Nonspecific DNA Binding and Bending by HU_αβ: Interfaces of the Three Binding Modes Characterized by Salt Dependent Thermodynamics

Abstract

Previous ITC and FRET studies demonstrated that Escherichia coli HU_αβ binds nonspecifically to duplex DNA in three different binding modes: a tighter-binding 34 bp mode which interacts with DNA in large (>34 bp) gaps between bound proteins, reversibly bending it 140° and thereby increasing its flexibility, and two weaker, modestly cooperative small-site-size modes (10 bp, 6 bp) useful for filling gaps between bound proteins shorter than 34 bp. Here we use ITC to determine the thermodynamics of these binding modes as a function of salt concentration, and deduce that DNA in the 34 bp mode is bent around but not wrapped on the body of HU, in contrast to specific binding of IHF. Analyses of binding isotherms (8, 15, 34 bp DNA) and initial binding heats (34, 38, 160 bp DNA) reveal that all three modes have similar log-log salt concentration derivatives of the binding constants (Sk_i) even though their binding site sizes differ greatly; most probable values of Sk_i on 34 bp or larger DNA are − 7.5 ± 0.5. From the similarity of Sk_i values, we conclude that binding interfaces of all three modes involve the same region of the arms and saddle of HU. All modes are entropy-driven, as expected for nonspecific binding driven by the polyelectrolyte effect. The bent-DNA 34 bp mode is most endothermic, presumably because of the cost of HU-induced DNA bending, while the 6 bp mode is modestly exothermic at all salt concentrations examined. Structural models consistent with the observed Sk_i values are proposed.

Introduction

Escherichia coli HU_αβ and its structural homolog IHF are major nucleoid associated-proteins (NAPs) in all phases of cell growth. Both HU and IHF function in various DNA transactions, including DNA compaction, recombination, and transcription, by modifying DNA conformation (e.g., bending, looping) ^{1; 2; 3; 4; 5}. Comparisons of thermodynamic and structural properties of HU and IHF in binding to duplex DNA are needed for a molecular understanding of similarities and differences in the physiological roles of these structurally homologous proteins: why does the cell retain both proteins in spite of their very similar architecture, and co-regulate the amounts of two proteins as a function of growth phase ^{6; 7; 8}? In addition, HU and/or IHF may serve as experimentally-tractable model systems to investigate structural and thermodynamic aspects of assembly and function of larger nucleoprotein complexes which involve significant bending or wrapping of DNA around protein surface, including the nucleosome ⁹.

Our previous ITC and FRET studies ¹⁰ of the nonspecific interactions between HU and duplex DNA oligomers in the length range 8 bp – 160 bp provide a comprehensive, quantitative framework for understanding and unifying previously-reported, sometimes contrasting effects of HU on DNA conformation (e.g. compaction, extension) and the DNA binding properties of HU (including site size, binding constant, cooperativity) observed in single molecule ^{11; 12; 13} and bulk solution studies ^{14; 15; 16; 17; 18; 19; 20}. At 0.15 M Na⁺ and 15 °C, we deduced that HU binds duplex DNA in three different modes depending on the ratio of total concentrations of HU to DNA ([HU]_total/[DNA]_total, abbreviated hereafter as [HU]/[DNA]) and DNA length. These modes differ in binding site size, binding constant, and binding enthalpy. Decreasing [HU]/[DNA] at constant DNA length or increasing DNA length at low [HU]/[DNA] drives binding mode transitions from smaller site size modes (e.g., smaller number of DNA base pairs occluded by HU) to larger site size modes. Our ITC characterization (at 15 °C and 0.15 M Na⁺) of the binding mode with the largest site size revealed that it occludes 34 bp and is the most endothermic (+ 7.7 kcal/mol). FRET studies using fluorescent probes at the ends of a 34 bp duplex DNA showed that the 34 bp mode bends the DNA by ∼ 140°. The other two modes with smaller binding site sizes occlude 10 bp and 6 bp with binding enthalpies of + 4.2 kcal/mol and − 1.6 kcal/mol, respectively, exhibit moderate intra- and intermode cooperativities, and do not induce detectable bending of a 34 bp duplex DNA in a FRET assay. Based on the binding mode transitions we observed as a function of [HU]/[DNA] ratio and DNA length, we proposed that the tighter-binding 34 bp mode interacts with vacant regions of nucleoid DNA in large (< 34 bp) gaps between bound proteins, reversibly bending it 140° and thereby increasing its flexibility, and that the two weaker, modestly cooperative small-site-size modes (10 bp, 6 bp) are used to fill gaps shorter than 34 bp between bound proteins.

No crystal or solution structure has yet been determined for any of these three nonspecific binding modes of HU, probably because binding constants are modest and competition between the modes leads to a mixed population of complexes under most conditions. The crystal structure of a tighter-binding complex of Anabaena HU with a duplex DNA 17-mer with 3 mismatched T:T appositions and 4 unpaired T ²¹ (see Fig. 8a) appears useful as a model for the 34 bp mode detected in our previous ITC and FRET studies, based on their similar binding site sizes and DNA bend angles ¹⁰. In the crystal structure, the β – saddle/arm region from each monomer binds the minor groove at the central region of the DNA spanning ∼ 10 bp. The conserved proline residues at the tips of the arms insert between DNA base pairs at the ends of the central 10 bp region, inducing sharp bending of the 5′- and 3′-terminal regions flanking the proline insertion points toward the α-helical body region of HU. Steric considerations based on the highly bent DNA trajectory suggested that binding of one HU could occlude up to 35 bp of a longer DNA even if the flanking DNA was not wrapped on the body of HU ^{1; 6; 21}. The 10 bp mode has been proposed to utilize the central portion of the binding interface observed in the crystal structure: the β – saddle/arms of HU interact with one helical turn (∼ 10 bp) of the DNA minor groove without proline insertion/DNA bending ^{6; 14; 16; 22}. No structural prediction has been made for the 6 bp mode.

Figure 8.

(A) Distribution of charged residues in the binding interface of the complex between Anabaena HU and the TR3 DNA 17mer containing 3 central mismatched T:T base pairs and 4 unpaired T bases (PDB code 1P71²¹). Positively charged side chains of K, R residues (blue sticks, present in both E.coli and Anabeana HU) and negatively charged side chains of D, E residues (red sticks, present in both E.coli and Anabeana HU) which are within 8 Å of anionic DNA phosphate oxygens (red sphere) are shown. (B) A model structure of the complex between a bent 34 bp DNA containing one nick and E.coli HU bound in the 34 bp mode constructed from the crystal structures of the Anabaena HU – TR3 DNA complex (A) and of the IHF – H′ DNA complex (PDB code 1IHF⁶⁵). Representation for distribution of charged residues in the binding interface of the complex is the same as that in (A). (C) The net charge on the DNA binding interface of HU as a function of cut-off for the distance between the charged residues of HU and DNA phosphate oxygens. The filled and empty bars represent the net charges over the entire binding interface and the interface between the central 10 bp region of DNA and the saddle/arm region of HU, respectively. Decomposition of the net charge for each cut-off distance into the number of cationic and anionic residues is given in (D). All structural illustrations (including figure 9) were created using Pymol⁸⁸.

Comprehensive thermodynamic studies for dependences of DNA binding mode transitions on solution variables have been reported for single strand DNA binding proteins from E.coli (SSB) ^{23; 24; 25; 26} and from Saccahromyces cerevisiae (scRPA) ²⁷ and for human or rat DNA polymerase β ^{28; 29}. Until recently ¹⁰, no corresponding information has been available for nonspecific binding of any NAP to double stranded DNA. For SSB and scRPA, changes in solution variables such as salt concentration and type, pH, and temperature are major driving forces for the binding mode transitions in addition to the [protein]/[DNA] mole ratio and DNA length ^{23; 25; 27}. In particular, both proteins exhibit remarkable changes in binding modes with varying salt concentration; small site size modes are replaced by large site size modes with increasing salt concentration. At very low or very high salt concentration, both SSB and scRPA utilize only one mode in binding to DNA. Do similar salt concentration driven binding mode transitions occur for interactions of HU with double stranded DNA?

As a first step to address the physiological and structural questions raised above, here we report the effects of salt concentration on the thermodynamic properties of the three different binding modes of HU observed in ITC data for forward titrations of 8, 15, and 34 bp DNA with HU and for initial heats of HU binding to 34, 38, and 160 bp DNA at different salt concentrations (0.06 – 0.15 M Na⁺ at 15 °C). Analyses of these titrations and initial binding heats provide binding constants, binding enthalpies, and cooperativities of all three binding modes ¹⁰. We find that the log – log salt concentration derivatives of binding constants k_i (i.e., Sk_i) for all three modes are similar within uncertainty, which indicates that the amount of salt ion release and therefore the number of DNA phosphates neutralized by positively charged groups on HU are similar for all three modes. The results provide the basis for proposals and tests of model structures for the complexes between HU and DNA in these binding modes.

Background on Coulombic salt effects and on Coulombic end effects

In the salt concentration range investigated here (0.06 M – 0.15 M), effects of NaCl on the binding constant (or standard free energy change) of a nonspecific protein-DNA interaction are proposed to be primarily Coulombic (and therefore primarily entropic effects in water) ^{30; 31; 32}. No large net contribution to K_obs or ΔG_obs° from non-Coulombic (Hofmeister, osmotic) effects of NaCl are expected ³³. Coulombic salt effects are typically manifested as a large negative SK_obs (i.e., ∂lnK_obs/∂ln[salt]) at low salt concentration and originate primarily from the reduction in the local salt cation (counterion) gradient near DNA phosphates (i.e., cation release) upon neutralization of these phosphates by binding of a cationic ligand or a cationic surface of a protein (the polyelectrolyte effect) ^{34; 35; 36; 37; 38}. Analysis of the Coulombic salt effect provides an estimate of the number of DNA phosphates in the interface and the effective net valence of the DNA binding site of a ligand or protein ^{34; 35; 37; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51}.

Experimental data, nonlinear Poisson-Boltzmann (NLPB) calculations, and Monte Carlo simulations of Coulombic salt effects on nonspecific binding of cationic oligopeptides (L^z+) to DNA (or RNA) oligomers have revealed large Coulombic end effects (CEEs), which cause the position-averaged site-binding constant (K_obs) and the magnitude of its salt concentration dependence (i.e., |SK_obs|) to increase strongly with increasing DNA length (up to approximately 40 phosphate charges) at low salt concentration ^{36; 52; 53; 54; 55; 56}. The CEE decreases in significance with increasing salt concentration, and is typically eliminated above 0.3 M salt. Similar behavior has been observed for nonspecific binding of human DNA polymerase β to single stranded polymeric and 16 nucleotide DNA in the salt concentration range 0.05 – 0.15 M Na⁺ with 1 mM Mg^{2+ 28}. Hence a significant CEE on binding of HU to 8 bp and 15 bp DNA (but not 34 bp or larger DNA) is expected in the range of salt concentration investigated here. However, no evidence for a significant CEE was obtained in our previous characterization of the thermodynamics of HU binding to these DNA fragments at 0.15 M Na^{+ 10}. Here we obtain circumstantial evidence for a significant CEE from analysis of the salt concentration dependences of the HU-DNA binding constants and explain why our previous experiments did not detect this CEE.

