise from measurement errors in the position of the ends and the middle of the MT. This is especially true when measuring short MTs, in which case noise may lead to an underestimation of the rigidity. The 12 MTs varied from 10 to 20 μm in length. No length dependence of κ was apparent over this range, but MTs shorter than 10 μm produced lower values for κ.
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0029775654
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p that is directed parallel to the axis of the MT. The contact angle with the wall does not play any role because the direction of the force is determined by the shape of the buckled MT, not by the normal to the wall. The Brownian ratchet model for a MT that grows by bending perpendicular to its axis is described in A. Mogilner and G. Oster, Biophys. J. 71, 3030 (1996).
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1842405221
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2. Note, however, that B is much smaller than A, implying that the effect of force is in any case dominated by a decrease in the on-rate, a result that is obtained for every positive value of q.
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1842371916
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note
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We thank T. E. Holy, S. Leibler, and K. Svoboda for discussions; K. Baldwin, T. E. Holy, and A. N. Pargellis for technical help; B. Shraiman and K. Svoboda for critical reading of the manuscript; and S. Leibler for use of his lab to prepare tubulin and MT seeds.
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