Kinetic Analysis of Pairing and Strand Exchange Catalyzed by RecA DETECTION BY FLUORESCENCE ENERGY TRANSFER*

RecA is a 38-kDa protein from Escherichia coli that polymerizes on single-stranded DNA, forming a nucleoprotein filament that pairs with homologous duplex DNA and carries out strand exchange in vitro . In this study, we measured RecA-catalyzed pairing and strand exchange in solution by energy transfer between fluorescent dyes on the ends of deoxyribo-oligonucleotides. By varying the position of the dyes in separate assays, we were able to detect the pairing of single-stranded RecA filament with duplex DNA as an increase in energy transfer, and strand displacement as a decrease in en- ergy transfer. With these assays, the kinetics of pairing and strand displacement were studied by stopped-flow spectrofluorometry. The data revealed a rapid, second order, reversible pairing step that was followed by a slower, reversible, first order strand exchange step. These data indicate that an initial unstable intermedi- ate exists which can readily return to reactants, and that a further, rate-limiting step (or steps) is required to effect or complete strand exchange. times duplex DNA and the background emission of the sample with only rhodamine- labeled DNA. The spectrum of the fluorescein-only reaction was normalized at 525 nm to the height of the energy transfer reaction. The spectrum of the rhodamine-only reaction was normalized to the energy transfer reaction using the emission at 585 nm with excitation at 558 n M . The sum of the normalized spectra was subtracted from the spectrum of the energy transfer reaction. The normalizations and subtrac- tion of background were performed according to the following formula.

RecA is a 38-kilodalton protein from Escherichia coli, which has been shown to be necessary for conjugal homologous recombination in vivo (1). In vitro, RecA protein polymerizes on single-stranded DNA in the 5Ј to 3Ј direction to form a righthanded helical structure in which the DNA is extended to 1.5 times its original length (2,3). Pairing with homologous duplex DNA results in a rapid uptake of the double-stranded DNA into a three-stranded complex, which can be kilobases in length (4 -6). Strand exchange results in displacement of the strand of duplex DNA that has the same sequence as the filament strand; the strand is displaced in the 5Ј to 3Ј direction (7)(8)(9). Homologs of RecA exist in eukaryotes from yeast to man and have been found to hydrolyze ATP, to form nucleoprotein filaments, to pair homologous DNA, and to carry out strand exchange in ways that are qualitatively similar to RecA protein (10 -15). Studies of the mechanisms of E. coli RecA may help to shed light on eukaryotic as well as prokaryotic recombination.
Most studies on the kinetics of RecA-catalyzed strand exchange have used phage DNA that is several kilobases in length (16 -20). RecA filaments formed on long single-stranded DNA generate coaggregates with duplex DNA that concentrate the DNA but also limit diffusion (21). Despite this complication, joint molecule formation displayed the saturation of rates with increasing substrate concentration that is typical of Michaelis-Menten kinetics (17). This observation suggested the existence of a reversible pairing step and a second, rate-limiting step in the reaction. Yancey-Wrona and Camerini-Otero (22) developed a solution assay for pairing and stable synapsis of a single-stranded oligonucleotide with duplex DNA in which a RecA filament formed in the presence of ATP␥S 1 protects a restriction site in the duplex target molecule. With this assay, they found that pairing was second order, reversible, and independent of the complexity of the target. They were also able to determine the equilibrium constant for pairing (22).
Several studies have used fluorescence resonance energy transfer to measure the kinetics of the formation or disruption of particular nucleic acid structures (23)(24)(25)(26). Energy transfer between two fluorescent dyes indicates their proximity, and in the case of DNA, the proximity of any two strands labeled with the dyes (27)(28)(29). We developed three assays based on energy transfer. These assays can be monitored in real time and presumably do not perturb the reaction. They allow the observation, by means of stopped-flow spectrofluorometry, of pairing, strand exchange, or both, depending on the placement of the two dyes (Fig. 1). An oligonucleotide system was chosen because of the ease of labeling the DNA with fluorescent dyes and the high yield of labeled DNA. Oligonucleotides also have the advantage of avoiding some of the more complicated aspects of strand exchange with long DNA substrates, such as the effects of coaggregate formation and the topological difficulties of strand displacement (18,21,30,31). Fitting of the stopped-flow data to a model with a reversible pairing step, followed by a reversible strand exchange step, allowed the determination of rate constants for the whole strand exchange reaction.

EXPERIMENTAL PROCEDURES
Materials-RecA was purified as described (32). T4 polynucleotide kinase was supplied by New England Biolabs. ATP, phosphocreatine, and phosphocreatine kinase were from Sigma. Bovine serum albumin was purchased from Boehringer Mannheim. Dithiothreitol was provided by Promega. Proteinase K was from American Bioanalytical.
Preparation of Oligonucleotide Substrates-All DNA concentrations are given in terms of moles of nucleotides. Oligonucleotides were synthesized on an Applied Biosystems DNA synthesizer (model 380B) at the Keck Biotechnology Resource Laboratory at Yale. Primary amines on C 6 linkers (Glen Research) were added to 83-mer oligonucleotides during synthesis for labeling with fluorescent dyes. Fluorescent oligonucleotides were produced by reacting 360 l of 5 mM DNA with 4 mg of 5-carboxyfluorescein or 5-and 6-carboxytetramethylrhodamine succinimidyl ester (Molecular Probes, Inc.) dissolved in 40 l of anhydrous dimethyl sulfoxide. The reaction was carried out in 250 mM carbonate buffer, pH 9, overnight at room temperature in the dark. Oligonucleotides were then precipitated in ethanol, dissolved in formamide, and purified by electrophoresis on a 12% denaturing polyacrylamide gel (33). The absorbance at 260, 496, and 558 nm of the oligonucleotides was measured to determine, respectively, the concen-* This work was supported by Grant R37 GM33504-13 from the National Institutes of Health. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Duplexes were 5Ј-end-labeled with 32 P using T4 polynucleotide kinase (35). Duplexes were checked for complete annealing by electrophoresis on an 8% nondenaturing polyacrylamide gel and quantitated by use of a Molecular Dynamics PhosphorImager. All duplexes used contained less than 5% single strands.
Standard Strand Exchange Reaction Conditions-Reactions were conducted at 37°C in buffer containing 33 mM PIPES acetate, pH 7.0, 1 mM magnesium acetate, 1.2 mM ATP, 2 mM dithiothreitol, and 100 g/ml bovine serum albumin. Stopped-flow fluorescence assays had no bovine serum albumin (to prevent bubbles) and had a final concentration of 16 mM phosphocreatine and 10 units/ml creatine phosphokinase for ATP regeneration. Filaments were formed on 10 M M(Ϫ) or R83 oligonucleotides (Sequences 1 and 5, Table I) by incubation with 3.33 M RecA for a minimum of 2 min. Magnesium was increased to 16 mM, and duplex 83-mer was added to a final concentration of 20 M. Unlabeled oligonucleotides still bore the primary amine linkage.
