INSTITUTE OF PHYSICS PUBLISHING
NANOTECHNOLOGY
Nanotechnology 17 (2006) 1217–1224
doi:10.1088/0957-4484/17/5/009
New magnetic tweezers for investigation of
the mechanical properties of single DNA
molecules
Chi-Han Chiou, Yu-Yen Huang, Meng-Han Chiang,
Huei-Huang Lee and Gwo-Bin Lee1
Department of Engineering Science, National Cheng Kung University, Tainan 701, Taiwan
E-mail: gwobin@mail.ncku.edu.tw
Received 4 October 2005, in final form 3 January 2006
Published 7 February 2006
Online at stacks.iop.org/Nano/17/1217
Abstract
This study reports new three-dimensional (3D) micromachined magnetic
tweezers consisting of micro-electromagnets and a ring-trap structure,
fabricated using MEMS (micro-electro-mechanical systems) technology, for
manipulating a single 2 nm diameter DNA molecule. The new apparatus uses
magnetic forces to exert over 20 pN with less heating, allowing the extension
of the DNA molecule over its whole contour length to investigate its entropic
and elastic regions. To improve the localized DNA immobilization efficiency,
a novel ring-trapper structure was used to handle the vertical movement of
magnetic beads which were adhered to the DNA molecules. One extremity of
the DNA molecule, which was bound to the thiol-modified magnetic bead,
could be immobilized covalently on a gold surface. The other extremity,
which was bound to another unmodified magnetic bead, could be
manipulated under a magnetic field generated by micro-electromagnets. The
important elastic modulus of DNA has been explored to be 453 pN at a low
ionic strength. This result reveals that DNA becomes more susceptible to
elastic elongation at a low ionic strength due to electrostatic repulsion. The
force–extension curve for DNA molecules is found to be consistent with
theoretical models. In addition to a single DNA stretching, this study also
successfully demonstrates the stretching of two parallel DNA molecules.
(Some figures in this article are in colour only in the electronic version)
described by [2]:
1. Introduction
The mechanical properties of DNA play a key role in molecular
biological functions. DNA can be viewed as a long, flexible,
and thin nano-scale spring polymer. Typically, the mechanical
response of a single DNA molecule to an applied force has
two regions: entropic and elastic [1]. The entropic response is
driven by thermal energy, and the elastic energy is generated
by base-pair interactions. In the entropic region, the stretching
force is less than 5 pN. The worm-like chain (WLC) model
can give a good description of DNA behaviour which could be
1 Author to whom any correspondence should be addressed.
0957-4484/06/051217+08$30.00
Felasticity P
1
R −2 1
R
1−
− +
=
Kb T
4
L
4
L
(1)
where Felasticity , L , R, K b T and P denote the stretching force,
the contour length, the extension length, the thermal energy,
and the persistence length, respectively. In the elastic region,
DNA behaves like an elastic rod. The stretching force against
the entropic response of the polymer ranges from 5 to 65 pN,
which is applied to the molecular chemical bonds. In this
region, the increase in length of the DNA molecule is due
to the slight distortion of its double-helical structure, making
the elasticity similar to that in a spring. Neglecting the
entropic contributions, the force–extension curve follows a
© 2006 IOP Publishing Ltd Printed in the UK
1217
C-H Chiou et al
(a)
(b)
Microelectromagnet
Ring trapper
Sample in
Gold surface
Felasticity λ -DNA
Magnetic bead
Sample out
z
x
Fmagnetic
Fgravity
Coverslip
Fluidic channel
Coverslip
Double side sticky tape
Oil objective
Figure 1. (a) Schematic illustration of the magnetic tweezers integrated with micro-electromagnets, a ring trapper, a fluidic channel, and a
gold-patterned surface. (b) Tethered-DNA magnetic bead is in equilibrium under the action of the magnetic force, DNA elastic force, and the
gravity force.
simple Hooke’s law [1]:
Felasticity = E Across
R
−1
L
(2)
where Across denotes the cross-sectional area, and E
represents the Young’s modulus of DNA. In real cases, the
entropic and elastic contributions must be taken into account
simultaneously. A modified model was then proposed by Odijk
for the interlinking between the entropic and elastic regions (2–
15 pN), and could be described as follows [3]:
1/2
R
1
Kb T
Felasticity
+
.
