Letter pubs.acs.org/macroletters
Stretching of Tethered DNA in Nanoslits Jia-Wei Yeh*,†,‡ and Kylan Szeto† †
School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, United States Department of Physics, University of California, San Diego, La Jolla, California 92122, United States
‡
S Supporting Information *
ABSTRACT: External forces and confinement are two fundamental and complementary approaches for biopolymer stretching. By employing micro- and nanofluidics, we study the force−extension dynamics by simultaneously applying external forces and confinement to single-DNA molecules. In particular, we apply external electric fields to stretch single DNA molecules that are attached to microspheres anchored at a nanoslit entrance. Using this method, we measure the force− extension relation of tethered DNA and describe this relation with modified wormlike chain models. This allowed experimental validations of several theoretical predictions, including the increase in the global persistence length of confined DNA with increasing degree of confinement and the “confined Pincus” regime in slit confinement. DNA under strong confinement when h ≤ 30 nm. As discussed below, this result can be explained by the inhomogeneity of surface-passivation polymers or the roughness of the nanoslit walls. We fabricated nanoslit devices on fused silica substrates using a differential etching process. The heights of the slits in our experiments were h = 30, 40, 55, 60, 90, and 130 nm. The fabricated nanoslits all have the same length ls = 30 μm (x-axis) and the width ws = 10 μm (y-axis). The two ends of each nanoslit are connected to microchannels that are 1 μm in height and 184 μm in width to load DNA samples and anchor microspheres (Figure S1). We sealed the device with fluidic inlets and outlets using a bonding technique described in the Supporting Information (SI). The DNA molecules used in our experiments are bacteriophage λ-DNA (48.5 kbp). They were fluorescently labeled with YOYO-1 fluorescent dye. We attached each DNA molecule to a 0.2 μm diameter microsphere (Figure 1, Methods in SI). The prepared samples of DNAbead-coupled molecules were loaded into the nanoslits and were subsequently stretched by an electrophoretic force along the direction of the nanochannels. In all experiments, one end of the DNA attached to the microsphere is held at the nanoslit opening. The other end of the DNA is extended in response to the applied electrophoretic field. To study the morphology of the stretched DNA, we imaged the sample with a fluorescence microscope and extracted its trajectory from the acquired data. A series of DNA molecules under various applied fields are shown in Figure 1b. We use the end-to-end projected DNA length l in the x-direction to characterize the DNA extension. We find three different regimes of the behavior of the DNA as
D
ynamics of single biopolymers through nanochannels and pores is an important and widely studied phenomenon. Such confined systems are highly relevant for many fascinating processes from viral DNA packaging1 and gene transfer between bacteria2 to the design of single-molecule sensors for detecting and analyzing genetic3 and epigenetic markers.4 Technical advancements have made it possible to manipulate individual biomolecules by external forces such as optical/ magnetic tweezers and flows.5−9 Moreover, nanofabrication has provided important experimental means to test theoretical predictions in fundamental polymer physics using single DNA molecules in confined spaces.10−14 Yet, how DNA molecules behave when they are stretched inside confinement remains poorly understood. The extension of polymers by external forces with both uniform and nonuniform tensions is well understood.15 For stretching in narrow channels, where the channel height (h) is comparable to or smaller than the radius of gyration (Rg) or persistence length (lp) of the polymers, force-induced deformation has been developed by blob theory for moderate confinements (h ∼ Rg),16−18 as well as for strong confinements (h ∼ lp).18−22 Compared to the progress on the theoretical front, experimental investigations of force-induced chain extension in strong confinement have remained behind. In the literature, analysis of force−extension measurements under confinement is limited to partial extensions.23,24 In this work, we studied the force−extension of individual DNA molecules in nanoslits. Our results present a quantitative picture that describes DNA extension resulting from the competition between strong confinement and the applied stretching force. The proposed model reveals how the stiffness, or the global persistence length of a DNA molecule in confinement, changes with the height of the nanoslits. In particular, we observed a reptation-like motion of stretched © XXXX American Chemical Society
Received: August 22, 2016 Accepted: September 15, 2016
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DOI: 10.1021/acsmacrolett.6b00639 ACS Macro Lett. 2016, 5, 1114−1118
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ACS Macro Letters
agreement with f rec ∼ h−4/3, a scaling theory prediction of a polymer in the extended de Gennes regime.26 An important result from the present work also concerns the third regime, in which the DNA extension is governed by the competition between the electrophoretic force and the elastic force of the DNA. For example, shown in Figure 3a is the DNA length l as a function of En (open squares). We find that l increases rapidly with increasing En at small applied electrophoretic forces (En ≲ 3 V/cm). At stronger fields (En ≳ 3 V/ cm), l plateaus. This trend is reminiscent of the DNA extension as a function of the flow speed found in previous work.13 A tethered DNA molecule stretching in unconfined fluid can be considered as a “stem and flower”.27 In this case, the stretched polymer is characterized by a stretching force gradient, where the tension is minimal at the free end and increases linearly toward the tethered end.5 The overall electrophoretic force applied on the entire molecule can be obtained by integrating the tension along the chain
Figure 1. (a) Schematic representation of a tethered biopolymer stretching in a nanofluidic channel along the direction of stretching. A micro/nanofluidic interface is used to anchor a biopolymer-attached bead, which is stretched by a constant electric field. (b) Images of a fluorescently labeled λ-DNA tethered in nanoslits (top view). The dashed line is the interface between the nanoslits and the microchannel.