Steady-state Fluorescence Resonance Energy Transfer (FRET) Assays-For the pairing assays ( Fig. 1), 10 M M(Ϫ)⅐3ЈF 2 (Sequence 1, Table I) Table I) was added and reacted for 2 min. In the case of the strand displacement assay, 25 M RecA was incubated with 75 M M(Ϫ)⅐3ЈNH 2 for 5 min in standard reaction buffer. The filament was added to M(Ϫ)⅐3ЈF/M(ϩ)⅐5ЈR duplex in reaction buffer with 16 mM magnesium acetate to produce 7.5 M M(Ϫ)⅐3ЈNH 2 filament with 2.5 M RecA and 10 M M(Ϫ)⅐3ЈF/M(ϩ)⅐5ЈR duplex DNA, which was reacted for 2 min. Two additional reactions were carried out for each assay with either the fluorescein-or the rhodamine-labeled strand replaced by an equivalent unlabeled, primary amine-tagged oligonucleotide.
Fluorescence emission spectra from 502 nm to 620 nm were taken with excitation at 493 nm on an SLM8000C spectrofluorometer (Spectronic Instruments, Inc.). Excitation and emission polarizers were aligned at 54.7°with respect to each other to help eliminate polarization artifacts (36). Reactions containing rhodamine were also observed from 565 nm to 620 nm with excitation at 558 nm. Buffer spectra under both conditions were subtracted from the data. The increase in emission by rhodamine due to FRET was calculated by subtracting both the background emission of the sample containing only fluorescein-labeled DNA and the background emission of the sample with only rhodaminelabeled DNA. The spectrum of the fluorescein-only reaction was normalized at 525 nm to the height of the energy transfer reaction. The spectrum of the rhodamine-only reaction was normalized to the energy transfer reaction using the emission at 585 nm with excitation at 558 nM. The sum of the normalized spectra was subtracted from the spectrum of the energy transfer reaction. The normalizations and subtraction of background were performed according to the following formula. S represents the spectrum taken with excitation at 493 nm, I represents the fluorescence intensity at a particular excitation and emission wavelength indicated by the subscript, and superscripts indicate the fluorophores present in a particular reaction. These calculations were based on work by Jares-Erijman and Jovin (37).
Stopped-flow Fluorescence Assays-Assays were performed on an Applied Photophysics DX.17MV sequential stopped-flow spectrofluorometer. One syringe contained an 83-mer oligonucleotide-RecA filament with an ATP-regeneration system, and the other contained duplex in buffer plus magnesium for the magnesium shift. The reaction conditions were standard, as described above. The contents of the syringes were mixed in equal proportions with a dead time of 50 ms or less. Excitation was at 493 nm, and an interference filter with maximum transmission at 520 nm and a 10-nm bandwidth (Corion) was used to select the emission wavelength observed. The time base for collection of data was split, so that half the data points were collected in the first 20 s. The control for photobleaching was performed with 10 M M(Ϫ)⅐3ЈF-RecA filament. The control for nonspecific quenching of fluorescein was conducted with 10 M M(Ϫ)⅐3ЈF-RecA filament and 20 M unlabeled duplex DNA. Heterologous controls were done with 10 M R83⅐3ЈF or R83⅐3ЈNH 2 as the filament strand and 20 M of the appropriate duplex. The data in Table II were generated using curve-fitting software supplied with the DX.17MV. The data in Figs. 5 and 7 were plotted and fit, and residuals were calculated using KaleidaGraph software (Abelbeck Software).
Mathematical Modeling of Stopped-flow Data-The kinetics of the reactions were further analyzed by comparison of the stopped-flow data with theoretical curves generated from the reaction scheme outlined in Fig. 1. Theoretical curves were computed by numerically resolving the system of derivative equations by the fourth order Runge-Kutta method. Starting at time t 1 , this method calculates the concentration change of each species during a short interval, ⌬t, based on the concentrations of all species at t 1 . In this way, one can calculate the concentration of all species at time t 2 from the concentrations at time t 1 by adding the concentration changes during the interval ⌬t. By repeating this operation from time t ϭ 0, one can compute the concentration of all species as a function of time. The method was numerically stable within a large range of ⌬t values. In general, we did not observe numerical instability using ⌬t ϭ 0.01 s. Furthermore, the concentrations approached the theoretical equilibrium values after sufficient reaction time, which supported the validity of the resolution method.
The concentrations of the species calculated by this method were then converted to fluorescence intensity for comparison with the experimental data. The maximum fluorescence change possible for either pairing assay 1 or the strand displacement assay was modeled by annealing of M(Ϫ)⅐3ЈF-RecA filament and M(ϩ)⅐5ЈR (see "Results"). The relationship between fluorescence changes and concentration changes assayed by gel electrophoresis was linear for both assays, so the change in concentration at any point on the theoretical curves could be converted to a change in fluorescence by multiplying it by the ratio of the maximum fluorescence change to the maximum concentration change. For the pairing assays, we assumed that the energy transfer for the intermediate was the same as for the annealed DNA. A better fit of the data for the strand displacement assay was obtained when a slightly smaller energy transfer for the intermediate was assumed.
The comparison of theoretical and experimental data was made by least square analysis. To find the best fit, the rate constants were systematically varied and the corresponding theoretical data were computed as described above. To reduce the number of parameters to be fitted and to estimate the value of the rate constants for the back reaction (k Ϫ1 and k Ϫ2 ), the equilibrium constants K eq1 for pairing and K eq2 for strand exchange were determined from the amount of strand exchange products determined by gel assay. K eq1 ϭ k 1 /k Ϫ1 ϭ C/(A ϫ B) and K eq2 ϭ k 2 /k Ϫ2 ϭ (D ϫ E)/C, where A and B represent the concentrations of the reactants, C is the concentration of the intermediate, and D and E are the products. This system of equations was also analyzed by the least square method to find the values of the equilibrium constants. The theoretical values were computed by numerical resolution of the equation system with the half-interval method (38).
