DNA Electrophoresis in Gellan Gels. The Effect of Electroosmosis and

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J. Phys. Chem. B 2002, 106, 2349-2356

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DNA Electrophoresis in Gellan Gels. The Effect of Electroosmosis and Polymer Additives Martin Markstro1 m,† Kenneth D. Cole,‡ and Bjo1 rn Åkerman*,† Department of Physical Chemistry, Chalmers UniVersity of Technology, S41296 Gothenburg, Sweden, and Biotechnology DiVision, NIST, Gaithersburg, Maryland ReceiVed: April 27, 2001; In Final Form: August 23, 2001

The polysacharide gellan forms hydrogels if a divalent ion such as calcium is added at millimolar concentrations. The gel can be reversed to solution by adding EDTA, which makes it a promising candidate for preparative electrophoretic separation of biomolecules. We have studied the electrophoretic migration of double-stranded T4 DNA (164 kilobase pairs) in gellan gels by velocity measurements and by linear dichroism spectroscopy studies of the DNA coil conformation during the migration. The gels either contained 0.3% of high molecular weight (5 × 106) poly(ethylene oxide) (PEO), to suppress the electroosmosis induced by the negative charges of the gellan polymer, or were free of such added polymer and therefore exhibited an electroosmotic flow which is opposite to the DNA migration. In both cases, the viral DNA migrate in an oscillatory manner between stretched and coiled states, because it becomes entangled with the gellan gel fibers. In the stretched state of the cycle, the molecules are substantially aligned with the field. As the field is turned off, the alignment relaxes first by a rapid (seconds) stretch relaxation along the aligned path in the gel, followed by a slower (minutes) end-on type of motion to the equilibrium isotropic coil state. The added PEO has two effects on the DNA migration. An indirect effect is that the quenched electroosmosis leads to a stronger stretching of the DNA and to shorter cycle period times because the ends of the molecules move faster in the absence of the counter flow. A direct effect is that the PEO itself retards the DNA motion, most likely because of a combination of hydrodynamic interactions and entanglement effects. The net result of these two opposing PEO effects is that the center-of-mass velocity of the DNA increases by a factor of about 2 upon addition of PEO.

Introduction The negatively charged polysaccharide gellan gum can be used to form hydrogels by employing divalent cationic gelling agents such as calcium ions or a diamine.1 In both cases, the gel can be reversed to solution by gentle chemical means, either by addition of EDTA to sequester the calcium or by raising the pH so that the cross-linking diamine becomes deprotonated. This possibility means that biomolecules can easily be recovered after the electrophoretic separation by cutting out the relevant piece of the gel and reversing it to solution under conditions where the molecules are likely to retain their biological activity. For instance, gellan gels can be used for size-separation of DNA in a size range similar to that available with agarose gels, and it has been demonstrated that after reverting the gel to solution the contained DNA can be used directly for restriction enzyme digestion, ligation, and transformation of bacteria.1 A disadvantage with the negative charge on the gellan polymer is the strong electroosmosis it causes in the gel. The flow is oppositely directed to the motion of negatively charged macromolecules such as DNA and, therefore, tends to slow their migration and separation compared to conventional gels such as agarose. Cole and co-workers2 have found that the electroosmosis in the gels can be reduced by adding neutral polymers, for instance poly(ethylene glycol) (PEO). The addition of such polymers indeed increases the rate of DNA migration and thus * To whom correspondence should [email protected]. Fax: 46317723858. † Chalmers University of Technology. ‡ NIST.

be

addressed.

E-mail:

separation,2 but the increase in DNA velocity was less than the decrease in electroosmotic flow, as measured independently. This suggests that the added polymer has a second effect on the DNA migration that tends to counteract the indirect effect operating through the reduction of the electroosmotic flow. One possibility is that the added polymer increases the effective viscosity of the solution in the gellan pores. This would indeed retard the electroosmosis but also the DNA molecules because they migrate in the same pores as the electroosmosis flows. However, our earlier analysis of the two effects of PEO2 was based on the assumption that the DNA and electroosmotic velocities simply are additive. This is accepted procedure in capillary electrophoresis and can be motivated in free solution on theoretical grounds,3 but the picture is less straightforward in gels because of how the gel network affects hydrodynamic interactions between polymer segments.4 For small solutes such as bromphenole blue, the subtraction procedure works well in gellan gels.2 With a large and flexible molecule such as DNA, on the other hand, the hydrodynamic and entanglement interactions with the gel fibers as well as with added PEO means that electrophoretic motion and a hydrodynamic flow may combine in a nonadditive manner. In this paper, we therefore attempt to resolve the two effects by measuring directly the retarding effect of the added PEO in absence of electroosmosis. We follow the Brownian motion of the DNA in the absence of an electric field, by first using a field to perturb (stretch) the DNA molecules and then monitor by spectroscopy their field-free relaxation after the cessation of the electroosmotic flow that is also induced by the perturbing field.

10.1021/jp011617l CCC: $22.00 © 2002 American Chemical Society Published on Web 02/09/2002

2350 J. Phys. Chem. B, Vol. 106, No. 9, 2002

Markstro¨m et al.

TABLE 1: Properties of the Polymers (in Aqueous Solution) chain radius r (nm) segment length b ) 2P (nm)c contour length Lc (µm) radius-of-gyration Rg (nm)d

T4 DNAa

PEOb

1 50 56.4 970

0.45 0.93 57.5 130

a Reference 29. b Reference 30. c P is the persistence length. d Rg ) (PLc/3)1/2.