= 1−
L
2 Felasticity P
E Across
(3)
To date, many experiments with a single DNA molecule
have shown good fit to the physical models [1, 4–9]. However,
the question of whether there is a difference or not in
mechanical properties between one single DNA molecule and
two single DNA molecules has raised broad interest in DNA
topology [10, 11]. In this paper, we describe a new approach
to study the mechanical properties for one and two DNA
molecules.
Magnetic tweezers have recently proven promising in
the study of the physical properties of biological materials
tethered to a magnetic bead [7–18]. Previous studies were
based on large-scale permanent magnets [7, 12, 13] or
electromagnets [9, 16–18], showing that the forces in the
piconewton range could be used on super-paramagnetic beads
attached to bio-molecules. Movable permanent magnets have
successfully moved tethered-bead DNA molecules [7, 12, 13].
Permanent magnets have the advantages of simplicity,
portability, and no power requirement. However, precisely
controlling the movement of magnetic beads is challenging
using permanent magnets. Alternatively, electromagnets are
preferred due to their excellent controllability during operation.
For example, one can turn on or off, or even change the
magnitude of the applied current to control the movement
of a magnetic bead bonded with a DNA molecule [8, 9].
However, for large-scale magnetic tweezers, the complexity
of the magnet assembly and the time-consuming alignment
process can overshadow their practical advantages. Most
importantly, they are bulky and lack the required versatility,
resulting in integration difficulty with micro systems.
1218
For magnetic bead micromanipulation on a chip, many
existing methods using MEMS technologies have been
reported [14, 19–22]. For example, a ring matrix made
up of Au wires, adopting planar conductor fabrication
techniques to trap and move magnetic nano-particles, has been
demonstrated [22]. However, magnetic tweezers based on
microcoils have high coil resistance, generating undesirable
Joule heating when applying high current [14]. Thus, a
DNA molecule cannot be stretched to its full contour length,
implying that it is difficult to study DNA structure transitions
from B-form to S-form.
Recently, to eliminate power
consumption and to improve the magnetic force, a microinductor integrated with magnetic permalloy, namely a microelectromagnet, has been proposed to successfully separate
magnetic beads [19–21]. Good performance in magnetic bead
movement has been reported without significant Joule heating.
This study proposes new, fully integrated, 3D magnetic
tweezers for manipulating single DNA molecules in the
entropic and elastic region. This apparatus can extend the
DNA molecule in excess of the contour length with low
power consumption. The essential platform technologies
include localized DNA immobilization, micro-electromagnet
fabrication and microfluidic channels, integrated to form a
micromachine-based DNA manipulation platform. A novel
DNA immobilization approach that employs the streptavidin
to biotin and thiol to gold affinity binding systems is developed
to enhance a highly efficient and specific anchoring.
2. Materials and methods
2.1. Design and fabrication
Figure 1 shows a schematic representation of the 3D magnetic
tweezers comprising six micro-electromagnets, a ring trapper,
a fluidic channel, and a gold-patterned surface. The extremities
of a single DNA molecule are first attached to two magnetic
beads, respectively. The extremity with the thiol-modified
bead can then be moved to the centre of the ring trapper,
on which the gold is deposited. In this approach a tetheredDNA magnetic bead can be immobilized onto a localized gold
pattern via a highly specific and strong Au–S covalent bond.
