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We report on the trapping, rotation, and in-situ growth of birefringent tetragonal lysozyme crystals in optical tweezers operating at a wavelength of 1070 nm. Variation of the pH and lysozyme concentration of the solution during growth was used to alter the length to width ratio of the crystals, and hence their orientation in the tweezers. Crystals with the optical axis skewed or perpendicular to the trapping-beam axis could be rotated by changing the orientation of linearly polarized light. We observed spontaneous spinning of some asymmetric crystals in the presence of linearly polarized light, due to radiation pressure effects. Addition of protein to the solution in the tweezers permitted real-time observation of crystal growth.
©2004 Optical Society of America
1. Introduction
Optical tweezers have been used to manipulate and investigate a wide variety of substances, including cells, viruses, individual proteins and inorganic particles[1–3]. A tightly focused beam of light impinges on a particle with a higher refractive index than the surrounding liquid. The gradient of the electric field intensity creates a net force toward the focal point of the beam in three dimensions. This allows manipulation and relocation of particles, application of calibrated forces to determine binding strengths, and trapping of particles for additional study with a variety of probes. Proper choice of the wavelength of the trapping beam (in a region of high transparency) minimizes damage of biological specimens, and use of a dichroic mirror permits the use of a white light source in conjunction with a CCD camera for imaging.
An elongated particle will tend to align along the axis of the trapping beam due to the gradient forces [4–5]. However, it is also possible to control the orientation of the particle in the plane perpendicular to the beam axis. Control of the orientation of particles in this plane may be achieved by using an asymmetric beam [6, 7] or polarized light together with particles having some external or internal anisotropy. Orientation effects due to the shape of the particle have been reported by Galajda et al. [8] in the presence of a polarized trapping beam, due to a slight anisotropy introduced to the trap by the polarization [9]. Additionally, polarization can be used to control the orientation of a particle in the case of symmetrically shaped birefringent particles [10, 11]. In the case of a birefringent material, circularly polarized light can be used to make a particle spin within the beam [12]. Spinning of particles using a rapidly rotating linearly polarized beam has also been reported [13]. Spontaneous rotation of asymmetric objects has also been reported in optical tweezers of an unspecified polarization state [14, 15].
Fig. 1. Morphology of tetragonal lysozyme, showing crystallographic axes and faces. The optical axis coincides with the c-axis. The aspect ratio is defined as l:w.
Lysozyme is a widely used model for studies of nucleation and growth of protein crystals to establish the fundamental understanding that can be applied to the crystallization of other proteins for structural characterization. These studies are a critical element in determination of biochemical function. In its most common (tetragonal) form, lysozyme is birefringent, and has a well-characterized morphology, as shown in Fig. 1. These characteristics suggest that optical tweezers can be used to immobilize and orient the crystals during observations of their growth. The difference in the indices along the a and c axes in the visible is 2.4×10-3, whereas the tensor elements of the optical activity are two orders of magnitude smaller [16], so chiral effects are minimal, especially at long wavelengths. The difference between the crystal and host liquid indices of refraction is also small (8×10-3) [17, 18]. The ratio of the length of the c-axis to the (110) face width in these crystals is affected by the pH and the supersaturation ratio of the host liquid during growth. We are therefore able to vary the aspect ratio of the crystals to choose the orientation that the crystals will assume in the tweezers.
The ability to relocate protein microcrystals with optical tweezers has been noted [19]. Here, we establish the birefringence of lysozyme in the infrared, and use this property to fix or rotate the orientation of lysozyme crystals, as desired, using the polarization of the trapping light. We demonstrate, for the first time, the growth of crystals within an optical trap. (Crystals could also be dissolved and regrown under changed conditions, allowing comparison of the quality of crystals from a single seed, used multiple times.) In addition, we observe spontaneous rotation of asymmetric and compound crystals.
2. Experiments
2.1 Optical tweezers
Two separate setups were used in the experiments described here; one for recording video of the rotation and the growth of the particles, and one for measurements of the ellipticity introduced into linearly polarized light passing through the lysozyme crystals. The system used in the ellipticity measurements is reported in [20], whereas the video recording setup is shown in Fig. 2. Linearly polarized light from an Yb-doped fiber laser operating at 1070 nanometers in the range of 200–500 mW was coupled into a 60x oil-immersion objective of numerical aperture 1.4. The laser light was guided to the objective using a dichroic mirror (DC), allowing viewing and recording of the crystals using the same objective and a white light source. A half-wave (HWP) or quarter-wave plate (QWP) in the beam path could be used to either adjust the direction of the plane of polarization or to produce a circularly polarized trapping beam.
2.2 Lysozyme crystal preparation
The microcrystals of lysozyme were prepared by the batch method. To promote heterogeneous nucleation, a concentrated solution of lysozyme was prepared from the as-delivered powder, and allowed to age for 2 weeks at room temperature, prior to crystal growth [21]. The lysozyme powder was dissolved in a 0.6M acetic acid/deionized water solution to a concentration of 487mg/ml. 20–100 µl of this protein concentrate was placed in 2ml bottles, and then varying amounts of a 5wt% solution of NaCl in water (titrated to a pH of either 7 or 9 using NaOH) were added. The ratio of the volumes of the protein:salt solutions was one to one, two, four, five, ten or twenty. During addition of the salt solution, the micropipette was used to agitate the solution vigorously by pumping the mixture in and out of the tip 10–20 times. This resulted in rapid formation of many nuclei in all but the most dilute solutions. The crystals were formed at, and stable at, room temperature over a period of weeks. Growth experiments were made by adding small amounts of the protein concentrate (approximately 1:4 by volume) to the solution in the optical tweezers. No attempt was made to control the solution pH accurately during these initial experiments.
