Kinetic Control of Mg²⁺-dependent Melting of Duplex DNA Ends by E. coli RecBC

Abstract

E. coli RecBCD is a highly processive DNA helicase involved in double strand break repair and recombination that possesses two helicase/translocase subunits with opposite translocation directionality (RecB (3’ to 5’) and RecD (5’ to 3’)). RecBCD has previously been shown to melt out ∼5−6 base pairs upon binding to a blunt-ended duplex DNA in a Mg²⁺-dependent, but ATP-independent reaction. Here we examine the binding of E. coli RecBC helicase (minus RecD), also a processive helicase, to duplex DNA ends in the presence and absence of Mg²⁺ in order to determine if RecBC can also melt a duplex DNA end in the absence of ATP. Equilibrium binding of RecBC to DNA substrates with ends possessing pre-formed 3’ and/or 5’-single stranded (ss)-(dT)_n flanking regions (tails) (n varying from zero to 20 nucleotides) was examined by competition with a fluorescently labeled reference DNA and by isothermal titration calorimetry (ITC). The presence of Mg²⁺ enhances the affinity of RecBC for DNA ends possessing 3’ or 5’-(dT)_n ss-DNA tails with n < 6 nucleotides, with the relative enhancement decreasing as n increases from zero to six nucleotides. No effect of Mg²⁺ was observed for either the binding constant or the enthalpy of binding (ΔH_obs) for RecBC binding to DNA with ss-DNA tail lengths, n ≥ 6 nucleotides. Upon RecBC binding to a blunt duplex DNA end in the presence of Mg²⁺, at least four base pairs at the duplex end become accessible to KMnO₄ attack, consistent with melting of the duplex end. Since Mg²⁺ has no effect on the affinity or binding enthalpy of RecBC for a DNA end that is fully pre-melted, this suggests that the role of Mg²⁺ is to overcome a kinetic barrier to melting of the DNA by RecBC and presumably also by RecBCD. These data also provide an accurate estimate (ΔH_obs = 8 ± 1 kcal/mol) for the average enthalpy change associated with the melting of a DNA base pair by RecBC.

Introduction

Helicases are a class of motor enzymes that play critical roles in all aspects of DNA and RNA metabolism. These enzymes catalyze the separation of double-stranded (ds) DNA (or RNA) to form the single stranded (ss) DNA intermediates required for DNA replication, recombination and repair via the coupling of energy from nucleoside triphosphate (NTP) binding and hydrolysis ^{1; 2; 3; 4}. To function processively, helicases must also translocate along the DNA filament. Such enzymes can also disrupt protein-DNA complexes ^{5; 6} and this appears to provide an important biological function ^{7; 8}.

The E. coli RecBCD helicase is responsible for the majority of recombinational repair at dsDNA breaks ^{9; 10}. RecBCD is a heterotrimeric enzyme consisting of the RecB (134 kDa), RecC (129 kDa) and RecD (67 kDa) subunits. Both the RecB and RecD subunits are superfamily 1 (SF1) DNA helicases ¹¹, but unwind dsDNA with opposite polarities; RecB is a 3’ to 5’ helicase/translocase ¹², while RecD is a 5’ to 3’ helicase/translocase ^{13; 14}. RecBCD binds and initiates DNA unwinding from a blunt or nearly blunt DNA end, the enzyme generates a 3’-ended ssDNA intermediate after encountering a recombination hotspot, called Chi (χ) (5’-GCTGGTGG-3’)^{15; 16; 17}. After Chi recognition, RecBCD then facilitates the loading of the RecA protein onto the unwound 3’-ssDNA ¹⁸. The RecA-bound ssDNA filament then forms a joint molecule with a homologous region of DNA to initiate a recombination event. The RecBC enzyme, lacking the RecD subunit, can also function as a processive helicase and is capable of facilitating homologous recombination in vivo ^{19; 20}. However, the nuclease activity of RecBC is greatly attenuated ^{21; 22; 23; 24} even though the nuclease site is located within the 30-kDa C-terminal domain of the RecB subunit ^{25; 26; 27}, indicating that the nuclease activity is stimulated by the RecD subunit.

Both RecBCD and RecBC enzymes initiate DNA unwinding from duplex ends, including blunt ends ^{28; 29; 30; 31; 32; 33}. Studies of initiation complexes formed between RecBCD and a blunt-ended duplex DNA show that the RecB subunit can be crosslinked to the 3’-strand of the duplex end while the RecC and RecD subunits can be crosslinked to the 5’-strand ³⁴. Furthermore, five to six base pairs (bp) at the duplex end within the RecBCD-dsDNA initiation complex become accessible to KMnO₄ attack in a Mg²⁺-dependent but ATP-independent manner ³⁵, suggesting that RecBCD melts out or unwinds 4−5 bp upon binding to a blunt DNA end. A crystal structure of a RecBCD-DNA complex, formed in the presence of Ca²⁺, but without ATP, shows a melting of ∼ four bp at the duplex DNA end ²⁷.

Equilibrium binding of both RecBCD and RecBC to duplex DNA ends is enhanced if the DNA end possesses pre-formed 3’ and/or 5’ ssDNA flanking regions³⁶, with RecBC showing optimal binding to a DNA end with both 3’-(dT)₆ and 5’-(dT)₆ tails, whereas RecBCD binds optimally to a DNA end with a 3’-(dT)₆ tail, but a 5’-(dT)₁₀ tail ³⁷. These results suggest that both enzymes are capable of disrupting ∼six bp upon binding to a blunt duplex DNA end ³⁷; however, melting of a duplex DNA end by RecBC has not been demonstrated. In the current study, we have compared the effects of Mg²⁺ on the equilibrium binding of RecBC to duplex DNA ends possessing variable lengths of pre-existing ssDNA tails as well as on the patterns of KMnO₄ protection. These results demonstrate that RecBC is also able to melt out at least four bp upon binding to a duplex DNA end in a Mg²⁺-dependent, but ATP-independent reaction. Our studies also suggest that the effect of Mg²⁺ is to relieve a kinetic block to DNA melting by RecBC, rather than to affect the equilibrium binding affinity of RecBC for the DNA.

Results

DNA substrate design

The experiments described here were performed using the series of 60-bp Cy3-labeled reference DNA (I to III) and the unlabeled DNA molecules (IV to VI) shown schematically in Figure 1a. The 60-bp duplex length ensures that one molecule of RecBC can bind independently to each duplex end without interference from protein binding to the other end ³⁷. The almost identical ends within each DNA duplex molecule simplify the data analysis as RecBC binds to both ends with the same affinity within experimental error ³⁷. The equilibrium constant for RecBC binding to an end of a Cy3-labeled reference DNA molecule (I to III) is referred to hereafter as K_BC,R, while K_BC denotes the equilibrium constant for RecBC binding to an unlabeled duplex DNA end (IV to VI). The sequences of DNA strands used to form the duplex DNA molecules in Figure 1a are given in Figure 1c.

Figure 1.

DNA molecules used for RecBC equilibrium binding studies. (a) Schematic representations of Cy3-labeled reference DNA molecules I through III and the non-fluorescent competitor series DNA IV to VI. (b) Structure of the Cy3 fluorophore and its covalent attachment to the phosphate group on the 5’-end of the DNA via a three-carbon linker. (c) Sequences of all DNA strands used to form DNA molecules shown in (a). Reference DNA I was formed from strands 1 and 2; reference DNA II was formed from strands 3 and 4; reference DNA III was formed from strands 5 and 6; DNA series IV was formed from strands 7 and 8; DNA series V was formed from strands 9 and 10; and DNA series VI was formed from strands 11 and 12.

Effects of Mg²⁺ on RecBC binding to reference DNA I

Generally, an increase in the bulk solution [NaCl] will decrease the equilibrium binding constant for most protein-DNA interactions due to the fact that the Na⁺ counterion is displaced from the DNA when the protein binds ^{38; 39; 40; 41}. If there is a mixture of Na⁺ and Mg²⁺ in the buffer and if Mg²⁺ interacts only with the DNA and not the protein, then the Mg²⁺ should compete with both the Na⁺ and protein for binding to the DNA. Thus, if Mg²⁺ were only serving as a competitor for DNA binding, then the protein-DNA binding constant measured in the presence of Mg²⁺ should always be less than or equal to the binding constant measured in the absence of Mg²⁺ at the same [NaCl] ^{42; 43}.

We examined the effects of Mg²⁺ on the [NaCl]-dependence of the equilibrium constant for RecBC binding to a duplex DNA end that we expect will be partially melted in the presence of Mg²⁺. For this purpose we examined RecBC binding to reference DNA I which has a Cy3 fluorophore on each 5’-end of the DNA and a 3’-(dT)₄ tail. Based on our previous studies ³⁷, RecBC binding to each end of this DNA is expected to melt an additional 2 bp in the presence of Mg²⁺. We first examined the dependence of the RecBC-DNA end binding constant, K_BC,R, on [NaCl] by performing “salt-back titrations” in the presence and absence of 10 mM MgCl₂ as described ^{44; 45} (see Materials and Methods) and the results are plotted in Figure 2. At the starting [NaCl] of 0.10 M, RecBC binds with higher affinity to the DNA end in the presence of 10 mM MgCl₂ (K_BC,R = (4.8 ± 0.3) × 10⁷ M⁻¹ in 10 mM MgCl₂ vs. (2.3 ± 0.2) × 10⁷ M⁻¹ in the absence of MgCl₂). Upon increasing the [NaCl] we observe a decrease in K_BC,R both in the presence and absence of 10 mM MgCl₂. Plots of log K_BC,R vs. log [NaCl] are linear within experimental error over the range from 0.1 to 0.85 M NaCl, with log-log slopes of −1.9 ± 0.4 in the presence of 10 mM MgCl₂ and −4.5 ± 0.6 in the absence of MgCl₂. Therefore, at any [NaCl], K_BC,R is always larger in the presence of 10 mM MgCl₂ with the relative effect of MgCl₂ increasing with increasing [NaCl] (Figure 2). This result is opposite to the expected result if Mg²⁺ were to bind only to the DNA and compete for binding of Na⁺ and RecBC since under those circumstances the values of K_BC,R should converge, rather than diverge at high [NaCl] ^{42; 43}. This result provides a clear indication that Mg²⁺ also binds directly to the RecBC protein and/or the RecBC-DNA complex, and facilitates RecBC binding to the DNA end. The simplest interpretation of the slopes of the plots in Figure 2 indicates that approximately five ions (Na⁺ and/or Cl⁻) are released upon RecBC binding to an end of reference DNA I in the absence of MgCl₂, while ∼two ions (Na⁺ and/or Cl⁻) are released when RecBC binds to a DNA I end in the presence of 10 mM MgCl₂.

