JOURNAL OF APPLIED PHYSICS 102, 074703 共2007兲
Single molecule ␭-DNA stretching studied by microfluidics
and single particle tracking
Jun Wang and Chang Lua兲
Department of Agricultural and Biological Engineering, School of Chemical Engineering,
Birck Nanotechnology Center, Bindley Bioscience Center, Purdue University,
West Lafayette, Indiana 47907, USA
共Received 3 May 2007; accepted 14 August 2007; published online 9 October 2007兲
DNA stretching has been an intensively studied topic due to its involvement in the cellular
functions. In this work, we studied DNA stretching based on microfluidics and single particle
tracking techniques. Microfluidics generates well-defined flow field within microscale channels and
potentially allows the incorporation of chemical and biological assays with the single molecule
experiments. Single DNA molecules were tethered to the channel bottom 共glass兲 at one end and to
fluorescent microbeads at the other end. The microscale flow exerted hydrodynamic force on the
microbead with a magnitude dependent on the flow rate. The force-extension curves of the single
DNA molecules were obtained by localizing the fluorescent microbead with nanometer precision at
different flow rates. We were able to obtain DNA force-extension curves which fit the wormlike
chain model very well. Furthermore, we also observed plateaus at low forces 共15– 30 pN兲 in these
curves when the hydrodynamic force was kept constant for a duration of 10 s at each flow rate. One
possible reason is that stretching force with long duration lowers the activation barrier for the
conformational changes of a double-stranded DNA molecule. We expect that this approach will be
useful for studying the force associated with biological events involving single DNA molecules in
general. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2786896兴
I. INTRODUCTION
New single-molecule manipulation techniques have allowed the studies of the mechanical properties of individual
macromolecules. A number of tools, such as optical
tweezers,1,2 atomic force microcope,3,4 magnetic tweezers,5,6
and flow field,7,8 have been applied to exert mechanical
forces 共⬃piconewton兲 on single molecules and study the
forces involved in single molecule biological events.
The mechanical properties of DNA have been intensively studied.2,3,6,9,10 The use of optical tweezers led to discovering the striking DNA overstretching transition from B
form to S form.2,9 At the force of ⬃65 pN, the doublestranded DNA 共dsDNA兲 extended to 1.7–1.8 times the length
of normal B form dsDNA. The highly cooperative overstretching transition plateau has only a narrow band of a few
piconewton. Above that, the stretching profile of dsDNA
converges with that of single-stranded DNA 共ssDNA兲. The
flexibility and elasticity of dsDNA and ssDNA can be characterized by wormlike chains 共WLCs兲 and freely joint chains
共FJCs兲, respectively.2,6,11 There are important reasons that
DNA stretching is a topic of a great deal of interest. The new
states created from DNA stretching are biologically significant since some of them are relevant to DNA-protein
interactions.12 The S-DNA was speculated to provide easier
access to the base pairs for transcription purposes.13
The WLC model has been applied to describe the elastic
behavior of dsDNA under lower stretching forces.11,14 The
formula below 关Eq. 共1兲兴 describes the relationship between
a兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-8979/2007/102共7兲/074703/6/$23.00
the extension x of a WLC and the exerted stretching force F
when the dsDNA is entropically stretched 共x 艋 16 ␮m for ␭
DNA兲,
冉 冊
FP 1
x
= 1−
k BT 4
L0
−2
−
1 x
+ ,
4 L0
共1兲
where kB is the Boltzmann constant, T is the temperature, P
is the persistence length, x is the DNA’s extension, and L0 is
the contour length. The stretching behavior of DNA is assumed to be inextensible in this equation. A different equation 关Eq. 共2兲兴 describes the enthalpical stretching of DNA in
its extensible WLC regime 共14艋 x 艋 17 ␮m for ␭ DNA兲
when x approaches the contour length L0 defined by B-DNA
geometry,15
冉 冊
1 k BT
x
=1−
2 FP
L0
1/2
+
F
,
S
共2兲
where S is the elastic stretch modulus. At extensions beyond
the two regimes, DNA undergoes overstretching.
