Escherichia coli Replicative Helicase PriA Protein-Single-stranded DNA Complex

Analyses of interactions of the Escherichia coli replicative helicase, PriA protein, with a single-stranded (ss) DNA have been performed, using the quantitative fluorescence titration technique. The stoichiometry of the PriA helicasezssDNA complex has been examined in binding experiments with a series of ssDNA oligomers. The total site-size of the PriAzssDNA complex, i.e. the maximum number of nucleotide residues occluded by the PriA helicase in the complex, is 20 6 3 residues per protein monomer. However, the protein can efficiently form a complex with a minimum of 8 nucleotides. Thus, the enzyme has a strong ssDNA-binding site that engages in direct interactions with a significantly smaller number of nucleotides than the total site-size. The ssDNA-binding site is located in the center of the enzyme molecule, with the protein matrix protruding over a distance of ;6 nucleotides on both sides of the binding site. The analysis of the binding of two PriA molecules to long oligomers was performed using statistical thermodynamic models that take into account the overlap of potential binding sites, cooperative interactions, and the proteinzssDNA complexes with different stoichiometries. The intrinsic affinity depends little upon the length of the ssDNA. Moreover, the binding is accompanied by weak cooperative interactions.

In the process of priming a DNA strand, the primosome, a multiple protein complex is formed, which can translocate along the DNA while synthesizing short oligoribonucleotide primers that are used to initiate synthesis of the complementary strand (1)(2)(3).The PriA protein is a key replication protein in Escherichia coli that plays a fundamental role in the ordered assembly of the primosome.Originally, the protein was discovered as an essential factor during the synthesis of the complementary DNA strand of phage X174 DNA (4,5).
The gene encoding the PriA protein has been cloned and sequenced and that of the encoded protein has been determined (13,14).Current biochemical data indicate that the native protein is a monomer, with a molecular mass of 81.7 kDa, which is proposed to be the predominant form of the protein in solution (7,9).
In vivo functions of the PriA helicase are related to the ability of the enzyme to interact with both ss-and dsDNAs (3, 7-10, 15, 16).Although the importance of understanding the PriA protein interactions with a nucleic acid has been recognized, little is known about the quantitative aspects of these interactions.Nothing is known about the stoichiometry, i.e. the total site-size of the PriA⅐ssDNA complexes with different ssand dsDNAs, base specificity, effect of solution conditions on the intrinsic affinity, the cooperativity of the binding process, and the structure of the complexes.Knowledge of the stoichiometry and structure of the helicase-nucleic acid complex and the mechanism of binding is a prerequisite for formulating any model of the mechanism of enzyme functioning in DNA replication (17,18).This includes enzyme translocation on the DNA, catalysis of DNA unwinding, as well as the functioning of the PriA helicase in the formation and translocation of the primosome (19 -20).
In this communication, we report, for the first time, quantitative analyses of the interactions of the PriA helicase with a ssDNA, using the quantitative fluorescence titration technique.We present evidence that the helicase binds the ssDNA as a monomer with the total site-size of the protein⅐ssDNA complex n ϭ 20 Ϯ 3 nucleotide residues.However, studies with a series of short oligomers indicate that the ssDNA-binding site on the enzyme, directly engaged in interactions with the nucleic acid, encompasses only 8 Ϯ 1 nucleotide residues, significantly less than the total site-size of the complex.The obtained results indicate that the enzyme has a single ssDNA-binding site, located in the central part of the protein molecule, with the protein matrix protruding over a distance of 6 Ϯ 1 nucleotide residues on both sides of the ssDNA-binding site.The data show the binding of PriA to the ssDNA is not accompanied by any significant cooperative interactions.

EXPERIMENTAL PROCEDURES
Reagents and Buffers-All solutions were made with distilled and deionized Ͼ18 megohms (Milli-Q Plus) water.All chemicals were reagent grade.Buffer C is 10 mM sodium cacodylate adjusted to pH 7.0 with HCl, 0.1 mM EDTA, 1 mM dithiothreitol, 25% glycerol.The tem-peratures and concentrations of salts in the buffer are indicated in the text.
Fluorescence Measurements-All steady-state fluorescence titrations were performed using SLM-Aminco 48000S or 8100 spectrofluorometers.In order to avoid possible artifacts, due to the fluorescence anisotropy of the sample, polarizers were placed in excitation and emission channels and set at 90 and 55°(magic angle), respectively (28 -35).The binding was followed by monitoring the fluorescence of the etheno derivatives of the nucleic acids ( ex ϭ 325 nm, em ϭ 410 nm).Numerical fits were performed using KaleidaGraph (Synergy, PA) and Mathematica (Wolfram, IL).
The relative fluorescence increase of the nucleic acid, ⌬F, upon binding the PriA protein is defined by Equation 1, where F i is the fluorescence of the nucleic acid solution at a given titration point "i," and F o is the initial value of the fluorescence of the same solution.Fluorescence emission spectra have been corrected for the instrumental factors using the software provided by the manufacturer.