Gel Electrophoresis Assay for Strand Exchange-The same DNA and RecA concentrations as in the FRET assay described above were used for the gel electrophoresis assay shown in Fig. 6. The M(Ϫ)⅐3ЈF strand (Sequence 1, Table I) of the duplex substrate used was 5Ј-end-labeled with 32 P as described above. Aliquots (10 l) of the strand exchange reaction were taken at different times and deproteinized as described (35). Loading buffer was added to produce a final concentration of 5% glycerol, 0.05% bromphenol blue, 0.05% xylene cyanol. Samples were loaded on an 8% native polyacrylamide gel and run 3 h at 275 V and room temperature. The gel was dried and quantitated by use of the Molecular Dynamics PhosphorImager to determine the extent of strand displacement.
The other gel electrophoresis assays that were used to calculate the concentrations of the products of strand exchange with the substrates for the three fluorescence assays were performed with 10 M singlestranded DNA, 3.33 M RecA protein, and 20 M duplex DNA under standard conditions. Two-fold, 3-fold, and 5-fold increases in the preceding concentrations were made for the substrates of the fluorescent strand displacement assay. In another set of titrations, the filament concentration was held constant at 10 M and the duplex concentration was 5, 7, 10, 20, or 30 M. In all cases, the final concentration of products was determined from an aliquot of the reactions taken at 3 min after the addition of duplex DNA. The aliquots were deproteinized, electrophoresed, and quantitated as described above.

Assays and Substrates Used to Monitor Pairing and Strand
Displacement-When fluorescein comes into proximity with tetramethylrhodamine, the overlap between its emission spectrum and the excitation spectrum of rhodamine allows the non-radiative transfer of energy to rhodamine by a process called fluorescence resonance energy transfer, or FRET (27)(28)(29). The maximum emission of fluorescein is around 525 nm in the presence of RecA. The emission of fluorescein at 558 nm, which coincides with the peak of the absorption spectrum of tetramethylrhodamine, is still half the maximum intensity observed at 525 nm; thus energy transfer can occur. Tetramethylrhodamine has a maximum of emission at 582 nm.
By varying the placement of the fluorescent probes attached to 83-mer oligonucleotides, we devised assays that separately measure homologous pairing and strand displacement promoted by RecA protein. We use the term strand displacement to indicate the apparent separation of the single-stranded product from the heteroduplex product of strand exchange without any deliberate deproteinizing treatment. We are unable to specify, however, if the displaced strand has completely dissociated from the heteroduplex, or if it is still in a common nucleoprotein complex, but is sufficiently removed or shielded from the duplex so that the dyes are unable to interact. Fig. 1 depicts the design of the three energy transfer assays. Two schemes were used to observe pairing. In the first, dubbed pairing assay 1, the RecA nucleoprotein filament was formed on the M(Ϫ) oligonucleotide to which fluorescein was attached at the 3Ј end via a 6-carbon linker arm (M(Ϫ)⅐3ЈF: Sequence 1, Table I). This filament was reacted with a duplex molecule consisting of the M(Ϫ) oligonucleotide that had no dye attached, but still bore a primary amine on a linker arm, and the M(ϩ) oligonucleotide with rhodamine on a linker at the 5Ј end (M(Ϫ)⅐3ЈNH 2 /M(ϩ)⅐5ЈR; Sequences 1 and 2, Table I). When attached in these positions, fluorescein and rhodamine should come together during pairing and remain together after strand exchange takes place, resulting in the quenching of fluorescein emission and the enhancement of rhodamine emission (Fig. 1). In pairing assay 2, the rhodamine was located on the 3Ј end of the M(Ϫ) strand of the duplex oligonucleotide, so that the emission of fluorescein should be quenched and the emission of rhodamine enhanced only during the phase of the reaction in which all three strands are in proximity within the filament (M(Ϫ)⅐3ЈF ϩ M(Ϫ)⅐3ЈR/M(ϩ)⅐5ЈNH 2 : Sequences 1 and 2, Table I The third assay was designed to measure only strand displacement. Unlabeled M(Ϫ) filament was reacted with a duplex oligonucleotide consisting of the M(Ϫ) oligonucleotide that was labeled at the 3Ј end with fluorescein and the M(ϩ) oligonucleotide that was labeled with rhodamine at the 5Ј end (M(Ϫ)⅐3ЈNH 2 ϩ M(Ϫ)⅐3ЈF/M(ϩ)⅐5ЈR: Sequences 1 and 2, Table  I). Before the reaction with single-stranded RecA filament, the dyes on the duplex DNA should undergo energy transfer because they are together. Energy transfer should decrease as the fluorescein-labeled strand leaves the three-stranded intermediate upon strand exchange, resulting in an enhancement of fluorescein emission and a decrease in rhodamine emission ( Fig. 1). With this set of three assays, pairing, pairing and strand displacement, or just strand displacement can be monitored by changes in energy transfer.
Energy transfer can be observed either as quenching of the donor (fluorescein) or enhancement of the acceptor (rhodamine). The quenching of fluorescein emission is much easier to measure than the enhancement of rhodamine emission, as can be seen from the steady-state spectra for pairing assay 1 in Fig. 2, which will be described further below. However, fluorescein is sensitive to its environment, and its emission may be quenched by other means than energy transfer, such as the formation of a filament on DNA by RecA protein (data not shown). In contrast, the increase in rhodamine emission due to energy transfer, called sensitized emission, cannot arise from any other source. These properties of the spectra led us to the following compromise. We studied the rapid kinetics of the reactions by monitoring the emission from fluorescein, but we measured the steady-state emission spectra to confirm that changes in fluorescein emission corresponded to changes in the sensitized emission of rhodamine.
Steady-state Emission Spectra- Fig. 2 contains the steady-

R83
A mixture of random 83-mers state spectra for pairing assay 1, depicted schematically in Fig.  1. Pairing assay 1 is used as an example of the energy transfer calculations carried out for all three assays. We reacted M(Ϫ)⅐3ЈF with one RecA monomer per three nucleotide residues for 2 min at 37°C for filament formation (Sequence 1, Table I). The filament was then reacted with an equimolecular quantity of M(Ϫ)⅐3ЈNH 2 /M(ϩ)⅐5ЈR duplex for 2 min (Sequences 1 and 2, Table I). Two emission spectra were taken, one with an excitation wavelength of 493 nm, which primarily excited fluorescein ( Fig. 2A), and another with an excitation wavelength of 558 nm, which exclusively excited rhodamine (data not shown). Since both fluorescein and rhodamine emit in the range of 580 to 585 nm when excited at 493 nm, the contribution by fluorescein at those wavelengths had to be subtracted to observe the sensitized emission of rhodamine. The sensitized emission of rhodamine was calculated by the use of singly labeled controls as described (37) (see "Experimental Procedures" for details). A fluorescein-only control (M(Ϫ)⅐3ЈF filament ϩ M(Ϫ)⅐3ЈNH 2 /M(ϩ)⅐5ЈNH 2 ) and a rhodamine-only control (M(Ϫ)⅐3ЈNH 2 filament ϩ M(Ϫ)⅐3ЈNH 2 / M(ϩ)⅐5ЈR) were carried out under the same conditions as the energy transfer reaction that contained both dyes ( Fig. 2A). The sum of the normalized spectra of the fluorescein-and rhodamine-only controls is plotted in Fig. 2B along with the spectrum of the energy transfer reaction, which contains both fluors. The difference between the two spectra in Fig. 2B is the sensitized emission of rhodamine, which is plotted in Fig. 2D. The difference between the fluorescein-only control and the energy transfer reaction at 525 nm is the quenching of fluores-cein as a result of energy transfer ( Fig. 2A), which is larger and much easier to observe than the sensitized emission. However, as indicated above, calculation of the sensitized emission was necessary to confirm that the quenching of fluorescein was not solely due to interactions with RecA protein or other means not related to energy transfer.
