A high-resolution magnetic tweezer for
Kipom Kim1and Omar A. Saleh1,2,*
1Materials Department and2Biomolecular Science and Engineering Program, University of California,
Santa Barbara, CA 93106, USA
Received May 1, 2009; Revised July 26, 2009; Accepted August 17, 2009
manipulation instruments that utilize a magnetic
field to apply force to a biomolecule-tethered
magnetic bead while using optical bead tracking
to measure the biomolecule’s extension. While
relatively simple to set up, prior MT implementa-
tions have lacked the resolution necessary to
observe sub-nanometer biomolecular configuration
changes. Here,we demonstrate
interference technique for bead tracking, and show
that it has much better resolution than traditional
resolution by fabricating optical coatings on all
reflecting surfaces that optimize the intensity and
implement feedback control of the focal position
to remove drift. To test the system, we measure
the length change of a DNA hairpin as it undergoes
a folding/unfolding transition.
Over the past 10 years, a variety of experimental
techniques have been developed that allow the mechanical
manipulation of a single biological molecule and the
sensing of its interactions with other biomolecules (1–3).
These single-molecule measurements are extraordinarily
sensitive, as they are capable of applying piconewton-
scale forces and measuring displacements of nanometers,
allowing them to provide direct data on the molecular-
scale workings of biological systems. Importantly, these
data are quantitative, and can thus be directly compared
to other information, such as crystallographic structures
or biochemical / biophysical theories, in order to attain
a complete understanding of biomolecular behavior.
The magnetic tweezer (MT) is a simple and stable tool
to stretch and twist biomolecules and to measure their
extension over time (4–8). It is based on the manipulation,
using magnetic fields, of a paramagnetic bead (1–5mm in
diameter) that is tethered to a glass surface through a
single biomolecule. The field applies a force to the bead
that stretches or twists the molecule. In a typical
experiment, a physical change to the tethered biomolecule
causes its extension to increase or decrease, raising or
lowering the vertical position of the bead. Traditionally,
bead height is measured by analyzing the bead’s
diffraction image when viewed in a transmitted light
geometry (9,10). Thus, the MT’s capability to measure
physical changes to the biomolecule depends on the
ability to relate variations in the diffraction image to the
position of the bead.
The resolution of any single-molecule technique is
impaired by two sources of noise: the Brownian motion
of the bead, which can be reduced by using small beads,
high forces, and short tethers, and the intrinsic resolution
of the instrument, which depends on the sensing technique
diffraction-based MT setups, the intrinsic resolution is
limited to ?1nm (10), which suffers in comparison to
high-resolution optical tweezer methods (11). This low-
resolution originates from the relatively small lateral
motion of the diffraction interference fringes with bead
height. Limited resolution is acceptable in the low-force
regime, where Brownian motion of the tethered bead
dominates the experimental noise. However, when using
high forces, Brownian motion is reduced and the intrinsic
resolution becomes limiting.
To overcome this limit, we have adapted Reflection
Interference Contrast Microscopy (RICM) to the MT.
interference pattern between rays reflecting from a glass
surface and those reflecting from an object in solution
located near to the surface (12,13). Bead height is
calculated by comparing the
pattern to a theoretical model that predicts the fringe
shape based on the optical geometry (13). Importantly,
the interference fringes from RICM have a much larger
variation with bead height than those from diffraction.
Indeed, prior applications of RICM have indicated
sub-nanometer accuracy in measured bead height is
illumination creates an
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Published online 3 September 2009 Nucleic Acids Research, 2009, Vol. 37, No. 20e136
? The Author(s) 2009. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/
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There are two difficulties in using RICM with an MT.
First, the optical properties are not ideal: both the
magnetic beads and the glass surface have a similar
refractive index as the surrounding solution. Without a
significant difference in refractive index, little light would
be reflected from each interface, allowing background
illumination (stemming from, e.g. internal reflections
within the bead) to obscure the RICM interferogram.