Determination of Thermodynamically Rigorous Binding Isotherms of the PriA Helicase⅐ssDNA Complexes-In this work, we followed the binding of the PriA protein to ssDNA oligomers, by monitoring the fluorescence increase, ⌬F obs , of their etheno derivatives upon the complex formation.To obtain rigorous estimates of the average degree of binding, ͚ i (number of the bound protein molecules per ssDNA oligomer) and the free protein concentration, P F , independent of any assumption about the relationship between the observed spectroscopic signal and ͚ i , we applied an approach previously described by us (19, 23-26, 29 -32).Briefly, the experimentally observed ⌬F obs has a contribution from each of the different possible i complexes of the PriA helicase with the ssDNA.Thus, the observed fluorescence increase is functionally related to ͚ i by Equation 2, where ⌬F i(max) is the molecular parameter characterizing the maximum fluorescence increase of the nucleic acid with the PriA protein bound in complex i.The same value of ⌬F obs , obtained at two different total nucleic acid concentrations, N T 1 and N T 2 , indicates the same physical state of the nucleic acid, i.e. the degree of binding, ͚ i , and the free PriA protein concentration, P F , must be the same.The value of ͚ i and P F is then related to the total protein concentrations, P T1 and P T2 , and the total nucleic acid concentrations, N T1 and N T2 , at the same value of ⌬F obs , by Equations 3 and 4, where x ϭ 1 or 2 (19, 29 -32, 34, 35).

RESULTS
Determination of the Total Site-size of the PriA Helicase⅐ssDNA Complex Using ssDNA Etheno Derivatives-Binding of the PriA helicase to the ssDNA homopolymers is not accompanied by an adequate change in the helicase fluorescence to perform quantitative analyses of the PriA-ssDNA interactions.However, we have found that formation of the complex between the enzyme and the etheno derivative of the adenosine polymer and oligomers causes a strong ϳ3-fold nucleic acid fluorescence increase.Because at 325 nm (excitation wavelength) the etheno adenine is predominantly excited, the observed fluorescence increase must result from the quantum yield increase of the nucleic acid.It should be noted that incorporation of ⑀A into the polymer induces an 8 -10-fold quenching of the ⑀A fluorescence, as compared with the free mononucleotide (36,37).Thus, the strong nucleic acid fluorescence increase, when bound to the PriA helicase, indicates that some of the quenching processes have been removed in the complex with the helicase (see "Discussion").
The dramatic enhancement of the ssDNA etheno derivative fluorescence provides an excellent signal to monitor the PriA-ssDNA interactions and to perform the high resolution measurements of the stoichiometry and mechanism of the helicase⅐ssDNA complex formation.However, quantitative fluorescence titrations of the etheno derivative of poly(dA) and poly(d⑀A), with the PriA helicase, were hindered by the fact that the protein-polymer nucleic acid complex precipitates at high concentrations of the protein and the nucleic acid (data not shown).Nevertheless, these data indicate that the total site-size of the helicase⅐ssDNA complex, i.e. the maximum number of nucleotides occluded by the enzyme in the complex, is lower than ϳ25 nucleotide residues.Therefore, to address the fundamental problem of the stoichiometry of the helicase⅐ssDNA complex, we performed a series of quantitative studies using several ssDNA oligomers with different numbers of nucleotide residues.
Fluorescence titrations of the 24-mer, d⑀A(p⑀A) 23 , with the PriA protein at two different nucleic acid concentrations, in buffer C (pH 7.0, 10 °C), containing 100 mM NaCl, are shown in Fig. 1a.At higher nucleic acid concentrations, a given relative fluorescence increase is reached at higher PriA concentrations.This increase results from the fact that, at higher DNA concentrations, more protein is required to obtain the same degree of binding, ͚ i .The selected nucleic acid concentrations provide separation of the binding isotherms up to the relative fluorescence increase of ϳ2.3.
To obtain binding parameters, independent of any assumption about the relationship between the observed signal and the degree of binding, ͚ i , the fluorescence titration curves, shown in Fig. 1a, have been analyzed, using the approach outlined under "Experimental Procedures" (19, 23-26, 29 -32).Fig. 1b shows the dependence of the observed relative fluorescence increase of the 24-mer as a function of the average degree of binding, ͚ i , of the PriA helicase.Short extrapolation to the maximum fluorescence change, ⌬F max ϭ 2.8 Ϯ 0.2, shows only one molecule of the PriA helicase binding to the 24-mer.The same 1:1 stoichiometry and the same affinities (see below) were obtained with higher and lower 24-mer concentrations providing direct thermodynamic evidence that the enzyme exists in our solution conditions predominantly as a monomer, and the monomer is the form that binds the ssDNA.This is in excellent agreement with early studies that indicated that the PriA helicase exists in solution as a monomer (7,9).Additionally, using the analytical ultracentrifugation technique, we determined that the sedimentation coefficient of the enzyme, s 20,w ϭ 5.9 Ϯ 0.15, remains constant, within experimental accuracy, over a large protein concentration range (data not shown).These results indicate that the PriA helicase exists as a monomer in the protein concentration range studied in this work.