Flow field has been explored as a tool for exerting piconewton force on single molecules due to its simplicity and
low requirement on instrumentation.6–8,16 Hydrodynamic
flow fields can generate forces within a very wide range
共0.1– 1000 pN兲. This tool potentially offers easy setup and
high throughput for observing a number of single molecules
simultaneously. In this study, we explore applying microfluidic channels to DNA stretching studies. Compared to homemade channels or chambers applied in previous work, microfabricated channels offer high fidelity and reproducibility in
their dimensions and these characteristics are very important
for the reproducibility of the inside flow field. Furthermore,
102, 074703-1
© 2007 American Institute of Physics
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074703-2
J. Wang and C. Lu
due to the high level of integration and automation allowed
on a microfluidic platform, chemical and biological assays
can be potentially coupled with single molecule force measurement. By tethering one end of a ␭ DNA to the glass
substrate and the other end to a fluorescent microbead, a
number of DNA molecules were attached to the bottom of a
microfluidic channel made of polydimethylsiloxane 共PDMS兲.
We changed the flow rate in the microfluidic channel to adjust the hydrodynamic force on the DNA molecules while
monitoring the change in the localization of the fluorescent
microbead. Using single particle tracking based on fluorescence microscopy we were able to localize the microbead’s
position with nanometer precision and therefore obtain information about the length of the DNA.17,18 We envision that
this simple method will become a routine tool for studies
related to biomolecule stretching and single molecule force
measurement. In addition, we also observed DNA forceextension plateau occurring at low forces 共15– 30 pN兲 instead of the commonly reported ⬃65 pN 共Ref. 2兲 or 110 pN
for unnicked and unwound DNA19 when the force changing
took place at the time scale of seconds.
II. EXPERIMENT
A. Microfluidic device fabrication
The general information about PDMS microfluidic chip
fabrication based on standard soft lithography was provided
in our previous publication.20 The dimensions of fabricated
microfluidic channels were 64 ␮m in the depth, 314 ␮m in
the width, and 25 mm in the length. Glass slips 共150 ␮m
thick, Fisher Scientific, Pittsburgh, PA, USA兲 were cleaned
in a basic solution 关H2O : NH4OH共27% 兲 : H2O2共30% 兲
= 5 : 1 : 1, volumetric ratio兴 at 75 ° C for 1 h and then rinsed
with de-ionized 共DI兲 water and blown dry. The PDMS chip
was then bonded to the clean glass slip after both surfaces
were oxidized. The microfluidic device was then ready for
subsequent tethering of DNA molecules.
B. DNA preparation and tethering
␭ phage DNA 共New England Biolabs兲 with 48 502 base
pairs is hybridized to have biotin and digoxigenin in different
ends with three oligonucleotides 共Oligos Etc.兲. A 3⬘ biotinmodified oligo 1 共5⬘-Agg TCg CCg AAA AAA AAA AAA
AAA AAA AA-biotin-3⬘兲 was annealed to a 5⬘ overhang of
␭ phage DNA, while unmodified oligonucleotide 2 共5⬘-ggg
Cgg CgA CCT ggA CAg CAA gTT ggA CCA-3⬘兲 grafted ␭
phage DNA with oligonucleotide 3 共5⬘-digoxigenin-AA
AAA AAA AAA AAA Atg gTC CAA CTT gCT gTC C-3⬘兲
关Fig. 1共b兲兴. The resulting dsDNA with biotin and digoxigenin
ends has 48 555 base pairs. The dsDNA construct can be
denatured to form ssDNA construct by heating in 2 mM
NaOH at 100 ° C for 5 min.21
200 ␮l carboxylate-modified 5 ␮m beads with a concentration of 0.5% W / V 共Spherotech Inc.兲 were centrifuged and
resuspended in 50 mM 2-共N-morpholino兲ethanesulfonic acid
共Sigma-Aldrich兲 buffer at pH 6.0 for activation. Then the
beads were functionalized in 200 ␮l 1-ethyl-3-关3共dimethylamino兲propyl兴 共EDTA兲-carbodiimide 共Pierce兲 at
5 mg/ ml for 15 min and washed in 0.2M borate buffer at pH
J. Appl. Phys. 102, 074703 共2007兲
FIG. 1. 共Color online兲 Schematic of the experimental setup and the beadDNA-substrate construction. 共a兲 The experimental setup 共not drawn to
scale兲. The microfluidic device was mounted on an inverted fluorescent
microscope with a 20⫻ objective. The hydrodynamic force was used to pull
on the bead. 共b兲 Schematic representation of the bead-DNA-substrate construct. The ␭ DNA was annealed and ligated to the cohesive ends with oligo
1 共one end tagged with biotin兲, oligo 2, and oligo 3 共one end tagged with
digoxigenin兲. The ␭ DNA molecule was bound to glass surface at one end
by biotin/streptavidin link and the other end to a fluorescent bead 共5 ␮m
diameter兲 by digoxigenin/antidigoxigenin link as illustrated.