Figure 2.

Effects of Mg²⁺ on the [Na⁺]-dependence of the equilibrium constant (K_BC,R) for RecBC binding to an end of reference DNA I. Values of log K_BC,R for reference DNA I are plotted as a function of log [Na⁺]. The data were obtained from “salt-back titrations” as described in Materials and Methods in buffer M at 25°C in the presence of 10 mM MgCl₂ (●) or in the absence of MgCl₂ (○). Data were also obtained from direct measurement of K_BC,R in buffer M plus the indicated [NaCl] in the presence of 10 mM MgCl₂ (▲) or in the absence of MgCl₂ (△). The solid and short dash lines are linear fits to the data obtained in buffer M with or without 10 mM MgCl₂, respectively. The slopes obtained from the linear fits are −1.9 ± 0.4 in the presence of 10 mM MgCl₂ and −4.5 ± 0.6 in the absence of MgCl₂.

Independent experiments indicated that the fluorescence intensity of the Cy3 labeled DNA is unaffected by increases in [NaCl], thus enabling us to use “salt back” titrations to obtain estimates of K_BC,R. As a further check, we also measured K_BC,R directly at 300 and 400 mM NaCl by determining a full binding isotherm (titrating RecBC into DNA I and monitoring the Cy3 fluorescence increase). The values of K_BC,R determined directly (triangles in Figure 2) and by the salt back titration (circles in Figure 2) agree within experimental uncertainty.

The pre-existing ss-(dT)_n tail length influence the effects of Mg²⁺ on RecBC binding to DNA ends

The data in Figure 2 show that K_BC,R for RecBC binding to a DNA end with a 3’-(dT)₄ ssDNA tail is increased in the presence of 10 mM MgCl₂. As mentioned above, we anticipate that two bp within the duplex region at the ss-ds-DNA junction should be melted upon RecBC binding to such a DNA end. We next determined the relative equilibrium constants for RecBC binding to DNA ends possessing different lengths of pre-existing ss-(dT)_n tails. For these studies we measured equilibrium constants, K_BC, for RecBC binding to the non-fluorescent DNA series IV (variable 3’-(dT)_n tail) and V (variable 5’-(dT)_n tail) in the presence and absence of 10 mM MgCl₂ using competition titration experiments. These experiments were performed by titrating a mixture of reference DNA I and one of the competitor DNA IV or V series molecules with RecBC as described ³⁷. For each competitor DNA molecule, three experiments were performed in which the concentration of reference DNA I was maintained constant (20 nM) while the concentration of the non-fluorescent competitor DNA molecule was increased in each successive experiment. Data from all three experiments were analyzed globally to obtain K_BC using non-linear least square (NLLS) methods as described ³⁷ and the values of K_BC are presented in Table 1. The competition binding isotherms obtained from a representative experiment performed using a DNA IV series molecule with n = 8 nucleotides are shown in Figure 3a. The relative fluorescence enhancement (ΔF_obs, defined in equation (2) in Materials and Methods) is plotted as a function of total [RecBC] together with simulated isotherms based on the best fit values of K_BC (Table 1) as described ³⁷.

Table 1.

Equilibrium constants (K_BC) for RecBC binding to the non-fluorescent DNA IV to VI series molecules at 25°C.

DNA IVa			DNA Va
3′-(dT)n tail length (n)	KBC (107 M−1) in 10 mM MgCl2	KBC (107 M−1) in 0 mM MgCl2	5′-(dT)n tail length (n)	KBC (107 M−1) in 10 mM MgCl2	KBC (107 M−1) in 0 mM MgCl2
0	1.6 ± 0.3	0.56 ± 0.05	0	1.6 ± 0.3	0.56 ± 0.05
2	4.3 ± 0.4	1.96 ± 0.2	2	2.2 ± 0.4	0.79 ± 0.05
4	18 ± 2	13 ± 2	4	3.8 ± 0.4	1.7 ± 0.3
6	39 ± 3	39 ± 3	6	4.8 ± 0.5	4.6 ± 0.4
8	19 ± 2	19 ± 2	8	4.7 ± 0.4	4.5 ± 0.4
10	8.2 ± 0.9	9.0 ± 0.9	10	5 ± 0.5	4.9 ± 0.3
20	0.82 ± 0.09	0.90 ± 0.06	20	4.7 ± 0.5	4.7 ± 0.4

DNA VI (twin-tails)b
(dT)n tail length (n)	KBC (106 M−1) in 10 mM MgCl2	KBC (106 M−1) in 0 mM MgCl2
6	13 ± 1	13 ± 1

^abuffer M plus 100 mM NaCl and the indicated [MgCl₂]

^bbuffer M plus 750 mM NaCl and the indicated [MgCl₂]

Figure 3.

Effects of Mg²⁺ on the equilibrium constants (K_BC) for RecBC binding to DNA ends containing pre-formed ss-(dT)_n tails. (a) Representative equilibrium competition titrations to determine K_BC for binding to the ends of a non-fluorescent DNA IV series molecule containing 3’-(dT)₈ tails. Mixtures of Cy3 labeled reference DNA I (20 nM) and the non-fluorescent DNA IV molecule was titrated with RecBC in buffer M, 10 mM MgCl₂ plus 100 mM NaCl at 25°C and the relative Cy3 fluorescence enhancement (ΔF_obs) is plotted as a function of total [RecBC]. Three separate titration experiments were performed in which a constant total reference DNA I concentration was used for all experiments but the total concentrations of the competitor DNA IV substrates were varied in each titration. (●) represents a titration performed in the presence of only reference DNA I (20 nM), while (○) and (■) represent experiments performed in the presence DNA I (20 nM) and 20 or 40 nM DNA IV with 3’-(dT)₈, respectively. Solid lines are simulations using the best fit values of K_BC (Table 1) as described previously ³⁷. (b) Ratios of K_BC measured in the absence of Mg²⁺ (Table 1) to K_BC measured in 10 mM MgCl₂ (Table 1) are plotted as a function of the length of pre-existing ss-(dT)_n tail (n). (○) represents ratios of K_BC for the DNA IV series with pre-existing 3’-(dT)_n tails; (■) represents ratios of K_BC for the DNA V series with pre-existing 5’-(dT)_n tails; and (△) represents ratio of K_BC for a DNA VI molecule with pre-existing twin-(dT)₆ tails.

Figure 3b shows plots of the ratio of K_BC measured in the absence of MgCl₂ to K_BC measured in the presence of 10 mM MgCl₂ as a function of the length of the preexisting ss-(dT)_n tail. The dependences of K_BC on the length of the pre-existing ss-(dT)_n tail are qualitatively similar in the presence or absence of 10 mM MgCl₂ (Table 1). In both cases, a maximum in K_BC is observed for a DNA end with a pre-existing 3’- or a 5’-(dT)_n tail with n ≥ 6 nucleotides. Importantly, the values of K_BC for the DNA IV and V series measured in the absence of MgCl₂ are lower than K_BC measured in 10 mM MgCl₂ when n < 6 nucleotides (Table 1); however, for n ≥ 6 nucleotides, K_BC is the same in the absence or presence of 10 mM MgCl₂. As shown in Figure 3b, the difference between K_BC measured in the absence and presence of MgCl₂ decreases as the length of the preexisting ss-(dT)_n tail increases from zero to six nucleotides, with the values of K_BC becoming independent of the presence of Mg²⁺ for n ≥ 6 nucleotides. The largest difference is observed for a blunt DNA end such that K_BC is ∼3 times higher in the presence of 10 mM MgCl₂. We also observed no effect of 10 mM MgCl₂ on the values of K_BC for a DNA VI molecule possessing pre-existing twin ss-(dT)₆ tails on both ends (open triangle in Figure 3b). Hence, Mg²⁺ only affects K_BC for RecBC binding to a DNA end with a 3’- or 5’-(dT)_n tail if n < 6 nucleotides. This suggests that the effect of Mg²⁺ is observed only when RecBC can potentially melt out some base pairs within a duplex DNA end.

Effects of Mg²⁺ on melting of a DNA end by RecBC as examined by chemical protection of DNA

Although the above binding studies suggest that RecBC melts some of the bp within the duplex DNA end region in the presence of Mg²⁺, we performed additional independent experiments to test this hypothesis. We performed KMnO₄ footprinting experiments on the RecBC-blunt-ended-DNA complex to examine if base pairs are melted out in a Mg²⁺-dependent manner. KMnO₄ preferentially oxidizes the C5-C6 double bond within unstacked thymine bases within DNA ⁴⁶ and thus should detect melting of a duplex region containing thymidine base pairs. In fact, this approach was used by Farah and Smith ³⁵ to demonstrate that RecBCD melts out four to five bp upon binding to a blunt duplex end. We used a blunt-ended DNA (the same DNA used in the fluorescence titration experiments discussed above) radiolabeled with ³²P at the 5’-end of the top strand (Figure 4). In addition to performing the experiments in buffer M in the presence or absence of 10 mM MgCl₂, we also performed experiments in both 30 and 100 mM NaCl to determine if this range of monovalent salt concentration influences bp melting. As shown in Figure 4, the thymine base at position four (T4) is significantly more susceptible to KMnO₄ attack in the presence of 10 mM MgCl₂ and RecBC, regardless of the [NaCl]. This is the only thymine base within the six base pair region from the end of the 5’-³²P-labeled strand. None of the other thymines at other positions (T8 and beyond in Figure 4) exhibit any enhancement in susceptibility to KMnO₄ attack in the presence of RecBC and 10 mM MgCl₂. This indicates that at least four base pairs at the end of a blunt-ended DNA are melted upon binding of RecBC in a Mg²⁺-dependent manner.

Figure 4.

Effects of Mg²⁺ on the chemical protection patterns of a blunt-ended DNA bound by RecBC. KMnO₄ footprinting experiments of the RecBC-blunt-ended-DNA complex were performed in buffer M plus the indicated [NaCl] and [MgCl₂] at 25°C as described in Materials and Methods. Lane 1 is a control with just the 5’-³²P-labeled ssDNA top strand alone. The contents of lanes 2 through 9 are indicated in the figure. The asterisk in the inset shows the position of the ³²P-label on the DNA. The reference DNA band is indicated by ref and the uncut sample DNA band is denoted by uncut.

