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Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, Connecticut 06520
Correspondence: Address reprint requests to Thomas D. Pollard, MCDB, KBT-548, Yale University, PO Box 208103, New Haven, CT 06520-8103. Fax: 203-432-6161; E-mail: thomas.pollard{at}yale.edu.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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; Fujiwara et al., 2002). The fluorescence signal is fourfold stronger with actin labeled on Cys-374 with Oregon green rather than rhodamine. To distinguish growth at barbed and pointed ends we used image drift correction and maximum intensity projections to reveal points where single N-ethylmaleimide inactivated myosins attach filaments to the glass coverslip. We estimated association rates at high actin concentrations and dissociation rates near and below the critical actin concentration. At the barbed end, the association rate constant for Mg-ATP-actin is 7.4 µM–1 s–1 and the dissociation rate constant is 0.89 s–1. At the pointed end the association and dissociation rate constants are 0.56 µM–1 s–1 and 0.19 s–1. When vitamin D binding protein sequesters all free monomers, ADP-actin dissociates from barbed ends at 1.4 s–1 and from pointed ends at 0.16 s–1 regardless of buffer nucleotide. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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), but these methods are limited because the signal depends not only on the polymer concentration, but also on the size of the filaments and the extent of cross-linking. In addition, viscometric measurements perturbed assembly by fragmenting filaments.
What was needed was a sensitive, spectroscopic assay to measure polymer concentration directly in real time. Actin labeled on Cys-374 with pyrenyl iodoacetamide filled this need (Kouyama and Mihashi, 1981), because the fluorescence of the polymer is 20 times higher than the monomer. This assay revolutionized actin research and has been the standard method for 20 years. However, this assay has limitations. First, it measures only the concentration of polymer. The direction of growth and number of filaments must be inferred, often with considerable uncertainty. Although capping proteins have been used to separate barbed from pointed end growth, these assays must assume a constant concentration of ends and thus ignore filament nucleation, annealing, and severing. Second, some proteins including myosin (Kouyama and Mihashi, 1981) and actin depolymerizing factor (ADF)/cofilin (Carlier et al., 1997) quench the fluorescence of pyrenyl-actin filaments. This is useful for binding studies, but makes it impossible to study how these proteins regulate actin polymerization. Labeling actin with 7-chloro-4-nitrobenzeno-2-oxa-1,3-diazole on Lys-373 (Detmers et al., 1981) circumvents the quenching problem, but not the uncertainty regarding the number of filaments or their direction of growth.
Fluorescence microscopy of filaments labeled with fluorescent-phalloidin (Blanchoin et al., 2000; Burlacu et al., 1992; Xu et al., 1999; Yanagida et al., 1984) reveals branches and allows measurement of filament lengths and direction of growth. Together with knowledge of the polymer concentration, this method makes it possible to calculate the number of filaments, but these insights are available only on static samples. Electron microscopy can be used to distinguish the growth at the two ends of actin filaments (Bonder and Mooseker, 1986; Pollard, 1986; Pollard and Mooseker, 1981; Woodrum et al., 1975), but this approach is also restricted to samples taken at particular time points and requires fixation in nonphysiological buffers.
An ideal assay would employ continuous observation of growing filaments, allowing documentation of the nucleation of new filaments (de novo or as branches) and growth at both ends. Fluorescence microscopy can image single actin filaments containing subunits labeled with a fluorescent dye (Cintio et al., 2001) and thus has many features of an ideal assay. To avoid interference from the sea of unlabeled actin monomers required in a polymerization experiment, the fluorescent filaments must be excited either with an evanescent wave by total internal reflection (TIR) (Amann and Pollard, 2001; Fujiwara et al., 2002) or by confocal illumination (Ichetovkin et al., 2002). Our improvements in fluorescent labeling of actin, microscope hardware, and image analysis software have made real-time microscopy of actin polymerization a routine assay applicable to a wide range of actin studies (Kovar et al., 2003). We describe these improvements and characterize the elongation and the steady-state treadmilling of actin filaments.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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). We carried out all steps at 0–4°C unless specified otherwise. The pellet was resuspended in buffer G (2 mM Tris-Cl, pH 8.0, 0.2 mM ATP, 1 mM NaN3, 0.1 mM CaCl2, 0.5 mM dithiothreitol, DTT), sonicated for 1 min in a bath sonicator, diluted to 6 mg/ml, and dialyzed against three changes of buffer G over 2 days. After centrifugation at 105x g for 2 h, the crude actin in the top 80% of the supernatant was gel filtered on Sephacryl S-300 (Amersham Biosciences, Piscataway, NJ) to separate monomers from oligomers and minor contaminants. We measured the concentration of unlabeled actin by absorbance using an extinction coefficient of 
(Houk and Ue, 1974).
