Gel-Shift Assays - American Chemical Society

J. Phys. Chem. B 2001, 105, 12879-12893

12879

Gel-Shift Assays: Migrative Dissociation of a RecA-Oligonucleotide Complex during Electrophoresis in Hydroxyethylated Agarose Gels Roine Svingen,† Masayuki Takahashi,‡ and Bjo1 rn A° kerman*,† Department of Physical Chemistry, Chalmers UniVersity of Technology, Go¨ teborg, Sweden, and Department of Biocatalysis, UniVersity of Nantes and Centre National de la Recherche Scientifique, Nantes, France ReceiVed: May 3, 2001; In Final Form: September 6, 2001

We investigate the dynamics of a protein-DNA complex under gel-shift assay conditions, in particular how the degree of gel confinement influences the complex stability during the electrophoretic analysis. The fiberlike complex between RecA proteins and a single-stranded oligonucleotide has been studied in hydroxyethylated agarose gels with the average pore radius being between 1 and 5 times larger than the radius of the rodshaped complex. The confining effect of the gel matrix slows down the dissociation of the complex, but in addition, migrative interactions (collisions) with the gel network during the electrophoresis perturbs the complex in two ways. At low gel concentrations, the protein-DNA complex is dismantled into free RecA and oligonucleotide with a half-time of the complex that decreases with increasing field strength in accordance with a migrative mechanism. At a given field strength, the half-time increases with increasing gel concentration despite more frequent interactions, probably because of a counteracting stabilizing cage effect from the gel. At high gel concentrations, a second type of perturbation is reflected in an increasing complex velocity over time, probably caused by trains of end-to-end attached fibers being broken up by interactions with the tight gels.

Introduction Many biological processes require the formation of macromolecular complexes, for example, the protein-DNA complexes involved in DNA transcription or DNA-DNA complexes such as triplexes formed in antigene approaches. A useful method to study the stoichiometry and thermodynamics of such complexes is the gel-mobility-shift (or gel-retardation) assay.1-5 The formation of a complex is monitored through an altered electrophoretic velocity of one of the components when it becomes complexed, which is detected as a shift of the position on an electrophoresis gel compared to the position of the component when it is free. Specific detection is accomplished by labeling one of the components, and in DNA-protein complexes, it is often the nucleic acid component that carries a radioactive or fluorescent marker.6 In porous gels, large mobility shifts often occur because of the larger size of the complex compared to the components, but it has been demonstrated recently that mobility-shift assays also can be performed in free solution by capillary electrophoresis.7,8 Comparison with DNase I foot-printing assays9 has shown that it is possible to measure binding constants by the gel-shift approach under suitable circumstances. In most studies to date, the approach has been to find conditions under which the equilibrium distribution between free and complexed forms is not affected by the electrophoretic analysis. Because the electrophoretic separation of the complex from the uncomplexed components disturbs the mass-action equilibrium, it is generally required that the dissociation rate of the complex is slow compared to the time needed for the electrophoretic separation. * To whom correspondence should be addressed. Tel: 46317723052. Fax: 46317723858. E-mail: [email protected]. † Chalmers University of Technology. ‡ University of Nantes and Centre National de la Recherche Scientifique.

An interesting but nontrivial approach to freezing the equilibrium distribution is cryoelectrophoresis in which the equilibrated sample is rapidly quenched and analyzed electrophoretically at subzero temperatures.10 Importantly, the gel itself may have a stabilizing effect because the complex lifetime in the gel is often found to be longer than that in free solution. This has been ascribed to a cage-effect.11 The gel network retards further separation in space of the components of complexes that have dissociated, and this leads to an enhanced probability of a reassociation compared to that in free solution. In addition, the dissociation step may be retarded by the gel, if the dissociation requires complex-complex interactions.12 Then, an extra gelstabilizing effect (sequestering) can be that the matrix reduces the probability of such encounters.13 Both effects can help to preserve the equilibrium distribution that was established in the sample before loading on the gel. These examples demonstrate that an understanding of the dynamics of macromolecular complexes in gels is important for developing the retardation assay, for example, for cases in which the complexes do dissociate on the time scale of the electrophoretic separation.14 Gels are also interesting model systems for studying the effects of confinement on the dynamics of macromolecular complexes. Association kinetics in gels has been measured by exploiting the fact that when the two components have different mobilities they can be mixed electrophoretically in the gel. This approach has been used, for example, to demonstrate the sequestering effect mentioned above for the binding of the lac repressor15 and the CAP protein13 to DNA. Dissociation rates, on the other hand, can be measured by monitoring the decreasing amount of complex as a function of electrophoresis time.16 With the lac repressor and the CAP protein, the dissociation of the complex was slower in the gel than in free solution and became slower as the gel was made denser in agreement with a stronger confinement of the separate

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12880 J. Phys. Chem. B, Vol. 105, No. 51, 2001 components. Furthermore in both cases, the rate of dissociation was independent of field strength, suggesting that it occurs by the same mechanism as in free solution but is retarded by the gel matrix. Here, we report a case in which a DNA-protein complex dissociates during gel electrophoresis with a rate that increases with increasing field strength. This behavior reveals a new type of macromolecular complex dynamics under conditions typical for gel-shift assays. The RecA-DNA complex that we investigate differs from many other complexes investigated by gel-shift assays in that the protein does not bind to a particular site of the DNA but instead covers the nucleic acid and forms a fiberlike complex.17,18 Because of its biological function as a catalyst for strand exchange during genetic recombination,19 the complex can contain up to three single strands of DNA.20 RecA is also an ATPase, and the hydrolysis of ATP is involved in the release of the protein component after strand exchange.21 Here, we focus on the simplest form of RecA-DNA complex, which contains one DNA strand, the so-called presynaptic complex. We use the nonhydrolyzable cofactor analogue ATPγS, which leads to a much more stable complex than that with ATP, a fact that has been used in studies of the structure and dynamics of the presynaptic complex.21,22 To promote the formation of only onestranded complexes, we used an excess of RecA. It was suspected that the spatial distribution of the unbound protein in the gel might affect the association and dissociation dynamics of the complex during the electrophoresis. In this study, we have therefore fluorescently labeled the protein component also but with a different color than that used for the nucleic acid so that the spatial distribution of the two components could be monitored independently. Tight gels such as polyacrylamide gels are used in gel-shift assays of RecA-DNA complexes.23 The small pore sizes promote efficient separation of complex and free DNA and allow the use of short, well-defined DNA targets such as oligonucleotides without having extensive band broadening due to diffusion. In fact, the pores can be made small enough to fully arrest DNA molecules that are covalently end-modified with a streptavidin by trapping the bulky protein.24 Here, we have instead used hydroxyethylated agarose gels, which have pore sizes in a similar range as polyacrylamide gels and which are useful in gel-shift applications.25 Our aim is to study gelstabilization and electrophoretic dissociation in tight gels in which the typical pore size is similar to the protein-DNA complex dimensions. To this end, we use the pore sizes of hydroxyethylated gels measured here for the first time and the well-known and uniform dimensions of the cylinder-like presynaptic RecA-DNA complex. An advantage with these agarose-type gels is that they are likely to form a more homogeneous matrix than the free-radical-polymerized polyacrylamide. The average pore size is therefore likely to be more representative of the degree of complex confinement than in polyacrylamide gels. Materials and Methods Chemicals. The 30-base single-stranded oligonucleotide with 5′-fluourescein label and the sequence Fl-5′-GTA-AGA-GCTTCT-CGA-GCT-GCG-CAA-GGA-TAG-3′ was obtained from Medprobe. Stock solutions of 8.7 mM (strands) were made up in water with concentrations determined by spectroscopy using an extinction coefficient of 296 200 M-1 cm-1 (strands). RecA was prepared as described previously.26 Stock solutions in 20 mM potassium phosphate (pH 6.8), 10 mM β-mercaptoethanol, and 50% glycerol were 107 µM in protein. Long-term storage