Dependence of DNA melting by RecBC on Mg²⁺ concentration

The effects of Mg²⁺ on the equilibrium constant for RecBC binding to a DNA end, K_BC,R and K_BC, indicate that the binding of Mg²⁺ to RecBC increases its affinity for DNA ends containing pre-existing ss-(dT)_n tails only if the tails are shorter than six nucleotides. The KMnO₄ chemical protection experiments indicate that base pair melting by RecBC is also dependent on the presence of Mg²⁺. Together, these results indicate that the binding of Mg²⁺ to RecBC and/or the RecBC-DNA complex is linked to base pair melting by RecBC as has been demonstrated previously to be the case for RecBCD ³⁵. To further study these two processes and to estimate the equilibrium constant for Mg²⁺ binding to the RecBC-DNA complex, we examined the fluorescence intensity of Cy3 labeled reference DNA molecules (DNA I through III) when pre-bound with RecBC as a function of [MgCl₂]. As shown in Figure 1a, DNA I has a Cy3 label on the 5’-end of the duplex and each end has a 3’-(dT)₄ tail, DNA II has twin 3’ and 5’-(dT)₂ tails and a Cy3 label at the end of the 5’-(dT)₂ tail and DNA III has twin 3’ and 5’-(dT)₆ tails and a Cy3 label at the end of the 5’-(dT)₆ tail. Therefore, we expect that RecBC will melt out 2 bp from each end of DNA I and 4 bp from each end of DNA II in a Mg²⁺-dependent reaction. Experiments were performed by first saturating each reference DNA with RecBC in the absence of MgCl₂ (buffer M plus 100 mM NaCl at 25°C) and then titrating with MgCl₂ while monitoring the Cy3 fluorescence signal.

The results of these experiments are presented in Figure 5a where the corrected Cy3 fluorescence (F_i,corr as defined in equation (1) in Material and Methods) is plotted as a function of the total [MgCl₂]. The fluorescence intensities of Cy3 within the RecBCDNA I and RecBC-DNA II complexes were enhanced upon titrating with MgCl₂. In contrast, the Cy3 fluorescence signal of the RecBC-bound reference DNA III, which has twin ss-(dT)₆ tails on both ends, does not change upon addition of MgCl₂. The largest enhancement in Cy3 fluorescence (∼58%) is observed for the RecBC-bound DNA I, which has a 3’-(dT)₄ tail, while the RecBC-bound DNA II, which has twin ss-(dT)₂ tails, exhibits a smaller Cy3 fluorescence enhancement (∼21%). Since the Cy3 fluorescence of reference DNA alone is independent of [MgCl₂] (data not shown), the observed enhancement of the Cy3 fluorescence signals of the RecBC-DNA I and RecBC-DNA II complexes upon titration with MgCl₂ is due to the effects of Mg²⁺ on the RecBC-reference DNA complexes. The final fluorescence levels for all RecBC-reference DNA complexes are the same within experimental error, indicating that the final environments of the Cy3 fluorophores in all RecBC-DNA complexes are the same. The fact that only the reference DNA with ss-(dT)_n tails shorter than six nucleotides (DNA I and DNA II) exhibit fluorescence enhancement suggests that the increase in Cy3 fluorescence is due to DNA melting. No enhancement of the Cy3 signal was observed for reference DNA III which has twin ss-(dT)₆ tails, consistent with the expectation that no additional base pair melting should occur upon RecBC binding.

Figure 5.

Effects of Mg²⁺ on the Cy3 fluorescence signal of a RecBC-reference DNA complex. (a) 10 nM of DNA I (■), DNA II (●) or DNA III (◇) was pre-bound with 2.4, 2.2 or 1.3 μM RecBC, respectively, and titrated with MgCl₂ in buffer M plus 100 mM NaCl at 25°C and the corrected Cy3 fluorescence (F_i,corr) was plotted as a function of total [MgCl₂]. The same experiments were performed in buffer M plus 400 mM NaCl for DNA I (□) and DNA II (○). Solid lines are simulations using equations (13) to (15) and the best fit values of $K_{\mathrm{Mg}}^{\mathrm{BD}}$ and $K_{\mathrm{Mg}}^{\mathrm{B}}$ ($(5\pm 2)\times {10}^2{\mathrm{M}}^{-1}$, and (8 ± 3) M⁻¹ respectively). (b) Comparisons of 10 nM of DNA I pre-bound with 2.4 μM RecBC titrated with MgCl₂ (●) or CaCl₂ (×) in buffer M plus 100 mM NaCl at 25°C. F_i,corr is plotted as a function of total [MgCl₂] or [CaCl₂]. 10 nM of DNA III pre-bound with 1.3 μM RecBC was also titrated with CaCl₂ (◇) in buffer M plus 100 mM NaCl at 25°C. (c) Comparisons of 10 nM of DNA I pre-bound with either 2.4 μM RecBC (●) or 2.4 μM RecB^ΔnucC (▽) and titrated with MgCl₂ in buffer M plus 100 mM NaCl at 25°C. F_i,corr from each experiment was normalized arbitrarily to one and plotted as a function of [MgCl₂].

We also performed a MgCl₂ titration of DNA I and DNA II in the presence of 400 mM NaCl, since this higher [NaCl] should further reduce Mg²⁺ binding to the DNA. As shown in Figure 5a, the results obtained in 400 mM NaCl are identical to the those obtained in 100 mM NaCl, thus the binding of Mg²⁺ to the DNA appears to be weak enough at these high [NaCl] that it does not compete with the binding of Mg²⁺ to the RecBC-DNA complex. To examine this further, we calculated the expected extent of Mg²⁺ binding to a DNA duplex under these salt concentrations using the values of the Mg²⁺ binding constant determined as a function of [NaCl] from the study of non-specific interactions between lac repressor and calf thymus DNA⁴² as well as pentalysine and T7 DNA ⁴³. Based on these results one can calculate the probability (P_Na) that a nucleotide within the duplex DNA has only Na⁺ and no Mg²⁺ associated with it when the duplex DNA is placed in a buffer containing both Na⁺ and Mg²⁺ (see Appendix). These calculations indicate that at 100 mM NaCl, P_Na ≈ 0.62 at the end of the titration when 10 mM MgCl₂ is present. At 400 mM NaCl, P_Na ≈ 0.95 at the end of the titration when 10 mM MgCl₂ is present. We also note that the equilibrium constants for Mg²⁺ binding to duplex DNA used in the above calculations were determined for Mg²⁺ binding to long duplex DNA. Since the DNA used in our experiments is only 60 bp long, there will be less Mg²⁺ binding to the shorter DNA than estimated from the calculations. Therefore we conclude that there should be relatively little Mg²⁺ bound to the DNA even at 10 mM Mg²⁺, especially at 400 mM NaCl. Although these results suggest that the binding of Mg²⁺ to the RecBC-DNA complex is relatively insensitive to the [NaCl], this may be complicated by any compensating effects due to the [NaCl]-dependence of Mg²⁺ binding to the DNA.

As shown in Figure 5a, the midpoint of the Mg²⁺ titrations for DNA I performed in either 100 or 400 mM NaCl is ∼ 1.6 (± 0.4) mM MgCl₂ while titrations for DNA II exhibit a midpoint of 1.8 (± 0.4) mM MgCl₂. This indicates that the melting of base pairs in both DNA I and II has the same dependence on MgCl₂ concentration despite the expectation that a different number of base pairs are melted in DNA I vs. II (2 vs. 4 bp, respectively).

To obtain estimates of the apparent equilibrium constant for Mg²⁺ binding to the RecBC and RecBC-DNA complex we analyzed the MgCl₂ titrations quantitatively using a simple model that assumes only one Mg²⁺ binding site per RecBC (see Scheme 1 and Materials and Methods). This model ignores any binding of Mg²⁺ to duplex DNA; however, as discussed above, this is expected to be small at the high [NaCl] (100 mM and 400 mM) used in our experiments. NLLS analysis of the data using equation (17) (see Materials and Methods) yields a value of $K_{\mathrm{Mg}}^{\mathrm{BD}}=(5\pm 2)\times {10}^2{\mathrm{M}}^{-1}$ for the equilibrium constant for Mg²⁺ binding to either a RecBC-DNA I or a RecBC-DNA II complex, and a value of $K_{\mathrm{Mg}}^{\mathrm{B}}=(8\pm 3){\mathrm{M}}^{-1}$ for the equilibrium constant for Mg²⁺ binding to RecBC, assuming only one Mg²⁺ binding site per RecBC.

Somewhat surprisingly, Ca²⁺ has identical effects on the Cy3 fluorescence signals of RecBC-DNA complexes as Mg²⁺. As shown in Figure 5b, the traces obtained from titrations of the RecBC-DNA I complex with CaCl₂ and MgCl₂ are identical within experimental uncertainty. Titration of the RecBC-DNA III complex with CaCl₂ also exhibits no change in Cy3 fluorescence intensity (Figure 5b). We also observed that RecBC binds to reference DNA I with the same affinity (K_BC,R = (4.8 ± 0.5) × 10⁷ M⁻¹) in either 10 mM MgCl₂ or 10 mM CaCl₂ (data not shown). These data indicate that the observed equilibrium constant for the RecBC-DNA complex binding to one Ca²⁺ ion is identical to that for Mg²⁺. Even though a crystal structure of RecBCD bound to a duplex DNA in the presence of Ca²⁺ shows that RecBCD can melt out four bp at the end of the duplex ²⁷, our quantitative studies are somewhat surprising since Mg²⁺ and Ca²⁺ binding sites on proteins are expected to be different ^{47; 48}.

Since a Ca²⁺ ion is observed bound at the RecB nuclease domain active site in the crystal structure of RecBC-DNA complex ²⁷, we next tested if this site is responsible for the observed binding of Mg²⁺ by examining RecB^ΔnucC, which was reconstituted from RecC and a RecB nuclease domain deletion mutant (RecB^Δnuc) ²⁶. Figure 5c shows that the [MgCl₂]-dependence of the normalized enhancement of the Cy3 fluorescence signal of a RecB^ΔnucC-DNA I complex is the same as observed for the normalized Cy3 fluorescence signal for a RecBC-DNA I complex. Therefore the nuclease domain of RecB is not responsible for the observed effect of Mg²⁺ on DNA melting.

