Probing the Ionic Atmosphere of Single-Stranded DNA Using

Dec 2, 2008 - Department of Chemistry, Colorado State University, Fort Collins, Colorado ..... photon counting avalanche photodiode detectors (PerkinE...
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Anal. Chem. 2009, 81, 465–472

Probing the Ionic Atmosphere of Single-Stranded DNA Using Continuous Flow Capillary Electrophoresis and Fluorescence Correlation Spectroscopy Keir Fogarty, Jeffrey T. McPhee, Eric Scott, and Alan Van Orden* Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 Two-beam fluorescence cross-correlation spectroscopy coupled with continuous flow capillary electrophoresis (2bFCCS-CFCE) was used to study the relationship between diffusion and effective charge of a fluorescently labeled 40-base polythymine single-stranded DNA (ssDNA) as a function of Mg2+ concentration. Crosscorrelation analysis of the fluorescence monitored from two spatially offset microscopic detection volumes revealed the diffusion and electrophoretic migration of ssDNA at a range of Mg2+ concentrations and electric field strengths. The effective charge of the ssDNA could then be determined using simple calculations. It was found that as the Mg2+ concentration in the buffer solution increased, the diffusion of the ssDNA also increased, while the effective charge of the ssDNA decreased. This was believed to be caused by increased association of the Mg2+ counterions with the negatively charged backbone of the ssDNA, which partially neutralized the negatively charged functional groups and allowed the ssDNA to adopt a more compact structure. To our knowledge, this is the first demonstration of the measurement of effective charge of ssDNA in relation to Mg2+ concentration.

The interaction of positive counterions with single-stranded DNA and RNA molecules in solution partially neutralizes the negative charged groups of the phosphate backbone. This gives rise to an effective charge of the molecule equivalent to the chemical charge (given by the number of negative charged functional groups on the DNA backbone) minus the collective charge of associated positive counterions. Effective charge is a key parameter to characterize the interactions between DNA and counterions in solution and provides quantitative information about the average number of interacting counterions under a given set of conditions. Remarkably, the effective charge of biomolecules in aqueous solution has proven to be a difficult quantity to measure. Most techniques used for this purpose are based on capillary zone electrophoresis (CZE) and have mainly been applied to the study of double-stranded DNA (dsDNA) interacting with monovalent counterions.14,15 CZE measures the electrophoretic mobility, µe, of charged species in aqueous solution due to their migration with respect to an applied electric field. The interaction of the molecules with the electric field is governed by the effective charge, Zeff, of the ion and its associated counterions. This effective charge is related to the electrophoretic mobility by the equation µe )

The ionic atmosphere of nucleic acid biopolymers plays an important role in their function and structure.1-8 In particular, many monovalent and divalent cations, such as Na+ and Mg2+, interact strongly with the nucleotide bases and phosphate backbone of RNA and DNA.9-13 These interactions affect the behavior of DNA and RNA in base-pairing, replication, secondary and tertiary structure formation, and interactions with other nucleic acids and proteins. * To whom correspondence should be addressed. E-mail: vanorden@ lamar.colostate.edu. (1) Bloomfield, V. A.; Crothers, D. M.; Tinoco., I., Jr., Nucleic Acids: Structure, Properties and Functions; University Science Books: Sausalito, CA, 2000. (2) Anderson, C. F.; Record, M. T., Jr Annu. Rev. Phys. Chem. 1995, 46, 657– 700. (3) Bloomfield, V. A. Biopolymers 1997, 44, 269–282. (4) Misra, V. K.; Shiman, R.; Draper, D. E. Biopolymers 2003, 69, 118–136. (5) Subirana, J. A.; Soler-Lopez, M. Annu. Rev. Biophys. Biomol. Struct. 2003, 32, 27–45. (6) Woodson, S. A. Curr. Opin. Chem. Biol. 2005, 9, 104–109. (7) Draper, D. E.; Grilley, D.; Soto, A. M. Annu. Rev. Biophys. Biomol. Struct. 2005, 34, 221–243. (8) Chen, S. J. Annu. Rev. Biophys. 2008, 37, 197–214. 10.1021/ac8019416 CCC: $40.75  2009 American Chemical Society Published on Web 12/02/2008

DZeffe kBT

(1)

where kB is the Boltzmann constant, T is the temperature, e is the unit charge, and D is the translational diffusion constant. The electrophoretic mobility is related to the migration velocity,Vx, of a species by Vx ) (µe + µEOF)E

(2)

where E is the applied electric field and µEOF is the contribution of electroosmotic flow (EOF) to the mobility.16 In conventional (9) Munoz, J.; Sponer, J.; Hobza, P.; Orozco, M.; Luque, F. J. J. Phys. Chem. B 2001, 105, 6051–6060. (10) Petrov, A. S.; Pack, G. R.; Lamm, G. J. Phys. Chem. B 2004, 108, 6072– 6081. (11) Sundaresan, N.; Pillai, C. K. S.; Suresh, C. H. J. Phys. Chem. A 2006, 110, 8826–8831. (12) Zhang, Y.; Huang, K. X. J. Mol. Struct.: Theochem. 2007, 812, 51–62. (13) Tan, Z. J.; Chen, S. J. Biophys. J. 2008, 95, 738–752. (14) Stellwagen, E.; Dong, Q.; Stellwagen, N. C. Biochemistry 2007, 46, 2050– 2058. (15) Stellwagen, E.; Stellwagen, N. C. Biophys. J. 2003, 84, 1855–1866.