Svingen et al. was at -80 °C and short-term storage of 100 µL aliquots was at -20 °C. Nile red and ATPγS from Sigma and Metaphor agarose from FMC BioProducts were used without further purification. Concentrations of oligonucleotide and complexes are given in strands. Complex Formation. Presynaptic filament between RecA and oligonucleotide was formed by mixing 10 µL of reaction buffer, 2.4 µL of stock oligomer solution (final concentration, 1 µM), 3.6 µL of stock RecA solution (final concentration, 19 µM), and 2.0 µL of stock ATPγS solution (final concentration, 2 mM). The reaction buffer was a mixture of equal volumes of 400 mM Tris-sodium acetate, 90 mM magnesium acetate, 1 M potassium acetate, 10 mM dithiothreitol, and 1µg/µL bovine serum albumin. TBE (50 mM borate, 50 mM tris, 1.25 mM EDTA, pH)8.2) buffer was then added to a final volume of 20 µL. An almost 2-fold excess of RecA was used to ensure that only complexes with one oligonucleotide strand were formed. This complex contains one RecA per three bases 27 or 10 RecA per oligonucleotide in our case. The sample was equilibrated at 37 °C for 1 h. Control experiments showed that under these conditions the fiber formation had reached equilibrium. For a final concentration of 9.6 µM of RecA, in the well 10 µL of the sample solution was mixed with 6 µL of TBE buffer and 4 µL of 15% Ficoll to a final volume of 20 µL. Bromophenol blue, usually used as an electrophoresis marker, was found to bind to RecA, so it was avoided in most experiments, although there was no detectable effect on the complex formation with DNA. The rate of dissociation of the complex in free solution was measured by adding a 20-fold excess of nonlabeled oligonucleotide to the presynaptic complex formed by the standard protocol to capture released protein. Aliquots of 14 µL were removed at regular intervals and analyzed by gel electrophoresis to measure the increase in the amount of noncomplexed labeled oligonucleotide. The dissociation was slow so that only a lower limit of 200 min could be determined for the half-time of the complex (with ATPγS). Electrophoresis. Gels were prepared by dissolving the appropriate amount of agarose powder in TBE and heating the solution under stirring to boiling for 5 min. Horizontal gels of various concentrations were cast to give wells for 10 samples and with a thickness of 8-10 mm and length of the lanes of 70 mm. Sometimes different gel concentrations were run in parallel by making multigels. Electrophoresis was run in submarine mode, and the electric field strength in the gel was measured by two platinum electrodes placed 1 cm apart. Electrophoresis was arrested at certain time intervals for scanning of the fluorescence, and each gel scan interrupted electrophoresis for about 2-3 min. In one type of experiment, the duration of migration in the well before entering the gel was varied by making a set of wells of different lengths in the field direction, varying between 1.5 and 7 mm (standard was 3 mm). The different wells were loaded with the same sample but with the volumes being proportional to the well length. Electrophoresis was then run for 31 min at 5 V/cm in the 2.5% gel. In some experiments, ATPγS was added to the electrophoresis buffer to test potential effects of electrophoretic transport of the cofactor. To save material, in those experiments, the gels were formed in a cylindrical glass capillary (inner diameter 3 mm, length 100 mm) that could be attached at each end to two separate buffer chambers containing the electrodes. The sample was loaded at one end of the capillary and locked into position by a gel plug before the capillary was assembled with the buffer

Gel-Shift Assays: Migrative Dissociation chambers. Also, the capillary was scanned intermittently during the electrophoresis, using the same scanning protocol as for the submarine gels. Control experiments under the conditions of the submarine experiments (without ATPγS in the gel and buffer chambers) were conducted by the same capillary method. In the submarine gels, the samples were introduced into a starting position a few mm into the gel by the same preelectrophoresis step at 3 V/cm for 20 min, to have the same initial conditions for the dissociation experiments conducted at different field strengths. The initial complex concentration at the starting position varied between different gel concentrations because the zone widths are affected by the relative velocity in the gel and in the well. Comparison of dissociation rates between different gel concentrations thus required the dissociation rates (see below) to be corrected for the effect of initial complex concentration at the starting position. (This was not necessary for comparisons at different field strengths at a given gel concentration). The effect of initial complex concentration was determined by loading the same volume of sample at different total concentrations on the same 2.5% gel, running the preelectrophoresis step and then measuring the rate of dissociation of the complex at 2 V/cm. The rate of complex dissociation was found to be linearly related to the complex concentration in the range of initial complex concentrations that was obtained at different gel concentrations (after pre-electrophoresis). The rates of dissociation were corrected to an initial concentration of 9 µM complex by a linear interpolation procedure. Scanning and Data Evaluation. Gels were scanned for fluorescence intensity with an FluorImager 595, Molecular Dynamics. With fluorescein (oligonucleotide), excitation was at 488 nm and detection was with a 530 ( 30 nm band-pass emission filter. Control gels showed that the integrated fluorescence signal was proportional to the loaded amount of (noncomplexed) oligonucleotide in a range that exceeded the amounts used in the dissociation studies by a factor of at least three. In the gel scans, as the complex dissociated into free oligonucleotide, the total integrated intensity over all of the bands in a given lane increased by less than 5% over time, probably because of a partial quenching of the fluorescein label by bound RecA as supported by experiments in microtiter plates at the same the scanner settings. The amount of oligonucleotide in the different components was taken to be proportional to the integrated intensity of the corresponding separated zone. To detect the position of the RecA, in some cases, the gel was stained with the fluorescent protein dye Nile red28 by submersing the gel first in a 0.05% SDS solution for 30 min and then in a 63 µM Nile red solution in 7.5% acetic acid. With Nile red, excitation was at 514 nm and emission was collected with a long pass filter of 630 nm. In general, each lane contained three components as monitored by the oligonucleotide label: the complex, free oligonucleotide, and between them a smear of oligonucleotide, which had been released from the complex during electrophoresis in the gel. The status of the oligonucleotides in the smear was investigated by running a perpendicular electrophoresis step. The gel was rotated by 90 degrees after the separation pattern in the first dimension had been scanned, and electrophoresis in the new direction was run at 10 V/cm for an additional 15 min. The migration velocity of the oligonucleotides in the smear was evaluated by determining the velocity of the sharp edge of the smear in the perpendicular direction. The integrated intensity of the three components was obtained from the intensity profiles along the lane after subtraction of a reference profile obtained from a neighboring sample-free lane.

J. Phys. Chem. B, Vol. 105, No. 51, 2001 12881 Resolution of the overlap between smear on one hand and the zones of the complex and the free oligonucleotide on the other hand was made by assuming symmetric peak shapes for the two distinct zones and ascribing the rest of the intensity to the smear. The data evaluated from each scan were the relative amount of oligonucleotide in the complex, the smear, and the zone of free oligonucleotide and the zone positions as defined by the position of the maximum intensity. The set of intensity and position data obtained from the repeated scans after different electrophoresis times was used to determine the rate of complex dissociation and the velocity of each of the zones. The rate of complex dissociation was evaluated from semilogarithmic plots of the integrated intensity of the complex zone, normalized to its initial intensity at the starting position. The velocity (as a function of time) was evaluated by numerically taking the derivative of the peak-position data with respect to time. Pore Sizes. Pore sizes were obtained by the Ogston approach as used by Slater and co-workers,29 in which the average pore radius at a certain gel concentration equals the radius-of-gyration of the DNA size, which in that gel has half the mobility of DNA in free solution. HaeIII restriction fragments of the ΦX174 plasmid were used as size probes and run at different gel concentrations between 0.5% and 3.5%, and the gel concentration at which each of the fragment sizes had half the freesolution mobility29 were determined by interpolation. The average pore radius was then obtained as the radius-of-gyration calculated from the known contour lengths with the wormlike chain model using a persistence length of 50 nm.30 This approach was chosen so that comparison could be made with pore sizes measured in other types of agarose gels. Results Gel Shifts for the Complex between RecA and Oligonucleotide. Figure 1a shows a fluorescence scan (490 nm excitation) of a gel after electrophoretic analysis of the complex between RecA and a 30-base fluorescein-labeled oligonucleotide (left lane). The gel shows two bands in the sample lane, and because only the oligonucleotide is visible at the wavelength used, this observation demonstrates that the oligonucleotide exists in two distinct states in the mixture with RecA. Comparison with the control sample containing noncomplexed oligonucleotide (right lane) indicates that the fast and slow components correspond to free and RecA-complexed oligonucleotide, respectively. The fast component has a mobility that is similar to the control, whereas the position of the slow component corresponds to a strong shift of the oligonucleotide toward the starting position, i.e., to a markedly reduced velocity compared to free oligonucleotide. Such a shift is consistent with the observation that the complex between RecA and an oligonucleotide is a fiberlike complex, which is thick17 and stiff31,32 compared to the oligonucleotide itself and therefore will experience a stronger retardation as a result of a stronger interaction with the gel network. The gel shift to lower velocities is in agreement with earlier results23 obtained in polyacrylamide gels. The band assignments given above are supported by observations of the protein distribution in the gel by protein-specific staining with the dye Nile red.28 The same gel used for DNA scanning (using fluorescein) was post-stained with Nile red and scanned with 514 nm excitation (Figure 1b). In the sample lane (left), RecA is seen to form a zone at the same position as the slow oligonucleotide component, whereas no RecA could be