The maximum stoichiometry of the enzyme-ssDNA oligomer is different in the case of the 30-mer, d⑀A(p⑀A) 29 , although this oligomer is only six nucleotide residues longer than the 24-mer.Fluorescence titrations of the d⑀A(p⑀A) 29 with the PriA helicase at two different nucleic acid concentrations, in buffer C (pH 7.0, 10 °C), containing 100 mM NaCl, are shown in Fig. 2a.Separation of the titration curves allowed us to determine the average degree of binding, ͚ i , up to ϳ1.6, a value significantly higher than in the case of the 24-mer.The dependence of the relative fluorescence increase of the 30-mer, as a function of the average degree of binding of the PriA helicase on the oligomer, is shown in Fig. 2b.Extrapolation to the maximum fluorescence increase ⌬F max ϭ 2.5 Ϯ 0.2 provides ͚ i ϭ 2.2 Ϯ 0.2.Thus, the presence of an extra six nucleotide residues in the 30-mer, as compared with the 24-mer, provides enough interaction space for the binding of the second PriA protein molecule.
However, the stoichiometry of the two PriA molecules bound per ssDNA oligomer is not changed when the length of the ssDNA oligomer is further increased by an additional 10 residues.Fluorescence titrations of the 40-mer, d⑀A(p⑀A) 39 , with the PriA helicase at two different nucleic acid concentrations, in buffer C (pH 7.0, 10 °C), containing 100 mM NaCl, are shown in Fig. 3a.Separation of the titration curves allowed us to determine the average degree of binding, ͚ i , up to ϳ1.5.The titration at high nucleic acid concentrations could not reach a plateau because of the precipitation of the protein-nucleic acid complex at high protein and nucleic acid concentrations for this longest ssDNA oligomer studied.The dependence of the relative fluorescence increase of the 40-mer, as a function of the average degree of binding of the PriA helicase on the oligomer, is shown in Fig. 3b.Extrapolation to the maximum fluorescence increase Quantitative analysis of the maximum stoichiometry of PriA⅐ssDNA complexes has been performed for a series of ssDNA oligomers.The dependence of the maximum number of bound PriA molecules per ssDNA oligomer, determined using the approach (see "Experimental Procedures") upon the length of the oligomer, is shown in Fig. 4. Oligomers from 8 to 26 nucleotide residues bind a single PriA molecule.Transition from a single enzyme bound per oligomer to two bound protein molecules per ssDNA occurs between 26-and 30-mers (Fig. 4).However, a further increase in the length of the oligomer, up to 40 residues, does not lead to an increased number of bound PriA molecules per ssDNA oligomer.These data provide the first indication that a total site-size of the PriA⅐ssDNA complex is less than 24 nucleotide residues, but it must contain at least 15 nucleotide residues per bound protein molecule (see below).
Number of Nucleotide Residues Directly Engaged in Interactions with the ssDNA-Binding Site of the PriA Helicase-The total site-size of a large protein ligand-DNA complex corresponds to the DNA fragment, which includes nucleotide residues directly involved in interactions with the protein, its DNA-binding site, and the nucleotides not engaged in direct interactions (38 -40).The latter are prevented from interacting with another protein molecule by the protruding protein matrix of the previously bound protein molecule over nucleotides adjacent to the binding site (37)(38)(39).This is clearly evident in the case of the PriA complexes with 8-and 26-mers (Figs. 3 and 4).Both oligomers can bind only a single enzyme molecule, yet the length of the 26-mer is more than three times longer than the length of the 8-mer.
An accurate estimate of the site-size of the PriA helicase⅐ssDNA complex, using ssDNA oligomers, requires the evaluation of the number of nucleotide residues directly engaged in interactions with the ssDNA-binding site of the helicase.Fluorescence titrations of the d⑀A(p⑀A) 13 , d⑀A(p⑀A) 9 , d⑀A(p⑀A) 7 , and d⑀A(p⑀A) 5 with the PriA helicase in buffer C (pH 7.0, 10 °C), containing 100 mM NaCl, are shown in Fig. 5. Titration curves of the 14-, 10-, and 8-mers show similar fluorescence increases, although slightly decreasing as the length of the nucleic acid decreases.Recall, a single molecule of the PriA helicase, binds to 14-, 10-, and 8-mers (Fig. 4).Moreover, the binding to these oligomers is characterized by very similar intrinsic affinities (Table I).A very dramatic drop in the affinity and the accompanying fluorescence increase occurs when the number of nucleotide residues is lower than eight, with the affinity of the 6-mer being beyond the quantitative analysis in our solution conditions (K Ͻ Ͻ 1 ϫ 10 3 M Ϫ1 ).These data clearly indicate that the number of nucleotide residues directly involved in interactions with the ssDNA-binding site of the PriA helicase, within the total site-size of the protein⅐ssDNA complex, is 8 Ϯ 1.Moreover, the fact that the helicase binds only a single 8-mer molecule indicates that the enzyme possesses only one strong ssDNA-binding site.