Subsequently, a series of micro-electromagnets are used to
manipulate the DNA molecule. A tethered-DNA magnetic
New magnetic tweezers for investigation of the mechanical properties of single DNA molecules
(a)
(b)
Microelectromagnet
(c)
Ring trapper
Sample in
Sample out
Pad slot
Gold surface
Fluorescence excitation
(d)
2 cm
(e)
Figure 2. Photographs showing (a) the fabricated micro-electromagnets (bottom layer) and ring trapper, (b) the electroplated permalloy and
via holes, (c) the electroplated via holes, (d) the top view of micro-electromagnets, and (e) the completed assembly of the 3D magnetic
platform.
bead can be moved around under the magnetic field generated
by the micro-electromagnets.
Six micro-electromagnets are designed in hexagonal
geometry for linear and angular movements of a magnetic
bead. A ring trapper is utilized to handle the vertical movement
of the magnetic bead. Thus, a 3D DNA manipulator can be
realized. Six micro-electromagnets and a ring trapper have
been first fabricated using standard lithography, electroplating,
and planarization processes [14]. The SEM pictures are shown
in figures 2(a)–(d). Notably, a micro-electromagnet comprised
of 3D coils wrapped with 30 turns, wound around a bar core of
high-permeability permalloy (Ni80 Fe20 ). The width, spacing
and thickness of the coils are 80, 100 and 25 µm, respectively.
A magnetic core has a size of 5.3 mm × 300 µm × 15 µm.
Significantly, the fabricated permalloy is easy to magnetize
and demagnetize, and hence requires a low magnetic field
strength. Thus, the permalloy can be applied to microelectromagnets involving repeated cycles of magnetization and
demagnetization, and enhances the magnetic flux density.
A gold surface for Au–S bonding was then patterned
using standard lift-off techniques. Thus, thiol-modified λDNA could be immobilized onto a localized gold pattern
and a highly specific and strong covalent bonding of Au–S
could be formed. Lastly, a fluidic channel was sealed with a
cover slip using double-sided sticky tape (60 µm thickness,
ARclearTM, Adhesives Research Inc., USA). As illustrated in
figure 1(b), the DNA molecule was anchored on the top of the
flow channel. Therefore, the distance between the anchoring
point of DNA and the cover slip was around 60 µm. Notably,
the thin cover slip (100 µm thickness, Erie Scientific Company,
USA) must be selected for flow cell construction because this
type granted an additional 70 µm of space when using a
170 µm corrected working distance, oil-immersion objective.
This can ensure that the manipulated DNA molecule is located
within the working distance of the objective. The dynamic
behaviour of a single DNA molecule could be observed under
a microscope, and calibration of the magnetic force could be
achieved with viscous drag forces acting on a bead. Figure 2(e)
shows the completed assembly of the 3D magnetic platform.
2.2. DNA sample preparation
The λ-phage DNA (New England Biolabs, USA) with a
complementary 12-base single-stranded 5 -overhang was used
in this study. It has 48 502 base pairs (bps) and a contour
length of 16.5 µm. To improve the efficiency of anchoring
the DNA on the localized gold surface, a new method for
DNA construction with two-bead binding was developed,
as illustrated in figure 3. Detailed information for DNA
construction will be described in the following sections.
2.2.1. Biotinylation of two extremities of DNA. First, a
complementary primer containing a biotin molecule at the 3
end and phosphorylation at the 5 end was custom-synthesized
(MDBio Inc., Taiwan). The oligonucleotide sequence is
5 AGGTCGCCGCCC-biotin3 . Prior to ligating the primer
onto the λ-DNA, the λ-DNA was heated to 70◦ for 15 min
to linearize any circular-forms. The synthesized primer was
then hybridized with the λ-DNA when the solution was cooled
down slowly from 70 ◦ C to 4 ◦ C for 2 h, followed by ligation
using T4 DNA Ligase and 10× Ligase buffer at 16 ◦ C for
6 h. Subsequently, the biotinylated λ-DNA was purified
using phenol/chloroform extraction and ethanol precipitation
to remove proteins and excess olignucleotides. The DNA of
150 µg ml−1 was dissolved in deionized distilled (DD) water
for the next ligation process.