The molecular origin of the CEE which makes K_obs and SK_obs for DNA binding of a cationic ligand or cationic site on a protein vary with DNA length is the axial dependence of the salt cation concentration gradient surrounding the DNA molecule ^{36; 56; 57; 58}. In particular, the surface concentration of Na⁺, which at low salt concentration (< 0.2 M) greatly exceeds the bulk Na⁺ concentration at all locations on DNA, is smaller in the vicinity of the 5 – 6 bp at each end of the molecule than in the interior where it is comparable to the surface Na⁺ concentration for interior regions of polymeric DNA. Except at high salt concentration, binding of a cationic ligand or protein at or near the end is disfavored relative to binding to any interior site due to a smaller amount of cation release; the difference in binding constants favoring interior binding increases with decreasing salt concentration because the contribution to the ensemble averaged SK_obs from interior binding is more negative than from end binding. Since the fraction of potential nonspecific binding sites for an oligocation or protein which are located within 6 bp of an end decreases with increasing DNA length, the contribution of the CEE to the position-averaged nonspecific site binding constant (and SK_obs) decreases with increasing DNA length and is not expected to be significant on 34 bp or longer DNA, as observed for binding of oligocations to DNA ^{36; 54; 55; 56}. This CEE also explains why an oligocationic ligand or the charges on a typical protein binding site do not contribute nearly as much to the SK_obs of DNA binding as do the similar number of DNA phosphates in the polymeric interior of DNA ³⁰. Predictions of the CEE are obtained from the analytical oligocation model (referred to hereafter as the model CEE case) ⁵⁶ and from numerical NLPB calculations on structural models of reactants and complexes (see the Discussion).

Results and Analysis

Qualitative features of ITC titrations of various lengths of DNA (8 bp – 160 bp) with HU: persistence of the three DNA binding modes of HU at all salt concentrations examined

The [HU]/[DNA] and DNA length dependences of nonspecific binding of HU to various lengths of DNA observed in ITC titrations have demonstrated the existence of three DNA binding modes of HU and [HU]/[DNA] driven transitions between them at 0.15 M Na^{+ 10}. Titrations at lower salt concentrations provide strong evidence for the persistence of all three binding modes of HU at all salt concentrations examined. Previous DSC and CD thermal scans of E.coli HU_αβ have demonstrated that unfolding of HU (αβ → I → α + β where I is a dimeric unfolding intermediate) does not occur until 25 °C in the salt concentration range 0.2 M to 1.0 M Na^{+ 59}. Extension of these DSC and CD experiments to the lower salt concentration range of the DNA binding experiments reported here demonstrates that HU remains a stable folded dimer at 15 °C. At or above 25 °C, folding of HU is coupled to binding, affecting the observed binding constant, enthalpy, and heat capacity change (Koh et al., in preparation) ⁶⁰.

Figure 1a shows the biphasic binding isotherms obtained in titrations of 15 bp DNA with HU at [Na⁺] from 0.06 M to 0.125 M, similar to that reported previously at 0.15 M Na⁺, but very different from the monophasic 1:1 binding isotherms obtained on 8 bp DNA at all [Na⁺] ¹⁰ (see Sfig. 1). As [Na⁺] is reduced the transition from endothermic to exothermic binding becomes steeper and occurs at lower [HU]/[DNA] (from [HU]/[DNA] = 1.3 at 0.15 M Na⁺ to 0.7 at 0.06 M Na⁺). The depth of the exothermic minimum increases from – 0.7 kcal/mol at 0.15 M Na⁺ to – 3.5 kcal/mol at 0.06 M Na⁺. The final phase of the isotherm, in which the heat signal decays to baseline, is also steeper at lower salt concentration, with a distinct inflection point at [HU]/[DNA] ∼ 2 (Fig. 1a). These biphasic binding isotherms of 15 bp DNA indicate a binding mode transition as a function of [HU]/[DNA] at all salt concentrations examined here, as observed previously at 0.15 M Na^{+ 10}. Initially, for [HU]/[DNA] < 1, HU binds noncooperatively in the endothermic 10 bp mode. Higher [HU]/[DNA] drives the binding mode transition to the cooperative, exothermic 6 bp mode ¹⁰. The traces of the electrical power, which represents the heat evolved or absorbed for each injection of HU as a function of time, show the complete return of the signal to the baseline over [HU]/[DNA] and the salt concentration range examined, indicating that the kinetics of binding of HU to 15 bp DNA in the two modes and the transition between them are rapid on the time scale of the ITC injections (Sfig. 2). The quantitative analysis in subsequent sections shows that the more abrupt and larger amplitude features of the isotherms at lower [Na⁺] are the consequence of large increases in binding constants of both 10 bp and 6 bp modes as [Na⁺] is reduced.

Figure 1.

[HU]/[DNA] and DNA length dependent DNA binding mode transitions of HU detected by ITC in the salt concentration range 0.06 M – 0.15 M Na⁺ at 15 °C. Data for 0.15 M Na⁺ were reproduced from Koh et al (2008). (A) Representative titrations of 15 bp DNA with HU monitored by ITC at 0.06 M (square), 0.082 M (cross), 0.1 M (circle), 0.125 M (triangle), and 0.15 M (diamond) Na⁺. Typical concentrations of HU in ITC injection syringe and of DNA in the reaction cell were 100 μM and 4 μM, respectively. Titration data were fit to Eq. 2 and 4 to obtain thermodynamic parameters listed in Table 2. Curves are simulated binding isotherms with the best fit parameters for k_{6, 15bp}/k_{6, 8bp} = 1. (B) DNA length (34 bp – 160 bp) dependence of the initial heat of binding at 0.06 M (square), 0.082 M (x), 0.1 M (circle), 0.125 M (triangle), and 0.15 M (diamond) Na⁺. Inset shows the representative titrations using high concentrations of DNA for determination of the initial heat of binding for 34 bp (black), 38 bp (red), and 160 bp (blue) DNA at 0.125 M Na⁺. The observed DNA length dependence at each salt concentration was analyzed using Eq. 1 to obtain the thermodynamic parameters listed in Table 3. Curves are the simulated DNA length dependence of the initial heat of binding with the best fit parameters at each salt concentration (simulations with different CEE assumptions are indistinguishable from each other). (C) Data from (B) were re-plotted as a function of salt concentration. (D) Representative titrations of 34 bp DNA with HU at 0.06 M (square), 0.1 M (circle), 0.125 M (triangle), and 0.15 M (diamond) Na⁺. Titration data were analyzed using the modified sequence generating function method (10) (Eq. 5 – 7) to obtain thermodynamic parameters listed in Table 4. Curves are simulated binding isotherms with the best fit parameters at each salt concentration for the no CEE case (black) and the model CEE case (blue).

Quantitative analysis of these binding isotherms involves six microscopic thermodynamic quantities: site binding enthalpies Δh₁₀ and Δh₆, position-averaged site binding constants k₁₀ and k₆, cooperativity ω₆, and cooperativity enthalpy Δh ω₆¹⁰. As defined previously ^{10; 61; 62}, these microscopic binding constants and enthalpies refer to the binding of HU in binding mode i (occupying n_i base pairs) to one of the N − n_i + 1 potential sites on a N bp DNA oligomer. (The quantity N − n_i + 1 is called the statistical factor.) The cooperativity ω₆ is defined as the ratio of binding constants for adjacent binding and isolated binding of HU in the 6 bp mode. These six quantities cannot all be determined by fitting the 15 bp DNA binding isotherms. Independent information regarding Δh₆ and k₆ for the 6 bp mode is required and available from titrations of 8 bp DNA with HU (Sfig. 1). While Δh₆ is expected to be independent of DNA length, k₆ is expected to increase with increasing DNA length because of the Coulombic end effect.

At 0.15 M Na⁺ and low [HU]/[DNA] (< 1), HU binds 34 bp and longer (38 bp and 160 bp) DNA primarily in the endothermic noncooperative 34 bp mode ¹⁰. An increase in DNA length from 34 bp to 38 bp or 160 bp at low [HU]/[DNA] favors the 34 bp mode relative to the two small site size modes because the statistical factor (i.e., the number of ways that one HU can bind in a particular binding mode to an unoccupied DNA oligomer, defined above) of the 34 bp mode increases much more (relative to its value on 34 bp DNA) than those of the small site size modes as the DNA length increases in this range ¹⁰. As a consequence, the initial heat of binding (i.e., the enthalpy change for formation of an ensemble of 1:1 complexes in the three modes (see Eq. 1 below)), increases as DNA length increases from 34 bp, approaching the binding enthalpy of the 34 bp mode at a DNA length of 160 bp. Figure 1b and c show that very similar DNA length dependences of the initial heat of binding are observed at lower salt concentrations (0.06 M – 0.125 M Na⁺), indicating the existence of all three DNA binding modes of HU at all [Na⁺] examined. At each [Na⁺], the initial heat of binding increases dramatically with increasing DNA length from 34 bp to 38 bp, and then increases only slightly for 160 bp DNA. For each DNA length, the initial heat of binding increases slightly with increasing [Na⁺].

Quantitative analysis of the observed DNA length (34 bp, 38 bp, and 160 bp) dependence of the initial heat of binding involves site binding enthalpies (Δh₃₄, Δh₁₀, and Δh₆) and position-averaged site binding constants (k₃₄, k₁₀, and k₆) of the three binding modes ¹⁰. The binding constants and enthalpies of the 10 bp and the 6 bp modes are available from titrations of 8 bp and 15 bp DNA with HU. Here the binding enthalpies of the two modes are expected to be independent of DNA length, while the binding constants are expected to be larger on 34 bp (and larger) DNA than on 8 bp or 15 bp DNA. The CEE is not expected to significantly affect position-averaged nonspecific binding constants for 34 bp and larger DNA, as discussed above.

At 0.15 M Na⁺, the ITC isotherm observed in a forward titration of 34 bp DNA with HU is biphasic, exhibiting a transition from endothermic to exothermic binding with increasing [HU]/[DNA] ¹⁰. Analysis of the isotherm reveals that as [HU]/[DNA] increases the binding mode switches from the 34 bp mode to the less endothermic 10 bp mode and the exothermic 6 bp mode, both of which are moderately cooperative ¹⁰. Figure 1d shows that these features become more pronounced as [Na⁺] is reduced, indicating that the transitions between the three binding modes as a function of [HU]/[DNA] persist at all salt concentrations examined. The transition from endothermic to exothermic binding heat shifts to lower [HU]/[DNA], becomes steeper, and exhibits a sharper exothermic minimum with decreasing salt concentration, as observed for 15 bp DNA binding isotherms. While the binding isotherms at [Na⁺] ≥ 0.125 M subsequently exhibit decay of the heat signal to the baseline, the isotherms at lower salt concentrations exhibit a second transition prior to decay to the baseline, reverting to endothermic binding with a distinctive inflection point at [HU]/[DNA] ∼ 3.5 (Fig. 1d). As observed in 15 bp DNA binding isotherms, the traces of the electrical power as a function of time indicate that the kinetics of binding of HU to 34 bp DNA in the three modes and transitions between them are rapid on the time scale of the ITC injections (Sfig. 2). Our quantitative analysis of these complex features of the 34 bp DNA binding isotherms reveals significant contributions from cooperativity enthalpies of the two small modes to the observed binding heat (see below for further discussion).