12882 J. Phys. Chem. B, Vol. 105, No. 51, 2001

(a)

(b)

(c)

Figure 1. Gel-electrophoretic analysis of RecA-oligonucleotide complex run. (a) Distribution of fluorescein-labeled oligonucleotide in agarose gel after electrophoresis (4 V/cm in 3% metaphor for 80 min) of sample containing the RecA-oligonucleotide mixture (C) and of the two control samples containing either RecA (R) or oligonucleotide (SS). The gel was scanned for fluorescence using excitation at 488 nm, and emission was measured with a 530 ( 30 nm band-pass filter. (b) Same gel scanned after staining with the fluorescent protein stain Nile red. Excitation was at 514 nm, and emission was measured with a 630 nm long-pass filter (where fluorescein emission is negligible as seen from the lack of intensity in the SS lane). (c) Concentration profiles for oligonucleotide (fluorescein) and protein (Nile red) (from part a and b, respectively) were measured as intensities (arbitrary units) along sample lane (thick line) and along corresponding control lanes (thin line), i.e., R lane for the Nile red and SS lane for the fluorescein scan. The Nile red profiles have been shifted upward for the sake of clarity.

detected at the position of the fast band, nor in the oligonucleotide control (right lane). The latter observation shows that Nile

Svingen et al. red does not bind to the nucleic acid component and thus can be used to specifically detect the location of the protein. The Nile red staining thus confirms that the slow oligonucleotide zone in the sample lane corresponds to the complex with RecA. Fluorescence intensity profiles obtained from Figure 1a,b (Figure 1c) show that the RecA distribution in the sample lane is somewhat broader than the width of the slow oligonucleotide zone. The difference in shape indicates that not all RecA is bound in an oligonucleotide complex, which is expected because an excess of RecA was used to ensure that only one-stranded complexes with the oligonucleotide are formed. Control experiments in which the ratio of RecA to oligonucleotide was varied confirmed that the approximate 2-fold protein excess is high enough to ensure that the complexes studied here contain one oligonucleotide (results not shown). Figure 1b also shows that the RecA control sample (middle lane) exhibits a similar protein zone at approximately the same position as the complex zone. The observed direction of migration of the free RecA is in agreement with the negative charge, which is expected for free RecA at the used pH of 8.2 because its isoelectric point is between 5 and 6.21 The observation that the position of the RecA-oligonucleotide complex is very similar to that of the RecA control band is in interesting contrast to the strong shift of the complex with respect to the oligonucleotide control. Below, we will discuss this and two additional observations that can be made from a more detailed inspection of the fluorescence intensity profiles of Figure 1c. Albeit to a much lesser extent than for the complex zone, also the fast sample zone (oligonucleotide) exhibits differences compared to the oligonucleotide control: the sample zone is more narrow and its position is slightly shifted to lower velocity compared to the control. Secondly, there is a smear of oligonucleotide (490 nm) between the fast- and slow-sample zones, which is not seen in the Nile red scan (514 nm) of the sample lane. Surface Properties of the Presynaptic Complex. The lack of gel shift for the complex with respect to free RecA is surprising because the RecA protein is comparable in size to the oligonucleotide and is therefore also expected to migrate faster through the pores of the gel than the considerably larger RecA-oligonucleotide complex. It could be argued that a higher friction for the RecA-oligonucleotide complex due to its bulkiness (compared to the RecA monomer) is expected to be partly offset by an increase in electric force on the complex due to the extra negative charge that is contributed by the oligonucleotide component. However, studies by isoelectric focusing33 have shown that free RecA and RecA-oligonucleotide complexes have the same isoelectric point, despite the extra negative charge from DNA phosphate groups. The effective charge of the complex in electrophoresis thus seems to be dictated by the RecA. This is reasonable because the electrokinetic properties (σ potential) of a particle are determined by its surface potential and both scanning tunneling microscopy (STM)17,18 and electron microscopy34,35 studies show that the protein covers a large fraction of the oligonucleotide. A similar effect is the observation that charged amino acids that are located internally in a protein may not contribute to its electrokinetic properties unless the protein is denatured.36 The DNA charges can therefore not be invoked to give a compensating stronger electric driving force to explain the similar electrophoretic mobilities of the complex and free RecA, which are observed despite the bulkiness of the fiber. Interestingly, it is known from small-angle neutron scattering (SANS) and electron microscopy studies that RecA forms helical fibers also in the absence of DNA.21 Such an extended structure is expected to experience

Gel-Shift Assays: Migrative Dissociation

J. Phys. Chem. B, Vol. 105, No. 51, 2001 12883

Figure 2. Electrophoretic velocity in the gel. Plots of position of zones vs electrophoresis time are shown for the fast (free oligonucleotide) (b) and slow (complex) ([) components of the sample and for the control oligonucleotide (9). Good fit to straight lines indicates normal migration with a constant velocity, which is calculated from the slope. Gel concentration was 2%, and field strength was 6 V/cm.

Figure 3. Dissociation of complex during electrophoresis in the gel. Oligonucleotide concentration profiles along the sample lane after indicated times of electrophoresis are shown. Position of intact complex (C) and border between complex zone and smear of free oligonucleotide (dotted line) are indicated. Field strength was 4 V/cm, and gel concentration was 2%.

much stronger interactions with the gel network than monomeric RecA. However, the state of aggregation is sensitive to environmental conditions,37-39 and the nature of the fiber inside a gel is not known. Furthermore, at least oligomeric states of the fiber are rather dynamic at room temperature,40 so it is uncertain whether the RecA-only fiber will remain intact during migration through a gel. A model in which the surface properties of the complex are dictated by the RecA can thus explain certain electrical properties, such as the isoelectric point, but cannot by itself explain the similar gel mobility for RecA and the complex. Still, it is clear that if a fraction of the RecA molecules dissociate from an oligonucleotide complex, it is likely to increase the electrophoretic velocity of the remaining complex. The reduction of the complex bulkiness will reduce friction, and a higher σ potential will result from the exposed DNA phosphate charges. The Fast Sample Component is Free Oligonucleotide from Which RecA Dissociated outside the Gel. The lack of RecA fluorescence at the position of the fast oligonuceotide band (Figure 1a,b, left lane) strongly indicates that this zone contains free oligonucleotide. This is surprising because the excess of RecA in the sample should ensure that the initial amount of free oligonucleotide is very low. Importantly, in our standard protocol, the complex formation has reached equilibrium before the sample is loaded on the gel because longer incubation times did not decrease the amount of oligonucleotide in the fast zone. However, the weak perturbation of the migration of the fast component compared to the oligonucleotide control (Figure 1c) suggests that these oligonucleotides have interacted with RecA. In principle, the fast component could contain oligonucleotides that carry a small amount of still-bound RecA, below the detection-limit of the Nile-red dye but still large enough to cause a weak retardation of the oligonucleotide. However, a plot of the position in the gel of the fast component and of the oligonucleotide control band as a function of electrophoresis time (Figure 2) shows straight lines with the same slope, i.e., the two bands have the same velocity through the gel. This observation supports that the fast band in the sample contains RecA-free oligonucleotide. If a small amount of bound RecA would be the cause of the position shift, the fast band should exhibit a lower slope compared to the control oligonucleotide, as is the case with the intact complex (Figure 2). The observed shift of the fast-sample component is instead seen to be the result of a downward offset of the curve compared to the control oligonucleotide, i.e., to a RecA-induced delay that occurred