8.5. After incubation for 4 h with 100 ␮l antidigoxigenin
共Roche Diagnostics兲 solution at 0.01 mg/ ml, the reaction
was quenched by washing the beads with 50 mM Tris solution and then stored in phosphate buffered saline 共PBS兲 共pH
7.4兲 with 0.5% bovine serum albumin 共BSA兲 and 0.1%
Tween-20.
2% 3-aminopropyl-triethoxysilane 共Pierce兲 in dry acetone was infused into the microfluidic device and incubated
for 5 min at room temperature. The solution was then removed by de-ionized water and the channel was cured at
110 ° C for 30 min. After a mixture of 1 ⫻ 10−4 mg/ ml
Streptavidin 共Sigma-Aldrich兲 and 10 mg/ ml EDTAcarbodiimide was infused to the channel and incubated for
10 min, the reaction was quenched by flowing 50 mM
NH4Cl solution in PBS through the channel. Then the channel was filled with blocking buffer 共10 mM Tris, 2 mM
EDTA, 10 mM NaCl, 0.1% Tween-20, 3 mM NaN3,
3 mg/ ml BSA, pH8.0兲 for 1 h. The biotin and digoxigenin
modified dsDNA or ssDNA was diluted to 10−10M in DNA
bonding solution 共50 mM Tris, 50 mM NaCl, 1 mM EDTA,
10% blocking buffer, pH 7.5兲 before infusing into the channel to allow biotin at one end of DNA bound to Streptavidin
for 30 min. The excessive DNA was washed by DNA bonding solution with a flow rate at 10 ␮l / h for 10 min. Finally
functionalized microbeads at 1.46⫻ 108 / ml were carefully
infused into the channel and incubated for 30 min. The unbound beads were flushed by the stretching buffer 共137 mM
NaCl, 2 mM KCl, 0.5% BSA, and 10 mM phosphate buffer兲
flowing at 10 ␮l / h. BSA at this concentration in the stretching buffer does not affect DNA elasticity based on previous
literature.21
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074703-3
J. Appl. Phys. 102, 074703 共2007兲
J. Wang and C. Lu
C. DNA stretching observation
To determine that the microbeads are specifically attached to the glass substrate by a DNA molecule, the buffer
was flowed in alternating directions at low flow rates
共⬍50 ␮l / h兲 and we observed the movement of the microbeads. The microbeads attached to the substrate by DNA
molecules were able to go either direction. We varied the
stretching force by changing the flow rate of the stretching
buffer 共137 mM NaCl, 2 mM KCl, 0.5% BSA, and 10 mM
phosphate buffer兲 provided by a syringe pump 共PHD infusion pump, Harvard Apparatus兲 with a constant interval of 3
or 10 s. Once the force versus extension curves are obtained,
we also fit the data using WLC model to confirm that single
DNA was responsible for the connection between the microbead and the substrate. The velocity profile inside the microfluidic channel was simulated by a commercial finite volume
package FLUENT 6 共Fluent Inc.兲.
