Cell, Vol. 59, 915-925, December 1, 1989. Copyright 0 1989 by Cell Press

One-Dimensional Diffusion of Microtubules Bound to Flagellar Dynein

Ronald D. Vale: David R. SolI,+ and I. Ft. Gibbons* *Cell Biology Program Department of Pharmacology University of California School of Medicine San Francisco, California 94143 t Department of Biology University of Iowa Iowa City, Iowa 52242 *Pacific Biomedical Research Center University of Hawaii Honolulu, Hawaii 98822

Summary

Dynein is a multisubunlt ATPase that powers mlcrotu- bule-based motlllty. We find that a dissociated dynein particle containing the p heavy chain subunit translo- cates microtubules unidirectionally over a glass sur- face In the presence of ATI? However, after nucleo- tide hydrolysis is inhlblted by vanadate, unidirectional trandocation ceases, and mlcrotubules Instead under- go irregular back-and-forth motion along their longitu- dinal axes. Ouantltatlve analysis reveals that this mo- tion is due to thermal-driven diffusion, but, unlike a particle undergolng Brownian motion, the diffusion is restricted to one dlmenslon. The properties of the dif- fusional movement indicate that dynein can interact with mlcrotubules in a way that permits the latter to diffuse only along their longitudinal axes. This weak binding Interaction may constitute an important inter- mediate state in dynein’s force-generating cycle.

Introduction

Dynein is the force-generating enzyme responsible for ciliary and flagellar movement (Gibbons, 1981) as well as other forms of microtubule-based intracellular motility, in- cluding retrograde axonal transport (Paschal and Vallee, 1987; Schroer et al., 1989) and possibly mitosis (Pratt, 1984). One of its best characterized forms is the outer-arm dynein from sea urchin sperm flagella that forms cross bridges between adjacent outer-doublet microtubules in the axoneme. The ATP-driven cyclic activity of these dynein cross bridges generates the sliding between outer- doublet microtubules that gives rise to normal flagellar beating. The outer-arm dynein is a complex structure of 1200 kd that by electron microscopy appears to consist of two globular heads connected by stalks to a common base (Sale et al., 1985). The two globular heads, which are com- posed of distinct a and 8 heavy chains (470 kd each) with different ATF’ase properties (Tang et al., 1982) are thought to be the important domains involved in force production. Linear mapping of the heavy chains indicates that the ATP binding site lies within a multiply folded region of

70-100 kd in the midregion of each heavy chain (Mocz et al., 1988; King and Witman, 1988).

The hydrolysis of ATP by dynein in intact flagella is tightly coupled to their motility (Brokaw and Benedict, 1988; Gibbons and Gibbons, 1972). Kinetic studies of the dynein ATPase cycle show that ATP binds to the catalytic site of dynein and is hydrolyzed rapidly. Release of the hy- drolysis products (ADP and Pi) is relatively slow, with the release of ADP being the fate-limiting step for dynein in solution (Johnson, 1985; Holzbaur and Johnson, 1989). The force-producing event is believed to be linked to the enhanced release of ADP and Pi upon rebinding of dynein to the microtubule (Omoto and Johnson, 1988) in a manner analogous to the rebinding of myosin to actin in the myosin cross bridge cycle (Cooke, 1988). However, al- though the binding of ATP to dynein has been shown to release dynein from a tight “rigor-like” interaction with microtubules (Gibbons and Gibbons, 1974; Porter and Johnson, 1983), the manner in which dynein interacts with microtubules at other stages of its ATPase cycle has not yet been defined.

The development of in vitro motility assays offers new opportunities for studying the kinetic interactions of dy- nein and other force-generating proteins with their corre- sponding cytoskeletal polymers (Warrick and Spudich, 1987; Vale, 1987). We (Vale and Toyoshima, 1988) and others (Paschal et al., 1987; Lye et al., 1987) have recently developed such assays for dynein, which involve adsorb- ing dynein onto a glass surface and then using video mi- croscopy to observe the ATP-dependent translocation of purified bovine brain microtubules over the surface.

In our present work, we use this in vitro motility assay to show that microtubules bound to dynein heads undergo continual thermal-driven movements along their longitu- dinal axes when nucleotide hydrolysis by dynein is in- hibited. Such one-dimensional diffusional motion involv- ing a protein and a biological polymer has not been reported previously, although it has been postulated to un- derlie the motion of kinetochores along microtubules (Hill, 1985; Koshland et al., 1988) and of DNA binding proteins (e.g., lac repressor) along DNA (Winter et al., 1981; von Hippel and Berg, 1989), possibly as a result of weak pro- tein-polymer bonds. A similar type of weak interaction ap- pears to permit dynein heads to maintain attachment to microtubules yet allow thermal-driven diffusion of the microtubules along their length. By quantitating the diffu- sional movements of microtubules in this in vitro system, we have been able to partially characterize this weak bind- ing interaction, which may represent an important inter- mediate state in the normal force-generating cycle of dynein ATPase.

Results

To elucidate the fundamental elements of the force-gen- erating process, it is advantageous to identify and utilize

Cdl 916

0 5 10 15 20 Fraction Number

Figure 1. Separation of a and 6-C Heavy Chain Subunits of Flagellar Outer-Arm Dynein and Assays for ATPase and Microtubule Transloca- tion Activity

The heavy chain subunits were dissociated by dialysis against a low ionic strength buffer and were separated from one another by sucrose density gradient centrifugation. (Top) The distribution of heavy chain subunits in the gradient by SDS-PAGE (fraction 1 corresponds to the bottom of the gradient and fraction 20 to the top); only the top portion of the gel is shown. The 6 chain sediments as a discrete peak at about 12s in fractions 10-14. The aggregated a heavy chain spreads across the lower region of the gradient in fractions l-10. (Bottom) The distribution of microtubule translocating (solid circles) and ATPase (open squares) activity in the same gradient. Four other gradients analyzed in the same manner demonstrated identical re- sults.

the minimal functional portion of a motor protein (Toyo- shima et al., 1987). Working toward this goal, we first dem- onstrate that the p-IC subunit of flagellar dynein is capa- ble of generating microtubule movement and then use this subunit in most of the subsequent experiments.

The p-K Subunit of Dynein Produces Microtubule Translocation The a and p heavy chain ATPase subunits of outer-arm dynein from sea urchin sperm flagella were dissociated by dialysis against a low ionic strength buffer and then sepa- rated by sucrose density gradient centrifugation (Figure 1, top). The ATPase activity (Figure 1, bottom) mostly cosedi- mented with the peak of the 9-IC complex, which consists of the 9 heavy chain complexed with one intermediate chain (Tang et al., 1982). The fractions containing the p-IC complex also produced movement similar to that described for intact outer-arm dynein in the in vitro motility assay (Paschal et al., 1987). The relative level of motility, deter- mined by measuring the maximum dilution of each frac- tion that supports movement, correlated closely with the distribution of the j3-IC subunit in the gradient (Figure 16). In the presence of 1 mM ATP, the velocity of microtubule

translocation induced by the p-IC subunit (3.9 * 0.6 Km/s; n = 120) was somewhat higher than that produced by in- tact outer-arm dynein (2.9 f 0.8 km/s; n = 100). Similar results for dynein from a different species of sea urchin were reported independently by Sale and Fox (1988).