before (or possibly upon) entering the gel. Therefore, those oligonucleotides have also been retarded by binding of RecA, but in this case, the RecA dissociated either during migration in the free solution in the well or during entry into the gel. When the length of the well was varied, the ratio of the amounts of oligonucleotide in the fast (free) and slow (complex) zones increased (results not shown). The fact that the relative amounts were affected at all supports that the noncomplexed oligomer in the fast band did not exist in the sample before electrophoresis because variations in the sample volume (at constant concentrations of the components) should not affect the degree of complex formation. The presence of the fast band is thus an effect of the electrophoresis. The fact that the relative amount of free oligonucleotide increased with increasing well length suggests that the dissociation occurred during the migration in the well, before entering the gel, because the average time the complexes spend migrating outside the gel then increases. We conclude that the fast-sample component corresponds to oligonucleotides that did form a complex but lost their RecA before entering the gel as an effect of fielddriven dissociation, most probably during migration in the free solution in the well. The main focus of this study, however, is on the complex stability inside the gel. Electrophoretic Dissociation of the Complex inside the Gel. Also in the gel, electrophoretic migration leads to dissociation of the RecA-oligonucleotide complex. The kinetics of this process was monitored by measuring the amount of the slow component (intact complex) as a function of migration time. Figure 3 shows the fluorescence intensity profiles (490 nm excitation) of the sample lane in a 2% gel after different times of electrophoresis at 4 V/cm. The intensity of the complex peak decreases with increasing time, and at the same time, there is a progressive buildup of the smear that extends downfield from the complex band down to the fast zone of free oligonucleotide (the latter was not included in Figure 3 for the sake of clarity). Figure 1c shows that most of the smear is outside the zone of RecA in the sample lane (as detected with Nile red). This strongly indicates that the smear contains RecA-free oligonucleotides, but again they may, in principle, still carry some RecA below the detection limit of Nile red. We therefore tried to measure the electrophoretic velocity of those oligonucleotides inside the gel, to compare it with that of the control oligonucleotide, as was used in Figure 2 for the fast component. In the present case, the dissociated oligonucleotides do not form a distinct zone so the velocity cannot be evaluated directly from


Figure 4. Semilogarithmic plot of the integrated intensity of the complex zone vs electrophoresis time. Data are from Figure 3.

the electrophoresis experiment. However, when subjected to a perpendicular field the sharp border of the smear which is now leading the migration had the same velocity as the control oligonucleotide (result not shown). This was true along the whole length of the smear, so we can exclude the possibility that the smear is formed by oligonucleotides with, for example, a decreasing amount of RecA bound to them. We thus conclude that the smear contains RecA-free oligonucleotides, which must have dissociated from the complex during migration inside the gel because they are found behind the fast band. The integrated intensity of the slow band in Figure 3, excluding the smear (see Materials and Methods) corresponds to the amount of remaining complex. The approximately linear dependence in a semilogarithmic plot of this entity vs electrophoresis time (Figure 4) reveals a monoexponential decay of the complex. This simple kinetic form was observed under all experimental conditions studied here. The results of the experiments on the electrophoretic dissociation in the gel will therefore be presented in terms of the effect of field strength and gel concentration on the half-time, τi, of the complex derived from the slope (τi ) ln 2/slope). A complication in those studies was the fact that the initial concentration of the complex at the starting position in the gel varied with gel concentration even though the samples were introduced into the gel by the same pre-electrophoresis step (see Materials and Methods). This is most likely due to the fact that the degree of band sharpening upon gel entry depends on the ratio of the velocity in free solution to that in the gel and hence the sharpening was more pronounced at high gel concentrations at which the migration velocity in the gel is lower. The resulting variations in starting concentration affect the dissociation rates measured in the gel. Figure 5 shows the results of dissociation experiments when the starting concentration of complex in the gel was varied intentionally by increasing the sample concentration in the well. The dissociation at constant conditions of field strength and gel concentration is clearly slower at higher starting concentration. To make possible relevant comparisons between dissociation time constants measured at different gel concentrations, the measured half-times had to be corrected to correspond to the same initial complex concentrations (see Materials and Methods). Figure 6 shows the collected data on the half-time, τi, after correction to an initial complex concentration of 9.0 µM. At a given gel concentration, τi is seen to decrease with increasing field strength, which evidences a field-driven dissociation. A log-log plot of these data (inset) reveals an approximate E-1 power law in the half-time at the two lower gel concentrations and a more complex dependence at the highest gel concentration.

Svingen et al.

Figure 5. Effect of complex concentration on the dissociation halftime evaluated from the slope of semilogarithmic plots as in Figure 4. Field strength was 2 V/cm, and gel concentration was 2.5%.

Figure 6. Effect of field strength on complex half-time at different gel concentrations (indicated). Complex concentration was 9 µM. Curves are a guide to eye only. Inset shows a log-log plot of the halftime data. Slopes for least-squares linear fits are 0.98 ( 0.05 (2%) and 0.86 ( 0.01 (3%).

Second, the half-time is seen to increase strongly with increasing gel concentration at a given field strength, evidencing a stabilizing effect as the gel network becomes denser. The halftime of the complex in free solution is at least 200 min under our conditions (see Materials and Methods), in agreement with earlier observations of the high stability of the presynaptic complex when formed with ATPγS.22 It is seen from Figure 6 that in most cases the complex half-time in the gel is considerably shorter than this. Still, the complex is clearly stabilized by the gel because the half-time increases with increasing gel concentration. As discussed below, we ascribe these two observations to the fact that the gel affects the complex by two opposing mechanisms: a stabilization due to the network itself and a destabilizing effect due to the motion of the complex through it during electrophoresis. In addition to providing a basis for correction of dissociation rates, the results in Figure 5 indicate the existence of a competing reassociation process, which is faster at higher sample concentration. A control experiment was therefore conducted to directly test whether the RecA-oligonucleotide complex can form during ongoing electrophoresis. A zone of RecA gel similar to the one observed in the middle lane of Figure 1b was created inside a 2.5% gel by loading RecA by itself (together with 2 mM ATPγS) and running electrophoresis for 40 min at 4 V/cm. After this step, uncomplexed oligonucleotide was loaded in the same well and its migration toward the zone of RecA was monitored by repetitive scanning of the gel during electrophoresis at 4 V/cm. When the oligonucleotide reached

Gel-Shift Assays: Migrative Dissociation the RecA zone about 50% of the oligonucleotide was complexed with RecA as evidenced by the formation of a slow-moving oligonucleotide zone. This result shows that the difference in velocity between oligonucleotide and RecA is not large enough to prevent the complex from forming during the migration. Thus reassociation of dissociated components during electrophoresis is clearly a possibility. Dissociation as a Function of Migrated Distance. An important clue to the understanding of the dissociation process during gel migration is obtained by further analysis of the dissociation time profiles. Figure 7a shows plots of the integrated intensity of the complex band as a function of electrophoresis time at different field strengths at a constant gel concentration of 2%. The dissociation is seen to become consistently faster as the field strength becomes stronger, as already summarized in Figure 6. However, if the dissociation curves are replotted as a function of migrated distance instead (Figure 7b), it is seen that the dissociation profiles obtained at different field strengths approximately superimpose to form a common curve. Also at the highest gel concentration of 5%, the dissociation profiles (except for the lowest field strength) exhibited a similar universal behavior when plotted as a function of migrated distance (Figure 7d) compared to a plot versus electrophoresis time (Figure 7c), and similar results were obtained at other gel concentrations (not shown). The degree of dissociation thus seems to be more closely related to the migrated distance than to the time of migration. One possibility is that the dissociation occurs as a result of interactions (collisions) with the gel fibers, the number of which should be approximately proportional to the number of traversed pores, i.e., to the migrated distance at a given gel concentration. From the plots versus distance, it is possible to evaluate a characteristic distance after which half of the complexes have dissociated. Table 1 shows that this dissociation length increases with increasing gel concentration. Complexes between single-stranded DNA and RecA are usually formed with the cofactor (ATPγS) in excess. We investigated whether electrophoretic removal of the cofactor from the complex zone in the gel may affect complex stability. Electrophoretic transport of ATPγS will be fast given its small size and high charge, so lack of cofactor may in such a case become a destabilizing factor after rather short electrophoresis times and may be more so the stronger the field becomes in accordance with the observed higher dissociation rate (Figure 6). Control experiments were therefore performed with ATPγS present in the electrophoresis gel and buffer, so that electrophoretic depletion in the complex band is counteracted by a compensating inflow of cofactor from the upfield part of the gel. To reduce the required amounts of the cofactor in those experiments, the submarine gel was replaced by a glass capillary in which the gel was formed. The results showed that the presence of ATPγS in the gel at the same 2 mM concentration as used in the incubation protocol had no detectable effect on the dissociation rate compared to the control electrophoresis in standard ATPγS-free gels run in the same capillary (not shown). The observations reported here are thus not due to this particular cofactor dependence of the RecA-DNA complex. Velocity Measurements. In addition to the intensity data presented above, information on the properties of the complex including its stability was also obtained from velocity measurements. An important piece of information comes from measurements of the electrophoretic velocity as a function of migration time. A time-independent velocity, as demonstrated in the 2% gel by the constant slopes in Figure 2 for the fast- and slow-sample


Figure 7. Dissociation profiles. Integrated complex concentration vs electrophoresis time (a) and migrated distance (b) at 2% gel concentration and indicated field strengths are shown. Parts c and d show the same relationships as parts a and b, respectively, at 5% gel concentration.

components as well as for the control oligonucleotide, indicates migration of a nonchanging component. Such a normal behavior was observed for the free oligonucleotides at all gel concentra-


Svingen et al.