Thus, it is necessary to adjust the properties of each
surface both to achieve optimal interferogram intensity
and contrast and to cut-off background light. Second, to
accurately model and analyze the RICM interference
pattern, the image plane of the microscope must be
stably maintained at a known, fixed position—in parti-
cular, at the glass-water interface. Thus, it is necessary
to minimize the defocusing effects of thermal and
mechanical drift. We overcame these difficulties by,
respectively, fabricating optical coatings on all reflecting
surfaces that optimize the intensity and contrast of the
interference image, and implementing feedback control
of the focal position to remove drift.
MATERIALS AND METHODS
DNA samples. DNA constructs with a single hairpin were
based on PAGE-purified DNA oligomers (Integrated
DNA Technologies) that have a hairpin sequence, and
non-palindromic ligation sequences at each end. The
hairpins (S20T8, S30T8) have 20-bp stem and 8-nt
Thymine-loop (S30T8), of which stem sequences are GA
GTCAACGTCTGGATCCTA and GAGGCGGTCGCC
The 50-end of the hairpin was ligated to an 800-bp
dsDNA handle with a 14-nt complementary overhang at
one end and a digoxigenin label at the other end, while the
30-end of the hairpin was annealed to a 15-nt oligomer
(Integrated DNA Technologies) with a 50biotin label.
The dsDNA handle (800bp) was prepared by means of
AutostickyPCR using Lambda-phage
digoxigenin-labeled primer (MWG Biotech), and one
primer with a 15-nt extension after a deoxyribose spacer
site (Integrated DNA Technologies) to achieve the
speciEed dsDNA length and 50-end (16). A 1738-bp
double-stranded DNA without a hairpin was prepared
by means of PCR using Lambda-phage DNA as the
template, andprimers containing,
digoxigenin and 50biotin labels (MWG Biotech).
oneas the template,50
Beads. Magnetic beads of 2.8mm diameter (Invitrogen
Dynal-M280) were used for the diffraction measurements
and 4.5mm-diameter magnetic beads (Invitrogen Dynal-
M450) were used for the RICM measurements. Dynal
M450 beads have 5% polydispersity in diameter. Our
simulation (see below) indicates that a 5% polydispersity
affects the measured bead height by <3%; direct
measurement of the individual tethered bead’s diameter
would reducethis error.One micrometer-diameter
polystyrene beads (Bangs Laboratories PS04N) were
used as reference objects stuck on the coverglass.
Optical enhancement of reflecting surfaces
To enhance each surface’s optical characteristics for
RICM, both the magnetic bead and the glass surface
were coated with nanofabricated thin layers (Figure 1).
To make beads with a half gold surface, the solution of
magnetic beads was dried on a flat solid surface. The
surface was coated sequentially with Ti (5nm) and Au
(50nm) using electron-beam metal evaporation; the
Ti layer acts as an adhesion layer between the polystyrene
of the bead and the gold. Half-coated beads were
resuspended in phosphate-buffered saline using sonica-
tion, and purified by magnetic separation. Separately,
the glass substrate was sequentially coated with TiO2
(50nm, n=2.5) and SiO2 (25nm, n=1.42) using
electron-beam dielectric evaporation. The coatings were
fabricated in the UCSB Nanofabrication Facility using
Temescal electron-beam evaporators.
Immobilization of DNA
The magnetic bead’s gold-coated surface was biotinylated
by incubating overnight in a biotinylation reagent (0.2%
w/v Sulfo-NHS-SS-Biotin in Phosphate-buffered saline,
pH 7.4): the Sulfo-NHS-SS-Biotin (Pierce Ez-Link) was
used after reducing the disulfide bond with TCEP
(Sigma). The biotinylated gold surface was then coated
with streptavidin (Roche Diagnostics). The coverglass’s
In both the diffraction and RICM measurements, the
biotin and digoxigenin labels on the DNA were bound,
respectively, to the streptavidin on the magnetic bead and
the anti-digoxigenin on the coverglass (Figure 1a).