The DNA tethered fluorescent microbeads in the microfluidic channel were observed on an inverted microscope
共IX-71; Olympus兲 with a 20⫻ objective. The fluorescent microbeads were illuminated by a 100 W mercury lamp filtered
by a filter set 共Exciter HQ480/40, emitter HQ535/50, and
beamsplitter Q505lp; Chroma technology兲. An area of 433
⫻ 330 ␮m2 was observed by a charge-coupled device 共CCD兲
camera 共ORCA-285; Hamamatsu兲. 50 images were taken at a
frame rate of 30 frames/ s for the fluorescent microbeads at a
given flow rate for the localization analysis.
D. Nanoscale localization of the microbeads
The images of fluorescent microbeads are fitted by two
dimensional 共2D兲 Gaussian function defined as
PG共x,y,z0,A,x0,y 0,s兲
冋
= z0 + A exp −
册
共x − x0兲2 + 共y − y 0兲2
,
2s2
共3兲
where z0 is constant due to background noise, A is the amplitude, x0 and y 0 are the bead’s fitted fluorescent center, and
s is standard deviation of the distribution.17,18 The images of
the fluorescent microbeads were fitted by minimizing least
squares via a Matlab 共MathWorks, Inc.兲 program written in
our lab. The parameters 共z0, A, x0, y 0, s兲 are found by nonlinear least-square fitting. The beads position was determined
by averaging x0 and y 0 from the images at a specific flow
rate.
III. RESULTS AND DISCUSION
In this study, microfluidics allows the exertion of piconewton force on microbeads which are tethered by singlestranded or double-stranded ␭ DNA to the substrate. We used
fluorescent microbeads which yielded enough signal/noise
ratio for us to localize the microbead with nanometer precision 共⬃4 nm兲 at the given moment under a specific hydrodynamic force. We increased the flow rate 共the hydrodynamic force兲 using the syringe pump while recording the
localization of the microbead. The length of the DNA can be
calculated from the localization of the microbead that the
FIG. 2. 共Color online兲 Steady state velocity profile viewed in the cross
section of the microfluidic channel. The profile was simulated using FLUENT
6. The velocity was normalized by setting 0 at the boundaries and 100 at the
center. The region in which tethered beads were monitored is labeled in the
figure.
DNA is tethered to. Such data will provide us with the force
versus extension data for single DNA molecules in the image
frame.
In our experiment, we imaged the DNA tethered fluorescent microbeads in the XY plane. In order to eliminate the
effects of the vertical walls on the velocity profile, we only
observe the stretching of microbead-DNA-substrate constructs in the center portion of the channel with a distance of
at least 50 ␮m from the two vertical walls. Figure 2 shows
the modeled velocity profile in the cross section of the microfluidic channel. At 50 ␮m from the vertical walls 共XY
planes兲, the no-slip boundaries do not affect the velocity profile any more. The DNA tethered beads being observed experienced essentially the same stretching force at a given
flow rate in the channel.
Using the protocol we had for DNA tethering to the microbead and the substrate, we typically had five to eight
DNA tethered beads that were stretched by the hydrodynamic force within the imaging window of 433⫻ 330 ␮m2
with a 20⫻ objective. This approach allows us to inspect a
small population of single DNA molecules to provide desired
statistical significance.
The centers of fluorescent microbeads were determined
by 2D Gaussian fitting of the fluorescent images as described
in the experimental section, similar to what is in the
literature.17,18 Figure 3 shows that the fluorescent image of a
microbead with 20 ms exposure time can be fit to a Gaussian
with a correlation coefficient of r2 = 0.997. The center, or
mean, value of the distribution can be found based on the
fitting. The uncertainty ␴, or the standard error of the mean
in each direction, was 4.2 nm. The fluorescent image allowed
us to precisely localize a microbead under a certain flow rate.