Another complementary primer (5 GGGCGGCGACCTbiotin3 , MDBio Inc., Taiwan) was ligated to the other
1219
C-H Chiou et al
(a) Step 1
λ phage DNA
(48,502 bps,16 µ m)
Biotin
G G G C G G C G A C C T
C C C G C C G C T G G A
Biotin
G G G C G G C G A C C T
C C C G C C G C T G G A
(a) Step 2
Streptavidin
λ phage DNA
Sulpho-NHS-SS-Biotin
Biotin
Thiol
Magnetic bead
gold
surface
Ring
trapper
Figure 3. Schematic illustration of DNA construction with two-bead binding. (a) Two sticky ends of a λ-DNA were hybridized with
biotinylated primers. (b) Two extremities were attached to magnetic beads. Using the ring trapper, one end was then immobilized onto the Au
surface via the thiol-modified bead.
biotinylated λ-DNA extremity using the same methods as
described above. The two-end, biotinylated λ-DNA was again
purified and stocked in a concentration of 100 µg ml−1 in TE
buffer (10 mM Tris-HCl (pH 8.0), 1 mM EDTA) for bead
attachments.
2.2.2. Fluorescent dye staining. In order to observe a single
DNA molecule, a cyanian dimer dye, YOYO-1 (Molecular
Probes Inc., USA), was used to stain λ-DNA for DNA
manipulation, and it was visualized using a fluorescence
microscope. To improve the signal-to-noise ratio, the base
pair to dye molecule ratio was kept at 5:1 for DNA solutions.
Under these conditions, the contour length of λ-DNA increases
to around 20 µm [23]. An oxygen scavenging system
containing 4% β -mercaptoethanol, 50 g ml−1 glucose oxidase,
10 g ml−1 catalase, and 2% glucose can be mixed with the
DNA solution to efficiently reduce photo-bleaching and photoscission effects. Typically, a single molecule can be observed
by constant illumination for a period of 10 min without
bleaching.
2.2.3. Thiolization of magnetic beads. The following step
was the magnetic bead activation with thiol-biotin reagents.
In this study, sulfo-NHS-SS-biotin (sulfosuccinimidyl-2(biotinamido)ethyl-1,3-dithiopropionate, Pierce Inc., USA)
was used because of its good solubility in water (up to
approximately 10 mM) and it enables thiolization in general
buffers. In this study, two super-paramagnetic, streptavidincoated beads, a 2.8 µm diameter bead (magnetic moment,
m sat ≈ 1.42 × 10−13 A m2 , M280, Dynal, Norway) and a
1.0 µm diameter bead (m sat ≈ 2.25 × 10−14 A m2 , MyOneTM ,
Dynal, Norway), were used. Subsequently, sulfo-NHS-SSbiotin of 10 mM in DD water was prepared immediately before
use. Partial beads that were desired to be modified with thiol
groups were mixed with sulfo-NHS-SS-biotin of 1 mM in PBS
buffer (0.1 phosphate, 0.15 M NaCl, pH 7.2). The reaction
was incubated at room temperature for 30 min, followed by
washing twice with PBS buffer for removal of the non-reacted
sulfo-NHS-SS-biotin. The thiol-modified beads were stocked
in the binding buffer (10 mM Tris-HCl (pH 8.0), 1 mM EDTA,
1220
10 mM NaCl, and 0.1% Tween 20) at 4 ◦ C for further DNA
attachment.
2.2.4. DNA attachment onto two-magnetic beads. The twoend biotinylated λ-DNA of 10 ng ml−1 was mixed together
with the modified beads of 5 × 106 ml−1 and unmodified beads
of 5 × 106 ml−1 in the binding buffer for 3–5 min. Significantly,
they still had a 1 in 4 probability of collisions among λ-DNA
molecules and beads, resulting in one end being bound to a
non-thiol-modified bead and the other end bound to a thiolmodified bead.