The Total Site-size of the PriA Helicase⅐ssDNA Complex, Model of PriA Protein-ssDNA Interactions-The transition from a single PriA molecule bound per ssDNA oligomer to two molecules bound per oligomer occurs between 26-and 30-mers, suggesting that the minimum, total site-size of the PriA⅐ssDNA complex is 15 nucleotide residues per bound protein (Figs. 2  and 4).On the other hand, binding studies with short oligomers  13 ; Ⅺ, d⑀A(p⑀A) 9 ; q, d⑀A(p⑀A) 7 ; E, d⑀A(p⑀A) 5 .Concentrations of 14-, 10-, 8-, and 6-mer are 4.5 ϫ 10 Ϫ7 M (oligomer).The solid lines are nonlinear least squares fits using a single-site binding isotherm (Equation 6) that takes into account the fact that the ssDNAbinding site engages only 8 nucleic acid residues in direct interactions.Intrinsic binding constants and maximum fluorescence increases accompanying the complex formation are included in Table I.
indicate that the protein engages only 8 nucleotide residues in interactions with its ssDNA-binding site (see above).These data strongly suggest that a significant part of the total sitesize of the complex (at least 7 residues) results from the protruding of the large protein molecule over the residues adjacent to the ssDNA-binding site.
If the ssDNA-binding site of the protein is located on one side of the molecule, with a part of the enzyme protruding over the extra 7 residues, then the 24-, 26-, and 40-mers would be able to accommodate two and three PriA molecules, respectively (Fig. 6).This is not what is experimentally observed.One PriA molecule binds to the 24-and 26-mers, and only two enzyme molecules bind to the 40-mer (Fig. 4).Therefore, the model presented in Fig. 6 cannot represent the PriA⅐ssDNA complex (see "Discussion").Next, we consider a model where the ssDNA-binding site, which engages 8 nucleotide residues, is located in the central part of the protein, as depicted in Fig. 7.The protein molecule now has two parts that are protruding over 6 nucleotide residues both sides of the ssDNA-binding site.In this model, only one PriA molecule can bind to the 24and 26-mers.This is because the first bound molecule can now block at least 14 nucleotide residues.For efficient binding, the second protein molecule also needs a fragment of at least 14 nucleotide residues, which is larger than the remaining 11 and 12 residues of the 24-and 26-mers, respectively.The two bound PriA molecules require at least 28 nucleotide residues of the ssDNA.On the other hand, this allows two molecules of the enzyme to bind to the 30-, 35-, and 40-mers (see Fig. 4).In the case of the 40-mer, the remaining fragment of 8 residues is 6 nucleotides too short, i.e. it does not provide efficient interacting space to allow the third PriA protein to associate with the oligomer.This is exactly what is experimentally observed (Fig. 4).Therefore, the model of the protein-ssDNA, presented in Fig. 7, adequately describes all experimentally determined stoichiometries of the PriA with the series of ssDNA oligomers examined in this work (see "Discussion").Moreover, these data and the analyses indicate that the actual total site-size of the PriA⅐ssDNA complex is 20 Ϯ 3 nucleotide residues and include 8 residues encompassed by the ssDNA-binding site of the enzyme, as well as ϳ12 residues occluded by the protruding protein matrix (Fig. 7).Examination of the intrinsic affinities of the enzyme to different ssDNA oligomers provides additional support for the proposed model of the PriA⅐ssDNA complex (see below).
Intrinsic Affinities of PriA-ssDNA Interactions-Binding of a single PriA molecule to 8-, 10-, 14-, 16-, 18-, 20-, 24-, and 26-mers can be analyzed using a single-site-binding isotherm described by Equation 5, where K N is the apparent binding constant characterizing the affinity for a given ssDNA oligomer, containing N nucleotide residues, and ⌬F max is the maximum relative fluorescence increase.Notice the value of K N contains a statistical factor resulting from the fact that the number of nucleotide residues engaged in interactions with the protein ssDNA-binding site, within the total site-size of the PriA⅐ssDNA complex, m ϭ 8. Knowing the number of residues engaged in direct interactions with the ssDNA-binding site of the enzyme allows us to properly extract the intrinsic binding constant, K i , for the ssDNA oligomers, which bind only a single PriA molecule.By using the intrinsic binding constant, K i , the equation describing the binding of PriA to ssDNA oligomers, which can accommodate only a single enzyme molecule, is defined as shown in Equation 6.
where N is the number of nucleotide residues in the ssDNA oligomer.It should be pointed out that Equation 6 is different from the isotherm, typically applied in the binding of a large ligand to a finite lattice, which takes into account the overlap of potential binding sites, although the mathematical form is the same (38 -40).The difference results from the fact that instead of the total site-size of the protein⅐ssDNA complex (n ϭ 20), the number of the nucleotide residues engaged in direct interactions with the ssDNA-binding site of the protein, m, enters the equation (in the case of PriA, m ϭ 8).
The solid lines in Fig. 1a are nonlinear least square fits of the experimental binding isotherm for the PriA-24-mer system using Equation 6, with N ϭ 24 and m ϭ 8, which provide K i ϭ (4.4 Ϯ 0.6) ϫ 10 4 M Ϫ1 .The lines are parametric plots where ⌬F, defined by Equation 6, is plotted versus total protein concentration, P Tot ϭ P F ϩ (͚ i )N Tot (Equation 4).The values of the intrinsic binding constants, together with the K N values for all studied ssDNA oligomers, are included in Table I.The value of K N , within experimental error, increases as the length of the ssDNA oligomers increase.This results from the increasing value of the hidden statistical factor in Equation 5.However, with the exception of the shortest oligomer (8-mer), the intrinsic binding constant is centered around the value of (5.5 Ϯ 2) ϫ 10 4 M Ϫ1 .Such behavior is expected for the binding constant characterizing intrinsic interactions that should be independent of the length of the nucleic acid oligomer, as long as the oligomer is longer than m.Also, these data indicate that there are no significant end effects in the PriA helicase binding to the ssDNA.