The spectroscopic approach is also used to investigate the mode of DNA migration in the novel gellan gels in terms of the DNA conformational dynamics during the electrophoresis, in particular regarding the effect of the electroosmosis. This approach has been used earlier to distinguish between different modes of DNA migration in agarose,5 where the comparably large DNA molecules used in the present study migrate by a cyclic conversion between extended and coiled states.6,7 Materials and Methods Samples and Gel Preparation. The linear DNA samples from T4 (166 kbp) and T7 (39 kbp) phages from Sigma contained 95% intact molecules as obtained by pulsed field agarose gel electrophoresis. The polymer additive PEO from Aldrich had a molecular weight of 5 × 106. The properties of PEO and T4 DNA are summarized in Table 1. The dimeric form of the fluorescent DNA-stain oxazole yellow (YOYO) was from Molecular Probes. Gellan gels were prepared using 5 mM calcium ions as gelling agent as described in detail elsewhere.1,2 Briefly, the required amount of gellan powder was dissolved in water by boiling for 5 min. The required amount of buffer, and in some cases PEO, was added as 10× stock aqueous solutions, and water was finally added to the required final volume. Gellan concentrations were 0.1 or 0.3% (w/v), and when present, the PEO concentration was 0.3% (w/v). Both velocity and alignment experiments were performed with and without 0.3% PEO, but the alignment measurements were limited to 0.3% gels. All experiments were performed in TB buffer (50 mM boric acid and 50 mM Tris) with 5 mM CaCl2, and with YOYOstained DNA (1 dye per 10 base pairs) as described elsewhere.7 Under present staining conditions, the dye increases the DNA length by almost 50% and reduces the electrophoretic charge by 15%.8 YOYO staining was employed for fluorescencemicroscopy imaging of the DNA as described earlier.7 Gel Electrophoresis and Electroosmosis. Slab gels were run in submarine mode with the Ca2+-containing gelation buffer as the circulation buffer in order to stabilize the gel. The electrophoretic velocity in constant field was calculated from the slope of distance vs migration time obtained by repeated scanning of the gel during electrophoresis. The electroosmotic flow was measured by using vitamin B12 as an uncharged marker, as described earlier.2 Linear Dichroism (LD). Electrophoretic alignment of T4 DNA was monitored in situ by LD measurement in a vertical electrophoresis cell9 containing a gellan gel prepared in the same way as the submarine gels for velocity experiments. The DNA was introduced into the measuring position in the bulk of the gel by field inversion gel electrophoresis (T+ ) 3 s and T-) 1 s at 7.5 V/cm) which separates degraded DNA from the major intact T4 DNA component. The DNA concentrations were in the range of 25-150 µM phosphate, as determined by absorption at 260 nm and the extinction coefficient 6600 M-1 cm-1. The average temperature in the gel was 20 ( 2 °C as monitored through the electric current. The LD measurements are presented

Figure 1. Electrophoretic velocity of T4 (160 600 bp) and T7 (39 000 bp) DNA during migration at 5 V/cm in 0.3% (left) or 0.1% (right) gellan gels, in the absence (black) or presence (hatched) of 0.3% (w/ w) of polyetylene oxide of molecular weight 5 × 106.

in terms of an orientation factor S which quantifies the average degree of DNA-helix orientation:10

S)

〈3 cos2 θ - 1〉 2

(1)

where θ is the angle between the DNA helix axis and the direction of the electric field and the brackets denote an average over all of the segments in all DNA molecules. For a randomly oriented sample, S ) 0, whereas when all DNA molecules are perfectly aligned with their helix axes parallel to the field, S ) +1. Results Electrophoretic Velocity. Figure 1 shows how the electrophoretic velocity of two sizes of double-stranded DNA in 0.3 and 0.1% gellan gels is affected by the addition of 0.3% (w/w) PEO. In all four cases, the DNA migrates faster in the presence of PEO, in accordance with the earlier study on mainly smaller DNA sizes in 0.1% gellan gels.2 The increase by a factor of 1.7 for T7 (39 kbp) in 0.1% gellan observed here compares well to a factor of 1.9 obtained for the similarly sized λ-DNA (48 kbp). The electroosmotic flow in the PEO-free gel was found to be (9.2 ( 0.1) × 10-5 cm2 V-1 s-1 under the present conditions. Here we have chosen to investigate further the migration of the larger T4 DNA (166 kbp) in the presence and absence of PEO by studying the DNA conformational dynamics in situ during electrophoresis by linear dichroism spectroscopy. When present, the PEO concentration was always chosen to be 0.3% because this is sufficient to completely quench the electroosmosis.2 DNA-Alignment Response. Figure 2 shows typical alignment responses of T4 DNA in a 0.3% gellan gel to a pulse of electric field of 15 V/cm as indicated by the field profile at bottom of Figure 2. The LD responses without and with PEO (-PEO and +PEO, respectively) are both positive and oscillatory, but the overall magnitude is higher with PEO present, and the oscillations are also more marked. The responses in Figure 2 were obtained at 260 nm, where the absorbance of DNA has a maximum. No LD signal was observed if the experiment was performed at a wavelength (320 nm) where DNA does not absorb or in a DNA-free gel. The observed LD responses can therefore9 be ascribed to a DNA alignment and are not the result