2.2.5. DNA anchoring on the gold surface. Finally, the twoend, tethered-bead λ-DNA molecules were introduced into the
microfluidic channel integrated with the 3D magnetic tweezers
using a syringe pump. When applying a current to the ring
trapper, the DNA molecules with magnetic beads were trapped
to the centre of the gold covered surface. Consequently, the
thiol-modified bead was immobilized on the gold surface. As
the magnetic force was released, the bead without thiol groups
precipitated away from the top Au surface due to the higher
density compared with the buffer solution, while the one with
thiol groups was firmly anchored onto the gold surface via Au–
S bonding.
2.3. Experimental setup
The fabricated device was mounted on top of an inverted
microscope (IX-70, Olympus, Japan) for DNA visualization,
which was equipped with a fluorescence source (75 W xenon
lamp, UXL-S75XE, Ushio Inc., Japan) and a standard YOYO1 filter set (excitation filter: 460–490 nm, dichroic mirror:
505 nm, emission filter: 515–550 nm, U-MWIBA, Olympus,
Japan). The fluorescence image of a single DNA molecule
was acquired by an oil-immersion objective lens (Plan Apo,
100×, NA = 1.35, Olympus, Japan), as well as a cooled
CCD (CCD-300T-RC, DAGE-MTI, USA), an image integrator
(Investigator, DAGE-MTI, USA) and a video recorder (NVF86TN, Panasonic, Japan). Finally, a frame grabber (Bandit-II
CV, Coreco Imaging, USA) and a personal computer (PC) were
used to digitize the recorded images.
New magnetic tweezers for investigation of the mechanical properties of single DNA molecules
y
y
z
x
(a)
x
z
(b)
Figure 4. Single molecule manipulation using 3D magnetic tweezers. (a) Stretching of a single DNA molecule linked to thiol-modified beads.
(b) DNA reciprocating motions by alternating applied current on opposite micro-electromagnets. The DNA molecule can be manipulated
upward and downward.
3. Results and discussion
In order to manipulate DNA molecules, the tethered-bead
DNA molecules were first manually transported into the fluidic
channel. One end of the DNA molecule should be anchored on
the centre zone of the magnetic tweezers such that the magnetic
force could act uniformly on the DNA molecule. Initially,
two magnetic beads bound to the same DNA molecule were
trapped after applying a current of 500 mA to the ring trapper.
Consequently, the thiol-modified bead was immobilized on the
localized gold surface via a highly specific and strong Au–
S covalent bonding, on which the magnetic field gradients
were generated. When the current was turned off, the bead
without thiol groups precipitated away from the top Au surface
due to the gravity, while the bead with thiol groups was
firmly anchored on the gold surface due to the Au–S covalent
bonding. Additionally, a shear flow could be applied to flush
the beads with non-specific binding. With this approach, one
end of the DNA molecule was linked to the central area of the
Au surface, while the other end was attached to a magnetic
bead which was suspended in the buffer solution. The magnetic
bead bound to the DNA molecule could be moved around
within the magnetic field generated by micro-electromagnets.
Consequently, the DNA molecule could be manipulated by
using the developed magnetic platform.
3.1. Single molecule manipulation
Figure 4(a) shows the stretching of a single DNA molecule
linked to a localized gold surface using the magnetic force
generated by applying current to the micro-electromagnet. The
DNA molecule was stretched to 14.74 µm as the applied
current gradually increased to 400 mA. DNA reciprocating
motions were achieved by alternating current applied to the
opposite micro-electromagnets, as shown in figure 4(b). One
end of the DNA molecule was attached to a 1 µm magnetic
bead linked to the gold surface. The other end was attached to
a 2.8 µm magnetic bead suspended in the solution. Initially,
the tethered-bead DNA molecule was in equilibrium. When
applying a 50 mA current to the upward coil, an initial
stretching of a DNA molecule was found in the upward
direction. When applying a 100 mA current to the downward
coil, the DNA molecule was stretched correspondingly. When
again applying a 200 mA current to the upward coil, the
DNA molecule was stretched and moved back upwards. The
y
z
17.47 µm
14.74 µm
x
6.50 µm
(a)
(b)
(c)
Figure 5. Versatile DNA stretching techniques at the same applied
current: (a) two DNA molecules simultaneously attached to magnetic
beads, (b) one DNA molecule attached to 1.0 µm magnetic beads,
and (c) one DNA molecule attached to 2.8 µm magnetic beads.
experimental results demonstrate a capability for versatile
DNA manipulation using alternating current inputs.
