Migration Behavior of Rodlike dsDNA under Electric Field in

Oct 24, 2013 - Tetra-PEG gel, which has a homogeneous network structure, was utilized as a model system, allowing us to systematically tune the polyme...
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Migration Behavior of Rodlike dsDNA under Electric Field in Homogeneous Polymer Networks Xiang Li, Kateryna Khairulina, Ung-il Chung, and Takamasa Sakai* Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan S Supporting Information *

ABSTRACT: We investigated the migration behavior of rodlike dsDNA in polymer gels and polymer solutions. Tetra-PEG gel, which has a homogeneous network structure, was utilized as a model system, allowing us to systematically tune the polymer volume fraction and molecular weight of network strand. Although we examined the applicability of the existing models, all the models failed to predict the migration behavior. Thus, we proposed a new model based on the Ogston model, which well explained the experimental data of polymer solutions and gels. The polymer volume fraction determined the maximum mobility, while the network strand governed the size sieving effect. From these results, we conclude that the polymer network with lower polymer volume fraction and smaller network strand is better in terms of size separation. The homogeneous polymer network is vital for understanding of particles’ dynamics in polymer network and a promising material for high-performance size separation.

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INTRODUCTION The dynamics of particles in viscoelastic media is governed by migration and diffusion. The former specifies the response to the external force and the latter to the spontaneous thermal fluctuations.1 The migration behavior of particles in liquid (free solution) is fully understood; the effects of temperature, pressure, particle size, and liquid viscosity are modeled and experimentally validated.2 One of the popular applications of this phenomenon is free solution electrophoresis, which enables separation of particles (e.g., ions and proteins), based on the balance of particle’s charge and the friction between particles and the solution. However, when particles have the same charge− friction balance, we cannot separate them. For instance, uniformly charged polyelectrolytes (e.g., DNA) migrate under electric field at the same mobility regardless of their sizes. For the separation of particles based on their size, polymer gels and solutions are conventionally used as separation media (gel electrophoresis). They act as stable (polymer gels) or transient (polymer solutions) networks and interact with polyelectrolytes in a complex manner, separating polyelectrolytes based on their size. This complex interaction, on the other hand, makes it challenging to fully understand the dynamics of polyelectrolytes in the presence of polymer network.3 Thus, understanding of the dynamics of polyelectrolytes in polymer network is one of the most important goals in polymer science and will help develop a highperformance separation media. These academic and industrial interests led to a number of researches on gel electrophoresis. Ogston first proposed theoretical prediction on this phenomenon.4 The Ogston model treats the network as an © 2013 American Chemical Society

assembly of randomly distributed pores formed with long stiff fibers. When a particle finds a pore larger than itself, it is able to pass through the pore. Chrambach et al. extended this model and predicted the migration of a variety of particles in obstacles with a variety of geometries.5 The reduced mobility is calculated as μe μe0

= exp( −K rϕ),

K r ∼ (R g + r ) g

(1)

where μe is the electrophoretic mobility in polymer network, μe0 is the free solution electrophoretic mobility, Kr is retardation coefficient, Rg is the gyration radius of particle, ϕ is polymer volume fraction, r is the smaller dimension of the obstacles, and g is a factor depending on the geometry of particles and obstacles. The validity of the Ogston model was experimentally confirmed in the system where the macroscopic pores exist and the polyelectrolytes are smaller than the average pore size: 2−10 kb double-stranded DNA (dsDNA) in 0.2−0.5% w/v agarose gel6 and 118−310 bp small dsDNA fragments in hydroxyethyl cellulose (HEC) solution with ϕ near or lower than the overlapping polymer volume fraction (ϕ*).7 However, the Ogston model seems invalid for dsDNA migration in flexible polymer network such as polyacrylamide gel or semidilute polymer solution,7,8 where polymer chains have excluded volume and fill the space.9 Received: September 4, 2013 Revised: October 10, 2013 Published: October 24, 2013 8657