Gradient fractions containing the other dynein head, the a subunit, supported neither movement nor microtubule attachment to the glass, even when used at a concentra- tion of 100 9glml. The isolated a subunit, however, demon- strated little ATPase activity, suggesting that it may not re- tain its native conformation after its separation from the j3 chain by low salt dialysis.

Microtubule attachment to glass and translocation both displayed a sharp threshold with respect to protein con- centration. After incubation of the glass with p-IC fraction at a concentration of 44 pglml or less, microtubules did not attach to the surface and no movement was observed; at 50 wglml, however, numerous microtubules attached and translocated at near-maximal velocity. Similar results were obtained with intact dynein. Assuming that the majority of dynein molecules bind to the glass (see Vale and Toyo- shima, 1989), this threshold corresponds to a surface den- sity of ~1000 dyneins per wm2. However, the density of functional heads capable of translocating microtubules in the assay is not known.

To determine the direction of translocation induced by 3-IC, microtubules of known polarity were obtained by polymerizing tubulin from the plus ends of flagellar axo- nemes (Vale and Toyoshima, 1988). Such microtubule- axoneme complexes always translocated with their plus ends leading (n = 110 microtubules), indicating relative movement of p-IC toward the minus end of the microtu- bule. This direction of movement is the same as that de- scribed for other dynein molecules (Sale and Satir, 1977; Paschal and Vallee, 1987; Vale and Toyoshima, 1988). Un- like the single-headed 14s dynein from Tetrahymena cilia (Vale and Toyoshima, 1988) neither intact outer-arm dy- nein nor the single-headed p-IC induced rotation of mi- crotubule-axoneme complexes. The microtubule translo- cation properties of p-IC thus resemble those of intact outer-arm dynein.

Although movement of long microtubules in the pres- ence of ATP was always unidirectional, short microtu- bules (<*3 pm) would occasionally pause and undergo apparently random back-and-forth motion for several sec- onds before resuming their translocation in the original direction (Figure 2). As described below, such back-and- forth motion becomes the predominant form of movement for all microtubules upon addition of inhibitors of dynein ATPase activity.

Back-and-Forth Motion of Microtubules Occurs after Inhibition of Dynein ATPase The unidirectional translocation of microtubules by dynein requires energy derived from ATP hydrolysis: upon addi- tion of 5 PM or more of the ATPase inhibitor vanadate, the unidirectional translocation induced by f3-IC or intact outer-arm dynein ceased completely. However, the micro- tubules did bind to the dynein-coated glass and undergo continual aperiodic backward and forward displacements

$nn-Dimensional Diffusion of Microtubules

the solution; the presence of ADP or vanadate alone did not suffice. In the presence of 200 uM vanadate, binding of microtubules to the glass coated with 84 required higher concentrations of ADP (500 uM) than of ATP (10 ufvt). Virtually all microtubules that bound to the glass in the presence of ATP and vanadate or ADP and vanadate exhibited the back-and-forth motion, and the movements displayed in ATP and vanadate or ADP and vanadate were indistinguishable. In the assays that included ADP, 1 mM diadenosine pentaphosphate, 100 U/ml hexokinase, and 10 mM glucose were added to the motility medium to in- hibit dinucleotide kinase and to convert any residual ATP to ADf?

The above results indicate that the back-and-forth mo- tion of microtubules requires the presence of nucleotide bound to the p-IC or dynein on the glass surface. Further- more, the finding that this motion occurs in the presence of the ATPase inhibitor vanadate combined with a highly purified preparation of ADP, which is not a substrate for hy- drolysis or motility, argues that motion does not require energy derived from nucleotide hydrolysis. To confirm this point, dynein nucleotidase activity was measured in the same chamber used for the motility assays. No detectable release of Pi (less than 1% of the normal level of ATP hy- drolysis) was observed under the identical conditions used to perform the motility assay (1 mM ADP and 200 uM vanadate). Taken together, these data indicate that chemi- cal energy derived from nucleotide hydrolysis is not re- quired for the back-and-forth motion of microtubules.

Glycerol (20% v/v), which is an inhibitor of dynein ATP- ase activity and thus slows Pi release from the dynein- ADP-Pi complex (Shimizu and Katsura, 1988), also inhib- ited ATP-driven unidirectional translocation of microtubules while permitting their back-and-forth motion (Table 1).

Figure 2. A Sequence of Dark-Field Images of a 3.4 urn Microtubule Undergoing Back-and-Forth Motion During a Pause in Its Earslocation on a Glass Surface Coated with 3-C in the Presence of 1 mM ATP

These frames display only the largest excursions of the microtubule in either direction. In the last two frames, the microtubule resumes trans- locating to the right. The positions of two stationary markers on the glass surface are indicated by arrows in the first panel, and the asterisk marks a reference point equidistant between these markers. Time (in seconds) is indicated in the upper right of each frame. Bar = 1 Wm.

along their longitudinal axes similar to those shown in Fig- ure 2. The observed longitudinal displacements of up to 1 urn were considerably larger than the ~50 nm length of a dynein molecule (Goodenough and Heuser, 1984; Sale et al., 1985) indicating that the microtubules were not sim- ply tethered to one or more dynein heads.

The back-and-forth linear movement of microtubules re- quired the presence of p-IC on the glass surface as well as nucleotide in the solution. No microtubules attached to the surface in the absence of p-IC or intact dynein ad- sorbed on the glass, nor in the presence of 8-IC and the absence of nucleotide (Table 1). Attachment occurred only with 8-IC or intact dynein adsorbed to the glass and either ATP ATP and vanadate, or ADP and vanadate present in

High Resolution Analysis of Microtubule Motion The insensitivity of the back-and-forth motion to inhibitors of dynein ATPase activity and the magnitude of the dis- placement distances indicate that this motion is not pro- duced by forward and reverse power strokes of dynein at- tached to the microtubules. An alternative hypothesis is that these movements are driven by thermal forces and re- flect one-dimensional diffusion of the microtubule along its axis while it is weakly bound to the dynein or p-IC on the surface. In such a case, the individual displacements of a given microtubule, measured with respect to its previ- ous position after successive equal intervals of time, will exhibit a Gaussian distribution about a mean of zero. In addition, the root-mean-square (RMS) displacement (stan- dard deviation of the Gaussian) should depend upon the time interval of measurement and the diffusion coefficient of the microtubule as predicted by the equation 22 = 2Dt for one-dimensional diffusion, where 2, D, and t are the RMS displacement, the diffusion coefficient of the parti- cle, and time, respectively (Berg, 1983).

