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Optical Tweezers: Application to the Study of Motor Proteins
|Optical Tweezers: Application to
the Study of Motor Proteins
Optical tweezers allow the study of interactions of
single molecules of motor proteins with the track,
actin or microtubules, on which they run. The mechanical
properties of cellular motors can only be studied
at the single molecule level, and for those that act in
organised structures, notably muscle, study at this
level avoids the complexity of interpreting the effect of
large numbers of motors acting in parallel and asynchronously.
This article concentrates primarily on the
use of the "bead-actin-bead dumbbell" method (Finer et al.
, 1994, Fig. 1) for studying actomyosin interactions,
which necessitates the use of a dual-beam trap.
This approach is particularly useful for nonprocessive
actin-based motors, but many of the principles are
equally applicable to processive actin and microtubule-
based motors. Sheetz (1998) has edited a useful
volume of articles on laser tweezers in biology.
|FIGURE 1 The dumbbell setup.
II. MATERIALS AND
- Optical table (~4 x 3 ft).
- Research-quality inverted microscope with provision
for epi-illumination, a xenon light source for
bright-field imaging, and an objective >60x and
≥1.25 NA with good transmission properties at 1064
- A high-quality piezo-controlled stage (e.g., Physik
Instrumente P-528) and a piezo-controlled
focussing device (e.g., Physik Instrumente P-723 or
with superior capacitative position sensor P-725).
- Nd:YAG laser ≥ 1W.
- Two 2-mm aperture electro-optic deflectors (EOD)
(Leysop) with associated high-voltage amplifiers
(Apex sells inexpensive high-voltage hybrid
- Two CCD cameras and one intensified camera for
- Dual-photodiode quadrant detector (QD) and
associated electronics with a frequency response
- One computer with DAQ board for primary data
acquisition and one with frame grabber for servocontrolled
stage feedback. (A single computer
might suffice for these two applications.) We use
National Instruments DAQ boards and frame grabbers
in association with Labview software.
III. OVERVIEW OF OPTICAL
The standard single-beam gradient setup is capable
of trapping small particles, e.g., 1-µm latex beads, of
higher refractive index than the surrounding medium.
The mode of operation has been explained in varying
degrees of detail in many review articles, including the
compilation by Sheetz (1998). Most modern microscopes
use infinity-corrected optics and we will
assume this to be the case in this article. To form a trap,
a parallel beam must fill the back focal plane of the
objective, i.e., be ~5mm in diameter. Most of the
common lasers used for trapping emit narrower beams
than this, which necessitates the use of a beamexpanding
telescope. This could be a proprietary item
but in order to place all the optical components in their correct positions, it is more convenient to use two
separate lenses for this purpose (Figs. 2 and 4). Outside
the beam-expanding telescope, it is the angle of
the laser beam that controls the position of the trap,
whereas within the beam-expanding telescope, i.e.,
, it is the lateral displacement of the
beam. The mirror in Fig. 2 is in a plane that is conjugate
to the back focal plane of the microscope so that
the amount of light entering the objective is independent
of the angle of the mirror. This mirror allows
initial positioning of the trap at the beginning of the
experiment. An electro-optic or acousto-optic deflector
at or near this position allows rapid control of trap
IV. PRACTICAL DESIGN
|FIGURE 2 Basic optics of the trapping beam (m = m3 in Fig. 3). Focal lengths are f and F and BFP is the back focal plane of the objective.
An optical trap setup has to fulfill several other
functions besides trapping. For actomyosin experiments, a bright-field image is required to visualise the
beads for trapping and a video-rate fluorescence image
is required for attaching the actin filaments to the
beads, which necessitates an intensified CCD camera.
The positions of the two beads of the dumbbell must
be measured with a precision of ≤1nm with a frequency of >
10 kHz, which is achieved most readily by
projecting a bright-field image of the beads onto two
QDs. A xenon arc is a favourable light source for this
purpose. If the position of the stage is to be servo controlled
to overcome drift, a CCD camera with a field
width of about 10µm is also required. Figure 3 shows
the various light paths.
|FIGURE 3 The main light paths. Dotted lines in the trapping panel correspond to the reflected light, which
is useful for alignment and in the fluorescence panel to the emitted fluorescence, d are dichroic mirrors and
p are beam splitting prisms.
