DNA-induced Dimerization of the Escherichia coli Rep Helicase ALLOSTERIC EFFECTS OF SINGLE-STRANDED AND DUPLEX DNA*

The Escherichia coli Rep helicase is a stable mon- omer (Mr = 72,802) in the absence of DNA; however, binding of single-stranded (8s) or duplex (ds) DNA induces Rep monomers to dimerize. Furthermore, a chemically cross-linked Rep dimer retains both its DNA-dependent ATPase and helicase activities, sug- gesting that the functionally active Rep helicase is a dimer (Chao, K., and Lohman, T. M. (1991) J. Mol. Biol. 221, 1165-1181). Using a modified "double-fil-tern nitrocellulose filter binding assay, we have ex- amined quantitatively the equilibrium binding of Rep to a series of ss-oligodeoxynucleotides, d(pN), (8 5 n I 20) and two 16-base pair duplex oligodeoxynucleo- tides, which are short enough so that only a single Rep monomer can bind to each oligonucleotide. This strat-egy has enabled us to examine the linkage between DNA binding and dimerization. We also present a statistical thermodynamic model to describe the DNA-induced Rep dimerization in the presence of ss- and/or ds-oligodeoxynucleotides. We observe quantitative agreement between this model and the experimental binding isotherms and have analyzed these isotherms to obtain the seven independent interaction constants that describe Rep-DNA binding and Rep dimerization.


77550.
7l ity of either ss-or ds-DNA to the free protomer of a half-saturated Rep dimer is clearly influenced by the conformation of DNA bound to the first protomer. These allosteric effects further support the proposal that the Rep dimer is functionally important and that the Rep-DNA species P2S2 and P2SD may serve as useful models for intermediates that occur during DNA unwinding. The ability of Rep to form the ternary complexes P2S2 and P2SD has important implications for how a Rep dimer may interact with a DNA replication fork and unwind DNA.
Duplex DNA is the stable form of the majority of DNA within a cell. However, duplex DNA must be unwound, at least transiently, to produce the single-stranded (ss)' DNA intermediates that are needed for processes such as replication, repair, and recombination. This DNA unwinding is catalyzed by a class of DNA-binding enzymes referred to as DNA helicases in a reaction that is coupled to ATP binding and hydrolysis. Helicases have been identified and isolated from a variety of prokaryotic and eukaryotic sources (for recent reviews see Matson and Kaiser-Rogers, 1990; Thommes and Hubscher, 1990;Matson, 1991;Lohman, 1992) and they appear to be ubiquitous. Although the unambiguous assignment of the function in vivo of any particular helicase can be difficult due to their large number (at least 10 different helicases have been identified in Escherichia coli) and the possibility for functional complementation (Fassler et al., 1985;Lee and Kornberg, 1991;Taucher-Scholz et al., 1983;Washburn and Kushner, 1991), helicases as a class are essential to most DNA metabolic processes.
The E. coli Rep protein was one of the first helicases to have been characterized genetically (Denhardt et al., 1967;Lane andDenhardt, 1974, 1975) and biochemically (Scott et al., 1977). Its role in DNA replication is well established since genetic studies indicate that E. coli rep mutants exhibit reduced rates of chromosomal replication fork movement and cannot support replication of ss-DNA bacteriophages such as dX174, P2, fl, and M13 (Denhardt et al., 1967;Lane andDenhardt, 1974, 1975). Although essential for the unwinding of duplex replicative form phage DNA during ss-DNA phage replication (Calendar et al., 1970;Lane and Denhardt, 1975), rep is not essential in E. coli (Colasanti and Denhardt, 1987). This probably reflects the participation of other essential helicases in replication, such as the DnaB protein (Lebowitz and McMacken, 1986). Other studies suggest that rep may also function in DNA repair (Calendar et al., 1970;Bridges and von Wright, 1981). Interestingly, rep/uurD double mu-The abbreviations used are: ss, single-stranded; ds, doublestranded; HPLC, high performance liquid chromatography. tants are lethal in E. coli (Washburn and Kushner, 1991).
The Rep helicase can unwind duplex DNA in uitro in the absence of DNA synthesis (Yarranton and Gefter, 1979;Kornberg et al., 1978;. In the absence of a phage accessory protein such as the 4x174 cis A or fl gene I1 protein, Rep requires a 3' ss-DNA region flanking the duplex DNA in order to initiate unwinding (Yarranton and Gefter, 1979;Lohman et al., 1989). Chao and Lohman (1991) have recently shown that although Rep remains monomeric (Mr = 72,802, Gilchrist and Denhardt, 1987) up to concentrations of at least 8 p M (monomer) even in the presence of nucleotide cofactors, binding of either ss-or duplex (ds) DNA induces Rep to dimerize. Furthermore, a chemically cross-linked Rep dimer retains its ss-DNA-dependent ATPase and DNA helicase activities, suggesting strongly that the active form of the Rep helicase is dimeric (Chao and Lohman, 1991).
A dimeric structure in a helicase has important implications for its mechanism of unwinding DNA (Chao and Lohman, 1991;Lohman, 1992). For example, it has been suggested that unwinding of duplex DNA might proceed via intermediates in which the helicase would interact simultaneously with both 9s-and ds-DNA at an unwinding fork (Yarranton and Gefter, 1979). Such a model would require a minimum of two separate DNA-binding sites, a requirement that can be readily satisfied by a dimeric helicase if each protomer of the dimer can bind DNA. Interestingly, essentially all helicases for which this property has been examined have an oligomeric assembly state, usually hexameric or dimeric. Hence, this may yet prove to be a property common to all helicases. It is plausible that such oligomeric structures provide helicases with the multiple DNA-binding sites which may be important for their mechanisms of DNA unwinding (Lohman, 1992).
In order to assess the importance of DNA-induced dimerization in the mechanism of Rep-catalyzed DNA unwinding, it is important to determine the stoichiometry of Rep-DNA binding and to resolve the thermodynamic linkages in the energetics of DNA binding and protein dimerization. Using a series of ssand ds-DNA oligonucleotides that are long enough to bind only a single Rep monomer to each oligonucleotide, we were able to determine all the equilibrium interaction constants for DNA binding and Rep dimerization independently. Such an approach required the development of a statistical thermodynamic model to describe the multiple binding and dimerization equilibria so that the individual interaction constants can be determined from experimental binding titrations. The results of this study suggest how Rep may bind to an unwinding fork at intermediate stages during DNA unwinding and provides the basis for additional studies on the modulation of DNA binding and Rep dimerization by ATP binding and hydrolysis.