Magnetic tweezer (MT)
The basic MT system is shown in Figure 2. We used an
inverted microscope (Nikon TE2000-U) with an oil-
immersion objective (Nikon Plan APO 1.4NA 100?).
The applied magnetic field is generated by a pair of
permanent (NdFeB) magnets (12.5mm cubes, DuraMag
NS-505050) located above the sample stage, separated by
1mm, and with their magnetic moments aligned anti-
parallel to each other. Variation of the field in the
sample plane is achieved by translating the magnets with
a DC servo motor (Physik Instrumente M-126.PD1) in the
range between 1 and 25mm from the stage. Magnetic
beads can be rotated about the illumination axis by
rotating the magnet pair with a DC servo motor (Physik
Instrumente C-150.PD); we use the trajectory of rotated
beads to exclude mis-tethered beads (17).
We calibrate the force applied to magnetic beads by
analyzing the power spectrum of measured lateral
fluctuations, as is standard for such techniques (9).
Based on that analysis, we estimate the uncertainty in
the measured force to be 10%.
e136Nucleic Acids Research, 2009,Vol.37, No. 20PAGE 2 OF 7
Illumination, imaging and tracking
Detail of the illumination scheme and stabilizing method
were as explained in Ref. (10,15). Briefly, there are
separate light sources to make the diffraction and inter-
ference image of the beads (Figure 2). A monochromatic
incident beam (red) from an LED enters through the gap
between the magnets and creates a diffraction pattern of
the bead on the image plane. A second monochromatic
beam for RICM (green) uniformly illuminates the image
plane by focusing the incident beam on the back focal
plane of the objective lens; the smallest achievable
illumination numerical aperture (INA) is 0.48. The
images were then acquired with a CCD camera (JAI
CV-A10CL), which has 60Hz frame rate and 3.3ms
minimum exposure. From each acquired image, lateral
center positions and height (x, y, h) and radial averaged
intensity profiles of the interference image I(r) of magnetic
beads were calculated and stored in real time using custom
written tracking software. In the diffraction method, h
was calculated in real-time from previously-acquired
calibration images. In RICM, h was estimated in
real-time by scaling the radius of the first interference
ring with a sensitivity factor pre-estimated numerically
for each bead. After completing the experiments, h
values for RICM were re-calculated from the stored I(r)
using custom written analysis software. The illumination
and the imaging method are chosen by switching the filter
block and the tracking-software.
The piezo objective positioner (Mad City Labs F-100)
on which the objective lens is mounted was used to
implement feedback control of the focal position for
RICM, and to make the calibration image for the
diffraction method; it has 0.2nm spatial resolution,
20ms time response and a 100mm travel range.
re-calculated from the stored I(r) after finishing an
experiment. Each acquired intensity profile I(r) was
compared with a series of intensity profiles IS (r,h)
simulated based on Ref. (13); simulated profiles were
calculated for every 1nm change in bead height. The
absolute squared differences ?2(h) for pairs of I(r) and IS
(r,h) were calculated, and the final value of h was selected
by interpolation in the vicinity of the minimum ?2(h).
RICM-based measurements,allh valueswere
Stabilization for RICM-based measurements
Low-frequency drift from the apparatus restricts the
low-frequency limit on measurable transition rates. To
minimize defocusing due to the low-frequency drift, we
implemented an active stabilizing method that uses
position through piezo-driven motion of the objective
controlof the focal
Figure 1. (a) Schematic diagram of optical and biochemical coatings.
(b) Electron micrograph of 4.5mm diameter gold-coated beads; the
bright half of each bead is the gold-coated surface. Scale bar: 2mm.
Figure 2. Schematic diagram of the experimental setup. AD: aperture
diaphragm, FD: field diaphragm, IF: incident bandpass filter, OF:
imaging bandpass filter, TL: tube lens, PL: parfocal lens, M: beam
splitter, P: piezo objective positioner, Obj: objective lens. CCD is a
CCD camera with 60Hz frame rate. The inset shows the geometry of
both the tethered bead and the transmitted and reflected beams.