A heterologous control for pairing assay 1 was performed to ensure that energy transfer was homology-dependent, and not the result of nonspecific binding. A mixture of 83-mers of random sequence, R83, was labeled with fluorescein and used in place of M(Ϫ) as the filament strand (R83⅐3ЈF ϩ M(Ϫ)⅐3ЈNH 2 / M(ϩ)⅐5ЈR: Sequences 1, 2, and 5, Table I). The emission spectra of this reaction and the sum of the normalized singly labeled control reactions are shown in Fig. 2C. In the case of the heterologous control, the two spectra almost completely overlap, and the difference between them, which is plotted in Fig.  2D, is less than one-sixth of the sensitized emission of the homologous reaction. Thus, pairing assay 1 resulted in energy transfer that depended on homology, as expected from the design of this assay (Fig. 1).
Pairing assay 2, depicted in Fig. 1, was performed under the same conditions as pairing assay 1. Steady-state spectra confirmed that the dyes behaved as expected and that a heterologous control led to no energy transfer (spectrum not shown). Because of the biphasic nature of the changes in energy transfer in this assay, we defer further consideration to the section below on stopped-flow analysis.
The strand displacement assay involved two sets of energy transfer calculations. First, the sensitized emission of the M(Ϫ)⅐3ЈF/M(ϩ)⅐5ЈR duplex was calculated with duplexes in which either the fluorescein-or the rhodamine-labeled strand had been replaced with an unlabeled strand of the same sequence. The spectrum of the doubly labeled duplex is shown in Fig. 3A, and the sensitized emission of that duplex is plotted in Fig. 3B. Then, M(Ϫ)⅐3ЈNH 2 that had been incubated with RecA protein in a separate Eppendorf tube was added in 1.5-fold excess to each of the three duplexes. After strand exchange had occurred, spectra were collected and the sensitized emission of rhodamine was calculated once more. The spectrum of the energy transfer reaction is shown in Fig. 3A for comparison with the spectrum with the original duplex DNA. The decrease in sensitized emission as a result of the separation of the strands of the duplex is evident from the plot of the sensitized emission before (duplex only) and after strand exchange (Fig.  3B). A heterologous control was performed with the Het(ϩ) oligonucleotide as the filament strand, and no change took place in the spectrum (Sequence 3, Table I, no spectrum shown). Thus, in the strand displacement assay, the energy transfer decreased as expected in a homology-dependent manner (Fig. 1).
Correlation of Sensitized Emission and Changes in Fluorescein Emission-Although the changes in sensitized emission occurred in all three assays, we needed to be able to compare the sensitized emission between assays and to determine how it was related to the changes in fluorescein emission. To compare energy transfer quantitatively in different assays, the ratio of the sensitized emission of rhodamine to the normalized emission of the rhodamine-only control was taken. This ratio, expressed as a percentage, should be independent of variations in concentration. The normalized sensitized emission is the percent increase in rhodamine emission for the two pairing assays, shown in Fig. 4 (A and B). For the strand displacement assay, shown in Fig. 4C, the percent decrease in rhodamine emission was calculated from the difference in the normalized sensitized emission before and after the M(Ϫ)⅐3ЈF/M(ϩ)⅐5ЈR duplex was reacted with M(Ϫ)⅐3ЈNH 2 .
To assess the correlation between changes in the sensitized emission of rhodamine and the emission of fluorescein, we had to know what portion of the changes in fluorescein emission was specific to energy transfer. In the case of the pairing assays, the quenching of fluorescein that was specific to energy transfer was determined from the difference in intensity at 525 nm between the fluorescein-only control and the reaction containing both dyes. Those two reactions were identical except for the presence of rhodamine in the doubly labeled sample, so the differences in emission should have been solely due to energy transfer. The nonspecific quenching was reflected in the difference between the total quenching observed during the course of the reaction containing both dyes and the specific quenching (Fig. 4, A and B). For the strand displacement assay, the nonspecific quenching was calculated from the change in emission of the fluorescein-only control before and after strand exchange. By comparing the sensitized emission, the specific quenching, and the nonspecific quenching of fluorescein, the reliability of the quenching of fluorescein as an indicator of energy transfer was determined.
Pairing assay 1 gave 37% specific quenching of fluorescein and 94% enhancement of rhodamine emission (Fig. 4A). The total quenching of fluorescein was 30%, indicating that all the quenching was the result of energy transfer. 3 The heterologous 3 The specific quenching was larger than the total quenching because separate reactions, the fluorescein-only control and the doubly labeled control for pairing assay 1 produced 5% nonspecific and 1% specific quenching of fluorescein, with 6% enhancement of rhodamine emission. These data demonstrated that there was a good correlation between the quenching of fluorescein and energy transfer as assessed by the sensitized emission of rhodamine for pairing assay 1. There was no energy transfer to rhodamine in the absence of the cofactor ATP, but there was 8% quenching of fluorescein, 5% of which appeared to be specific (Fig. 4A). This specific component might be an artifact produced by slight differences in concentration between the fluorescein-only sample and the doubly labeled sample. The overall quenching was probably the result of RecA binding DNA even in the absence of a cofactor (39,40). In any event, the controls for the requirement of homology and ATP were satisfactory.