MATERIALS AND METHODS
Reagents and Buffers-All solutions were made with reagent grade chemicals using Milli-Q H20, i.e. distilled H20 that was subsequently deionized and further purified through a Milli-Q Water Purification System (Millipore Corporation, Bedford, MA). Standard titration buffer is 20 mM Tris-HC1, pH 7.5, at 4 "C, 6 mM NaC1, 5 mM 2mercaptoethanol, 1 mM Na3EDTA, 10% (v/v) glycerol (spectrophotometric grade, Aldrich). Kinase buffer contained 50 mM Tris-HC1, pH 7.5, at 25 "c, 10 mM MgC12, 10 mM 2-mercaptoethanol. C,, buffer contained 100 mM Tris-HC1, pH 7.5, at 25 "C, 10 mM triethylammonium bicarbonate (TEAB), pH 7.5,l mM Na3EDTA. All buffers were made from 0.5 M Tris stocks titrated to the appropriate pH at the indicated temperature. The pH reported for each buffer was measured at the final buffer concentration and temperature used in the experiment. ATP was obtained from Calbiochem (La Jolla, CA). [y-"PI ATP (3000 Ci/mmol) was obtained from Du Pont-New England Nuclear.
Proteins and Enzymes-E. coli Rep protein was purified to >99% purity from E. coli MZ-l/pRepO (Colasanti and Denhardt, 1987) as described Chao and Lobman, 1991). Its concentration was determined spectrophotometrically, using an extinction coefficient for the monomer of = 8.47 X lo4 M" cm" . T4 polynucleotide kinase was purchased from U. S. Biochemical Corporation (Cleveland, OH).
Oligodeoxynucleotides-All oligodeoxynucleotides were synthesized by the Washington University School of Medicine Protein Chemistry Laboratory (St. Louis, MO) using an AB1 model 380A Automated DNA Synthesizer (Applied Biosystems Inc., Foster City, CA). Singlestranded oligodeoxynucleotides, dT8, dTI2, dT14, dT16, dT20, dT7AT8, d A l f i , dCI6, KL3 (5"GACTCGTTACCTGAGT) and KL4 (5"ACT-CAGGTAACGAGTC) were purified to >99% purity as described . A hairpin oligodeoxynucleotide, HP (5'-GACTCGTTACCTGAGT-T4-ACTCAGGTAACGAGTC), was purified by electrophoresis through a 15% acrylamide, 1.5% bisacrylamide, 8 M urea gel in TBE at 60 "C. The DNA was recovered by electroelution using an Elutrap apparatus (Schleicher & Schuell) and further purified on a Maxi-Clean CIS cartridge (Alltech Associates, Deerfield, IL) as described (Wong et al., 1991). The duplex oligodeoxynucleotide, KL34, was formed by annealing KL3 and KL4 (200 p M each) at room temperature in 10 mM Tris-HC1, pH 7.5, 1 mM EDTA, 150 mM NaCl and was purified away from unannealed ss-DNA by electrophoresis through a nondenaturing 24% acrylamide, 0.8% bisacrylamide gel in TBE. DNA was recovered by electroelution and purified using Maxi-Clean cartridges as described above. The sequence of KL34 is identical to the sequence of the 16-base pair duplex region of the hairpin, HP. All DNA stocks were dialyzed or desalted on a Bio-Gel P2 column into Milli-Q H20 for storage. Purity was determined by analytical polyacrylamide gel electrophoresis. Single-stranded DNA was visualized by autoradiography using 5' end-labeled DNA. Double-stranded DNA was visualized after treatment with Stains-All (Bio-Rad) since T4 polynucleotide kinase preferentially phosphorylates protruding 5'-hydroxyl groups relative to blunt ends.
Radiolabeled oligodeoxynucleotides were prepared using 45 units of T4 polynucleotide kinase, 150 pCi of [y-32P]ATP, and 100 pmol of DNA in 25 pl of kinase buffer. Following incubation at 25 "C for 45 min, reactions were quenched by the addition of 5 pl of 500 mM EDTA. C18 buffer (150 pl) was then added and the entire volume loaded onto a mini-column containing 100 pl of Sample Pack CIS column packing (Alltech Associates, Deerfield, IL) prewetted with HPLC grade methanol and equilibrated in CIS buffer. Unincorporated label was eluted from the column by washing with 1.5 ml of Milli-Q H20. Labeled DNA was eluted with 50% (v/v) methanol (150-200 pl) and desalted by passing through a 1-ml Bio-Gel P2 column equilibrated in Milli-Q H20.
Concentrations of oligodeoxynucleotides were determined spectroscopically in 10 mM Tris-HC1, pH 7.5,l mM EDTA, 150 mM NaCl at 25 "C using the following extinction coefficients (per DNA molecule): dT,, E260 = n X 8,100 M" cm"; KL3, €260 = 132,800 M" cm"; KL4, epMl = 131,200 M" cm"; KL34, 6260 = 214,400 M" cm"; HP, czfi0 = M" cm". The extinction coefficients for ss-DNA were calculated by nearest neighbor analysis (Cantor et al., 1970). For ds-DNA, a melting experiment was first performed. The extinction coefficient was then determined by linear extrapolation of the high temperature base line to 25 "C followed by application of the nearest neighbor analysis to the denatured single strands (Senior et al., 1988).
The oligodeoxynucleotide, 5'-dT7tATs, containing the fluorescent adenosine analog, etheno-adenosine (EA), was prepared from 5'-dT,AT, by a modification of the protocol of Giedroc et al. (1991). HPLC purified 5'-dT7ATs, 200 pM, was incubated in 4.5 M chloroacetaldehyde (Aldrich) at pH 4.5, 42 "C for 12 h with constant stirring. The pH must be maintained at 24.5 since we observed significant depurination below pH 4.5. The DNA was then extracted three times with chloroform and once with diethylether and desalted by passage over a Bio-Gel P-2 column, pre-equilibrated with Milli-Q H20. DNA was then dried using a Speed-Vac (Savant), redissolved in 0.5 ml of Milli-Q H20 and dialyzed against 1 liter of Milli-Q H 2 0 overnight.