To analyze the motion of microtubules in order to test this hypothesis, their positions had to be measured ac- curately. Manual tracking proved inadequate owing to the difficulty of determining the precise position of microtu- bule ends in still video frames. To circumvent this prob-

Cell 916

Table 1. Nucleotide Dependence of Microtubule Attachment and Movement

Movement

Nucleotide Attachment Unidirectional Back-and-Forth

None no no no 1 mM ATP yes Yes ye* 1 mM ATP + 200 uM vanadate yes no 9s 1 mM ATP + 20% glycerol yes no yes 1 mM ADP no no no 1 mM ADP + 200 pM vanadate Yes no yes 200 uM vanadate no no no

The assay conditions are those described in Experimental Procedures, except that purified bovine brain microtubules were introduced along with the indicated concentration of nucleotide, phosphate analog, or glycerol. Attachment of microtubules to the dyneincoated surface was scored as negative if, after a 10 min incubation, an average of fewer than two microtubules were bound per 1200 pm* field of view. ADP was purified by reverse-phase HPLC. In the assays that included ADP, 1 mM diadenosine pentaphosphate, 100 U/ml hexokinase, and 10 mM glucose were added to the motility medium to inhibit dinucleotide kinase and to convert any residual ATP to ADP. a Back-and-forth motion in the presence of ATP and no vanadate is intermittent and occurs only for microtubules less than 3 pm long.

lem, a small number of streptavidin-coated colloidal gold spheres 20 nm in diameter were bound to microtubules polymerized from biotinylated tubulin (Figures 3A and 38). The centroid of such a gold sphere provides an excel- lent marker of microtubule position, and its viscous drag

A

E

100 “In

coefficient is negligibly small compared to that of the typical-length microtubule to which it becomes attached (see Experimental Procedures for the calculation). The level of background noise, resulting from electronic and mechanical instability in the system, was determined by measuring the apparent displacements of the centroid of a stationary gold sphere attached directly to the glass sur- face. In our system, the apparent RMS displacements of stationary gold spheres were ~15 nm in 0.2 s intervals (Figure 3E), well below the RMS displacements of up to 170 nm for typical microtubules exhibiting back-and-forth motion (Figure 3C). Microtubules often continued their longitudinal back-and-forth movement in the same linear path for several minutes or more, although they would oc- casionally exhibit abrupt angular deflections up to about 209 and then start back-and-forth movement along the new line of their longitudinal axes (Figure 3D).

Quantitation of the displacements measured parallel and perpendicular to the longitudinal axis of a typical microtubule undergoing back-and-forth motion confirms that the movement is essentially confined to the longitudi- nal axis of the microtubule (Figure 4). Data averaged from eight microtubules at 0.2 s intervals gave an average RMS

Figure 3. Analysis of Back-and-Forth Microtubule Motion on a Glass Surface Coated with 3-C Colloidal gold particles (20 nm) coupled with streptavidin were bound to microtubules polymerized from biotin-labeled tubulin and used as a marker of microtubule position. (A) A schematic of the linkage (“A’ and ‘6” represent avidin and biotin, respectively). (B) An actual dark-field image of a gold particle attached to a 6.4 urn microtubule. (C) The centroid positions of a gold particle attached to a 4.6 urn microtubule undergoing back-and-forth motion in the presence of 1 mM ATP and 200 uM vanadate measured at 0.2 s intervals; note that movement is essentially confined to a linear path. (D) The same as (C) except that the microtubule, measured at 0.06 s intervals, moves back-and-forth along a linear path for a while and then undergoes an abrupt angular deflection, followed by more back-and- forth motion along its new path. (E) The centroid positions of two typical stationary gold particles at- tached to the glass surface were used to calibrate the noise level of the system. A 100 nm scale bar for the centroid analyses in panels (C), (D), and (E) is shown in the lower right.

;;;Dimensional Diffusion of Microtubules

0.4

5 0.0

8 UJ -0.4

2

; o,4;l

20 Time (set)

Figure 4. Quantitation of the Back-and-Forth Motion of a 2.3 nm Microtubule in Directions Perpendicular and Parallel to Its Longitudinal Axis The centroid of the gold bead attached to the microtubule was deter- mined at 240 successive 0.2 s intervals. The net displacements parallel (A) and perpendicular (8) to the microtubule longitudinal axis are shown for each 0.2 s time interval. The RMS displacements for this mo- tion are 191 nm and 15 nm, respectively, corresponding to diffusion coefficients of 9.1 x lo-lo cm% and 0.09 x IO-r0 cm*/s.

displacement of 170 f 30 nm for motion parallel to their longitudinal axes and only 20 f 4 nm for motion perpen- dicular to their long axes. The latter is scarcely above the noise level of our system.

To test whether the back-and-forth motion is random, the distribution of net longitudinal displacements was ex- amined. The net displacements, measured for 2725 suc- cessive intervals of 0.1 s, of a typical microtubule in the presence of ATP and vanadate are plotted as a histogram in Figure 5. The mean net displacement for this microtu- bule is -0.1 nm and the RMS displacement is 91 nm. A Gaussian curve with these parameters fit the distribution of the displacements reasonably well, with the exception that the number of displacements less than 20 nm ex- ceeded the predicted values by approximately 25% (cor- responding to MO? of all displacements). Data obtained from 70 other microtubules all displayed distributions similar to that shown in Figure 5 with mean net displace- ments less than 5 nm; the number of excess displace- ments smaller than 20 nm exceeded the predicted Gaus- sian value by 2%-8% of the total displacements. The excess number of displacement values close to zero may reflect times when displacement is blocked by a non- specific interaction of the microtubule with some compo- nent on the glass surface.

t ' I '

300

t 250

t

t 200

E

z 150 0

100

50

0 1

Net Displacement (nm)

Figure 5. Net Displacement Distances Measured at 2725 Successive 0.1 Set Time Intervals for a 3 pm Microtubule Undergoing Back-and- Forth Motion in the Presence of 1 mM ATP and 200 pM \Fanadate Net displacements were grouped into 20 nm bins. The histogram shows the number of displacements failing into each bin. The mean and standard deviation of the data are -0.1 nm and 91 nm, respec- tively. The curve represents the values of a theoretical Gaussian curve generated for this number of data points with the same mean and stan- dard deviation. The degree of fit for the complete data has a x2 value of 96, corresponding to a probability of less than 10e4. With the two central points deleted, the value of x2 is 55, corresponding to a proba- bility of ~0.1.

The temporal drstribution of the changes in the direction of microtubule movement was examined in order to deter- mine whether there was a tendency for persistent motion in a given direction. For all the microtubules analyzed, the resultant distribution of the number of time intervals be- tween successive reversals in direction closely matched that calculated on the basis of random reversals (data not shown). The above data combined indicate that, at the fre- quency of observation used (0.1 s), changes in direction of movement occur at random intervals with no tendency toward persistent movement in a given direction, and that the magnitudes of net displacements have a nearly Gaus- sian distribution.

To determine whether the spread of the Gaussian curve increases with longer time periods between measure- ments, as predicted for a diffusion-based process, the po- sition of a single microtubule was measured at different time intervals ranging from 0.1 s to 0.9 s. The correspond- ing mean-square displacements (XT increased linearly with the length of the time interval (Figure &A), as pre- dicted by the diffusion equation. Five other microtubules analyzed similarly yielded essentially identical results.