An inverting microscope is generally preferred
because it allows the majority of optical components
to be close to the optical table and is generally more
stable. Furthermore, beads floating in solution tend to
fall towards the coverslip, the region useful for exploring
myosin interactions. The trapping beam is introduced
into the optical system via a dichroic mirror (d1 in Figs. 3 and 4). The best location for this dichroic is immediately below the objective (Lang et al., 2002), but
can be combined with the fluorescence excitation beam
or before the dichroic of the fluorescence cube. The
dumbbell assay requires two traps that can be created
either by temporal sharing of a single beam (Visscher et al., 1993) or by using polarising beam splitters. We
will describe the simplest possible version of the latter
approach (Fig. 4). The wavelength of Nd:YAG lasers
(1064nm) is suitably distant from the absorption of
most biological materials, yet near enough to the
visible spectrum for the performance of standard
microscope objectives to be adequate. The first λ/2
waveplate controls the relative intensities of the two
beams. Mirrors m1 and m2 control the position and
angle of the laser beam. Mirrors m3 are at a distance
f away from lenses L1 and are thus conjugate with
the back focal plane of the objective. They allow
positioning of the two traps at the beginning of the
experiment to tension the dumbbell to the desired
level. Because the angular deviation from the EODs is
small, the entry of the beam into the back focal plane
of the microscope is affected negligibly, provided that
they are positioned close to the mirrors m3. Path a
needs a λ/2 wave plate on both sides of the EOD to
rotate the plane of polarisation by 90° and back again
as the EODs have a preferred polarisation direction.
The dichroic d1 reflects wavelengths above 900nm.
The YAG rejection filter avoids reflected trapping laser
light, contributing to the bright-field QD signal. The
dichroic d2 reflects below 550nm for the exciting
Hg lamp. Pellicle beam splitters p provide light for the
low and high magnification bright-field cameras. The dichroic d3 reflects light >555nm to pick out the
emitted fluorescence, which then passes through the
emission filter. The light path of the trapping laser
must be enclosed to avoid movement of the laser beam
due to air currents in the room. This is done most easily
by a combination of tubes and a box around the square
of the beam splitting prisms (grey box in Fig. 4).
|FIGURE 4 Diagram of the trap setup.
On the first occasion, alignment of the two trapping
beam can cause frustration, but the following protocol
works even if the trap is being constructed from
scratch rather than being based on a microscope. It is
based on the principle of sending a HeNe or similar
visible laser beam backwards through the microscope
to define the optical axes of the various light paths.
Laser safety glasses are required during the alignment
- Check that the microscope stage is horizontal
with a spirit level.
- Establish a rough vertical optical axis by dropping
a plumb line from the ceiling to the centre of the
- To refine the line of the beam, attach a tiltable
mirror at the ceiling so that the HeNe beam can be
reflected back to the objective. Place a mirror on the
stage and adjust the position of the HeNe beam on
the ceiling mirror and the angle of that mirror so that the beam is hitting the centre of the objective and is
being reflected back along itself.
- Before extension of the optic axis to the trapping
laser, remove lenses L1 and L2 and the EODs from
their provisional positions. Replace the microscope
objective with a ~4-mm aperture (readily made from
an old objective) to let the reference beam through.
This defines the back aperture of the objective.
- Centre two apertures on the HeNe beam, as
widely spaced as possible between the microscope
and the recombining prism (positions i and ii in
- Switch on the trapping laser and make the two
paths collinear with the HeNe laser beam. For path a,
orientation of m1 allows the trapping beam to be made
coincident with the reference beam at m2, and the orientation
of m2 allows it to be made collinear with the
reference beam. For path b, a small rotation of the first
polarising beam splitter together with orientation of its
prism table allows the trapping beam of path b to be
made concident with the reference beam at m3b, and
orientation of m3b allows the beams in path b to be
made collinear. Any CCD cameras attached to microscope
ports now show the beam in the centre and those
not on microscope ports should be centred at this time.
The focus of the cameras should be adjusted to correspond
to that of the microscope eyepiece.
- Replace the objective aperture with the objective,
place a dry flow cell (construction described later) on
the stage and focus on the inner surface of the cover
slip. The alignment should be adequate to see the
reflected laser beam with a low-magnification,
infrared-sensitive CCD camera. Fine-tune the alignment
of the trapping beams to make the diffraction
pattern around the reflected image symmetrical.
- Lens L2 can now be inserted at its focal length F
(~300mm) from the back focal plane of the objective
and positioned laterally so that the reversed beam still
impinges on the trapping laser and the reflected image
remains symmetrical. Note that L2 focusses the trapping
beam at the back focal place of the objective. The
laser beam should be turned down to minimum intensity
to avoid damage.