fe =
∫0
L
fe (s)ds /L = λE
∫0
L
(L − S)ds /L = λEL /2 (1)
where fe(s) represents the stretching force at position s; L is the molecule contour length; and λ is the effective charge per unit length. Here, the relationship between En and the applied voltage V sensitively depends on the slit geometry and thus has to be determined carefully (see SI). Furthermore, the value of λ has been reported to span a wide range from 0.29 e−/nm28 to 1.47 e−/nm29 in various systems and buffer conditions. Since the experimental conditions of Keyser et al.29 are similar to ours, we set λ = 1.47 e−/nm for the current work. Following the Marko−Siggia force−extension result of the WLC model,15 the elastic force of the molecule fels can be determined as
the applied electrostatic force increases (Figure 2). When the applied field (En), hence the electrophoretic force (fe), is
fels =
⎤ ⎞ kBT ⎡ 1 ⎛ 1 ⎢ ⎜ − 1⎟ + X ⎥ 2 ⎥⎦ lp ⎢⎣ 4 ⎝ (1 − X ) ⎠
(2)
23
where lp = 66 nm is the DNA persistence length previously determined by magnetic tweezers with similar buffer conditions. The persistence length measured in our work is consistent with the value found in a recent atomic force microscopy study, in which lp ∼ 57 nm. This value is unaffected by the intercalation dye YOYO-1.30 However, the classical WLC model does not account for the confinement effect and thus applies only to unconfined systems. Recent WLC-based Monte Caro simulations31 have reported the approximated force−extensions in two-dimensional (2D) and three-dimensional (3D) cases, corresponding to the lower (2D) and upper (3D-unconfined) bounds of the force−extension relations observed in our experiments. These force−extension relations can be expressed in terms of the dimensionless electric field ε ≡ λE(lp)2/kBT
Figure 2. Extension l versus the applied field across a nanoslit (h = 55 nm). Each data point is averaged over 14 frames. (i) In the weak field regime (En → 0), the entropic force is dominant. (ii) When En = E*, the external force overcomes the entropic force, and the DNA stays in the nanoslits. (iii) In the high field regime, DNA extends gradually with the applied field. Inset shows the threshold fields E* versus the height of the slit h (red, green, orange, and blue circles for h = 130, 90, 60, and 40 nm, respectively). The dashed line represents E* ∼ h−4/3.
smaller than the DNA recoil force (f rec), fe ≤ f rec, the molecule stays outside the nanoslits for entropic reasons. When these two forces become comparable fe ≈ f rec, the DNA molecule is pulled into the slit but remains relaxed. As fe further increases to fe ≫ f rec, the DNA is stretched by the applied field and exhibits elastic resistance ( fels) in response to its extension. The crossover between these three regimes is characterized by the DNA extension as a function of En as shown in Figure 2. In the second regime, we plot the relation between the average threshold field E* and the slit height h in the Figure 2 inset. From these results, it is apparent that as h is decreased both the threshold field25 and the entropic forces23 increase, in good
⎧ 2l p ⎡ ⎤ 1 ⎪ ⎢ 1 X − + ⎥ , (a) 3D‐WLC ⎦ ⎪ L ⎣ (1 − X )2 ε=⎨ ⎪ 2l p ⎡ 1 1 3 ⎤ − + X ⎥ , (b) 2D‐WLC ⎪ ⎢ 2 4 2 ⎦ ⎩ L ⎣ 4(1 − X )
(3)
We expect the confinement effect on elasticity in the high field regime to be negligible since the polymer has less interactions with the slit walls [as shown in Figure 2(iii)], thus 1115
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Figure 3. (a) Typical field-length curve (□) for h = 130 nm nanoslits was fitted with eq 2 (green dashed dotted line), eq 3(a) (purple dotted line), eq 3(b) (blue dotted line), eq 4 (solid red line), and EV-WLC21 (orange dashed line). The values of L are 22.3 ± 0.03, 24.9 ± 0.15, 22.3 ± 0.03, 21.9 ± 0.18, and 21.24 ± 0.12 (s.e.m.) μm for eqs 2, 3a, 3b, 4, and EV-WLC, respectively. The L value we used for rescaling extension length is from eq 4. (b) Shown here are the rescaled field-extension trajectories x = l/L (gray traces) of 32, 16, 25, and 20 molecules and their average extension ⟨x⟩ for slit h = 130 (blue circles), 90 (orange circles), 60 (green circles), and 40 (red circles) nm nanoslits, respectively (error bars: standard deviation).