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For the relatively large polyelectrolytes, a relationship μe ∼ n−1 was observed in agarose gel (>0.5% w/v),10 polyacrylamide gel,11 and concentrated polymer solution,12 where n is the base number of dsDNA. In order to explain this phenomenon, two research groups13,14 independently proposed two ideas inspired from “the reptation in tube” concept introduced by de Gennes.9 Viovy et al. finally integrated these ideas and proposed the biased reptation with fluctuations model (BRF model).15−17 In this model, they assume that there is a tubelike path formed by a random sequence of pores inside the polymer network and polyelectrolytes migrates inside the tube. Other than the models proposed above, Smisek and Hoagland found the relationship μe ∼ n−γ with 1 < γ < 3,18 which is out of prediction of both the Ogston and BRF models. They claim that this phenomenon is attributed to the internal entropy of polyelectrolytes, and the “entropic trapping” dominates the migration when the gyration radius of the polyelectrolyte and the size of pores are comparable. Slater et al. have done further study, but the detailed mechanism of entropic trapping is not fully understood.19,20 These three models assume the porelike structure in polymer networks. The porelike structure might be adaptable for fibrous physical gels. Indeed, the AFM measurement on agarose gel showed submicrometer-sized pore structure.21 A series of pores can compose a tubelike structure. As we described above, the experimental data of gel electrophoresis suggest the validity of Ogston and BRF models in fibrous physical gels. In contrast, in flexible polymer solution or chemical gels, porelike structure has never been observed. In such flexible polymer networks, two different correlation lengths are experimentally observed (Figure 1). One is the concentration blob characterized by the

However, it is difficult to control ϕ and Ns independently and precisely in a conventional polymer network system. In physical gels and polymer solutions, ϕ is the only available parameter. On the other hand, in chemical gels, though both ϕ and Ns could be tuned, there was no discussion on the relationship between Ns and μe.24,25 One of the reasons inhibiting the theoretical investigation of the effect of Ns is its uncontrollability, which is caused by the heterogeneous nature of conventional polymer gels.26 Because of the heterogeneity, conventional polymer gels have ununiformly distributed Ns. Furthermore, the degree of heterogeneity is enhanced with an increase in the cross-linking concentration.27 Therefore, it is practically impossible to investigate the pure effect of ϕ and Ns on μe. Recently, we have succeeded in fabricating a homogeneous gel system (Tetra-PEG gels) by the A−B type cross-link coupling of two mutually reactive tetra-arm poly(ethylene glycol) units (Tetra-PEG prepolymers).28 Although some extent of heterogeneity was observed in our small-angle neutron scattering and NMR measurements,22,29 the degree of heterogeneity was extremely lower than that in conventional polymer gels. In addition, we can precisely control ϕ and Ns by tuning polymer volume fraction and the molecular weight of prepolymers, respectively. A series of precisely controlled polymer networks will be helpful in understanding the migration mechanism of polyelectrolyte in polymer gels. In this paper, we conducted electrophoresis in Tetra-PEG gel with a series of precisely tuned ϕ and Ns for dsDNA in the range 10−160 bp. These dsDNA are smaller than the persistence length of dsDNA (approximately 50 nm), so that they can be simply regarded as stiff rods. We investigated the effect of ϕ and Ns on μe and proposed a new migration mechanism of rodlike dsDNA in polymer network.