Effects of [Na⁺] on binding of HU to 8 bp DNA in the 6 bp mode are analogous to those on binding of an octacation (L⁸⁺) to a similar DNA oligomer

Microscopic binding constants and enthalpies for the 6 bp mode on 8 bp DNA (k₆, Δh₆°) obtained from fitting the previous ITC titration data ¹⁰ (Sfig. 1) to the 1:1 binding model (Eq. 2, 3) in the salt concentration range 0.06 M to 0.125 M Na⁺ are presented in Table 1 together with previously published k₆ and Δh₆° at 0.15 M Na^{+ 10}. At 15 °C, for all salt concentrations examined, the primary thermodynamic driving force for binding of HU to 8 bp DNA in the 6 bp mode is the positive entropy change even though the enthalpy change is also favorable and significant. Reduction in [Na⁺] from 0.15 M to 0.06 M increases k₆ by almost two orders of magnitude (from 3.4 × 10⁴ M^-1 to 2.7 × 10⁶ M^-1): the log-log salt concentration derivative of k₆, Sk₆ = (∂lnk₆/∂ln[Na⁺]) = − 4.9 ± 0.3 (Fig. 2a and Table 5). Values of Sk₆ are expected to be more negative (larger in magnitude) on larger DNA as a result of the CEE (see above). A reduction in [Na⁺] from 0.15 M to 0.06 M increases the favorable entropic contribution to binding (TΔs₆°) from 4.4 kcal/mol to 6.4 kcal/mol and makes the binding enthalpy Δh₆° slightly more exothermic (from – 1.6 kcal/mol to – 2.1 kcal/mol) (Table 1); Δh₆° extrapolates linearly to – 2.3 kcal/mol at the low salt limit (Fig. 2b).

Table 1. Thermodynamics of binding of HU to 8 bp DNA in the 6 bp mode as a function of salt concentration ([Na⁺]) at 15 °C.

[Na+] (M)	k6 (M-1)	Δh6° (kcal/mol)	Δg6° (kcal/mol)c	TΔs6° (kcal/mol)d
0.06a	2.7 (± 0.3) × 106	- 2.1 ± 0.2	- 8.5 ± 0.1	6.4 ± 0.2
0.082a	8.0 (± 1.1) × 105	- 1.8 ± 0.2	- 7.8 ± 0.1	6.0 ± 0.2
0.1a	3.3 (± 0.9) × 105	- 1.7 ± 0.3	- 7.3 ± 0.2	5.6 ± 0.3
0.125a	7.1 (± 1.7) × 104	- 1.5 ± 0.1	- 6.4 ± 0.1	4.9 ± 0.2
0.15b	3.4 (± 1.4) × 104	- 1.6 ± 0.3	- 6.0 ± 0.2	4.4 ± 0.3

^aITC data from Koh et al. (2008) were analyzed using the 1:1 binding model. Uncertainties were determined from at least three independent measurements.

^bFrom Koh et al. (2008)

^cΔg₆° = – RT ln k₆.

^dTΔs₆° = Δh₆° – Δg₆°.

Figure 2.

Salt concentration dependences of the binding constant (A) and the binding enthalpy (B) of the 6 bp mode on 8 bp DNA in the salt concentration range 0.06 M – 0.15 M Na⁺ at 15 °C. These quantities (Table 1) were determined from forward ITC titrations of 8 bp DNA with HU (Koh et al., 2008: see supplemental figure 1) by fitting the titration data to a 1:1 binding model (Eq. 2 and 3). Lines represent linear regression of lnk₆ with respect to ln[Na⁺] (A) and of Δh₆° with respect to [Na⁺] (B).

Table 5. Ranges of salt concentration dependences of the binding constants $({\text{Sk}}_{\text{i}}\equiv \frac{{\text{d}ln\text{k}}_{\text{i}}}{\text{d}ln[{\text{Na}}^{+}]})$ and binding enthalpies $(\frac{\text{d}\Delta {\text{h}}_{\text{i}}°}{\text{d}[{\text{Na}}^{+}]})$ of the three nonspecific DNA binding modes of HU at 15 °C.

Mode	8 bp DNA	Ski 15 bp DNA		34 bp and longer DNA
		k6,15bp/k6,8bp = 1	k6,15bp/k6,8bp = max.	no CEE	model CEE
34 bp mode	-	-	-	- 5.3 ± 0.5	- 7.8 ± 0.7
10 bp mode	-	- 4.9 ± 0.3	- 7.2 ± 0.4	- 4.9 ± 0.3	- 7.4 ± 0.4
6 bp mode	- 4.9 ± 0.3	- 4.9 ± 0.3	- 7.4 ± 0.4	- 4.9 ± 0.3	- 7.5 ± 0.4
Mode	8 bp DNA	$\frac{\text{d}\Delta {\text{h}}_{\text{i}}°}{\text{d}[{\text{Na}}^{+}]}$ 15 bp DNA		34 bp and longer DNA
		k6,15bp/k6,8bp = 1	k6,15bp/k6,8bp = max.	no CEE	model CEE
34 bp mode	-	-	-	10.9 ± 4.6	11.4 ± 4.9
10 bp mode	-	7.0 ± 2.0	8.2 ± 2.1	7.0 ± 2.0	8.2 ± 2.1
6 bp mode	5.4 ± 2.2	5.4 ± 2.2	5.4 ± 2.2	5.4 ±2.2	5.4 ±2.2

These thermodynamic aspects of binding of HU in the 6 bp mode to 8 bp duplex DNA (14 phosphate charges) are analogous to those of binding of an octacation L⁸⁺ (KWK₆) to single stranded nucleic acid oligomers with 14 phosphate charges, for which SK_obs = − 4.8 ± 0.3 ⁵⁵. In general, binding of oligocations (L^z+) to single- or double-stranded nucleic acids is entropically driven at low salt concentration; this entropic driving force (the polyelectrolyte effect) increases as the salt concentration is reduced ^{35; 41; 42; 43}. Extrapolated binding free energies at 1 M salt (a useful but hypothetical reference state) are typically small in magnitude (close to zero ^{35; 41; 42; 43; 55}) as we observe for binding of HU to 8 bp DNA in the 6 bp mode (Δg₆° (1 M) = − 0.6 ± 0.3 kcal/mol). The binding enthalpy of the 6 bp mode (approximately – 2 kcal/mol, typically insensitive to salt concentration) is also comparable to ΔH_obs° for L^z+ – nucleic acid interactions: for interaction of (Lys)₅CO₂ with T7 DNA, ΔH_obs° = − 1.3 ± 0.7 kcal/mol ³⁹ and for interaction of (Lys)₅(Trp)_1∼3NH₂ with poly(U), ΔH_obs° = − 2.0 ± 1.5 kcal/mol after correction for the Trp interaction enthalpy ⁴¹.

Binding of HU to 15 bp DNA: [Na⁺] dependent thermodynamics of the 10 bp mode and competition between the 10 bp and the 6 bp modes

Statistical thermodynamic analysis ¹⁰ of the observed binding isotherms of 15 bp DNA, using the binding enthalpy (Δh₆) and a range of possible values of the position-averaged binding constant (k₆) of the 6 bp mode on 15 bp DNA as inputs to Eq. 2 and 4, yields the binding enthalpy (Δh₁₀) and the corresponding range of the binding constant (k₁₀) of the 10 bp mode at each salt concentration (Table 2). The fit also yields the cooperativity enthalpy (Δh_ω6) and the corresponding range of the cooperativity factor (ω₆) of the 6 bp mode (cooperativity factors involving the 10 bp mode (ω₁₀ and ω_10/6) are quantified from analysis of the 34 bp DNA binding isotherms, given below). Initially, the values of k₆ determined from titrations of 8 bp DNA were used in analysis of HU binding isotherms for 15 bp DNA, as done previously at 0.15 M Na^{+ 10} Although excellent fits at all salt concentrations investigated here are obtained using these values of k₆ (Fig. 1a), we subsequently found that equally good fits to the 15 bp DNA binding isotherms were obtained using a range of larger values of k₆ as inputs (Fig. 3). While only a small range of values of k₆ (approximately two-fold) yields acceptable fits to 15 bp DNA binding isotherms at 0.15 M Na⁺, a much larger range of k₆ (approximately twenty-fold) is consistent with isotherms at 0.06 M Na⁺ (black curves in Fig. 3). These ranges (maximum acceptable values) of the ratio k_{6,15 bp DNA} / k_{6,8 bp DNA} are listed in Table 2 for all salt concentrations examined. (Values of k_{6,15 bp DNA} / k_{6,8 bp DNA} < 1 also provide satisfactory fits but are nonphysical and hence not considered further.) Analyses using values of k_6,15bp/k_6,8bp greater than the maximum values in Table 2 systematically fail to fit the initial transition from endothermic to exothermic heat signal and the final relaxation to the baseline at all salt concentrations examined (red curves in Fig. 3).

Table 2. Thermodynamics of binding of HU to 15 bp DNA in the 10 bp and the 6 bp modes as a function of salt concentration ([Na⁺]) at 15 °C^a.

[Na+] (M)	k6, 15bp/k6,8bpb	k6 (M-1)	Δh6° (kcal/mol)	k10 (M-1)	Δh10° (kcal/mol)	Δg10°d (kcal/mol)	TΔs10°e (kcal/mol)	ω 6	Δhω6° (kcal/mol)
0.06	1	2.7 × 106	- 2.1	1.0 (± 0.2) × 107	3.5 ± 0.2	- 9.2 ± 0.1	12.7 ± 0.2	54.6 ± 8.5	1.9 ± 0.3
	20	5.4 × 107	- 2.1	1.2 (± 0.2) × 108	3.3 ± 0.2	- 10.6 ± 0.1	13.9 ± 0.2	4.4 ± 2.0	2.5 ± 0.5
0.082	1	8.0 × 105	- 1.8	2.2 (± 0.7) × 106	3.7 ± 0.4	- 8.4 ± 0.2	12.1 ± 0.4	49.5 ± 8.7	1.2 ± 0.4
	7	5.6 × 106	- 1.8	9.5 (± 3.3) × 106	3.5 ± 0.4	- 9.2 ± 0.2	12.7 ± 0.4	5.4 ± 1.2	1.6 ± 0.5
0.1	1	3.3 × 105	- 1.7	1.0 (± 0.1) × 106	3.8 ± 0.2	- 7.9 ± 0.1	11.7 ± 0.2	44.0 ± 6.7	1.5 ± 0.4
	5	1.7 × 106	- 1.7	3.4 (± 0.3) × 106	3.7 ± 0.2	- 8.6 ± 0.1	12.3 ± 0.2	6.9 ± 1.0	1.9 ± 0.4
0.125	1	7.1 × 104	- 1.5	2.7 (± 0.6) × 105	3.9 ± 0.2	- 7.2 ± 0.1	11.1 ± 0.2	36.2 ± 9.8	1.2 ± 0.3
	3	2.1 × 105	- 1.5	5.6 (± 1.2) × 105	3.8 ± 0.2	- 7.6 ± 0.1	11.4 ± 0.2	6.1 ± 1.9	1.3 ± 0.2
0.15c	1	3.4 × 104	- 1.6	1.1 (± 0.2) × 105	4.2 ± 0.3	- 6.6 ± 0.1	10.8 ± 0.3	24.0 ± 11.0	- 0.3 ± 1.0
	2	6.8 × 104	- 1.6	1.7 (± 0.3) × 105	4.1 ± 0.4	- 6.9 ± 0.1	11.0 ± 0.4	7.2 ± 3.8	- 0.8 ± 1.4

^aAnalysis floats k₁₀, Δh₁₀°, ω₆, and Δh_ω6°, fixing k ₆ and Δh₆° as indicated. Uncertainties were determined from at least three independent measurements.