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CZE, the migration velocity of an analyte is determined from the retention time of the analyte band, and the contribution of EOF is often determined from the retention time of a neutral marker. As shown in eq 1, the electrophoretic mobility depends on both the translational diffusion constant, D, and the effective charge, Zeff. Hence, determination of Zeff from CZE measurements of the electrophoretic mobility requires that D also be known. It is difficult to determine both the electrophoretic mobility and the diffusion constant from CZE measurements alone. In CZE, translational diffusion is one of several factors that produce broadening, or variance, of the electropherogram peak widths. If D could be obtained from the peak variance, Zeff could then be determined from the electrophoretic mobility. However, several other variables also contribute to peak variance besides translational diffusion. These include sample plug injection, detection zone broadening, Joule heating, non-ideality of the flow profile, and interactions of the analyte plug with the capillary walls.16-21 It is often not possible to isolate the diffusion contribution to peak variance in the presence of these other variables, and thereby characterize the diffusion properties and effective charge of molecules based on CZE alone. Isolating the diffusion contribution from other sources of variance is only possible using specialized CZE techniques.16,22 For example, a technique that has been used previously to measure DNA effective charge is stopped-migration CZE.17,23-30 In stopped-migration CZE, the electric field driving the analyte molecules through the separation channel is switched off midway through the separation. During this zero-field interval, the analyte plug becomes broadened because of translational diffusion of the analyte molecules. Since translational diffusion is the only contribution to peak broadening during this interval, the diffusion properties of the molecules can be isolated from other sources of variance because of the excess broadening that occurs. The success of stopped-migration CZE depends on the reproducibility of the other experimental variance contributions, which has been shown to be difficult to achieve.31 In addition, the dwell time in stopped migration CZE experiments is often unreasonably long, particularly for larger molecules, which often require dwell times of 10 h or more.23,24,28 Although stopped migration CZE has been (16) Handbook of Capillary Electrophoresis, 2nd ed.;Landers, J. P., Ed.; CRC Press: Boca Raton, 1997; p 894. (17) Yao, Y. J.; Li, S. F. Y. J. Chromatogr. Sci. 1994, 32, 117–120. (18) Foret, F.; Deml, M.; Bocek, P. J. Chromatogr. 1988, 452, 601–613. (19) Ali, I.; Aboul-Enein, H. Y.; Gupta, V. K. Anal. Lett. 2006, 39, 2345–2357. (20) Huang, X.; Coleman, W. F.; Zare, R. N. J. Chromatogr. 1989, 480, 95–110. (21) Roberts, G. O.; Rhodes, P. H.; Synder, R. S. J. Chromatogr. 1989, 480, 35–67. (22) Musheev, M. U.; Javaherian, S.; Okhonin, V.; Krylov, S. N. Anal. Chem. 2008, 80, 6752–6757. (23) Walbroehl, Y.; Jorgenson, J. W. J. Microcolumn Sep. 1989, 1, 41–45. (24) Nkodo, A. E.; Garnier, J. M.; Tinland, B.; Ren, H.; Desruisseaux, C.; McCormick, L. C.; Drouin, G.; Slater, G. W. Electrophoresis 2001, 22, 2424– 2432. (25) Kenndler, E.; Schwer, C. Anal. Chem. 1991, 63, 2499–2502. (26) Maichel, B.; Gas, B.; Kenndler, E. Electrophoresis 2000, 21, 1505–1512. (27) Stellwagen, N. C.; Magnusdottir, S.; Gelfi, C.; Righetti, P. G. Biopolymers 2001, 58, 390–397. (28) Stellwagen, E.; Stellwagen, N. C. Electrophoresis 2002, 23, 2794–2803. (29) Stellwagen, N.; Gelfi, C.; Righetti, P. G. Electrophoresis 2002, 23, 167– 175. (30) Muijselaar, P. G.; van Straten, M. A.; Claessens, H. A.; Cramers, C. A. J. Chromatogr., A 1997, 766, 187–195. (31) Schaeper, J. P.; Sepaniak, M. J. Electrophoresis 2000, 21, 1421–1429.