Labeled actin
Crude monomeric actin was dialyzed against two changes of buffer G without DTT for 1 h each. After clarification at 500x g for 5 min, actin was polymerized by mixing an equal volume of cold 2x label buffer (2x = 50 mM imidazole, pH 7.5, 0.2 M KCl, 4 mM MgCl2, 6 mM NaN3, 0.6 mM ATP). After 5 min polymerized actin was diluted to 1 mg/ml with cold 1x label buffer. A fresh 10-mM stock solution of Oregon green 488 iodoacetamide (Molecular Probes, Eugene, OR) was prepared in N,N-dimethylformamide. A 12- to 15-fold molar excess of Oregon green was added dropwise to the actin while stirring, and the solution was stirred gently overnight. Labeled actin was clarified at 500x g for 5 min and centrifuged at 105x g for 2 h to pellet actin filaments. The pellet was resuspended in buffer G, sonicated for 1 min, diluted to 6 mg/ml, and dialyzed for 1.5 days against two changes of buffer G and one change of buffer G6.5 (5 mM PIPES-Tris, pH 6.5, 0.2 mM ATP, 1 mM NaN3, 0.1 mM CaCl2, 0.5 mM DTT). After centrifugation at 105x g for 2 h, the supernatant was loaded onto a 1 x 5.5-cm column of DEAE-cellulose DE52 (Whatman, Kent, UK) equilibrated with buffer G6.5 and eluted with a 200-ml gradient of 0–300 mM KCl in buffer G6.5 to separate unlabeled from labeled actin. The peak fraction and following fractions down to 30% of the peak concentration were pooled, dialyzed overnight against polymerization buffer (5 mM imidazole, pH 7.5, 0.1 M KCl, 2 mM MgSO4, 0.5 mM, 0.3 mM, 0.5 mM, 1 mM NaN3, and centrifuged at 105x g for 2 h. The pellet was resuspended in buffer G, sonicated for 1 min, and dialyzed for 2 days against three changes of buffer G to depolymerize actin. We separated labeled actin monomers from oligomers by centrifugation at 105x g for 2 h and gel filtration on a Sephacryl S-300. Fractions were stored at 4°C and remained active for up to 4 weeks. The concentration of labeled actin was measured by absorbance at 290 and 491 nm using the extinction of OG at 491 nm 
and a correction for OG absorbance at 290 nm of 
The ratio of labeled actin to total actin is 
Myosin
Rabbit skeletal muscle myosin (Kielley and Harrington, 1959) was stored at –20°C in 50% glycerol. Aliquots of 
10 µM myosin were dialyzed against 10 mM imidazole, pH 7, 0.5 M KCl, 10 mM EDTA for 2 h. After incubation with 1 mM NEM for 1 h on ice, 1 mM DTT was added for 1 h on ice. Myosin was dialyzed against 50% glycerol in 10 mM imidazole, pH 7, 0.5 M KCl, 10 mM EDTA, 1 mM DTT overnight, and stored at –20°C.
Slide preparation
Flint glass slides of 25 x 75 x 1 mm (Erie Scientific, Portsmouth, NJ) were cleaned by a modified acid wash technique. Slides in glass vertical staining jars were sonicated for 45 min in 2% (v/v) Versaclean detergent (Fisher Scientific, Hampton, NH) in hot tap water, rinsed 10 times in hot water, and sonicated an additional 30 min. Slides were rinsed 10 times with distilled water, incubated for 3 h in 1 M KOH at 42°C, rinsed three times in double distilled (dd) water, and incubated overnight in 1 M HCl at 42°C. Jars were cooled to room temperature, rinsed five times in dd water, sonicated for 30 min in dd water, rinsed twice in 1 mM EDTA, and sonicated for 30 min in EDTA to reduce calcium contamination. Slides were rinsed twice in 70% ethanol, sonicated for 30 min, rinsed twice in absolute ethanol, sonicated for 30 min, and rinsed in absolute ethanol. Clean slides were stored in absolute ethanol in screw-top plastic jars and were used within two weeks.
Flow cell preparation
Flow cells containing 3–5 µl of fluid were prepared each day as in Kron and Spudich (1986). Two-and-one-quarter-inch strips of parafilm were stretched to approximately three times their length and placed across the long axis of a 24 x 50-mm, No. 1 coverslip (VWR International, West Chester, PA), leaving a 2-mm gap. A clean, 25 x 75 x 1-mm flint glass slide was removed from ethanol, flamed dry, cooled, and placed perpendicular across the parafilm strips. The parafilm strips were compressed by firm hand pressure on the top of the slide to seal the sides of the chamber. The chamber was flamed again briefly and cooled to stick the protruding parafilm strips to the open coverslip surface. For an inverted microscope, chambers were used with the coverslip down, facing the objective lens, and slide up, supporting the prism. Solutions were loaded directly into the chamber via capillary action. The solution in the chamber was changed by placing 2x chamber volumes of solution at one end and then pulling it through with a piece of filter paper on the other side. To prevent fluid flow onto the top of the slide, hydrophobic "corrals" were drawn across the top edges of the slide, above the entrance and exit ports with room temperature VALAP (1:1:1 vaseline/lanolin/paraffin).
Polymerization experiments
Unlabeled and labeled Ca-ATP-actin were dialyzed overnight against buffer G, centrifuged at 105x g for 2 h, the supernatant concentrations measured, and mixed with buffer G to the desired labeled fraction at 2.22 times the final concentration. Ca-ATP-actin was converted to Mg-ATP-actin for each experiment by adding 1/10 part of 10x Mg exchange buffer (10 mM EDTA, 1 mM MgCl2) to give two times the final actin concentration and incubating on ice for 5 min. NEM-inactivated myosin was diluted to 0.2 µM in high salt Tris-buffered saline (HS-TBS, 50 mM Tris-Cl, pH 7.6, 600 mM NaCl) containing a 10–4 dilution of 200 nm crimson fluorescent microspheres (Molecular Probes) and 5 µl were loaded into a freshly prepared flow cell. After 1 min at room temperature flow cells were washed with 10 µl 1% (w/v) bovine serum albumin (BSA) in HS-TBS followed by 10 µl 1% BSA in low-salt Tris-buffered saline (50 mM Tris-HCl, pH 7.6, 50 mM NaCl). Mg-ATP-actin (2x) was mixed 1:1 with 2x TIR buffer (100 mM KCl, 2 mM MgCl2, 2 mM EGTA, 20 mM imidazole, pH 7.0, 200 mM DTT, 0.4 mM ATP, 30 mM glucose, 1% methylcellulose, 40 µg/ml catalase, 200 µg/ml glucose oxidase) and 10 µl were immediately loaded into the chamber and placed on the microscope.
