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.
II. MATERIALS AND INSTRUMENTATION
III. OVERVIEW OF OPTICAL TWEEZERS
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., between L1 and L2, 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 position.
IV. PRACTICAL DESIGN
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 >
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).
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 procedure.
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 PERFORMANCE
A. Positive Feedback of Bead Position to Trap Position
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).
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
1-Ethyl-3-(3-dimethylaminopropyl) carbodiimide (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
Neutravidin - Biotin Latex Beads
B. Preparation of Biotin-Tetramethyl Rhodamine-Actin
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 coverslip surface.
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 -20°C
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 20 mMNaN3
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