its extension behavior follows the 3D case in eq 3(a). Conversely, if the field or slit height h is small, confinement will constrain the motion of the polymer in one lateral dimension. In this limit, the polymer behavior is more accurately described by the 2D case in eq 3(b). Based on these insights, we describe the crossover from the 3D system to the 2D case by modifying the 3D-WLC model eq 3(a). To do so, we include the entropic force and confinement effects in the force−extension relation in terms of the dimensionless electric field ε as ε≅
⎤ 2(lp)2 ⎡ 1 1 ⎢ − + X − X 0 ⎥ + Cr(h) 2 2 Llc ⎣ (1 − X ) (1 − X 0) ⎦ (4)
where x0 = l0/L is the equilibrium relative extension; lc(h) is the DNA segmental correlation length (or global persistence length) in the elongation direction; and Cr(h) ≡ 2l2pf rec(h)/ kBTL describes the entropic force contribution [the f rec and Cr term in eq 4 are only present when fe is less than or close to the recoil force, as shown in Figure 2]. Here, the intrinsic elasticity of DNA is altered by the nanoconfinement, where the rigidity of the chain depends on the confining geometry.20,22,32−34 The equilibrium extension length l0 is finite due to confinement effects even when fels = 0.11,17,18,21,35 In the large extension limit, our modified model recovers the equation for the 3D bulk case [eq 3(a)]. To investigate how well the modified-WLC model can describe the confined DNA extension behavior, we compared five different models in Figure 3a. We find that the modified3DWLC yields a great fit indicating a significant confinement effect is present at h = 130 nm. We then repeated our extension measurements for three smaller slit heights (90, 60, and 40 nm) and obtained X(ε) = l(ε)/L [Figure 3(b)]. These results are presented in Figure 4(a). To be noted, the EV-WLC21 also provides an excellent fit to the data, especially at the smaller force regime. An initial difference of two models is the uniform and nonuniform stretching mechanisms. Our case is the nonuniform stretching of wormlike chains in slits, where forces gradually increase from the free end to the tethered end. Direct comparisons show that the confinement effectively enhances the DNA elongation at a constant applied external field. Moreover, the slope of x(ε) in the high field (large ε) regime becomes smaller when the slit is shallower. The reduced slope suggests a higher rigidity induced by confinement.
Figure 4. (a) Averaged extension as a function of dimensionless electric field ε in nanoslits for h = 40 (red circle), 60 (green circle), 90 (orange circle), and 130 (blue circle) nm nanoslits (error bars: standard error). Dotted and dashed-dotted lines correspond to the 2DWLC and 3D-WLC models with an external field in eq 3. The dash lines correspond to the modified-3DWLC models in eq 4. The solid pink lines show the confined Pincus regime21 and the Pincus regime,36 respectively. (b) The global persistence length lc versus slit height h. Dotted line studied by Brownian dynamics simulation20 and the brown dashed line from the results in ref 22.