DNA-induced Rep Dimerization
quartz cuvettes (NSG Precision Cells, Inc., Farmingdale, NY). After each addition of titrant, a polyethylene stirring rod (NSG Precision Cells, Inc., Farmingdale, NY) was used to mix the solution. The observed fluorescence after the ith addition of Rep, Fi,oba, was taken 2.5 min after the addition of protein to allow the solution to equilibrate. Equilibrium was assumed to have been reached in this time based on the observation that the fluorescence signal no longer increased. A parallel titration was performed by addition of Rep to a second cuvette containing only buffer without DNA to obtain the value of the background fluorescence, Fi.blank. The corrected fluorescence emission intensity, Fi,corr, at each concentration of Rep is then given by Equation 1 Fi,corr = (Fi,obs -Fi,bIank)( VdVd where Vi is total volume after the ith addition and Vo is the initial volume at the start of the titration. Neither photobleaching nor innerfilter effects were observed in these experiments. We assumed that the fluorescence enhancement, Fi.,,,, is directly proportional to the fraction of DNA bound, an assumption which was validated by direct comparison with binding isotherms obtained by nitrocellulose filter binding (see "Results"). Therefore, the fraction of bound DNA, &/ST, after the ith addition of Rep can be calculated from Equation 2 Sb/ST = (Fi,corr -Fo,corr)/(Ff,con -F~,corr) (2) where s b and ST denote the concentrations of bound and total ss-DNA, respectively, and Fo,c,,, and Ff,eorr denote the corrected fluorescence emission intensities in the absence of Rep and in the presence of saturating concentrations of Rep, respectively.
"Double-filter" Nitrocellulose Filter Binding Assay-A modification of the standard nitrocellulose filter binding method (Riggs et al., 1970) was used to obtain equilibrium binding isotherms for the interactions of Rep with a series of ss-and ds-oligodeoxynucleotides. ' The modified double-filter procedure involves the use of sheets of nitrocellulose and DEAE paper and a 96-well dot-blot apparatus in order to take advantage of direct @-emission imaging technology. This procedure is significantly more rapid since it eliminates the manipulation of large numbers of filters and the long times required to quantitate each filter separately by liquid scintillation counting and improves significantly the accuracy and precision of the method.
Modification of a Dot-blot Apparatus for Use in Nitrocellulose Filter Binding-Filter binding was carried out using a modified 96-well dotblot apparatus (Minifold I, Schleicher & Schuell, Keene, NH) as described? On the top plate of the unmodified apparatus, a rubber O-ring surrounds each of the 96 wells. These O-rings provide tight seals between the wells and the membrane. However, when used in this configuration for filter binding, we observed significant lateral diffusion of radiolabel on the membranes. This diffusion was eliminated by installing an inverted top plate below the membrane, such that each sample well has an O-ring seal above and below the membrane.
By using this modified apparatus, an entire binding isotherm consisting of a duplicate or triplicate set of 20-24 concentration points of 20-25 pl each can be obtained on a single 4.5 X 5-inch filter. Samples were applied to 6-9 wells at a time. Immediately before samples were loaded to each subset of 6-9 wells, the designated wells were flushed with 100 pl of ice-cold binding buffer using a Repipet, Jr. fixed volume dispenser (Labindustries, Inc. Berkeley, CA). Vacuum was applied just long enough to draw the flush solution through the membrane. Samples were then loaded and vacuum reapplied to draw the samples through. As soon as the samples have been drawn through the membrane, the wells were washed immediately with another 100 pl of ice-cold binding buffer. A flow rate of 5-6 ml/min was maintained using a house vacuum line (12-15 inch Hg). Timing constraints limited the number of samples processed to 6-9 wells each time. First, it was necessary to load the sample as soon as possible after the initial cooling flush to ensure that the temperature of the membrane did not increase significantly, and second, it is imperative that the wells be rinsed as quickly as possible following sample application in order to minimize the background retention. The entire membrane was then imaged by direct &emission detection using a Betascope 603 Blot Analyzer (Betagen, Waltham, MA). 32P-Labeled DNA retained by the nitrocellulose at each concentration point was quantitated by "boxing" and integrating the p-emission detected within the area of the corresponding "dot" by digital manip-I. Wong and T. M. Lohman, manuscript in preparation. ulation of the image using software supplied by the manufacturer. This allowed the simultaneous quantitation of an entire set of titration points in 30 min.
Pretreatment of Nitrocellulose Membranes-Nitrocellulose membranes were obtained in precut sheets (4.5 X 5 inch, Schleicher & Schuell) to fit the Minifold I apparatus. To reduce the binding of free ss-DNA to the nitrocellulose filters, the filters were presoaked for 10 min in 0.4 M KOH followed by continuous rinsing in Milli-Q H20 until the pH returned to neutral (Smolarsky and Tal, 1979). Filters were then equilibrated in standard titration binding buffer at 4 "C for a minimum of 1 h prior to use.
Preparation of Samples for Nitrocellulose Filter Binding-All samples for nitrocellulose filter binding were prepared in standard buffer (20 mM Tris, pH 7.5,6 mM NaCI, 1 mM EDTA, 5 mM 2-mercaptoethanol, 10% glycerol) at 4 "C. Titrations were performed either at constant Rep concentration, varying DNA concentration, or vice versa. The titrant whose concentration was being varied was serially diluted to span the necessary concentration range. Typically, titrations at constant DNA concentration required serial dilution of the Rep by factors of 0.75-0.85 while titrations at constant Rep concentration required serial dilution of the DNA by factors of 0.65. Titrations at a constant Rep concentration 2 1 p~ required a slightly different protocol in mixing to prevent precipitation problems. Here, the Rep was prepared in 5 X buffer containing 50% glycerol in onefifth final volume. The remaining four-fifths volume was contributed by the addition of DNA which was in Milli-Q H20. Samples were mixed by repeated pipetting and then incubated at 4 "C for 10 min. Equilibrium was reached within this time based on the observation in control experiments that the extent of binding did not change beyond this time. All samples were maintained at 4 "C constantly throughout the titration.
Double-filter Technique-As a further improvement to the standard nitrocellulose filter binding assay, an anion-exchange membrane made of DEAE-cellulose (NA45,4.5 X 5 inch, Schleicher & Schuell) was installed below the nitrocellulose filter. This DEAE membrane binds all of the DNA that passes through the nitrocellulose membrane, thus providing a means to determine the unbound, or free, DNA. The amount of radioactivity present in each dot on the DEAE membrane was analyzed as described above for the nitrocellulose membrane.
Direct quantitation of the amount of DNA that passes through the nitrocellulose membrane, which is related to the unbound DNA (see Equation 4), improves the precision and the accuracy of the method. First, the total DNA in each titration sample can be determined by summing the radioactivity retained on the nitrocellulose and DEAE filters. This allows one to compensate for pipetting errors, since for each titration point the DNA bound by the nitrocellulose filter can be normalized to the total amount of DNA that was loaded onto the filters. Second, since the radioactivity retained by the DEAE filter is directly related to the amount of free DNA, it provides a more accurate parameter for the determination of nonspecific background counts retained by the nitrocellulose. Traditionally, the amount of background DNA retained on the nitrocellulose has been determined by performing a parallel set of titrations in the absence of protein.
These background values would then be subtracted directly from those obtained in the presence of protein. However, this method of correcting for background assumes that the nonspecifically bound counts are a function of the total DNA concentration rather than of the free DNA concentration. However, when protein is present during a titration, the relationship between total and free DNA is not linear, hence the traditional method would usually overestimate the extent of DNA bound nonspecifically to the nitrocellulose and thus each point in the titration would be overcorrected for this background. Therefore, the background counts derived from loading the total DNA on a filter without protein would overestimate the actual background counts.
To circumvent this problem, a linear standard curve is constructed by plotting the DNA counts retained on the nitrocellulose filter as a function of the DNA counts retained on the DEAE filter in the absence of protein. The slope, u, of this standard curve can be used to determine the amount of background DNA as a function of the concentration of free DNA. In the presence of protein, the proteinbound DNA counts Cbound,i, and the free DNA counts, Cfree.i, for the ith titration point, are therefore given by Equations 3 and 4 Cbound,i = CNC.~ -UCDEAE,~ where CNC,~ and CDEAE,~ are the counts retained on the nitrocellulose and DEAE membranes, respectively. The concentration of DNA bound to protein, [DNA]bund.i, is then given by Equation 5.
Equations 3-5 are strictly valid only when the protein-nucleic acid complexes are retained on nitrocellulose with 100% efficiency as is true for the Rep-oligodeoxynucleotide complexes studied here. The DEAE membranes were regenerated by soaking in three changes of 1 M NaCl for 10 min each followed by a 1 min rinse in 0.5 M NaOH followed by rinsing in Milli-Q H20 until the pH has returned to neutral.
Non-linear Least Squares Analysis and Simulation of Binding Zsotherms for the DNA-induced Rep Dimerization Model-The equilibrium interaction constants (see "Theory") and their error estimates were derived from analysis of equilibrium binding isotherms using the non-linear least squares analysis method of Johnson and Frasier (1985) on a Hewlett-Packard 9000 computer. The error estimates represent 67% confidence limits. In cases where the error estimates were asymmetric, we have given the range based on the larger value.
The function used to model the extent of binding in these analyses is described under "Appendix." The experimental data points for a binding isotherm were weighted equally. However, in order to resolve the three interaction constants (e.g. K1s, L2s, and it was necessary to perform a simultaneous analysis of multiple isotherms (see "Results"). Theoretical binding isotherms, based on the statistical thermodynamic model presented under "Theory," were simulated using KaleidaGraph (Synergy Software, Reading, PA) on an Apple Macintosh IIfx computer.