TABLE 1: Pore Radius and Dissociation Distance for RecA-DNA Complexes in Hydroxyethylated Agarose Gels gel concentration (%)

Rpa (nm)

Ldb (mm)

number of poresc (106)

2 10.1 7(1 0.34 3 4.9 11 ( 2 1.1 5 1.9 22 ( 1 5.5 a Average pore radius calculated from eq 1. b The migrated distance when half of the complexes have dissociated, obtained from plots of dissociation degree versus migrated distance (Figure 7b). c The number of traversed pores when half of the complexes have dissociated, calculated as Ld/Rp.

Figure 9. Effect of field strength on time-dependent complex velocity. Position (a) and velocity (b) of the complex zone versus electrophoresis time in 5% gel at indicated field strengths are shown. Curves in part b represent fits to a single-exponential growth profile from V0 (at t ) 0) to Vss (at infinite time) and with a half-time τv. Arrow shows (timeindependent) velocity of noncomplexed oligonucleotide at 5% and 2 V/cm.

Figure 8. Effect of gel concentration on time-dependent complex velocity. (a) Position of complex zone versus electrophoresis time at indicated gel concentrations and 2 V/cm is shown. Linear fit worked well for 2% (R) 0.9997 and 5% (0.9995) but poorly for 4% (0.978) and 5% (0.990). (b) Electrophoretic velocity calculated by taking the numerical derivative of data in part a is shown.

tions and field strengths but not always for the complex. Figure 8a shows plots of position vs time for the slow band (complex) at four different gel concentrations, at a constant field strength of 2 V/cm. At 2% and 3%, normal migration is indicated by the linear plots, but it is seen that at the higher gel concentrations of 4% and 5% there is a distinct upward curvature. The time derivative of these curves (Figure 8b) shows that the velocity of the complex clearly increases with increasing time at the high gel concentrations, whereas at low gel densities, the velocity is approximately constant. The increasing velocity of the complex zone at high gel concentrations shows that the complex experiences an increase in the effective charge and/or a decrease in the friction coefficient with time. This suggests that the complex undergoes some kind of perturbation, which only occurs if the gel concentration is high enough, i.e., if the pores are small enough. Under these conditions, there are strong retarding interactions with the gel as is evident from the fact that the (average) velocity is overall considerably lower at the higher gel concentrations (Figure 8b).

The rate of this perturbation process can be estimated from the rate of velocity increase, and its dependence on the electric field was investigated in the 5% gel in which the velocity increase is most marked. Figure 9 shows the position (part a) and corresponding velocity (part b) of the complex band as a function of time in 5% gel at five different field strengths. The clear nonlinearity of the position curves at 5% gives rise to a time-dependent velocity at all fields, whereas the corresponding position data at 2% gave time-independent velocities at all fields (not shown). The velocity curves exhibit a growth phase, which is shorter at stronger field strength, followed by an approximate steady-state phase. Importantly, at a given field strength, the limiting velocity, Vss, is about a factor of 4 lower than that of the free oligonucleotide (as illustrated for 2 V/cm in Figure 9b), so it is clear that the velocity-detected perturbation does not result in free oligonucleotide being produced. The growth phase could be adequately described by a simple exponential profile with a characteristic half-time, τv, and Figure 10 shows that τv decreases with increasing field strength according to an approximate power law of τv ∝ E-1.8(0.1 (see inset). Data on the half-time τi for the complex dissociation (Figure 6) are included in Figure 10 for the sake of comparison. It is seen that for a given field strength the half-time for the velocity increase (τv) is smaller than τi. Figure 11 shows a plot of the velocity (normalized to Vss) versus migrated distance instead of versus time. The result is an approximate merging of the dissociation curves measured at different field strengths, as was the case for the intensity data (Figure 7b), although the velocity data scatter considerably more because the numerical derivation tends to enhance the noise.



Figure 10. Half-time τv calculated from the increase in velocity (from fits in Figure 9b) versus field strength (b), plotted together with the half-time τi (2) for complex dissociation obtained from the decrease in intensity (from Figure 6). Gel concentration was 5%. Inset shows a log-log plot of τv data.

Figure 11. Velocity data in 5% gel at indicated field strengths (from Figure 9b), normalized to the steady-state velocity, Vss, and plotted versus migrated distance.

Still the velocity behavior at different field strengths is significantly closer to universal as a function of distance than as a function of time. Figure 11 shows that the characteristic length for the velocity-changing process is only a few millimeters, i.e., considerably shorter than the dissociation length of 22 mm derived from Figure 7. Thus, on average, the velocity increase occurs prior to the complex dissociation, both as a function of electrophoresis time (Figure 10) and migrated distance (Figure 11). A second piece of information comes from comparing the electrophoretic velocity, V, at different field strengths. The complex velocity is proportional to the field strength in the range of gel concentrations studied here (Figure 12a), i.e., the mobility, µ ) V/E, is independent of field. The same observation was made for the free oligonucleotide (not shown). The fieldindependent mobility indicates that the RecA-oligonucleotide fiber does not undergo the field alignment and/or molecular deformation that occurs with (noncomplexed) double-stranded DNA41 for which the mobility depends strongly on the field strength when pore sizes are comparable to the coil dimensions. Such effects could not be ruled out beforehand for the RecADNA complex because at the highest gel concentrations used here the pore diameters (see below) are comparable to the diameter of the RecA-oligonucleotide fiber. Finally, the velocity of the complex at different gel concentrations can be used to estimate the electrophoretic velocity in free solution, for example, in the well before entering the gel.

Figure 12. Effect of field strength and gel concentration on the electrophoretic velocity of the complex. (a) Complex velocity versus field strength at indicated gel concentrations is shown. The two curves for 5% show the initial (V0, 0) and final (Vss, 9) velocities (cf. Figure 9b). The arrow indicates the increase in complex velocity over time in 5% gel. The electrophoretic velocity of complex in free solution ([) is also indicated. (b) Ferguson plot of logarithm of velocity of complex versus gel concentration at 5 V/cm is shown. Extrapolation to zero gel concentration gives a free solution velocity of 1 ( 0.2 mm/min.

Figure 12b shows a plot of the logarithm of the complex velocities at 5 V/cm vs gel concentration. (The data point for 5% is the time-averaged velocity). According to the Ogston model,42 such a Ferguson plot43 is predicted to be linear for DNA if the molecules do not undergo a migrative perturbation.44 The dissociation into free oligonucleotide does not affect the applicability of the model because Figure 12b is only based on the velocity of the still-intact complexes, whereas the timeincreasing velocity may affect the Ferguson plot as will be discussed below. The free-solution velocity is obtained by extrapolation of the Ferguson plot to zero gel concentration, which gives an approximate value of 1 ( 0.2 mm/min at 5 V/cm. Measurements of the Average Pore Size. The strong effect of gel concentration on the nature and rate of electrophoretic migration and dissociation indicates that the confinement and retardation effects of the gel vary strongly with gel concentration. It was therefore deemed essential to estimate the pore size at different concentrations of the relatively new types of hydroxyethylated gels used here. There are several variants of the Ogston approach to this problem, such as the extended model 45 and the approach of Slater and co-workers.29 We choose the latter because it allowed comparison with pore data of unmodified29 and other types of hydroxyethylated gels46 obtained by the same method. It should also be noted that the Ogston approach tends to underestimate the pore sizes in nonmodified agarose gels by approximately a factor of 2 compared to direct measurements by atomic force microscopy (AFM).47,48 It is not


Svingen et al.