- Insert the two lenses L1 at a distance (f + F)
further back from L2 so that L1 and L2 form beamexpanding
telescopes (Fig. 2). Adjust their lateral position
so that the reflected image is again symmetrical.
If the objective is replaced by the aperture, the parallel
beam should hit the ceiling mirror at the same point
as the HeNe laser.
- The apparatus should now be able to trap 1-µm
beads. A small adjustment of axial position of lenses L1 can be used to fine control the z position of each
- Adjust the orientation of the mirrors m3 to position
the two traps for the dumbbell experiment ~6µm
- Position the electro-optic deflectors (EOD) as
near as possible to the mirrors m3. EODs are convenient
because, in the absence of an applied voltage, the
beam is not deflected. If an AOD is used rather than
an EOD, typically the angle of the beam will change at
this point, which will need some realignment. Some
AODs are more convenient in that they have the far
face cut so that refraction compensates for the diffraction
and at the centre frequency the first-order beam
remains parallel to the input beam.
- The relative intensities of the two beams can be
monitored using an adequately large (~1 cm) photodiode
mounted above the field stop of the condenser and
equalised by rotation of the λ/2 plate positioned prior
to the first beam splitter. The stiffness of the two traps
should now be roughly equal.
- Equalise the height at which the two beads are
trapped by final positioning of the lenses L1. Move the
lenses L1 closer to the microscope to move the trapped
bead further from the surface of the coverslip.
- Transimpedance amplifiers are used to convert
the currents from the individual quadrants of the photodetector
to voltages. A signal that is almost linearly
proportional to, for example, the horizontal bead displacement
for movements up to about one-third of a
bead diameter is gained by summing the two left-hand
and the two right-hand quadrants and taking the difference
signal between these values. This signal needs
to be converted from volts into bead movement in
nanometers. First, it is necessary to convert volts to
micrometers movement of the bead image at the quadrant
detector by moving the QD to a series of positions
with a micrometer-driven slide. Magnification of the
microscope from the stage to the quadrant detector
then allows conversion of QD volts to bead movement
in nanometers. As an accurate calibration using the
micrometer is time-consuming, we apply a 2-Hz
square wave to a stepper motor to rotate a thin
(~0.5 mm) microscope slide ±7.5° so as to give a constant
lateral displacement of the bead image (see
Fig. 5), which can be measured.
- A variety of methods have been described for
measuring the trapping strength, but probably the
most robust one for routine use is to apply a square
wave to the traps. The bead position record is then
averaged over a sufficient number of cycles to give a smooth trace and a rate λ fitted to the exponential
decay. The trap stiffness is then 6πrηλ (r being the
radius of bead and η the viscosity). It should be noted
that η is quite temperature dependent and also that the
bulk value is only applicable if the trapped bead is a
few bead diameters away from the coverslip. Other
methods of measuring trap stiffness have been
described by Svoboda and Block (1994).
|FIGURE 5 Calibration using the "flipper" to provide known lateral movement of the bead image.
VII. THE DUMBBELL EXPERIMENT
A. Assembling the Dumbbell
Preparation of the components is described in
Section X. The first step is to trap two beads: if one can
be found that has already stuck near to the end of a 5-
to 8-mm-long actin filament, so much the better. In the
absence of such good fortune, the piezo stage is moved
in order to catch a suitable filament near its end. The
spacing of the beads is then adjusted to match the filament
prior to attaching the loose end by aligning the
actin filament using movement of the stage to induce
flow past the stationary beads. If the beads and actin
filaments have been prepared properly, attachment to
the second bead should occur almost instantly because
of the constraining influence of the flow. It soon
becomes apparent that the correct concentration of
beads and actin filaments is critical for successful
assembly and use of dumbbells. If there is an inadequate
supply of either, too much time is spent searching
for beads or actin, if the concentration of one of
these is too high, the perfect dumbbell is liable to be
spoilt by the capture of extra beads or actin filaments.
Due to the effect of radiation pressure, beads enter the
trap from the objective side (beads about to be caught
look blacker than in their trapped position), which has
the fortunate repercussion that the required beads are
normally caught ~10µm deep, whereas in the operating position, 1.5µm above the surface of the coverslip,
uninvited beads rarely enter the trap. However, actin
filaments can float past and become attached. The
traps naturally accumulate all forms of small particles
that can seriously increase the noise when measuring
bead position. All solutions should be filtered and/or
centrifuged prior to use.