The viscous drag on a microtubule is proportional to its length and to the solution viscosity (see Experimental Procedures). The observed effect of viscosity (altered by addition of glycerol to the assay buffer) on the back-and- forth motion shows that the reciprocal of the mean-square displacement was proportional to the viscosity of the solu-

Time (Set)

2 4 6 6 10

Viscosity (cP)

4 . , . , , . , . . . , . I- O 1 2 3 4 5 6 7

Microtubule Length (pm)

Figure 6. Dependence of the Mean-Square Displacement of the Back- and-Forth Motion of Microtubules on the Time Period Used for Mea- surement, the Viscosity of the Solution, and the Length of the Micro- tubule

(A) The mean-square displacement of a single microtubule determined at time periods ranging from 0.1 to 0.9 s over a total time of 250 s, in standard motility buffer with 1 mM ATP and 200 KM vanadate; the slope of the line corresponds to a diffusion coefficient of 5 x IO-lo cm2/s. (B) The mean-square displacement in a solution containing 60 mM (rather than 40 mM) KCI and 0%. lo%, 15%, 20%, 40%. or 60% (w/v) glycerol. Between 5 and 15 microtubules (1.5-2.5 Km in length) were analyzed for each glycerol concentration. The mean-square displace ment of each microtubule was determined from 150-300 measure- ments of net displacement taken at 0.2 s intervals. The reciprocal of the average of mean-square displacements is plotted against the vis- cosity, with the corresponding reciprocal of the diffusion coefficient shown on the right axis. (C) The reciprocal of mean-square displacements (determined from 150-250 net displacement measurements at successive 0.2 s inter- vals) of 26 individual microtubules is plotted versus their lengths. In all cases, the lines represent the best fit by linear regression.

tion (Figure 6B). Data from individual microtubules of different lengths showed that the reciprocal of the mean- square displacement increased with increasing microtu- bule length (Figure 6C), although there was considerable scatter in these data for reasons that are unclear. The Gaussian distribution of the displacements and the ef- fects of time, viscosity, and microtubule length on the RMS displacement provide strong evidence that back- and-forth motion of microtubules is driven by thermal diffusion.

The observed mean-square displacement corresponds to an average diffusion coefficient of approximately 5 x lo-lo cm% for a 2 urn microtubule on a surface coated with p-IC in standard assay buffer containing 40 mM KCI. Under these same assay conditions, the observed diffu- sion coefficient of microtubules on a surface coated with intact outer-arm dynein was 0.9 x lo-lo cm2/s, indicating that the a subunit may contribute significant resistance to one-dimensional diffusion.

Effect of Ionic Strength on Microtubule Diffusion The one-dimensional diffusion of microtubules bound to p-IC in the presence of ATP and vanadate was affected by the concentration of salt in the assay buffer. The diffu- sion coefficient for microtubules (average length of 2.5 urn) increased from 1.6 x lo-lo cm2/s with no KCI in the buffer to 6.5 x lo-lo cm2/s in the presence of 60 mM KCI (Figure 7). At 100 mM KCI, microtubules remained at- tached to the glass coated with 6-IC and exhibited back- and-forth motion for only a few seconds before dissociat- ing into the solution. At 125 mM KCI, no attachment of microtubules to the surface was observed. These results indicate that increasing salt concentration decreases the resistance to diffusional motion of the microtubules, pos- sibly by weakening the interaction between microtubules and dynein.

Discussion

SinglaHeaded Dynein Can Induce Microtubule Movement The dynein molecules from flagella and cilia (Johnson and Wall, 1963; Goodenough and Heuser, 1964; Sale et al., 1965) and from bovine brain cytoplasm (Vallee et al., 1966) contain either two or three globular heads, with each head being composed of a single distinct heavy chain polypeptide (Johnson, 1965). In this study, we have shown that the single-headed p-IC heavy chain complex of a two-headed dynein from sperm flagella can induce microtubule translocation in an in vitro motility assay; similar results have been obtained independently by Sale and Fox (1966). A two-headed proteolytic fragment of the three-headed dynein from Tetrahymena cilia was also re- cently reported to induce microtubule movement (Vale and Toyoshima, 1969). These studies indicate that the complete multiheaded structure of outer-arm dynein is not essential for motility, and that at least the head containing the 6 heavy chain has the potential to produce transloca- tion of microtubules in vitro, either by itself or in coopera- tion with other 6-IC subunits. Whether or not all of the dis-

$r;-Dimensional Diffusion of Microtubules

01 1. I I , . !o 0 20 40 60 80 100

KCI Cont. (mM)

Figure 7. The Effects of KCI Concentration on the Diffusional Motion of Microtubules and on Surfaces Coated with f3-IC

The indicated concentration of KCI was added to a buffer containing 3 mM Mg&, 10 mM Tris-HCI (pH 7.5) 1 mM EGTA, and 1 mM ATP, in the presence of 200 uM vanadate. The mean-square displacements of diffusional motion were measured for 5-15 microtubules at each KCI concentration (150-300 measurements per microtubule at 0.2 s time intervals); the right axis shows the corresponding diffusion coeffi- cients.

tinct heads in a dynein molecule have this potential remains to be determined.

One-Dimensional Diffusion Reflects a Weak Dynein-Microtubule interaction A most unexpected finding of this study was the observa- tion of back-and-forth motion displayed by microtubules on glass surfaces coated with either intact outer-arm dynein or the separated fi-IC complex. A variety of evi- dence indicates that this back-and-forth motion of microtu- buies is driven by thermal forces rather than by dynein- driven power strokes: First, back-and-forth motion persists after dynein ATPase activity is inhibited by the phosphate analog vanadate or by glycerol. It also occurs in the pres- ence of vanadate and ADP which is not a substrate for hy- drolysis (Gibbons, 1966). Thus, unlike unidirectional trans- location, the back-and-forth movements do not derive their energy from nucieotide hydrolysis. Second, analysis at high spatial resolution shows that the net displace- ments of a microtubule examined at successive time inter- vals can be fit reasonably well by a Gaussian curve with a mean net displacement very close to zero, and that the mean-square displacement increases in proportion to the time interval between measurements. These data indicate that the motion is a one-dimensional random walk. Third, the mean-square displacement decreases with increas- ing viscosity of the solution and with increasing length of the microtubule, both of which increase the viscous drag force on the microtubule. As a result of these data, we con- clude that back-and-forth movement of the microtubules on the glass is a one-dimensional diffusional motion driven by thermal forces.

The attachments of dynein to the microtubule, however, clearly exert a significant constraining influence on this

thermal-driven motion. For a 2 urn microtubule associated with p-IC on the glass in 80 mM KCI, the observed longitu- dinal diffusion coefficient of 8.5 x lo-lo cm% is a factor of about 8 less than the calculated diffusion coefficient of 67 x lo-lo cm2/s for completely unconstrained one- dimensional motion adjacent to a surface (see Experi- mental Procedures for the calculation). This observed diffusion coefficient decreases lo-fold under conditions that presumably increase the affinity of dynein for the microtubule, such as lower ionic strength or the presence of the a subunit in the two-headed intact dynein. Thus, dynein exerts a moderate, but not negligible, frictional re- sistance to diffusional motion of microtubules along their long axes.