DNA Electrophoresis in Gellan Gels

Figure 2. 2. Alignment response (LD at 260 nm) of T4 DNA in 0.3% gellan gel to an electric pulse (E) of constant electric field strength 15 V/cm, in the absence (-PEO) or presence (+PEO) of added poly(ethylene oxide) (0.3% w/w). The orientation factor S quantifies the degree of alignment (see Materials and Method section). The inset shows the expanded view of the oscillatory build-up in the presence of PEO, with the definition of the amplitude ∆S of the oscillation. A similar but weaker oscillatory response is observed in the absence of PEO. The concentration of DNA is 93 µM phosphate. The DNA is stained with YOYO at one dye per 10 base pairs.

of a gel-distortion. The positive sign of the orientation factor S shows that the DNA coils are preferentially aligned along the field direction,10 as is the case during migration in agarose gels.11 The magnitude of the steady-state value Sss with PEO present (S ) 0.076) reflects a significant deformation of the DNA coils from the isotropic equilibrium state (S ) 0), although the field alignment is far from perfect (S ) 1). The alignment at 15 V/cm is about 8-fold weaker in the absence of PEO. The build-up to the steady state occurs by an oscillatory response (inset), which shows that the DNA molecules are undergoing nonmonotonic conformational dynamics as a response to the electric field. In addition to a smaller amplitude of the oscillation in the absence of PEO, Figure 2 also shows that the overshoot occurs later. When the field is removed (at t ) 50 s), the field alignment relaxes, first rapidly so that S is reduced by half within a few seconds and then by a slow process which lasts for several minutes. In this work, we have studied the relaxation phase in order to monitor the Brownian (field-free) motion of the DNA in the gellan gel, but the field-induced response is also important because the oscillatory LD contains information on the mechanism of DNA migration. Only this understanding allows us to make molecular interpretations of the DNA motion during the relaxation process and how PEO affects it. We will first present the data on the field-induced response and then the relaxation measurements. Steady-State Alignment. Figure 3 shows the degree of migrative DNA alignment in the steady state (Sss) as a function of field strength with or without PEO present in the 0.3% gellan gel. In both cases, the degree of DNA orientation increases with increasing field. This is expected from the corresponding increase in the pulling electric force, and the same effect is observed in agarose gels.11 Notably, PEO has a marked effect on the degree of alignment because it is between 4- and 10fold higher in the presence of the polymer additive, depending on the field strength. Build-Up Dynamics. The nonmonotonic LD response (overshoot) is similar to that observed in agarose gels.11 In agarose, the oscillations in the DNA alignment reveal a cyclic type of

J. Phys. Chem. B, Vol. 106, No. 9, 2002 2351

Figure 3. Steady-state electrophoretic alignment of T4 DNA in 0.3% gellan gel vs field strength, in the presence (solid) and absence (open) of 0.3% PEO.

Figure 4. Relative amplitude of the alignment oscillation vs field strength, with (solid) or without (open) added PEO. The Sss values are from Figure 3, and the amplitude ∆S is defined in Figure 2.

migration7 which has been demonstrated by direct microscopy observation of individual DNA molecules.6 Starting from an equilibrium coil, the DNA molecules are stretched into a U-shaped conformation hooked on a gel fiber, because when the field was applied the two DNA ends chanced to pick paths through the gel on different sides of this particular obstacle. The continued application of the (constant) electric field leads to a subsequent tug-of-war between the arms of the U which is finally resolved by the sliding of the shorter arm around the hooking point. Once the transient anchoring is lost, the entropic tension in the chain leads to a collapse into a coiled state, from which the cycle can start again. Here we will focus on the initial phase of U formation, where the DNA alignment is driven by the independent motion of the two ends of the DNA molecule. Attempts to verify by microscopy that the migration of DNA is cyclic in nature also in gellan gels failed because of the high (millimolar) concentration of divalent cations used as gellingagents. As a result, the microscopy dye YOYO, which to a large extent binds to the DNA by electrostatic interactions,12 dissociated from the DNA before images could be obtained. When the magnitude ∆S of the oscillations (inset of Figure 2) is normalized by the steady-state orientation (∆S/Sss), it exhibits a maximum as a function of field strength (Figure 4), in agreement with earlier observations in agarose gels.11 It is also seen that even when the overshoot amplitude is normalized to the higher overall alignment in the presence of PEO, it is higher than in the unmodified gel, where in fact a monotonic build-up (∆S ) 0) is observed at low field strengths.

2352 J. Phys. Chem. B, Vol. 106, No. 9, 2002

Figure 5. Time to alignment overshoot vs field strength in the presence (solid) and absence (open) of added PEO. Inset shows log-log plot of the data. The slopes of the least-squares fits are -1.1 ( 0.1 with PEO and -1.5 ( 0.1 without PEO.

Figure 6. Semilogarithmic plots of the field-free decay of the DNA alignment in the presence and absence of PEO (indicated). The field is turned off at time t ) 0, and the orientation function S(t) has been normalized to its steady-state value during the field pulse.