Figure 13. Average pore radius of hydroxyethylated agarose versus gel concentration measured by the Ogston-model approach (see Materials and Methods). Inset shows a log-log plot of the data. Linear fit gives a slope of -1.8 ( 0.1.

known whether this difference also holds for gels formed by hydroxyethylated agarose. Figure 13 shows how the pore radius of the gel type used here increases with decreasing gel concentration, c, in a manner that in fact is unusually strong for an agarose-type gel. The log-log plot in the insert of Figure 13 shows an approximate power law

Rp ) 35 nm c-1.8(0.1

(1)

This scaling with gel concentration is considerably stronger than for unmodified agarose (an exponent of about -0.6)29 and for less hydroxyethylated Nusieve agarose (-1.4).46 This strong dependence on gel concentration is probably not an effect of the chosen experimental approach, because even if AFM and the Ogston methods disagree on the magnitude of the pore size they do agree on the gel-concentration dependence.47,48 Discussion The Degree of Confinement. The subject of the present investigation is the electrophoretic dynamics of a protein-DNA complex under conditions typically used in gel-shift assays. In particular, we are interested in the dynamics under conditions of tight confinement, i.e., when at least one of the dimensions of the complex is smaller than the pore size. The relatively strong influence of gel concentration on the average pore radius of hydroxyethylated gels (Figure 13) allows us to vary the degree of confinement in a relevant range. Pores in the commonly used polyacrylamide gels also can be varied in a large range, but the bimodal nature of the pore size distribution49 leads to an uncertainty regarding which pore size the complex actually senses. The RecA-olignucleotide complex has a well-defined cylinderlike structure. The radius of the presynaptic fiber has been estimated to be 4-5 nm from STM images of coated17 and uncoated18 RecA-DNA complexes. The fiber formed by RecA itself has an approximate radius of 3.1 nm32 as calculated from its crystal structure.50 The length of the RecA complex with single-stranded DNA is also well-known. Recent singlemolecule experiments in solution32 have confirmed earlier electron-microscopy reports51 that it is 5.3 Å/base. For the 30base oligonucleotide used here, the length of a single fiber then is about 16 nm. Because the persistence length of the RecADNA fiber is over 900 nm,32 the complexes studied here can be viewed as rigid rods. In the most dense gels used here (5%), the average pore radius according to the Ogston method is 1.9 nm (Figure 13). Taking

into account the difference of a factor of about two between Ogston-derived values and measurements by AFM on nonmodified agarose,47,48 the pore radius is about 4 nm and thus close to the fiber radius. At the lowest concentration (2%), the Ogston-derived pore radius is about 10 nm so that the actual average pore radius probably is about 6 times larger than the fiber radius and somewhat larger than the fiber length. The strongly varying degree of confinement of the RecA-oligonucleotide complex is reflected in the strong effect of the gel concentration (pore size) on both dissociation time (Figure 6) and on the amplitude (Figure 12a) and time dependence (Figure 9) of the velocity. Caging and Dissociation in the Gel. The fact that the halftime of the complex increases strongly with increasing gel concentration (Figure 6) indicates a stabilizing effect of the gel. In free solution, the dissociation rate of the RecA-DNA complex decreases (weakly) with increasing complex concentration,22 in contrast to the increase observed for the DNA complex with the CAP protein13 and the lac repressor.15 The sequestering mechanism13 that operates in the latter two cases is therefore unlikely to be responsible for the stabilization of the RecA complex in the gel, and the most probable mechanism is then stabilization by a cageing mechanism.11 We have not quantified the degree of gel stabilization of the RecA-DNA complex, however. Usually, the effect is evaluated by comparing the stability in the gel during electrophoresis with the free-solution dissociation in the absence of an electric field.13,16 However, the formation of the fast-sample zone of free oligonucleotide (Figure 1) indicates an electrophoretic dissociation is possible outside the gel as well. The electric field itself may thus affect the stability of the complex, and the effect of the gel on the complex stability can therefore only be judged by comparing with the free-solution dissociation time measured in the presence of the same electric field. In fact, such a destabilizing effect of the field may explain why dissociation times measured in the gel during electrophoresis sometimes are reported to be intriguingly short when compared to the fieldfree dissociation in solution.13 More detailed dissociation studies in free solution in the presence of an electric field are needed to resolve this question. This study is instead focused on the electrophoretic dissociation of the complex in the gel. That electrophoretic dissociation occurs is evident from the field dependence in the dissociation rates (Figure 6) and from the existence of an oligonucleotide smear extending downfield from the complex zone (Figure 1c) in agreement with theoretical predictions.52 It is also clear from both Nile-red staining and the perpendicular electrophoresis assay that the final result of the dissociation is a complete dismantling of the presynaptic complex into oligonucleotides free of RecA. One possible field-dependent dissociation mechanism is that the electric field simply overrides the stabilizing effect of the gel by pulling one of the dissociated components out of the cage, which in the present case would be the oligonucleotide with its high velocity compared to RecA. Below, we show that the experimental results on the RecA-DNA complex are not agreement with this mechanism, and instead suggest a dissociation mechanism based on collisions with the gel structure. Finally, we discuss the relation between the complex dissociation and the increase in complex velocity with time that is observed at high gel concentrations. Kinetic Models. The time profiles of the dissociation (Figure 7a,c) will be analyzed on the basis of the scheme in Figure 14, which shows a model for the reaction and transport processes in which the RecA and oligonucleotide are involved during


J. Phys. Chem. B, Vol. 105, No. 51, 2001 12889 TABLE 2: Electrophoretic Removal and Dissociation Times for RecA-DNA Complexes in Hydroxyethylated Agarose Gels gel concentration (%) removal timea (min) dissociation timeb (min) 2 3 5

5 6 8

20 50 230

Figure 14. Reaction-transport model for complex electrophoresis. The square box represents the complex zone in the gel, in which complex (SS‚R) is in dynamic exchange with noncomplexed oligonucleotide (SS) and RecA (R). Oligonucleotides that have escaped the complex zone are denoted SSr. Noncomplexed RecA remains in the zone because its velocity is very similar to that of the complex.

a Calculated as Lz/(2Voligo) where the zone width is Lz ) 3 mm and Voligo is the oligonucleotide velocity at 2 V/cm. b At 2 V/cm from Figure 6.

electrophoresis. The primary process (rate r-) is the dissociation of the complex (SS‚R) into RecA (R) and oligonucleotide (SS). This step is counteracted by a reassociation (r+) of the protein and oligonucleotide. The existence of the latter process is deduced from the observation that the rate of dissociation depends on the starting concentration of the complex (Figure 5) and the demonstration by the electrophoretic-mixing experiments that complexes indeed can form also during migration. In addition, there are those oligonucleotides (SSr) which have escaped electrophoretically from the zone (rr) because of the high oligoucleotide velocity compared to that of the complex. Throughout the smear, these oligonucleotides are free from RecA, and they are thus no longer involved in complex formation. By contrast, all dissociated RecA are assumed to stay in the complex zone because the velocity of RecA and that of the complex are very similar (Figure 1c). Released RecA molecules therefore remain available for reassociation with those oligonucleotides that still have not left the zone. The central kinetic competition in the scheme is thus for the oligonucleotide, and it occurs between the processes of reassocition with RecA in the complex zone and electrophoretic removal of the oligonucleotide from the zone. The scheme of Figure 14 suggests that there are two principally different mechanisms by which an electric field can lead to complex dissociation. One possibility (case 1) holds if the exchange between complex and free RecA/oligonucleotide is rapid compared to migrative transport so that electrophoretically removed oligonucleotides are rapidly replaced by dissociation from the complex pool through mass action. Then, the rate-limiting step for complex dissociation is the electrophoretic removal of released oligonucleotides from the complex zone. This case represents an indirect electrophoretic effect on the complex stability acting through removal of dissociation products. By contrast, if electrophoretic removal is fast (Case 2), the rate-limiting step would instead be the actual dissociation step (r-) into free RecA and oligonucleotide, where the latter component is rapidly removed from the zone once it is formed. In this case, the experimental observation that the net dissociation rate depends on the electric field strength would indicate that the field stimulates the rate-limiting step (r-) in a direct fashion, for example, by migrative dissociation due to collisions with gel fibers. To allow for this possibility, it will be assumed that the rate r- in Figure 14 may depend on the field strength. Migrative Dissociation. We have limited the kinetic analysis of the scheme in Figure 14 to the evaluation of the predicted complex-dissociation time profiles in the two cases outlined above. The analysis (see appendix) shows that in both case 1 and case 2 the rate of dissociation should increase linearly with the field strength (i.e., half-times scaling as E-1) and that plots of the degree of dissociation versus migrated distance (as opposed to time) should be independent of field strength. Both predictions are in agreement with our observations on the dissociation process (Figures 6, inset, and 7b), except for the stronger than 1/E dependence in the half-time at 5% gel