The constraining influence of the dynein-microtubule interaction is still more apparent in motion perpendicular to the long axis. The theoretical diffusion coefficient for movement of a microtubule perpendicular to its long axis is 33 x lo-lo cm%, only 2-fold less than for movement parallel to this axis (Brennen and Winet, 1977). However, the observed transverse diffusion coefficient of a 2 pm microtubule associated with p-IC is less than 0.1 x lo-lo cm% (Figure 4)-a value more than two orders of magni- tude lower than the theoretical diffusion coefficient and only slightly above the noise level of our system. Further- more, microtubules rarely diffuse away from the dynein- coated surface even after several minutes of observation. Thus, the interaction of dynein with microtubules imposes a considerable restraint to lateral movement and dissocia- tion of the microtubule, while contributing much less resis- tance to diffusional movement along the longitudinal axis of the microtubule.

Properties of the Weak Dynein-Microtubule interaction The nucleotide requirements of one-dimensional diffu- sion provide information on the dynein-nucleotide com- plex that underlies the weak binding interaction. The oc- currence of longitudinal diffusion of microtubules in the presence of vanadate and either ATP or ADP is consistent with previous evidence that the slowly dissociating dy- nein-ADP-vanadate complex can be formed either from ADP or ATP (Shimizu and Johnson, 1983). The trapped dynein-ADP-vanadate complex that exhibits one-dimen- sional diffusion is thought to simulate the transient dy- nein-ADP-Pi state that occurs in the normal dynein ATP- ase cycle. Consistent with this hypothesis, longitudinal diffusion of microtubules is observed also in the presence of ATP and glycerol, an agent that decreases the rate of Pi release from the dynein catalytic site (Shimizu and Katsura, 1988).

In this in vitro system, both the attachment of microtu- buies to dynein on the surface and the magnitude of their subsequent diffusional movement depend strongly upon salt concentration, suggesting that weak electrostatic forces play an important role in this dynein-microtubule interaction. As discussed by von Hippel and his col- leagues for the case of lac repressor sliding along DNA (Winters et al., 1981; von Hippel and Berg, 1989), elec- trostatic interactions between a protein and a polymer can

Cdl 922

provide a high energy barrier to lateral diffusion or dissoci- ation, while contributing a relatively low energy barrier to linear diffusion of the protein along the polymer lattice. A similar model could account for the one-dimensional diffusion of dynein heads relative to the tubulin lattice of the microtubule.

An alternative model is that dynein heads are retained in close proximity to the microtubule by rapid cycles of as- sociation and dissociation. Accurate calculation of the ki- netic constants would require knowledge of the mean number of dynein heads interacting with the microtubule as it diffuses. We have no data for this number, but the oc- casional abrupt angular deflections of microtubules sug- gest that the number is low enough that statistical fluctua- tions occasionally reduce it to a single attachment about which pivoting of the microtubule can occur (Figure 3). By considering the limiting case of a microtubule interacting with a single, rigid dynein, one can estimate a lower bound for the dissociation rate constant. The ratio of the ob- served diffusion coefficient of a microtubule interacting with the dynein (5 x lo-lo cm*/s in 40 mM KCI) to its the- oretical value for unconstrained diffusion (67 x lo-‘0 cm*/@ could be interpreted to indicate that the microtu- bule is bound to a dynein head for 92% of the time. As- suming that a dynein on the glass is able to recapture a dissociated microtubule if the latter has diffused away from the surface by a distance of less than 15 nm (the ap- proximate size of a dynein head), then the microtubule (moving with its unconstrained transverse diffusion coeffi- cient of 33 x lo-lo cm*/@ could be dissociated for a mean time of 0.17 ms and still have a 95% probability of remaining within the capture radius. The corresponding mean time of 2.1 ms for which the microtubule would be bound to the dynein equates to a lower bound for the dis- sociation rate constant of 430 s-l. A similar calculation using the observed diffusion coefficient for our intact two- headed dynein yields a lower bound for the dissociation rate constant of 77 s-l.

It should be emphasized that these calculations of the slowest possible dissociation rates require assumptions regarding the number of interacting dyneins as well as the capture radius and flexibility of individual dynein mole- cules. Nonetheless, these values are both significantly faster than the dissociation rate of 0.6 s-l for the 22s Tetrahymena dynein-microtubule complex, determined by a light scattering assay in the presence of ATP and vanadate (Shimizu and Johnson, 1963). This disparity may be due in part to the presence of the third microtubule binding head in 22s Tetrahymena dynein and in part to the different experimental assay systems.

Role of Weak Binding Interactions in Motile Protein Systems The observed thermal motion of microtubules may play a significant role during normal ATP-induced microtubule movement produced by dynein. In this in vitro system, dynein weakly bound to microtubules, either by elec- trostatic interactions or rapid on-off kinetics, could be dis- placed to adjacent tubulin monomers by thermal fluctua- tions at a rate (k) of up to 10,600 s-l (k = 2DI[Ax]*, where

D is the experimental diffusion coefficient of 6.5 x lo-lo cm*/.s and Ax [the step size] is the monomer spacing of tubulin subunits in the microtubule polymer lattice [4 nm]). If ATP hydrolysis could provide the energy for dynein to act as a ratchet that captures thermal movements in one direction and prevents them in the opposite direction (analogous to a Maxwell demon; see Feynman et al., 1963) then the observed diffusion coefficient for microtu- bules could account for unidirectional sliding speeds of up to 22 t.4m/s.

In the axoneme, microtubules under mechanical stress presumably undergo little thermal motion, but an elastic dynein molecule may be stretched and displaced by ther- mal forces to adjacent tubulin monomers along the microtubule polymer lattice at comparable or even faster rates. Such a mechanism was suggested by A. F. Huxley (1957) in his original theory for muscle contraction. The bacterial flagellar motor, driven by a proton gradient across the membrane, is another example of a biological machine that may operate on such principles (Khan and Berg, 1963). This hypothesis differs from the conventional articulating cross bridge model in which product release during the ATPase cycle causes a flexing between do- mains within the cross bridge that changes its effective orientation relative to the cytoskeletal polymer (Huxley, 1969; Vibert and Cohen, 1988). Further work will be needed to distinguish between these two models.