Overall, our experimental data are in good agreement with the modified-3D-WLC model fittings [eq 4] as shown by the dashed lines in Figure 4(a). All measured extension relations reside in a regime between the 3D-WLC and 2D-WLC approximations. At higher forces, our results are qualitatively consistent with the Bandpass model24 and de Haan and Schendruck’s result,22 in which the DNA fluctuations are allowed in one or two lateral dimensions in nanoslits. At weaker forces and shallower slits, our results show that excluded volume becomes important and leads to a “confined Pincus” regime, which predicts x ∼ f1/3;21 to our knowledge, this is the first experimental confirmation of that prediction (Figure 4(a)). The observed nonlinear asymptotic extensions are well fitted by the modified-3D-WLC model [eq 4]. The fitted lines intersect at nonzero values corresponding to the extensions due to entropic force at ε = 0. We found that lc increases with decreasing h, and the observed trend is consistent with the empirical scaling proposed by previous simulations (dashed lines) (Figure 4b).20,22 Furthermore, when h is comparable to 1116
DOI: 10.1021/acsmacrolett.6b00639 ACS Macro Lett. 2016, 5, 1114−1118
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ACS Macro Letters chain persistence length lp, change in lc leads to a substantial modification to the DNA conformation, consistent with theoretical predictions.19,20,22,32,33 To characterize how surface interactions affect the stretching mechanism of biopolymers, we further reduced the slit height down to h = 30 nm. In this case, the highly confined DNA exhibited a reptation-like trajectory, drastically different from the contour shapes of the less confined (h ≥ 40 nm) DNA molecules (see Section IV of SI, Figure S2, and movie S2 for further discussion). The reptation-like motion has also been observed when the DNA is purely retracted by entropic forces in similar highly confined environments,37 which might be caused by the surface passivation agent polyvinylpyrrolidone (PVP). In summary, we investigated mechanical and conformational properties of tethered DNA force−extension in strong confinements. Our experimental data allowed direct tests of previous theoretical predictions. We found the DNA force− extension behavior at the higher force regime is consistent with the 3D-WLC and 2D-WLC models for both high and low extension limits, respectively.31 At the lower force regime, our data confirm the existence of a “confined Pincus regime” in strong slit confinement.21 Based on this observation, we developed a modified 3D-WLC model, which described the force−extension behavior. Also important, our experiments provide the first experimental evidence that confinement effectively modifies the global persistence length of the confined DNA molecules.19 This ultimately leads to a different force−extension relation, in agreement with the predictions by previous simulations.20,22,33 Our experiments also revealed a reputation-like trajectory of electrophoretically stretched DNA under ultrastrong confinements (h = 30 nm), which might arise from the surface passivation polymer effect or surface charge inhomogeneity. We expect our study of force−extensions in confined spaces will stimulate further theoretical and experimental investigations, as well as single-molecule analysis38 and biotechnological applications.
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Nanofabrication Facility (CNF) of NNIN supported by NSF (ECCS-0335765).