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successful at measuring electrophoretic mobility, diffusion constants, and effective charges of biological macromolecules, an ideal technique would measure these parameters simultaneously, quickly, and independent from other sources of variance present in conventional CZE. An alternative to separations-based CZE involves monitoring the flow and diffusion properties of individual molecules as they migrate continuously through an electrophoresis capillary. Techniques based on this concept are referred to as continuous-flow capillary electrophoresis (CFCE). CFCE-based techniques are advantageous because they eliminate the need for sample plug injection and chemical separation and monitor analyte migration on shorter timescales than CZE. These features allow for simultaneous determination of the diffusion properties of the molecules and their migration velocities. Detection methods for CFCE include dynamic light scattering (DLS),32-34 sequential singlemolecule fluorescence detection,35 single-molecule fluorescence imaging,36-38 and fluorescence correlation spectroscopy (FCS).39-47 FCS is the most versatile detection technique for CFCE because it can be used for a wider variety of analytes and over a broader range of concentrations compared to the other techniques mentioned above. FCS also exhibits improved signal-to-noise ratio and greater temporal resolution.43,48 FCS detection in CFCE can be implemented using single focus fluorescence autocorrelation spectroscopy or with dual focus fluorescence cross-correlation spectroscopy (2bFCCS).39,41-43 In the latter technique, two femtoliter sized focal volumes are positioned a few micrometers apart in an electrophoresis capillary. Migration of fluorescent analyte molecules is monitored by measuring their transit times between the two foci, which typically occurs on the time scale of ∼100 µs to ∼10 ms. The migration velocity measured by 2bFCCSCFCE is directly related to the electrophoretic mobility, whereas the dispersion of the cross-correlation function is related to the translational diffusion. Hence, 2bFCCS-CFCE can be used to simultaneously monitor the electrophoretic mobility and translational diffusion of an analyte, as demonstrated explicitly by Ra¨dler and Bayer in a recent study of double-stranded DNA migrating through a sieving matrix. 45 In addition, 2bFCCS-CFCE can be used to resolve different analyte components in a multicomponent mixture into separate electropherogram peaks based on differences in molecular transit times.42,46,47 It can also be used to (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48)

Ware, B. R.; Flygare, W. H. Chem. Phys. Lett. 1971, 12, 81–85. Ware, B. R.; Flygare, W. H. J. Colloid Interface Sci. 1972, 39, 670–675. Semenov, S. N. Z. Fizicheskoi Khimii 1995, 69, 2070–2073. Castro, A.; Shera, E. B. Anal. Chem. 1995, 67, 3181–3186. Shortreed, M. R.; Li, H.; Huang, W.-H.; Yeung, E. S. Anal. Chem. 2000, 72, 2879–2885. Anazawa, T.; Matsunaga, H.; Yeung, E. S. Anal. Chem. 2002, 74, 5033– 5038. Lee, J.-y.; Li, H.-W.; Yeung, E. S., J. Chromatogr., A 2004, 1053, 173–179. Van Orden, A.; Keller, R. A. Anal. Chem. 1998, 70, 4463–4471. Brinkmeier, M.; Doerre, K.; Stephan, J.; Eigen, M. Anal. Chem. 1999, 71, 609–616. LeCaptain, D. J.; Michel, M. A.; Van Orden, A. Analyst 2001, 126, 1279– 1284. LeCaptain, D. J.; Van Orden, A. Anal. Chem. 2002, 74, 1171–1176. Fogarty, K.; Van Orden, A. Anal. Chem. 2003, 75, 6634–6641. Sonehara, T.; Kojima, K.; Irie, T. Anal. Chem. 2002, 74, 5121–5131. Bayer, J.; Raedler, J. O. Electrophoresis 2006, 27, 3952–3963. Schiro, P. G.; Kuyper, C. L.; Chiu, D. T. Electrophoresis 2007, 28, 2430– 2438. Brister, P. C.; Weston, K. D. Analyst 2006, 131, 303–310. Schimpf, M. E.; Semenov, S. N. Anal. Chem. 2003, 75, 5062–5070.