^bMinimum and maximum values of ratio of the binding constant of the 6 bp mode on 15 bp DNA to that on 8 bp DNA (Table 1) at each salt concentration yielding statistically and visually similar fits to 15 bp DNA binding isotherms

^cReanalysis of data of Koh et al. (2008)

^dΔg₁₀° = – RT ln k₁₀.

^eTΔs₁₀° = Δh₁₀° – Δg₁₀°.

Figure 3.

Analysis of 15 bp DNA binding isotherms of HU for cases in which the binding constant of the 6 bp mode on 15 bp DNA is equal to or greater than that on 8 bp DNA at each salt concentration (i.e., k_{6, 15bp}/k_{6, 8bp} ≥ 1; k_{6, 15bp}/k_{6, 8bp} is shown as r in the figures for simplicity). A range of the ratio k_{6, 15bp}/k_{6, bp} (Table 2) provides statistically and visually similar fits to the binding isotherm at each salt concentration (black curves) while the values of k_{6, 5bp}/k_{6, 8bp} beyond this range significantly degrade the fits (red curves). This analysis yields the ranges of the binding constants and the binding enthalpies of the 10 bp mode and the ranges of the cooperativities and cooperativity enthalpies of the 6 bp mode (Table 2).

Table 2 reveals that the enthalpies Δh₁₀ and Δh_ω6 do not change significantly as k₆ is systematically varied, while fitted values of k₁₀ increase proportionately at all salt concentrations investigated. For all values of k₆ yielding acceptable fits to 15 bp DNA binding isotherms, the ratio k₁₀/k₆ = 2.8 ± 1. Increasing k₆ causes the best fit value of the cooperativity ω₆ to decrease so that the product k₆ω₆ remains relatively constant within uncertainty at each salt concentration. These correlations of fitting parameters result because for the conditions investigated (relatively high [DNA] and low to moderate [Na⁺]), the initial heat of binding (see below) is a function of the ratio k₁₀/k₆ and not the individual values of k₁₀ and k₆. In the late stages of the isotherm, binding is mostly in the cooperative 6 bp mode with equilibrium constant k₆ω₆ and therefore if k₆ is increased, the fitted value of ω₆ is reduced to maintain a constant k₆ω₆.

The observation that the ratio k₁₀/k₆ does not vary significantly with [Na⁺] or with the choice of k_6,15bp used in fitting 15 bp DNA binding isotherms indicates that binding constants of these two modes have the same log-log dependences on [Na⁺] (i.e., Sk₁₀ = Sk₆) on 15 bp DNA. As k_{6, 15bp} is increased from k_6,8bp, Sk₆ on 15 bp DNA decreases (i.e., increases in magnitude) from − 4.9 ± 0.3 to − 7.4 ± 0.4. As a consequence, k₁₀ increases and Sk₁₀ decreases (from − 4.9 ± 0.3 to − 7.2 ± 0.4) on 15 bp DNA. Over the entire range of possible values of k_6,15bp, Sk₁₀ and Sk₆ are the same within the experimental uncertainty (Fig. 4a and Table 5).

Figure 4.

Ranges of salt concentration dependences of the binding constants (A) and the binding enthalpies (B) of the 10 bp (circle) and the 6 bp (triangle) modes on 15 bp DNA in the salt concentration range 0.06 M – 0.15 M Na⁺ at 15 °C. Closed and open symbols represent the cases for k_{6, 15bp}/k_{6, 8bp}=1 and k_{6, 15bp}/k_{6, 8bp}=the maximum value, respectively. Solid and dashed lines represent linear regression of lnk_i (or Δh_i°) with respect to ln[Na⁺] (or [Na⁺]) for k_{6, 15bp}/k_{6, 8bp}=1 and k_{6, 15bp}/k_{6, 8bp}=the maximum value, respectively, and define lower and upper limits of SK_obs on 15 bp DNA (Table 5).

For all salt concentrations examined (at 15 °C), the primary thermodynamic driving force for binding of HU to 15 bp DNA in the 10 bp mode is the positive entropy change whereas the enthalpy change is unfavorable. With a reduction in Na⁺ concentration from 0.15 M to 0.06 M, the entropic contribution to the binding free energy (TΔs₁₀°) becomes more favorable (more positive) by 2-3 kcal/mol, while the binding enthalpy (Δh₁₀) becomes less unfavorable (less positive) by about 0.8 kcal/mol (Table 2), extrapolating linearly to ∼ 3.0 kcal/mol at the low salt limit (Fig. 4b). Inspection of Table 2 shows that the driving force for the cooperativity of the 6 bp mode is primarily entropic at all salt concentrations investigated.

Population distributions of the 10 bp and the 6 bp (isolated and cooperative) modes on 15 bp DNA at 0.06 M and 0.125 M Na⁺ based on the fitting results with k_6,15bp/k_6,8bp = 1 (Table 2) are shown in Figure 5a (other values of k_6,15bp/k_6,8bp between 1 and the maximum value also yield the similar population distributions at a given salt concentration). Because the ratio of binding constants between the two modes is found to be independent of salt concentration (k₁₀/k₆ ∼ 2.8), the ratio of populations between the two modes is not strongly affected by changing salt concentration for [HU]/[DNA] < 0.5, the regime where HU forms mostly 1:1 complexes with 15 bp DNA. This result, together with the weak salt concentration dependences of the binding enthalpies of both modes (Table 5), explains the absence of any significant salt concentration dependence of the initial heat of binding. The transition from endothermic to exothermic binding with increasing [HU]/[DNA] (occurring at [HU]/[DNA] = 0.7 at 0.06 M Na⁺ and at [HU]/[DNA] = 1.3 at 0.15 M Na⁺; see Fig. 1 a) is primarily attributed to replacement of the endothermic 10 bp mode (Δh₁₀ ∼ + 3.5 kcal/mol) by the exothermic 6 bp mode (Δh₆= ∼ – 2.0 kcal/mol) (Fig. 5b). Increases in the binding constants of the 10 bp and the 6 bp modes with decreasing salt concentration result in a sharper transition from the 10 bp to the 6 bp mode, shifted to lower [HU]/[DNA], at lower salt concentration (Fig. 5a and b). For example, at 0.06 M Na⁺, the average number of HU bound in the 10 bp mode per DNA decreases strongly from 0.34 at [HU]/[DNA] = 0.85 to 0.05 at [HU]/[DNA] = 1.7. However, at 0.125 M Na⁺, the average number of HU bound in the 10 bp mode is almost invariant (0.34 to 0.32) in the same range of [HU]/[DNA]. The increase in the binding constant of the 6 bp mode also contributes to the steeper decay of the heat signal to the baseline at saturation and to the more pronounced exothermic minimum and the inflection point observed at lower salt concentration.

Figure 5.

(A) [HU]/[DNA] dependent population distributions (from a simulation using Eq. 4 and thermodynamic quantities for k_6,15bp/k_6,8bp=1 in Table 2) of the 10 bp mode (blue), the 6 bp mode (red), and the contact point between nearest neighbor HU molecules cooperatively bound in the 6 bp mode (magenta) on 15 bp DNA at 0.06 M (solid) and 0.125 M (dotted) Na⁺. (B) Corresponding [HU]/[DNA] dependences of the contributions to the observed binding heat signal (black) from the 10 bp mode (blue), the 6 bp mode (red), and the contact point of the 6 bp mode (magenta) at 0.06 M (solid) and 0.125 M (dot) Na⁺.

As reviewed in the Background, the molecular basis for expecting a larger value of k₆ and a more negative Sk₆ for 15 bp DNA than for 8 bp DNA is the Coulombic end effect (CEE). The CEE is expected to be primarily entropic, consistent with the observation that values of Δh₆ from analysis of the 8 bp DNA titrations (Table 1) do not need correction to fit the 15 bp (also 34 bp and larger; see below) DNA binding isotherms. Based on the analogy between binding of HU to 8 bp DNA in the 6 bp mode and binding of L⁸⁺ to an oligonucleotide with the same number of phosphate charges (see above), HU was modeled as a simple oligocation with a net charge of +8 for theoretical estimation of the CEE on binding of HU to oligomeric DNA in the 6 bp mode. This so-called “model CEE” analysis, previously successfully used to predict the CEE on interactions of oligocations with oligonucleotides ⁵⁶, is used here to estimate the increase in k₆ on 15 bp DNA as compared to 8 bp DNA at each salt concentration (see Materials and Methods). Predicted ratios k_6,15bp/k_6,8bp decrease from 21 at 0.06 M Na⁺ to 5 at 0.15 M Na⁺. Except at 0.06 M Na⁺, these predicted values are about two-fold larger than, but the same within uncertainty as, the maximum values of these ratios that provide acceptable fits to the 15 bp DNA binding isotherms. (For example, reducing the length of the end region in the model CEE analysis ⁵⁶ from 12 to 11 phosphate charges, reduces these predicted ratios by two-fold.)

Binding of HU to 34 bp and longer DNA: analysis of the initial heat of binding as a function of DNA length and salt concentration indicates that the three binding modes of HU have similar salt concentration dependences of binding constants, Sk_i

Analysis of the initial heat of binding of HU to 34 bp and selected larger DNAs provides a direct way to determine the binding enthalpy and the range of possible binding constants for the 34 bp mode, free of contributions from the cooperativities of the 10 bp and the 6 bp modes ¹⁰. Moreover, Coulombic end effects are not significant for interpretation of position-averaged nonspecific HU binding constants for 34 bp or larger DNA (see Background). The analysis of initial binding heats requires that only 1:1 complexes between HU and DNA molecules be present and that the free HU concentration be negligibly small (i.e., stoichiometric binding) ¹⁰ To achieve this condition, the concentration of DNA in the ITC reaction cell is increased until the initial heat signal reaches a [DNA]-independent plateau for each DNA length (Fig. 1b inset). At the [DNA]-independent plateau, the initial heat of binding for each DNA length (N bp) is given by:

$${\text{Q}}_{\text{initial},\text{N bp DNA}}={\sum }_{\text{i}=6,10,34}\Delta {\text{h}}_{\text{i}}\frac{({\text{N}-\text{n}}_{\text{i}}+1){\text{k}}_{\text{i}}}{{\sum }_{\text{i}=\mathrm{6.10.34}}({\text{N}-\text{n}}_{\text{i}}+1){\text{k}}_{\text{i}}}$$ (Eq. 1)

where n_i is the binding site size of the binding mode i and $\frac{({\text{N}-\text{n}}_{\text{i}}+1){\text{k}}_{\text{i}}}{{\sum }_{\text{i}=\mathrm{6.10.34}}({\text{N}-\text{n}}_{\text{i}}+1){\text{k}}_{\text{i}}}$ is the fractional population of the 1:1 complex in the binding mode i ¹⁰. Division of both numerator and denominator by k₆ rearranges Eq. 1 in terms of the ratios k₃₄/k₆ and k₁₀/k₆.