Figure 5 compares the relationship of the force–extension
with the various DNA stretching techniques at the same level
of applied current. As shown in figure 5(a), when raising the λDNA concentration in the bead-binding buffer, 1 µm magnetic
beads may lead to interactions between two DNA molecules,
and two single molecules could be simultaneously attached
to two magnetic beads. When applying a current of 400 mA
to the micro-electromagnet, two DNA molecules attached to
the 1 µm magnetic bead were stretched to 6.50 µm. For
comparison, a single DNA molecule could be elongated to
14.74 µm as shown in figure 5(b). These two DNA molecules
could be regarded as parallel springs.
Table 1 summarizes the results of DNA stretching,
including one single and two parallel DNA molecules. The
behaviour of the two parallel DNA molecules is clearly
different from that of one single DNA molecule. The extension
of two parallel DNA molecules is much lower than that of a
single DNA molecule. This phenomenon may be speculated
due to entwinement/curling, variation of attachment points,
or even nicking. According to the experimental observation,
two DNA molecules may be slightly entwined and are not
absolutely parallel bindings. This phenomenon would cause
a higher spring constant. Although the extension length of
1221
C-H Chiou et al
Relative extension
λ -DNA
Figure 6. Schematic of force calibration using the modified
Stokes’ law.
Table 1. Comparison of the force–extension relationships of DNA
stretching for one single and two parallel DNA molecules.
Applied force
Stretching of two
DNA molecules
(µm)
7.61
10.96
13.00
14.74
3.10
4.23
5.96
6.50
DNA can be precisely calibrated from the difference between
the y coordinates of the beginning and end fluorescence values
in an image, the attachment points for two parallel DNA
molecules cannot be well controlled or well defined on the
magnetic beads. This would lead to errors in determining the
extension length and cannot stretch absolutely parallel DNA
molecules. In addition, a possible explanation is that the
two parallel molecules have larger temporal fluctuation energy
against the stretching force. Half of the applied force was
applied to one of the DNA molecules, causing the transverse
spring constant of the DNA to become smaller. Thus, the
larger transverse fluctuations of the DNA were easily driven
by thermal motion. This transverse fluctuation energy can be
against the stretching force, leading to a smaller extension. On
the other hand, DNA nicking is an inevitable effect, especially
for DNA–dye complexes, leading to a smaller spring constant.
Therefore, the stretching of two parallel DNA molecules
reveals significant change in spring constants when compared
to the stretching of a single DNA molecule.
Moreover, 2.8 µm magnetic beads were also used for
tensile testing. As shown in figure 5(c), the single DNA
molecule could be extended to 17.47 µm at the same applied
current. In the cases of figures 5(b) and (c), the applied
magnetic forces are 0.542 and 2.049 pN, respectively. The
results indicate that the 2.8 µm magnetic bead used in
manipulating the DNA could generate a bigger magnetic force
to stretch the DNA molecule than the 1.0 µm magnetic bead.
This is because the 2.8 µm magnetic bead has a higher
magnetic moment than the 1 µm bead, enabling the same
magnetic field gradient to induce a larger magnetic force.
There is an appreciable discrepancy between the measured
force and the calculated force. The result may be due to the
difference in the level of magnetization for a 2.8 µm diameter
bead and a 1.0 µm diameter bead.