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EXPERIMENTAL SECTION

Synthesis of Prepolymers. Tetra-amine-terminated poly(ethylene glycol) (Tetra-PEG-NH2) and tetra-OSu-terminated poly(ethylene glycol) (Tetra-PEG-OSu) were prepared from tetrahydroxyl-terminated poly(ethylene glycol) with equal arm lengths. Here, OSu stands for N-hydroxysuccinimide. The detailed preparation methods were reported elsewhere.28,30−33 The molecular weights of Tetra-PEG-NH2 and Tetra-PEG-OSu were matched to each other (Mn = 10, 20, and 40 kg/mol), so that Ns were 113, 227, and 454. Fabrication of Tetra-PEG Gels and Poly(ethylene glycol) (PEG) Solution. The stoichiometric ratios of Tetra-PEG-NH2 and Tetra-PEG-OSu (ϕ: 0.034−0.081) were dissolved in Bis-Tris/ACES buffer (25 mM Bis-Tris, 25 mM ACES, 1 mM 2Na-EDTA, 11.3 mM NaOH, pH7.0). Two Tetra-PEG prepolymer solutions were mixed with conditioning mixer (AR-100, Thinky, Japan). The capillary internal wall was conditioned with 1 M NaOH for 5 min and with distilled deionized water for 5 min. The mixture of two prepolymers solution was sucked into the conditioned capillary with the aspirator. Both ends of capillary were clogged with clay and placed at room temperature for 1 day to finish the gelation reaction. Poly(ethylene glycol) (PEG) with molecular weight 200 kDa (Sigma-Aldrich) (ϕ: 0.034−0.081) was dissolved into Bis-Tris/ACES buffer and filled into capillary using the same method as Tetra-PEG gels. All buffers and polymer solutions were filtered through 0.45 μm filter (Millex-HA, Merck Millipore) and degassed under 0.02 MPa with sonication for 2 min before use. Sample. dsDNA markers in the range 20−1000 bp by 20 bp difference (20 bp Molecular Ruler, Bio-Rad) were dissolved in Bis-Tris/ ACES buffer at the final concentration of 66.6 μg/mL. Capillary Electrophoresis. We made a custom-made capillary electrophoresis system. The system contained a fluorescent microscope (IX71, Olympus, Japan), a photoamplitude tube (H5784, Hamamatsu Photonics, Japan), a high voltage power supply (PS375, Stanford Research Systems), and data acquisition and instruments control software

Figure 1. Schematic representation of (A) fibrous polymer network and (B) flexible polymer network. Fibrous polymer network consists of macroscopic pores, whereas flexible polymer network consists of concentration blobs and elastic blobs.

size of ξc. Concentration blob has been known in polymer solutions, but we experimentally confirmed its presence in the polymer gels. In polymer gels, ξc is independent of polymerization of network strand (Ns) and depends only on the ϕ as ξc ∼ ϕ0.78 in the semidilute regime,22 well corresponding to the theory of scaling of blob size in semidilute solution (ξc ∼ ϕ3/4).9 The other is the elastic blob observed by mechanical testing in polymer gels. The elastic modulus of swollen and deswollen polymer gels indicated that the elastic blob size (ξel) corresponds to the length of a network strand with polymerization degree of Ns, which obeys the scaling prediction for gyration radius of polymer chain in semidilute solution, ξel ∼ Nsν(ϕ/ϕ*)−1/8,23 where ν is the excluded volume exponent. Thus, in order to understand the migration behavior in flexible polymer network, we should investigate μe of various polymer networks with controlled ϕ and Ns. 8658

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Figure 2. The n dependence of μe in Tetra-PEG gel and PEG solution with ϕ (ϕ: 0.034, open circle; 0.050, square; 0.066, triangle; 0.081, rhombus). The error bars are hidden when the error bar is smaller than the symbol size. (LabView 2011, National Instruments). Fused silica capillaries (Polymicro Technologies) with 75 μm internal diameter, 375 μm outside diameter, and 5 cm length were used. The distance from the end of capillary to the detector was 2.5 cm. Capillaries with Tetra-PEG gel or PEG solution were equilibrated with Bis-Tris/ACES buffer containing 1 μg/mL ethidium bromide (Sigma-Aldrich) at 100 V/cm for 30 min. The sample was injected electrokinetically at 100 V/cm for 2 s and separated at 25−100 V/cm. Temperature was controlled at 25.0 ± 0.5 °C with a custom-made thermoelectric Peltier air conditioner box (Hayashi Watch-Works CO., Ltd., Japan).