In addition to a possible role in force production, the weak binding interaction described in this study would al- low the subset of dynein heads that are not generating force and are poised to undergo a power stroke to main- tain contact with the microtubule, yet contribute little fric- tional resistance to the microtubule sliding produced by the other subset of dynein molecules actively engaged in force production. Indeed, electron micrographs of cilia (Goodenough and Heuser, 1984) and flagella (Sale et al., 1985) show that virtually all of the outer-arm dynein heads remain in contact with the Et-tubule of the adjacent doublet while the cilium is beating normally in the presence of ATP

In addition to the present evidence for a weak binding interaction of microtubules with dynein, there is consider- able indirect evidence for a weak binding interaction be- tween myosin and actin filaments (reviewed in Cooke, 1986). Tension measurements, for example, indicate that relaxed muscle with myosin in its ATP or ADP-Pi state is stiff when subjected to a rapid stretch (0.1 ms) but compli- ant when subjected to aslow stretch (Brenner et al., 1982). These and other experiments suggest that myosin is in a rapid equilibrium between attached and detached states whenever ATP or ADP-Pi are bound to the active site of the molecule (Schoenberg, 1985). Thus, a weak polymer binding state may be an important general property of the ATPase cycle in force-transducing molecules. It is not known whether the weak binding intermediate of myosin allows one-dimensional diffusion of actin filaments, al- though it should be possible to examine whether such events occur by using an analogous in vitro myosin assay (Kron and Spudich, 1986).

Weak binding interactions may also play important roles

f;s-Dimensional Diffusion of Microtubules

in other systems by allowing translocating molecules to maintain their attachment to the polymer for extended periods of time. For example , one-dimensional diffusion has been implicated as a general mechanism of enhanc- ing association rates between proteins and their targets (Adam and Delbriick, 1966; von Hippel and Berg, 1969) and as a means by which chromosomes move along microtubules (Hill, 1965; Koshland et al., 1966). There is kinetic evidence for one-dimensional diffusion of DNA binding proteins, such as the lac repressor, along DNA (Winter et al., 1961) and of microtubule-stabilizing proteins along microtubules (Pabion et al., 1964), although there was no direct visual observation of diffusion. Moreover, DNA helicases (Yarranton et al., 1979; Endlich and Linn, 1965; Lasken and Kornberg, 1966) and the 40s subunit of eukaryotic ribosomes (Kozak, 1960) are thought to un- dergo energy-dependent progression for hundreds of base pairs along DNA or RNA without detaching, and a single kinesin molecule can move a microtubule for a time corresponding to several hundred cycles of ATP hydroly- sis (Howard et al., 1969). Since Brownian movement would rapidly separate a dissociated translocating protein from its polymer within a millisecond, the protein and poly- mer must maintain contact for the majority of the translo- eating cycle. The combination of a weak binding interaction to maintain attachment and a strong binding interaction to generate force or movement may be used by many types of protein translocating systems.

Experimental Procedures

Materials ADP from Boehringer Mannheim was purified by Cl6 reverse-phase HPLC to remove a trace (0.02%) contamination of ATP A succinimidyl ester of biotin with a long chain spacer (biotin XX succinimidyl ester; #B-1606) was obtained from Molecular Probes, Inc. Colloidal gold (20 nm) coupled with streptavidin was obtained from Polysciences, Inc. Taxol was a generous gift of Dr. Matthew Suffness at the National Can- cer Institute. All other enzymes and chemicals were from Sigma Chem- ical Co.

Sodium orthovanadate (Fisher Chemicals) was prepared as a 20 mM stock solution in 25 mM Tris-HCI (pH 6).

Pmparatlon of flagellar Dyneln and p-IC Subunlt Outer-arm dynein was extracted from sperm flagella of the sea urchin Tripneustes gratilla with 0.6 M NaCl and purified by sucrose gradient density centrifugation (Tang et al., 1962). The a and 6-IC subunits were isolated by low salt dialysis followed by density gradient centrifu- gation (Tang et al., 1962). The specific ATPase activity of the peak frac- tion of &IC was 0.57 pmol of Pi per minute per milligram. Unless specified, all experiments described in the text were performed with the isolated 5-IC complex.

Pmparatlon of nbulln and MIcrotubules Bovine brain tubulin, purified according to Weingarten et al. (1975) was polymerized into microtubules by addition of 1 mM GTP 4 mM MgClz, and 10% DMSO for 30 min at 3pC and subsequently stabi- lized by addition of 20 pM taxol. When appropriate, tubulin was cova- lently modified with biotin XX succinimidyl ester to a stoichiometry of approximately 0.5 mol of biotin per mol of tubulin, according to the pro- cedure of Kristofferson et al. (1966).

Motlllty Assay The routine assay for motility was essentially as described for Tetra- hymena dyneins by Vale and Toyoshima (1966). A 10 pl perfusion chamber was prepared by placing two parallel lines of Apiezon M grease on a glass slide (Gold Seal, Clay Adams) with fragments of #O

glass cover slips as spacers and an 16 x 16 mm #1 glass cover slip (Corning) on top. Purified 21s dynein or f3-IC complex was introduced into the chamber at a concentration of 150 &r/ml and allowed to stand for 2 min, followed by flushing with 50 pl of motility buffer (40 mM KCI, 10 mM Tris-HCI IpH 7.51, 3 mM MgClz, 1 mM EGTA, 1 mM dithiothrei- tol). Fifty microliters of a 30 pg/ml suspension of the taxol-stabilized microtubules in motility buffer was then perfused into the chamber. Microtubules were visualized on a Zeiss IM-35 microscope with dark-field illumination using a 100 W mercury light source, heat- reflecting and absorbing filters, a UV cutoff filter, an Olympus 1.2-1.33 NA dark-field condenser, and a Nikon 50x plan 0.5-0.65 NA objective. The image was projected onto the target of a Hamamatsu C2400 SIT camera using a 25x ocular and recorded using a Sony 5600H U-matic video tape recorder.

The following modifications were used to quantitate the diffusional movement of micmtubules. Microtubules polymerized from biotinyl- ated tubulin were diluted to a final concentration of 30 @ml tubulin into motility buffer and then sheared into l-5 nm fragments by passing the suspension three times through a 27 gauge needle. The biotin- ytated microtubules (100 pl) were then incubated for 5 min with 2 PI of the stock suspension of avidin-coupled 20 nm gold particles, which resulted in approximately 20% of the microtubules binding at least one gold particle.

Motion Analysis of Mkrotubules The velocity of unidirectional microtubule translocation in the pres- ence of ATP was measured by a semiautomated tracking program de- veloped by Dr. Steve Block (Sheet2 et al., 1966). Analysis of micmtu- bule-gold particle complexes undergoing back-and-forth diffusional movement was performed by first digitizing the video image with a VP100 real-time digitizer (Motion Analysis Corp., Santa Rosa), as de- scribed previously (SOIL 1966). The contrast threshold of the digitizer was adjusted so that only the edge of the 20 nm gold particle was de- tected, and the pixel coordinates defining the edge of the gold particle were then stored in a data file in a SUN Ill computer. The rate of data acquisition was either 5 or 10 per set of videotape, as given in the text. The position of the centroid of the bead in each frame digitized was subsequently calculated using the custom software package of the Dy- namic Morphology System (DMS, SVUI. Iowa City, Iowa) (SOIL 1966). This position was used to obtain the net displacement of the micmtu- bule between the successive frames analyzed, with the direction of positive or negative movement being chosen arbitrarily for each micmtubule. A similar strategy was used by Gelles et al. (1966) to track kinesincoated beads moving along microtubules.