Effects of Mg²⁺ on the observed enthalpy and heat capacity changes for RecBC binding to DNA ends

As shown above, for RecBC binding to a DNA end possessing a pre-existing twin-ss-(dT)₆ tail (DNA VI), there is no effect of Mg²⁺ on K_BC and thus on the standard state binding free energy change, ΔG°_obs= −RT ln K_BC, (Figure 3b and Table 1). While this suggests that there is no effect of Mg²⁺ on the energetics of the RecBC-DNA VI (n = 6) interaction, it is possible that there is an enthalpy/entropy compensation under the conditions used resulting in similar values of K_BC. We therefore performed isothermal titration calorimetry (ITC) experiments to measure ΔH_obs for RecBC binding to the ends of a DNA VI molecule with n = 6 in the presence and absence of 10 mM MgCl₂ over a temperature range from 5 to 25°C. We also compared the ΔH_obs for RecBC binding to a DNA VI molecule with n = 6, for which no bp melting is expected, to that for RecBC binding to a blunt-ended DNA molecule (DNA VI with n = 0) for which bp melting is only expected to occur in the presence of Mg²⁺.

The results of two representative ITC experiments are shown in Figure 6a and b where the heat of each injection normalized to the amount of DNA injected (ΔQ_i,norm as defined in equation (20) in Materials and Methods) is plotted as a function of the ratio of total [DNA]/total [RecBC] (Buffer M, 100 mM NaCl). The data were analyzed (see equations (18) to (20) in Materials and Methods) and the values of the observed enthalpy change (ΔH_obs) for RecBC binding to one DNA end are presented in Table 2 and Figure 6c. In the temperature range between 5 to 25°C, ΔH_obs for RecBC binding to a DNA end containing twin-ss-(dT)₆ tails (DNA VI with n = 6) is the same within experimental error, in the absence or presence of 10 mM MgCl₂. This indicates that the complete thermodynamic profile (ΔG°_obs, ΔH_obs, ΔS°_obs, and ΔC_p,obs) for RecBC binding to the pre-melted ends of DNA VI (with n = 6) is identical in the absence or presence of MgCl₂. Hence, Mg²⁺ has no effect on the energetics of RecBC binding to a fully pre-melted DNA end over the temperature range from 5 to 25°C. RecBC binding to the DNA with twin-ss-(dT)₆ tails (DNA VI with n = 6) exhibits the same ΔC_p,obs in the presence or absence of 10 mM MgCl₂ ((−1.6 ± 0.3) and (−1.6 ± 0.4) kcal mol⁻¹ K⁻¹, respectively).

Figure 6.

Effects of Mg²⁺ on the temperature dependence of the observed enthalpic change (ΔH_obs) for RecBC binding to one end of the DNA VI series molecules with n = 0 or 6. Experiments were performed in buffer M plus 100 mM NaCl and the indicated [MgCl₂] at the indicated temperature. (a) and (b) are representative ITC experiments to determine the enthalpic change for RecBC binding the ends of DNA VI series molecules with n = 0 or 6 in the presence of 10 mM MgCl₂ at 25°C. The heat of each injection normalized to the amount of DNA injected (ΔQ_i,norm as defined in equation (20)) is plotted as a function of total [DNA]/total [RecBC]. (a) 710 nM RecBC was titrated with 15.2 μM DNA VI with n = 0; (b) 885 nM RecBC was titrated with 9 μM DNA VI with n = 6. Solid lines are simulations using equations (18) to (20) and the best fit values of ΔH_obs (Table 2) and K_BC = (1.6 ± 0.3) × 10⁷ M⁻¹ in (a) while K _BC ≥ 10⁹ M⁻¹ in (b). (c) Effects of Mg²⁺ on values of ΔC_p,obs for RecBC binding to a DNA end. ΔH_obs for RecBC binding to an end of DNA VI with n = 6 in the presence of 10 mM MgCl₂ (●) or in the absence of MgCl₂ (○) and ΔH_obs for RecBC binding to a blunt DNA end in the presence of 10 mM MgCl₂ (■) or in the absence of MgCl₂ (□) are plotted as a function of temperature (°C). Straight lines represent results obtained from linear least-square analysis of each set of data and the value of ΔC_p,obs obtained from each set of data is presented in Table 2. (d) Effects of Mg²⁺ on the temperature dependence of equilibrium constant (K_BC) for RecBC binding to a blunt DNA end measured by competition fluorescence titration experiments. Experiments were performed in buffer M, 100 mM NaCl with or without 10 mM MgCl₂ at the indicated temperature. Values of ln K_BC measured in 10 mM MgCl₂ (●) or 0 mM MgCl₂ (○) are plotted as a function of temperature (°C). The solid and broken lines are simulations using equation (22) and the ΔH_obs and ΔC_p,obs values obtained from ITC experiments in the presence or absence of 10 mM MgCl_2, respectively (Table 2).

Table 2.

Temperature dependence of the observed enthalpic change (ΔH_obs) for RecBC binding to one end of the DNA VI series molecules with n = 0 or 6. Observed heat capacity change (ΔC_p,obs) values are obtained from linear least-square analyses of the observed enthalpic change data. (buffer M plus 100 mM NaCl and the indicated [MgCl₂])

Temperature (°C)	DNA with twin (dT)6 tails		Blunt-ended DNA
	ΔHobs (kcal mol−1) in 10 mM MgCl2	ΔHobs (kcal mol−1) in 0 mM MgCl2	ΔHobs (kcal mol−1) in 10 mM MgCl2	ΔHobs (kcal mol−1) in 0 mM MgCl2
5	−32 ± 3	−31 ± 3	ND	ND
10	−38 ± 3	−35 ± 3	ND	ND
15	−48 ± 3	−47 ± 3	−3 ± 3	−7 ± 3
17	ND	ND	−5 ± 3	−8 ± 3
20	−56 ± 3	−53 ± 2	−8 ± 3	−9 ± 3
25	−64 ± 3	−61 ± 2	−15 ± 2	−11 ± 2

ss-(dT)n tail length (n)	ΔCp,obs (kcal mol−1 K−1) in 10 mM MgCl2	ΔCp,obs (kcal mol−1 K−1) in 0 mM MgCl2
0	−1.2 ± 0.2	−0.5 ± 0.3
6	−1.6 ± 0.3	−1.6 ± 0.4

On the other hand, we observe a definite effect of Mg²⁺ on the values of ΔH_obs and its heat capacity change (ΔC_p,obs= (dΔH_obs/dT)_P) for RecBC binding to a blunt DNA end (DNA VI with n = 0) (Table 2 and Figure 6c) measured over the temperature range from 15 to 25°C. Interestingly, ΔC_p,obs for RecBC binding to a blunt-ended DNA in the presence of 10 mM MgCl₂ is very similar ((−1.2 ± 0.2) kcal mol⁻¹ K⁻¹), to ΔC_p,obs for RecBC binding to the twin-ss-(dT)₆ tailed DNA, although the values of ΔH_obs are much smaller in magnitude for RecBC binding to the blunt DNA end. In contrast, ΔC_p,obs for RecBC binding to a blunt-ended DNA in the absence of MgCl₂ ((−0.5 ± 0.3) kcal mol⁻¹ K⁻¹) is about 2.5 times smaller in magnitude. Hence, a larger negative value of ΔC_p,obs is observed under conditions where the final state of the DNA has 6 unpaired bases when bound to RecBC.

We also used the competition fluorescence titration experiments to examine the effects of 10 mM MgCl₂ on K_BC for RecBC binding to a blunt DNA end (DNA VI with n = 0) at 5, 15 and 25°C and compared these values with the predicted temperature dependence of K_BC based on the ΔC_p,obs and ΔH_obs values obtained from the ITC studies (Table 2). The results are presented in Table 3 and plotted in Figure 6d. The lines in Figure 6d are simulations using equation (22) and the ΔH_obs and ΔC_p,obs values from Table 2. As shown in Figure 6d, there is excellent agreement between the measured values of ln K_BC both in the presence and absence of MgCl₂ and those calculated using the parameters obtained from the ITC studies.

Table 3.

Temperature dependence of the equilibrium constants (K_BC) for RecBC binding to a blunt-ended DNA. (buffer M plus 100 mM NaCl and the indicated [MgCl₂])

Temperature (°C)	KBC (107 M−1) in 10 mM MgCl2	KBC (107 M−1) in 0 mM MgCl2
5	2.0 ± 0.7	0.8 ± 0.1
15	3.7 ± 0.7	0.8 ± 0.1
25	1.6 ± 0.3	0.56 ± 0.05

Enthalpic cost of base pair melting

We next performed a series of experiments to obtain an estimate of the ΔH_obs for melting a base pair within the RecBC-DNA end complex. For this purpose, we measured ΔH_obs for RecBC binding to the ends of the series of DNA VI molecules containing twin ss-(dT)_n tails, with n = 0, 2, 4, 6, 8, 10 and 20, in the presence of 10 mM MgCl₂. We reasoned that, in the presence of MgCl₂, six base pairs should be melted upon RecBC binding to a blunt DNA end (DNA VI with n = 0), while no base pairs should be melted upon RecBC binding to a DNA end with twin ss-(dT)_n tails, where n ≥ 6. Thus the difference between ΔH_obs for RecBC binding to a blunt DNA end and ΔH_obs for RecBC binding to a DNA end with twin ss-(dT)₆ tails should provide a measure of the enthalpic cost for melting six base pairs. Of course, this assumes that the energetic state of the final RecBC-DNA complex (with 6 bp melted) is unaffected by DNA base composition.

The results of these experiments are presented in Table 4 and Figure 7. ΔH_obs for RecBC binding to one end of DNA VI is always negative and decreases linearly from (−17 ± 4) kcal mol⁻¹ to (−64 ± 3) kcal mol⁻¹ as the lengths of the pre-formed twin ss-(dT)_n tails increase from zero to six nucleotides; however, ΔH_obs remains unchanged at (−64 ± 3) kcal mol⁻¹ for n ≥ 6 nucleotides. A linear fit to the length dependence of ΔH_obs for n = 0 to 6 yields a value of −8 (± 1) kcal mol⁻¹. Therefore, the average enthalpic cost of melting one DNA base pair by RecBC is (8 ± 1) kcal mol⁻¹ bp⁻¹.

Table 4.