Statistical Thermodynamic Model for DNA-induced Rep
Dimerization-Equilibrium binding of Rep to DNA was examined using oligodeoxynucleotides that are sufficiently short to preclude contiguous binding of Rep monomers or dimers to a single oligodeoxynucleotide (e.g. d(pN), with 8 5 n 5 20) (Chao and Lohman, 1991). Binding equilibria were analyzed using the DNA-induced Rep dimerization model shown in  Table I. The free Rep dimer, Pz, is not populated under the conditions of these experiments. The bored region represents the equilibria involved in binding of only ss-oligodeoxynucleotides.
of both ssand ds-DNA, five possible dimeric Rep species can form: the half-saturated dimers, PzS and P2D or the fully saturated dimers, P2Sz, PzDz or the mixed ligated dimer, PzSD; 6) dimerization of Rep is negligible in the absence of DNA since LP 5 lo4 M" (Chao and Lohman, 1991).
For clarity we will first discuss the simplified case in which only one type of DNA is present (either S or D). The case in which only ss-DNA is present is represented by the boxed portion of Fig. 1. In general, the six equilibria defined in Equations 6a-6f describe this case where K is the macroscopic equilibrium binding constant and L is the macroscopic Rep dimerization constant (see Equations A-13 under "Appendix" for the relationship to the intrinsic interaction constants). The first subscript of both K and L indicates the assembly state of the Rep protein, either monomeric (1) or dimeric (2). The second subscript indicates the type of DNA (single-stranded, S, or duplex, D) that is bound to the Rep monomer or dimer. The presence of a third subscript (S or D) indicates that a second oligodeoxynucleotide is bound to a Rep dimer.
However, only three of these equilibrium constants are needed to describe the Rep-ss oligodeoxynucleotide binding for the following reasons. 1) Since the Rep dimer does not form in the absence of DNA at Rep monomer concentrations less than 8 p~, Lz 5 lo4 M" (Chao and Lohman, 1991), the two equilibria represented in Equations 6c and 6e can be eliminated from consideration under the conditions of our experiments. 2) The remaining four equilibrium constants are not all independent since they are related by the thermodynamic cycle at the top of Fig. 1. We have chosen to describe the equilibrium binding of Rep to short ss oligodeoxynucleotides using the three equilibrium constants Kls, LZs, and Kzss. LZss can then be calculated from Equation 7. (7) We express the experimentally determined extents of DNA binding in either one of two forms: 1) the moles of ss-DNA bound/Rep monomer, Sb/PT or 2) the fraction of total ss-DNA bound, St&, depending on whether the protein or DNA is held constant throughout the experiment. For the binding of ss-DNA to Rep in the absence of duplex DNA, the expressions for these quantities are given in Equations 8 and 9.

LPSS = LzsKzss/K~s
(1 + KlSS/(l + 2LSP/(l + K Z S S S , ) ) ) W S T = (K1sP/(1 + &sP/(l + ZGssS/)))/ In the presence of both ss-DNA and ds-DNA, we must consider the formation of the mixed ligation state Rep dimer, PZSD, in which ss-DNA is bound to one subunit of the Rep dimer while ds-DNA is bound simultaneously to the other Rep subunit as shown in Fig. 1. PZSD can be formed either by binding of S to PzD, with binding constant K Z D S or by binding of D to P2S with binding constant KZsD; however, only one of these equilibria is needed to define the equilibria involving PzSD. We have chosen to use K~s D , from which K Z D S can be calculated using Equation 10.
The species, PZSD, can also be formed by the interaction of PS and PD, described by dimerization constant LDs (see "Appendix"). Therefore, a total of seven independent equilibrium constants (K1s, Ls, KBS To determine these seven interaction constants experimentally, we have adopted the following strategy. First, binding isotherms determined using only ss-DNA are used to determine Kls, LZS, and KZss. Second, binding isotherms determined using only duplex DNA are used to determine KID, L~D , and K Z D D . Third, to determine the last interaction constant, KzsD, experiments are performed to measure the competitive binding of ss-DNA and duplex DNA for Rep. By constraining the six interaction constants (Kls, LZs, KZSS, KID, L D , and K z D D ) to their values determined from the two sets of independent experiments, the competition experiments can be analyzed to determine K~s D .

Nitrocellulose Filter Assay to Obtain Equilibrium Binding Isotherms for Rep-Oligodeoxynucleotide
Interactions-Nitrocellulose filter binding has been used extensively to measure equilibrium binding constants for sequence specific protein-DNA interactions (Riggs et al., 1970;Winter et al., 1981;Barkley et al., 1981). However, its use to measure nonspecific DNA-protein interactions is not as widespread due mainly to the fact that for such nonspecific interactions multiple protein molecules can usually bind to each DNA molecule (Clore et al., 1982;Woodbury and von Hippel, 1983). To avoid this problem, we used 16-nucleotide (or base pair) long synthetic oligodeoxynucleotides that are long enough to bind only one Rep monomer/DNA (Chao and Lohman, 1991).
The utility of nitrocellulose filter binding as a quantitative method can also be dependent upon the particular proteinnucleic acid system under study due to a number of systemdependent variables that must first be determined (e.g. efficiency of filter retention and background retention of DNA). Furthermore, the use of this method to study a nonspecific DNA-binding protein such as Rep that also undergoes a DNAinduced dimerization raises additional questions such as 'It is probable that a ss-oligodeoxynucleotide binds to a Rep subunit with a unique orientation with respect to its backbone polarity, whereas a ds-oligodeoxynucleotide is likely to bind to a Rep subunit in either orientation. If this is the case, then the values of KID, &DO, and KZs0 each contain a statistical factor of 2, relative to K I S , K S S , and K~Ds.
whether the efficiency of filter retention differs for DNA that is bound to Rep monomers or dimers. The efficiency of retention of protein-bound DNA was determined to be 100 f 5% by direct measurement over a wide range of Rep to ss-DNA ratios, under the standard conditions used here . Consistent with this finding, we observe that the fraction of DNA bound by Rep always reaches unity at saturation for both 8s-and duplex oligodeoxynucleotides (e.g. see Figs. 5A and 7A). As a further control we also compared the isotherms obtained by nitrocellulose filter binding with those obtained by an independent, spectroscopic method. The fluorescently labeled ss-oligodeoxynucleotide, 5'dT7tATs, prepared as described under "Materials and Methods," shows a 2.75-fold enhancement of its etheno-A fluorescence (Lx = 320 nm; L,,,,,, = 400 nm) upon binding Rep in our standard conditions at 4 "C. Using this fluorescence enhancement to monitor binding, we obtained isotherms from fluorescence titrations performed at two different concentrations of dT7tATs, 0.2 and 1.0 pM and compared them directly with isotherms obtained by nitrocellulose filter binding of radiolabeled dT7tAT8. The isotherms obtained by both methods are superimposable at both concentrations; the isotherms obtained at 1.0 p~ dT7cATs are compared directly in Fig. 2. We conclude that the nitrocellulose filter binding method can be used to determine true equilibrium binding isotherms for the interaction of Rep with ss-and duplex oligodeoxynucleotides (see below) under the conditions reported here.
Also shown in Fig. 2 is an isotherm determined at 0.1 pM dT7tATs using the nitrocellulose filter binding method. Both isotherms, determined at DNA concentrations differing by a factor of 10, are well described by the DNA-induced Rep dimerization model (see "Theory") with the same interaction constants: Kls = 3.9 X lo6 M-', LZs = 1.1 X lo8 M-', and K2ss = 2.0 x lo6 M-'. For comparison we have included in Fig. 2 the best-fit isotherm obtained by assuming that a single Rep monomer binds to one molecule of dT7tATs to form a simple 1:l complex (dashed line; see Equation A-5). Clearly a simple 1:l binding model fails completely to describe the experimen-  . 1) using the following values for the interaction constants: K1s = 3.9 X lo6 M-', LZS = 1.1 X l@ "I, and KZss = 2.0 X lo6 id-', which were obtained from non-linear least-squares analysis of the four isotherms shown in Fig. 4. The dashed curue shows the best non-linear least squares fit to a simple 1:l binding model with K = 8.3 X lo6 "I. tal binding isotherm obtained at 0.1 p~ and also 1 p M dT7eATa (curve not shown).
Binding Isotherms Determined at Constant Rep Concentration-In Fig. 3, we show R e p -d (~T )~~ binding isotherms determined at constant Rep concentration (0.2 pM monomer) plotted as the fractional saturation of DNA-binding sites, S b / PT, versus the total d (~T )~6 concentration, ST. Isotherms were obtained under standard conditions (6 mM NaC1, pH 7.5, 4 "C) in the presence or absence of 25 mM MgC12. In the absence of M e (Fig. 3A), a clear saturation point was reached at 1 ~( P T )~~ molecule bound/Rep monomer, indicating that: 1) the efficiency of filter retention was loo%, 2) all Rep monomers in solution are active in binding d ( p T h , and 3) both subunits of the Rep dimer can bind d ( p T )~. Data from two independent experiments are shown in Fig. 3A indicating the excellent reproducibility of these binding isotherms. In the presence of 25 mM M$+ (Fig. 3B) Determination of Kls, K2ss, and L2s for Rep Binding to ssoligodeoxynuckotides-As discussed under "Theory," three independent interaction constants are needed to describe the DNA-binding and DNA-induced Rep dimerization equilibria in the presence of a single conformation of oligodeoxynucleotide, e.g. K1s, K2ss, and L2s for ss-DNA. However, since these parameters are correlated, particularly Kls and L2s, it is\necessary to perform multiple titrations spanning a wide rknge of both protein and DNA concentrations in order to resolve all three constants. One binding isotherm obtained at a single concentration of Rep or DNA does not contain sufficient information to resolve all three constants unambiguo sly. Since the three equilibria described by Kls, K2ss, and LZs how different dependences on DNA and Rep concentration P information on both the Rep and DNA concentration dependence of the binding isotherms must be obtained. This requires multiple titrations since an individual titration provide9 information on the concentration dependence of only on# titrant.