Statistical Thermodynamic Models of the PriA Helicase Binding to the ssDNA 30-, 35-, and 40-mers, Intrinsic Affinities, and Cooperativities-Quantitative analysis of the PriA helicase binding to a 30-mer and longer oligomers is much more complex.The partition function, Z N , for these PriA-ssDNA oligomer systems must account for the potential overlap of the binding sites and the possible cooperative interactions between the bound protein molecules.The situation is additionally complicated by the fact that the PriA protein can efficiently associate with ssDNA oligomers, which are significantly shorter than the total site-size of the protein⅐ssDNA complex.Thus, two enzyme molecules associate with the 30-mer, although the length of the oligomer is shorter than the sum of the two total site-sizes of the PriA⅐ssDNA complex (see above).Moreover, we know that the number of nucleotide residues engaged in inter- actions with the ssDNA-binding site of the enzyme is m ϭ 8 and that the protein protrudes over a distance of 6 Ϯ 1 nucleotides on both sides of the binding site (Fig. 7).For instance, the PriA protein can bind to the 5Ј or 3Ј end of the ssDNA, occluding only 14 nucleotide residues instead of 20 (Fig. 7).The considered complex binding mechanism is unique and, to our knowledge, never before analyzed.Such a binding system cannot be directly treated by the exact combinatorial theory for large ligand binding to a finite linear, homogeneous lattice that exclusively uses the total site-size of the protein-lattice complex (38 -40).The partition functions for the 30-, 35-, and 40-mers, Z N , have been obtained by examining all possible states of the given PriA⅐ssDNA oligomer complexes.In the case of the 30-mer, the complete partition function of the PriA-30-mer system, Z 30 , which takes into account the overlap of potential sites and the formation of the PriA⅐ssDNA complexes lower than the total site-size, as depicted in Fig. 7, is described by Equation 7, (Eq. 7) FIG. 6.Schematic model for the binding of the PriA helicase to the ssDNA, based on the minimum site-size of the protein-nucleic acid complex, n ‫؍‬ 15, and the size of the binding site engaged in protein ssDNA interactions, m ‫؍‬ 8.The helicase binds the ssDNA in a single orientation with respect to the polarity of the sugar-phosphate backbone of the ssDNA.The ssDNA-binding site, which encompasses 8 nucleotide residues, is located on one side of the enzyme molecule, with the rest of the protein matrix protruding over the extra 7 nucleotide residues, without engaging in thermodynamically significant interactions with the DNA (black ribbon) (a).When bound at the ends of the nucleic acid, or in its center, the protein can occlude 8 or 15 nucleotides (b).Therefore, this model would allow the binding of two molecules of the PriA helicase to the ssDNA 24-mer and three molecules of the enzyme to the 40-mer (c).However, as shown is this work, this is not experimentally observed.FIG. 7. Schematic model for the binding of the PriA helicase to the ssDNA, based on the total site-size of the protein-nucleic acid complex, n ‫؍‬ 20, and the size of the ssDNA-binding site engaged in protein-ssDNA interactions, m ‫؍‬ 8.The helicase binds the ssDNA in a single orientation with respect to the polarity of the sugar-phosphate backbone of the ssDNA.The ssDNA-binding site of the PriA helicase, which encompasses only 8 nucleotide residues, is located in the center of the enzyme molecule (a).The protein matrix protrudes over 6 nucleotide residues on both sides of the ssDNA-binding site without engaging in interactions with the nucleic acid (black ribbon).When bound at the 5Ј or the 3Ј end of the nucleic acid, the protein always occludes 14 nucleotide residues, whereas in the complex in the center of the ssDNA oligomer, 20 nucleotide residues are occluded (b).This model would allow the binding of only one molecule of the PriA helicase to the 24-mer and only two molecules of the enzyme to the 30-, 35-, and 40-mers (c).This is in complete agreement with all of the experimental results described in this work.
where is the parameter characterizing the cooperative interactions between bound protein molecules.Analogous partition functions for the 35-and 40-mers are shown in Equation 8, and Equation 9, The average degree of binding, ͚ i , is then obtained by using the standard statistical thermodynamic expression, ͚ i ϭ ѨlnZ N /ѨlnP F (38 41).For the binding of PriA to the 30-, 35-, and 40-mers, one obtains Equations 10 -12.
