Dual-beam Optical Trap Research Articles

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

Single-molecule techniques for stretching DNA of contour lengths less than a kilobase are fraught with experimental difficulties. However, many interesting biological events such as histone binding and protein-mediated looping of DNA1,2, occur on this length scale. In recent years, the mechanical properties of DNA have been shown to play a significant role in fundamental cellular processes like the packaging of DNA into compact nucleosomes and chromatin fibers3,4. Clearly, it is then important to understand the mechanical properties of short stretches of DNA. In this paper, we provide a practical guide to a single-molecule optical tweezing technique that we have developed to study the mechanical behavior of DNA with contour lengths as short as a few hundred basepairs. The major hurdle in stretching short segments of DNA is that conventional optical tweezers are generally designed to apply force in a direction lateral to the stage5,6, (see Fig. 1). In this geometry, the angle between the bead and the coverslip, to which the DNA is tethered, becomes very steep for submicron length DNA. The axial position must now be accounted for, which can be a challenge, and, since the extension drags the microsphere closer to the coverslip, steric effects are enhanced. Furthermore, as a result of the asymmetry of the microspheres, lateral extensions will generate varying levels of torque due to rotation of the microsphere within the optical trap since the direction of the reactive force changes during the extension. Alternate methods for stretching submicron DNA run up against their own unique hurdles. For instance, a dual-beam optical trap is limited to stretching DNA of around a wavelength, at which point interference effects between the two traps and from light scattering between the microspheres begin to pose a significant problem. Replacing one of the traps with a micropipette would most likely suffer from similar challenges. While one could directly use the axial potential to stretch the DNA, an active feedback scheme would be needed to apply a constant force and the bandwidth of this will be quite limited, especially at low forces. We circumvent these fundamental problems by directly pulling the DNA away from the coverslip by using a constant force axial optical tweezers7,8. This is achieved by trapping the bead in a linear region of the optical potential, where the optical force is constant-the strength of which can be tuned by adjusting the laser power. Trapping within the linear region also serves as an all optical force-clamp on the DNA that extends for nearly 350 nm in the axial direction. We simultaneously compensate for thermal and mechanical drift by finely adjusting the position of the stage so that a reference microsphere stuck to the coverslip remains at the same position and focus, allowing for a virtually limitless observation period.

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

Single-molecule techniques for stretching DNA of contour lengths less than a kilobase are fraught with experimental difficulties. However, many interesting biological events such as histone binding and protein-mediated looping of DNA, occur on this length scale. In recent years, the mechanical properties of DNA have been shown to play a significant role in fundamental cellular processes like the packaging of DNA into compact nucleosomes and chromatin fibers. Clearly, it is then important to understand the mechanical properties of short stretches of DNA. In this paper, we provide a practical guide to a single-molecule optical tweezing technique that we have developed to study the mechanical behavior of DNA with contour lengths as short as a few hundred basepairs. The major hurdle in stretching short segments of DNA is that conventional optical tweezers are generally designed to apply force in a direction lateral to the stage (see Fig. 1). In this geometry, the angle between the bead and the coverslip, to which the DNA is tethered, becomes very steep for submicron length DNA. The axial position must now be accounted for, which can be a challenge, and, since the extension drags the microsphere closer to the coverslip, steric effects are enhanced. Furthermore, as a result of the asymmetry of the microspheres, lateral extensions will generate varying levels of torque due to rotation of the microsphere within the optical trap since the direction of the reactive force changes during the extension. Alternate methods for stretching submicron DNA run up against their own unique hurdles. For instance, a dual-beam optical trap is limited to stretching DNA of around a wavelength, at which point interference effects between the two traps and from light scattering between the microspheres begin to pose a significant problem. Replacing one of the traps with a micropipette would most likely suffer from similar challenges. While one could directly use the axial potential to stretch the DNA, an active feedback scheme would be needed to apply a constant force and the bandwidth of this will be quite limited, especially at low forces. We circumvent these fundamental problems by directly pulling the DNA away from the coverslip by using a constant force axial optical tweezers. This is achieved by trapping the bead in a linear region of the optical potential, where the optical force is constant-the strength of which can be tuned by adjusting the laser power. Trapping within the linear region also serves as an all optical force-clamp on the DNA that extends for nearly 350 nm in the axial direction. We simultaneously compensate for thermal and mechanical drift by finely adjusting the position of the stage so that a reference microsphere stuck to the coverslip remains at the same position and focus, allowing for a virtually limitless observation period.

Measuring the complete force field of an optical trap

The use of optical traps to measure or apply forces on the molecular level requires a precise knowledge of the trapping force field. Close to the trap center, this field is typically approximated as linear in the displacement of the trapped microsphere. However, applications demanding high forces at low laser intensities can probe the light-microsphere interaction beyond the linear regime. Here, we measured the full nonlinear force and displacement response of an optical trap in two dimensions using a dual-beam optical trap setup with back-focal-plane photodetection. We observed a substantial stiffening of the trap beyond the linear regime that depends on microsphere size, in agreement with Mie theory calculations. Surprisingly, we found that the linear detection range for forces exceeds the one for displacement by far. Our approach allows for a complete calibration of an optical trap.