Fits of initial heats of HU binding to 34 bp, 38 bp, and 160 bp DNA to Eq. 1 (Fig. 1 b), using binding enthalpies (Δh₁₀, Δh₆) and binding constant ratios k₁₀/k₆ as inputs, yield the binding enthalpy (Δh₃₄) and relative binding constants (k₃₄/k₆ and k₃₄/k₁₀) of the 34 bp mode as a function of [Na⁺]. In this analysis, binding enthalpies for the 10 bp and the 6 bp modes determined from analyses of the 15 bp and the 8 bp DNA binding isotherms (Table 1 and 2) are directly used and ranges of binding constants (therefore k₁₀/k₆) for the two modes derived from various assumptions regarding CEEs are examined. As one limiting case (that specified as “no CEE” in Table 3), we assume that k₆ and k₁₀ are independent of DNA length so that values of these quantities determined from analyses of 8 bp and 15 bp DNA titrations neglecting CEEs (from Table 2) are directly applicable to 34 bp and larger DNA. In other analyses, values of k₆ and k₁₀ are increased from their values on 15 bp (and 8 bp) DNA given in Table 2. The maximum increase in k₆ from 8 bp to 15 bp DNA at each salt concentration consistent with the ITC results (see Table 2), which is also most consistent with that predicted by the model CEE analysis (see above), was considered as the most plausible case. Likewise, the most plausible increases in k₆ and k₁₀ from 15 bp to 34 bp DNA were estimated at each salt concentration based on the model CEE predictions, and are listed in Table 3 (model CEE).

Table 3. Thermodynamics of binding of HU to 34 bp and longer DNA in the 34 bp mode (and the other two modes) as a function of salt concentration ([Na⁺]) at 15 °C obtained from analysis of initial heat of binding (34 bp, 38 bp, and 160 bp DNA)^a.

[Na+] (M)		k6,15bp/k6,8bp	k6,34bp/k6,15bp	k10,34bp/k10,15bp	k34/k6	k34/k10	k34 (M-1)	Δh34° (kcal/mol)	Δg34°e (kcal/mol)	TΔs34° f (kcal/mol)
0.06	no CEEb	1	1	1	74.1 ± 28.7	20.0 ± 7.7	2.0 (± 1.0) × 108	6.7 ± 0.9	- 10.9 ± 0.3	17.6 ± 0.9
	model CEEc	20	2.1	3.4	78.6 ± 30.3	21.4 ± 8.1	9.0 (± 4.5) × 109	6.7 ± 1.0	- 13.1 ± 0.3	19.8 ± 1.0
0.082	no CEEb	1	1	1	58.8 ± 22.8	21.4 ± 8.2	4.7 (± 1.8) × 107	7.2 ± 0.6	- 10.1 ± 0.2	17.3 ± 0.6
	model CEEc	7	2.0	3.1	62.2 ± 24.1	23.4 ± 9.0	7.0 (± 2.8) × 108	7.1 ± 0.6	- 11.7 ± 0.2	18.8 ± 0.6
0.1	no CEEb	1	1	1	75.8 ± 26.4	25.0 ± 8.3	2.5 (± 1.1) × 107	7.2 ± 0.9	- 9.8 ± 0.3	16.9 ± 0.9
	model CEEc	5	2.0	3.0	78.4 ± 27.2	25.4 ± 8.4	2.6 (± 1.1) × 108	7.2 ± 0.8	- 11.1 ± 0.2	18.3 ± 0.8
0.125	no CEEb	1	1	1	70.4 ± 24.4	18.5 ± 6.2	5.0 (± 2.2) × 106	7.7 ± 0.7	- 8.8 ± 0.3	16.5 ± 0.7
	model CEEc	3	1.9	2.9	73.8 ± 25.6	18.0 ± 6.0	2.9 (± 1.3) × 107	7.7 ± 0.6	- 9.8 ± 0.2	17.5 ± 0.6
0.15d	no CEEb	1	1	1	55.9 ± 10.3	17.3 ± 2.9	1.9 (± 0.4) × 106	7.8 ± 0.4	- 8.3 ± 0.1	16.1 ± 0.4
	model CEEc	2	1.8	2.7	58.3 ± 10.8	15.7 ± 2.6	7.2 (± 1.2) × 106	7.8 ± 0.4	- 9.0 ± 0.1	16.8 ± 0.4

^aAnalysis floats k₃₄/k₆ and Δh₃₄, fixing Δh₁₀ and Δh₆ (Table 2), and k₁₀/k₆ as dictated by the CEE assumptions.

^bk₆ and k₁₀ assumed to be independent of DNA length

^cIncreases in k₆ and k₁₀ from 8 bp to 15 bp DNA and from 15 bp to 34 bp DNA estimated from oligo-model of the CEE⁵⁶

^dReanalysis of data of Koh et al. (2008)

^eΔg₃₄° = – RT ln k₃₄.

^fTΔs₃₄° = Δh₃₄° – Δg₃₄°.

Significantly, Table 3 reveals that the fitted values for ratios of position-averaged site binding constants k₃₄/k₆ (69 ± 12) and k₃₄/k₁₀ (21 ± 5), valid for 34 bp and larger DNA, are relatively independent of both [Na⁺] and the assumptions about CEE used in the analyses. These results show that the log-log [salt] derivatives of the binding constants (Sk_i) of the three modes are the same within uncertainty, independent of assumptions regarding the magnitudes of k₆ and k₁₀ as functions of DNA length. Values of Sk_i for the three modes on 34 bp and longer DNA are − 4.9 ± 0.3, − 4.9 ± 0.3, and − 5.3 ± 0.5 for the 6 bp, the 10 bp, and the 34 bp modes, respectively, if there is no DNA length dependence of k₆ and k₁₀ (Fig. 6a and Table 5). If k₆ and k₁₀ have the DNA length dependences predicted by the model CEE analysis, more negative Sk_i are obtained: Sk₆ = − 7.5 ± 0.4, Sk₁₀ = − 7.4 ± 0.4, and Sk₃₄ = − 7.8 ± 0.7 (Fig. 6a and Table 5).

Figure 6.

Salt concentration dependences of the binding constants (A) and the binding enthalpies (B) of the 34 bp (square), the 10 bp (circle) and the 6 bp (triangle) modes on 34 bp or longer DNA in the salt concentration range 0.06 M – 0.15 M Na⁺ at 15 °C. Closed and open symbols represent the no CEE and the model CEE cases, respectively. Solid and dashed lines represent linear regression of lnk_i (or Δh_i°) with respect to ln[Na⁺] (or [Na+]) for these two cases, respectively (Table 5).

Fitted values of the binding enthalpy Δh₃₄ for the bent 34 bp mode are completely insensitive to assumptions about CEE on k₆ and k₁₀ used in the analyses and are more endothermic at all salt concentrations than observed for the smaller-site-size modes. For all salt concentrations examined (15 °C), the primary thermodynamic driving force for binding of HU to 34 bp and longer DNA in the 34 bp mode is the positive entropy change whereas the enthalpy change is unfavorable. With a reduction in Na⁺ concentration from 0.15 M to 0.06 M, the favorable entropic driving force (TΔs₃₄°) increases from 16.9 kcal/mol to 21.0 kcal/mol for the model CEE case (Table 3). (Alternatively, if k₆ and k₁₀ were assumed to be independent of DNA length (no CEE), then a somewhat smaller increase in TΔs₃₄° is predicted: 16.5 kcal/mol at 0.15 M Na⁺ to 19.3 kcal/mol at 0.06 M Na⁺.) The binding enthalpy (Δh₃₄) decreases from 7.8 kcal/mol at 0.15 M Na⁺ to 6.7 kcal/mol at 0.06 M Na⁺, extrapolating linearly to 6.2 kcal/mol at the low salt limit (Fig. 6b). In addition to the two choices described above and listed in Table 3, we examined the entire ranges of DNA length dependent values of k₆ and k₁₀ consistent with both initial binding heats and the entire 34 bp DNA binding isotherms and found that the conclusions regarding Δh₃₄ and ΔSk_i are not significantly affected (see supplemental information).

[Na⁺] effects on the competition between the three binding modes of HU on 34 bp DNA: evidence for exothermic cooperative interactions of HU involving the 10 bp mode (ω₁₀, ω_10/6)

The entire 34 bp DNA binding isotherms were analyzed using the modified sequence generation function method (SGF) (Fig. 1d) previously developed to describe the competition between the 34 bp, the 10 bp, and the 6 bp modes on 34 bp DNA (Eq. 5–7) ¹⁰. In this analysis, values of k₃₄, k₁₀, k₆, Δh₃₄, Δh₁₀, Δh₆, ω₆, and Δh_ω6 determined from analyses of 8 bp and 15 bp DNA binding isotherms and of initial heats of binding for 34 bp, 38 bp, and 160 bp DNA with different assumptions of CEEs (see above) were used to obtain the cooperativities involving the 10 bp mode (10 bp mode (ω₁₀) and intermode (ω_10/6)) and their associated enthalpies (Δh_ω10 and Δh_ω10/6) (Table 4). Equivalently acceptable fits describing all the features of the binding isotherm were obtained for both the model CEE and the no-CEE cases at each salt concentration (Fig. 1d). At all salt concentrations examined, the increases in k₁₀ and k₆ reduce ω₁₀ and ω_10/6 without significantly affecting values of Δh_ω10 and Δh_ω10/6 (Table 4), as observed in analysis of 15 bp DNA binding isotherms.

Table 4. Cooperativities and cooperativity enthalpies involving the HU 10 bp mode as a function of [Na⁺] obtained from analysis of the entire 34 bp DNA binding isotherms using the modified sequence generating function method ^a.

CEE assumption	[Na+] (M)	ω10	ω10/6	Δhω10 ° (kcal/mol)	Δhω10/6° (kcal/mol)
no CEE	0.06	54.2 ± 17.8	41.7 ± 18.9	- 6.8 ± 0.5	- 2.9 ± 1.5
	0.1	44.3 ± 9.9	12.7 ± 5.4	- 5.4 ± 0.4	- 2.8 ± 1.2
	0.125	28.6 ± 8.5	4.2 ± 2.9	- 4.9 ± 0.3	- 4.1 ± 2.0
	0.15	17.5 ± 9.9	10.8 ± 7.1	- 3.0 ± 1.1	- 3.0 ± 1.7
model CEE	0.06	16.9 ± 7.7	11.1 ± 5.7	- 6.9 ± 0.8	- 2.4 ± 1.3
	0.1	20.1 ± 3.4	5.0 ± 2.9	- 5.3 ± 0.4	- 3.1 ± 1.3
	0.125	12.2 ± 3.8	2.5 ± 1.5	- 5.2 ± 0.4	- 3.6 ± 2.0
	0.15	13.6 ± 9.1	5.6 ± 3.7	- 3.4 ± 1.1	- 2.8 ± 1.2

^aValues of k₃₄, k10, k₆, Δh₃₄°, Δh₁₀°, Δh₆°, ω₆, and Δh_ω6° determined from analyses of 8 bp and 15 bp DNA binding isotherms and of initial heats of binding to 34 bp, 38 bp and 160 bp DNA for different assumptions of CEEs (Tables 1 – 3) were used in this analysis.