Actin filament seeds marked for polarity
Marked actin filament seeds were created as follows: 10 µM Mg-ATP-actin was mixed 1:1 with 2x TIR buffer, incubated at room temperature for 10 min to form filaments 30 µm long, fragmented for 1 min in a bath sonicator, and incubated for 10 min. Chambers coated with NEM-myosin and microspheres were washed once with 10 µl of 1x TIR buffer and 1 µl of seed mixture was flowed into the chamber in the reverse direction to form a gradient of seed densities on the surface. After 1 min, 10 µl of freshly prepared Mg-ATP-actin at 0.5x, 1x, or 2x the labeled fraction of seeds was mixed 1:1 with 2x TIR buffer, loaded into the flow chamber in the forward direction, and allowed to polymerize for a short time. Mg-ATP-actin was diluted to two times the desired concentration, mixed 1:1 with 2x TIR buffer, and 10 µl were loaded in the forward direction into a chamber containing preformed filaments.
Depolymerization
Twenty-five percent labeled, 3 µM Mg-ATP-actin was mixed 1:1 with 2x ATP-TIR buffer, loaded into a flow chamber coated with NEM-myosin and microspheres, and incubated for 10 min. Chambers were washed with 25% labeled 0.18 µM Mg-ATP-actin in 1x ATP-TIR buffer, and incubated for 22 min to convert filaments to Mg-ADP-actin. Chambers were washed with 50% labeled 1.5 µM Mg-ATP-actin for 1–2 min, and washed with either 1x ATP- or ADP-TIR buffer containing 5 µM vitamin D binding protein (DBP) (Calbiochem, San Diego, CA).
Microscope
An Olympus IX-71 microscope (Olympus America, Melville, NY) on an optical bench was modified for prism-based TIRF illumination (Fig. 1). A single-mode optical fiber (Oz Optics, Carp, Ontario, Canada) transmitted light at 488 nm from a mechanically isolated 100 mW argon-ion laser (Midwest Laser Products, Frankfort, IL). The 3-mm beam was passed through a 5x beam expander and an active phase scrambler (a transparent plastic petri dish spinning at >1000 rpm) to remove interference patterns due to stray light and produce even excitation illumination. Two dielectric mirrors steered the beam to the microscope stage at a 13° angle from the horizontal, where it was focused with an f = 100 mm convex lens onto a right-angle prism attached to a flow cell by a thin layer of glycerol. The exit beam was absorbed by a beam block. Optics and optomechanics were from Thorlabs (Newton, NJ). Uniblitz shutters (Vincent Associates, Rochester, NY) controlled the illumination from the laser and arc lamp. A motorized filter turret (Olympus) switched filter cubes, and a Mac 5000 stepper motor controlled focus (Ludl Electronic Products, Hawthorne, NY). Images were captured with an Orca-ER charge-coupled device camera (Model C4742-95-12ER, Hamamatsu, Bridgewater, NJ). A custom-designed image acquisition plug-in for the public domain image analysis program, ImageJ (National Institutes of Health, http://rsb.info.nih.gov/ij/), controlled the microscope filter wheel, shutters, focus, and camera.
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was convolved with a derivative of a Gaussian filter. The resulting x- and y-derivative images were summed, squared, and added together to form a single focus value at each z-position,
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 | (2) |
was similarly defined in the y-direction, and W and H were the image width and height, respectively. A Gaussian width of 
was used. The z-value, which maximized 
was estimated using parabolic interpolation of the sampled maximum focus value 
and its two nearest neighbors 
and 
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The best-focus position was further refined by using the estimated z-value as the center position of eight new epifluorescent images, spaced 
apart, and the focus function and best-focus position are recalculated. Because this autofocusing process is very insensitive to noise, short exposure times could be used, and the entire focus process was completed in <5 s.
Drift correction
The drift correction algorithm was written in Java as a plug-in for ImageJ. Drift was typically corrected in two phases. In the first phase, a single bright fluorescent speckle was roughly tracked by hand through every frame. The tracking was refined to the center of the speckle at each frame as follows. The image was smoothed by convolution with a Gaussian kernel of 
pixels in radius to reduce image noise. Local pixels within a certain radius (typically 5–20) of the initial track point were searched for the maximum intensity. The position of the peak intensity was further refined to subpixel accuracy in both x- and y-directions by parabolic interpolation between the peak pixel 
and its two neighbors in either x or y as follows. Given an x-position of m, the discrete first and second derivative of the intensity in the x-direction are
and 
respectively. The new x-position of the peak of the parabola is estimated from 
The y-position of the peak 
is estimated in the same way. Once the speckle centers were refined in each frame, the position of the speckle in the first frame was subtracted to obtain the drift over time. Each image was shifted in the opposite direction, using bilinear interpolation to estimate the intensity of fractional pixel positions.
In the second correction pass, the positions of several particles were roughly marked in the first frame. The centers of each particle were then found in each frame using the radial search and parabolic refinement above. The average change in position of all particles was then calculated as the average drift of the entire image sequence. Each image was again shifted in the opposite direction using bilinear interpolation of the old image to obtain the new pixel intensities.
Data analysis
We wrote filament snapping and length measurement algorithms in Java as plug-ins for ImageJ. For each experiment, we performed drift correction on the entire image sequence and created an MIP of the entire sequence that was added to the end of the image sequence stack. Each pixel in the MIP represented the maximum intensity of that pixel over all time points. We selected single filaments for analysis, one at a time. A straight line drawn across the filament's myosin restriction point in the MIP was recorded as the cutting line. For each time point, we traced the filament with a rough, freehand polygon, taking care to accurately mark the filament endpoints. The filament trace was refined through several steps. The curve was first smoothed by downsampling a Cartesian Fourier descriptors representation of the polygon (Jähne, 2002) as follows. The freehand polygon was converted to a "closed" curve by doubling each point such that the curve was traced first in the forward direction, then the opposite direction. Each original endpoint was further replicated in place twice to "fix" its position. The x- and y-positions of each point 
in the closed curve of N points were combined into a complex number representation 
The sequence of z-values was converted into a Fourier series representation by calculating P = N Fourier coefficients using a discrete Fourier transform
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represents successive approximations of the curve. The original curve could be reconstructed from these Fourier coefficients by means of an inverse Fourier transform
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The original curve was smoothed by reconstruction from fewer Fourier coefficients. To reduce the number of points to half, only the first P/2 coefficients are used to reconstruct the curve. The polygon curve was then converted to an "open" curve by removing the second half of its points, effectively tracing the path only in the forward direction.