deswelling hardly occurs in the capillary tube with extremely high aspect ratio. μe was an exponential function of ϕ for each Ns and n, which well corresponds to the Ogston model prediction. The deviation from the fitting curve at low ϕ region is probably due to the imperfection of the network reported previously,22,29 which decreases interaction with dsDNA and increases the μe. According to the Ogston model, the extrapolation and slope in Figure 3 correspond to μe0 and Kr, respectively. The values of μe0 for each Ns are plotted against n in Figure 4. μe0 decreased with an increase in n and has no obvious trend with Ns. This relatively large fluctuation in the value of μe0 is caused by the estimation method of μe0: the extrapolation of an exponential fitting, which has large fitting error in nature. Thus, in the following analyses, we used the average value of μe0 at each n, which is obtained by averaging the value of μe0 for different Ns. The decrease in μe0 with an increase in n has been confirmed on other polymer network systems as well.8,34 However, this tendency is different from the theoretical prediction or those of the direct measurement. Theoretically, μe0 is predicted as μe0 = Q/f ∼ n/n, where Q is the total charge of the polyelectrolyte and f is the friction drag exerted by the system. As both Q and f are proportional to n, μe0 is independent of n.16 On the other hand, the direct measurement in free solution shows μe0 was a increasing function of n in the range 20−160 bp.35 The reason for this discrepancy is not clear at this stage. Examination of the Ogston Model and Proposal of a New Semiempirical Model. We refitted Figure 3 using eq 1 with the average value of μe0 at each n and confirmed that the fit worked well (SFigure 2), suggesting the validity of our treatment. The values of Kr estimated from the fit are displayed against n in Figure 5. The values of Kr increased with an increase in n, and the increasing rate decreased with an increase in Ns. In order to examine the validity of the Ogston model, we investigated the relationship Kr1/g ∼ Rg + r, with g = 1, 2, 3, which is derived from eq 1.

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RESULTS AND DISCUSSION Migration Behavior of dsDNA. We conducted capillary gel electrophoresis for dsDNA fragments with n from 20 to 160 bp in Tetra-PEG gels and PEG solution by tuning ϕ and Ns (Figure 2). μe was calculated from the migration velocity (v) as μe = v /E (2) where E is the electric field strength. Under the moderate E, μe is independent of E; however, under the strong E, E affects μe due to the Joule heating or DNA orientation along the electric field. In order to eliminate these undesirable effects, we tuned E in the range 25−100 V/cm for each experimental condition and confirmed the independence of μe on E around the experimental condition (SFigure 1). The n dependence of μe is displayed in Figure 2. The larger DNA had lower μe. The increase in ϕ or the decrease in Ns lowered μe as well. These results indicate that the large DNA or the dense network lead to strong interaction and result in decreased μe. Ferguson Plot: Estimation of Free Solution Mobility (μe0). Figure 3 shows the semilogarithm plots of μe against ϕ (Ferguson plot)16 for various Ns and n. We assumed that the polymer volume fraction of polymer gel did not change from that of prepolymer solution because subsequent swelling or 8659

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Figure 3. The ϕ dependence of μe in Tetra-PEG gel and PEG solution with dsDNA size n (n: 20 bp, circle; 40 bp, square; 60 bp, triangle; 80 bp, rhombus; 100 bp, full circle; 120 bp, full square; 140 bp, full triangle; 160 bp, full rhombus). The error bars are hidden when the error bar is smaller than the symbol size.

Figure 4. The n dependence of μe0 in Tetra-PEG gel and PEG solution with Ns (Ns: 113, open circle; 227, square; 454, triangle; PEG solution, rhombus; the average value of μe0 at each n for different Ns, full circle).

Figure 5. The n dependence of Kr in Tetra-PEG gel and PEG solution with Ns (Ns: 113, open circle; 227, square; 454, triangle; PEG solution, rhombus). The dotted line is the fitting curve showing the relation Kr = α(Ns)nβ(Ns).