A further control was performed to demonstrate that the energy transfer observed for homologous substrates was not due to an artifact generated by end-to-end aggregation rather than homologous alignment. In this control, rhodamine was placed at the 3Ј end of the M(ϩ) in the duplex DNA, so that rhodamine and fluorescein would be on opposite ends of the heteroduplex product of strand exchange (M(Ϫ)⅐3ЈF ϩ M(Ϫ)⅐3ЈNH 2 /M(ϩ)⅐3ЈR). This would make energy transfer impossible unless there was nonspecific aggregation of ends. Only 5% quenching of fluorescein and 8% enhancement of rhodamine was observed, which was comparable to the heterologous background, suggesting that end-to-end aggregation may have been responsible for most of the heterologous signal at those concentrations of DNA and RecA (Fig. 4A).
When a 10-fold excess of unlabeled heterologous duplex oligonucleotide (Sequences 3 and 4, Table I) was added to filament formed on M(Ϫ)⅐3ЈF before the M(Ϫ)⅐3ЈNH 2 /M(ϩ)⅐5ЈR duplex DNA was added, 3% nonspecific and 29% specific quenching of fluorescein, as well as 41% enhancement of the rhodamine emission still occurred. This demonstrated that the RecA filament took up heterologous sequences, but that homologous ones were able to compete with the heterologous DNA (Fig. 4A). This competition might have been more effective if the reaction time were longer and ATP regeneration had been used.
Pairing assay 2 produced 7% specific quenching, 14% nonspecific quenching of fluorescein, and 20% enhancement of rhodamine emission (Fig. 4B). The nonspecific component of the quenching of fluorescein was larger relative to the specific quenching than in pairing assay 1, apparently because the energy transfer was far less (compare Figs. 4A and 4B). There were no energy transfer-related changes in fluorescence for the heterologous control for pairing assay 2 (Fig. 4B). Since the nonspecific quenching in pairing assay 2 was similar in magnitude for homologous and heterologous DNA, most of the nonspecific quenching was probably caused by interaction of the duplex DNA with the RecA filament that was independent of homology, such as end-to-end aggregation. The correlation between the quenching of fluorescein and energy transfer seems less good for pairing assay 2 than for pairing assay 1, but the spectra could not be taken when energy transfer was the greatest in pairing assay 2 because of the biphasic changes that occur in that assay (see below).
In the strand displacement assay, the fluorescein emission increased 370%, 350% of which was specific to energy transfer, and the sensitized emission of rhodamine decreased 62% (Fig.  4C). The heterologous control for strand displacement produced no changes at all. Since no strand exchange could take place with these substrates, this result was expected. In general, pairing assay 1 and the strand displacement assay were better than pairing assay 2 in terms of having few or no changes in fluorescein emission that were not related to energy transfer.
Stopped-flow Analysis of Pairing and Strand Displacement Rates-Having established that changes in fluorescein emission were correlated with homology-dependent changes in energy transfer, we used changes in fluorescein emission as observed by stopped-flow spectrofluorometry to study the rapid kinetics of homologous pairing and strand exchange. Samples were excited at 493 nm, and the emission of fluorescein at 520 nm was observed. A control for photobleaching of fluorescein showed less than 2% of the change in fluorescence observed for any of the assays. Heterologous controls for the assays performed with R83⅐3ЈF or R83⅐3ЈNH 2 produced no fluorescence change beyond background noise. A control for nonspecific quenching of fluorescein yielded a change in fluorescence that was 6% of the amplitude change in pairing assay 1 and 16% of the change in pairing assay 2 (see "Experimental Procedures" for further details of the controls).
Pairing assay 1 yielded a single, rapid decrease in fluorescein emission, as predicted by the scheme in Fig. 1 (Fig. 5A). Pairing assay 1 was performed with a range of concentrations of singlestranded oligonucleotide ranging from 5 M to 50 M and duplex DNA from 10 M to 100 M in 1-to-1 ratios of filament to duplex. Also, the filament concentration was held constant at 10 M and the concentration of duplex DNA was varied 4-fold. For initial analysis of rates, the time courses for pairing assay 1 at different concentrations were fit with single exponential functions or the sum of two exponential functions. The general reaction, were used to calculate the specific quenching, and there might have been slight differences in concentrations between the two reactions. equations used for fitting the data were I ϭ A 1 ⅐exp(Ϫk 1 ⅐t) ϩ C or A 1 ⅐exp(Ϫk 1 ⅐t) ϩ A 2 ⅐exp(Ϫk 2 ⅐t) ϩ C, where I ϭ fluorescence intensity, t ϭ time, k ϭ first order rate constant, A ϭ amplitude, and C ϭ end point of the curve. The results are listed in Table II. Residuals for the single or double exponential fits are plotted beneath the data to indicate how well the data are described by exponential functions (Fig. 5A). The residual for the single exponential fit for pairing assay 1 deviated considerably from zero in the first 30 s, whereas the residual for the double exponential fit deviated less and at later times (Fig. 5A). The failure of a single exponential to fit the data indicated that pairing assay 1 was not detecting a first order process. The apparent first order rate constants, k obs(a) and k obs(b) , varied about 3-fold with concentration (Table II), indicating that the sum of two exponential functions also did not adequately describe the reaction.
Controls were performed with constant concentrations of DNA (10 M single strand and 20 M duplex) and with one RecA monomer to six nucleotides or one nucleotide (data not shown). The rates were the same as for the reaction with one RecA monomer to three nucleotides, within the error of the measurements. These controls demonstrated that the concentration dependence of the rate constants was not just the result of changes in protein concentration. Additionally, when the control for nonspecific quenching was subtracted from the data for 10 M filament and 20 M, k obs(a) remained the same and k obs(b) increased by only 0.01 s Ϫ1 . The lack of fit to a single exponential function and the variation in constants with concentration confirmed that the pairing reaction was not first order, which is consistent with the pairing reaction being a bimolecular process.
In contrast to pairing assay 1, pairing assay 2 demonstrated two phases: a decrease in fluorescein emission upon pairing and increase with displacement of the rhodamine-labeled strand, as predicted in Fig. 1 (Fig. 5B). Also in contrast to pairing assay 1, pairing assay 2 was well fit by the sum of two exponentials. The residual shows the quality of the fit, with no significant deviations from zero (Fig. 5B). The apparent first order rate constants k obs(c) and k obs(d) varied little with concentration (Table II). These observations suggest that pairing assay 2 may be reflecting two first order processes. This is difficult to reconcile with pairing assay 1, unless two or more intermediates exist, and pairing assay 2 is scoring a different, later intermediate from assay 1. See "Discussion" for further details.