Biochemkal Procadums Dynein and tubulin protein concentrations were determined using the Bradford dye-binding assay. Electrophoresis was performed on 3%- 5% polyacrylamide gel gradients in the presence of SDS (Laemmli. 1970). Dynein ATPase activity in the motility chamber was measured by incubating motility buffer (10 ~1) together with 1 mM ATP or ADP in the presence or absence of 200 pM vanadate for l-15 min. After the incubation, the fluid was removed from the chamber with a Pipetman. The phosphate released by nucleotide hydrolysis was determined by the assay of Kodama et al. (1966).

Cakulatlon of VISCOUS Drag Forces The diffusion coefficient (D) for any shaped particle is given by the Einstein-Smoluchowski equation D = kT/y, where y is the drag coeffi- cient, k is the Boltzmann constant, and T is absolute temperature (Berg, 1963). For a long cytinder of length I and radius r moving parallel to its long axis at height h above a surface, y = 2nnllln(2h/r) (Brennen and Winet, 1977). Thus, a microtubule of length 2000 nm and radius 12 nm moving parallel to its long axis at an estimated height (based on the molecular dimensions of dynein [Goodenough and Heuser, 1964; Sale et al., 19651) of 50 nm above the surface, in a medium of viscosity(n) 0.01 g/cm per second, at 293OK, has a drag coefficient of 6.0 x 1O-6 g/s, corresponding to a calculated diffusion coefficient of 67 x lo-j0 cm2/s. Similarly, the drag coefficient for motion perpendic- ular to the long axis of the microtubule is y = 4nnf/ln(2hh), which leads to a diffusion coefficient of 33 x lo-r0 cm*/s. The drag coefficient for the 20 nm gold spheres used as markers of microtubule position is given by Stokes law, y = 6xnr, and has a value of 0.19 x 10v6 g/s, which is negligibly small compared to that of the microtubule.

We are grateful to Dr. W.-J. Tang, Cheryl Phillipson, Pat Harwood, and Steve Coulson for technical assistance. We are also indebted to Ed Voss for his assistance with the motion analysis and to Dr. A. Hyman for his advice on attaching colloidal gold to microtubules. Dr. Joe Howard, Dr. Barbara Gibbons, and Mr. Fady Malik provided helpful comments on the manuscript. This work was supported by National In- stitutes of Health grant GM38499 and a Searle Scholarship to Ft. D. V, by NIH grant HD18577 to D. R. S., and by NIH grants GM30401 and HDO8585 to I. R. G. and Barbara Gibbons.

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 USC. Section 1734 solely to indicate this fact.

Received May 22, 1989; revised September 25, 1989.

References

Adam, G., and Delbriick, M. (1988). Reduction of dimensionality in bio- logical diffusion processes. In Structural Chemistry and Molecular Bi- ology, A. Rich and N. Davidson, eds. (New York: W. H. Freeman and Co.), pp. 198-215.

Berg, H. C. (1983). Random Walks in Biology (Princeton, New Jersey: Princeton University Press), p. 142.

Brennen, C., and Winet, H. (1977). Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339-398.

Brenner, B., Schoenberg, M., Chalovich, J. M., Greene, L. E., and Eisenberg, E. (1982). Evidence for cross-bridge attachment in relaxed muscle at low ionic strength. Proc. Natl. Acad. Sci. USA 79,7288-7291.

Brokaw, C. J., and Benedict, B. (1968). Mechanochemical coupling in flagella. I. Movement-dependent dephosphorylation of ATP in glyceri- nated spermatozoa. Arch. Biochem. Biophys. 725, 770-778.

Cooke, R. (1986). The mechanism of muscle contraction. CRC Crit. Rev. Biochem. 21, 53-118.

Endlich, B., and Linn, S. (1985). The DNA restriction endonuclease of Escherichia coli B. I. Studies of the DNA translocation and the ATPase activities. J. Biol. Chem. 260, 5720-5728.

Feynman, R. I?, Leighton, R. B., and Sands, M. (1963). The Feynman Lectures on Physics (Reading, Massachusetts: Addison-Wesley Pub- lishing Co.), pp. 46-1-46-5.

Gelles, J., Schnapp, B. J., and Sheet& M. P (1988). Tracking kinesin- driven movements with nanometer-scale precision. Nature 337, 450- 453.

Gibbons, B. H., and Gibbons, I. R. (1972). Flagellar movement and adenosine triphosphatase activity in sea urchin sperm flagella de membranated with Triton X-100. J. Cell Biol. 54, 75-97.

Gibbons, B. H., and Gibbons, I. R. (1974). Properties of flagellar “rigor waves” formed by abrupt removal of adenosine triphosphate from ac- tively swimming sea urchin spermatozoa. J. Cell Biol. 63, 970-985.

Gibbons, I. R. (1966). Studies on the adenosine triphosphatase activity of 14 S and 30 S dynein from cilia of Tetrahymena. J. Biol. Chem. 241, 5590-5598.

Gibbons, 1. R. (1981). Cilia and flagella of eukaryotes. J. Cell Biol. 91, 107a-124a.

Gibbons, I. R., Cosson, M. P., Evans, J. A., Gibbons, B. H., Houck, B., Martinson, K. H., Sale, W. S., and Tang, W.-J. (1978). Potent inhibition of dynein adenosine-triphosphatase and of the motility of cilia and sperm flagella byvanadate. Proc. Natl. Acad. Sci. USA 75,2220-2224.

Goodenough, U., and Heuser, J. (1984). Structural comparison of puri- fied dynein proteins with in situ dynein arms. J. Mol. Biol. 780, 1083- 1118.

Hill, T. L. (1985). Theoretical problems related to the attachment of microtubules to kinetochores. Proc. Natl. Acad. Sci. USA 82, 4404- 4408. Holzbaur, E., and Johnson, K. (1989). Microtubules accelerate ADP re- lease by dynein. Biochemistry 28, 7010-7015. Howard, J., Hudspeth, A. J., and Vale, R. D. (1989). Movement of microtubules by single kinesin molecules. Nature, in press.

Huxley, A. F. (1957). Muscle structure and theories of contraction. Prog. Biophys. Chem. 7, 255-318.

Huxley, H. E. (1969). The mechanism of muscle contraction. Science 164, 1356-1366.

Johnson, K. A. (1985). Pathway of the microtubule-dynein ATPase and structure of dynein: a comparison with actomyosin. Annu. Rev. Bio- phys. Chem. 14. 161-188.

Johnson, K. A., and Wall, J. S. (1963). Structure and molecular weight of dynein ATPase. J. Cell Biol. 96, 669-678.

Khan, S., and Berg, H. C. (1983). Isotope and thermal effects in chemi- osmotic coupling to the flagellar motor of Streptococcus. Cell 32, 913-919.

King, S. M., and Witman, G. W. (1988). Structure of the a and p heavy chains of the outer arm dynein from Chlamydomonas flagella: location of epitopes and protease-sensitive sites. J. Biol. Chem. 263, 9244- 9255.