When the macromolecule is smaller than its persistence length, Rg is given by Kratky−Porod formula36 as Rg ∼ n, leading to the relationship Kr1/g ∼ n + r. We plotted Kr1/g against n but could not find any linear relationship between them for g = 1, 2, 3 (SFigure 3), suggesting the failure of the Ogston model in this experimental range. The migration behavior observed in this study has the same ϕ dependence but a different n dependence with the Ogston model. Although the linear relationship in Ferguson plots is sometimes regarded as the proof for the Ogstonmodel-based migration behavior,37,38 the present study clearly demonstrates that the linear Ferguson plot is not sufficient to validate the Ogston model. In contrast to the Ogston prediction, Kr was a simple power law function of n; Kr = 6.4n0.34 (Ns = 113); Kr = 8.1n0.22 (Ns = 227); Kr = 10.5n0.11 (Ns = 454); Kr = 12.7n0 (PEG solution)

(Figure 5). Thus, μe/μe0 is semiempirically represented as follows: μe /μe0 = exp( −K rϕ)

(3)

K r = α(Ns)n β(Ns)

(4)

where α(Ns) and β(Ns) are variables depending only on Ns. The similar power law relationship (Kr ∼ n1/3) was previously observed in polyacrylamide gel for dsDNA in the range 47− 350 bp.39 The Ns dependence of α(Ns) and β(Ns) is shown in Figure 6. The data of the PEG solution are shown as dotted lines. With an increase in Ns, α(Ns) increased and β(Ns) decreased. Both α(Ns) and β(Ns) asymptotically reached the constants that 8660

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Figure 6. The Ns dependence of α(Ns) and β(Ns). The dotted line is the value of PEG solution.

correspond to those of PEG solution (α = 12.7 and β = 0). These data strongly suggest that the PEG solution can be practically treated as a polymer network with infinite Ns, and the migration behavior is not critically influenced by the gelation threshold. The continuous change in diffusion coefficient of particles was previously observed in semidilute polystyrene solution and gel.40 Polymer Volume Fraction Determines the Maximum Electrophoretic Mobility. Let us focus on μe/μe0 of the PEG solution, which corresponds to the polymer gel with infinite Ns. The zero value of β in the PEG solution indicates that μe/μe0 is defined only by ϕ, and represented as μe /μe0 = exp( −12.7ϕ)

(5)

Figure 7 shows μe/μe0 of the PEG solutions. Practically, the values of μe/μe0 did not depend on n and well predicted by eq 5. These data strongly suggests that μe/μe0 of polymer gels is defined only by ϕ, regardless of Ns and n, when Ns is large enough. ϕ itself does not influence the size sieving. Because Kr increases with a decrease in Ns (Figure 5), the value expected by

Figure 7. The ϕ dependence of reduced electrophoretic mobility (μe/μe0) in PEG solution with dsDNA size n (n: 20 bp, open circle; 40 bp, square; 80 bp, triangle; 160 bp, rhombus). The dotted curve is the guide of the relation μe/μe0 = exp(−12.7ϕ).

Figure 8. The Ns dependence of μe/μe0 in Tetra-PEG gel and PEG solution with dsDNA size n (n: 20 bp, open circle; 40 bp, square; 80 bp, triangle; 160 bp, rhombus). The dotted line shows the average value of PEG solution. 8661