/
We have used two approaches to resolve all three interaction constants. In the first approach, the requisite Rep and DNA concentration ranges can be spanned by performing a series of titrations of a single type, e.g. titrating a constant DNA concentration with Rep at several DNA concentrations. However, this approach is relatively inefficient. While each titratipn provides substantial information on the concentration ddpendence of one species (Rep), information at only one DNA concentration is obtained. Using this approach, we found tyPically that it was necessary to perform titrations at a minimum of three, but often more, DNA concentrations.
An example of this approach is shown in Fig. 4 (0.1, 0.2, 1.0, and 5.0 PM). Simultaneous analysis of these isotherms by non-linear least squares methods was able to resolve all three interaction constants: Kls = 3.9(&0.5) X IO6 The second approach, which we have adopted for routine use, proved to be a more efficient method for resolving the three interaction constants since it involved performing only two titrations: one at constant DNA concentration and the other at constant Rep concentration, such as those shown in Fig. 5. This combinatorial approach hinges on the fact that the two different types of titrations sample the concentration dependence of a different titrant, hence the concentration dependence of both titrants can be obtained from the combination of these two isotherms. The interaction constants determined by this approach based on non-linear least squares analysis of the two isotherms shown in Fig. 5 are: Kls = 4.5(f lo6 M-' as listed in Table I. These values are in excellent agreement with those determined from the series of experiments shown in Fig. 4. The curves describing the isotherms in Fig. 5 are theoretical isotherms using the DNA-induced dimerization model and these interaction constants.   Effects of Single-stranded DNA Length-The number of nucleotides occluded by a Rep monomer bound to ss-DNA (apparent site size) has been estimated to be 16 k 2 nucleotides in experiments with ss-homopolynucleotides Chao and Lohman, 1991). This apparent site size provides an estimate of the number of nucleotides occluded/Rep monomer; however, it does not provide an estimate of the length of the oligodeoxynucleotide, m, needed so that all contacts are made with the protein (Kelly et al., 1976;Draper and von Hippel, 1978). In order to examine this, we have measured Kls, Kzss, and Lzs, using nitrocellulose filter binding as described above, for a series of oligodeoxythymidylates, d(pT),, with n = 8, 12, 14, 16, and 20 in standard buffer (6 mM NaCl, pH 7.5,4 "C). Each of these oligodeoxynucleotides binds with a stoichiometry of one oligonucleotide/Rep monomer. The interaction constants are plotted in Fig. 6 as a function of ss-DNA length and are given in Table 11. While all three interaction constants increase with increasing ss-DNA length, the two Rep-DNA-binding constants, K1s and KzSs, exhibit abrupt 5-and 16-fold increases, respectively, upon increasing the ss-DNA length from n = 12 to n = 14 nucleotides. In contrast, the Rep dimerization constant LZS shows only a gradual increase from 6.6(f1.6) X lo7 M-' to 2.7(f0.9) X 10' M" over the range of lengths tested from n = 8 to 20. These results suggest that d(pT)12 is not long enough to make all of the contacts within the Rep-binding site, whereas all contacts are made with d(pT)14. Therefore, we conclude that 12 < m I 14, which is consistent with the observed occluded site size of 16 k 2 nucleotides on ss-DNA. An interesting feature of Fig. 6 is that KZSS, the apparent equilibrium constant for binding a second ss-oligodeoxynucleotide to the half-ligated Rep dimer, PzS, decreases by a factor of 4 upon increasing the ss-DNA length from n = 16 to n = 20. This effect is not observed for K1s, the affinity of a Rep monomer for an oligodeoxynucleotide, which actually displays a slight increase. Therefore, it seems unlikely that the decrease in Kzss reflects a direct effect on the intrinsic Rep-ss-DNA binding affinity. Since d(pT)20 is slightly longer than the occluded site size, it seems more likely that when bound to one subunit in the P2S complex, it can also partially occupy the unfilled DNA-binding site on the second Rep subunit thereby inhibiting the binding of a second molecule of dTzo at that site. In light of these results, we performed experiments comparing ss-and ds-DNA with oligodeoxynucleotides that are 16 nucleotides or base pairs in length.

Effects of DNA Sequence and Base Composition on Rep-ss-DNA Interactions-The E. coli Rep helicase is a nonspecific
DNA-binding protein that can unwind duplex DNA independent of its sequence. We examined the interactions of Rep with several 16-nucleotide long ss-oligodeoxynucleotides in order to determine the effect of base composition on the Rep equilibrium binding and dimerization constants. Three of these, d(pT),s, d(p&, and ~( P C )~~, are homo-oligodeoxynucleotides and a fourth, KL3, has a mixed sequence with 50% GC content (see "Materials and Methods"). Table I11 indicates that the interaction constants, Kls, Kzss, L2s, and L s s , for ~( P T )~~, d(pC)16, and the mixed sequence oligodeoxynucleotide KL3 are identical within experimental error. Binding of d (~A )~6 to Rep shows a 2-3-fold lower affinity (both for K1s and K2ss) relative to the other oligodeoxynucleotides examined, although the Rep dimerization is unaffected. Based on these data, we conclude that the equilibrium binding of Rep to ss-DNA is independent of ss-DNA sequence under the conditions of these experiments (6 mM NaCl, pH 7.5, 4 "C) and that experiments performed with oligodeoxythymidylates reflect the general binding properties of Rep to ss-DNA. This might have been anticipated for a protein that binds nonspecifically to ss-DNA, although most well-characterized ss-DNA-binding proteins, such as the E. coli SSB protein (Overman et al., 1988), the T4 phage gene 32 protein (Newport et al., 1981), and the fd phage gene 5 protein (Sang and Gray, were determined for Rep binding to a series of oligodeoxythymidy-Iates, dT,, with n = 8, 12, 14, 16, and 20, under standard conditions (6 mM NaC1, pH 7.5,4 "C) based on the simultaneous analysis of two different types of isotherms for each oligodeoxynucleotide as shown in Fig. 5. The interaction constants, which are also listed in Table I, are plotted as a function of DNA length, n.
1989) display a surprisingly large dependence of affinity on ss-DNA base composition.