Once we obtained a smooth, downsampled version of the rough filament trace, the trace was refined to the centerline of the filament as follows. The entire image was smoothed by convolution with a Gaussian convolution kernel of pixels in radius. For each point along the line 
the estimated direction tangent to the filament was obtained by vector subtraction of the next and previous points 
The direction perpendicular to the filament at that point was then 
The smoothed image was sampled at 1-pixel increments along this perpendicular direction for a radius of 5 pixels in either direction. The intensities of fractional pixel positions were estimated by bilinear interpolation to obtain the intensity profile perpendicular to the line. This profile was searched for a local maximum intensity that was closest to the original point. The maximum intensity along this perpendicular direction was further refined by one-dimensional parabolic interpolation with its two nearest neighbors in the profile. The position of this maximum intensity was taken as the filament center, and the current point was moved to this point. This refinement process could be iterated a second time to further define the center of the filament. When filament density was high, the refinement process would occasionally cause the filament trace to "jump" to a nearby filament. In these instances, the filament could be traced again, the search radius could be decreased to 3 pixels in either direction, or the refinement process could be limited to one iteration.
The refined filament trace was used to measure the length of the entire filament and the lengths on either side of the cutting line defined earlier. The polygon representing the filament trace was followed from start to finish. The length of each segment of the polygon was calculated, and each segment was tested for intersection with the cutting line. Each time an intersection was found, the segment was cut at that point, the current length from either the filament start or the last intersection point was recorded, and the process continued from the intersection point until the other end of the filament was reached. Kymographs were produced by segmenting the refined filament trace polygon into 1-pixel-long intervals. The intensity at each vertex was estimated with bilinear interpolation of the nearest four pixels. The entire process of image smoothing, refinement of the hand trace, and length measurement took roughly 1 s. For each filament, the measurement process was repeated at each time point to obtain the total filament length over time and lengths between both ends and the cutting line.
Instantaneous rates were calculated with a windowed derivative filter. For each filament end, the measured lengths L at each frame t were combined into a list, Lt. Any missing frames were filled by linear interpolation of the two closest measured lengths. The beginning of the list was extended backward in time by linear extrapolation of the first two length measurements. The end of the list was extended forward in a similar fashion. The entire list was convolved with a derivative of a Gaussian filter,
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, of two to three frames and divided by the average time between frames for the experiment. This simultaneously smoothed the data and calculated the change in length. Instantaneous rates for extrapolated frames were thrown out. |
RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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) (Fig. 1). An inexpensive (BK7) right-angle glass prism served as well as a quartz Pellin Broca prism. An active phase scrambler consisting of clear plastic plate spinning at >1000 rpm after the beam expander scrambled the laser polarization and smoothed out intensity variations in the total internal reflection fluorescence (TIRF) illumination due to interference patterns and stray light. An automated filter cube turret and shutters for both the laser and arc lamp light sources allowed rapid switching between TIRF and epifluorescence illumination. A stepper motor attached to the microscope fine focus wheel permitted automated focusing of the TIRF image.
Actin labeled with Oregon green 488 on Cys-374 incorporates into growing filaments
The work described here was done with actin labeled on Cys-374 with the stable fluorescein derivative, Oregon green 488 iodoacetamide (OG-actin). OG-actin copolymerized with unlabeled actin. The emission intensity of polymerized OG-actin was 4.5 times that of actin filaments labeled on Cys-374 with rhodamine maleimide, the conjugate used by Amann and Pollard (2001) and others (Fujiwara et al., 2002).
TIRF microscopy allowed imaging of individual actin filaments polymerizing from mixtures of OG-actin monomers and unlabeled actin monomers (Fig. 2 A). We observed the growth of filaments in the presence of 0.5–5 µM total Mg-ATP-actin including 10–50% OG-actin. The contrast was excellent even with micromolar concentrations of unpolymerized fluorescent actin in solution. On the other hand, the high background fluorescence of unpolymerized molecules prevented imaging of polymerizing OG-actin filaments by epifluorescence microscopy.
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Myosin attachment points distinguished growth at barbed and pointed ends
A fiducial mark is required on each filament to distinguish the growth at the two ends. We used single N-ethylmaleimide (NEM)-inactivated myosin II molecules to attach filaments to the chamber surface (Amann and Pollard, 2001), but locating and using these tethers as external reference marks required correction of stage drift. We developed software to track several stationary fluorescent particles in the field of view (Fig. 3 A) with subpixel accuracy. We took the average motion of these particles as the total drift over the course of an experiment and used this measurement to shift each image in the opposite direction and stabilize the entire movie (Fig. 3 C). We combined each TIRF microscopy sequence into a single image with a maximum intensity projection (Fig. 3, B and C), where each pixel in the projection image corresponded to the maximum intensity projection (MIP) at that location over all time points. The MIP image exposed the history of each filament and revealed constriction points where the Brownian motion of a swiveling filament was negligible (Fig. 3 C, arrows). We verified that these restriction points were fixed at a point on the filaments by changing the mol fraction of OG-actin midway through a polymerization experiment. Such sharp steps in fluorescence intensity rarely moved with respect to the constriction point of the filament, even over several hours (Fig. 3 C). We used constriction points to separate the two ends during length measurements. We assumed that barbed ends grow faster than pointed ends.