The time tos to reach the overshoot is a useful parameter because it corresponds to the average time for the DNA molecules to reach the U shape.7 The effect of the field strength on the overshoot time is shown in Figure 5, where a rather limited number of data points are given for gels without PEO because in this case the overshoot was absent at low fields. The time for U formation is seen to decrease with increasing field strength, which is simply because the ends migrate faster.13 The log-log plots of the data in the inset of Figure 5 reveal a power law tos ∝ E-1.1(0.1 for gels with PEO. The field-dependence seems to be stronger in the absence of PEO (a scaling exponent for tos of about -1.5), but the few data points and a more narrow field range make this observation rather uncertain. The data in Figure 5 also shows that at a given field strength the U formation is faster with PEO present than in the absence of added polymer, i.e., that the ends move faster by a factor of about 1.6 when electroosmosis is suppressed Field-Free Brownian Motion of the DNA. To investigate to what extent the PEO polymer directly affects DNA motion, we studied the effect of PEO on the Brownian (field-free) relaxation of the aligned DNA. The main rationale for this approach is that the electroosmosis is a field-driven process, so by studying DNA motion in the absence of field, the indirect effect of the PEO could be eliminated. Figure 6 shows a semilogarithmic plot of the field-free relaxation of DNA in gellan gels with or without added PEO.

Markstro¨m et al.

Figure 7. Terminal relaxation time constants from linear fit to longtime part of the normalized relaxation data (as in Figure 6) in the absence (open) or presence (solid) of PEO. Error bars (or sizes of symbol) show uncertainty in the fitted time constants.

The orientation factors S(t) have been normalized to the value Sss which was reached in the steady state during the preceding pulse (22.5 V/cm). In neither case is the relaxation process a single exponential, and the presence of a fast (seconds) phase followed by final relaxation over minutes is again very similar to the observation in agarose gels.11 This behavior is due to the fact that in gels the conformation of long DNA can relax on many different length scales, ranging from the average pore size to the contour length of the chain, and this leads to a correspondingly wide distribution of relaxation times14,15 Ultimately the relaxation is singly exponential, however, as indicated by the approximate linear behavior for long enough times in Figure 6. The slope of the long-time linear fit gives the terminal relaxation time, and the zero-time intercept gives the relative contribution (AR) by this final process to the overall relaxation amplitude. The main observation is that the PEO has little effect on the time constant, but that its presence reduces the relative contribution from the terminal relaxation-process substantially. The terminal relaxation time constants in the presence and absence of PEO are shown at different field strengths in Figure 7. The observed magnitude of several minutes indicates that the long-time relaxation occurs by reptation, i.e., end-on motion of the DNA chain.16 This mode of terminal field-free relaxation for the T4 DNA used here has been demonstrated in agarose gels,14,17 where it occurs on a similar time scale. The fact that the time constant τR is only weakly dependent on the electric field and if anything increases with increasing field also supports this conclusion (see below). It is also seen from Figure 7 that there is no significant effect of the added PEO on the rate of reptation. Figure 8 shows the relative relaxation amplitude AR (timezero intercept in Figure 6) of the final process vs field strength. It is seen that in the absence of PEO reptation is responsible for a larger fraction (10-25%) of the relaxation compared to the values below 5% when the polymer is present. However, as shown in the inset, the corresponding degrees of absolute DNA alignment (SR ) ARSss) with and without PEO are rather similar. The parameter SR is a measure of the degree of alignment of the global DNA path between the gel obstacles (the so-called primitive path16). The increase in SR, with increasing field (inset of Figure 8) shows that a stronger electric force results in that the DNA follows a more straight path though the gel, as is the case in agarose gels.14,15 The remaining relaxation amplitude Sstr ) (1 - AR)Sss represents the DNA

DNA Electrophoresis in Gellan Gels

J. Phys. Chem. B, Vol. 106, No. 9, 2002 2353

Figure 8. Relative amplitude AR of long-time (reptation) contribution to the field-free relaxation vs field strength of the perturbing pulse, in the absence (open) or presence (solid) of PEO. AR values are obtained from the zero-time intercepts of linear fits as in Figure 6. Inset: corresponding absolute relaxation amplitude SR ) ARSss, where Sss values are from Figure 2.

Figure 9. Time needed for relaxation of 70% of the induced DNA alignment vs field strength in the perturbing pulse, in the absence (open) and presence (solid) of PEO.

TABLE 2: T4 DNA Orientation Parameters at 7.5 V/cm

Sstrb Sssc ARd d

0.3% gellan, no PEO

0.3% gellan, with 0.3% PEO

1% agarose, nativea

1% agarose, affinity modifieda

0.0024 0.003 0.24

0.03 0.03 0.05

0.124 0.133 0.07

0.160 0.183 0.13

a Reference 21. b Obtained as S c str ) (1 - AR)Sss. From Figure 3. From Figure 8.

alignment which relaxes by the fast process and can be ascribed to stretching of the DNA along this path.14,13 Table 2 gives the values of Sstr at 7.5 V/cm with and without PEO (together with the corresponding values in native and affinity-modified agarose for later reference). It is seen that the DNA stretching is about 10-fold weaker in the absence of PEO. A single-exponential terminal decay (as in Figure 6) is predicted by theories for reptation in an array of fixed obstacles.16 The data on the faster part of the relaxation could not be fitted to a simple sum of exponentials, in fact a stretched exponential has been used to describe the corresponding experimental data in agarose gels.14 However, in the absence of a supporting theory for the latter mathematical form, we have instead chosen to characterize the fast part of the relaxation by evaluating the time τ70 after which 70% of the steady-state alignment (Sss) has relaxed.11 Figure 9 presents the data on τ70 in 0.3% gellan gels as a function of the perturbing field strength, both in the presence and absence of PEO. It is seen that the relaxation time τ70 decreases with increasing strength of the field, in contrast to the reptation time (Figure 7) and, second, that at a given field strength the relaxation time is shorter in the presence of PEO than in its absence. Discussion Two Opposing Effects of PEO on DNA Mobility. Figure 10 shows the electrophoretic mobilities of T4 DNA in 0.3% gellan gels without and with added PEO (from Figure 1) together with the DNA mobility which is expected in the PEO-free gellan gel in the absence of electroosmosis (obtained by adding the electroosmotic mobility 9.2 × 10-5 cm2 V-1 s-12) and the mobility in 1% agarose. The first observation is that the electroosmosis-corrected mobility in the PEO-free gellan gel is about 3-fold higher than in 1% agarose gel. This indicates that