Determination of KID, K~DD, and LZD for Rep Binding to
Duplex Oligodeoxynucleotides-The dimerization of Rep monomers is also induced by the binding of duplex DNA (Chao and Lohman, 1991); hence, we also determined the equilibrium interaction constants for the binding of duplex oligodeoxynucleotides to Rep. All experiments were performed in standard buffer (6 mM NaC1, pH 7.5,4 "C) and the interaction constants, KID, KZDD, and Lzo, were resolved based on analysis of the two isotherms shown in Fig. 7. The Rep-duplex DNA experiments were performed with two different oligodeoxynucleotides, both containing the identical 16-base pair duplex region. KL34 was formed by annealing the two complementary 16-base long mixed sequence ss-oligodeoxynucleotides, KL3 and KL4, as described under "Materials and Methods." The other duplex, referred to as HP, is a hairpin containing four deoxythymidylates in its loop region. The equilibrium binding isotherms obtained with these two duplex oligodeoxynucleotides were indistinguishable under these solution conditions as shown in Fig Table I).
The value of LZD, however, is comparable to the value of L2s, whereas LzDD = 1.9 X lo7 "I, is a factor of -10 lower than Lzss.
Since ds-DNA binds with lower affinity to Rep than does ss-DNA, the presence of small amounts of contaminating ss-DNA in the ds-DNA titrations would interfere with our determination of the Rep-ds-DNA interaction constants. To be sure that the ds-oligonucleotides were annealed under our binding conditions, we determined the thermal melting properties of both the HP and KL34 duplexes as a function of salt and DNA concentrations. Due to the large effect of temperature on the pKa of Tris, 10 mM potassium phosphate was substituted for Tris in these thermal melting studies. The melting profiles for KL34 showed the expected dependence on DNA concentration with T , values of 38 and 42 "C at 0.18 and 1.5 gM, respectively, in 6 mM NaC1. In contrast, the melting profiles for the HP duplex were independent of HP concentration from 0.1 to 2 JLM, with T, values of 73 and 50 "C in the presence and absence of 200 mM NaC1, respectively, at both DNA concentrations (data not shown). While all binding isotherms reported here were carried out at 4 "C, well below the T,,, of both duplexes, the lower T,,, of the dimer duplex, KL34, precludes future studies with this DNA at   higher temperatures where significant strand dissociation is likely to occur.

DNA-induced Rep Dimerization
On the other hand, we also had some initial concerns about the suitability of the hairpin duplex for these studies stemming from: 1) the potential "single-stranded" nature of the dT, loop, and 2) the possibility that two H P molecules might dimerize to form a 36-base pair duplex containing a dT, bulge in the middle. The finding that the HP and KL34 duplexes display identical binding isotherms suggests strongly that the dT, loop does not contribute to the Rep-duplex interactions. Furthermore, the lack of a concentration dependence of the melting profile for the H P duplex indicates the absence of significant dimeric duplex structures. Based on these findings, we conclude that both the hairpin duplex and the duplex dimer are suitable models for the Rep-ds-DNA equilibrium interaction at 4 "C. However, the hairpin duplex is the more appropriate molecule to use to examine duplex DNA binding to Rep over a wide range of solution conditions, e.g. at higher temperatures or lower DNA concentrations.

Competitive Binding of Single Strand and Duplex DNA to
the Rep Protein-In order to determine whether ss-DNA and ds-DNA bind to the same or separate DNA-binding sites, we examined the characteristics of the competitive binding of d(pT)1~ and the HP duplex to Rep. These experiments were performed under standard buffer conditions (6 mM NaCl, pH 7.5, 4 "C) starting with preformed R e p -d (~T )~~ complexes (4 p M Rep monomer plus 4 PM ~( P T )~G ) which were then titrated with H P duplex. Two parallel experiments were performed under identical conditions. In one case, preformed R e~-~' p -~( P T )~~ complexes were titrated with unlabeled H P duplex, while the extent of 32P-d(pT)16 bound to Rep was monitored. In the second experiment, preformed R e p -d (~T )~~ complexes were titrated with 32P-HP duplex and the binding of the 32P-H P duplex to Rep was monitored. The results of both experiments are shown in Fig. 8A and indicate that HP binding completely displaces ~( P T )~, indicating that ss-and ds-DNA bind to the same sites on Rep monomers and dimers.
The data in Fig. 8A were also analyzed to determine the extent to which the mixed ligation species P2SD can form under these conditions. Simulation of these competition curves based on the DNA-induced Rep dimerization model requires independent knowledge of the seven interaction constants, &SD, Kls, KZSS, L2s, KID, KZDD, and L S D (see "Theory" and "Appendix"). However, six of these, Kls, K2ss, L2s and K I D , K~DD, and LZD, have already been determined from the independent binding experiments performed separately with d(pT)lG and the hairpin duplex oligodeoxynucleotides. Therefore, the competition experiments can be analyzed to obtain the remaining interaction constant, KZsD. Using the values of K1s, LZs and KID, KZDD, and LZD listed in Table I,  8A also shows simulated curves for a value of K2sD = 5 x lo4 M" (dashed lines) indicating the sensitivity of these competition isotherms to the value of K 2 s~. The agreement between the simulated curves based on the DNA-induced Rep dimerization model and the experimental competition isotherms lends additional support to our conclusion that this model provides an excellent quantitative description of the binding of both duplex and ss-oligodeoxynucleotides to the Rep protein. Fig. 8B shows the predicted population distributions of the three doubly ligated Rep dimer species, P2S2, P2D2, and PzSD, based on Equations A-3 and the seven interaction constants.

DISCUSSION
The E. coli Rep helicase is a stable monomer up to concentrations of at least 8 ~L M monomer, even in the presence of  Table I Table I (6 mM NaC1, pH 7.5,4 "C). Significant accumulation of the mixed-ligation state, PzSD, occurs under these conditions. nucleotide cofactors ; however, the protein is induced to dimerize upon binding either 9s-or duplex DNA (Chao and Lohman, 1991). Furthermore, a chemically cross-linked Rep dimer retains its ss-DNAdependent ATPase and DNA helicase activity (Chao and Lohman, 1991), which suggests strongly that the dimer is the active form of the Rep helicase. Higher order assembly states beyond the dimer have not been observed. However, these previous studies did not determine whether both subunit.s of the Rep dimer are able to bind DNA simultaneously. In an attempt to understand how a DNA-induced Rep dimer might function to unwind duplex DNA, we sought to determine the stoichiometries and affinities of the various Rep-DNA com-plexes, with the ultimate goal of determining whether these might be influenced by ATP binding and subsequent hydrolysis. For this purpose we have developed a statistical thermodynamic model that describes DNA binding to Rep monomers and the coupled DNA-induced Rep dimerization. Using a modified double-filter nitrocellulose filter binding method: which improves significantly the quality of binding isotherms and the ease of data acquisition, we have examined the equilibrium binding of Rep to a series of single-and doublestranded oligodeoxynucleotides. These studies were performed with oligodeoxynucleotides that were sufficiently short so that only one Rep monomer can bind to each oligodeoxynucleotide, thus enabling us to examine true DNAinduced dimerization in the absence of adventitious binding of two monomers to a single DNA molecule.
The major results of our studies are as follows. 1) Monomers of Rep can bind both ss-and duplex DNA, both of which induce Rep dimerization. Under the conditions used in these studies (6 mM NaC1, pH 7.5, 4 "C), ss-DNA binds with higher affinity than duplex DNA (see Table I).
We have been able to resolve all seven interaction constants needed to describe Rep binding to ss-and duplex oligodeoxynucleotides and the DNA-induced Rep dimerization as defined by the statistical thermodynamic model in Fig. l. 2) Rep monomers are induced to dimerize upon binding ssor ds-DNA. The dimerization constant for DNA-bound Rep increases by at least a factor of -lo4 (L2s, L P~ and LPss -1-3 X 10' M-') (6 mM NaC1, pH 7.5, 4."C), since its maximum value in the absence of DNA is L2 5 lo4 M" (Chao and Lohman, 1991). Fig. 9 shows a plot of the fraction of Rep protein in the dimeric form as a function of total Rep concentration in the presence of an equal molar concentration of d(pT)IG. Fully 90% of the Rep protein is in a dimeric form at Rep and d(pT)lG concentrations of 100 nM. Since Rep must be bound to DNA in order to function as a helicase these results are consistent with a dimer as the active form of the Rep helicase.
3) Rep dimerization enhances dramatically its affinity for for both ss-and ds-DNA. 4) Both protomers of a Rep dimer can bind ss-or ds-DNA to the same sites.