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We eliminated from analysis filaments that moved from their constriction points, due to detachment from myosin or incorrect assignment of an attachment point. Sliding of nongrowing filaments would appear as coordinated movements of the two ends relative to the point chosen as the constriction point. Detection of sliding is more difficult for growing filaments. Filament sliding would appear as coordinated movements of the two ends superimposed on their linear growth curves (Fig. 4, A and C), but would not affect the total filament length. We detected nonlinearities in length traces by subtracting the length estimated by linear regression from the measured length. We used such residual plots to search for coordinated nonlinear movement of the barbed and pointed ends of a filament, and linear growth of the entire filament. Plots of length residuals at the two ends of filaments as a function of time revealed two classes of filaments.
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Other filaments slid along their lengths relative to their constriction points. Plots of length as a function of time deviated from linearity at both ends (Fig. 4, B and D), with coordinated fluctuations in the distances between the constriction point to the two ends (Fig. 4 F). The residuals from barbed end length measurements and the negative residuals from pointed end length measurements were correlated (Fig. 4 F). If the difference between the two end residual measurements was >130% of the measurement error for the total filament length (equivalent to the sum of the two end residuals), the filament was defined as not fixed at the constriction point and rejected as unsuitable for measuring growth at the two ends.
Autofocusing
We used subresolution crimson fluorescent beads as autofocusing targets during long-term TIRF recordings of actin filaments. We coated flow cells with 5–20 beads per field concurrently with NEM-myosin-II. Before acquiring each TIRF image, the microscope took a Z-series of epifluorescent images of the beads at a longer wave length, using short exposures and low light levels to avoid bleaching of Oregon green. We measured focus using a standard sharpness function. Because a focused image is sharper than an out-of-focus image, the total image derivative (dI/dx)2 + (dI/dy)2 summed over all pixels is maximal at the correct focal plane. This two-pass autofocusing step proved robust even for extremely noisy images, took <5 s, and kept filaments in focus more than several hours. This method avoids bleaching that would occur if the microscope were focused on the filaments before acquiring each image.
Speckles
Fluorescent speckles are an alternative to single molecule tethers as fiducial marks. With the mol fractions of labeled actin employed here, "speckles" of nonuniform labeling along filaments were rarely discernable in single images (Fig. 2 A) but were obvious in straightened intensity kymographs of filaments (Fig. 2 B) as persistent dark patches. Because speckle contrast was often low (Fig. 2 B, arrowheads) and filament overlap could also produce speckles (Fig. 2 B, arrow), myosin tethers were used as fiducial marks for this study. Nevertheless, these dark speckles rarely moved relative to the myosin tether points (not shown), verifying that our constriction point method of end separation was also valid for a single mol fraction of label.
Steady growth interrupted by pauses
The total length of most filaments increased at a constant rate for many minutes (Fig. 2 C) indicating that the actin monomer pool was not depleted. Pauses interrupted periods of steady growth at all concentrations of monomers (Fig. 2, C and E, arrowheads). We removed obvious pauses of three or more frames (24–90 s depending on the frame rate) from rate analysis measurements.
We analyzed the elongation data in experiments such as Fig. 2 in three ways: 1), individual filament slopes; 2), pooled filaments slope; and 3), distribution of instantaneous growth rates. For 1.5 µM (30% labeled) Mg-ATP-actin, individual filaments (method 1; Fig. 2 C) elongated at an average of 3.9±0.4 subunits x s–1 (N = 13 filaments). Using the same data, all filaments in the field were combined as the change of length of each filament with time (method 2; Fig. 2 D). All of the points fell along the same line with a slope of 3.914±0.010 subunits·s–1 (N = 925 data points), indicating that growth was uniform throughout the field. Alternatively, we smoothed each filament length trace with a Gaussian window and calculated the change in length over each four-frame interval (Fig. 2 E) to obtain a distribution of rates (method 3). The instantaneous rates had a Gaussian distribution (Fig. 2 F) with an average change in length of 4.0 ± 1.5 subunits·s–1 (N = 925 data points). We consider the merits of each approach below.
OG-actin monomers incorporate into filaments but do not contribute to elongation rates
Like actin labeled with rhodamine on Cys-374 (Amann and Pollard, 2001), actin labeled on Cys-374 with Oregon green 488 depended on unlabeled actin for polymerization. At both 1 µM and 2.5 µM total Mg-ATP-actin, the elongation rates at the barbed end were inversely proportional to the fraction of labeled actin (Fig. 5 C). Extrapolation of this linear trend line to 0% label gave polymerization rates expected for native, unlabeled actin (Pollard, 1986). Linear extrapolation of this data gave no barbed end elongation at 90% label, similar to rhodamine-Cys-374-actin (Amann and Pollard, 2001). Noise obscured any dependence of pointed end elongation rates on the fraction of labeled actin (Fig. 5 D). We were unable to obtain 100% labeled OG-actin to demonstrate directly its incapacity of polymerize.
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In each of three experiments, plots of elongation rates versus total actin concentration (labeled + unlabeled) were linear but the slopes differed between experiments. Fitting the average instantaneous growth rate (method 3; Fig. 2 F) at each concentration to a line gave superior correlation coefficients than either fitting to individual filaments (method 1; Fig. 2 C) or pooled filaments (method 2; Fig. 2 D) at each concentration. For 30% labeled actin, the barbed end association rate constants for trials 1–3 were 
and 3.4±0.2 µM–1 s–1, respectively, and the barbed end dissociation rate constants for trials 1–3 were 
and 1.8±0.8 s–1. Knowing that labeled actin did not contribute to elongation rates, we combined the rates for all measured actin concentrations and labeled fractions (Fig. 5, A–D) into a single plot of rate versus concentration of unlabeled Mg-ATP-actin. For barbed ends (Fig. 8 C, circles), every filament showed the same dependence of rate on the concentration of unlabeled actin, regardless of the concentration of OG-actin in the experiment. From this combined plot, the barbed end association rate constant for unlabeled actin was 
and the dissociation rate constant was 
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and 0.79±0.16 µM–1 s–1 and 
and 1.0±0.5 s–1, respectively. A combined plot of rate as a function of unlabeled actin (Fig. 8 D, circles) gave rate constants of 
and 
Subunit dissociation from barbed and pointed ends in the absence of free Mg-ATP-actin monomers
To measure subunit dissociation in the absence of association, we used 5 µM vitamin D binding protein (DBP) (Kd 1 nM for ADP-actin monomers; McLeod et al., 1989) to sequester monomers as they dissociated from filament ends. Actin filaments assembled on the slide from 25% labeled Mg-ATP-actin were aged under treadmilling conditions (0.18 µM Mg-ATP-actin monomers) for 22 min (5x half-times for phosphate release) to convert them predominantly to ADP-actin. We marked barbed ends briefly with 50% labeled Mg-ATP-actin, before washing out actin monomers and adding DBP in buffer containing either ATP or ADP. Although different labeled fractions at barbed ends might complicate measurements, less than one-third of the measured filaments were marked, and the brightly labeled segments depolymerized quickly. Because depolymerization of some filaments slowed or stopped after 20 min, we measured depolymerization rates during the first 1000 s.