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(1) Smith, D. E.; Tans, S. J.; Smith, S. B.; Grimes, S.; Anderson, D. L.; Bustamante, C. Nature 2001, 413 (6857), 748−752. (2) Chen, I.; Christie, P. J.; Dubnau, D. Science 2005, 310 (5753), 1456−1460. (3) Venkatesan, B. M.; Bashir, R. Nat. Nanotechnol. 2011, 6 (10), 615−624. (4) Aguilar, C. A.; Craighead, H. G. Nat. Nanotechnol. 2013, 8 (10), 709−718. (5) Perkins, T. T.; Smith, D. E.; Larson, R. G.; Chu, S. Science 1995, 268 (5207), 83−87. (6) Smith, S. B.; Finzi, L.; Bustamante, C. Science 1992, 258 (5085), 1122−1126. (7) Smith, D. E.; Babcock, H. P.; Chu, S. Science 1999, 283 (5408), 1724−1727. (8) Perkins, T. T.; Smith, D. E.; Chu, S. Science 1994, 264 (5160), 819−822. (9) Kim, K.; Saleh, O. A. Nucleic Acids Res. 2009, 37, 136. (10) Tegenfeldt, J. O.; Prinz, C.; Cao, H.; Chou, S.; Reisner, W. W.; Riehn, R.; Wang, Y. M.; Cox, E. C.; Sturm, J. C.; Silberzan, P.; Austin, R. H. Proc. Natl. Acad. Sci. U. S. A. 2004, 101 (30), 10979−10983. (11) Reisner, W.; Morton, K. J.; Riehn, R.; Wang, Y. M.; Yu, Z. N.; Rosen, M.; Sturm, J. C.; Chou, S. Y.; Frey, E.; Austin, R. H. Phys. Rev. Lett. 2005, 94 (19), 196101. (12) Turner, S. W. P.; Cabodi, M.; Craighead, H. G. Phys. Rev. Lett. 2002, 88 (12), 128103. (13) Bakajin, O. B.; Duke, T. A. J.; Chou, C. F.; Chan, S. S.; Austin, R. H.; Cox, E. C. Phys. Rev. Lett. 1998, 80 (12), 2737−2740. (14) Lin, P. K.; Fu, C. C.; Chen, Y. L.; Chen, Y. R.; Wei, P. K.; Kuan, C. H.; Fann, W. S. Phys. Rev. E 2007, 76 (1), 011806. (15) Marko, J. F.; Siggia, E. D. Macromolecules 1995, 28 (26), 8759− 8770. (16) Tang, J.; Levy, S. L.; Trahan, D. W.; Jones, J. J.; Craighead, H. G.; Doyle, P. S. Macromolecules 2010, 43 (17), 7368−7377. (17) Jun, S.; Thirumalai, D.; Ha, B. Y. Phys. Rev. Lett. 2008, 101, 13. (18) Taloni, A.; Yeh, J. W.; Chou, C. F. Macromolecules 2013, 46 (19), 7989−8002. (19) Odijk, T. Phys. Rev. E 2008, 77 (6), 060901. (20) Chen, Y. L.; Lin, P. K.; Chou, C. F. Macromolecules 2010, 43 (24), 10204−10207. (21) Li, X. L.; Dorfman, K. D. J. Chem. Phys. 2016, 144 (10), 104902. (22) de Haan, H. W.; Shendruk, T. N. ACS Macro Lett. 2015, 4 (6), 632−635. (23) Yeh, J.-W.; Taloni, A.; Chen, Y.-L.; Chou, C.-F. Nano Lett. 2012, 12 (3), 1597−1602. (24) Lin, J.; Persson, F.; Fritzsche, J.; Tegenfeldt, J. O.; Saleh, O. A. Biophys. J. 2012, 102 (1), 96−100. (25) Daoudi, S.; Brochard, F. Macromolecules 1978, 11 (4), 751−758. (26) Dai, L.; Maarel, J. v. d.; Doyle, P. S. Macromolecules 2014, 47 (7), 2445−2450. (27) Brochardwyart, F. Europhys. Lett. 1995, 30 (7), 387−392. (28) Smith, S. B. Biopolymers 1990, 29, 1167−1173. (29) Keyser, U. F.; Koeleman, B. N.; Van Dorp, S.; Krapf, D.; Smeets, R. M. M.; Lemay, S. G.; Dekker, N. H.; Dekker, C. Nat. Phys. 2006, 2 (7), 473−477. (30) Kundukad, B.; Yan, J.; Doyle, P. S. Soft Matter 2014, 10 (48), 9721−9728. (31) Manca, F.; Giordano, S.; Palla, P. L.; Cleri, F.; Colombo, L. J. Chem. Phys. 2012, 137 (24), 244907. (32) Cifra, P.; Benkova, Z.; Bleha, T. Phys. Chem. Chem. Phys. 2010, 12 (31), 8934−8943. (33) Cifra, P.; Benkova, Z.; Bleha, T. J. Phys. Chem. B 2008, 112 (5), 1367−1375. (34) Tree, D. R.; Reinhart, W. F.; Dorfman, K. D. Macromolecules 2014, 47 (11), 3672−3684.
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.6b00639. Experimental details and methods (PDF) Movies demonstrating the single fluorescence DNA stretching (AVI) Movies demonstrating the single fluorescence DNA stretching (AVI)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was accomplished under the guidance of Prof. Harold G. Craighead. The authors thank Dr. Neil Y.C. Lin and Profs. Suckjoon Jun and Yeng-Long Chen for helpful discussions and insightful suggestions. This research was supported by National Institutes of Health Grant (R01 DA030329-03). The work was performed in part at Cornell 1117
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ACS Macro Letters (35) Saleh, O. A.; McIntosh, D. B.; Pincus, P.; Ribeck, N. Phys. Rev. Lett. 2009, DOI: 10.1103/PhysRevLett.102.068301. (36) Pincus, P. Macromolecules 1976, 9 (3), 386−388. (37) Yeh, J.-W.; Taloni, A.; Sriram, K. K.; Chen, Y.-L.; Chou, C.-F. Quantitative analysis of reptation of partially extended DNA in sub-30 nm nanoslits. unpublished (arXiv:1502.05115). (38) Sriram, K. K.; Yeh, J. W.; Lin, Y. L.; Chang, Y. R.; Chou, C. F. Nucleic Acids Res. 2014, 42 (10), e85.
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