This process of Gaussian fitting yields precision of several
nanometers which is much smaller than the experimental uncertainty caused by Brownian motion, flow irregularities, and
mechanical drift.17 At low flow rates 共⬍500 ␮l / h兲, Brownian motion of the microbead was significant in the transverse
direction which is perpendicular to the flow and parallel to
the substrate. We took 50 images within 1.5 s and calculated
the mean position of the microbead based on all the images.
By gathering the position of the same microbead at dif-
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074703-4
J. Wang and C. Lu
FIG. 3. 共Color online兲 Point-spread function 共PSF兲 of an individual fluorescent microbead tethered to a single DNA at flow rate 100 ␮l / h. A 2D Gaussian 共solid lines兲 fits the PSF surface very well 共R2 = 0.997兲 and this enables
the center to be determined with uncertainty within 4.2 nm.
ferent flow rates, we were able to establish the relationship
between the flow rate and the DNA extension length. In Fig.
4, we increased the flow rate every 3 s between the data
points. The force versus extension curve of a dsDNA molecule matched WLC behavior very well below 1700 ␮l / h.
When the dsDNA was stretched by over 1700 ␮l / h, melting
hesteresis happened. At 2600 ␮l / h, the DNA was dramatically extended to be 1.77 times of the contour length
共⬃16.5 ␮m兲 where it has a plateau in the extension curve.
We started to relax the same dsDNA after reaching the flow
rate of 3000 ␮l / h. The relaxing process was carried out by
decreasing the flow rate at the same time interval of 3 s. The
relaxing process displays hysteresis and the extension curve
of the relaxed dsDNA closely resembles that of ssDNA
stretching with flow rates higher than 500 ␮l / h. This suggests that the hysteresis was likely related to the ss nicks
presence in the dsDNA. These facts agree with what was
described in early literature.2
Next we calibrate the relationship between the flow rate
FIG. 4. Flow rate/force vs extension for dsDNA and ssDNA in a microfluidic channel. The flow rate was increased 共stretching兲 or decreased 共relaxing兲 every 3 s. The dsDNA stretching data is compared to a WLC model
共dash lines兲 with persistence length of 53 nm and contour length of
16.5 ␮m.
J. Appl. Phys. 102, 074703 共2007兲
FIG. 5. Force−1/2 vs extension for a single dsDNA molecule. The linear
relation between the two in the region of 14– 16 ␮m supports strong stretching WLC behavior. Only the data between 14 and 16 ␮m was used to
generate the trend line.
and the hydrodynamic force exerted on the microbead. In our
microfluidic channel, we assume that the hydrodynamic
force on the microbeads is proportional to the volumetric
flow rate as suggested in the literature 共F = ␻V兲.8 We use Eqs.
共1兲 and 共2兲 to fit the dsDNA stretching data in Fig. 4 at x
艋 16 ␮m and 14艋 x 艋 17 ␮m, respectively. The parameters
involved in the two equations 共P, L0, and S兲 and the conversion factor ␻ between the hydrodynamic force F and the
volumetric flow rate V were then obtained based on the fitting using least-squares method in a Matlab program. We
found the persistence length P at 52.88 nm, the contour
length L0 at 16.52 ␮m, and the elastic stretch modulus S at
1278.58 pN. The conversion factor ␻ was 0.0257 pN h / ␮l
with the particular microchannel applied in the experiment.
We could then calibrate the hydrodynamic force at different
flow rates 共Fig. 4兲. The persistence length P and the contour
length L0 we obtained from the fitting were consistent with
the values in the literature.6,14
Figure 5 shows that when the force−1/2 is plotted against
extension based on the dsDNA stretching data presented in
Fig. 4, there is a strong linear relationship between the two
parameters in the 14– 16 ␮m range. Such linearity is a clear
signature of WLC elasticity.11,22 The possible interaction between the substrate surface and the DNA bead, if existent,
does not seem to affect the WLC elasticity. It needs to be
noted that WLC model is an approximation to pure DNA
elasticity due to coupled hydrodynamic drag on DNA molecule even in uniform flow.23 In our settings, shear flow may
also play a role in determining DNA stretching behavior.