B. Tensioning the Dumbbell
The success of an experiment is dependent upon the
movement of the actin filament being transmitted to
the trapped beads, which requires that the compliance
between the segment of actin interacting with the
myosin and the bead be low compared to that of the
myosin head. The compliance of actin itself is low, and
the limiting feature is the link between the actin and
the bead. The compliance of this link is very nonlinear,
and to achieve the required value (>1pN/nm), a significant
pretension (>5pN) is necessary. One way of
doing this is to align the quadrant detectors, apply a
triangular wave to one of the traps, and monitor
whether the other bead faithfully follows the first. If
not, the dumbbell tension is increased using one of the
mirrors m3. One problem is that for a weak trap
(0.02 pN/nm) and a 1-µm bead this is quite close to the
maximum force. Moreover, the stiffness along the
beam (z) axis is several times weaker than the x,y stiffness
and is reduced further when the bead is at the
edge of the trap. The overall result is that the beads
become rather unstable, particularly in the z direction,
and the quality of the results is degraded. The application
of positive feedback, outlined later, significantly
helps limit this problem.
A myosin, suitably positioned near the top of a fixed
1.5-µm glass bead, now needs to be found to allow
interaction with the actin. The initial search can be
done with a mouse-driven stage but it is very convenient
to be able to move the actin ±300nm along the y axis (regarding the axis of the actin filament as x) using
a potentiometer so that the filament can be placed
exactly above the myosin to get the maximum rate of
interaction. At realistic values of dumbbell tension,
thermal motion results in the standard deviation of the
position of the middle of the actin filament being about
40nm, so the actin needs to be positioned in the y and
z axes to within ~20nm of its optimal position. At this
point it is desirable to servo control the position of the
stage relative to the traps so that the rate of interaction
becomes reasonably constant. Typically 100 second
data files are recorded (normally at 10kHz with a
5-kHz antialias filter).
VIII. IMPROVEMENT OF
A. Positive Feedback of Bead Position to
For a simple trap the maximum force provided by
a trap is directly related to its stiffness, with the width
of the energy well being controlled by the size of the
trapped bead and of the diffraction limited spot. It is
advantageous to carry out actomyosin experiments
with traps that are considerably more compliant than
the myosin head to provide a good contrast in the variance
of bead position between periods of actin attachment
and detachment, which limits the extent that the
dumbbell can be pretensioned to a somewhat suboptimal
level. One way to get around this problem is to
feedback a fraction α of the bead position to the trap
position (Xt = αXb) (Steffen et al., 2001). Such positive
feedback broadens the energy well and reduces the
stiffness by a factor of α, which allows the intensity of
the trapping beam to be increased by this factor to
restore the stiffness to its original value. Both the
maximum force and the stiffness in the y and, more
importantly, the z directions are increased due to this
increase in beam intensity. This procedure works well
for modest values of α (~2), but considerable care
needs to be taken if larger values are used because
noise other than that arising from the thermal motion
of the bead is also amplified.
B. Stage Feedback
The stability of optical microscopes is comparable
to the resolution, i.e., slightly submicrometer. The
monomer periodicity of actin is 5.5 nm and this will not
be resolved unless the stability of the position of the
stage with respect to the objective is around the 1-nm level during the period of data collection. This is only
possible by servo-controlling the stage position. We
have used a combination of piezo-positioned stage and
objective, but piezo stages, which have adequate
movement in the z as well as the x,y directions, are now
available (e.g., Physik Instrumente: P-562.3CD) and
are probably the most convenient solution. It is advantageous
to bolt the objective directly below the stage
so as to minimise thermal drift. Positioning in all three
directions can be controlled on the basis of video
images, but the noise level is probably slightly lower
if an image of the fixed, myosin-bearing bead is projected
onto a third quadrant detector to control the x,y
position. For most applications, speed of the feedback
loop is not the issue. A simple Labview program is
available for download from traps.rai.kcl.ac.uk.
IX. ANALYSIS OF DATA
The activity of nonprocessive motors is usually
detected on the basis of the reduction of variance of
bead position during periods of attachment (Molloy et al., 1995). If both the compliance of at least one of the
actin bead links and of the myosin is more than five
times the combined stiffness of the traps, at least the
longer events will be readily visible on an oscilloscope
trace. In these circumstances, detection of events on the
basis of reduction of the variance of the bead position
is relatively straightforward. We use a program developed
by Smith et al. (2001), which carries out a
maximum-likelihood analysis of the whole trace and
assigns the rates of attachment, f, and detachment, g,
as well as the periods of attachment. By comparison of
the covariance and autovariance of the bead positions
during periods of attachment and detachment, the
program also deduces the compliance of the two actin
bead links and of the myosin link and corrects the
observed working stroke for the effect of these compliances.