Marked barbed ends of ADP filaments shortened at rates of 2 s–1 in ATP buffer, whereas pointed ends shortened at 0.2 s–1. Based on this 10-fold difference in depolymerization rates, we designated the rapidly depolymerizing ends of unmarked filaments as barbed ends and combined marked and unmarked filaments for further analysis. The distribution of smoothed instantaneous rates at barbed ends was Gaussian with a mean dissociation rate of 1.23±2.88 s–1 (mean±SD; Fig. 6 A). The distribution was skewed slightly toward a dissociation rate of zero, consistent with long pauses in depolymerization observed for several filaments. All pointed end depolymerization rates clustered in one peak with a mean of 0.06±1.89 s–1 (Fig. 6 B). In buffer containing ADP Mg-ADP-actin filaments also shortened faster at their barbed ends (1.52±2.86 s–1; Fig. 6 C) than at their pointed ends (0.26±2.20 s–1; Fig. 6 D).
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) and measurements of rate constants verified (Pollard, 1986; Pollard and Mooseker, 1981) that once actin filaments reach a steady state, the concentration of Mg-ATP-actin monomers is slightly above the critical concentration at the barbed end and well below the critical concentration at the pointed end. Under these conditions a population of filaments has net elongation of barbed ends matched by net shortening of pointed ends. Although total polymer concentration remains constant, subunits treadmill through filaments from the barbed to the pointed end. Fujiwara et al. (2002) were the first to observe single filaments growing at their barbed ends and shrinking at their pointed ends by TIRF microscopy.
We extended this work by observing the behavior of filaments over a range of Mg-ATP-actin monomer concentrations from 0.025 to 0.2 µM. Under these conditions the critical concentration at the barbed end is 0.1 µM and the critical concentration at the pointed end is 0.8 µM. To distinguish the two ends of these filaments, we pulse-labeled long filaments with 50% labeled actin at the pointed end and 35% labeled actin at the barbed end, then exchanged the solution in the chamber with a low concentration of 25% labeled actin monomers to observe filaments under treadmilling conditions (Fig. 7). The ends of the filaments changed length very slowly. For example, in 150 nM Mg-ATP-actin, pointed ends take 40 min to shorten 1 µm. Thus, accurate measurements of treadmilling rates by TIRF microscopy required autofocusing to collect images for more than an hour.
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100 nM (75 nM unlabeled actin), both ends shortened. At slightly higher concentrations, barbed ends elongated and pointed ends shortened. Fig. 7 A shows time series of four filaments treadmilling in 150 nM total monomeric actin. At this concentration, barbed ends elongated at 0.839±0.013 s–1 (N = 10 filaments), faster than the average rate of shortening of pointed ends, 0.125±0.012 s–1 (N = 10 filaments). "Straightened" kymographs of these filaments (Fig. 7 B) show that barbed ends elongated at a constant rate, whereas pointed ends shortened intermittently. Uncertainty in the measurements of length changes at pointed ends precluded a detailed analysis of these pauses. To avoid potential effects of marked ends on treadmilling, we used filaments uniformly labeled with a single mol fraction OG-actin and myosin attachment points as fiducial marks. Uniformly labeled filaments treadmilled like end-labeled filaments (not shown). At low concentrations of Mg-ATP-actin monomers, barbed end elongation rates depended on the mol fraction of unlabeled actin monomers, as at high concentrations. The effect of labeled subunits on elongation at the pointed ends was ambiguous due to the scatter of the depolymerization rates.
Assigning ends from polymerization rates is ambiguous at low actin concentrations. Although barbed ends grow faster at all concentrations above the critical concentration, they also shorten faster than pointed ends below some "crossover" concentration owing to a higher dissociation rate constant. To determine the crossover concentration, we swapped barbed and pointed end assignments for concentrations at or below some arbitrary concentration and reanalyzed the rate as a function of concentration data for both ends. The best linear fits, measured from the sum of the correlation coefficients (R2 values) at both ends, were achieved with a crossover concentration of 50 nM unlabeled actin 
Below this concentration barbed ends depolymerized faster.
Plots of elongation rate versus concentration of unlabeled Mg-ATP-actin at these low actin concentrations (Fig. 8, A and B) gave the following rate constants: barbed end association rate constant 
barbed end dissociation rate constant 
pointed end association rate constant 
and pointed end dissociation rate 
We did not observe balanced barbed end polymerization and pointed end depolymerization at any concentration, thus filaments never reached a steady state with the monomer pool during our observation window. Although barbed ends switched from depolymerization to elongation at higher concentrations, pointed ends did not elongate under these conditions.