Values of ω₁₀ and ω_10/6 obtained from analysis of the entire 34 bp DNA binding isotherms are moderate to weak depending on the CEE assumption used in the analysis at all salt concentrations examined (Table 4). The corresponding enthalpies are significantly exothermic for any case at all salt concentrations examined (Table 4) and are primary driving forces for the 10 bp mode and intermode cooperativities, in contrast to the entropically driven and enthalpically unfavorable 6 bp mode cooperativity (Table 2). With decreasing salt concentration from 0.15 M to 0.06 M Na⁺, ω₁₀ increases ∼ 3-fold for the no-CEE case and is more or less constant if the model CEE case is used, whereas ω_10/6 does not show a monotonic dependence on salt concentration with the minimum value at 0.125 M Na⁺. Δh ω₁₀ decreases by ∼ 4 kcal/mol from 0.15 M to 0.06 M Na⁺ whereas Δh ω_10/6 does not show any systematic salt concentration dependence with an average value of ∼ − 3.0 kcal/mol.

The exothermic cooperativity enthalpy of the 10 bp mode significantly contributes to the transition from endothermic to exothermic binding heat observed in the first half of 34 bp DNA titrations (Fig. 7c, d) because the population of the contact point between two adjacent HU molecules bound in the 10 bp mode increases cooperatively with increasing [HU]/[DNA] (i.e., positive curvature in the average number of contact points per DNA, Fig. 7a, b). After this transition, the observed binding heat reflects the net conversion of cooperatively bound HU molecules in the 10 bp mode to those in the 6 bp mode (Fig. 7c, d). The endothermic dissociation of cooperative clusters of HU in the 10 bp mode is the primary origin of the endothermic peaks observed at low salt concentrations (Fig, 7a, c). The enthalpy of the intermode cooperativity is important in determining the details of the shape of the exothermic minimum and the endothermic maximum (Fig. 7c, d). All of these features become more pronounced as the salt concentration is reduced, because the increases in binding constants of all modes cause the binding mode transitions to become sharper, as observed for 15 bp DNA binding isotherms. The 34 bp mode contributes to the population distribution and to the observed binding heat only at low [HU]/[DNA], as observed previously ¹⁰.

Figure 7.

(A, B) Simulated equilibrium population distributions (based on the modified SGF analysis of the 34 bp DNA binding isotherms for the model CEE case) of the 34 bp mode (blue), the 10 bp mode (green), and 6 bp mode (red), and those of the 10 bp mode contact point (cyan), the 6 bp mode contact point (magenta), and the intermode (10 bp – 6 bp) contact point (brown) on 34 bp DNA as a function of [HU]/[DNA] at 0.1 M Na⁺ (A) and 0.15 M Na⁺ (B). (C, D) Corresponding [HU]/[DNA] dependence of the contribution to the observed binding heat signal (black) from the heat of formation of each equilibrium species calculated in (A) and (B).

Discussion

DNA binding mode transitions of E.coli HU_αβ as a function of [HU]/[DNA] and DNA length are observed at all salt concentrations examined

ITC studies of nonspecific binding of HU to DNA oligomers at low to moderate salt concentration (0.06 M – 0.15 M Na⁺, 15 °C) demonstrate the existence of three (6 bp, 10 bp, 34 bp) binding modes differing in position-averaged, nonspecific site binding constant k_i at a constant salt concentration. Significantly, the binding constant ratios k₃₄/k₁₀ and k₃₄/k₆ on 34 bp and longer DNA are found to be independent of salt concentration and of the assumptions made regarding the Coulombic end effect (CEE), within experimental uncertainties. Therefore, the log-log [salt]-derivatives of the binding constants, Sk_i, are the same for all three binding modes on 34 bp and larger DNA within uncertainty.

However, values of Sk_i for the individual modes do depend sensitively on the role assigned to the CEE, because the characterizations of the small site size modes were performed with short DNA oligomers. To unambiguously determine k_i for the 6 bp mode as a function of salt concentration and therefore obtain Sk_i for this mode requires using a DNA shorter than 10 bp to avoid binding of HU in the 10 bp mode. We obtain Sk_i ∼ – 5 for the 6 bp mode on 8 bp DNA; reducing [Na⁺] from 0.15 M to 0.06 M increases k₆ by about two orders of magnitude. But the CEE is predicted to be most significant for such short oligomers. If there were no CEE, and Sk_i for the 6 bp mode were – 5 for all DNA lengths, then we would conclude that Sk_i are also – 5 for the 10 bp and the 34 bp modes for all DNA lengths. On the other hand, use of the model CEE analysis yields calculated values of Sk_i of approximately – 8 for all three modes on polymeric DNA (≥ 34 bp).

In this range of salt concentration, binding enthalpies of the three modes are insensitive to the magnitude of the CEE and decrease linearly (i.e., become more exothermic) with decreasing salt concentration. The largest site size (34 bp) mode exhibits the largest dependence of the binding enthalpy on salt concentration.

Because the ratios of the binding constants between different modes are independent of salt concentration, [HU]/[DNA] and DNA length (34 bp to 160 bp) driven binding mode transitions observed previously at 0.15 M Na^{+ 10} occur at all other salt concentrations examined in this study. Binding enthalpies of the three modes differ significantly from each other in magnitude at all salt concentrations investigated, allowing the binding mode transitions to be readily detected by ITC. Binding mode transitions driven by the [HU]/[DNA] ratio are the origin of the multiphasic features of the HU binding isotherms for 15 bp and longer DNA (Fig. 1). These features become more pronounced at lower salt concentration because the increases in binding constants of all modes cause sharper transitions between the modes as a function of [HU]/[DNA]. For example, the [HU]/[DNA] ratio where fractional populations of the 10 bp and the 6 bp modes on 34 bp DNA are equal shifts from 11.0 at 0.15 M Na⁺ to 3.7 at 0.06 M Na⁺ (Fig. 7b and Sfig. 3a). Similar salt concentration dependent features have been reported in a recent single-molecule force extension measurement study ⁶³ where the transition from compaction to stiffening of DNA with increasing HU concentration becomes less pronounced at higher salt concentration.

Salt concentration driven binding mode transitions are observed in interactions between E.coli SSB and single stranded DNA as a consequence of the large differences in values of SK_obs for the different modes ^{23; 24; 25}, in contrast to the similar SK_obs values for all three DNA binding modes of HU. The transition from the 35 nucleotide (nt) mode to the 65 nt mode on poly(dT) is driven by increasing NaCl concentration with ΔSK_{obs, transition} = SK_{obs, 65} – SK_obs,35 = + 8, interpreted as the net uptake of ∼ 8 salt ions (6 Na⁺, 2 Cl^-) ²⁵. A stable complex with the intermediate site size of 56 nt was also observed in this binding mode transition. Because ΔSK_{obs, transition} is large, SSB binds poly(dT) exclusively in the 35 nt mode at low salt concentration ([NaCl] < 0.01 M) and in the 65 nt mode at high salt concentration ([NaCl] < 0.2 M), and exhibits [SSB]/[DNA] dependent transitions between these modes at intermediate salt concentration (0.01 M < [NaCl] > 0.2 M) ⁶⁴. Uptake of cations in the transition from the 35 nt to the 65 nt mode is found to be necessary to reduce the charge repulsions caused by bringing phosphate residues in close proximity upon further wrapping of ssDNA (i.e., negative cooperativity within the ssDNA binding sites of SSB), overriding the release of cations from neutralization of additional DNA phosphates by SSB ^{25; 65; 66}.

Binding of scRPA (yeast single stranded DNA binding protein) to poly(dT) was observed to behave similarly to SSB ²⁷. At low salt concentration ([NaCl] < 0.1 M), scRPA utilizes the 19 nt mode in the interaction with poly(dT) whereas the 27 nt mode is the dominant mode at high salt concentration ([NaCl] > 1 M). Human DNA polymerase β exhibits 16 nt and 5 nt binding modes for ssDNA at all salt concentrations examined ²⁸, but the appreciable difference in SK_obs between the two modes (ΔSK_obs ∼ 3) predicts that only single binding mode may be observed at sufficiently low or high salt concentration.

The presence of multiple binding modes and transitions between them may be general features for nonspecific single or double stranded DNA binding proteins including IHF (Koh et al., in preparation) ⁶⁰, other NAPs, and the nucleosome. Indeed, the nucleosome has been observed to be dynamic in terms of the extent of wrapping of DNA on its surface, populating at least two different conformations, wrapped and partially unwrapped forms ^{67; 68; 69}. These different modes have been proposed to be important for regulatory proteins to gain access to their target DNA sequences in the nucleosome ^{67; 68; 69}. Equilibrium constants for partial unwrapping were recently determined by FRET, and range from ∼ 0.02 to ∼ 0.1 in the salt concentration range 0.1 M to 0.15 M ⁶⁸. For converting the bent (but not wrapped) 34 bp mode to the unbent 10 bp mode of binding of HU, we find k₁₀/k₃₄ = 0.05 (Table 3), comparable to these nucleosome results.

Interpretation of Sk_i for formation of the DNA binding modes of HU: DNA in the 34 bp mode is bent, but not wrapped, around the α–helical body region of HU

It is remarkable that the observed salt concentration dependences (Sk_i) of binding constants of the three DNA binding modes of HU are similar, given the large differences in the binding site sizes between these modes. What insight does this observation provide regarding the structures of these modes and molecular processes involved in the transitions between them? Sk_i may be interpreted in terms of a long-range Coulombic salt effect; the net Hofmeister-osmotic contribution to Sk_i should be minimal because all the titrations were performed at low to moderate concentration of NaCl ^{32; 33} and because the extent of dehydration of HU and DNA upon binding in these three nonspecific modes appears to be small (see below for discussion of salt concentration dependences of binding enthalpies) ^{32; 70; 71}. Therefore, the net charge on the DNA binding interface of HU is expected to be a key determinant of Sk_i. Here, we propose model structures for the complexes between HU and DNA in the three binding modes based on the thermodynamic observations, analyze distributions of charged residues in their binding interfaces, and finally examine Coulombic salt effects on stabilities of these model structures by NLPB calculations.