WLC model was also applied to describe DNA stretching in
a shear flow 共when DNA was tethered to a surface at one end
and free at the other end兲.24 Although it is still different from
the case of DNA attaching to a bead at one end 共as in our
study兲, this is potentially relevant to the fact that the overall
stretching we observe here matches the WLC model.
In Fig. 6共a兲, we show force versus extension curves of
dsDNA taken by varying the flow rate every 10 s 共totally
⬃5 min from 100 to 3000 ␮l / h兲. The average loading rate is
calibrated to be as low as 0.257 pN/ s. These curves can be
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074703-5
J. Appl. Phys. 102, 074703 共2007兲
J. Wang and C. Lu
slow stretching processes are likely to be involved in real
biomolecule functioning for them to work efficiently to reduce unnecessarily energy dissipation through molecular
friction. Second, strictly speaking, the DNA bead system experiences the extensional force generated by the flow-bead
interaction and in the meantime it is also sheared in Poiseuille flow between the channel floor and ceiling. It is possible that the shear flow can influence the DNA stretching in
a more significant way when the loading rate is low and the
flow rate is high. Furthermore, the interaction between the
DNA-bead with the substrate surface can vary with different
flow rates. These factors could potentially contribute to the
plateau change.
IV. CONCLUSION
FIG. 6. 共Color online兲 Flow rate/force vs extension for a number of single
dsDNA molecules in a microfluidic channel. The flow rate was increased
every 10 s. 共a兲 The force vs extension curves of several single dsDNA
molecules. 共b兲 These curves compare very well to WLC model 共dash lines兲
when the hydrodynamic force is lower than 15 pN.
fitted using Eq. 共1兲 with Pearson correlation coefficients better than 0.9 共95% or higher confidence兲 when the force was
lower than 15 pN as shown in Fig. 6共b兲. These curves exhibit
multiple transitions and force versus extension plateaus at
low forces in the range of 15– 30 pN, compared to ⬃65 pN
reported when the force was varied at the rate of 60 pN/ ␮m
using optical tweezer.25 There can be a couple of possible
reasons for such behavior. First, the force plateau has been
suggested to be associated with either DNA conformational
transitions9,26 or DNA melting.27 In our case, the possible
mechanism for the plateaus at low forces is due to the force
displacement over large time scale 共force changed every
10 s兲. It is known from ligand-receptor pair that its unbinding force depends on both the molecular fundamental property and the loading rate.28 The unbinding force is smaller if
the load on the complex increases at a sufficiently slow rate,
because there is more time for thermal fluctuations to drive
the system over the energy barrier. The low force needed for
dsDNA stretching plateau is consistent with the prediction
that low force with long duration can accelerate thermal activation over a free energy barrier stabilizing dsDNA.29 Such
We validate the application of microfluidics and single
particle tracking for the study of DNA stretching. Microfabrication provides devices with highly reproducible dimensions that are ideal for establishing flow field for single DNA
molecule stretching. The DNA length is obtained by localizing the fluorescent microbead attaching to the one end of a
single DNA molecule 共the other end tethered to the substrate兲. The high signal to noise ratio of the fluorescent microbead allows nanometer localization with a common CCD
camera. We found the multiple transitions and plateau taking
place in the stretching curve. The study of the DNA stretching based on microfluidics provides a versatile platform for
incorporating chemical and biological assays during force
measurement. Further theoretical and experimental work will
need to be carried out to precisely characterize the forces and
interactions experienced by DNA molecules in the settings of
our method.
ACKNOWLEDGMENTS
The authors thank Dr. Chengde Mao at Purdue University and Dr. Min Wu at Yale University for helpful discussions about the experimental procedures. The research was
supported by Purdue University.
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