determine the direction of analyte migration, which allows simultaneous monitoring of both positive and negative ions migrating in opposite directions.43 This paper demonstrates the use of 2bFCCS-CFCE to elucidate the role of Mg2+ counterions in modulating the effective charge and diffusion properties of single-stranded DNA (ssDNA). To our knowledge, this is the first demonstration of the measurement of effective charge of ssDNA in relation to Mg2+ concentration. We examined the diffusion constants, migration velocities, and migration direction of 40-nucleotide polythymine (polyT40) labeled with a rhodamine 6G derivative at varying Mg2+ concentrations and electric field strengths. By accounting for electroosmotic flow and temperature, we determined the effective charge of the ssDNA under each set of conditions. This “snapshot” into the Mg2+-DNA interaction reveals the potential of 2bFCCS-CFCE in the fundamental study of biological macromolecules interacting with their ionic atmospheres. EXPERIMENTAL SECTION Sample Preparation. 40-oligo poly(dT) single-stranded DNA (ssDNA) labeled at the 5′ end with Rhodamine 6G (R6G-ssDNA, Operon Biotechnologies, Huntsville, AL) was diluted to a concentration of ∼10 nM in tris-glycine buffer at pH 8.3 (3 mM TrisHCl, 3 mM Glycine, Sigma, St. Louis, MO). Magnesium chloride (Fisher Scientific, Houston, TX) was added to the buffer in concentrations that ranged from 0 to 3 mM. The buffer solutions also contained 0.125 wt % poly(vinylpyrrolidone) (PVP, MW ≈ 106 g/mol, Sigma), which served as a dynamic coating to suppress EOF and prevent adsorption of the ssDNA to the capillary walls.49 Once prepared, the buffer solutions were boiled to denature any possible deoxyribonuclease contamination prior to introducing the ssDNA. Capillary Coating. Square bore fused silica capillaries were used in these experiments (Polymicro, Phoenix, AZ). The crosssectional area of the inner space of the capillaries was 50 × 50 µm2. The total cross-sectional area was 375 × 375 µm2. The outer surfaces of the capillaries were coated with polyimide. A procedure adopted from Belder et al.50 was used to apply a coating of poly(vinyl alcohol) (PVA, MW ≈ 4 × 104 g/mol, Sigma) to the interior walls of the capillaries to further suppress EOF and ssDNA adsorption. A clean, 25 cm long capillary was filled with an acidified aqueous glutaraldehyde solution, prepared from 200 µL of 50 wt % aqueous glutaraldehyde (Fisher, Houston, TX) in 800 µL of 1 M hydrochloric acid (Mallinckrodt, Hazelwood, MO). A plug of 2.5 wt % PVA in 0.6 M hydrochloric acid was injected into the glutaraldehyde-filled capillary using 0.5 MPa of N2 for 10 s. The capillary was then emptied and dried with continuous nitrogen flow for ∼4 h, after which it was ready for use. Instrumentation. Our 2bFCCS-CFCE apparatus (Figure 1) has been described previously.42,43 A 514.5 nm laser beam from an air-cooled, continuous wave Ar+ laser (Midwest Laser Products, Frankfort, IL) was split and then recombined into two nearly parallel beams by two 50/50 beamsplitters (Newport, Irvine, CA). The two beams were adjusted in power to 43 µW (49) Gao, Q.; Yeung, E. S. Anal. Chem. 1998, 70, 1382–1388. (50) Belder, D.; Deege, A.; Husmann, H.; Koehler, F.; Ludwig, M. Electrophoresis 2001, 22, 3813–3818.

Figure 1. Schematic representation of the two-beam fluorescence cross-correlation/continuous flow capillary electrophoresis experiment. The optical setup was designed to position two diffraction limited laser foci in the center of a square capillary, separated by a distance of ∼2 to 3 µm. The capillary is filled with sample solution using applied gas pressure, which is then turned off and voltage is applied for the electrophoresis experiment. Fluorescence signal from each focus is collected and used for the analysis of auto and cross-correlation.

using the appropriate absorptive neutral density filters (Newport), reflected by a 530 nm long pass dichroic beamsplitter (CVI, Albuquerque, NM), and focused by a 100 ×, 1.25numerical aperture oil immersion microscope objective (Edmund Industrial Optics, Barrington, NJ) through a small window created in a 25 cm length of the PVA coated capillary. The window was created by dissolving a small section of the outer polyimide coating in concentrated sulfuric acid heated to a temperature of 75 °C. Electric potentials were applied across the capillary by means of platinum electrodes connected to a high voltage power supply (Spellman, model CZE1000R, Plainview, NY). Fluorescence from each focal region was collected by the microscope objective, split by a 50/50 cubic beamsplitter (Thorlabs, Newton, NJ), spatially filtered by 50 µm pinholes (Thorlabs, Newton, NJ), and filtered by 535 nm long pass interference filters (Omega Optical, Brattleboro, VT), through which fluorescence was transmitted to two single photon counting avalanche photodiode detectors (PerkinElmer Optoelectronics, model SPCM-AQR-14, Wellesley, MA). The photocounts from the two detectors were cross-correlated using an ALV-6010/160 digital correlator card (ALV, Langen, Germany) mounted in a Pentium computer. Temperature was monitored using a Digi-Sense Benchtop Thermistor Temperature Controller (model EW-89000-10, Cole Parmer). The two laser beams formed nearly identical diffraction-limited focal regions, positioned near the center of the inner capillary space (∼25 µm from the inner surfaces), and separated along the axis of the capillary by a distance, R. From autocorrelation analysis of a standard 5-carboxy-tetramethylrhodamine (TAMRA) solution, the e-2 focal radius in the radial dimensionof the focal volume, ω0, was determined to vary from 0.2198 ± 0.0033 µm to 0.2567 ± 0.0037 µm. The ratio, κ0, of the radial and axial e-2 focal beam radii (κ0 ) ω0/z0, where z0 is the axial radius) was also determined and found to be 0.104 ± 0.002 µm. The separation distance, R, between the two foci was determined by crosscorrelation analysis to vary from 2.379 ± 0.045 µm to 2.581 ± 0.050 µm. The position of the laser beam foci relative to the inner surface of the capillary was reproducibly controlled using Analytical Chemistry, Vol. 81, No. 1, January 1, 2009