The core Fortran program and a Matlab
program that calls them and analyses batches of files
and plots out the most useful aspects of the analysis is
available from traps.rai.kcl.ac.uk.
Two parts of the standard output are shown in
Fig. 6 (obtained from separate experiments). Figure 6a
shows a histogram of the positions of interactions for
a dumbbell that is kept stationary with respect to the
myosin for the duration of the 100-s record. In general,
it is necessary to servo control the stage position to be
able to associate each interaction as being with a specific
actin monomer. Patlak (1993) proposed a method
of analysis of ion channel data based on mean-variance
histograms and he has adapted the method for actomyosin data (Guilford et al., 1997). We have not used
the method for final analysis of data but find that plotting
the standard deviation against the mean for time
slices of bead position data provides a very valuable
initial check on data quality. Such a plot is shown in
Fig. 6b. In this record the dumbbell has been moved
past five target zones of the actin filament (a target
zone is a region in which monomers are suitably oriented
to interact with actin). The plot readily identifies
both the target zones and the underlying actin
monomers. Such plots reveal inhomogeneities among
target zoned and monomers. Analysis methods have
been reviewed by Knight et al. (2001).
|FIGURE 6 (a) Histogram of the position of interactions with a stationary dumbbell and a relatively weak
trap so that two target zones are accessed. The myosin is halfway between the two target zones. (b) A plot
of the standard deviation versus the mean position of 5-ms time slices of a data record in which the dumbbell
is moved past five target zones during the 100s of data collection.
A. Preparation of Latex Beads
The preparation of neutravidin-coated latex beads
is a straightforward procedure and, in our hands,
appears to be superior to commercial products. By first
generating latex beads covalently cross-linked to
biotin, one can generate a stock of beads that can be
stored for many months. Once coated with neutravidin
the beads are used for a period of 2-3 weeks.
Buffer, Solutions, and Materials
Carboxylated latex beads (Sigma, L3905, 1µm in
diameter, 2.5% solids)
Eppendorf reaction vials, screw top
(EDAC) (Sigma, E1769)
50mM phosphate buffer, pH 7.0
2mg/ml biotin-x-cadaverine (Molecular Probe, A1594)
in dimethyl sulfoxide, aliquots stored at -80°C
5mg/ml neutravidin (Molecular Probe, A-2666,
aliquots stored at -80°C)
Biotinylated Latex Beads
- Centrifuge 250-µl latex beads in a 1.5-ml Eppendorf
reaction vial at 6000g preferably in a swingout
rotor (e.g., Sorvall RSA) for 10min.
- Aspirate supernatant without disturbing the
- Resuspend beads in 500µl of 50mM phosphate
buffer, pH 7.0, place in sonicating bath for 10
seconds, and centrifuge as in step 1.
- Repeat washing step.
5. Resuspend beads in 250µl of phosphate buffer,
- Add 25µl of 2mg/ml biotin-x-cadaverine and
- Add ~2mg of EDAC cross-linker, mix, and incubate
at room temperature for 30min.
- Add 500µl of phosphate buffer and centrifuge as
in step 1.
- For the washing step, resuspend beads in 500µl
phosphate buffer, sonicate in a bath for 10s, and
centrifuge as in step 1.
- Repeat washing step at least five-times.
- After final wash, resuspend beads in 500µl phosphate
buffer containing 0.02% NaN3 and store in a
Neutravidin - Biotin Latex Beads
- Resuspend 25 µl of biotinylated 1-µm latex beads
(see earlier discussion) in 175µl phosphate buffer.
- Centrifuge at 6000g for 10min.
- Aspirate supernatant.
- Resuspend beads in 100µl of phosphate buffer
containing 0.1M glycine.
- Add 15 µl of 5 mg/ml neutravidin and incubate at
room temperature for 20min (mix intermittently).
- Add 100µl phosphate buffer and centrifuge as in
- For the washing step, resuspend beads in 500ml
phosphate buffer, sonicate in a bath for 10s, and
centrifuge as in step 2.
- Repeat washing step at least five-times.
- After final wash, resuspend beads in 200ml phosphate
buffer containing 0.02% NaN3 and store in a
- Test beads in a binding assay (fluorescence
microscopy) by mixing beads with 1-4µg/ml
biotinylated F-actin at a ratio of 1:50.