)
We observe dramatic allosteric effects in this system. The affinity for DNA of one protomer of a Rep dimer is Rep concentration. This fraction of Rep dimer is defined as (2P2S + ZPzSz)/(PS + 2PzS + 2P2Sz) and is calculated using the interaction constants in Table I (6 mM NaC1, pH 7.5, 4 "C). dependent on the type of DNA (8s or duplex) that occupies the other protomer. 6) The minimum length of ss-DNA needed to form all contacts with a Rep monomer is 12 c m I 14 nucleotides.

7)
Little dependence of Rep-ss DNA affinity on base composition or sequence is observed (see Table 111), consistent with the role of Rep as a nonspecific DNA-binding protein and its ability to unwind duplex DNA independent of sequence.
We discuss these points in more detail below. Analysis of Binding Isotherms to Determine Equilibrium Interaction Constants-Quantitative determination of the various interaction constants that describe the multiple Rep-DNA equilibria is essential for obtaining a molecular understanding of the functional energetics of the DNA unwinding process. We have found that only two titrations, one at constant DNA and one at constant Rep concentration, are necessary in principle to determine the three independent equilibrium constants that describe the interaction of Rep with a single conformation of oligodeoxynucleotide, e.g. ss-DNA. The reason for this is apparent from inspection of  Table I for  10 that the population distributions for the three Rep-DNA species differ dramatically for the two types of titrations. Typically, binding isotherms obtained by varying the Rep concentration at a constant DNA concentration are not sensitive to K~S S since the formation of PzSz requires high DNA to Rep ratios, a condition that applies only for the initial few points of the isotherm, whereas at higher Rep concentrations, the formation of P2S is favored (see Fig. 1OA). Consequently, PzSz is only sparsely populated except in titrations performed at extremely high DNA concentrations. However, these binding isotherms, if obtained at low enough DNA concentration, are sensitive to both Kls and LS and therefore can be used to resolve these two constants independently. For example, a change in Kls shifts the isotherm along the Rep concentration axis, whereas a change in h s affects the steepness of the isotherm. On the other hand, Fig. 1OB shows that a titration at constant Rep concentration provides the necessary information to determine K2sS since the second half of such an isotherm (at high DNA concentration) is dominated by the formation of P2Sz. Therefore, the two constants Kls and L Z S can be resolved based solely on the isotherm obtained at constant DNA concentration, whereas the isotherm obtained at constant Rep concentration provides the major constraint needed to determine Kzss. Of course, in the case of Rep, the independent determination of these three constants is facilitated by the fact that Lzs is at least a factor of 100 larger than either Kls or Kzss. The population distributions for the Repds-DNA species, corresponding to the isotherms in Fig. 7, are shown in Fig. 11. The excellent agreement between our experimental binding isotherms and the DNA-induced Rep di- merization model (Fig. 1) indicates that this is the minimal scheme needed to describe the multiple equilibria for this system. The use of the double-filter nitrocellulose filter binding assay' has facilitated greatly our ability to resolve the seven independent interaction constants that describe the DNAinduced Rep dimerization. The introduction of a DEAE membrane and the use of a dot-blot apparatus, coupled with direct counting of the radioactivity on both the nitrocellulose and DEAE membranes are modifications that should be generally applicable for use with any protein-nucleic acid interaction that can be studied by nitrocellulose filter binding.
Rep Dimers Bind DNA with Substantially Higher Affinity Than Rep Monomers- Chao and Lohman (1991) have shown that the affinity of ss-DNA for a chemically cross-linked Rep dimer is substantially higher than for a Rep monomer. We cannot measure directly the affinity of an unliganded Rep dimer for DNA, since unliganded Rep dimers are not populated at the concentrations used in our experiments ( Lz 5 lo4 M-'; Chao and Lohman, 1991). However, we can estimate lower limits for KZs and KzD, the macroscopic binding constants for ss-and ds-oligodeoxynucleotide binding to an isolated Rep dimer, based on the estimate of Lz and the relationship K~s = KI&s/L2. We estimate that both k2s/k1s and k2D/ klD 2 7 X lo3, i.e. a nearly 10,000-fold increase in intrinsic binding affinity results from dimerization (see Equations A-13 in "Appendix" for definitions of the intrinsic constants). The fact that Rep dimerization is induced upon binding DNA is reflected directly in the magnitude of the ratio of these binding constants. These substantial differences may be functionally important, since they indicate that a Rep dimer can remain tightly bound to DNA with one protomer while the other protomer can exchange DNA as, for example, during an unwinding reaction. Allosteric Effects on DNA Binding to the Rep Dimer-Our results indicate that two molecules of either ssor ds-DNA can bind to a Rep dimer to form the ternary complexes PzS2 or P2DZ, respectively. Furthermore, a Rep dimer can also form the mixed ligation species PzSD, in which one molecule each of 8s-and ds-DNA is bound to the Rep dimer simultaneously. Furthermore, our results also show that 9s-and ds-DNA both compete for the same binding sites on the Rep dimer. This differs from the conclusion reached by  that individual Rep monomers possess distinct sites for ss-and ds-DNA, although their studies were carried out with polymeric ssand ds-DNA.
Significant allosteric effects are also apparent in this system, ie. the binding of ss-or ds-DNA to the second protomer of a half-saturated Rep dimer is clearly influenced by the type of DNA that occupies the first subunit (see Table I). The following general conclusions can be drawn (6 mM NaC1, pH 7.5, 4 T ) : (i) The affinity of either ss-or duplex DNA to the second protomer is always higher if the first protomer is filled with ss-DNA (e.g. KZss = 4KzDs and KzsD =: 7KZDD); (ii) ss-DNA always binds to the second protomer with higher affinity than duplex DNA (K2ss =: 12K2s~ and KzDs = 20K2DD). These allosteric effects suggest that different conformations of the Rep protein are stabilized by the type of bound DNA and this likely involves communication across the Rep dimer interface. The observation of such allosteric effects suggests to us the possibility that these ternary complexes may mimic intermediate complexes that can occur at an unwinding fork and that are important in DNA unwinding.
Implications for Rep-catalyzed DNA Unwinding-The ability of the Rep protein to dimerize has important implications for how this helicase might interact with an unwinding fork (Chao and Lohman, 1991). Since each Rep protomer can bind DNA, then at an unwinding fork, the dimer is likely to bind two different regions of DNA simultaneously to form ternary complexes. The formation of ternary structures in which the Rep dimer binds either two regions of ss-DNA (P&) or a region of ss-DNA and a region of duplex DNA (PzSD) would seem to be the most likely models for intermediates at a replication fork. Three possibilities for such ternary complexes are depicted in Fig. 12. In Fig. 12A, both Rep protomers are bound to ss-DNA, one on the leading strand and the other on the lagging strand, whereas in Fig. 12B, both Rep protomers are bound to ss-DNA, but on the same (leading) strand. Although both protomers might also be bound to the lagging strand (not shown), the apparent 3' to 5' polarity of unwinding observed for Rep (Yarranton and Gefter, 1979;Lohman et al., 1989; suggests that this binding mode is not productive. Finally, Fig. 12C depicts a mixed ligation binding mode in which one protomer is bound to ss-DNA on the leading strand while the other protomer is bound to ds-DNA ahead of the fork. We consider it unlikely that a Rep dimer would bind two regions of duplex DNA simultaneously at an unwinding fork due to the intrinsic stiffness of duplex B-form DNA (Hagerman, 1988); hence, we do not consider a P2Dz species to be important functionally. The mixed ligation species, PzSD, is of special interest since the transient formation of a ternary complex consisting of Rep, ds-DNA, and ss-DNA has been postulated in models for unwinding (Lohman, 1992).