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eq 5 is the maximum μe/μe0 at the specific ϕ, which is not influenced by Ns and n. What is the molecular picture expected from these results? The ϕ-dependent and Ns-independent characteristic reminds us of a molecular picture of the concentration blob. Polymer solutions and polymer gels in semidilute solution are closely packed system of concentration blobs. Because ξc (0.5−3 nm)22 is smaller than Rg of dsDNA (7−54 nm), dsDNA may migrate in the packed concentration blobs, which cause a friction against dsDNA. Because the dsDNA may be treated as the free-draining rodlike structure, the friction against dsDNA from concentration blobs will be proportional to n. This n dependence will be canceled by the effect of electric force, which is also proportional to n, resulting in the loss of size-sieving effect. This expectation corresponds well to the experimental results that the n dependence was not practically observed in the PEG solution (β = 0). Elastic Blobs Interact with the Contour of Rodlike dsDNA. Finally, we show the effect of Ns and n on μe/μe0. The Ns dependence of μe/μe0 is displayed in Figure 8. With a decrease in Ns, μe/μe0 decreased from the value predicted by eq 5, and the decrease was remarkable in dsDNA with large n. These data indicate that the Ns and n determine the degree of retardation from the maximum (eq 5). Because the elastic blob is characterized by Ns, it is expected that the elastic blobs interact with the contour of dsDNA. The direct influence of Ns on the n dependence of Kr seen in eq 4 also supports the strong interaction between the elastic blob and the contour of dsDNA.

gray; 100 V/cm, white); SFigure 2: refitting of Figure 3 with the average value of μe0 at each n (all symbols are the same with Figure 3); SFigure 3: n dependence of Kr1/g in Tetra-PEG gel and PEG solution with Ns (Ns: 113, open circle; 227, square; 454, triangle; PEG solution, rhombus). This material is available free of charge via the Internet at http://pubs.acs.org.

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Corresponding Author

*E-mail: [email protected] (T.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

The authors appreciate the advice of Dr. K. Sumitomo and Dr. K. Mayumi. This work was supported by the Japan Society for the Promotion of Science (JSPS) through the Grants-in-Aid for Scientific Research, the Center for Medical System Innovation (CMSI), the Graduate Program for Leaders in Life Innovation (GPLLI), the International Core Research Center for NanoBio, Core-to-Core Program, A. Advanced Research Networks and the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST program); the Ministry of Education, Culture, Sports, Science, and Technology in Japan (MEXT) through the Center for NanoBio Integration (CNBI); and the Japan Science and Technology Agency (JST) through the S-innovation program, and Grant-in-Aids for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (no. 12J07977 to X.L., no. 23700555 to T.S., and no. 24240069 to U.C.).

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CONCLUSION We investigated the migration behavior of rodlike dsDNA under moderate electric field in Tetra-PEG gel and PEG solution. We observed the continuous change in reduced electrophoretic mobility from Tetra-PEG gel to PEG solution; the gelation threshold did not critically influence the migration behavior. The migration behavior of rodlike dsDNA did not obey any existing models but did obey a new model based on the Ogston model. Through the model analysis, we confirmed that ϕ and Ns independently influence the migration behavior in different manners. ϕ equally retarded the migration of rodlike dsDNA regardless of their size and determined the maximum migration rate; the “concentration blob” may interact with dsDNA in a freedrain manner. On the other hand, Ns determined the size dependence of dsDNA migration in polymer network and thus governed the size sieving effect of polymer network; the “elastic blob” may interact with the contour of rodlike dsDNA. Our data clearly showed that the existing model assuming porelike structure could not predict the migration of rodlike dsDNA in the flexible polymer network. These results also give us a clear strategy in designing high-performance separation media for small particles. The smaller ϕ results in shorter separation time, while the smaller Ns increases the sieving resolution. In order to achieve such small ϕ and small Ns, we need to make a dense polymer network with a small amount of material. This material design is identical to that of homogeneous polymer network. Thus, we conclude that homogeneous polymer networks are the promising candidates for high-performance separation media.

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AUTHOR INFORMATION

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ASSOCIATED CONTENT

S Supporting Information *

SFigure 1: n dependence of μe in Tetra-PEG gel and PEG solution with f ( f: 0.034, open circle; 0.050, square; 0.066, triangle; 0.081, rhombus) under E (E: 25 V/cm, black; 50 V/cm, 8662

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