concentration, which will be discussed below. These observations can thus not be used to distinguish between the two limiting cases above, but the analysis also shows that case 2 leads to a monoexponential decrease of the complex concentration, as we observe experimentally (Figure 4), whereas case 1 instead leads to a decrease of the complex concentration that is linear in time. The applicability of case 2 to the present system is also supported by the fact that its condition of fast transport compared to the dissociation rate seems to be fulfilled in the case of RecA-DNA complexes in hydroxyethylated agarose gels. The average time for electrophoretic removal from the zone will be t ) Lz/2Voligo, where Lz is the width of the zone in the field direction (about 3 mm, Figure 1c) and Voligo is the electrophoretic velocity of the oligonucleotide in the gel. By the use of velocity data at 2 V/cm (not shown) at which the velocity is the lowest, the estimated removal times are given in Table 2. These removal times are all short compared to the lower estimate of 200 min for the complex dissociation half-time in free solution obtained from the competition experiments and will be even shorter at higher field strengths. This supports the overall picture that under our conditions electrophoretic removal is fast compared to the inherent dissociation rate of the complex. A more relevant comparison is with the half-times in the actual gel network at 2 V/cm. Table 2 shows that also those are longer than the removal time under the same conditions. It therefore seems reasonable to assume that the removal process in general is fast compared to dissociation rates of the complex also in the gel, in accordance with the conditions for case 2. The data in Table 2 also show that changing the gel concentration affects removal rates in a different way (less strongly) than the measured dissociation rates, which should not be the case if electrophoretic removal is the rate-limiting step (case 1). We conclude that a direct field effect on the dissociation step is the most likely mechanism. An interesting comparison can be made with studies of zone widths for (nondissociating) macromolecules during gel electrophoresis. The degree of zone broadening measured at different field strengths correlated well with the migrated distance but not with migration time.53 This type of field-independent behavior as a function of distance was used to demonstrate that zone widths are determined by the interactions (collisions) with the gel matrix and not by diffusion. The similar fieldindependent correlation between the degree of dissociation and migrated distance observed here (Figure 7b,d) supports that such interactions are important in destabilizing the macromolecular complexes. The approximate inverse field scaling, τi ∝ E-1, for the dissociation at low gel concentrations (Figure 6, inset) also supports this conclusion. The average time between collisions will decrease as 1/E because the velocity increases linearly with field strength (Figure 12a, see Appendix). The more complex field dependence in the 5% gel (Figure 6) with a stronger than E-1 variation (Figure 6, inset) is not due to a nonlinear increase in the velocity with field strength

12890 J. Phys. Chem. B, Vol. 105, No. 51, 2001 because this relation is linear also in the 5% gel (Figure 12a). The complex dissociation thus seems to be enhanced at high gel concentrations and field strengths, and one possibility is a coupling to the process that underlies the observed velocity increase (Figure 9b) because it only occurs at high gel concentrations and because its rate has a comparatively strong field dependence, E-1.8 (Figure 10a, inset). If the changes in the complex that bring about the increase in velocity also lead to a more efficient loss of RecA, the total effect would be an enhanced field dependence in the rate of formation of free oligonucleotide. Such a coupling is clearly possible because the experiments show that the two effects do not exclude each other: the smear and a time-dependent velocity are observed simultaneously at high gel concentration. The Velocity Increase. An increase in the velocity of the complex over time, as observed at high gel concentrations (Figure 9b), could in principle be explained by the loss of RecA from the RecA-DNA complex fiber because this would reduce the complex size and lead to a higher degree of exposure of the DNA charges. However, it is clear that the velocity increase is not just another manifestation of the complex-dismantling process because the rate of the latter (as monitored by the concentration of remaining complex) differs from the rate of the velocity increase both in the magnitude (Figure 11b) and the field dependence (insets of Figures 6 and 10a). In addition, there are conditions (low gel concentrations) in which dismantling of the fiber is possible without such a velocity increase. The velocity increase must thus be caused by some other change in the properties of the complex, although it seems likely that also this change is caused by collisions with the gel network. This is concluded from the observation that within experimental uncertainty the velocity profiles become field-independent when plotted as a function of distance (Figure 11a), just as was the case for the RecA dissociation from the fiber (Figure 7b) and for zone broadening.53 Two important clues are that the velocity increase only occurs at high gel concentrations (Figure 8) and that its rate is particularly strongly influenced by an increase in the field strength (slope of -1.8 in the inset of Figure 10a) compared to the dismantling process (inset Figure 6). Both observations indicate that the underlying changes in the complex occur only when it is subjected to strong perturbing forces, because the frictional forces between complex and gel are maximized in narrow pores at high fields. One possibility is then dissociation of RecA molecules that are internally placed in the fiber, as opposed to removal of proteins from the ends. Internal RecA molecules are known to be more strongly bound to the DNA than proteins at the ends of the fiber54 most likely because an internal RecA makes attractive contacts with two neighboring proteins.21 The particularly strong forces from the gel at high fields and narrow pores might be enough to strip internal RecA from the fiber. However, the velocity-detected process as such does not lead to a full dissociation of the complex because the product has a final velocity, Vss, that is much lower than that of the free oligonucleotide control (Figure 9b). It is unclear why RecA removal should come to a halt before it has proceeded to completion just because it has been initiated in the internal parts of the fiber. Such a gradual and partial removal of RecA from the presynaptic complex therefore seems to be a less likely explanation for the velocity increase, although we cannot rule it out. A second possibility is that the velocity increase reflects another type of complex alteration than removal of RecA from the fiber. The characteristic time, τv, for the velocity increase

Svingen et al. is shorter than that for the formation of free oligonucleotide (τi) (Figure 11b), so on average the complex alteration which causes the velocity increase occurs faster than the RecA falls off. This observation suggests that the increase in velocity is due to changes in the properties of a still-RecA-covered fiber. Then, the surface charge is essentially retained during the process, and the fact that the velocity increases then indicates a decrease in the size of the complex. One possibility is then that it reflects a breaking up of the trains of end-to-end attached oligonucleotide-RecA fibers, which tend to form in solution according to microscopy and hydrodynamic experiments.33 From a steric point of view, it is reasonable that such a perturbation occurs when the typical pore radius becomes smaller than the length of individual fibers. An increase in velocity is expected because train dissociation would lead to a shorter effective fiber length, but the velocity would still be low compared to the velocity of the free oligonucleotide because the bulkiness of the presynaptic complex is retained. For nonchanging macromolecular complexes, their size can be estimated from the slope of the Ferguson plot.55 In our case, with a complex for which velocity increases over time, the Ferguson plot (Figure 12b) is based on the average velocity during the electrophoresis and thus cannot be used to evaluate the change in complex size over time as the velocity increases. However, the corresponding decrease in complex size can be estimated in the following way. In the investigated field range, the average increase in velocity, Vss/V0, in the 5% gel (Figure 9b) is by a factor of 2.4 ( 0.5. The same increase in (average) velocity would be obtained by decreasing the gel concentration from 5% to 3.4 ( 0.4% according to Figure 12b. According to eq 1, this in turn is equivalent to an increase in pore radius from 1.9 to 4 ( 0.8 nm or by a factor of 2.1 ( 0.4. Because mobilities of particles in gels are generally governed by the ratio between particle and pore size,56 such an approximate doubling of the equivalent pore radius corresponds to a reduction of the effective complex size (at constant pore radius) by the same factor of about 2. Interestingly, with unmodified oligonucleotides, each train may contain tens of individual fibers, but with a 5′ modification such as the fluorescein label used here, the trains are considerably shorter and contain just a few oligonucleotides.33 One interpretation is thus that the velocity increase typically corresponds to breaking up of a dimer train into monomer, which would explain why the velocity does not continue to increase. Other combinations of initial and final train lengths are possible, of course, because no absolute value on the final complex size is obtained by the present approach. Attempts to estimate the absolute complex size were made by exploiting the fact that the radius R of a spherical particle can be obtained from velocity data such as those in Figure 13 by using the Ogston-model prediction29 πR

V ) Vfreee e- 4 Rp

(2)

where Rp is the average pore radius and Vfree is the velocity in free solution. However, a plot of ln(V/Vfree) versus 1/Rp2 (not shown) was not linear for the RecA-DNA complexes, indicating that the Ogston model for a sphere fails to describe the electrophoretic behavior of the rodlike complexes. This is not surprising; a similar deviation in terms of a downward curvature has been observed for rodlike tobacco mosaic viruses in agarose gels.55 (This effect may be related to changes in the gel structure as well.)45 The reduction in average complex size by a factor of about 2 during migration is estimated from pore sizes