Observed enthalpic change (ΔH_obs) for RecBC binding to one end of the DNA VI series molecules. (buffer M plus 10 mM MgCl₂ and 100 mM NaCl at 25°C)

(dT)n tail length (n)	ΔHobs (kcal mol−1) for DNA VI (twin tails)
0	−17 ± 4
2	−34 ± 3
4	−49 ± 3
6	−64 ± 3
8	−63 ± 3
10	−65 ± 3
20	−64 ± 3

Figure 7.

Enthalpic cost of base pair melting by RecBC upon binding to a duplex DNA end. The observed enthalpic change (ΔH_obs) for RecBC binding to one end of the DNA VI series containing twin ss-(dT)_n tails with n varying from zero to 20 nucleotides were measured in buffer M plus 10 mM MgCl₂ and 100 mM NaCl at 25°C . ΔH_obs for RecBC binding to one end of the DNA DNA VI series (●) are plotted as a function of pre-existing ss-(dT)_n tail length (n).

Discussion

Previous studies of RecBCD binding to a blunt DNA duplex end have shown that the last four to five bp at the end of the duplex become accessible to KMnO₄ attack in a Mg²⁺-dependent but ATP-independent manner ³⁵. The last four bp of a blunt ended duplex DNA are also observed to be unpaired in a crystal structure of a RecBCD-DNA complex formed in the presence of Ca^{2+ 27}. Equilibrium binding studies performed in the absence of ATP also show that RecBCD binds tightest to a DNA end containing preexisting 3’-ss-(dT)₆ and 5’-ss-(dT)₁₀ tails ³⁷. These observations indicate that RecBCD is capable of melting out the last four to six base pairs upon binding to a blunt duplex DNA end in a divalent cation-dependent, but ATP-independent reaction. Here we have shown that RecBC is also able to carry out a similar bp melting reaction upon binding a blunt-ended DNA.

Base pair melting by RecBC is Mg²⁺-dependent

Divalent cations such as Mg²⁺ can always compete with monovalent cations and protein for the binding of DNA and thus the presence of Mg²⁺ will generally decrease the equilibrium constant for protein binding to DNA and the magnitude of its dependence on [NaCl] ^{40; 41}. Although for RecBC binding to DNA I we observe that the dependence of the equilibrium constant (K_BC,R) on [NaCl] is affected by the presence of 10 mM MgCl₂, the effects are very different from those expected if Mg²⁺ only acted as a competitor. The fact that K_BC,R measured in the presence of Mg²⁺ is always higher than K_BC,R measured in the absence of Mg²⁺ at all [NaCl] examined indicates that Mg²⁺ facilitates RecBC binding to DNA. This Mg²⁺-dependent increase in K_BC,R is consistent with the hypothesis that RecBC requires Mg²⁺ in order to melt a region of the duplex DNA end upon binding.

The effects of varying the lengths of the pre-existing tails on K_BC for the DNA IV and V series in the absence of MgCl₂ are qualitatively similar to the effects observed in the presence of 10 mM MgCl₂. Therefore, these data by themselves cannot be used to conclude whether RecBC melts out six base pairs in a Mg²⁺-dependent manner. However, the quantitative differences between K_BC measured in the absence and presence of MgCl₂ are consistent with the hypothesis that six base pairs at the blunt DNA end are melted out by RecBC only in the presence of Mg²⁺. For DNA ends with pre-existing (dT)_n tails shorter than six nucleotides, the difference between K_BC measured in the presence and absence of Mg²⁺ is expected to increase in magnitude as the lengths of the pre-existing (dT)_n tails decreases because the number of base pairs melted by RecBC (6 − n) increases as n decreases. Indeed we observe that the magnitude of the difference between K_BC measured in the presence and absence of 10 mM MgCl₂ decreases as the length of the pre-existing tail increases from zero to six nucleotides, whereas no difference was observed in K_BC for DNA possessing ss-(dT)_n tails with n ≥ 6 nucleotides. The KMnO₄ footprinting data also directly shows a Mg²⁺-dependent melting by RecBC of at least four base pairs at the end of a blunt DNA end.

The effects of [MgCl₂] on the Cy3 fluorescence of DNA I through III molecules when pre-bound with RecBC also indicate that binding of Mg²⁺ by RecBC facilitates base pair melting at the end of DNA. The RecBC-DNA III complex, which possesses pre-existing twin ss-(dT)₆ tails and therefore no melting is expected to occur upon binding of RecBC, failed to show an increase in the Cy3 fluorescence, whereas both RecBC-bound DNA I and II (with ss-DNA tails shorter than six nucleotides) exhibit an enhancement in Cy3 fluorescence upon titration of MgCl₂ consistent with bp melting being associated with the fluorescence enhancement upon addition of MgCl₂. The same final fluorescence level exhibited by all RecBC-DNA complexes at the end of titration indicating that all the RecBC-DNA complexes are in the same final state (i.e., six base pairs at the end are unpaired) at the end of titration.

Mg²⁺ overcomes a kinetic barrier to facilitate base pair melting by RecBC

For RecBC-induced melting of duplex DNA to occur, the favorable free energy change accompanying RecBC binding to DNA (ΔG°_bind) must be sufficient to overcome the unfavorable free energy change associated with base pair melting (ΔG°_melt). One potential explanation for the requirement of Mg²⁺ for this process is if Mg²⁺ increases the affinity of RecBC for the final fully melted DNA product so that (ΔG°_bind + ΔG°_melt < 0), whereas in the absence of Mg²⁺, (ΔG°_bind + ΔG°_melt > 0). However, the fact that ΔG°_obs (= −RT ln K_BC) for RecBC binding to a DNA end possessing pre-existing ss-(dT)_n tails with n ≥ 6 nucleotides is the same with or without 10 mM MgCl₂ indicates that there is already sufficient binding free energy available from the RecBC-DNA interaction even in the absence of Mg²⁺, to achieve a melted structure. Yet, bp melting by RecBC does not occur in the absence of Mg²⁺. Therefore, our results suggest that base pair melting by RecBC binding to DNA is thermodynamically favored in the presence and absence of Mg²⁺, but is kinetically blocked in the absence of Mg²⁺.

Interestingly, the Cy3 fluorescence data suggest that Ca²⁺ can also facilitate base pair melting by RecBC. This observation is consistent with the fact that four bp are unpaired in the RecBCD-blunt-ended DNA crystal structure formed in the presence of Ca^{2+ 27}. The one surprising observation is that the effect of Ca²⁺ is indistinguishable from Mg²⁺. Even if Ca²⁺ and Mg²⁺ bind to the same site to facilitate bp melting, it is not expected that they would have the same affinity for the same site on RecBC or the RecBC-DNA complex given the distinctly different ion sizes and requirements for Ca²⁺ and Mg²⁺ binding sites within proteins ^{47; 48}. In fact, Ca²⁺ is observed bound in the expected Mg²⁺ binding site within the RecB nuclease domain ²⁷ and does inhibit the nuclease activity of RecBCD ⁴⁹. It is possible that there are multiple sites for Mg²⁺ and Ca²⁺ and that there is a fortuitous compensation of effects such that the apparent affinity of Mg²⁺ and Ca²⁺ appear to be the same. Since both Ca²⁺ and Mg²⁺ appear to function to relieve a kinetic block associated with DNA melting by RecBC and RecBCD, this could potentially mask any difference in affinity of these two ions for the RecBCD-DNA complex.

A Ca²⁺ ion is observed bound at the Mg²⁺ binding site within the nuclease domain in the crystal structure of a RecBCD-DNA complex ²⁷. Yet, our data indicate that deletion of the nuclease domain to form RecB^ΔnucC, has no influence on the ability of Mg²⁺ to facilitate DNA melting by RecBC. Therefore the site for Mg²⁺ binding that facilitates bp melting by RecBC is not located on the nuclease domain of RecB. The ATP binding site on RecB is a potential site for binding Mg²⁺ but it is also possible that the Mg²⁺ binding site is present on the RecC subunit. The structural fold of RecC is similar to that of RecB and it has been suggested that RecC may have been a defunct RecB helicase ⁵⁰.

Thermodynamics of RecBC-DNA complex formation and base pair melting

We observe that ΔC_p,obs for RecBC binding to a blunt DNA end in the presence of Mg²⁺ (−1.2 ± 0.2 kcal mol⁻¹ K⁻¹) is very similar to the ΔC_p,obs for RecBC binding to a DNA end possessing two pre-existing twin-(dT)₆ tails (DNA VI with n = 6 nucleotides) (−1.6 ± 0.3 kcal mol⁻¹ K⁻¹ in 10 mM MgCl₂ and −1.6 ± 0.4 kcal mol⁻¹ K⁻¹ in no MgCl₂). This similarity suggests that there is little heat capacity change associated with bp melting, at least as it occurs within the RecBC complex. This is consistent with the conclusion that unstacking of bases does not contribute significantly to the ΔC_p,obs of duplex disruption ⁵¹. In contrast, ΔC_p,obs for RecBC binding to blunt DNA end in the absence of Mg²⁺ is less negative (−0.5 ± 0.3 kcal mol⁻¹ K⁻¹). The potential origins of the heat capacity change associated with any protein-DNA complex or any macromolecular interaction are numerous ^{52; 53; 54; 55; 56; 57}, and a determination of the origins of ΔC_p,obs for this system are beyond the scope of this work. Further studies are required to elucidate the linked equilibria responsible for the large and negative ΔC_p,obs for RecBC binding to DNA ends and the difference between ΔC_p,obs for the formation of the “melted” versus “un-melted” complexes.