Kodama, T., Fukui, K., and Kometani, K. (1986). The initial phosphate burst in ATP hydrolysis by myosin and subfragment 1 as studied by a modified malachite green method for determination of organic phos- phate. J. Biochem. 99, 1465-1472.

Koshland, D. E., Mitchison, T. J., and Kirschner, M. W. (1988). Pole wards chromosome movement driven by microtubule depolymeriza- tion in vitro. Nature 331, 499-504.

Kozak, M. (1980). Role of ATP in binding and migration of 405 ribosomal subunits. Cell 22, 459-467.

Kristofferson, D., Mitchison, T. J., and Kirschner, M. W. (1988). Direct observation of steady-state microtubule dynamics. J. Cell Biol. 102, 1007-1019.

Kron, S. J., and Spudich, J. A. (1986). Fluorescent actin filaments move on myosin fixed to a glass surface. Proc. Natl. Acad. Sci. USA 83, 6272-6276.

Laemmli, U. K. (1970). Cleavage of structural proteins during the as- sembly of the head of bacteriophage T4. Nature 227, 880-685.

Lasken, R. S., and Kornberg, A. (1988). The primosomal protein n’ of Escherichia coli is a DNA helicase. J. Biol. Chem. 263, 5512-5518.

Lye, R. J., Porter, M. E., Scholey, J. M., and McIntosh, J. R. (1987). Identification of a microtubule-based cytoplasmic motor in the nema- tode C. elegans. Cell 51, 309-318.

Mocz, G., Tang, W.-J. Y., and Gibbons, I. R. (1988). A map of photolytic and tryptic cleavage sites on the B heavy chain of dynein ATPase from sea urchin sperm flagella. J. Cell Biol. 106, 1607-1814.

Omoto, C. K., and Johnson, K. A. (1986). Activation of the dynein adenosinetriphosphatase by microtubules. Biochemistry 25, 419-427.

Pabion, M., Job, D., and Margolis, R. L. (1964). Sliding of ST0P pro- teins on microtubules. Biochemistry 23, 6642-8648.

Paschal, B. M., and Vallee, R. B. (1987). Retrograde transport by the microtubule-associated protein MAP 1C. Nature 330, 181-183.

Paschal, B. M., King, S. M., Moss, A. G., Collins, C. A., Vallee, R. B., and Witman, G. B. (1987). Isolated flageilar outer arm dynein translo- cates brain microtubules in vitro. Nature 330, 672-674.

Porter, M. E., and Johnson, K. A. (1983). Transient state kinetic analy- sis of the ATP-induced dissociation of the dynein-microtubule complex. J. Biol. Chem. 258, 65826587. Pratt, M. M. (1984). ATPases in mitotic spindles. Int. Rev. Cytol. 87, 83-105.

Sale, W. S., and Fox, L. A. (1986). The isolated p-heavy chain subunit of dynein translocates microtubules in v&o. J. Cell Biol. 707, 1793- 1798.

Sale, W. S., and Satir, F’. (1977). Direction of active sliding of microtu- bules in Tetrahymena cilia. Proc. Natl. Acad. Sci. USA 74, 2045-2049.

Sale, W. S., Goodenough, U. W., and Heuser, J. E. (1985). The sub structure of isolated and in situ outer dynein arms of sea urchin sperm flagella. J. Cell Biol. 107, 1400-1412.

Schoenberg, M. (1985). Equilibrium muscle cross-bridge behavior. Theoretical considerations. Biophys. J. 48, 467-475.

Schroer, T. A., Steuer, E. R., and Sheetz, M. P. (1989). Cytoplasmic dynein is a minus end-directed motor for membranousorganelles. Cell 56, 937-946.

&rr5eDimensional Diffusion of Microtubules

She&z, M f?, Block, S. M., and Spudich, J. A. (1966). Myosin move- ment in vitro: a quantitative assay using oriented actin cables from Nitella. Meth. Enzymol. 734, 531-544.

Shimizu, T., and Johnson, K. A. (1963). Presteady state kinetic analysis of vanadate-induced inhibition of the dynein ATPase. J. Biol. Chem. 258, 13633-13646.

Shimizu, T, and Katsura. T (1966). Steady-state kinetic study on the inhibition of the adenosinetriphosphatase activity of dynein from Terre- hymena cilia by glycerol. J. Biochem. 703, 99-105.

Soll, D. Ft. (1966). “DMS,” a computer-assisted system for quantitating motility, the dynamics of cytoplasmic flow, and pseudopod formation: its application to Dictyosfelium chemotaxis. Cell Motil. Cytoskel. 10. 91-106.

Tang, W.-J. T., Bell, C. W., Sale, W. S., and Gibbons, I. R. (1982). Struc- ture of the dynein-l outer arm in sea urchin sperm flagella. J. Biol. Chem. 257, 506-515.

Toyoshima, Y. Y., Kron, S. J., McNally, E. M., Niebling, K. R., Toyo- shima, C., and Spudich, J. A. (1967). Myosin subfragment- is suffi- cient to move actin filaments in vitro. Nature 328, 536-539.

Vale, R. D. (1967). Intracellular transport using microtubule-based mo- tors. Annu. Rev. Cell Biol. 3, 347-376.

Vale, R. D., and Toyoshima, Y. Y. (1966). Rotation and translocation of microtubules in vitro induced by dyneins from Tetrahymena cilia. Cell 52, 459-469.

Vale, R. D., and Toyoshima, Y. Y. (1969). Microtubule translocation properties of intact and proteolytically digested dyneins from 7&a- hymena cilia. J. Cell Biol. 708, 2327-2334.

Vallee, R. B., Wall, J. S., F’aschal, B. M., and Shpetner, H. S. (1968). Microtubule-associated protein 1C from brain is a two-headed cytosolic dynein. Nature 332, 561-563.

Vibert. P. and Cohen, C. (1966). Domains, motions and regulation in the myosin head. J. Muscle Res. Cell Motil. 9, 296-305.

von Hippel, P H., and Berg, 0. G. (1969). Facilitated target location in biological systems. J. Biol. Chem. 264, 675-676.

Warrick, H. M., and Spudich, J. A. (1967). Myosin structure and func- tion in cell motility. Annu. Rev. Cell Biol. 3, 379-421.

Weingarten, M. D., Lockwood, A. H., Hwo, S., and Kirschner, M. W. (1975). A protein factor essential for microtubule assembly. Proc. Natl. Acad. Sci. USA 72, 1666-1862.

Winter, R. B.. Berg, 0. G., von Hippel, P H. (1981). Diffusion-driven mechanisms of protein translocation of nucleic acids. 3. The Esche- richia co/i lac repressor-operator interaction: kinetic measurements and conclusions. Biochemistry 20, 6961-6977

Yarranton, G. T, Das, R. H., and Gefter, M. L. (1979). Enzymetata- lyzed DNA unwinding. Mechanism of action of helicase Ill. J. Biol. Chem. 254, 12002-12006.