Global analysis of combined elongation data
We combined our elongation data for all actin concentrations to arrive at a global fit of rate as a function the concentration of unlabeled actin monomers (Fig. 8, C and D). The barbed end association rate constant was 
and the dissociation rate constant was 
The pointed end association rate constant was 
and the dissociation rate constant was 
The linear fit to the barbed end data (R2 = 0.83) was more robust than the pointed end data (R2 = 0.39). Table 1 compares our TIRF microscopy measurements with rate constants measured by electron microscopy.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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; Fujiwara et al., 2002). This required a new actin labeling scheme, autofocusing, drift correction, and improvements in filament length measurement. Actin labeled on Cys-374 with Oregon green 488 iodoacetamide is brighter than rhodamine labeled actin used in earlier TIRF studies. Like rhodamine actin, OG-actin incorporated into actin filaments but did not contribute to the elongation rate. We extrapolated the rate constants measured at several mol fractions of labeled actin to obtain the rate constants for native actin polymerization, which depended solely on the concentration of unlabeled actin in the reaction.
Each filament needs a stable fiducial mark to distinguish growth at the two ends. For this purpose Fujiwara et al. (2002) used bright fiducial spots on rare actin filaments to demonstrate steady-state treadmilling. We used two methods to distinguish barbed and pointed ends of numerous filaments. In some experiments we pulse-labeled filaments with different fractions of labeled actin to mark a stable boundary. For uniformly labeled filaments, we located points where NEM-inactivated myosin attached filaments to the glass surface as stable external fiducial marks. Residual analysis of growth curves distinguished these myosin attachment points from nonspecific binding of filaments to glass. Although subtle, the intensity variations along each filament revealed by kymographs (Fig. 2 B) are internal fiducial marks that are potentially superior to external marks.
We used these methods to obtain simultaneously the rate constants for both filament ends in each experiment, allowing measurement of hundreds of filaments. At all actin monomer concentrations occasional pauses separated periods of constant growth or shrinkage. Although pauses were more frequent at barbed ends, pauses also occurred during long-term pointed end depolymerization under filament treadmilling conditions. Measurement noise likely obscured many pointed end pauses, owing to very slow changes in length relative to measurement errors.
What accounts for these pauses? Contaminating capping protein (McLean-Fletcher and Pollard, 1980) might cause barbed end pauses, but the 38-s average half-life of barbed end pauses (not shown) is far shorter than the 4500-s half-time for capping protein dissociation (Schafer et al., 1996). Furthermore, reducing capping protein contamination by double gel filtration of actin did not reduce the frequency or duration of pauses. Association with inactive myosin might cause pauses. Many growing filaments paused when an end affixed to a single point, consistent with myosin binding. Some filaments shortening at low actin concentrations also paused at a presumptive NEM-myosin attachment point. Since we and others (Fujiwara et al., 2002) observed pauses in the absence of myosin, pauses are more likely due to nonspecific, unfavorable interactions of filament ends with the glass surface. Consistent with this interpretation, growth pauses and filament attachment (seen as decreased Brownian motion) are more common in winter, when lower humidity can increase electrostatic charges on the glass surfaces.
Real-time fluorescence microscopy confirmed that the rate constant for elongation of barbed ends by Mg-ATP-actin of 7.4±0.5 µM–1 s–1 is 10 times larger than the pointed end association rate constant of 0.56±0.10 µM–1 s–1. These values fall within the range of previous measurement, for example 3.4–12.3 µM–1 s–1 at the barbed end (see Pollard, 1986; Table 2). Both TIRF microscopy values are 65% the values measured by electron microscopy. Undetectable pauses could partially account for the lower rates measured by TIRF microscopy, but EM measurements could have overestimated growth rates. For electron microscopy, filaments were grown from blunt-ended fragments of Limulus acrosomal processes and bundled with poly-L-lysine. The maximum length of the tapered bundle was measured at each time point. Given the distribution of filament growth rates we observed in individual TIRF experiments (see Fig. 5, A and B), it is likely that measuring the longest filament in EM overestimated growth rates. Fitting our rate constants to the fastest filament in each experiment (Fig. 8, C and D, circles) gave rate constants (
of 10.7 µM·s–1 and 
of 1.5 µM·s–1) similar to the EM method.
Polymerization rate constants measured by fluorescence microscopy varied from experiment to experiment (Fig. 5). Environmental conditions such as humidity, temperature, and charge on the glass substrate are more likely to explain the variation in our measurements than differences in actin activity, because we obtained trials 2 and 3 on successive days using the same actin preparation. Thus, internal controls are essential when using microscopy to study the effects of solution conditions or regulatory proteins on actin polymerization rates. As TIRF microscopy becomes a standard method for actin kinetics, polymerization rates of actin alone should be routinely remeasured for each set of experimental conditions.
Methods to measure dissociation rate constants
Previous estimates of subunit dissociation rates relied on bulk samples with unknown numbers of filament ends (Carlier et al., 1986; Teubner and Wegner, 1998) or on microscopic measurements of elongation rates at actin monomer concentrations above the critical concentration and linear extrapolation of these rates to zero monomer (Pollard, 1986). We observed subunit dissociation directly in excess vitamin D binding protein to sequester monomers and preclude association reactions. This allowed us to test the effects of nucleotides on subunit dissociation.
Dissociation rate constants obtained by extrapolation of linear plots of growth rates versus actin monomer concentrations to zero monomer concentration are inherently more sensitive to measurement noise than those obtained by direct measurement. Our association rate constants varied 2.5-fold between different trials, whereas our dissociation rate constants obtained by extrapolation varied 10-fold between trials. Over seven trials of Mg-ATP-actin growth by EM, Pollard (1986) observed a 1.3-fold range of barbed-end association rate constants and a 10-fold range of extrapolated barbed-end dissociation rate constants.
Depolymerization at barbed ends
We created Mg-ADP-actin filaments by incubating filaments assembled from Mg-ATP-actin monomers for 22 min in a concentration of ATP-actin monomers where pointed ends depolymerized and barbed-end polymerization was slow and stochastic, growing at most 500 subunits (not shown). During this ageing step most subunits in the filaments hydrolyzed their bound ATP (1000 half-lives) and dissociated the 
-phosphate (five half-lives) to become ADP-actin. Short barbed end caps that grew during ageing consisted of a mixture of Mg-ATP- Mg-ADP-Pi- and Mg-ADP-actin. Some of these short caps broke off when the actin monomers were washed out; the rest depolymerized within 300 s.