We estimated the average enthalpic cost of melting six base pairs at a blunt DNA end by RecBC in the presence of Mg²⁺ from the measurements of ΔH_obs for RecBC binding to a DNA end possessing pre-existing twin ss-(dT)_n tails (DNA VI) with n varying from 0 to 6 nt. This estimate is based on two assumptions. The first is that the end state of a RecBC-DNA VI complex is the same for 0 ≤ n ≤ 6 in the presence of 10 mM MgCl₂, i.e. the last six base pairs are unpaired in 100% of the RecBC-DNA complexes. The second assumption is that ΔH_obs is independent of base sequence and composition. With these assumptions, we estimate a value of 47 ± 7 kcal mol⁻¹ for the enthalpic cost to melt out the last six base pairs at the blunt DNA end used in our experiments, which consists of four G/C and two A/T base pairs. This corresponds to a value of (8 ± 1) kcal mol⁻¹ bp⁻¹ for the average enthalpic cost of melting out one base pair at 25°C. Since this estimate is based on the difference in ΔH_obs for binding of a series of RecBC-DNA VI complexes, the contributions to ΔH_obs from the RecBC-DNA interactions should cancel if the final RecBC-DNA complexes are the same and independent of base composition. Previous estimates of ΔH_obs for base pair melting are: 4.3 to 9 kcal mol⁻¹ bp^{−1 58}, 5.2 to 15 kcal mol⁻¹ bp^{−1 51} and ∼7 kcal mol⁻¹ bp⁻¹ from the nearest neighbor model ⁵⁹. Our value of (8 ± 1) kcal mol⁻¹ bp⁻¹ falls within this range. Since determinations of ΔH_obs for base pair melting from DNA melting experiments is generally difficult due to the uncertainties associated with obtaining accurate baselines at low and high temperatures, our determination may represent a more accurate estimate of this average quantity.

Implications for the helicase mechanism of RecBC and RecBCD

We have shown that when RecBC binds the end of a blunt-ended DNA, it melts out six base pairs at the DNA end in a Mg²⁺-dependent but ATP-independent manner. Our results suggest that Mg²⁺ functions by overcoming a kinetic barrier to the RecBC-mediated DNA melting process. The binding of RecBCD to a blunt DNA end also results in the unpairing of the last 4 to 5 base pairs at the end of the duplex DNA ³⁵. The number of base pairs melted out by RecBCD upon binding to a blunt DNA end is very similar to the “kinetic step size” of 3.9 ± 0.6 bp s⁻¹ estimated for RecBCD unwinding of DNA from pre-steady state kinetic studises of DNA ^{31; 32; 33}. Recall that a kinetic unwinding step size of 4 bp indicates that some rate-limiting step in the unwinding process is repeated every 4 bp on average during the unwinding process. The similarity between these two values suggests that DNA unwinding by RecBCD may occur in a two-step process in which 4−6 base pairs of DNA are melted upon binding of RecBCD to the duplex region independent of ATP, followed by more rapid ATP-dependent translocation of RecBCD to the newly formed ss/dsDNA junction ^{31; 32; 33}. Since RecBC also melts out base pairs upon binding to a duplex DNA end, it is possible that RecBC also unwinds DNA by this same mechanism, such that the RecBC binding alone is sufficient to actively open the next 4 bp.

Materials and Methods

Buffers

Buffers were made from reagent grade chemicals using double-distilled water that was further deionized with a Milli-Q purification system (Millipore Corp., Bedford, MA). Buffer C contains 20 mM potassium phosphate (pH 6.8), 0.1 mM 2-mercaptoethanol (2-ME), 0.1 mM EDTA, 10% (v/v) glycerol. Buffer M contains 20 mM MOPS-KOH (pH 7.0), 1 mM 2-ME, 5% (v/v) glycerol. The concentration of MgCl₂ stocks was determined by measuring the refractive index of a stock solution in water using a Mark II refractometer (Leica Inc., Buffalo, NY) and a standard table relating refractive index to [MgCl₂] ⁶⁰.

Proteins

E. coli RecB and RecC proteins were purified and reconstituted to form RecBC as described ³². RecB^Δnuc was purified and reconstituted with RecC to form RecB^ΔnucC as described ⁶¹. RecBC and RecB^ΔnucC concentrations were determined spectrophotometrically in buffer C using extinction coefficients of ε₂₈₀ = 3.9 × 10⁵ M⁻¹ cm^{−1 32} and ε₂₈₀ = 3.4 × 10⁵ M^{−1 61}, respectively. All protein concentrations reported refer to the RecBC or RecB^ΔnucC heterodimer. Bovine serum albumin (BSA) was from Roche (Indianapolis, IN) and its concentration was determined using an extinction coefficient of ε₂₈₀ = 4.3 × 10⁴ M⁻¹ cm⁻¹ in buffer C ³⁷. All proteins were dialyzed into the particular reaction buffer before use. Dialyzed RecBC or RecB^ΔnucC were stored at 4°C for up to five days, since a loss of activity (∼15%) was observed after five days at 4°C.

Oligodeoxynucleotides

Oligodeoxynucleotides were synthesized using an ABI model 391 synthesizer (Applied Biosystems, Foster City, CA) using reagents and phosphoramidites from Glen Research (Sterling, VA). A first purification step of each single-stranded oligodeoxynucleotide was performed using polyacrylamide gel electrophoresis under denaturing conditions followed by removal of the DNA from the gel by electroelution ⁶². The resulting oligodeoxynucleotides were then further purified chromatographically by reverse phase HPLC using an XTerra MS C18 column (Waters, Milford, MA). The concentration of each DNA strand was determined by completely digesting the strand with phosphodiesterase I (Worthington, Lakewood, NJ) in 100 mM Tris-Cl pH 9.2, 3 mM MgCl₂, at 25°C and measuring the absorbance of the resulting mixture of mononucleotides at 260 nm as described ⁵¹. The extinction coefficients at 260 nm used in this analysis are: 15340 M⁻¹ cm⁻¹ for AMP, 7600 M⁻¹ cm⁻¹ for CMP, 12160 M⁻¹ cm⁻¹ for GMP, 8700 M⁻¹ cm⁻¹ for TMP ⁶³ and 5000 M⁻¹ cm⁻¹ for Cy3 (Glenn Research). Duplex DNA substrates were prepared by mixing equimolar concentrations (usually 3 μM) of the appropriate DNA strands in reaction buffer, which was subsequently heated to 90°C for five minutes followed by slow cooling to 25°C. Reference DNA I (Figure 1a) was formed from strands 1 and 2 (Figure 1c); reference DNA II was formed from strands 3 and 4; reference DNA III was formed from strands 5 and 6; competitor DNA series IV was formed from strands 7 and 8; competitor DNA series V was formed from strands 9 and 10; and competitor DNA series VI was formed from strands 11 and 12. The sequences of the oligodeoxynucleotides used in this study are given in Figure 1c.

Fluorescence Titrations

Fluorescence titrations were performed as described ³⁷ using a PTI QM-4 fluorometer (Photon Technology International, Lawrenceville, NJ) equipped with a 75 watt Xe lamp. All slit widths were set at 0.5 mm. The temperature of sample in the 10-mm pathlength Type 3 quartz fluorometer cuvette (3 mL) (NSG Precision Cells Inc., Farmingdale, NY) was controlled using a Lauda RM6 recirculation water bath (Brinkmann, Westbury, NY). Stirring was maintained throughout each experiment using a P-73 cylindrical cell stirrer with a diameter of 8 mm (NSG Precision Cells Inc., Farmingdale, NY). The corrected Cy3 fluorescence intensity (F_i,corr) after the i-th addition of protein and the initial corrected Cy3 fluorescence of the reference DNA (F_0,corr) were obtained as described previously ³⁷. Briefly, F_i,corr is defined as in equation (1):

$$F_{i,\mathrm{corr}}=(F_i-F_{\mathrm{b}})\frac{V_i}{V_0}$$ (1)

where F_i is the fluorescence intensity after the i-th addition of titrant, F_b is the background fluorescence of the buffer which is always negligible ³⁷, V_i is the volume of the i-th addition and V₀ is the volume before the first addition.

The observed relative fluorescence change (ΔF_obs) is defined as in equation (2),

$$\Delta F_{\mathrm{obs}}=\frac{F_{i,\mathrm{corr}}-F_{0,\mathrm{corr}}}{F_{0,\mathrm{corr}}}$$ (2)

ΔF_obs reaches its maximum value (ΔF_max) when both ends of the reference DNA are bound with protein. Hence ΔF_obs/ΔF_max (0 ≤ F_obs/ΔF_max ≤ 1) equals the average of protein molecules bound per DNA end, and thus the average number of protein molecules bound per DNA molecule is given by (2ΔF_obs/ΔF_max).

“Salt-back” titrations

“Salt-back” titrations ^{44; 64} were performed after completion of a regular titration, i.e., after all additions of RecBC have been made. A buffer containing the same components as the reaction buffer but with 4 M NaCl was titrated into to the cuvettes and fluorescence measurements were made as described above. Data from “salt-back” titration experiments were analyzed using the same model used to describe the binding of RecBC to the ends of reference DNA, which has been described in detail ³⁷. In this model, RecBC (hereafter referred to as B) binds to each end of reference DNA (D) with the same binding constant, K_R, because the reference DNA has nearly identical ends. The binding polynomial for this model, which has two independent and identical sites, is given in equation (3),

$$P=1+2K_{\mathrm{R}}{\mathrm{B}}_{\mathrm{f}}+K_{\mathrm{R}}^2{\mathrm{B}}_{\mathrm{f}}^2$$ (3)

where B_f is the free concentration of protein.

The average number of protein molecules bound per DNA molecule is given by equation (4),

$$\frac{{\mathrm{B}}_{\text{bound}}}{{\mathrm{D}}_{\mathrm{T}}}=\frac{2K_R{\mathrm{B}}_{\mathrm{f}}}{1+K_R{\mathrm{B}}_{\mathrm{f}}}=2\frac{\Delta F_{\mathrm{obs}}}{\Delta F_{\max }}$$ (4)

where B_bound = ([DB]+2[B₂D]), [DB] is the concentration of D with only one of its ends bound by B and [B₂D] is the concentration of D with both of its ends bound by B.

As described previously ³⁷, ΔF_obs/ΔF_max can be expressed explicitly in terms of total protein concentration (B_T), total reference DNA concentration (D_T) and K_R as in equation (5).

$$\frac{\Delta F_{\mathrm{obs}}}{\Delta F_{\max }}=\frac{1+K_{\mathrm{R}}({\mathrm{B}}_{\mathrm{T}}+2{\mathrm{D}}_{\mathrm{T}})-\sqrt{4K_{\mathrm{R}}{\mathrm{B}}_{\mathrm{T}}+{(1-K_{\mathrm{R}}{\mathrm{B}}_{\mathrm{T}}+2K_{\mathrm{R}}{\mathrm{D}}_{\mathrm{T}})}^2}}{4K_{\mathrm{R}}{\mathrm{D}}_{\mathrm{T}}}$$ (5)

Experimental fluorescence titrations, plotted as ΔF_obs vs. [B_T], were obtained at three different reference DNA concentrations, D_T, and analyzed by global non-linear least squares (NLLS) analysis using equation (5) to obtain the best fit values of K_R and ΔF_max.