The strand displacement assay resulted in a single increase in fluorescein emission, as expected ( Figs. 1 and 5C). The time course of the strand displacement assay was described as well by a single exponential as by the sum of two exponentials (Fig.  5C). The residuals for both fits show trends away from zero at early times (Fig. 5C). This may be the result of changes in fluorescence that take place as the duplex is taken up into the RecA single-stranded DNA filament. The rates varied only from 0.05 Ϯ 0.02 to 0.07 Ϯ 0.01 s Ϫ1 over a 10-fold concentration change, which suggested a first order reaction mechanism, despite the problems with fitting the data to a single exponential (Table II). A first order mechanism is consistent with the proposed model, in which the pairing intermediate goes on to complete strand exchange and displacement. The change in fluorescence for the strand displacement assay was slower than for pairing assay 1 or the first phase of pairing assay 2, but was almost the same as the second phase of pairing assay 2. This indicates that the strand displacement assay and the latter half of pairing assay 2 probably detect the same step of strand exchange. Controls with different RecA to nucleotide ratios, like those performed for pairing assay 1, indicated that the rates changed only when there was less than one monomer of RecA to three nucleotides (data not shown). At one RecA to six nucleotides, the rate dropped to 0.02 s Ϫ1 , which suggested that incomplete filament formation had more of an effect on strand exchange than on pairing.
Calibration of Stopped-flow Data with Gel Assays for Strand Exchange-The preliminary analysis above indicated that at least one step in the strand exchange process is concentrationdependent. A link between the fluorescence assays and an independent assay for the concentrations of the species had to be established for further kinetic analysis, described below. The fluorescence assay for strand displacement was compared with the more traditional gel electrophoresis assay to establish whether they both detected the same step of the strand exchange reaction. We used the same substrates in both assays to observe the time course of strand exchange. In the fluorescence assay, the emission of fluorescein at 525 nm was monitored; in the gel electrophoresis assay, aliquots of the reaction were taken at various times and deproteinized with SDS and proteinase K. The deproteinized DNA was then run on a nondenaturing polyacrylamide gel, and the percent strand exchange determined. The two assays were independently normalized to a maximum of 100% (Fig. 6). The time courses of strand exchange measured by fluorescence assay and by gel assay coincided. According to the simplest interpretation, the two assays measure the same step of strand exchange.
The gel assay was also used to measure the absolute yield of strand exchange with the same substrates that were used for the fluorescence assays. Knowledge of the equilibrium constants for the strand exchange reaction reduced the number of rate constants that had to be independently varied in the mathematical modeling of the stopped-flow data below. Two sets of experiments were conducted to discover the effect on yield of varying substrate concentration. When the filament concentration was held constant at 10 M and the duplex DNA concentration increased from 5 M to 30 M, the yield of heteroduplex increased from 16 to 68% (data not shown). The yield at one filament to one duplex was 56%. These results indicate that pairing is reversible (k Ϫ1 0); otherwise, the yield should have reached maximum at one filament to one duplex, rather than continuing to increase even though the duplex was no longer the limiting substrate. The data from this experiment were used to calculate the relationship between the equilibrium constants for pairing and strand exchange as described under "Experimental Procedures" under "Mathematical Modeling of Stopped-flow Data." In other experiments, the concentration of DNA and RecA protein was increased up to 5-fold while the 1-to-1 ratio of single-stranded to double-stranded DNA was maintained, and the percent of strand exchange remained constant at an average of 54 Ϯ 3% (data not shown). This result also suggested that an equilibrium existed in the overall reaction, including the strand exchange step, which supported the modeling of strand exchange as reversible, with k Ϫ2 0 (see below).
We measured the yield of strand exchange with the substrates for the different assays to see if the dyes themselves affected the reactions. Under the conditions of the steady-state fluorometric assays, in the absence of an ATP regeneration system, the gel assay revealed that the respective yields were 40 Ϯ 10%, 30 Ϯ 10%, and 40 Ϯ 10% for pairing assays 1 and 2 and the strand displacement assay. Substrates that lacked any modification, even the primary amine, gave 30 Ϯ 10% products. The dyes did not seem to significantly affect the yield of strand exchange.
We also wanted to confirm that fluorescence changes in the reactions were proportional to concentration changes, so that we could convert concentration to fluorescence to compare theoretical curves generated by mathematical modeling of the reactions with the stopped-flow data. To calibrate changes in fluorescein emission with changes in concentration, we used RecA-catalyzed annealing of 10 M M(Ϫ)⅐3ЈF filament and 10 M M(ϩ)⅐5ЈR to model the maximum amplitude for pairing assay 1 and the strand displacement assay. The annealing reaction was performed under the same conditions as the other stopped-flow fluorescence measurements. The amplitude of the change in fluorescein emission observed with the strand displacement assay was 62% of the amplitude observed with the annealing reaction, which is close the yield of strand exchange assayed by gel electrophoresis (54%). Pairing assay 1 produced an amplitude that was 75% of the annealing amplitude, which was higher than expected from the results of the gel assay. The pairing assay may have detected intermediates that had not gone on to complete strand exchange, and thus were not detected by the gel assay. The amplitudes of the assays relative to the annealing reaction were used to convert concentrations to fluorescence emission, as described under "Experimental Procedures." Mathematical Modeling of the Assays to Obtain Equilibrium and Rate Constants-From the preliminary analysis of the data by fitting with exponential expressions, it was clear that there were at least two steps in the strand exchange reaction and the first step was probably a second order process. We have further analyzed the kinetic data based on the reaction scheme shown in Fig. 1 by comparison of experimental data with theoretical curves generated as described under "Experimental Procedures." The analysis was done with concentrations in terms of molecules of DNA, so all constants derived are in those terms. The strand exchange reaction was modeled as a completely reversible reaction. This assumption was made on the basis of the observations noted above in the results of the gel assays. The equilibrium constants for pairing and strand exchange, K eq1 and K eq2 , were determined from the analysis of the variation in the amount of products with substrate concentrations as described under "Experimental Procedures" and elsewhere (38). The fit was reasonable when the K eq1 value was between 1 ϫ 10 6 and 1 ϫ 10 7 M Ϫ1 , and the best fit was obtained with K eq1 ϭ 5 ϫ 10 6 M Ϫ1 (data not shown). This analysis provided the relationship between K eq1 and K eq2 values that was used to estimate the rates of the back reaction (k Ϫ1 and k Ϫ2 ), and thus decrease the number of kinetic parameters to be fitted from 4 to 3.