Z 30 (Eq. 10) The observed fluorescence increase, ⌬F, of d⑀A(p⑀A) 29 , d⑀A(p⑀A) 34 , and d⑀A(p⑀A) 39 as a function of the PriA concentration is then defined by Equations 13-15, where ⌬F 1 and ⌬F max are relative, molar fluorescence increases accompanying the binding of the one and two PriA molecules to the ssDNA oligomer, respectively.The values of ⌬F 1 and ⌬F max can be independently determined from the dependence of the nucleic acid fluorescence upon the average number of PriA molecules bound per oligomer, ͚ i as depicted in Figs.2b and 3b for the 30-and 40-mers.The plots are linear, indicating that the same fluorescence increase accompanies the binding of the first and the second PriA molecule to the 30-and 40-mers.The same is true for the 35-mer (data not shown).As we pointed out, such dependence of the observed spectroscopic signal, as a function of the degree of binding, should be determined and not a priori assumed (19, 29 -32, 34, 35).For the 30-mer, ⌬F 1 ϭ 1.25 and ⌬F max ϭ 2.5.The solid lines in Fig. 2a are nonlinear least square fits using Equations 7 and 13, with only two fitted parameters K i and .The obtained values are Analogous analyses of the binding of the PriA protein to 35and 40-mers (e.g.Fig. 3a) provide similar values of the intrinsic binding constants, although a slightly lower cooperativity parameter (Table II).A similar value of K i , obtained with ssDNA oligomers of different lengths, indicates similar types of intrinsic interactions between the PriA protein and the nucleic acid in the studied complexes.This is predicted by the proposed model of the protein⅐ssDNA complex, which takes into account the total site-size of the protein-nucleic acid complex, n, the number of the nucleotide residues engaged in interactions with the ssDNA-binding site, m, and the location of the ssDNAbinding site within the protein matrix (Fig. 7, Equations 7-15).The obtained value of ranging between 11 Ϯ 3 and 0.8 Ϯ 0.3 also indicates that the binding of the PriA helicase to the ssDNA is not accompanied by significant cooperative interactions (see "Discussion").

DISCUSSION
The physiological role of the PriA helicase is related to the ability of the enzyme to interact with both ss-and dsDNA (1-3).Yet, little is known about the quantitative molecular mechanism of the PriA helicase-nucleic acid interactions.In this communication, we provide extensive, quantitative studies of the stoichiometry, free energy of binding, and cooperativity of the PriA protein interactions with the ssDNA.
Application of Etheno Derivatives of the ssDNA to Quantitatively Study Helicase-Nucleic Acid Complexes-Quantitative studies of the interactions of the PriA helicase with ssDNA are greatly facilitated by the finding that binding of the protein to the fluorescent etheno analog (⑀A) of adenosine homopolymers is accompanied by a strong nucleic acid fluorescence increase (19, 28 -31).A similar effect of a helicase on the fluorescence of the etheno derivatives has been previously found in the case of the E. coli hexameric DnaB helicase and was extensively used by us to quantitatively examine the thermodynamics and kinetics of the DnaB helicase interactions with the ssDNA (19, 29 -32, 42).
The fluorescence of ⑀A is not very sensitive to the polarity of the environment (25)(26)(27)(28)43).However, as compared with the free ⑀AMP, the emission of etheno oligomers is predominantly quenched (8 -10-fold), via the dynamic process of an intramolecular collision (36,37,44).The observed strong fluorescence increase of the etheno derivative oligomers, upon binding to the PriA helicase, most probably results from the large conformational change of the nucleic acid leading to the increased separation and restricted mobility of the nucleic acid bases in the complex with the enzyme (19,20,37).A large fluorescence increase of ⑀A derivatives, in the complexes with both PriA and DnaB helicases, indicates that the structural changes of the ssDNA, induced by the complex formation with different helicases, are similar.This is particularly interesting in light of the fact that PriA and DnaB are fundamentally different in their helicase activity.The DnaB protein is a 5Ј 3 3Ј helicase, i.e. it unwinds the duplex DNA in a 5Ј direction, while PriA is a 3Ј 3 5Ј helicase (1-3).Thus, independently of the direction of dsDNA unwinding, a helicase induces very similar conformational changes in the bound ssDNA.
The Single ssDNA-Binding Site of the PriA Helicase Encompasses 8 Ϯ 1 Nucleotide Residues-In the complex with the polymer ssDNA, a large protein ligand will block the access of other protein molecules to n number of nucleotide residues (38 -40).This nucleic acid fragment, a fundamental quantity for proper analysis of the energetics and structure of the protein-nucleic acid complexes, is referred to as the total site-size of the protein-nucleic acid complex (31, 38 -40).Because PriApolymer ssDNA complexes precipitate at high protein and nucleic acid concentrations, we could not quantitatively determine the total site-size of the protein⅐ssDNA complex by directly using the polymer nucleic acid.Nevertheless, the obtained data with polymer ssDNA, limited to the protein concentrations where the precipitation was not yet present (ϳ4 ϫ 10 Ϫ5 M), already indicated that the binding density (number of protein molecules bound per nucleotide residue) reached the value of ϳ0.04.This value shows that the total site-size of the PriA⅐ssDNA complex cannot be larger than ϳ25 nucleotides (38 -40).
The major aspect of the experimental strategy used in this work is the application of the large series of ssDNA oligomers of well defined length.Oligomers range from a length shorter than the number of nucleotide residues encompassed by the ssDNA-binding site of the enzyme to ssDNA oligomers that can accommodate two PriA molecules.Such an approach dramatically increases resolution of the binding experiments and allows us to determine not only the total site-size of the protein⅐ssDNA complex, n, but also the number of nucleotide residues directly engaged in interactions with the ssDNA-binding site of the protein, m.In other words, it allows us to determine the size of the ssDNA-binding site of the enzyme.Only when these two parameters are known can the proper statistical factors be obtained and the intrinsic binding constants extracted (Tables I and II).Moreover, the possibility of analyzing the stoichiometries of protein⅐ssDNA complexes with different oligomers enables us to get insight into the location of the ssDNA-binding site within the protein matrix.