To calculate K_R at each [NaCl] during a “salt-back” titration, equation (5) is rearranged and ΔF_obs is substituted using equation (2) to become equation (6),

$$K_{\mathrm{R}}=\frac{\frac{\Delta F_{\mathrm{obs},\left[\mathrm{NaCl}\right]}}{\Delta F_{\max }}}{\left(\frac{\Delta F_{\mathrm{obs},\left[\mathrm{NaCl}\right]}}{\Delta F_{\max }}-1\right)\left(2{\mathrm{D}}_{\mathrm{T}}\frac{\Delta F_{\mathrm{obs},\left[\mathrm{NaCl}\right]}}{\Delta F_{\max }}-{\mathrm{B}}_{\mathrm{T}}\right)}$$ (6)

where ΔF_obs,[NaCl] is the relative fluorescence change observed after each addition of NaCl and ΔF_max is determined previously from an independent titration experiment of reference DNA with RecBC.

Competition methods to determine equilibrium binding to non-fluorescent DNA

Equilibrium constants for RecBC binding to non-fluorescent DNA molecules (N) were obtained from analysis of competition binding studies ⁶⁵. The analysis of competition data has been described previously ³⁷ and the same analysis is used here. Briefly, three separate titration experiments were performed at three different non-fluorescent competitor DNA concentrations (N₁, N₂ or N₃). In each titration experiment, a constant concentration of competitor DNA (N₁, N₂ or N₃) was added to a cuvette containing a Cy3 labeled reference DNA at 20 nM and then titrated with protein. Since the competitor DNA molecules used here have nearly identical ends (DNA IV and V), B should bind to both ends of N with binding constant K_N. Then B_T and B_f can be related to the total concentration of non-fluorescent DNA concentration (N_T), K_N, K_R and D_T as shown in equation (7),

$${\mathrm{B}}_{\mathrm{T}}={\mathrm{B}}_{\mathrm{f}}\left(1+2\left(\frac{K_{\mathrm{N}}{\mathrm{N}}_{\mathrm{T}}}{{(1+K_{\mathrm{N}}{\mathrm{B}}_{\mathrm{f}})}^2}+\frac{K_{\mathrm{R}}{\mathrm{D}}_{\mathrm{T}}}{{(1+K_{\mathrm{R}}{\mathrm{B}}_{\mathrm{f}})}^2}\right)+2{\mathrm{B}}_{\mathrm{f}}\left(\frac{K_{\mathrm{N}}^2{\mathrm{N}}_{\mathrm{T}}}{{(1+K_{\mathrm{N}}{\mathrm{B}}_{\mathrm{f}})}^2}+\frac{K_{\mathrm{R}}^2{\mathrm{D}}_{\mathrm{T}}}{{(1+K_{\mathrm{R}}{\mathrm{B}}_{\mathrm{f}})}^2}\right)\right)$$ (7)

Data from the three titration experiments at competitor DNA concentrations N₁, N₂ and N₃ were analyzed simultaneously using equations (4) and (7) and the “implicit fitting” NLLS algorithm in Scientist (Micromath, St Louis, MO) without the need to obtain an explicit expression for B_f. The value of K_N was allowed to float in this analysis while the values of K_R and ΔF_max were fixed at values determined from the analysis of independent titrations with reference DNA in the absence of competitor. The uncertainties for the independently determined values of K_R and ΔF_max were propagated into the reported uncertainties in K_N.

Equilibrium binding of Mg²⁺ to RecBC and RecBC-Reference DNA complex

The MgCl₂ titration data were analyzed by assuming there is one Mg²⁺-binding site on RecBC as well as RecBC bound at one end of the reference DNA and no significant binding of Mg²⁺ ions to the reference DNA. This model is sufficient in describing the data (Figure 5a) and therefore we did not consider more complicated models involving more than one Mg²⁺-binding site per RecBC. This one-Mg²⁺-site model is represented in Scheme 1, where K_{1,no Mg} and K₁ are the stepwise macroscopic binding constants for forming BD (D with only one of its ends bound by B) in the absence and presence of MgCl₂, respectively, while K_{2,no Mg} and K₂ are the stepwise macroscopic

Scheme 1.

binding constants for forming B₂D (D with both of its ends bound by B) in the absence and presence of MgCl₂, respectively. The equilibrium constant of B binding to D in the presence of Mg²⁺ (K_R) is related to K₁ and K₂ as described in equation (8),

$$K_1=2K_{\mathrm{R}}\text{and}{K}_2=K_{\mathrm{R}}∕2$$ (8)

Similarly, K_{1,no Mg} and K_{2,no Mg} can be expressed in terms of equilibrium constant for B binding to D in the absence of Mg²⁺ (K_{R,no Mg}) as given in equation (9):

$$K_{1,\mathrm{no}\mathrm{Mg}}=2K_{\mathrm{R},\mathrm{no}\mathrm{Mg}}\text{and}{K}_{2,\mathrm{no}\mathrm{Mg}}=K_{\mathrm{R},\mathrm{no}\mathrm{Mg}}∕2$$ (9)

$K_{\mathrm{Mg}}^{\mathrm{B}}$ is the equilibrium constant for one molecule of B binding to one Mg²⁺ ion while $K_{\mathrm{Mg}}^{\mathrm{BD}}$ is the equilibrium constant for one molecule of B bound at one end of D binding to one Mg²⁺ ion. Expressions for B_T, D_T and total Mg²⁺ concentration (Mg_T) in terms of B_f, D_f, free Mg²⁺ concentration (Mg_f), K_R, K_{R,no Mg}, $K_{\mathrm{Mg}}^{\mathrm{B}}$ and $K_{\mathrm{Mg}}^{\mathrm{BD}}$ are given in equations (10), (11) and (12) respectively:

$${\mathrm{B}}_{\mathrm{T}}={\mathrm{B}}_{\mathrm{f}}(1+K_{\mathrm{Mg}}^{\mathrm{B}}{\mathrm{Mg}}_{\mathrm{f}}+2(K_{\mathrm{R}}{K}_{\mathrm{Mg}}^{\mathrm{B}}+K_{\mathrm{R},\mathrm{no}\mathrm{Mg}}){\mathrm{D}}_{\mathrm{f}}+2{\mathrm{B}}_{\mathrm{f}}{\mathrm{D}}_{\mathrm{f}}{K}_{\mathrm{R},\mathrm{no}\mathrm{Mg}}^2{(1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}})}^2)$$ (10)

$${\mathrm{D}}_{\mathrm{T}}={\mathrm{D}}_{\mathrm{f}}(1+2{\mathrm{B}}_{\mathrm{f}}(K_{\mathrm{R}}{K}_{\mathrm{Mg}}^{\mathrm{B}}{\mathrm{Mg}}_{\mathrm{f}}+K_{\mathrm{R},\mathrm{no}\mathrm{Mg}})+{\mathrm{B}}_{\mathrm{f}}^2{K}_{\mathrm{R},\mathrm{no}\mathrm{Mg}}^2{(1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}})}^2)$$ (11)

$${\mathrm{Mg}}_{\mathrm{T}}={\mathrm{Mg}}_{\mathrm{f}}(1+K_{\mathrm{Mg}}^{\mathrm{B}}{\mathrm{B}}_{\mathrm{f}}(1+2K_{\mathrm{R}}{\mathrm{D}}_{\mathrm{f}})+2K_{\mathrm{R},\mathrm{no}\mathrm{Mg}}^2{\mathrm{B}}_{\mathrm{f}}^2{\mathrm{D}}_{\mathrm{f}}(1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}}))$$ (12)

In our experiment, since all the reference DNA molecules were bound with two molecules of RecBC before addition of Mg²⁺, [BD] = [BD]•Mg²⁺ = 0 and D_T = [B₂D] + [B₂D] •Mg²⁺ + [B₂D] •(Mg²⁺)₂. Therefore equations (10) to (12) become equations (13) to (15):

$${\mathrm{B}}_{\mathrm{T}}={\mathrm{B}}_{\mathrm{f}}(1+K_{\mathrm{Mg}}^{\mathrm{B}}{\mathrm{Mg}}_{\mathrm{f}})+2{\mathrm{D}}_{\mathrm{T}}$$ (13)

$${\mathrm{D}}_{\mathrm{T}}={\mathrm{D}}_{\mathrm{f}}{\mathrm{B}}_{\mathrm{f}}^2{K}_{\mathrm{R},\mathrm{no}\mathrm{Mg}}^2{(1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}})}^2$$ (14)

$${\mathrm{Mg}}_{\mathrm{T}}={\mathrm{Mg}}_{\mathrm{f}}(1+K_{\mathrm{Mg}}^{\mathrm{B}}{\mathrm{B}}_{\mathrm{f}}+2K_{\mathrm{R},\mathrm{no}\mathrm{Mg}}^2{K}_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{B}}_{\mathrm{f}}^2{\mathrm{D}}_{\mathrm{f}}(1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}}))$$ (15)

By combining equations (13) through (15), one obtains equation (16),

$${\mathrm{Mg}}_{\mathrm{T}}={\mathrm{Mg}}_{\mathrm{f}}\left(1+\frac{K_{\mathrm{Mg}}^{\mathrm{B}}({\mathrm{B}}_{\mathrm{T}}-2{\mathrm{D}}_{\mathrm{T}})}{1+K_{\mathrm{Mg}}^{\mathrm{B}}{\mathrm{Mg}}_{\mathrm{f}}}+\frac{2K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{D}}_{\mathrm{T}}}{1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}}}\right)$$ (16)

which relates Mg_T to Mg_f, B_T, D_T, $K_{\mathrm{Mg}}^{\mathrm{B}}$ and $K_{\mathrm{Mg}}^{\mathrm{BD}}$.