Since the preliminary exponential analysis indicated that the strand displacement step followed first order kinetics and the k 2 value was about 0.06 s Ϫ1 , regardless of the concentration of substrate, we have analyzed the data from pairing assay 1 using this k 2 value. To find the best fit, we have systematically varied the K eq1 and k 1 values. The K eq2 value, and thus the k Ϫ2 value, was estimated from the relationship between the K eq1 and K eq2 values. This procedure was performed on the data for all the concentrations listed in Table II except for the lowest concentration, which was at the limit of detection and had a low signal-to-noise ratio. We obtained a good fit for all cases, and Fig. 7A is one example. The K eq1 and k 1 values calculated from each data set were independent of substrate concentrations (Table III). The ability to fit the data from pairing assay 1 to a model with a second order pairing step and to obtain rate and equilibrium constants that are independent of concentration supports a model in which the pairing step is bimolecular.
The best fit for k 1 was about 1 ϫ 10 6 M Ϫ1 s Ϫ1 and for K eq1 was 1 ϫ 10 7 M Ϫ1 . The K eq1 value thus determined was close to the value determined from the analysis of amount of strand exchange products at the end of the reaction (5 ϫ 10 6 M Ϫ1 ). This consistency in the value of K eq1 obtained by different methods further supports the validity of our analysis. Uncertainty in the value of the yield of strand exchange (Ϯ10%), and thus the change in fluorescence intensity, affected the K eq1 value, but did not significantly alter the k 1 value obtained. In some cases we also varied the k 2 value to examine the effect of its uncertainty on the determination of k 1 value. The variation of k 2 value from 0.04 to 0.12 s Ϫ1 did not significantly affect the analysis, showing that pairing assay 1 provides mainly information about the first step of the reaction, as we expected from the design of the assay (Fig. 1).
FIG. 6. Comparison of time courses for strand exchange assayed by fluorescence and gel electrophoresis. q, strand exchange measured by monitoring fluorescein emission at 520 nm upon excitation at 493 nm with the strand displacement assay; Ⅺ, strand exchange with the same conditions assayed by gel electrophoresis following deproteinization. Percentages have been normalized for each assay so that the maximum is 100.
We then analyzed the data from the strand displacement assay, taking into account the first step of the reaction to more accurately estimate the k 2 value. We searched for the best fit by systematically varying k 2 value and using the values for K eq1 and k 1 determined above. The average of the best fits for all concentrations (except the highest) was k 2 ϭ 0.06 Ϯ 0.02 s Ϫ1 (Table III). The fit became better when one assumed that the energy transfer between two strands of the duplex DNA decreased by about 20% upon binding to the RecA-singlestranded DNA filament (Fig. 7C). Several observations have demonstrated that the structure of duplex DNA is modified upon the binding to RecA-single-stranded DNA complex (41)(42)(43)(44)(45). Our results indicated that the modification occurred immediately after the binding, or perhaps only the duplexes that had randomly assumed a different conformation interacted with RecA (see Fig. 1). Uncertainty in the yield of strand exchange and K eq2 values (2 ϫ 10 Ϫ7 to 3 ϫ 10 Ϫ7 M) affected the determination of the value of k 2 .
Finally, we analyzed the data from pairing assay 2 using the values of the constants determined above from the other two assays. We obtained a relatively good fit with these values, indicating that the reaction scheme is roughly correct. The best fit for the data from pairing assay 2 was obtained with smaller k 1 and k 2 values than those determined from the data for the other assays (Fig. 7B, Table III). However, the analysis of the data from pairing assay 2 is complicated by the smaller amplitude of the fluorescence changes and the larger nonspecific changes in fluorescence relative to pairing assay 1 and the strand displacement assay. Consequently, the rate constants cannot be estimated more precisely from the data for pairing assay 2.

Development of Assays for RecA-catalyzed Pairing and Strand Exchange Based upon Fluorescence Energy Transfer-
From the beginning of studies in vitro on the recombination activities of RecA protein, it has been clear that there is an initial phase of the reaction in which homologous recognition occurs, followed by a slower phase during which extensive strand exchange occurs (9). The observation that homologous recognition occurred without any free ends in the DNA substrates demonstrated that recognition does not require that the strands of nascent heteroduplex DNA be truly be intertwined, as in Watson-Crick duplex DNA (41-44, 46 -48). However, little or no success has attended efforts to isolate the initial intermediate or even to demonstrate that strand exchange at or near the site of recognition is an event that is distinct and separable from recognition. Indeed, studies from several laboratories have supported the hypothesis that localized switching of bases from parental to recombinant pairs is the mechanism of homologous recognition (49 -51). The present kinetic studies, which make use of fluorescence energy transfer and topologically simple oligonucleotides, provide insights on the staging of events in the overall reaction, demonstrating two or possibly three distinct steps.
We developed a set of three assays that detected pairing, strand displacement, or both, depending on the location of the fluorescent dyes fluorescein and tetramethylrhodamine (Fig.  1). These assays are performed in solution without the disruption of intermediates, and stopped-flow analysis can be used to measure the rates of the separate phases of the reaction. Although we cannot exclude steric effects of the probes themselves, the yield of strand exchange did not differ significantly between dye-labeled and unlabeled substrates. Since the fluorescence assays use oligonucleotides, they suffer the same drawbacks as any assay that uses RecA and oligonucleotides, namely that RecA does not bind as well to oligonucleotides as to long DNA (52,53). However, the length of the oligonucleotides is more than sufficient for homologous pairing and strand exchange (33, 54 -56). Since reactions with oligonucleotides are not complicated by the formation of coaggregates (18,21,30) or by topological barriers to strand displacement (31), they provide a simplified model system that is amenable to kinetic analysis.
Model of Pairing and Strand Exchange-When the stoppedflow data were fit to the model in Fig. 1, the assumption was made that the strand exchange reaction with oligonucleotides is reversible, which is supported by several lines of evidence.

TABLE III
Equilibrium and rate constants from analysis of stopped-flow data Constants were derived from fitting stopped-flow data to the kinetic scheme outlined in Fig. 1.   Rosselli and Stasiak (55) demonstrated that, when the products of strand exchange with 52-mer oligonucleotides were fixed with glutaraldehyde, protein-free heteroduplex was released as soon as heteroduplex appeared upon deproteinization, while the displaced single-strand remained bound by RecA. These observations were confirmed by us with a filter assay in which protein-bound DNA was retained by a filter on the basis of size. 4 As a result, the displaced strand was available for another round of strand exchange (55). In addition, we were able to show that in a strand exchange reaction at completion, the addition of excess single-stranded product to drive the reaction back established a new equilibrium governed by the same K eq as the initial reaction. 4 Further evidence of reversibility came from the experiments reported here. As noted under "Results," the yield of strand exchange remained near 50% over a 5-fold change in the concentration of the substrates while the molecular ratio of filament to duplex was kept constant, which indicated that an equilibrium existed for the reaction and that k Ϫ2 was significant ( Fig. 1). Also, the yield of heteroduplex continued to increase as the duplex/single-strand ratio exceeded 1, which demonstrated that k Ϫ1 0 (Fig. 1). The assumption of reversibility was supported by previous studies, gel electrophoresis data in the current study, and most of all by the fact that the stoppedflow data could be fit to such a model.