PAGE 3 OF 7Nucleic Acids Research, 2009,Vol.37, No. 20 e136
lens (15), where the feedback control automatically
adjusted the objective position every 1s. As shown in
our prior work, this feedback method decreased the
drift-induced apparent fluctuations in bead height to a
standard deviation of 0.12nm (at a 60Hz frame rate)
and was stable over tens of minutes.
The high-frequency limit on measurable transition rates
is set by the time-response of the bead (e.g. how fast can
the bead move after a step-like change in tether extension),
or by the frame rate of the camera (16ms), whichever is
less. Here, due to the high forces and short tethers used,
the frame rate of the camera is the limiting parameter.
RESULTS AND DISCUSSION
Effect of optical coating
To optimize the quality of the interference image, we
coated the magnetic bead and the glass surface with
nano-fabricated layers that
surface of the magnetic bead increased the reflectance to
80% and completely removed background light from
internal reflections within the bead. A further advantage
of the gold coating was that it retains biochemical
functionality through thiol chemistry. A high refractive
layer on the coverglass increased the
reflectance of that surface, while the SiO2capping layer
enabled biochemical functionality. In combination, the
gold and dielectric coatings increased the interference
pattern’s intensity 16-fold and its contrast by 60%
(Figure 3). As result of these improvements, we can
apply RICM based tracking for bead heights up to
1mm, corresponding to 3kbp dsDNA tethers.
Comparison with traditional method
To evaluate our RICM-based method and to compare it
to the traditional diffraction-based method, we performed
MT measurements of the force-induced folding/unfolding
transition of a DNA hairpin structure (Figure 4a) (18).
Figure 5 and Supplementary Figure S1 show that the
hairpins repeatedly fold and unfold at a constant applied
force near the critical force. The critical forces are
10±1pN for S20T8 and 12±1pN for S30T8. Based
on the hairpin length and the elasticity of ssDNA (19),
the expected changes in extension for the folding transi-
tion are 17.4±0.8nm for S20T8 and 27.8±0.6nm for
Sensitivity comparison. We tested the relative sensitivity of
the two approaches by comparing the radial intensity
profiles from diffraction to those from RICM for two
bead heights, corresponding to the open and closed state
of the DNA hairpin S20T8 (Figure 4b and c). For the
same change in bead height, the RICM fringes varied
much more than the diffraction fringes, indicating the
method. In particular, the first diffraction fringe shifted
by 3.8nm in the sample plane, while the first RICM
fringe shifted by 62nm (Figure 4d and e). Thus, our
RICM strategy provides roughly a 16-fold improvement
in instrumental resolution. Given the ?1nm intrinsic
resolution of diffraction (10), we expect the RICM-based
MT will have an intrinsic resolution well below 1nm.
Accuracy calibration. The diffraction-based measurement,
while less precise, has the virtue of relying on an accurate
experimental calibration scheme that relates bead height
to fringe motion (9). In contrast, calibration of the RICM
fringes relies on a theoretical model (13). To experimen-
tally verify the accuracy of the model, we compared the
diffraction- and RICM-measured extension difference
between the folded and unfolded states of the hairpins
(Figure 5 and Supplementary Figure S1). Figure 5 shows
diffraction- and RICM-measured time traces and height
distributions for beads tethered by hairpin S20T8
stretched near its critical force (similar data on hairpin
S30T8 is included in the Supplementary Figure S1).
