1LSA Biophysics, University of Michigan, 2LSA Biophysics, Department of Physics, University of Michigan
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Raghunathan, K., Milstein, J. N., Meiners, J. -. Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers. J. Vis. Exp. (56), e3405, doi:10.3791/3405 (2011).
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.
1. Tweezers Setup
2. Calibrating Apparent Size of the Bead to Axial Position
3. Mapping the Optical Potential of the Manipulation Beam
4. Stretching a DNA Sample
5. Representative Results:
We present force extension curves for two DNA sequences: a 1298 bp and a 247 bp sequence, the latter being the shortest sequence we have been able to stretch reproducibly. For short stretches of DNA, the conventional Worm-Like Chain (WLC) model does not fully explain the force extension relationship because at these length scales one must account for finite-size effects and zero force extension arising from boundary constraints. The force extension measurements, therefore, have to be fit using a modified WLC model which has an effective persistence length and a zero force extension as fit parameters, described further in the supplementary materials. For large contour lengths of dsDNA, the effective persistence length is simply the nominal persistence length (˜50 nm) and the zero force extension can be neglected. However, as the contour length becomes shorter the effective persistence length decreases well below 50 nm and the DNA, even under zero force, shows a significant extension.
The data and the corresponding fits of the force extension curves are shown in Fig. 5 for the two sequences. From the modified WLC fits, we have determined the effective persistence lengths to be 35 nm for the 1298 bp DNA and 25 nm for 247 bp DNA. For illustrative purposes, we are presenting single measures of the force extension curves for each sequence. In practice, one would repeat the measurements multiple times and obtain the average results along with the standard errors. It must also be noted that after obtaining each curve it is imperative to ensure that the microsphere remains trapped and properly positioned within the linear region, otherwise the microsphere must be realigned as previously described in the protocol.
Figure 1 Principle of Axial Optical Tweezers. (Left) Conventional optical tweezers trap near the focus. The bead is then moved lateral to the coverslip to exert tension. (Right) In axial optical tweezers, a microsphere is trapped away from the focus, in the linear region of the optical potential. In this configuration, the polymer is held under constant tension for a range of extensions. Moreover, increasing the laser intensity moves the microsphere in the axial direction.
Figure 2 Schematic Representation of Axial Optical Tweezers. Laser light (1064nm Nd:YvO4) is split into two beams by passing through a polarizing beam splitter (PBS). The manipulation beam, passes through an acousto-optical deflector (AOD) and the calibration beam can be adjusted independently using telescopic lenses. The two beams are then recombined using another PBS and focused onto the sample by a high N.A. objective. Simultaneously, brightfield illumination used to track the microsphere,passes through the sample, is infrared (IR) filtered and is then imaged by two CCD cameras, one of which takes measurements while the other acts as part of a feedback control system.
Figure 3 Axial Position Calibration. To calibrate the axial position, we acquire defocused images of a bead stuck to the chamber coverslip at varying axial positions of the stage. The size of the microsphere is given by the distance between its center and the position of peak intensity about the bright ring formed around the image of the microsphere. The inset presents the radial intensity distribution which gives the size of the bead.
Figure 4 Principle Behind Mapping the Optical Potential. To map out the optical force of the manipulation beam, the axial displacement that it induces on a microsphere trapped within a much stronger calibration beam is measured. The center of the linear region where this displacement is a maximum is located. The Optical Force vs. Axial Position curve can be integrated to find the optical potential.
Figure 5 Force Extension Curve. Data is shown for a random 1298 bp and 247 bp (inset) segment of dsDNA stretched by axial optical tweezers. The data points were fit to the modified WLC model of Eq. 3 (solid lines) and yielded effective persistence lengths of 34 nm and 25 nm for the 1298bp and 247bp respectively.
Conventional optical tweezers rely upon either analog or computer-controlled feedback to apply a constant force on a refractile object. These active feedback systems have difficulty performing under conditions where sudden changes in the extension of the specimen occur, for instance, from the binding of a protein to DNA or the rapid stepping of a molecular motor along a filament. Various passive methods for applying constant forces have recently been developed. One such method, used to resolve the stepping of RNA polymerase at basepair resolution, involved working within the linear region of the optical potential of a Gaussian laser beam12. We have adapted this method for the manipulation of short biomolecules by creating a constant-force axial optical tweezers.
Axial optical tweezers can be used to study short stretches of DNA that are inaccessible to manipulation by conventional optical methods. They have been used to study the elasticity of short DNA molecules as small as a few hundred base pairs8 and to probe the effects of elastic tension on protein-mediated DNA loops13,14. On short length scales, sequence dependent effects arising from variations in hydrogen bonding and stacking energies, may strongly contribute to the elastic properties of DNA. Axial optical tweezers are an ideal tool for uncovering these sequence dependent effects on DNA elasticity15. Moreover, axial optical tweezers will be a sensitive tool for studying the wrapping of DNA around individual histones and for probing the activity of any rapidly processing molecular motor, and would prove to be a valuable new technique in the single-molecule toolbox.
No conflicts of interest declared.
We thank Dr. Yih-Fan Chen for help with the axial optical tweezers and for contributing some of his stretching data to this manuscript. This work was sponsored by NSF grant PHY-0957293 and FOCUS grant PHY-0114336.
|Nd:YVO4 laser||Spectra Physics||T40-Z-106C|
|Microscope Objective||Olympus||PlanApo||60X, NA 1.4|
|Piezo stage||Mad City Labs||Nano-LP100||XYZ stage|
|Polystyrene Beads||Spherotech||SVP-08-10||800nm, streptavidin coated|
|Primers||MWG operon||Custom oligos||One primer: biotin Other : digoxigenin|
|PCR reagents||New England Biolabs||TAQ polymerase, dNTPs|
|Other chemicals for buffer||Fisher Scientific|
A. Hydrodynamic Friction Coefficient
For determining the hydrodynamic friction coefficient of the microsphere near a surface one can use the following expansion5,10:
where the following shorthand has been introduced:
The friction coefficient is defined in terms of the fluid viscosity η and the radius of the microsphere, with the microsphere’s center located a distance η above the surface. The summation converges reasonably well when expanded to about ten terms.
B. Influence of Axial Position on Stiffness Calibration
The calibration of the trap stiffness involves a tradeoff between the accuracy of the calibration, which increases with increasing distance from the surface, and the actual axial position where the trap is used experimentally. In general, the trap is calibrated at around 800-1000 nm from the surface, which is higher than the actual experimental condition.
C. Modified Worm-Like Chain (WLC) Model
The force extension curves can be fit to a modified WLC model that accounts for volume exclusion effects at zero optical force as follows:
where Fopt is the optical force, xo is a fit parameter for the zero force extension,xopt is the extension under force, l is the contour length of the DNA, and l*p is a second fit parameter for an "effective" persistence length. Fwlc is given by the usual WLC model11 where ε is the relative DNA extension.