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a submicrometer resolution differential micrometer (Newport) mounted on the z-axis of the sample stage. Additionally, a precision rotation stage (Newport) was mounted on the sample stage to allow adjustment of the flow axis relative to the axis defined by the position of the two laser beams. The optimum position of the two laser beam foci relative to the z-position of the capillary and the flow axis could be confirmed by crosscorrelation analysis. Electroosmotic Flow Measurements. The EOF was determined prior to any 2bFCCS-CFCE experiments using a procedure adopted from Zare et al.51 A buffer was prepared containing low concentrations of tris-glycine and magnesium chloride. The capillary was then filled with this lower ionic strength buffer, while the higher ionic strength sample buffer was placed at the anode end of the capillary. A potential was applied across the capillary, and the voltage drop across a 100 kΩU resistor placed between ground and the capillary was monitored using a Labview program written in-house. As the higher ionic strength sample buffer flowed into the capillary because of electroosmotic flow, more current flowed through the resistor, resulting in a continual increase in the voltage. When the higher ionic strength buffer completely filled the capillary, measured voltage reached a steady value. The electroosmotic flow velocity was obtained from the length of the capillary divided by the risetime of the voltage. Viscosity Measurements. Solvent viscosity was measured for each solvent using a size 50 Cannon-Fenske Viscometer (Technical Glass Products, Dover, NJ) in a temperature controlled water bath (Labortechnik AG, Flawil, Switzerland). The primary safety hazards of this experiment are electric shock due exposure to the high voltage electrodes and eye injury from exposure to laser light. The entire experiment was placed inside an enclosure to block stray laser light. Access to the enclosure was interlocked to the high-voltage power supply to prevent exposure to the high voltage electrodes during the operation of the experiment. RESULTS AND DISCUSSION Cross-Correlation Analysis. Cross-correlation of the fluorescence detected from the two confocal observation regions results in a cross-correlation function, GC(τ), plotted versus the lagtime, τ. The cross-correlation function of a given species is a pseudoGaussian shaped peak positioned near the average transit time of the molecules between the two observation regions. The width of the cross-correlation peak is characteristic of the translational diffusion of the molecules as they migrate through the capillary. Hence, the peak position characterizes the uniform translational flow of the molecules in one dimension, and the peak width characterizes the translational diffusion. This enables both the diffusion and flow properties of the ssDNA molecules to be determined from a single measurement of the cross-correlation function. The equation used to analyze the cross-correlation functions is given below.40,43,52,53 (51) Huang, X.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1988, 60, 1837–1838. (52) Brinkmeier, M. Cross-correlated flow analysis in microstructures. In Fluorescence Correlation Spectroscopy: Theory and Applications; Elson, E. S., Ed.; Springer: Berlin, 2001; Vol. 65, pp 379-395. (53) Jung, J.; Van Orden, A. J. Phys. Chem. B 2005, 109, 3648–3657.

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GC(τ) - 1 )

(

1 1 N 1 + τ ⁄ τd

)(

1 1 + κ02τ ⁄ τd

) [ 1⁄2

exp

-r2(1 - τ ⁄ τF)2 1 + τ ⁄ τd

] (3)

Here, τ is the lag time, τd is the average transit time of molecules through one of the focal volumes due to translational diffusion only, r is the ratio R/ω0, τF is the average transit time for the molecules to flow between the two focal volumes, and N is the average number of molecules occupying one of the focal regions. The parameters N, τd, τF, and r are obtained for each sample by fitting the observed cross-correlation function to eq 3. The parameter κ0 was held fixed to the value determined from control experiments. Adjusting this parameter made a negligible contribution to the other fitted parameters in both the auto- and cross-correlation analyses. Figure 2 shows representative cross-correlation functions obtained for three ssDNA solutions migrating through the capillary under the influence of a 15 kV applied potential. The red, green, and blue cross-correlation functions were obtained from solutions containing 0, 1.5, and 3.0 mM MgCl2, respectively. The diamonds represent the experimental data, and the solid lines were obtained by fitting to eq 3. The fitted parameters are presented in Table 1. The appearance of the cross-correlation peaks in the “forward” correlation channel is consistent with the negatively charged DNA molecules migrating toward the anode.44 The black baseline shows the “reverse” correlation channel. The inset of Figure 2 shows the trends observed in the τF parameter for a series of cross-correlation functions obtained at various Mg2+ concentrations and applied fields. As depicted in eq 3, the τF parameter decreases as the migration velocity of the ssDNA increases. Hence, the rate of ssDNA migration slows down with increasing Mg2+ concentration and speeds up with the applied field strength. These trends can be explained by the fact that at higher concentrations of Mg2+,

Figure 2. Representative “forward” channel cross-correlation experimental data (points) and corresponding fitting curves (lines) from polythymine samples at three conditions; 0 mM Mg, 15 kV (diamonds), 1.5 mM Mg, 15 kV (triangles), and 3 mM Mg, 15 kV (circles). “Blank” cross-correlation from the “reverse” channel can be seen as solid black baselines. The inset is a graph of the τF parameter versus magnesium obtained from fitting of cross-correlation data to eq 3. The data was taken at three different voltages; 10 kV (diamonds), 12.5 kV (triangles), and 15 kV (circles).

Table 1. Parameters Determined from Cross-Correlation Analysis of Representative Dataa,b polythymine

τF(ms) r 1/N τd(ms) standard errorc

0 mM Mg, 15kV

1.5 mM Mg, 15 kV

3 mM Mg, 15 kV

1.3257(82) 11.94(36) 0.420(27) 0.245(22) 8.81 × 10-5

3.396(40) 11.75(36) 0.634(47) 0.215(18) 4.95 × 10-5

3.935(58) 10.96(31) 0.647(47) 0.180(15) 4.18 × 10-5

a Parameters correspond to the fitting analysis in Figure 2. b Values in parentheses are the 95% confidence intervals for the last digits. c Standard errors from each curve fitting are estimated using residual sum-of-squares.