Single Cell Refractive Index Measurements for Optical Biomechanics

Accurate measurements of the optical properties of living cells are essential for both therapeutic and diagnostic applications of biomedical optics. Changes in the index of refraction of red blood cells, for example, have been used to chart the progress of the malaria parasite (1). The cellular index of refraction is also of critical importance in cellular biomechanics measurements. In the optical stretcher, a dual-beam optical trap, small variations in the index of refraction can lead to substantial errors in the assessment of single-cell elasticity. To determine the cell-to-cell variation of the index of refraction, we have integrated a Mach-Zehnder interferometer with a conventional transmitted light microscope to obtain high-resolution interferograms of individual cells. Quantitative phase images are obtained by performing a Hilbert transform and using Goldstein's algorithm to unwrap the wrapped phase image. The decoupling technique of Rappaz et al. was used to obtain cell height and index of refraction maps (2). By employing several laser sources, the cellular index of refraction can be measured as function of wavelength. Measurements of multiple cell lines at several wavelengths indicate that the refractive index can, in fact, vary significantly from cell-to-cell. Along with these results we will discuss the implications for accurate single-cell biomechanical measurements made with the optical stretcher. 1. Park et al. Proc. Natl. Acad. Sci. USA 105, 1730 (2008) 2. Rappaz et al. Opt. Express 13, 9361 (2005) Supported by NIH P20 RR16469 from the National Center for Research Resources (NCRR) and NIH R15 GM085776

Optohydrodynamic theory of particles in a dual-beam optical trap

We present an optohydrodynamic theory to treat optical interactions of particles. When applied to dielectric microsphere particles in a dual-beam optical trap, the theory explains the inhomogeneous self-organization and the spontaneous emergence of self-sustained oscillations. In the presence of small-scale symmetry breaking, self-sustained oscillations are shown to occur spontaneously from an exchange between the optical scattering and the gradient optical forces, in the absence of inertia that is central to the dynamics of ion traps. Experiments are provided that agree quantitatively with the theory. The optohydrodynamic theory is generally applicable to optical-particle configurations, and it is an important step toward explaining other physical phenomena that arise from optical interactions.

Theory of dielectric micro-sphere dynamics in a dual-beam optical trap

We investigate the dynamics of an array of polystyrene micron-sized spheres in a dual-beam fiber-optic trap. Experimental results show non-uniform equilibrium particle spacing and spontaneous self-sustained oscillation for large particle numbers. Results are analyzed with a Maxwell- Stress Tensor method using the Generalized Multipole Technique, where hydrodynamic interactions between particles are included. The theoretical analysis matches well with the experimentally observed equilibrium particle spacing. The theory shows that an offset in the trapping beams is the underlying mechanism for the oscillations and influences both the oscillation frequency and the damping rate for oscillations. The theory presented is of general interest to other systems involving multi-particle optical interactions.

Visualization of optical binding of microparticles using a femtosecond fiber optical trap

At the microscopic level, light-matter interactions can organize colloidal matter via a process known as optical binding. Optical binding refers to the creation of arrays of microparticles formed in the presence of laser fields, the inter-particle spacing being determined by the refocusing and/or scattering of the laser fields by the microparticles. In this paper we investigate one-dimensional optically bound arrays of microparticles using a femtosecond dual-beam optical fiber trap, and develop a means to visualize the field intensity distributions responsible for the optical binding using two-photon fluoresence imaging from fluorescein added to the host medium. The experimental intensity distributions are shown to be in good agreement with numerical simulations, thereby validating our new approach to visualizing the fields responsible for optical binding, and the physical model of optical binding as due to refocusing of the fields by the microparticles.

Self-aligned Dual-Beam Optical Laser Trap Using Photorefractive Phase Conjugation

We report what is to our knowledge the first experimental demonstration and theoretical analysis of an optical laser trap that uses a pair of mutually phase-conjugate beams. A primary trapping beam derived from an argon laser (514.5 nm) together with its counterpropagating phase-conjugate beam creates a self-aligned dual-beam laser trap that provides stable three-dimensional confinement for micrometer-sized dielectric particles. The transverse trapping efficiency, experimentally measured for low-numerical-aperture (N.A. 0.40–0.85) objective lenses, is found to be comparable with that produced by a single-beam gradient force trap. A theoretical analysis, which compares the performance of the self-aligned dual-beam trap against that of single-beam gradient force and conventional counterpropagating dual-beam laser traps, shows that phase-conjugate trapping provides a slight improvement in axial trapping efficiency over the other trapping geometries. The advantages of combining laser trapping with photorefractive optical phase conjugation for simultaneous sample micromanipulation and optical image processing are discussed.