Figure 10. Electrophoretic mobility of T4 DNA (at 5 V/cm) in PEOfree 0.3% gellan gel before (black) and after (checkered) correction for electroosmosis (see text) compared with the T4 DNA mobility in the gellan gel containing 0.3% PEO (white) and with its mobility in a 1% agarose gel (striped).

the pore size of 0.3% gellan gel is substantially larger than the value 250 nm measured for 1% agarose,36,37 as expected from the lower gel content. Second, it is seen that the observed increase in DNA mobility upon addition of PEO (Figure 1) is the net result of two comparably large but counteracting effects: a velocity increase because of the decrease in electroosmotic drag, which is almost compensated by a retardation of the DNA motion because of the PEO itself. This conclusion relies on the assumption that the effect on DNA velocity of a reduced electroosmotic flow is simply additive. One aim of this study was to measure directly the second, retarding, effect of the PEO, and this was achieved in two steps. First we establish in which manner the electrophoretic migration in gellan gels perturbs the DNA conformation. Then, we use the rate of fieldfree relaxation of this perturbed conformation to measure how added PEO affects the friction against DNA motion in absence of electroosmosis. DNA Migration in Gellan is Cyclic. The oscillatory LD response (Figure 2) is very similar to the alignment behavior of T4 DNA in agarose gels. This strongly indicates that migration occurs by the same cyclic stretching-coiling mechanism which has been established by microscopy in agarose,6,7 although we could not confirm it in gellan by such direct observation. The maximum in the relative overshoot ∆S/Sss as a function of field strength (Figure 4) is another characteristic of the cyclic migration.11 At low enough fields, the molecule have time to slip out of the hooking situation before becoming appreciably stretched (low ∆S). At high enough fields, the

2354 J. Phys. Chem. B, Vol. 106, No. 9, 2002 stretching in the U conformation saturates because the molecules cannot be stretched beyond their contour length.13 An elevated field can still increase the average stretching Sss over the cycle, however, by reducing the duration of the coiled phase of the cycle (where alignment is still low). Thus, ∆S/Sss in effect decreases at high fields. Overshoot Time. The similar mode of DNA migration means that the extensive understanding of the dynamics of long DNA in agarose gels10,18 can be applied in gellan as well. The DNA alignment during electrophoresis in gels is caused by the migrative transport,10 which means that the kinetics of the coildeformation process measured by LD is closely linked to the velocity of the DNA molecules. For instance, the time tos of the overshoot (after field application) reflects the velocity by which the two DNA ends drag the molecule into the U conformation of the cycle.13 The observation that tos exhibits a somewhat stronger than inverse field dependence (Figure 5) is again very similar to the behavior in agarose gels.11 A strict inverse dependence is predicted if the field only affects the velocity of the ends along the path in the gel, because the applied force dragging the ends increases linearly with field strength. The somewhat stronger field dependence that is observed has been ascribed to that an elevated field also leads to the ends choosing a somewhat more field-aligned path through the gel.13 The correspondingly more direct route to the U at a higher field means that it is reached in a time which decreases slightly faster than the applied force increases. The similar slopes indicate the field-effect on the path alignment is comparable to that in agarose. The faster overshoot in the PEO-modified gel means that the DNA ends migrate faster in the absence of electroosmosis, which is in agreement with that the macroscopic electrophoretic velocity of DNA measured on slab gels is higher with PEO present (Figure 1). The center-of-mass velocity (Vcom) increases more, by a factor of 2.3 compared to about 1.7 for the velocities of the ends (Figure 5). The two velocities are not simply related, however, because Vcom is an average over the whole migrative cycle. The cyclic conformational dynamics complicates the interpretation of Vcom for instance by leading to a strongly nonlinear dependence on the field strength,13 whereas the overshoot time has a simple molecular interpretation. Overshoot Amplitude and DNA-Gellan Interactions. The maximum relative overshoot in the gellan gel (Figure 4) is less than 0.1 in the presence of PEO and as small as 0.01 in its absence and, thus, considerably smaller than in agarose where it is 0.4 (11). The oscillation amplitude in LD is sensitive to the degree of coherence in the responses of the different molecules of the ensemble that contribute to the spectroscopic average.7,19 Even though it is known from microscopy observations that each molecule continues to migrate in an oscillatory fashion, usually only one LD oscillation (overshoot and undershoot) is observed because the coherence necessary for an oscillatory response of the whole ensemble is lost after about one migrative cycle.7 The reason is that the gel interactions which cause the cycling by leading to hooking of the DNA are stochastic because of gel heterogeneity. The distribution of period times therefore is wide, with a width similar to its mean,7 resulting in that the initially coherent cycles performed by different molecules become out of phase already after about one period.20 One mechanism that may increase the heterogeneity in DNA-gel interactions is attractive interactions between the DNA and gel. This is illustrated by observations in agarose gels that have been covalently modified with ethidium bromide, a