Oligomeric Nature of Helicases-The results reported here as well as previous results which have shown that a crosslinked Rep dimer retains helicase activity (Chao and Lohman, 1991) suggest that the functionally active form of the Rep helicase is a dimer. Furthermore, it has been suggested that the active forms of most helicases might be oligomeric (Loh-   , 1992). Other examples of oligomeric helicases include hexamers such as E. coli DnaB (Reha-Krantz and Hurwitz, 1978), SV40 large T antigen (Mastrangelo et al., 1989), E. coli Rho (Finger and Richardson, 1982), and dimers such as E. coli Helicase I11 (Yarranton et al., 1979), phage T7 gene 4 protein, a human (HeLa) helicase (Seo et al., 1991), and HSV-1 origin binding protein (Bruckner et al., 1991). The RecBCD protein, a helicase involved in recombination (Smith, 1990;Roman andKowalczykowski, 1990a, 1990b) forms at least a heterotrimer, although one measurement of its native molecular weight is consistent with it being a hexamer, i.e. (RecBCDL (Dykstra et al., 1984). E. coli Helicase I1 ( u u~D )~ and the phage T4 gene 41 protein (Liu and Alberts, 1981) also oligomerize, although the final assembly state as well as its assembly state on the DNA has not yet been defined. In fact, for the few cases of helicases that appear to be "monomeric," the assembly state of these helicases when bound to DNA has not been examined. Since Rep is clearly induced to dimerize only upon binding DNA (Chao and Lohman, 1991), this needs to be examined for other helicases that appear to be monomeric in the absence of DNA.
The fact that helicases appear generally to be oligomeric suggests that this is an important feature for their mechanism of action. Such oligomeric structures would provide a relatively simple means to generate multiple DNA-binding sites within a helicase (Lohman, 1992). The fact that both DNAbinding sites of a Rep dimer can accommodate either ss-or duplex DNA suggests unwinding mechanisms in which the two sites on the Rep dimer alternate binding of ss-and duplex DNA, modulated by the binding and subsequent hydrolysis of ATP (Lohman, 1992).' Such unwinding mechanisms may be used generally by helicases that contain multiple DNAbinding sites provided by oligomeric structures. Definition of Equilibrium Interaction Constants-The statistical thermodynamic model used to describe the DNAinduced Rep dimerization in the presence of both ss-and dsoligodeoxynucleotides that are short enough to preclude multiple binding of Rep monomers to a single oligodeoxynucleotide is depicted in Fig. 1 and is defined explicitly by 11 equilibria among eight distinct states (see Fig. 1 and "Theory"). Therefore, seven independent equilibrium interaction constants are needed to describe these equilibria and we have chosen the seven macroscopic interaction constants defined in Equations (A-1). where S , P, and D represent ss-oligodeoxynucleotide, Rep monomer, and ds-oligodeoxynucleotide, respectively, and the free DNA and Rep monomers are designated explicitly with the subscript f. Since Rep dimers do not form in the absence of DNA binding up to Rep monomer concentrations of at least 8 PM, indicating that Lz 5 IO4 M" (Chao and Lohman, 1991) Simulation of the Binding Isotherm in the Absence of Competition-In the presence of only one conformation of DNA (either ss or ds), the number of protein states reduces to 4 (e.g. P, P S , PzS and PzSz). In this case only three of the seven interaction constants are needed. We have used KIS, LZS, and K2sS to describe the ss-DNA binding equilibria and R D , LD, and K2DD for the ds-DNA binding equilibria. We describe below the methods for simulation of Rep binding isotherms obtained in the presence of only ss-DNA; however, exactly analogous equations apply in the case of only ds-DNA.
The extent of ss-oligodeoxynucleotide binding can be expressed either as the fraction of bound ss-DNA, S&T, or as the fractional saturation of DNA-binding sites assuming one binding site/Rep monomer, s b / P T . In practice, binding is normalized with respect to the species (protein or DNA) whose concentration is held constant during the titration. Thus, extent of binding is described in terms of S b / S T in titrations at constant DNA concentration and S b / P T in titrations at constant Rep concentration. In the absence of ds-DNA, the expressions for S b / P T and S b / S T are given in Equations A-4. (1 + K*sss/~PT~I"2~/4~Kl~2ss/~1 + K 2 S S S f ) ) For titrations performed at constant DNA concentration, the value of ST is known and remains invariant throughout the titration. We can therefore use Equation A-7a to calculate Sf explicitly for an assumed value of Pr. For each (Sf, Pf) pair, the fraction of DNA bound, &,/ST, and the total concentration of Rep monomer, PT, are easily calculated using Equations A-4b and A-6b, respectively. An entire binding isotherm can therefore be simulated by repeating this process iteratively while incrementing Pfi To simulate binding isotherms for titrations at constant total Rep monomer concentration, PT, Equation A-7b can be used to calculate Pf explicitly for an assumed value of Sf, and the binding isotherm is generated by solving for Sb/PT and ST using Equations A-4a and A6-a, respectively. Using this algorithm, binding isotherms can be simulated with relative ease and compared graphically with isotherms obtained experimentally. However, using this algorithm, both the abscissa, either PT or ST, and the ordinate, either Sb/PT or &,/ST, of the isotherm are derived values, i.e. the algorithm does not define an explicit relationship between the two. As a result, this algorithm, although intuitive, cannot be used to calculate directly the extent of binding for a given total concentration of titrant, PT or ST, whereas this capability is useful for computational purposes related to non-linear least squares analysis.
To derive the free concentrations of both titrants, Pf and Sf, from the known total concentrations, PT and ST, requires simultaneous solution of the two quadratic equations given in Equations A-6a and A-6b. To do this, we use the Newton-Raphson numerical method of root finding to solve iteratively for Pf for a given PT and S T . The root-finding function, F(Pf), which can be substituted into Equation A-8. This substitution eliminates Sf and the need to search simultaneously for Pf and Sf, and consequently greatly improves the robustness of the root-finding algorithm. A Fortran implementation of this algorithm, used in conjunction with the non-linear leastsquares fitting algorithm NONLIN (Johnson and Frasier, 1985), provides direct error estimates for the best-fit parameters.
Simulation of Binding Isotherms in the Presence of Both SSand ds-oligodeoxynucleotides-In the presence of both S and D, all seven interaction constants listed in Equations A-1 are needed to describe the system in a set of three simultaneous quadratic equations as defined by the mass conservation Equations A-10). + K~SDQ)) + K~D D / (~ + 2PfL20(1 + &DDD/))] -PT However, unlike the case described above for root finding in one dimension, numerical methods for root finding in multidimensions are typically not robust. In practice, convergence is guaranteed only in the immediate vicinity of the root. Therefore, very good initial guesses are required. By ensuring that each incremental change in Df is sufficiently small, we are guaranteed to be always near a root. Therefore, the previous values of Sf and Pf would always provide good initial guesses for the search for the new values of Sf and Pf. Starting at an initial value of Df = 0, Sf and Pf are calculated as described above in the absence of ds-DNA. We then increase D/ in small (5%) increments starting with an initial value equal to 0.02Sfi Each time Df is incremented, new values of Sf and Pf are derived iteratively using the old values as initial guesses. Following convergence, SdPT, Db/PT, and DT are calculated using Equations A-lla, A-llb, and A-lob, respectively. Df is then incremented logarithmically until the calculated value of Db/PT exceeds 0.95. A Fortran program was written to implement this algorithm. We were unable to solve directly for the binding isotherms from the experimentally relevant total concentrations of the three titrants. To do so required the simultaneous solution of three quadratic equations. All attempts to search in three dimension for D/, Sf, and Pf by Newton-Raphson led invariably to singular matrices.
Intrinsic Interaction Constants-The interaction constants defined above are macroscopic constants and hence have statistical factors incorporated into them. However, the free energy changes associated with each process are related to the intrinsic interaction constants which we have designated by lower case k and 1. The relationships between the intrinsic and the macroscopic constants are given in Equations A-13. Note that all of the macroscopic duplex DNA-binding constants, K I D , K~D , K~D o , and KZSD, contain an additional statistical factor of 2, relative to the single-stranded macroscopic binding constants, based on our assumption that a duplex DNA is likely to be able to bind in two orientations, whereas ss-DNA is likely to bind in a unique orientation with respect to its backbone polarity.