The kinetic order of the steps in strand exchange was also supported both by the fit of the data to the model and by the more qualitative preliminary analysis of the stopped-flow data with exponential functions. When the stopped-flow data from pairing assay 1 were fit to a model with a second order, reversible pairing step, the rate constants and the equilibrium constant K eq1 varied little with substrate concentration, which supported the model (Table III). Likewise, the first order rate constants determined by fitting the data from the strand displacement assay to a reversible first order step were constant (Table III). The model in Fig. 1 is supported not only by general observations but also by the quality of the fit of the data from pairing assay 1 and the strand displacement assay to the model.
The equilibrium and rate constants derived from the data for pairing assay 1 and the strand displacement assay describe a two-step process for the detection of homology. The value of k 1 , 1 ϫ 10 6 M Ϫ1 s Ϫ1 , determined from the stopped-flow data for pairing assay 1, is about the same as the rate constant for the annealing of complementary 16-mer oligonucleotides in the absence of protein (26). The value of k Ϫ1 (0.10 s Ϫ1 ) is close to the value of k 2 for strand displacement (0.06 s Ϫ1 ). Thus, the pairing intermediate has an equal probability of dissociating or going on to strand displacement. The back reaction for strand displacement (k Ϫ2 ϭ 2-3 ϫ 10 5 M Ϫ1 s Ϫ1 ) is significant compared with the rate constant, k 1 , for the initial pairing step. In light of the reversibility of both steps in strand exchange, discrimination between homologous and heterologous substrates could occur at either or both steps.
Pairing Assay 2 and the Possible Existence of Another Intermediate-Pairing assay 2, however, did not completely fit the kinetic scheme outlined in Fig. 1. Pairing assay 2 was biphasic, as expected (Fig. 5B). The second phase of pairing assay 2 was first order and had almost the same rate as strand displacement (Tables II and III); thus, it probably also reflected strand displacement, as predicted. Surprisingly, however, the first phase of pairing assay 2 also appeared to be first order. The data were perfectly fit by a single exponential function (Fig.  5B), and the rate constants were independent of concentration (Table II). In clear contrast, the data for pairing assay 1 were well described by a second order model. Since the initial homologous interactions should be second order, we infer that the first exponential phase of pairing assay 2 represents events that occur after those detected by assay 1. The simplest explanation is that pairing assay 2 detects a third step in the strand exchange reaction between initial pairing and strand displacement.
The two pairing assays might have detected different intermediates because of differences in the placement of the fluorophores. A priori, there is no reason why pairing assay 1 and pairing assay 2 should detect the same intermediate. In pairing assay 1, rhodamine was on the complementary strand, and the expected second order kinetics were observed (Fig. 1). On the other hand, in pairing assay 2, rhodamine was on the identical strand of the duplex, and first order kinetics were seen. The identical strand of the duplex may have been just outside the radius of energy transfer during the initial pairing step. Perhaps the filament strand is close to its complement during the initial second order pairing step, which is followed by a first order conformational change that brings identical strands into proximity. Finally, the second pairing intermediate goes on to complete strand exchange in a first order reaction. Further studies of pairing assay 2 are needed to evaluate this three-step model.
Comparison with Rates for Human Rad51-Preliminary studies have been done on the strand exchange reaction catalyzed by Rad51 protein, a human homolog of RecA, using the assay system described in this paper (15). Surprisingly, the apparent first order rate constants for pairing assay 1 and the strand displacement assay were the same. 5 From these initial studies of Rad51, it seems that either pairing assay 1 does not detect the initial pairing step catalyzed by human Rad51, or pairing and strand exchange are the same step, and all discrimination of homology occurs at the strand exchange step. Further studies are needed to distinguish between these possibilities. If pairing and strand exchange are simultaneous, Rad51 might be less selective, or the process of finding homology might be less efficient than for RecA.
Comparison with Previous Studies of Kinetics-In previous studies with long DNA substrates, joint molecule formation was assayed by a nitrocellulose filter assay that favored the survival of joints that had already undergone limited strand exchange (16 -20, 57). Thus, the formation of such joints was probably more closely related to strand exchange as measured in the present study. Published data support this interpretation; the first order rate constant for joint molecule formation determined by Julin et al. (20) was 0.014 s Ϫ1 , which is only slightly less than the k 2 value observed here (0.06 s Ϫ1 ).
Yancey-Wrona and Camerini-Otero (22) developed an assay for the stable synapsis of an oligonucleotide with a longer duplex target. In their assay, the protection of a restriction site in a 57-mer oligonucleotide duplex by a shorter RecA-oligonucleotide complex formed in the presence of ATP␥S was measured following an 8-min digestion with restriction endonuclease. They used a standard Michaelis-Menten model to analyze the data and found that the equilibrium constant for the homologous pairing ranged from 7.7 ϫ 10 6 to 1.3 ϫ 10 7 M Ϫ1 , which is in agreement with the value of K eq1 determined in this study (1 ϫ 10 7 M Ϫ1 ). However, the rate constant they measured for stable synapsis was 2 orders of magnitude lower than the strand exchange rate observed in this study, which may have been related to the use of ATP␥S as a cofactor.
The Role of the RecA Filament in Reversibility-Reversibility is presumably advantageous in vivo. In the cell, RecA or some other protein has to be able to dissociate whatever joint molecule has been formed in the face of topological constraints on strand displacement or in the event that the substrates are not completely homologous. This has been observed in vitro with long DNA substrates that do not have a free end to displace, such as distal joints or medial joints formed with 3Ј single strand ends, which undergo cycles of formation and dissociation (6,58,59). These joints may involve localized base pair switching because they can be isolated following deproteinization. Uptake of duplex DNA into the RecA filament unwinds the DNA and eliminates favorable stacking interactions between bases (41)(42)(43)(44)(45)(46)(47)(48). Perhaps the role of the unique structure of the RecA filament is to ensure the instability of the heteroduplex, without losing the specificity of Watson-Crick base pairing, so that the energetic barrier in either direction of pairing and strand exchange is lower. The reduction of the stability of heteroduplex may raise the threshold for stabilization of joints, ensuring a more perfect fit before strand exchange is allowed to proceed. The structure of the filament itself is thus the instrument of reversibility and fidelity.