A structural model of the HU-DNA 34 bp binding mode

The similar values of Sk_i observed for the three binding modes of HU most simply indicate that the charge-charge interactions and the extent of salt ion release in formation of the binding interfaces for these modes are similar. Therefore, bending of DNA and consequent additional interactions that distinguish the bent 34 bp mode from the unbent 6 bp and 10 bp modes must increase the steric binding site size greatly without increasing the number of charge-charge interactions and the extent of salt ion release. The FRET-determined DNA bend angle in the 34 bp mode complex is ∼ 140° ¹⁰. This bend angle, which is similar to that observed in the crystal structure of the complex between Anabaena HU (AHU) and a mismatched duplex DNA ²¹, must be large enough to bring the 5′ and 3′ terminal flanking regions of 34 bp DNA sufficiently close to the α – helical body region of HU to prevent binding of another HU molecule. However, this bend angle is not as large as that observed for the IHF – H′ DNA specific complex ^{32; 72} which allows tight wrapping of the flanking DNA regions on the body of the protein and formation of additional charge-charge interactions. Therefore, the experimentally-determined Sk_i for the formation of the 34 bp mode must result primarily from the salt ion release that accompanies formation of the binding interface between DNA and the HU β – arm/saddle region which is also thought to be the binding interface of the 10 bp mode ^{6; 14; 16; 22}.

To model the 34 bp binding mode complex formed by E.coli HU (EHU) and 34 bp DNA, we began with the crystal structure of the AHU-DNA complex ²¹ (Fig. 8a). The short (17mer) mismatched DNA oligomer in that structure was replaced by the bent 34 bp duplex DNA from the crystal structure of the IHF – H′ DNA complex (in which the DNA is nicked at one proline insertion site) ⁷². The overall bend angle of the DNA was reduced from 163° (IHF) to 140° (HU) (Fig. 8b). AHU amino acid side chains were converted to those of EHU as described in Materials and Methods.

Figure 8c and d summarize the numbers of positively and negatively charged residues of HU as a function of distance (from 3 Ǻ to 10 Ǻ) from the nearest anionic DNA phosphate oxygen in this model of the HU-DNA 34 bp mode. The net charge (i.e., the difference between the numbers of cationic and anionic residues) on the DNA binding interface of HU increases from +3 to +10 as the distance defining the contact interface in the complex is increased from 3 to 8 Ǻ. Additional increase in this distance from 8 to 10 Ǻ causes the net charge to decrease from +10 to +9 because there are more anionic residues than cationic residues at this distance range. Significantly, for any distance defining the contact interface, most of the interactions between charged residues of HU and DNA phosphates are located in the interface formed between the central 10 bp region of DNA and the β – arm/saddle region of HU, making at least 80 % contribution to the net charge on the DNA binding interface (Fig. 8c). This center biased distribution of the net charge is consistent with our proposal that salt ion release (primarily Na⁺ release from the DNA) in forming the 34 bp mode HU-DNA complex occurs primarily in the binding interface formed by the arm/saddle region of HU since DNA is bent toward, but not wrapped on, the body of HU. (See below for further discussion of the charged residues of HU in the DNA binding interface.)

Recent studies of relaxation kinetics of the IHF – H′ DNA complex perturbed by laser induced temperature jump showed that the forward rate constant for the step where a specific but unbent complex converts into a final specific IHF – DNA complex through bending and subsequent wrapping of DNA does not depend on salt concentration ⁷³ Based on this observation, it was proposed that there is no salt ion release in the formation of the transition state in which DNA is bent, but not yet wrapped on the α – helical body region of IHF. The 34 bp mode of HU observed in our ITC studies may therefore resemble the transition state of the IHF-DNA complex observed in the DNA bending/wrapping step.

A structural model of the HU-DNA 10 bp binding mode

The interface formed between the β – saddle/arm region of HU and the central region of DNA observed in the crystal structure (Fig. 8a) (and in the proposed model of the 34 bp mode (Fig. 8b)) spans ∼ 10 bp and has been proposed to be the binding interface of the 10 bp mode ^{6; 14; 16; 22}. Because the DNA bound in the 10 bp mode is unbent, the conformations of the HU arms must differ in the 10 bp and the 34 bp modes. Indeed, substituting a linear 34 bp DNA for the bent 34 bp DNA in the model structure of the 34 bp mode (Fig. 9a) results in significant steric clash between the arm of HU and the DNA phosphate backbone/bases (purple circle in the foreground of fig. 9a). For this model, the binding site size defined by the arms is approximately 14 bp, not 10 bp. [The origin of the clash is the narrower minor groove for the linear duplex DNA than for the bent DNA near the bending point.] NMR spectroscopy studies revealed that the arms of free Bst HU (residues 55 to 74), each of which consists of two β strands and an intervening loop, are highly flexible, populating multiple conformations ^{74; 75}. The pair of highly conserved alanine residues at 57 and 73 serves as a hinge between the flexible arm and the rigid body/saddle region ^{74; 76; 77}. The observed flexibility of the arms, which is consistent with the absence of electron density for these regions in crystal structures of free HU ^{22; 59; 76; 78}, indicates that the arms may readily change their conformations in the transition between the different binding modes.

Figure 9.

(A) Model structures for the 34 bp (left panel, reproduced from fig. 8B) and the 10 bp (right panel) modes (see text for detailed discussion). Representation for distribution of charged residues in the binding interface of the complex is the same as that in figure 8. (B) Model structures for the 10 bp (left panel, a top view of the 10 bp mode shown in (A)) and the 6 bp modes (right panel). (C) The net charges on the DNA binding interfaces of HU for the three modes as a function of cut-off for the distance between the charged residues of HU and DNA phosphate oxygens.

Figure 9a illustrates one plausible conformation of the flexible arm in the 10 bp mode (purple arrow) that minimizes steric clash with the phosphate backbone and bases of unbent DNA; this conformation displays a binding site size of approximately 10 bp. In this model of the 10 bp mode, the tips (the intervening loops) of the HU arms are pulled out of DNA minor groove. As a consequence, the two proline “levers” (green sticks in the 34 bp mode model) are not inserted into DNA base-pairs, which is compatible with the unbent DNA conformation. Most of the interface involving the arm/saddle of HU and the central region of DNA is conserved between the model structures of the 34 bp and the 10 bp modes (Fig. 9a). Therefore, at any contact distance the net charge on the DNA binding interface of HU is similar for these two models (Fig. 9c).

A structural model of the HU-DNA 6 bp binding mode

The simplest interpretation of the similar values of Sk_i for the 6 bp mode and the other two larger modes is that the charged region of the arm/saddle of HU is also the primary DNA binding interface for the 6 bp mode, possibly in a different orientation from that observed in the other two modes. For example, rotating the HU molecule in the model structure of the 10 bp mode around the axis perpendicular to the DNA helical axis by ∼ 50° reduces the binding site size from 10 bp to 6 bp (Fig. 9b). The net charge on the DNA binding interface at any distance in this model structure is similar to those obtained for the 34 bp and the 10 bp modes (Fig. 9c). Alternatively, or in addition, conformational changes in the HU arms may occur in the conversion from the 10 bp to the 6 bp mode as a means of reducing the binding site size while maintaining the relative orientation of HU and the primary binding interface observed in the 34 bp and the 10 bp modes.

Possibly the similarity between values of Sk_i for the 6 bp mode and the larger modes on polymeric DNA is only a coincidence and does not imply that the same region of the saddle and arms is the binding site; the binding site for DNA could be on the body of HU. However, there is no evidence for such an interpretation, and several arguments against it. All the binding isotherms on 15 bp and larger DNA obtained in this study are well interpreted in terms of competition between these three modes for binding to DNA; such competition is most simply explained if all three modes utilize similar binding surfaces of HU. In particular, experiments in DNA excess provide no evidence for a binding stoichiometry of 1 HU:2 DNA, as would be expected if the site for the 6 bp mode were distinct from that of the 10 bp and 34 bp modes. Moreover, no other region on the surface of HU has a local excess of cationic side chains similar to that of the site in the saddle/arm for the 34 bp and 10 bp modes. In particular, the flanking regions on the body of HU, used by IHF to wrap DNA in its specific 34 bp mode, are not sufficiently positively charged to be a binding site, and indeed do not contact DNA in the bent but not wrapped 34 bp mode of HU. Further structural and thermodynamic studies are required to establish a complete model for the 6 bp mode.

The different orientations of the bound HU molecule proposed for the 10 bp and the 6 bp modes indicate that the cooperative HU-HU interactions on DNA must occur through different regions of HU in the two modes. Remarkably different thermodynamic origins of the cooperativities for the two modes (ω₁₀ vs. ω₆) support this hypothesis (Table 2 and 4): cooperative interactions between two adjacent HU molecules bound in the 10 bp mode are enthalpically driven at all salt concentrations examined whereas cooperative interactions for the 6 bp mode are entropically driven. Moreover, Δh_ω10 becomes more exothermic with decreasing salt concentration while Δh_ω6 becomes more endothermic. A conserved hydrophobic patch centered on residue 45V (or I) in the turn between β strand 1 and 2 was previously proposed to be a putative protein-protein interaction surface ^{22; 77}. This patch is located on the “side” (yellow circles in fig. 9a) of the HU molecule where contact points may readily form between adjacent HU molecules bound in the 10 bp mode.

Nonlinear Poisson – Boltzmann (NLPB) calculations using the structural models to interpret experimental salt concentration dependences of the binding constants (Sk_i) for the three DNA binding modes of HU

The similar distributions of the net charge on the binding interface for the model structures of the three DNA binding modes of EHU are consistent with the similar Sk_i of the three modes determined from analysis of ITC data. To test these structural models further, we performed all-atom nonlinear Poisson – Boltzmann (NLPB) analysis ⁷⁹ of salt concentration dependences of Coulombic free energy changes for formation of the model complexes (see Materials and Methods for details). NLPB calculations of Coulombic free energies of HU, DNA oligomers, and their complexes in each binding mode as a function of salt concentration yield the thermodynamic extents of salt ion accumulation for these components (n_HU, n_DNA, n_complex). The difference (n_complex − n_HU − n_DNA) yields the predicted value of Sk_NLPB. For a given DNA length, we find that NLPB-predicted values of Sk_NLPB for all three binding modes are the same within ∼ 10 %, and also the same as those obtained from analysis of ITC data using the model CEE case (Table 5). For binding to 15 bp DNA, we find that Sk_NLPB = -7.1 and -7.5 for the 6 bp and the 10 bp modes, respectively. For binding to unbent 34 bp DNA, we find that Sk_NLPB = -7.3, -8.2, and -8.3 for the 6 bp, the 10 bp, and the 34 bp modes, respectively. The calculated Sk_NLPB for binding of HU to a pre-bent DNA to form the 34 bp mode complex (with no additional DNA bending) is -8.9; the calculated Sk_NLPB for bending 34 bp of initially-linear DNA by ∼ 140° is + 0.6, yielding Sk_NLPB = -8.3 for forming the bent 34 bp complex from HU and linear 34 bp DNA. [The small positive value of Sk_NLPB which we calculate for DNA bending indicates that charge repulsions caused by bringing DNA phosphates closer to each other at the narrowed central minor groove and at the underside of the proline insertion site do not contribute significantly to Sk₃₄.]

The value of Sk_{6, NLPB} for 8 bp DNA (-5.7), which is comparable to the ITC-determined value (-4.9), demonstrates a very significant Coulombic end effect for the 6 bp mode as compared to Sk_{6, NLPB} for 15 bp DNA. Both Sk_{6, NLPB} and Sk_{10, NLPB} are predicted to change only slightly with increasing DNA length from 15 bp to 34 bp DNA (see above). Hence, position-averaged values of Sk_NLPB calculated for the 6 bp and the 10 bp modes on 15 bp DNA are close to the polymeric (≥ 34 bp) limit; the CEE is predicted by NLPB analysis to be of great significance only for binding of HU to 8 bp DNA.