3. Results and discussion
The birefringence of our crystals in the visible was confirmed by examining them in the optical tweezers setup using crossed polarizers (oriented parallel to the edges of the image), as shown in Fig. 3. The trapping laser was turned off for this experiment.
Fig. 3. Images of lysozyme crystals (pH 7.0, 1:20 protein:salt solution) taken in the tweezers setup under a) crossed polarizers and b) linearly polarized light. The polarizer axes are aligned with the image edges.
3.1 Birefringence at 1064nm
Linearly polarized light was incident on the crystals, and the induced ellipticity upon passage through the crystal was measured according to the method described in [7] using a Nd:YAG laser. The thickness of the crystals, along with the angle of the c-axis relative to the polarization was combined with the ellipticity to yield a value for the difference in the indices of refraction along the [001] and [110] directions. We determined the refractive index difference Δn of the lysozyme at 1064nm to be 1.66×10-3, somewhat smaller than the value reported in the visible. Figure 4 shows the calculated momentum transfer per photon (normalized by thickness) derived from the ellipticity measurement, along with the curve calculated for the Δn given above.
3.2 Orientation control
Experiments were then performed to verify that the crystal orientation could be controlled using polarization. We expect to see a combination of the effects of shape anisotropy and crystalline birefringence. For crystals with aspect ratios (l:w) greater than ~2 the c-axis aligned with the beam axis upon capture. In this case, the alignment of the optical axis precluded any polarization effects due to birefringence. The shape anisotropy due to the square cross-section of the crystals was too weak to allow changes in orientation upon rotation of the half-wave plate. However, for smaller aspect ratios, crystals could be trapped with the optical axis perpendicular or skewed to the trap beam. In these cases, the crystals could be rotated using a half-wave plate. The maximum momentum transfer for this case was determined to be on the order of 0.1 ħ per photon. Rotation occurs for crystals with shape anisotropy (regular hexagonal faces) less than that of the c-axis aligned ones, indicating that the rotation is due to birefringence. The maximum momentum transfer for circular polarization was calculated to be between one and two orders of magnitude smaller than that for the half-wave plate rotation. Indeed, we were not able to rotate the crystals using circularly polarized light; the torques were not large enough to overcome the viscous forces for particles of this size.
Fig. 4. Measured and calculated values of the momentum transfer vs. angle for several crystals (solid line is for Δn=1.66×10-3). Each symbol represents a distinct crystal.
3.3 Autorotation
Asymmetric and compound (two or more adhered) crystals picked up by the tweezers showed spontaneous rotation in the presence of linearly polarized light. As reported by Higurashi et al[15], particles with parallel faces at different distances from the center of rotation lead to unbalanced torques, and can induce quite rapid rotation, due to refractive effects alone. This has also been noted in glass shards, when they are trapped two-dimensionally against a surface [13]. Figure 5 shows autorotation for a compound crystal.
Fig. 5. Movie of autorotation of a compound lysozyme crystal in a linearly polarized trapping beam. Rotation continued for ~10 minutes before slowing and stopping. (730 kB)
When crystals displayed spontaneous rotational behavior, after a period of five to ten minutes, the rotation slowed, then stopped. If the crystals were released and retrapped in the same orientation, there was no resumption of the rotation, but if the retrapping event resulted in a different orientation of the crystal, rotation was seen to resume in many cases. Close observation of the crystals showed that there was some erosion of the edges of the crystal during rotation; proteins in the crystals are weakly bound, and can be removed by rheological forces. This erosion presumably reduced the asymmetry of the crystals until there was no longer adequate torque to cause rotation. Spinning of well-formed crystals, by rotating a half-wave plate could potentially be used to measure the effects of convection on the dissolution of protein crystals.
3.4 In-situ growth of crystals
There is considerable interest in the protein crystal growth community in observing the habit of crystals in a controlled, but changing environment. Past efforts have been hampered by the difficulty of reliably examining a particular crystal seed as conditions are changed. The use of optical tweezers makes this possible. To establish this, we increased the protein concentration of the solution while observing a trapped crystal. In the presence of small seed crystals, the bulk of the excess lysozyme should induce additional growth of existing crystals, rather than the nucleation of new ones.
Figure 6 shows a time-lapse movie of a trapped crystal during the protein concentration change described above. It can be seen that the crystal grows primarily by addition of material on the {110} faces, as would be expected at a high protein concentration [22].
Fig. 6. Growth of lysozyme seed (from pH 7, 1:4 protein:salt solution) in the tweezers after addition of protein concentrate. Total elapsed time is 1 minute 12 seconds. (567 kB movie)
4. Conclusions and summary
We have used the birefringence of lysozyme crystals to control their orientation in optical tweezers. Alignment of the crystals in the plane perpendicular to the trapping beam axis can be achieved based either on their anisotropic shape, or the birefringence of the tetragonal crystals. The ability to immobilize and align the crystals during changes of the host solution (temperature, protein or salt concentration), suggests the use of optical tweezers for studies of protein crystal growth made either by video observation or x-ray diffraction.
Acknowledgments
We would like to acknowledge the support of NASA grant NAG8-1590, the University of Queensland and the Australian Research Council. We are indebted to Timo Nieminen, Norman Heckenberg and Simon Parkin for their contributions.
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