Figure 3. Representative electroosmotic flow (EOF) data obtained by the measurement of the voltage drop across a resistor placed between the capillary and ground, which corresponded to the anode end of the experiment. As a higher ionic strength buffer migrates from the anode to the cathode, it displaces lower ionic strength buffer in the capillary, which results in an increase of current flowing through the capillary (and resistor). In this figure, the higher ionic strength buffer completely displaced the lower ionic strength buffer at ∼4100 s, which is indicated by the voltage reaching a steady state.

more counterions are associated with the ssDNA, partially neutralizing the negative charge. In addition, as can be inferred from eq 4, the electrophoretic migration velocity of the polythymine is directly proportional to the electric field strength. The τd parameter can be used to determine the diffusion constant, D, of the poly(T)40 DNA using D ) ω02/(4τd). The analyte flow velocity is obtained using Vx ) (rω0)/τF. This velocity is related to the electrophoretic mobility and electroosmotic flow according to eq 2 above. Substituting the value for Vx into eqs 1 and 2 above, we obtain the following equation for the electrophoretic mobility of the ssDNA: µe )

(rω0 ⁄ τF) - VEOF E

(4)

The effective charge can then be determined by substituting eq 4 and the expression for D into eq 1 and solving for Zeff: Zeff )

4τdµekBT ω02e

(5)

As predicted by eqs 4 and 5, the value of Zeff depends on temperature, the applied electric field, and the EOF, in addition to the electrophoretic flow velocity and diffusion constant. The electric field strength was determined from the potential applied across the capillary and the capillary length. The next two sections discuss our efforts to control VEOF and T. Determination of EOF. To measure the electrophoretic migration of the ssDNA molecules independently from EOF contributions, it was necessary to measure the magnitude of the EOF occurring in the capillary from day to day as described above. Figure 3 shows a representative measurement used to determine the EOF before cross-correlation analysis was performed. For this measurement the low ionic strength buffer contained 2 mM TrisHCl, 2 mM glycine, with 1 mM magnesium chloride, while the high ionic strength buffer contained 3 mM Tris-HCl, 3 mM glycine with 1.5 mM magnesium chloride. The measured voltage for this experiment reached a steady state at 4118 ± 12 s, corresponding to the moment when the higher ionic strength buffer completely displaced the lower ionic strength buffer in the capillary. This end point time was then used, along with the length of the capillary to calculate VEOF, which was determined to be 5.66 (±0.12) × 10-3 cm/s. Statistical information was obtained by performing multiple experiments and averaging the results. In general, it was found that the magnitude of the EOF velocity was small compared to the overall migration velocity of the ssDNA, such that the VEOF correction in eq 4 was on the same order of magnitude as the experimental error in the Vx term. Hence, in most cases the EOF contribution to the migration velocity could be neglected without significantly altering the measurement of the effective charge. This was due to suppression of EOF by the coatings applied to the inner walls of the capillary, as described above. Joule Heating. To determine the effective charge of the DNA molecules, the temperature inside the capillary must be known. The temperature inside an electrophoresis capillary can be greater than the ambient room temperature because of Joule heating. To investigate whether our results were influenced by Joule heating, we used photon counting histogram (PCH) analysis to determine the specific brightness of tetramethyl rhodamine (TMR) labeled DNA molecules flowing through the capillary at different electric fields and ionic strengths. Steady state spectrofluorometry measurements confirmed that the fluorescence intensity of TMR decreases with temperature over a temperature range of 5 to 80 °C (see Supporting Information). Therefore, if Joule heating is prevalent in our experiments, the PCH measurements would reveal a decrease in the specific brightness of the TMR molecules when an electric field is applied. Our results showed no significant changes in specific brightness because of the application of an electric field (see Supporting Information). This was the case for all electric field and ionic strengths. According to our PCH measurements, the maximum temperature increase that may have occurred because of Joule heating was within experimental error of room temperature and therefore insufficient to alter the outcome our measurements. Hence, we assumed the temperature inside the capillary was equivalent to the ambient temperature of our laboratory in our calculations. The capillaries we used in our experiments were immersed in index matching fluid, which, in turn, was in thermal contact with a microscope objective mounted Analytical Chemistry, Vol. 81, No. 1, January 1, 2009

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Figure 4. Diffusion constant, D (top), viscosity, η (middle), and hydrodynamic radius, RH (bottom) versus Mg2+ concentration at different applied voltages; 0 kV (diamonds), 10 kV (triangles), 12.5 kV (circles), and 15 kV (squares). All diffusion constants were calculated from parameters determined from fitting of auto and crosscorrelation data. Viscosities of sample solutions were measured at the temperatures that the correlation data was taken. Hydrodynamic radii were calculated from diffusion, viscosity, and temperature data.