3.2. Force calibration
Since some important variables such as temperature, ionic
strength and the presence of the dye molecule can affect the
1222
0.3
0.4
0.5
0.6
0.7
0.8
0.9
10
12
14
16
18
Drag force
WLC model
0.8
0.6
0.4
0.2
0.0
4
6
8
DNA extension length (µm)
(pN)
0.057 (±3.0%)
0.090 (±3.1%)
0.281 (±3.2%)
0.543 (±3.2%)
DNA elastic force (pN)
νf
Stretching of one
DNA molecule
(µm)
1.0
h
0.2
Figure 7. Force–extension curve for a single λ-DNA molecule using
the drag force on a 1 µm bead. When the contour length of λ-DNA is
20 µm at the base pair to YOYO-dye molecule ratio of 5:1, the
persistence length is 53 nm at a monovalent sodium salt
concentration of 10 mM, and the thermal energy is 4.1 × 10−21 J at a
temperature of 25 ◦ C. The measurement data fit well with the WLC
model. The overall errors were estimated to be 3–4%.
DNA flexibility, an experiment was conducted to check these
controllable variables. A simple DNA stretching technique was
performed in the developed platform, as illustrated in figure 6.
A DNA molecule, attached to a 1 µm magnetic bead, was
stretched by the drag force from an applied flow. The DNA
stretching force can be directly estimated from the drag force
acting on the bead using the modified Stokes’ law [24]:
Fmagnetic
9r
= 6πηr νf 1 +
16h
(4)
where η denotes the viscosity of the solution, r denotes the
radius of the magnetic bead, νf denotes the flow velocity,
and h denotes the distance from the centre of the bead to
the wall. The experimental conditions were controlled and
described as follows: the temperature was 25 ◦ C, the base
pair to YOYO-dye molecule ratio was 5:1, and the sodium
salt concentration was 10 mM. Notably, if the monovalent
sodium ions were raised to a concentration of 100 mM, the
dye molecules were difficult to intercalate onto the DNA [25].
Under these conditions, the values K b T = 4.1 × 10−21 J,
L = 20 µm, and P = 53 nm, were used and were
substituted into the WLC model to obtain a curve fit to the
WLC model (equation (1)). Figure 7 shows the relationship
between the stretching force and extension length of a single
DNA molecule. The measurement data obtained by the drag
force fit well with the WLC model, and are in agreement with
most previous literature [2, 4]. It reveals that the variables for
DNA manipulation have been well controlled, allowing further
magnetic tweezers experiments. This technique provides a
simple and direct method to stretch a single DNA molecule and
to measure its force-curve. The error of the DNA stretching
force mainly depends on the accuracy in determining the flow
velocity and the bead size. The overall errors have small values
of 3–4%.
New magnetic tweezers for investigation of the mechanical properties of single DNA molecules
Relative extension
0.0
DNA elastic force (pN)
100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
14
16
18
20
22
3-D magnetic tweezers
WLC model
Odijk's model
Hooke's law
10
1
0.1
0.01
0.001
0
2
4
6
8
10
12
DNA extension length (µm)
Figure 8. Force–extension curves for a single λ-DNA molecule. 3D
magnetic tweezers can stretch DNA in the entropic and elastic
regions. The elastic modulus of DNA is measured to be 453 pN.
3.3. Force–extension curve of DNA
Figure 8 shows the force–extension relationship for a single
DNA molecule, and the comparison with the theoretical
models. The 3D magnetic tweezers could stretch a single
DNA molecule in the entropic and elastic regions. In order
to fit the measurement data in the elastic region, Hooke’s
law (equation (2)) and Odijk’s model (equation (3)) were
used. According to classical elasticity theory and the condition
for thermal bending equilibrium, two crucial parameters for
characterizing DNA flexibility, the persistence length ( P ) and
elastic modulus ( S = E Across ), are correlated in worm-like
DNA molecules [26, 27]:
P=
Sd 2
.