For S20T8, the measured changes in extension are
17.5±0.2nm for diffraction and 17.4±0.2nm for
RICM, while for S30T8, they are 27.6±0.1nm for
diffraction and 27.4±0.2nm for RICM. Thus, within
the experimental error, the results are in agreement both
with each other and with the expected extension change,
Figure 3. Interference images formed by reflected beams from the surfaces of (a) an uncoated bead and a coverglass, (b) a gold-coated bead and an
uncoated coverglass and (c) a gold-coated bead and a dielectric coated coverglass. In image (b), the intensity of interference below the bead is
saturated because of the high reflectance of the gold surface. The intensity in (c) is about 16 times higher than that of (a), and the contrast in (c) is
?60% higher than that of (a). For the image in (c), a 16? neutral density filter is placed in the optical path of the incident illumination, which
reduces background reflection intensity and prevents saturation of the CCD. Scale bar 2mm in (c).
e136Nucleic Acids Research, 2009,Vol.37, No. 20PAGE 4 OF 7
indicating that our RICM calibration scheme is reliable.
The RICM-based measurement shown in Figure 5b and d
has a larger variance than that of the diffraction
measurement (Figure 5a and c); this is not related to the
arguments indicate that the larger bead size used here
for the RICM-based measurement leads to a larger
predicted Brownian fluctuation (20), which dominates in
the force regime used in this calibration experiment.
At constant applied force and tether length, smaller
beads have less thermal noise; thus it is desirable to use
smaller beads in the RICM measurement. The RICM
0.7 0.80.9 1.0
2.1 2.22.3 2.4
0.51.0 1.52.0 3.0
Figure 4. Comparison of diffraction- and RICM-based methods. (a) Schematic of DNA hairpin experiment. (b) Radial intensity profiles of
diffraction patterns from a 2.8mm diameter bead. (c) Radial intensity profiles of reflected-interference patterns from a 4.5mm diameter bead. In
(b) and (c), the solid (dashed) line corresponds to an intensity profile from the closed (open) state of the DNA hairpin S20T8; the boxed areas
highlight the motion of the first fringe. (d) and (e) are magnifications of the boxed area in (b) and (c), respectively. In (b), the x-axis starts at 1.5mm
to exclude the region in which the light is blocked by the sphere.
500ms median filtered
raw date (60 Hz)
Figure 5. (a and b) Bead height versus time of a bead tethered by a dsDNA containing hairpin S20T8 measured at a constant applied force near the
critical force using (a) diffraction from a 2.8mm diameter magnetic bead and (b) RICM from a gold-coated 4.5mm diameter magnetic bead. (c and d)
Distributions of bead height calculated from the raw data in the (a) and (b), respectively.
PAGE 5 OF 7 Nucleic Acids Research, 2009,Vol.37, No. 20 e136
strategy described here (i.e. the illumination and detection
scheme and the height calibration method) can be applied
to smaller beads without any changes in protocol.
However, the RICM method requires a smooth bead
surface to generate a clean interferogram; thus far, we
have found only the Dynal 4.5mm diameter beads (and
not the Dynal 1 or 2.8mm diameter beads) to have an
adequately smooth surface. Future work is needed to
either identify a manufacturer of small, smooth magnetic
beads, or to fabricate them directly.
We demonstrate the resolution of the RICM-based
magnetic bead immobilized directly on the coverglass
and a magnetic bead tethered by a single 1738-bp DNA
molecule. Figure 6a shows a time trace of the apparent
height of the immobilized bead in the absence of applied
force. Using active stabilization, which uses a melted
polystyrene bead as a reference mark (15), the focal
position of the objective is maintained in the vicinity of
the solution/coverglass interface. However, it is impossible
for the focal position to be maintained in a perfectly stable
fashion. Furthermore, non-specifically immobilized beads
are known to undergo small motions (21). Thus, we
attribute the fluctuations in Figure 6a to the imperfect-
ness of both the active stabilization and the bead
immobilization method. The data thus indicates that the
instrumental resolution of RICM is below 0.2nm in
standard deviation (Figure 6c and e).