We did not confirm that the ATP in the buffer slows dissociation of Mg-ADP-actin subunits at the barbed end as reported by Teubner and Wegner (1998). When vitamin D binding protein sequestered free subunits, Mg-ADP-actin dissociated from barbed ends at 1.2 s–1 in ATP buffer and 1.5 s–1 in ADP buffer. A two-tailed student's t-test showed little significant difference between these two conditions (p-value of 0.071).
Inferred dissociation rate constants at barbed ends
To evaluate the dissociation rate constants for Mg-ATP-actin, we observed changes in the length of filaments at Mg-ATP-actin monomer concentrations near or below the critical concentration. Under these conditions, Mg-ATP-actin associates with barbed ends at a rate proportional to its concentration. Because the half times are 2 s for hydrolysis (Blanchoin and Pollard, 2002) and 5 min for phosphate dissociation (Melki et al., 1996), most terminal subunits will have bound ATP or ADP-Pi (Bindschadler et al., 2004). Linear extrapolation of the rate of elongation (including negative values below the critical concentration) of plots of rate versus actin concentration to zero actin gave a dissociation rate constant of 0.9 s–1 for these species on the end of the filament. This is two-thirds the average rate of ADP-actin dissociation we observed in the presence of DBP to sequester monomers. Thus, even rare associations of ATP monomers protect barbed ends from the higher rate of ADP-actin dissociation.
Previous estimates of Mg-ATP-actin barbed end dissociation rate constants based on extrapolation of polymerization conditions showed similar rate constants of 1.4 s–1 (Pollard, 1986) or 0.14–4.6 s–1 (Carlier et al., 1986). Our direct measurement of Mg-ADP-actin dissociation from barbed ends was only 1.5-fold higher than the "ATP-actin" dissociation rate, rather than the three- to fourfold higher values for Mg-ADP-actin than Mg-ATP-actin dissociation reported previously (7.2 s–1, Pollard, 1986; 6.0 s–1, Carlier et al., 1986; or 11.5 s–1, Teubner and Wegner, 1998).
Depolymerization at pointed ends
Similar to the barbed end, the rates of subunit dissociation from the pointed ends were equivalent in buffer with ATP or ADP at 0.16 s–1. Although the mean dissociation rate of Mg-ADP-actin was greater (0.06 s–1) in ATP buffer than ADP buffer (0.26 s–1), a two-tailed Student's t-test showed that these two distributions were indistinguishable (p-value of 0.082). A possibility of small effect of ATP in the buffer on pointed end depolymerization is intriguing and merits further study, because the nucleotide or phosphate exchange seem more plausible at pointed ends where the nucleotide binding cleft is more exposed on the terminal subunits (Fig. 9) than at barbed ends (Holmes et al., 1990). However, events at the pointed end are likely to remain enigmatic, because the reactions are slow and the mol fraction of subunits occupying either end is miniscule compared with internal subunits (Blanchoin and Pollard, 2002).
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). Linear extrapolation of the rate of pointed end length changes with time (including negative values below the critical concentration) to zero actin gave a dissociation rate constant of 0.19 s–1 for the mixture of species on the end of the filament, similar to the average rate of 0.16 s–1 seen for Mg-ADP-actin. Unlike the barbed end, Mg-ATP- or Mg-ADP-Pi-monomers do not protect the pointed end from depolymerization.
Subunit diffusion on filament ends
Our main approach was to measure rate constants directly. An alternative pioneered by Fujiwara et al. (2002) is to observe changes in the length of single actin filaments at steady state. Fujiwara et al. analyzed such changes as one-dimensional Fick's diffusion processes. They estimated a diffusion coefficient of 25 sub2 s–1 with 0.7 µM Ca-ATP-actin at steady state. From this diffusion coefficient, they estimated barbed end rate constants for Ca-ATP-actin of 
and 
at steady state. A similar analysis with 0.3 µM Mg-ATP-actin gave a diffusion coefficient of 29 sub2·s–1 at steady state and elongation rate constants of 
and 
These values were 40-fold larger than those obtained from measurements of filament elongation.
We, too, observed changes in length of actin filaments at Mg-ATP-actin monomer concentrations near the steady-state critical concentration. We confirmed that single filaments can treadmill, g
, dashed line, measured length minus fitted length), negative residuals of the pointed end (•, solid line, fitted minus measured length), and residuals of total filament length (x, dotted line, measured minus fitted total length). (A, C, and E) An example of a filament fixed at its constriction point with no correlation between barbed and pointed end residuals. (B, D, and F) An example of a filament sliding over its constriction point with correlated barbed end and pointed end residuals.
). Eight to 15 filaments fixed at their constriction points were selected at each concentration. Barbed and pointed end lengths of each filament were measured over 10–60 frames, and rates were obtained by averaging smoothed instantaneous growth rates for every measurement. Three trials using two different actin preparations are shown. Rate constants (
(•, dashed line) for trial 2 of 
and (
, dashed-dotted line) for trial 3 of 
were obtained by linear regression. Standard distributions of instantaneous rate measurements are shown for trial 3. Similar distributions were seen for trial 1 and trial 2. Trials 2 and 3 were from the same preparation on separate days. (C and D) Dependence of elongation rates at the (C) barbed end and (D) pointed end on the mol fraction of labeled actin. Mg-ATP-actin with 10–50% of the molecules labeled was polymerized at (
were obtained by linear regression. Mg-ATP-actin depolymerization rates (•) are shown for comparison. (C and D) Global summary of the polymerization rates at (C) barbed ends and (D) pointed ends as a function of unlabeled actin concentration for low (x) and high (
were obtained by linear regression. The linear regression is the solid line and the upper and lower 95% confidence intervals are dashed lines.