B. Preparation of Biotin-Tetramethyl
F-actin (~50 µM) is modified with a 0.5-1 molar ratio
of biotin-PEAC5-maleimide (Dojindo) in a buffer consisting
of 10mM NaHCO3, basically as described by
Ishijima et al. (1998). It is taken through two depolymerisation
cycles before adding 2mg/ml trehalose
and flash freezing 10-µl aliquots. An aliquot is polymerised
with a small molar excess of tetramethyl
rhodamine phalloidin overnight. The next morning,
excess dye and any monomeric actin are removed
by spinning through 200µl of 10% sucrose (29,000g,
30min: 30,000rpm in Beckman TLA 100.1 rotor) to
remove monomeric actin, and the filamentous actin is
resuspended with 0.1 mole rhodamine phalloidin per
mole of actin.
C. Preparation of Fixed-Bead Microscope
Slides (Flow Cell)
To allow myosin to access the actin of the dumbbell,
it must be raised above the surface of the cover slip.
This is achieved most simply by applying a suspension
of 1.5-µm glass beads in a nitrocellulose solution to the
- Apply 2µl of glass microspheres (1.5µm) suspended
in 0.05% nitrocellulose in amyl acetate to
coverslips (#1.5:22 x 22 mm). Spread the suspension
evenly using the edge of a second coverslip
mounted on a cocktail stick. Allow to dry.
- On a microscope slide lay down two thin strips of
vaseline (spacing ~8mm) using a syringe (~22-gauge needle).
- Place nitrocellulose-coated coverslips on top of the
slide and press down lightly to produce a gap of
about 30µm. (Thick aluminium foil can be used as
- Secure the four corners of the coverslip with
D. Sample Preparation
Buffers and Solutions
Deoxygenation system (Harada et al., 1990):
1 mg/ml catalase (Sigma, C-100) and
5mg/ml glucose oxidase (Sigma, G7141)
1 mM phalloidin (Sigma, P2141) in methanol, store at
100 mM N a-ATP
Buffer A: 25 mM K-HEPES, pH 7.6, 25 mM KCl, 4mM MgCl2, 0.02% NaN3
Reaction mix (RM) freshly prepared before every
experiment: 1 ml buffer A, 20 µl of 5 mg/ml glucose
oxidase, 20µl of 1 mg/ml catalase, 20µl of 100mg/
ml glucose, 1 µl β-mercaptoethanol (BME), 0.5 µl of
1 µM phalloidin, and 1 µM ATP or other nucleotides
at concentration of choice
Blocking solution: 1 ml buffer A and 20µl of 50mg/ml
bovine serum albumin
Buffer B (make fresh every day):
1 ml buffer A,
1 µl of 1 mM phalloidin, and
2 µl BME
Actin freshly diluted 1:200 in buffer B
10x actin polymerisation buffer: 50mM phosphate, pH
7.5, 500mM K-acetate, 20mM Mg-acetate, and
- Add 1-5µg/ml of myosin in buffer B to flow cells
and incubate for 1 min.
- Wash out excess myosin with 30µl of buffer B followed
by 30µl of blocking solution. Incubate with
blocking solution for 1 min.
- Wash with 30ml of buffer B.
- Apply 30µl of final reaction mix containing 1-µl
neutravidin-coated latex beads, 1-2nM biotinylated
actin, and the chosen concentration of ATP. If the
ATP concentration is less than 10µM, addition of
a regenerating system (1mM phosphocreatine,
20µg/ml creatine phosphokinase) is advisable.
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molecule mechanics: Piconewton forces and nanometre steps. Nature 368, 113-119.
Guilford, W. H., Dupuis, D. E., Kennedy, G., Wu, J., Patlak, J. B., and
Warshaw, D. M. (1997). Smooth muscle and skeletal muscle
myosins produce similar unitary forces and displacements in the
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Harada, Y., Sakurada, K., Aoki, T., Thomas, D. D., and Yanagida, T.
(1990). Mechanochemical coupling in actomyosin energy transduction
studied by in vitro movement assay. J. Mol. Biol. 216,
Ishijima, A., Kojima, H., Funatsu, T., Tokunaga, M., Higuchi, H.,
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Knight, A. E., Veigel, C., Chambers, C., and Molloy, J. E. (2001).
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to actomyosin interactions. Prog. Biophys. Mol. Biol. 77, 45-72.
Lang, M. J., Asbury, C. L., Shaevitz, J. W., and Block, S. M. (2002). An
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Molloy, J. E., Burns, J. E., Kendrick-Jones, J., Tregear, R. T., and White,
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