ΔF_obs,[Mg] in this experiment reaches its maximum value (ΔF_max,[Mg]) when Mg²⁺ ions are bound at both ends of B₂D to form B₂D•(Mg²⁺)₂. Hence, ΔF_obs,[Mg]/ΔF_max,[Mg] (0 ≤ ΔF_obs,[Mg]/ΔF_max,[Mg] ≤ 1) equals the average number of Mg²⁺ ions bound per RecBC-bound DNA end. The average number of Mg²⁺ ions bound per RecBC-saturated DNA molecule is given by equation (17):

$$\frac{{\mathrm{Mg}}_{\text{bound}}}{{\mathrm{D}}_{\mathrm{T}}}=\frac{2K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}}}{1+K_{\mathrm{Mg}}^{\mathrm{BD}}{\mathrm{Mg}}_{\mathrm{f}}}=2\frac{\Delta F_{\mathrm{obs},\left[\mathrm{Mg}\right]}}{\Delta F_{\max ,\left[\mathrm{Mg}\right]}}=2\frac{F_{i,\mathrm{corr},\left[\mathrm{Mg}\right]}-F_{0,\mathrm{corr},\left[\mathrm{Mg}\right]}}{F_{\max ,\mathrm{corr},\left[\mathrm{Mg}\right]}-F_{0,\mathrm{corr},\left[\mathrm{Mg}\right]}}$$ (17)

where Mg_bound = 2([B₂D•(Mg²⁺)] + [B₂D•(Mg²⁺)₂]), F_i,corr,[Mg] is the corrected fluorescence intensity after the i-th addition of Mg²⁺, F_0,corr,[Mg] is the corrected fluorescence intensity before the addition of Mg²⁺ and F_{max,corr,[Mg]} is the maximum value reached by F_i,corr,[Mg] after Mg²⁺ ions are bond at both ends of B₂D. Data were analyzed using equations (16) and (17) and the “implicit fitting” NLLS algorithm in Scientist (Micromath, St. Louis, MO) without the need to obtain an explicit expression for Mg_f. In this analysis, the values of $K_{\mathrm{Mg}}^{\mathrm{BD}}$, $K_{\mathrm{Mg}}^{\mathrm{B}}$ and F_{max,corr,[Mg]} were allowed to float. All uncertainties are reported at the 68% confidence limit (±one standard deviation).

Isothermal titration calorimetry

ITC experiments were performed in a VP-ITC calorimeter (Microcal, Northampton, MA) as described ³⁷. The analysis of the calorimetric data has been described in detail ³⁷ and the same analysis is used here. Briefly, experiments were carried out by titrating RecBC (0.7 to 1.1 μM in the sample cell) with 10 μL aliquots of DNA (8 to 14 μM in the syringe) at four-minute intervals and at a stirring rate of 140 rpm. All samples were degassed prior to use. The heat of reaction was obtained by integration of the peak obtained after each injection of titrant, using the software (Origin 7.0) provided by the manufacturer. Separate control experiments were performed to determine the heat of dilution for each injection by injecting the same volumes of DNA into the sample cell containing only buffer. The observed heat for the i-th injection (ΔQ_i) was obtained after correcting for the heat of dilution as described ⁶⁶ and is related to the total heat after the i-th injection (Q_i^tot) as in equation (18):

$$\Delta Q_i=Q_i^{\mathrm{tot}}-Q_{i-1}^{\mathrm{tot}}+\frac{\mathrm{d}{V}_i}{2V_0}(Q_i^{\mathrm{tot}}+Q_{i-1}^{\mathrm{tot}})$$ (18)

where dV_i is the volume of the i-th injection and V₀ is the active cell volume (1.43 mL). Since the DNA molecules used here have nearly identical ends (DNA VI series in Figure 1a), the same model of two identical and independent sites (see equation (7)) was used to analyze Q_i^tot, as given by equation (19):

$$\begin{array}{cc}\hfill Q_i^{\mathrm{tot}}& =\Delta H_{\mathrm{obs}}{V}_0{\mathrm{D}}_i^{\mathrm{T}}\frac{2K_{\mathrm{N}}{\mathrm{B}}_i^{\mathrm{f}}}{1+K_{\mathrm{N}}{\mathrm{B}}_i^{\mathrm{f}}}\hfill \\ \hfill & =\Delta H_{\mathrm{obs}}{V}_0{\mathrm{D}}_i^{\mathrm{T}}\frac{1+K_{\mathrm{N}}({\mathrm{B}}_i^{\mathrm{T}}+2{\mathrm{D}}_i^{\mathrm{T}})-\sqrt{4K_{\mathrm{N}}{\mathrm{B}}_i^{\mathrm{T}}+{(1-K_{\mathrm{N}}{\mathrm{B}}_i^{\mathrm{T}}+2K_{\mathrm{N}}{\mathrm{D}}_i^{\mathrm{T}})}^2}}{2K_{\mathrm{N}}{\mathrm{D}}_i^{\mathrm{T}}}\hfill \end{array}$$ (19)

where ΔH_obs is the observed enthalpy change for RecBC binding to one end of DNA, D_i^T is the total DNA concentration in the cell after the i-th injection, K_N is the binding constant for RecBC binding to one DNA end and B_i^f and B_i^T are the concentrations of free and total RecBC, respectively, in the cell after the i-th injection. ΔH_obs and K_N were obtained from NLLS analysis using equations (18) and (19) and the ITC NLLS algorithm contained within the Origin 7.0 software as described ⁶⁶.

In Figure 6a and b, the observed heat released upon the i-th injection normalized to the amount of injected DNA (ΔQ_i,norm) is obtained using equation (20):

$$\Delta Q_{i,\mathrm{norm}}=\frac{\Delta Q_i}{\mathrm{d}{V}_i{\mathrm{D}}^{\mathrm{T}}}$$ (20)

where D^T is the concentration of DNA in the syringe. The continuous lines in Figure 6a and b are simulations based on equations (18) to (20) and the best fit values of ΔH_obs (Table 4) and K_N indicated in the figure legends.

Observed heat capacity change (ΔC_p,obs) was obtained from a linear regression of ΔH_obs obtained at different temperature using equation (21),

$$\Delta H_{\mathrm{obs}}=\Delta H_{\mathrm{obs},\mathrm{ref}}+\Delta C_{\mathrm{p},\mathrm{obs}}(T-T_{\mathrm{ref}})$$ (21)

where ΔH_obs,ref is the observed enthalpy change at some reference temperature (T_ref). The dependence of K_BC on temperature is described by the van't Hoff equation ∂ln K_BC/∂(1/T = −δH_obs/R, where R is the gas constant. By substituting equation (21) into the van't Hoff equation and integrating it between T_ref to T, one can express ln K_BC in terms of ln K_BC,ref, ΔH_obs,ref, ΔC_p,obs, T_ref and T as shown in equation (22),

$$\ln K_{\mathrm{BC}}=\ln K_{\mathrm{BC},\mathrm{ref}}+\frac{\Delta C_{\mathrm{p},\mathrm{obs}}{T}_{\mathrm{ref}}-\Delta H_{\mathrm{obs},\mathrm{ref}}}{R}\left(\frac{1}{T}-\frac{1}{T_{\mathrm{ref}}}\right)+\frac{\Delta C_{\mathrm{p},\mathrm{obs}}}{R}\ln \frac{T}{T_{\mathrm{ref}}}$$ (22)

KMnO₄ footprinting

A 5’-³²P-labeled blunt-ended DNA (Figure 5) was made by annealing an unlabeled DNA strand 10 (n = 0) (Figure 1c) with a 5’-³²P-labeled DNA strand 9 (n = 0) (Figure 1c) as described above. Strand 9 was labeled using T4 polynucleotide kinase (US Biochemical Corp., Cleveland, OH) and γ-³²P-ATP (Perkin Elmer, Wellesley, MA) followed by purification as described ⁶². 2 nM of this 5’-³²P-labeled dsDNA was incubated with 1 μM of RecBC in buffer M plus the indicated [MgCl₂] and [NaCl] over ice for 20 min. Freshly prepared KMnO₄ solution was added to the RecBC-DNA mixture to a final concentration of 2 mM. This reaction was allowed to proceed for 3 min at 25°C and was quenched by adding 2-ME to a final concentration of 2 M. A 5’-³²P-labeled ssDNA strand 9 with n = 15 nucleotides was also added at this point to a final concentration of 2 nM as a control. DNA was then extracted by phenol extraction as described ⁶⁷ and followed by ethanol precipitation and piperidine digestion as described elsewhere ⁶⁸. The samples were run on a 20% polyarcrylamide gel with 7 M urea at 55°C for one hour as described ⁶⁸ and the gel was exposed to a phosphor screen and quantified with a Storm 840 system (Molecular Dynamics, Sunnyvale, CA).

Appendix

The probability of a nucleotide within a duplex DNA is bound with only Na⁺ and no Mg²⁺ when the duplex DNA is placed in a buffer containing both cations is calculated using equation A(1) as described ⁴²; ⁴³.

$$P_{\mathrm{Na}}=\frac{\left[{\mathrm{D}}_0\right]}{\left[\mathrm{D}\right]}=\frac{2}{1+\sqrt{1+4K_{\mathrm{obs}}^{\mathrm{Mg}}\left[{\mathrm{Mg}}^{2+}\right]}}$$ A(1)

where [D] is the total nucleotide concentration, [D₀] is the concentration of nucleotides associated with only Na⁺ and $K_{\mathrm{obs}}^{\mathrm{Mg}}$ is the observed intrinsic constant for Mg²⁺ binding to each DNA site. As shown by equation A(1), P_Na equals one before any addition of Mg²⁺ and it will decrease as [Mg²⁺] increases, indicating an increasing probability of Mg²⁺ binding to the DNA. The dependence of $K_{\mathrm{obs}}^{\mathrm{Mg}}$ on [NaCl] has been determined from the non-specific interactions between lac repressor and duplex DNA ⁴² as well as pentalysine and duplex DNA ⁴³ and given in equations A(2) and A(3), respectively:

$$\log K_{\mathrm{obs}}^{\mathrm{Mg}}=-1.75\log \left[\mathrm{NaCl}\right]+0.35$$ A(2)

$$\log K_{\mathrm{obs}}^{\mathrm{Mg}}=-(1.7\pm 0.1)\log \left[\mathrm{NaCl}\right]+(0.3\pm 0.2)$$ A(3)

In the presence of 100 mM NaCl, using either equation A(2) or A(3), one obtains an estimate for $K_{\mathrm{obs}}^{\mathrm{Mg}}\approx 100{\mathrm{M}}^{-1}$. Thus in the presence of 10 mM MgCl₂ and 100 mM NaCl one obtains a value of P_Na ≈ 0.62 using equation A(1). Similarly, in the presence of 400 mM NaCl, $K_{\mathrm{obs}}^{\mathrm{Mg}}\approx 9.5{\mathrm{M}}^{-1}$ and P_Na ≈ 0.95 when 10 mM MgCl₂ is present.