Markstro¨m et al. DNA intercalator which provides points of affinity between DNA and gel21 and where the overshoot amplitude is reduced compared to the unmodified gel. Interestingly, one possible reason for the reduced overshoot in gellan gels is an attractive DNA-gel interaction mediated by calcium ions forming electrostatic bridges between DNA phosphate charges and the negative charges of the gellan fibers. Such interactions could also explain the low velocity in gellan gels, because similar retardation is observed in the affinity-modified agarose.21 However, the agarose system also shows that the transient affinity-anchoring to the gel network gives rise to an increase in DNA stretching (Sstr) compared to gels without affinity (Table 1). In contrast, the DNA stretching is unusually weak in native gellan gels (without PEO) when compared to (native) agarose gels (Table 1), where no attractive DNA-gel interactions are believed to occur. This is a strong argument against that attractive interactions between DNA and gellan gels cause the slow migration. A more likely explanation for the unusually low degree of DNA stretching in gellan gels is instead that the hooked DNA chain will experience a drag force from the electroosmotic flow which is opposed to the stretching electric force. Similar compressing effects by electroosmotic flows on anchored DNA have been used22 to explain an unexpectedly weak stretching23 of such tethered chains in electric fields. This mechanism would also explain the low overshoot amplitude without the need for attractive interactions, because the overshoot is due to stretching of the DNA in the transiently anchored U formation.15 PEO Effects on the Drag on DNA. The fast component of the field-free relaxation reflects the release of chain tension as the stretched DNA polymer contracts along its path in the gel. This sliding motion is similar to the end-on stretching and sliding motion which occur during migration.7,13 The rate of field-free relaxation of DNA can thus be used to study the effect of PEO on a migration-mimicking DNA motion but which occurs in the absence of an electric field. This allows the direct PEO effect to be investigated separate from the indirect PEO effect, but only if the electroosmotic flow ceases faster than the DNA relaxation process so the latter occurs in the absence of the flow. The relaxation time for the electroosmotic flow can be estimated from a study of its dynamics in capillaries used for microelectrophoresis.24 In a 1 mm capillary, the electroosmosis relaxation time in water is shorter than 1 s. The relaxation time has a quadratic dependence on the diameter of the channel,24 so in a 100 nm channel (estimated pore size), the electroosmosis should cease in less than a millisecond. This time scale is much shorter than the typical relaxation times of seconds or longer for the DNA conformation (Figure 6), and the electroosmotic flow therefore should have a negligible effect on the DNA relaxation. The results of Figure 9 shows that at a given field strength the relaxation is faster in the presence of PEO. This suggests that the resistance to DNA motion is lower when PEO is present, in apparent agreement with the enhancing effect of PEO on the center of mass (Figure 1) and end velocity (Figure 5) of the DNA. However, the comparison of relaxation rates must take into account the fact that the relaxation time decreases markedly with increasing field. Recent single-molecule experiments in free solution (no gel) show that the relaxation modes of a stretched DNA polymer have time constants which decrease with increasing tension in the molecule.25 This supports theoretical predictions26 that the relaxation times become fielddependent when a polymer is stretched to the extent that the restoring entropic elastic force becomes nonlinearly dependent on coil extension. Single-molecule stretching experiments27

DNA Electrophoresis in Gellan Gels

Figure 11. Time constant for the fast field-free relaxation vs the degree of DNA alignment at the start of the field-free relaxation. Data on time constants with (solid) and without (open) PEO are from Figure 8, and steady-state orientation factors at corresponding field strengths are from Figure 3.

show that such non-Hookean behavior occurs approximately when the end-to-end distance of the DNA exceeds one-third of the contour length. Direct microscopy measurements of the endto-end distances during migration in agarose gels7 show that the typical electrophoretic field strengths used here are strong enough to cause such degrees of coil deformation, which explains the strong field-dependence in the relaxation rates in agarose.11,14 The degree of stretching in gellan gels is lower (Table 1), but it is likely that the field dependence in τ70 (Figure 9) has a similar origin. This is supported by the observation that the field dependence is weaker in the absence of PEO where the stretching also is weaker and by the fact that the reptation time does not exhibit such a decrease with increasing field (Figure 7) because the tension in the DNA has relaxed when this process occurs. The effect of added PEO on the fast relaxation process can therefore only be found by comparing the rates with and without PEO when the relaxation occurs from the same initial degree of coil stretching (as opposed to occurring at the same field strength). This can be accomplished by plotting τ70 vs the orientation factor Sss, which characterizes the degree of coil alignment at the start of the relaxation process, when the field is turned off. Figure 11 shows the data of Figure 9 plotted in this fashion. It is seen that the two data sets fail to overlap, which is because the degree of migrative coil deformation is overall considerably higher in the presence of PEO (Figure 3). However, Figure 11 also shows that within each of the data sets there is a monotonic variation of the relaxation time with the degree of DNA alignment, as expected from a model based on a non-Hookean restoring force. Therefore, a slight extrapolation over the small gap of nonoverlapping Sss values in Figure 11 can be made safely, to state that the relaxation time is longer in the presence of PEO if compared at the same degree of initial stretching. We thus conclude that the PEO indeed slows down the DNA sliding motion during field-free Brownian relaxation in the gellan gel. On the basis of the closest points in the two sets of data, the difference in relaxation rate is lower by approximately a factor of 7 ( 1, which reflects the increased drag because of the PEO. This should be compared to the fact that the velocity in the presence of PEO is lower than the velocity in PEO-free gel by a factor of 6.3, when the latter is corrected for electroosmosis