Figure 6b shows a time trace of the tethered bead
subject to ?23pN of applied force. The corresponding
standard deviation (Figure 6d and f) indicates the actual
resolution: 0.62nm at 8ms exposure and 60Hz frame rate,
the heightof botha
and 0.2nm using a 500ms window median filter. Here,
the resolution is limited by the Brownian fluctuations
allowed by the finite elasticity of the tether; they are
well-accounted for by the Langevin theory (17), which
predicts a standard deviation of 0.61±0.05nm at 8ms
When the applied force reduces the bead’s Brownian
fluctuations below 0.25nm, we expect the RICM-based
measurement can resolve sub-nanometer changes in bead
height with a signal to noise ratio (SNR) >4. This is
emphasized by the data in Figure 7a, which indicates the
standard deviations of the trace in Figure 6b as a function
of the window size of the median filter. In practice,
σ = 0.17 nm
σ = 0.63 nm
σ = 0.11 nm
σ = 0.20 nm
500ms median filtered
raw date (60 Hz)
Figure 6. (a and b) Measured bead height versus time of (a) a bead immobilized on the coverglass and (b) a bead tethered to the coverglass by a
1738bp dsDNA. Each data point was calculated from RICM data acquired with 8ms exposure and 60Hz frame rate (dots) and median filtered with
a 500ms window (solid lines). The force applied to the tethered bead is about 23pN. (c–f) Histograms of bead height from the traces in (a) and (b);
(c) and (d) are calculated using the 60Hz raw data, while (e) and (f) are calculated using the median filtered data. The distributions are fitted by a
Gaussian function (solid lines), with best-fit standard deviations shown.
Window size (ms)
1000 400600800 200
Figure 7. (a) Standard deviations of the time trace in Figure 6b as a
function of the window size of the median filter. (b) SNR for a 1nm
step versus window size. The dashed line indicates the condition for
which a 1nm change in bead height can be resolved with an SNR of 4.
e136Nucleic Acids Research, 2009,Vol.37, No. 20PAGE 6 OF 7
resolving step-like extension changes requires an SNR >4
(22); furthermore, the choice of window size will be
determined by the kinetics of the studied extension-
changing process. Thus Figure 7b indicates that, for a
1738bp tether under 23pN of force, 1nm steps can be
resolved by RICM if they occur more slowly than
We have demonstrated a high resolution MT based on
RICM with a greater than 10-fold resolution increase
over the traditional diffraction method. This improvement
was enabled by the intrinsically higher sensitivity of the
RICM fringes, the inclusion of thin films that enhanced
the quality of the RICM interferograms, and the use of an
active stabilization routine. We used a biomolecular
calibration based on DNA hairpin unfolding to show
that the RICM measurement of the length change is
accurate. Our results show that the RICM-based MT
system is well suited to precision measurements of
configuration-changing biomolecular activity. We expect
this system will provide a simple and powerful tool for the
investigation of the physical properties of biological
Supplementary Data are available at NAR Online.
The authors thank N. Ribeck for comments.
1R21GM079584-01A1]. A portion of this work was
done in the UCSB nanofabrication facility, part of the
Nanotechnology Infrastructure Network. Funding for
open access charge: National Institutes of Health [grant
Conflict of interest statement. None declared.
1. Greenleaf,W.J., Woodside,M.T. and Block,M. (2007)
High-resolution, single-molecule measurements of biomolecular
motion. Annu. Rev. Biophys. Biomol. Struct., 36, 171–190.
2. Neuman,K.C. and Nagy,A. (2008) Single-molecule force
spectroscopy: optical tweezers, magnetic tweezers and atomic force
microscopy. Nat. Meth., 5, 491–505.
3. Lionnet,T., Dawid,A., Bigot,S., Barre,F.X., Saleh,O.A., Heslot,F.,
Allemand,J.F., Bensimon,D. and Croquette,V. (2006) DNA
mechanics as a tool to probe helicase and translocase activity.
Nucleic Acids Res., 34, 4232–4244.
4. Strick,T.R., Allemand,J.F., Bensimon,D., Bensimon,A. and
Croquette,V. (1996) The elasticity of a single supercoiled DNA
molecule. Science, 271, 1835–1837.