As we discussed above, in direct interactions, the ssDNAbinding site of a protein may engage a significantly smaller number of nucleotide residues than the total site-size of the complex.This number of nucleotide residues encompassed by the ssDNA-binding site of the protein, m, can be estimated in experiments with short ssDNA oligomers.The minimum value of m corresponds to the length of the shortest ssDNA oligomer that still forms a complex with the protein, with an affinity similar to the affinity of longer oligomers.In other words, such an oligomer, although shorter than the total site-size, must form all crucial, interacting contacts with the ssDNA-binding site of the enzyme (31).By using this approach, we established that the ssDNA-binding site of the E. coli replicative helicase, the DnaB protein, encompasses only 6 -7 nucleotide residues although the total site-size of the protein⅐ssDNA complex is 20 Ϯ 3 nucleotides (31).In the case of the PriA helicase, in order to efficiently form a complex with the ssDNA-binding site, the ssDNA oligomer must have a length of m ϭ 8 Ϯ 1 nucleotide residues, a value significantly shorter than the total site-size.Thus, the difference of 2 nucleotide residues between 6-and 8-mers makes the affinity of the shorter oligomer for the binding site barely detectable (Fig. 5).However, the same difference between 8-and 10-mers does not lead to any decrease of the free energy of binding (Table I).
For the examined series of ssDNA oligomers, the PriA helicase forms complexes with a stoichiometry of 1:1 with oligomers of 8 -26 nucleotide residues in length (Fig. 4).As discussed above, the number of nucleotide residues encompassed by the ssDNA-binding site of the enzyme, m, is the minimum number of nucleotides necessary for the protein and a nucleic acid to efficiently form a complex.Knowing the value of m allows us to properly address the statistical factor in these complexes and to extract the intrinsic binding constant K i that should be independent of the length of the nucleic acid.Thus, the values of the apparent binding constants for studied oligomers, obtained using Equation 5, show, within experimental accuracy, an increasing trend with the increasing length of the studied oligomer, as a result of the increasing value of the statistical factor (Table I).However, intrinsic binding constants, determined using Equation 6, which take into account the statistical factor, show no such trend as a function of the length of the ssDNA and are centered around (5.5 Ϯ 2) ϫ 10 4 M Ϫ1 .This is exactly what is expected for the binding constant that characterizes intrinsic interactions between the protein and the nucleic acid, not affected by the statistical factors.
The Total Site-size of the PriA Helicase Complex with ssDNA Is 20 Ϯ 3 Nucleotide Residues-A transition from the stoichiometry of 1:1 to the stoichiometry of two PriA molecules bound per ssDNA occurs between the complexes with 26-and 30-mers (Fig. 4).The fact that two PriA molecules bind to the 30-mer would suggest that the total site-size of the enzyme⅐ssDNA complex is 15 nucleotides, yet only two protein molecules bind to the 35-and 40-mers, which would suggest a site-size larger than 15.However, knowing that the ssDNA-binding site on the protein binds only 8 nucleotide residues opens the possibility of more accurately determining the total site-size of the protein⅐ssDNA complex.Moreover, the obtained extensive data on the stoichiometries of the enzyme-ssDNA oligomer, over the entire spectrum of the length of the oligomer, provide insight into the structure of the protein-nucleic acid complex.
It is clear that if the ssDNA-binding site of the PriA helicase is located at one end of the protein molecule and the site-size is n ϭ 15, then two molecules of the enzyme would bind to the 24and 26-mers (Fig. 6, a-c).This is because the first bound PriA can form a complex with the nucleic acid where only 15 residues are blocked, with 9 or 11 residues remaining free.These ssDNA fragments would be long enough to accommodate another protein molecule that can bind, with a very similar intrinsic binding constant, to a stretch of only 8 residues (Fig. 6c).The same analysis shows that if the total site-size is 15 residues long and the ssDNA-binding site is located as depicted in Fig. 6, then the 40-mer should bind three PriA molecules.However, the experimental data show that only one and two PriA molecules bind to the 24-and 40-mers, thus contradicting this model.
The schematic model of the PriA protein⅐ssDNA complex, which agrees with all thermodynamic data described in this work, is shown in Fig. 7.The ssDNA-binding site, encompassing 8 nucleotide residues, is located in the center of the protein molecule.On both sides of the ssDNA-binding site the protein matrix protrudes over a distance of 6 residues, giving a total site-size of the protein⅐ssDNA complex as n ϭ 20.A characteristic feature of this model is that the bound protein always blocks either 20 or a stretch of 14 nucleotide residues in the complex with the ssDNA (Fig. 7b).As a result, in the complex with the 24-and 26-mers, the bound PriA blocks a stretch of at least 14 residues, leaving only 11 and 12 residues free, respectively.This is not enough for the second PriA molecule to associate with the ssDNA.With the 30-mer, the protein can form a complex where the stretch of 16 residues is free, making the binding of the second protein molecule possible (Fig. 7c).In the case of the 40-mer, two PriA molecules can form a complex with the oligomer where 34 residues are blocked, leaving only a stretch of 6 residues free.Once again, this is not enough for the third molecule of the enzyme to associate with the nucleic acid (Fig. 4).
