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.

1. Tweezers Setup
<ol>
	<li>The beam from a 1064 nm laser is split into two orthogonally polarized beams. One is used to manipulate the biomolecule while the other is used for calibration purposes (see Fig. 2).</li>
	<li>The intensity of the manipulation beam is controlled by an acousto-optic deflector (AOD), while the position and focus of each beam is independently controlled by beam steering mirrors and optical telescopes, respectively.</li>
	<li>The beams are then recombined with another polarizing beam splitter an...

<ol>
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Matter. 19, 293-302 (2006).</li><li>Kaplan, N. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+DNA-encoded+nucleosome+organization+of+a+eukaryotic+genome.">The DNA-encoded nucleosome organization of a eukaryotic genome.</a> Nature. 458, 362-366 (2009).</li><li>Garcia, H. G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Biological+Consequences+of+Tightly+Bent+DNA:+The+Other+Life+of+a+Macromolecular+Celebrity.">Biological Consequences of Tightly Bent DNA: The Other Life of a Macromolecular Celebrity.</a> Biopolymers. 85, 115-130 (2006).</li><li>Neuman, K. C., Block, S. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Optical+trapping.">Optical trapping.</a> Rev. Sci. 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C. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Entropic+boundary+effects+on+the+elasticity+of+short+DNA+molecules.">Entropic boundary effects on the elasticity of short DNA molecules.</a> Phys. Rev. E. 80, 020903-020903 (2009).</li><li>Chen, Y. F., Chu, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Tethered+Particle+Microscopy+(TPM)+Protocol.">Tethered Particle Microscopy (TPM) Protocol.</a> Meiners Lab. , (2011).</li><li>Brenner, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=The+slow+motion+of+a+sphere+through+a+viscous+fluid+towards+a+plane+surface.">The slow motion of a sphere through a viscous fluid towards a plane surface.</a> Chem. Eng. Sci. 16, 242-251 (1961).</li><li>Marko, J. F., Siggia, E. 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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 polymer...

<table border="1">
	<tbody>
		<tr>
			<th>Reagent/Equipment</th>
			<th>Company</th>
			<th>Catalog number</th>
			<th>Comments </th>
		</tr>
		<tr>
			<td>Nd:YVO4 laser</td>
			<td>Spectra Physics</td>
			<td>T40-Z-106C</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td>Acousto-optic deflector</td>
			<td>IntraAction</td>
			<td>DTD-274HA6</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td>Microscope Objective</td>
			<td>Olympus</td>
			<td>PlanApo </td>
			<td>60X, NA 1.4</td>
		</tr>
		<tr>
			<td>Piezo stage</td>
			<td>Mad City Labs</td>
			<td>Nano-LP100</td>
			<td>XYZ stage</td>
		</tr>
		<tr>
			<td>CCD camera</td>
			<td>PixeLink</td>
			<td>PL-A741</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td>Photodetector</td>
			<td>Electro-Optics Tech</td>
			<td>ET-3020</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td>Polystyrene Beads</td>
			<td>Spherotech</td>
			<td>SVP-08-10</td>
			<td>800nm, streptavidin coated</td>
		</tr>
		<tr>
			<td>Anti-digoxigenin</td>
			<td>Roche</td>
			<td>11333089001</td>
			<td>From sheep</td>
		</tr>
		<tr>
			<td>Primers</td>
			<td>MWG operon</td>
			<td>Custom oligos</td>
			<td>One primer: biotin 
Other : digoxigenin 
</td>
		</tr>
		<tr>
			<td>PCR reagents</td>
			<td>New England Biolabs</td>
			<td>TAQ polymerase, dNTPs</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td>Coverglass</td>
			<td>Fisher Scientific</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
		<tr>
			<td>Other chemicals for buffer</td>
			<td>Fisher Scientific</td>
			<td>&nbsp;</td>
			<td>&nbsp;</td>
		</tr>
	</tbody>
</table>
Supplementary Materials
A. Hydrodynamic Friction Coefficient
For determining the hydrodynamic friction coefficient of the microsphere near a surface one can use the following expansion5,10: 
<img src="/files/ftp_upload/3405/3405eq1.jpg" alt="Equation 1" />
where the following shorthand has been introduced: 
<img src="/files/ftp_upload/3405/3405eq2.jpg" alt="Equation 2" />
The friction coefficient is defined in terms of the fluid viscosity &eta; and the radius of the microsphere, with the microsphere's center located a distance &eta; 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: 
<img src="/files/ftp_upload/3405/3405eq3.jpg" alt="Equation 3" />
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 
<img src="/files/ftp_upload/3405/3405eq4.jpg" alt="Equation 4" /> 
where &epsilon; is the relative DNA extension.

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.

Watch this Scientific Journal Video about Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers at JoVE.com

Stretching Short Sequences of DNA with Constant Force Axial Optical Tweezers

We illustrate the use of a constant force axial optical tweezers to explore the mechanical properties of short DNA molecules. By stretching DNA axially, we minimize steric hindrances and artifacts arising in conventional lateral manipulation, allowing us to study DNA molecules as short as ~100 nm.

Single-molecule techniques for stretching DNA of contour lengths  less than a kilobase are fraught with experimental difficulties. However, many ...

stretching-short-sequences-dna-with-constant-force-axial-optical

Research

JoVE Journal

Bioengineering

13.0K visualizações.  University of Michigan. Ilustramos o uso de uma constante de força axial pinças ópticas para explorar as propriedades mecânicas das moléculas de ADN curtas. Esticando DNA axialmente, minimizamos impedimento estérico e artefatos provenientes de manipulação laterais convencional, o que nos permite estudar moléculas de DNA tão curto quanto ~ 100 nm.