5. van der Heijden,T., van Noort,J., van Leest,H., Kanaar,R.,
Wyman,C., Dekker,N.H. and Dekker,C. (2005) Torque-limited
RecA polymerization on dsDNA. Nucleic Acids Res., 33,
6. Taneja,B., Schnurr,B., Slesarev,A., Marko,J.F. and Mondrago ´ n,A.
(2007) Topoisomerase V relaxes supercoiled DNA by a constrained
swiveling mechanism. Proc. Natl Acad. Sci., 104, 14670–14675.
7. Lia,G., Semsey,S., Lewis,D.E., Adhya,S., Bensimon,D., Dunlap,D.
and Finzi,L. (2008) The antiparallel loops in gal DNA. Nucleic
Acids Res., 36, 4204–4210.
8. Saleh,O., Mcintosh,D., Pincus,P. and Ribeck,N. (2009) Nonlinear
low-force elasticity of single-stranded DNA molecules. Phys. Rev.
Lett., 102, 068301.
9. Gosse,C. and Croquette,V. (2002) Magnetic tweezers:
micromanipulation and force measurement at the molecular level.
Biophys. J., 82, 3314–3329.
10. Ribeck,N. and Saleh,O.A. (2008) Multiplexed single-molecule
measurements with magnetic tweezers. Rev. Sci. Instrum., 79,
11. Abbondanzieri,E.A., Greenleaf,W.J., Shaevitz,J.W., Landick,R. and
Block,S.M. (2005) Direct observation of base-pair stepping by
RNA polymerase. Nature, 438, 460–465.
12. Curtis,A.S.G. (1964) The mechanism of adhesion of cells to glass: a
study by interference reflection microscopy. J. Cell Biol., 20,
13. Wiegand,G., Neumaier,K.R. and Sackmann,E. (1998)
Microinterferometry: three-dimensional reconstruction of surface
microtopography for thin-film and wetting studies by reflection
interference contrast microscopy (RICM). Appl. Opt., 37,
14. Ra ¨ dler,J. and Sackmann,E. (1993) Imaging optical thicknesses and
separation distances of phospholipid vesicles at solid surfaces.
J. Phys. II France, 3, 727–748.
15. Kim,K. and Saleh,O.A. (2008) Stabilizing method for reflection
interference contrast microscopy. Appl. Opt., 47, 2070–2075.
16. Ga ´ l,J., Schnell,R., Szekeres,S. and Ka ´ lma ´ n,M. (1999) Directional
cloning of native PCR products with preformed sticky ends
(Autosticky PCR). Mol. Gen. Genet., 260, 569–573.
17. Klaue,D. and Seidel,R. (2009) Torsional stiffness of single
superparamagnetic microspheres in an external magnetic field.
Phys. Rev. Lett., 102, 028302.
18. Woodside,M.T., Behnke-Parks,W.M., Larizadeh,K., Travers,K.,
Herschlag,D. and Block,S.M. (2006) Nanomechanical
measurements of the sequence-dependent folding landscapes of
single nucleic acid hairpins. Proc. Natl Acad. Sci., 103, 6190–6195.
19. Smith,S.B., Cui,Y. and Bustamante,C. (1996) Overstretching
B-DNA: the elastic response of individual double-stranded and
single-stranded DNA molecules. Science, 271, 795–799.
20. Gittes,F. and Schmidt,C.F. (1998) Thermal noise limitations on
micromechanical experiments. Eur. Biophys. J., 27, 75–81.
21. Carter,A.R., King,G.M., Ulrich,T.A., Halsey,W., Alchenberger,D.
and Perkins,T.T. (2007) Stabilization of an optical microscope to
0.1nm in three dimensions. Appl. Opt., 46, 421–427.
22. Wallin,A.E., Salmi,A. and Tuma,R. (2007) Step length
measurement – theory and simulation for tethered bead
constant-force single molecule assay. Biophys. J., 93, 795–805.
PAGE 7 OF 7 Nucleic Acids Research, 2009,Vol.37, No. 20e136