Gel-Shift Assays: Migrative Dissociation measured with DNA molecules, which do obey the Ogston model. The indirect nature of the approach and the still unresolved question of the applicability of the Ogston model to hydroxyethylated agarose57 mean that the absolute values for the complex size could not be determined. From the known structure of the presynaptic filament, it is clear that the hypothesized train-breakup process neither excludes a concomitant removal of RecA from the fiber nor is a prerequisite for it, in agreement with the fact that depending on gel concentration the RecA loss can occur by itself as well as concomitantly with the velocity increase. In fact, accumulation of more but shorter trains could enhance the overall rate of RecA loss from the fibers if protein removal occurs preferentially from the ends. The extra binding affinity for internal RecA has been invoked to explain why in free solution RecA exhibits a strong tendency to dissociate from the end of the presynaptic complex.54 Similar end effects in the gel could mean that breaking-up of trains at high fields enhances the rate of RecA dissociation from the fiber and explain the extra strong field dependence in the rate of fiber dismantling (i.e., formation of RecA-free oligonucleotide) in 5% gels (Figure 6, inset). Finally, it should be noted that the collision hypothesis cannot explain all the observations on the dissociation processes. For instance, the number of pores that has to be traversed to dissociate half of the complexes into free oligonucleotide can be calculated as the ratio between the dissociation lengths (Table 1) and the average pore size (Figure 13). The results (Table 1) show that this number is not constant as might be expected if the dissociation process was only governed by the number of collisions with gel fibers. However, there is the additional effect of enhanced stability in the gels due to the cage effect, which is likely to be stronger as the pore sizes become smaller. In this interpretation, the presence of the gel thus has two effects. It stabilizes the complex compared to free solution especially at high gel concentrations but also provides obstacles for a fielddriven dissociation of the complex through collisions. Conclusions In conclusion, we have shown that electrophoretic migration under typical conditions of gel-shift assays may perturb a DNAprotein complex through interactions with the gel structure. Two types of perturbations have been detected, one directly through measurements of the concentrations of intact and dissociated complexes, one indirectly through changes in the electrophoretic velocity of the complexes. Because cofactor-dependent dissociation mechanisms have been excluded, the dissociation mechanisms reported here probably are general enough to occur also with other DNA-protein complexes, at least under some conditions. The migrative dissociation of the fiber occurs when the pore size is similar to the complex size, and this processes adds to the list of electrophoretic perturbations of macromolecules that may occur under conditions of strong confinement in gels. Another example is the electrophoretic deformation of a flexible polymer chain, which occurs during migration in gels that have pore sizes comparable to the coil size.58 In that case, the electric field forces the coils to adapt to the gel network by field extension of the chain. One result of this field alignment is that the velocity increases nonlinearly with the electric field.41 In the present case, the electric field instead forces a macromolecular complex to adapt to the tight pores by dissociation, and the result is a velocity that increases over time but is linear in the field strength. This difference in effect on the velocity might be related to the fact that the characteristic length scale for

J. Phys. Chem. B, Vol. 105, No. 51, 2001 12891 dissociative perturbation corresponds to migration through many pores (Table 1), whereas the coil alignment occurs on the length scale of coil size, i.e., after only a few pores have been traversed. Acknowledgment. The financial support from the Swedish National Research Council is greatly appreciated. Appendix In this appendix, kinetic expressions for the dissociation of the RecA-oligonucleotide complex are derived for the reactiontransport scheme of Figure 14 in the two limiting cases given in the main text. The basic approach is to combine the rate equations for interconversion between the complex and its two constituents with those of electrophoretic and diffusive transport.59 The components are regarded as being either in the complex zone or outside it (i.e., in the oligonucleotide smear), and only their average concentrations in these two regions are considered. The analysis therefore does not provide the detailed spatial profiles of the components (i.e., band shapes), which require the solution of the coupled transport and chemical rate equations as functions of space coordinates.52 The time evolutions of the spatially averaged concentrations are sufficient for our purposes because we only evaluate the integrated concentrations of the separated components. We neglect diffusion and use a coordinate system that moves with the zone of the complex. Then the only transport that has to be taken into account is the electrophoretic transport of the free oligonucleotide, because the velocity of free RecA is very similar to that of the complex. With the use of the notations R‚SS for the complex, R for RecA, SS for oligonucleotides that are still in the complex zone, and SSr for oligonucleotides that have been removed from this zone by electrophoresis, the following rate laws can be stated for the reaction/transport scheme of Figure 14:

r+ ) k+[R][SS]

(A1a)

r- ) k-[R‚SS]

(A1b)

rr )

d[SSr] ) kr[SS] dt

(A1c)

where [ ] denotes spatially averaged concentration and where the following field-dependent expressions for k- and kr are derived below.

k- ) R

µE Rp

µoligoE kr ) Rr Lz

(A2a)

(A2b)

The expression A2a for the rate constant k- takes into account the possibility of collision-induced dissociation of the complex where it is assumed that the average time between collision with the gel network is given by Rp/V where Rp is the pore radius and V ) µE is the electrophoretic velocity of the complex expressed in terms of its electrophoretic mobility, µ, and the electric field strength, E. The mobility is independent of the field strength because the complex velocity varies linearly with E (Figure 12). The parameter R corresponds to the fraction of collisions that are successful in dissociating the complex. The expression A2b for the rate constant kr for electrophoretic removal was obtained by calculating the number, ∆n, of


Svingen et al.

oligonucleotides that leave the electrophoretic zone in a time, ∆t11

∆n ) [SS]AVoligo∆t

(A4)

The rate constant kr (eq A2b) is obtained by including a factor Rr that takes into account effects due to the averaging over the zone and that should be close to unity. In the analysis, the rate constant for association, k+, is assumed to be independent of the field strength. This assumption could be tested by performing electrophoretic mixing experiments (see Materials and Methods) at different field strengths, but this has not been done in this study. Case 1. If the exchange between complex R‚SS and the free components SS and R is fast compared to electrophoretic removal, a steady-state assumption can be made for the concentration of free oligonucleotide in the zone. Equations A1a-c then give

0)

d[SS] ) k-[R‚SS] - k+[SS][R] - kr[SS] dt

[R‚SS] ) [R‚SS]0 e-t/τ2

(A3)

where Voligo ) µoligoE is the electrophoretic velocity of the oligonucleotide and µoligo is the corresponding mobility, which also is independent of the field strength because Voligo varies linearly with E (not shown). A is the cross sectional area of the zone perpendicular to the electric field so that the volume of the zone is V ) ALz where Lz is the length of the zone in the field direction. With the use of eq A3, the electrophoretic transport leads to a change of oligonucleotide concentration per unit time in the zone of

∆[SS] ∆n [SS]AVoligo∆t µoligoE ) ) ) [SS] rr ) ∆t V∆t ALz∆t Lz

which gives

(A5)

where the time constant τ2 ) 1/k- is given by (cf. eq A2a)

τ2 )

which with eq A5 and eq A2b becomes

µoligoE d [R‚SS] [SS] ) -kr[SS] ) -Rr dt Lz

t [SS] τ1

(A7)

(A8)

where [R‚SS]0 is the initial concentration of complex and where

τ1 )

Lz µoligoRr

E-1

(A9)

The complex concentration decreases linearly in time with a time constant that scales as τ1 ∝ E-1. Case 2. If electrophoretic removal is fast compared to reassociation, we can make the approximation r+ ) 0, and the dissociation step (r-) will be rate-limiting. Then eq A1a gives

d[R‚SS] ) r+ - r- ) -k-[R‚SS] dt

(A13)

where

λ2 )

Rp R

(A14)

The dissociation is exponential in the migrated distance with a characteristic dissociation length, λ2, which is independent of field strength and which is related to the number of pores the complex has to cross on the average before it dissociates. A universal decay behavior for different field strengths is not unique for case 2 however. The linear time profile (eq A8) of case 1 can be expressed in the distance, x, migrated by the complex as

[R‚SS] ) [R‚SS]0 -

x [SS] λ1

(A15)

where the characteristic decay length is

L zµ Rµoligor

(A16)

in which case there is no obvious interpretation of the decay length. References and Notes

With [SS] approximately constant according to the steady-state assumption, the solution to eq A7 is

[R‚SS] ) [R‚SS]0 -

(A12)

[R‚SS] ) [R‚SS]0 e-x/λ2

λ1 ) (A6)

Rp -1 E Rµ

The dissociation is exponential in time with a characteristic time constant scaling as τ2 ∝ E-1. By use of the fact that the distance migrated by the complex is x ) Vt ) µEt, the solution of eq A11 can be written

The dissociation rate for the complex is

d[R‚SS] ) r+ - r- ) k+[R][SS] - k-[R‚SS] dt

(A11)

(A10)

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