J. Phys. Chem. B, Vol. 106, No. 9, 2002 2355 (Figure 10) assuming it makes an additive contribution. The fact that the two values agree within experimental uncertainty supports this correction procedure. In this picture, the faster U formation (Figure 5) with PEO as well as the increase in centerof-mass velocity (Figure 1) is thus the net outcome of two opposing and additive effects: an indirect effect in terms of a decreased electroosmotic drag and a direct one causing an increase in the resistance to DNA motion which is due to the PEO chains themselves. Mechanism of Electroosmosis Reduction and Drag Increase by PEO. One possible mechanism for PEO to reduce electroosmosis is that it adsorbs to the gellan fibers, because adsorption of PEO to negatively charged silica surfaces is used to reduce electroosmosis in capillary electrophoresis.28 Interestingly, this would also explain why the reptation time is essentially unaffected by the PEO (Figure 7), because the PEO would not be present in the gellan pores. Contradicting this explanation is the observation that the gellan gel is intact even if enough PEO is added so that the electroosmosis is quenched completely, i.e., all negative charges have been rendered inactive. It is also difficult to explain how the PEO could reduce the rate of field-free relaxation so strongly (Figure 11), if it is not present in the pores. An alternative explanation is that the PEO is not adsorbed but retains its free-solution radius of gyration of 130 nm (Table 1), which is likely to be large enough for the PEO coils to be entangled with the gellan gel. In such a case, they would not move with the electroosmostic flow but rather add to the hydrodynamic resistance of the network by spanning the pores in which the electroosmosis is flowing. This would explain why the indirect PEO effect on DNA velocity (reduced electroosmotic drag) is nearly compensated by the direct one because the DNA is moving through the same pores as the flow and therefore will experience a similarly enhanced hydrodynamic drag because of the added PEO. Enhanced hydrodynamic drag would explain the fact that the field-free stretch relaxation is slower in the presence of PEO (Figure 11) but should also retard reptation in contrast to observation (Figure 7). A hydrodynamic picture of the direct PEO effect may be an oversimplification, however. The PEO concentration of 0.3% is slightly above the overlap concentration for the present PEO size.31 If nonadsorbed, the PEO can thus be expected to give rise to a second network by itself inside the gel, through which the DNA molecules are moving (at dilute concentrations, the overlap concentration for T4 is 0.15 mM phosphate11). Entanglements with the PEO network would cause retardation of migrating DNA, in a manner which resembles how such PEO solutions are used as sieving media in capillary electrophoresis.32 Relaxing DNA would also be affected but potentially to a different extent for the different phases of the field-free relaxation depending on the lifetime of the DNA-PEO entanglements. A comparison can be made with how transient gel contacts in affinity-modified agarose gels21 does retard the stretch relaxation, because the lifetime of the DNA-gel attachments (about 0.1s) is comparable to the seconds time scale of this process, but have no detectable effect on the subsequent reptation step because the attachment points are renewed many times on the time scale of minutes for this process. The lifetime of the DNA entanglements in a nondilute PEO solution will be determined by the dynamics of the PEO network. To our knowledge, there are no studies of PEO confined in a gel, but a rough picture of the PEO dynamics can be obtained by comparison with the more well-studied case of DNA in gels. The longest relaxation time of the PEO network

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Markstro¨m et al.

would be the reptation time of the PEO given by16

τR )

ζb (Nb)3 a2π2kT

(2)

where N, b, and ζ are the number, length, and friction coefficient of the polymer segments, respectively, and a is the effective pore size of the gellan gel. For DNA τR is about 300 s (Figure 7), and the value for PEO can be estimated by comparing the parameters in eq 2 for DNA and PEO, assuming that the effective mesh size (a) is the same. Table 1 shows that the contour length (Nb) is very similar for T4 DNA and the PEO used here but that the segment length is about 50 times lower for PEO. The segment friction coefficient will also be lower for PEO, by a factor of about 6 as estimated from the data in Table 1 when used in the expression for a rigid rod of length b and radius r

ζ)

6πηb ln(b/r) - 0.3

(3)

where η is the viscosity assumed to be the same for DNA and PEO. The predicted reptation time for PEO will therefore be about 300 times lower than for DNA, i.e., on the order of a second.33 The confining effect of the PEO network on the DNA will thus relax fast on the time scale of DNA reptation, but the PEO-DNA entanglements would survive at least partially on the time scale of the stretch relaxation. This could explain why in analogy with transient affinity21 the PEO retards destretching (Figure 10), as well as the build-up of DNA alignment which occurs on the same time scale of seconds (Figure 5) but has no detectable effect on the reptation (Figure 7). Effect of Electroosmosis on DNA Migration. In addition to slowing DNA down, the main effect of electroosmosis is to reduce the degree of DNA alignment (Figure 3). This occurs through a considerable weakening of the stretching of the DNA along the path in the gel (Table 2), whereas the alignment of the path itself is little affected by the added polymer (Inset Figure 8). These conclusions are as deduced by comparison with PEO-modified gellan. The alternative possibility that the large difference in stretching is due to that entanglements with added PEO gives rise to an unusually strong DNA stretching is unlikely, because Table 2 shows that the degree of stretching also with PEO is small when compared to that in agarose gels. As discussed above, a decreased electrophoretic stretching is expected from the counter-directed electroosmotic flow, acting on the length of the whole chain. The path alignment, on the other hand, only involves the very leading end of the DNA, because it is this part of the molecule which selects the next path segment.18 The electric field tends to orient the head of the DNA molecule, which leads to a more field-aligned tube as the field is increased as is observed (inset of Figure 8). The electroosmotic flow will create an opposing torque on the orienting head, but because the length of DNA involved is only about one pore size, the corresponding lever is short. The effect