to a large metal optical table via metal optics mounts. This served as an effective heat sink to dissipate any heat generated inside the capillary by Joule heating. In short, we have shown that it is possible to carry out these experiments in such a way that EOF and Joule heating make a negligible contribution to the results. Trends in the Diffusional Motion. Figure 4 displays diffusion constants calculated from the auto- and cross-correlation parameters for ssDNA samples containing a range of Mg2+ concentrations and electric field strengths. Also shown are the solvent viscosity, η, and hydrodynamic radius, RH, of the ssDNA observed for each sample. Hydrodynamic radii were calculated from the diffusion constants and solvent viscosities based on the Stokes-Einstein relation: RH ) kBT/6πηD. Measurements were performed in the absence of an applied potential and at applied potentials of 10, 12.5, and 15 kV. The diffusion constants at zero field were determined by autocorrelation analysis of freely diffusing ssDNA. The cross-correlation analysis technique described above was used to determine the diffusion constants of ssDNA molecules flowing through the electro470

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phoresis capillary under the influence of an applied field. The experimentally determined diffusion constants ranged from ∼4.6 × 10-7 in the absence of Mg2+ to ∼8.7 × 10-7 cm2/s at the highest Mg2+ concentration. The corresponding hydrodynamic radii were ∼4.1 to ∼2.3 nm. These values are in good general agreement with previous studies on the diffusion properties of similar sized ssDNA.24,28,54,55 The most important trend observed in Figure 4 shows that the rate of ssDNA translational diffusion increases with increasing Mg2+ concentration. The presence of Mg2+ has relatively little effect on the diffusion rate at lower Mg2+ concentrations but increases significantly above 1 mM Mg2+. The diffusion rate begins to level off between 2 and 3 mM Mg2+. The reverse trend is observed for the hydrodynamic radius, indicating the ssDNA is becoming more compact with increasing Mg2+ concentration. Previous studies have shown that as the concentration of small counterions increases, negative charges on the backbone of ssDNA are neutralized.54,56-59 This lowers the self-repulsion between nucleotides and allows the ssDNA to adopt more compact structures with larger diffusion constants and smaller hydrodynamic radii. Our results suggest that a threshold concentration of ∼1 mM Mg2+ exists, at which point the ssDNA begins to become more compact in its structure. The fact that the diffusion constants level off at Mg2+ concentrations above 2 or 3 mM, suggests the charge shielding starts to becomes saturated at these concentrations. Another trend that is apparent in Figure 4 is that the diffusion constants measured at zero applied electric field are noticeably smaller than those measured for ssDNA migrating under the influence of an electric field. The observed differences are within experimental error for samples with lower Mg2+ concentration, but they become significant at elevated Mg2+ concentrations. This seems to contradict previous experiments by Nkodo et al. showing no electric field dependent changes in the diffusion constants of ssDNA undergoing free zone electrophoresis.24 Nkodo et al. investigated similar sized ssDNA and similar electric field strengths compared to the present study. However, the buffer conditions were much different from ours, and no divalent cations were present. This makes direct comparison of the results difficult. Nonetheless, our observations deviate from those of Nkodo et al. only for the highest concentrations of Mg2+. It may be that in the presence of divalent cations, the electric field changes the ionic atmosphere surrounding the ssDNA, which, in turn, could affect the ssDNA structure and diffusion rate. Further studies are needed to clarify this issue. Finally, the differences in diffusion constant observed for the three different electric field strengths were within experimental error of each other. Trends in the Effective Charge. The electrophoretic mobilities and effective charges of the ssDNA molecules in each sample were calculated from the cross-correlation parameters using eqs (54) Doose, S.; Barsch, H.; Sauer, M. Biophys. J. 2007, 93, 1224–1234. (55) Stellwagen, E.; Lu, Y.; Stellwagen, N. C. Biochemistry 2003, 42, 11745– 11750. (56) Murphy, M. C.; Rasnik, I.; Cheng, W.; Lohman, T. M.; Ha, T. J. Biophys. J. 2004, 86, 2530–2537. (57) Tinland, B.; Pluen, A.; Sturm, J.; Weill, G. Macromolecules 1997, 30, 5763– 5765. (58) Caliskan, G.; Hyeon, C.; Perez-Salas, U.; Briber, R. M.; Woodson, S. A.; Thirumalai, D., Phys. Rev. Lett. 2005, 95, 268303. (59) Mills, J. B.; Vacano, E.; Hagerman, P. J. J. Mol. Biol. 1999, 285, 245–257.

Figure 5. Representative electrophoretic mobility (top) and effective charge (bottom) data versus magnesium concentration at the applied potential of 10 kV. Electrophoretic mobility and effective charge (in units of elementary charge) were calculated from parameters obtained from fitting cross-correlation data and from control experiments. Table 2. Parameters for Determining Effective Chargea polythymine

ω0(µm)b D (10-7 cm2/s)c VEOF (10-5 m/s)d E (105 V/m)e µDNA (10-9 m2/V s)f Zeff (e-)

0 mM Mg, 15kV

1.5 mM Mg, 15 kV

3 mM Mg, 15 kV

0.2197(33) 4.94(31) 6.68(14) 6.20(57) 3.04(29) 15.5(1.7)

0.2197(33) 5.66(43) 5.66(12) 6.44(63) 1.10(11) 4.90(62)

0.2384(48) 7.92(55) 6.31(14) 6.44(63) 0.935(95) 2.99(37)

a Values in parentheses are the 95% confidence intervals for the last digits. b Obtained from autocorrelation analysis of standard TAMRA solutions. c Calculated according to the equation, D ) ω20/(4τd). d Obtained from EOF control experiments. e Obtained from applied voltage divided by length of capillary. f Calculated using eq 5.