As we mentioned above, independence of intrinsic binding constants characterizing interactions of the enzyme with the ssDNA oligomers that accommodate only one protein molecule upon the oligomer length strongly support the proposed model of the PriA⅐ssDNA complex (Table I).Additional support of the model of the PriA⅐ssDNA complex, shown in Fig. 7, comes from the determined intrinsic binding constants for oligomers that bind two PriA molecules, 30-, 35-, and 40-mers.The determined values of K i are similar for all these oligomers.Moreover, the values of K i are also similar to the values of K i determined for the short oligomers (Tables I and II).This could only happen if the statistical factors that enter the partition function and that are strongly dependent on the total site-size and size of the ssDNA-binding site are correctly determined (Equations 7-15).
There Are Very Weak Cooperative Interactions in the Binding of the PriA Helicase to the ssDNA-Binding of the PriA helicase to the ssDNA is characterized by the cooperativity parameter, ϳ0.8 -11 which indicates very weak cooperative interactions between bound protein molecules (Table II).Similar low values of characterize the binding to the ssDNA of another E. coli replicative helicase, the DnaB protein (19,34).The DnaB protein is the only other helicase for which the value of is known.We believe that the fact that the DnaB hexamer and the PriA monomer are unable to form long protein clusters, when bound to the ssDNA, may reflect a general aspect of functioning of the replicative helicase (19,34).The unwinding of the dsDNA at the junction between ss-and dsDNA does not require clusters of helicase molecules.Very weak or nonexistent protein-protein interactions may be a simple evolutionary adaptation of a replicative helicase, which allows the enzyme to perform functions requiring only a single protein molecule (19,20).

FIG. 1 .
FIG.1.a, fluorescence titrations of the 24-mer d⑀A(p⑀A)23 with the PriA protein ( ex ϭ 325 nm, em ϭ 410 nm) in buffer C (pH 7.0, 10 °C), containing 100 MNaCl, at two different nucleic acid concentrations: f, 4.7 ϫ 10 Ϫ7 M; Ⅺ, 1.2 ϫ 10 Ϫ5 M (oligomer).The solid lines are nonlinear least squares fits of the titration curves, using a single-site binding isotherm (Equation6) that takes into account the fact that the ssDNAbinding site engages only 8 residues of the nucleic acid in direct interactions.Intrinsic binding constant K i ϭ 4.4 ϫ 10 4 M Ϫ1 and relative fluorescence change ⌬F max ϭ 2.8.b, dependence of the relative fluorescence of the 24-mer, ⌬F, upon the average number of bound PriA proteins (f).The solid line follows the experimental points and has no theoretical basis.The dashed line is the extrapolation of ⌬F to the maximum value of ⌬F max ϭ 2.8.FIG. 2. a, fluorescence titrations of the 30-mer d⑀A(p⑀A) 29 with the PriA protein ( ex ϭ 325 nm, em ϭ 410 nm) in buffer C (pH 7.0, 10 °C), containing 100 mM NaCl, at two different nucleic acid concentrations: f, 4.7 ϫ 10 Ϫ7 M; Ⅺ, 2.1 ϫ 10 Ϫ6 M. The solid lines are nonlinear least squares fits of the titration curves, using the statistical thermodynamic model for the binding of two PriA molecules to the 30-mer, described by Equations 7, 10, and 13.The intrinsic binding constant K i ϭ 1.3 ϫ 10 5 M Ϫ1 , cooperativity parameter ϭ 11, and relative fluorescence change ⌬F 1 ϭ 1.25, and ⌬F max ϭ 2.5.b, dependence of the relative fluorescence of the 30-mer, ⌬F, upon the average number of bound PriA proteins (f).The solid line follows the experimental points and has no theoretical basis.The dashed line is the extrapolation of ⌬F to the maximum value of ⌬F max ϭ 2.5.

FIG. 3 .FIG. 4 .
FIG. 3. a, fluorescence titrations of the 40-mer d⑀A(p⑀A) 39 with the PriA protein ( ex ϭ 325 nm, em ϭ 410 nm) in buffer C (pH 7.0, 10 °C), containing 100 mM NaCl, at two different nucleic acid concentrations: f, 4.6 ϫ 10 Ϫ7 M; Ⅺ, 4 ϫ 10 Ϫ6 M. The solid lines are nonlinear least squares fits of the titration curves, using the statistical thermodynamic model for the binding of two PriA molecules to the 40-mer, described by Equations 9, 12, and 15.The intrinsic binding constant K i ϭ 6 ϫ 10 4 M Ϫ1 , cooperativity parameter ϭ 0.8, and relative fluorescence change ⌬F 1 ϭ 1.7, and ⌬F max ϭ 3.5.b, dependence of the relative fluorescence of the 40-mer, ⌬F, upon the average number of bound PriA proteins (n).The solid line follows the experimental points and has no theoretical basis.The dashed line is the extrapolation of ⌬F to the maximum value of ⌬F max ϭ 3.5.