16 K b T
(5)
When modelling DNA as an elastic rod with d = 2 nm
and choosing P = 53 nm, the elastic modulus is predicted to
be 869 pN by using equation (5). Correspondingly, P = 53 nm
and S = 869 pN are substituted into the Hooke’s law and
the Odijk’s model to obtain the curve fits for these equations,
as shown in figure 8. There is an appreciable discrepancy
between the data involving the 3D magnetic tweezers and
the fitting data involving Hooke’s law. The measured elastic
modulus of DNA was determined to be 453 pN by using the
Hooke’s law, significantly below a value of 869 pN calculated
from equation (5). The experimental results reveal that DNA
becomes more susceptible to elastic elongation. The measured
value is consistent with the previous value of 450 pN reported
by Baumann et al (at low ionic strength of 9.3 mM Na+ ) [5],
while having appreciable deviation from a value of 1087 pN
as reported by Smith et al (at a high ionic strength of 150 mM
Na+ ) [1]. This phenomenon may be due to the fact that the high
ionic strength can neutralize the majority of negative charges
along the DNA backbone and may cause the DNA elasticity to
change.
According to the preliminary experiments, those variables
in equation (5) have been precisely controlled and defined
except for the elastic modulus ( S ) and the DNA diameter (d ).
In order to make equation (5) consistent with the measured S
and P values, the diameter of DNA must be increased from 2
to 2.77 nm, which seems unreasonably large. Another possible
explanation is that the DNA structure is not a perfectlyhomogeneous, cylindrical rod. Instead, it could be a nonuniform cylindrical rod with a varying diameter, especially,
when the manipulated DNA molecule is a DNA–dye complex.
The intercalated dye molecules may lead to a slight increase
in DNA diameter (for example, ethidium bromide may cause
an increase of 0.06 nm in diameter) [28]. In any event, the
reduced elastic modulus is not dominated by dye contribution
or structural deviation. Electrostatic interactions must be taken
into consideration in DNA models. Therefore, such a simple
and classical formula as equation (5) cannot explain real DNA
behaviour.
DNA is a negatively charged polyelectrolyte. At a low
ionic strength, a charged DNA molecule would become a
relaxed Hookean spring owing to electrostatic repulsion among
the DNA phosphate groups, resulting in a decrease in its
elastic modulus. Baumann et al [5] proposed another possible
explanation for the decrease in the elastic modulus. They
reported that at a certain ionic strength there was localized
melting in A-T rich regions [5]. Increases in the ionic
strength would reduce both local melting and intra-molecular
electrostatic repulsion, thus simultaneously increasing the
elastic modulus and decreasing the persistence length. The
elastic modulus obtained from 3D magnetic tweezers (as in this
study) and obtained from optical tweezers seems to support the
Baumann’s explanation [1, 5, 6].
4. Conclusion
In conclusion, DNA elastic properties are not governed by
macroscopic elasticity theory, i.e., DNA does not behave like
a classical macroscopic cylinder. The developed 3D magnetic
tweezers used a simple and reliable fabrication process. The
developed system provides physical insight into the physical
characteristics of DNA. In additional to the stretching of one
single DNA molecule, stretching of two DNA molecules has
also been demonstrated. With these methods, the size of the
apparatus can be reduced markedly, allowing the magnetic
tweezers platform to be mass-produced at low cost. Most
significantly, the microfabricated system can be simplified
without losing sensitivity and functionality, unlike in other
methods such as the use of large-scale magnetic tweezers and
optical tweezers. The outcome of this study could provide a
powerful tool for exploring the bio-physical properties of biomolecules, bio-polymers and cells, which will make substantial
impact on the development of bio-nanotechnology.
Acknowledgments
The authors gratefully acknowledge the financial support
provided to this study by the National Science Council, Taiwan
(Grant number NSC 94-2212-E-006-023) and MOE Program
for Promoting Academic Excellence of Universities (Grant
number EX-91-E-FA09-5-4). The authors also thank the
Center for Micro/Nano Technology Research, National Cheng
Kung University under projects from the Ministry of Education
and the National Science Council (NSC 93-212-M-006-006).
1223
C-H Chiou et al
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