4 and 5. These parameters are plotted in Figure 5 as a function of Mg2+ concentration, and representative parameters are shown in Table 2. Only data collected using an applied potential of 10 kV are shown in Figure 5. It was found that, within experimental error, the effective charge did not depend on the applied potential. The electrophoretic mobilities varied from a minimum value of ∼9.4 × 10-5 cm2/V s at the highest Mg2+ concentration to a maximum of ∼3.0 × 10-5 cm2/V s in the absence of Mg2+.

These values fall within the range of previous measurements of the electrophoretic mobility of ssDNA.24,45,60 As shown in Figure 5, the electrophoretic mobility declined sharply with Mg2+ for the lowest Mg2+ concentrations, and then decayed slowly thereafter. Likewise, the effective charge of the ssDNA attained a maximum value of ∼-16 in the absence of Mg2+, declined sharply with Mg2+ at low Mg2+ concentrations, then decayed to a minimum value of ∼-3.0 at ∼3 mM Mg2+ concentration. Even in the absence of Mg2+, the counterions present in the background electrolyte neutralized more than half the charge on the 40-nt ssDNA backbone. For comparison purposes, we estimated the effective charge of 75-nt polythymine ssDNA in an electrophoresis buffer using data from Nkono et al.24 These authors studied the electrophoretic mobilities and diffusion rates of ssDNA undergoing free solution electrophoresis, in the absence of divalent cations. On the basis of µe ) 1.83 × 10-4 cm2/V · s and D ) 4.65 × 10-7 cm2/s, a value of Zeff ≈ 10 is obtained. This suggests the 75-nt ssDNA experiences even greater charge neutralization than our 40-nt ssDNA in the absence of Mg2+. The background buffer used by Nkodo et al. had a higher concentration of electrolytes than our buffer, which could explain the greater amount of charge neutralization. In any case, it is apparent that the counterions present in the background buffer solution have the ability to significantly quench the ssDNA charge, even in the absence of divalent cations. Divalent cations further neutralize the remaining charge to the point where the ssDNA is almost completely neutralized in the presence of ∼3 mM Mg2+. Comparison of Figure 4 and 5 shows the relationship between the diffusion properties of the molecules and their effective charge at different Mg2+ concentrations. In particular, there is a threshold for the effective charge above which the ssDNA structure becomes more compact. At low Mg2+ concentration, the effective charge declines sharply with Mg2+ concentration, but the diffusion properties of the ssDNA do not change significantly. The change in diffusion properties become more pronounced, signifying the formation of more compact structures, when the Mg2+ concentration reaches ∼1.5 mM. At this concentration, the effective charge of the ssDNA is ∼6 e-. This suggests that most of the charged groups on the ssDNA backbone must be neutralized for the ssDNA to adopt the most compact structure. CONCLUSIONS In summary, we have demonstrated that 2bFCCS-CFCE can be used to determine the effective charge of single-stranded DNA in the presence of Mg2+ counterions. Knowledge concerning the effective charge of biological macromolecules yields important insight into the role that small counterions play in their structure and function. The advantage that 2bFCCS-CFCE has over other electrophoresis techniques in this area is its ability to simultaneously monitor diffusion and electrophoretic migration. It was found that increasing Mg2+ concentration increased the rate of DNA diffusion while also lowering the effective charge. This result indicates that neutralization of the negative charges on the ssDNA backbone allows it to overcome self-repulsion to adopt more compact conformations. Work in progress includes using simul(60) Dong, Q.; Stellwagen, E.; Dagle, J. M.; Stellwagen, N. C. Electrophoresis 2003, 24, 3323–3329.

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taneous analysis of autocorrelation, photon counting histogram, and cross-correlation, and extending the temporal resolution of the techniques into the nanosecond regime. Accomplishing this would allow the interrogation of the ionic atmosphere fluctuations that possibly contributed to the dependence of diffusion on electric field strengths. In addition, the technique has the potential to comprehensively study DNA-counterion kinetics. Investigation of dye-quencher interactions on specifically labeled biological macromolecules can also provide a window into the impact of ionic atmosphere on the active conformations of proteins, DNA, and RNA.

RR017025), the American Chemical Society Petroleum Research Fund (Grant 46878-AC5), and the National Science Foundation Collaborative Research in Chemistry Program (Grant 0628260).

ACKNOWLEDGMENT This research was supported by the National Institutes of Health-National Center for Research Resources (Grant R33

Received for review September 13, 2008. Accepted November 6, 2008.

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SUPPORTING INFORMATION AVAILABLE Further details are given in Figures S1-S3. This material is available free of charge via the Internet at http://pubs.acs. org.

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