of quenching the flow is therefore expected to be small, which could explain why the increase in tube alignment when PEO is added is small (inset of Figure 8) compared to the effect on the overall alignment (Figure 3). References and Notes (1) Cole, K. BioTechniques 1999, 26, 748. (2) Cole, K. D.; Tellez, C. M.; Nguyen, R. B. Appl. Biochem. Biotech. 1999, 82, 57. (3) Long, D.; Viovy, J. L.; Ajdari, A. Phys. ReV. Lett. 1996, 76, 3858. (4) Stigter, D. Macromolecules 2000, 33, 8878. (5) Magnusdottir, S.; Åkerman, B.; Jonsson, M. J. Phys. Chem. 1994, 98, 2624. (6) Smith, S. B.; Aldridge, P. K.; Callis, J. B. Science 1989, 243, 203. (7) Larsson, A.; Åkerman, B. Macromolecules 1995, 28, 4441. (8) Carlsson, C.; Larsson, A.; Jonsson, M. Electrophoresis 1996, 17, 642. (9) Jonsson, M.; Åkerman, B.; Norden, B. Biopolymers 1988, 27, 381. (10) Norden, B.; Elvingsson, C.; Jonsson, M.; Åkerman, B. Quart. ReV. Biophys. 1991, 24, 103. (11) Åkerman, B.; Jonsson, M.; Norden, B.; Lalande, M. Biopolymers 1989, 28, 1541-1571. (12) Larsson, A.; Carlsson, C.; Jonsson, M.; Albinsson, B. J. Am. Chem. Soc. 1994, 116, 8459. (13) Åkerman, B. Electrophoresis 1996, 17, 1027. (14) Mayer, P.; Sturm, J.; Weill, G. Biopolymers 1993, 33, 1347. (15) Mayer, P.; Sturm, J.; Weill, G. Biopolymers 1993, 33, 1359. (16) Doi, M.; Edwards, S. F. Theory of Polymer Dynamics; Clarendon Press: Oxford, U.K., 1986. (17) Pernodet, N.; Tinland, B.; Sturm, J.; Weill, G. Biopolymers 1999, 50, 45. (18) Viovy, J. L. ReV. Mod. Phys. 2000, 72, 813. (19) Deutsch, J. M. J. Chem. Phys. 1989, 90, 7436. (20) Carlsson, C.; Larsson, A. Electrophoresis 1996, 17, 1425. (21) Åkerman, B. J. Am. Chem. Soc. 1999, 121, 7292-7301. (22) Stı´gter, D. Biopolymers 1991, 31, 169. (23) Smith, S. B.; Bendich, A. J. Biopolymers 1990, 29, 1167. (24) Minor, M.; van der Linde, A. J.; van Leeuwen, H. P.; Lyklema, J. J. Coll. Interface Sci. 1997, 189, 370. (25) Quake, S. R.; Babcock, H.; Chu, S. Nature 1997, 388, 151. (26) Tanner, R. I. Engineering Rheology; Clarendon Press: Oxford, U.K., 1985; Chapter 5. (27) Bustamante, C.; Smith, S. B.; Liphardt, J.; Smith, D. Curr. Opion. Struct. Biol. 2000, 10, 279. (28) Preisler, J.; Yeung, E. S. Anal. Chem. 1996, 68, 2885-2889. (29) Nya Crothers (30) Kawaguchi, S.; Imai, G.; Suzuki, J.; Miyahara, A.; Kitano, T.; Ito, K. Polymer 1997, 38, 2885-2891. (31) Madabhushi, R. S.; Vainer, M.; Dolnik, V.; Enad, S.; Barker, D. L.; Harris, D. W.; Mansfield, E. S. Electrophoresis 1997, 18, 104. (32) Wei, W.; Yeung, E. S. J. Chromatogr. B 2000, 745, 221-230. (33) In this analysis, the effects of PEO-PEO entanglements on the PEO reptation are incorporated in the effective mesh size a. To our knowledge, PEO-network dynamics have only been studied in the melt where reptation times on a similar time scale of seconds or faster are observed,34,35 although it should be remembered that the melt exists at higher density and higher temperature than the PEO solutions used here. (34) Cohen Addad, J. P.; Guillermo, A. J. Chem. Phys. 1999, 111, 71317138. (35) Kimmich, R.; Seitter, R. O.; Beginn, U.; Mo¨ller, M.; Fatkullin, N. Chem. Phys. Lett. 1999, 307, 147-152. (36) Pernodet, N.; Maaloum, M.; Tinland, B. Electrophoresis 1997, 18, 55. (37) Maaloum, M.; Pernodet, N.; Tinland, B. Electrophoresis 1998, 19, 1606.