The effective net charges (Z_L,eff) on the binding interfaces of the three modes were estimated using the values of Sk_NLPB on 34 bp DNA (i.e., polymeric Sk_NLPB) and the relation, Skpolymeric = – 0.89Z_L,eff, from the charged cylindrical DNA – oligocation binding model ^{34; 35; 36; 39} The estimated values of Z_L,eff are +8, +9, and +10 for the 6 bp, the 10 bp, and the 34 bp modes, respectively, which are consistent with the net charges calculated from the numbers of the charged residues of HU within 8 Ǻ of DNA phosphates in the model complexes (Fig. 9c). [For estimation of Z_L,eff for the 34 bp mode, the value of Sk₃₄, NLPB before the correction for the effect of salt concentration on DNA bending (Sk₃₄, NLPB = – 8.9) was used.] There are 13 cationic residues (αK51, αR55, αR58, αR61, αK83, αK86, βK53, βR55, βR58, βR61, βR80, βK83, βK86) and 3 anionic residues (αE57, αE68, βE68) in the 8 Ǻ-defined DNA binding interface of the 34 bp mode (Fig. 8b, d). All these residues except αK83 and βK83 are located in the interface formed between the central 10 bp region of DNA and the arm/saddle region of HU. In the 10 bp mode, unbending of DNA removes αK83 and βK83 from the 8 Ǻ-defined binding interface while the conformational change of the HU arm removes α/βR61, αE57, and βE68 from this interface but adds an additional cationic residue αK67 (Δnet charge_{34→10bp mode} = -1). From the 10 bp mode to the 6 bp mode, rotating the bound HU molecule removes αK67, αK86, and αE68 from the binding interface (Δnet charge₁₀→6_{bp mode} = -1). Many of the charged residues of EHU found in the 8 Ǻ-defined DNA binding interfaces of the model complexes are also present in the binding interface for the crystal structure of the AHU-mismatched 17 bp DNA complex (Fig. 8a: αR55, αR58, αR61, αR86, βR53, βR55, βR58, βR61, βR86).

Four cationic residues in the proposed binding interfaces (R55, R58, R61, and R or K86) are highly conserved in HU homologues from different organisms and have been proposed and shown to play important roles in DNA binding ^{22; 75; 76; 80; 81; 82; 83}. For example, mutation of either R55, 58, or 61 into glutamate significantly reduced (3 to 7-fold in filter binding assays) the apparent DNA binding constant of the wild type Bst HU whereas conservative mutation into lysine did not have any significant effect ⁸². E.coli HU with mutations of R58 and R61 into glycines was also observed to be eluted at lower salt concentration than the wild type in DNA affinity chromatography ⁸³.

Interpretation of salt concentration dependences of ΔH_obs° for formation of the DNA binding modes of HU

For two large-interface protein-DNA complexes in which DNA is wrapped on the protein surface, binding enthalpies increase with increasing salt concentration, strongly in Cl^-and Br^- salts, and modestly in F^- and Glutamate salts ^{32; 84; 85; 86; 87} At 25 °C, the binding enthalpy of SSB in the 65 nt mode to one (dT)₇₀ or two (dT)₃₅ increases from − 150 kcal/mol at low salt concentrations of NaCl or NaBr (< 0.1 M) to − 94 kcal/mol at 2.0 M NaCl and to −70 kcal/mol at 2.0 M NaBr but is unaffected by increasing concentration of NaF up to 0.6 M ⁸⁴ For the specific complex of IHF with H′ DNA, in which 34 bps are wrapped around the protein ⁷², ΔH_obs° at 20 °C increases from − 20 kcal/mol at 0.04 M KCl to − 9 kcal/mol at 0.33 M KCl and from − 22 kcal/mol at 0.04 M KF to − 17 kcal/mol at 0.38 M KF ³² For IHF binding to H′ DNA, ΔH_obs° is a linear function of salt concentration (∂ΔH_obs°/∂[MCl] = 38 kcal/mol/M), as expected for a Hofmeister effect, and the positive slope is attributed to disruption of weak, enthalpically favorable Hofmeister interaction of Cl^- anions (and to a lesser extent F^- and Glu^- anions) with the surface on the free protein that is buried in the interface of the complex ³² Therefore, the magnitude of salt concentration dependence of ΔH_obs° is proportional to the amount of surface area buried (ΔASA) in complexation.

The situation is quite different for HU. Binding enthalpies of all three DNA binding modes of HU in NaCl increase modestly with increasing [NaCl] (Table 5), with slopes of ∼ 11.2, 7.6 and 5.4 for the 34 bp, the 10 bp and the 6 bp modes, respectively. The ΔASA for the model structure of the HU 34 bp mode is only half as large in magnitude as for the IHF – H′ DNA complex (-2880 Ǻ² vs. -5340 Ǻ²) due to the absence of tight wrapping of the flanking DNA regions on the body of HU. Since values of ∂ΔH_obs°/∂[MCl] for IHF and HU binding differ by more than three-fold, it is likely that there is also less dehydration per A² of surface buried in forming the nonspecific HU-34 bp DNA complex than in forming the specific IHF-34 bp H′ DNA complex. The ratio of ∂ΔH_obs°/∂[MCl] values comparing the 34 bp and the 10 bp modes of HU (∼ 1.5) is comparable to the ratio of ΔASA calculated from the corresponding model structures (2880Ǻ² / 1840Ǻ² ∼ 1.6), but significantly smaller than the ratio of the binding site sizes of the two modes (3.4), consistent with the absence of tight wrapping of the flanking DNA regions around the body of HU in the 34 bp mode.

The more positive binding enthalpy of the 34 bp mode as compared to the 10 bp mode in the salt concentration range examined here (and extrapolated to 0 M salt) may reflect the net effect of the interactions involved in bending the DNA by the HU “machinery”: loss of base stacking (ΔH° > 0) ^{88; 89}, gain of interactions between unstacked bases and the proline (ΔH° < 0), and release of ordered water molecules from the DNA minor groove upon burial of the tip of the HU arm containing the proline (ΔH° > 0) ⁹⁰. The moderately endothermic binding enthalpy of the 10 bp mode may be also attributed to release of ordered water molecule from the DNA minor groove interacting with the saddle and the lower arm regions. Molecular interpretation of the binding enthalpy of the 6 bp mode (and unambiguous dissection of Δh₃₄ and Δh₁₀) requires further structural and thermodynamic characterizations.

Conclusion

Using salt concentration as a probe, we examined the thermodynamic basis of stabilities and the characteristics of the HU-DNA interfaces for the 34 bp, the 10 bp, and the 6 bp binding modes by ITC. All three modes are significant at all salt concentrations examined and exhibit very similar dependences of their stabilities (Δg_i°) on salt concentration (similar values of dΔg_i°/dln[salt] = -RT Sk_i). As a consequence, binding mode transitions driven by changes in [HU]/[DNA] ratio and in DNA length occur at all salt concentrations examined. Our comprehensive analyses of ITC data for different lengths of DNA also provide circumstantial evidence for Coulombic end effects on binding of HU to short DNA oligomers (≥ 15 bp). The similar values of Sk_i for the 6 bp, the 10 bp and the 34 bp modes indicate that the binding interfaces in these complexes involve similar numbers of charge-charge interactions and that the DNA flanking the central 10 bp region which interacts with the saddle and arms of HU is bent toward, but not wrapped on, the body of HU. This structural proposal is corroborated by the observation that the ratio of values of ∂ΔH_obs°/∂[MX] for the 34 bp and 10 bp modes is smaller than the site size ratio and that ∂ΔH_obs°/∂[MX] for the 34 bp mode is much smaller than that of the tightly wrapped H′ DNA -IHF complex ³² [The difference in the extent of DNA bending between HU and IHF also results in strikingly different temperature dependences of the binding enthalpies for these two proteins (Koh et al., in preparation) ⁶⁰.]

The relatively weak binding constant (at ∼ 0.15 M Na⁺) and the absence of tight wrapping of DNA in the 34 bp mode complex presumably mean that DNA bending by this mode is rapidly reversible, consistent with the lack of detectible kinetics in the ITC titrations and with the observation of a greatly reduced persistence length (stiffness) of DNA in vivo⁹¹. This increased flexibility doubtless contributes to dynamic compaction of chromosomal DNA in vivo. HU bound in the 34 bp mode should also facilitate formation of DNA loops and bends required for “action at a distance” occurring in Gal repressosome ⁹² and Mu transpososome ⁹³.

While the physiological significance of the 34 bp mode in DNA compaction and in regulation of other DNA transactions is clear, the occurrence and the significance of the modestly cooperative, relatively unbent 10 bp and 6 bp modes are currently unknown. In exponential growth, the average gap size on the nucleoid is estimated to be at least 160 bp with a ratio [HU]/[160 bp DNA gap] ∼ 0.6 (or [DNA bp]/[HU] ∼ 270) if the other abundant DNA binding proteins (FIS, H-NS, IHF, RNA polymerase, and CRP) are assumed to be all bound and distributed randomly on the nucleoid ¹⁰. For this condition similar to that for determination of the initial binding heat for 160 bp DNA, the 34 bp mode is predicted to be dominant (i.e., 127k₃₄/(127k₃₄+151k₁₀+155k₆) ∼ 0.93 using values in Table 3; the proportionality of each k_i is the statistical factor of each binding mode), though heterogeneity in gap size would affect this calculation. We expect that gaps smaller than 34 bp can be efficiently filled by the two smaller-site-size, modestly-cooperative modes. The population distribution between the three modes could be shifted by changes in growth conditions or by the presence of other DNA binding proteins ¹⁰. Information about in vivo distributions of HU and other NAPs on the nucleoid as a function of growth conditions and growth phase ⁷ and investigation of possible interactions between the different HU binding modes and other DNA binding proteins ⁹⁴ will improve our understanding of the physiological significance of each of these modes.

Materials and Methods

Materials

All the chemicals used in these studies were prepared and obtained as described previously ¹⁰. E.coli HU_αβ and DNA oligomers

• (8 bp DNA: 5′- CTCGCGAG -3′;

• 15 bp DNA: 5′- CGGTCAGTTCAAGGC –3′;

• 34 bp DNA: 5′ – GCCAAAAAAGCATTGCTTATCAATTTGTTGCACC –3′;

• 38 bp DNA: 5′ – CGGTCAGTTCAAGCCCTTCTAAGTTTGTAGACACCAGC –3′;

and 160 bp calf thymus DNA) were also prepared and purified as described previously (8 bp – 38 bp DNA oligomers were initially synthesized and purified by Integrated DNA Technologies (Coraville, IA)) ¹⁰. The purities and binding activities of HU and DNA were essentially the same for independent preparations.

ITC titrations

Samples for ITC experiments were extensively dialyzed (three changes, > 36 hours total) against binding buffer (0.010 M Na₂HPO₄, 0.001 M Na₂EDTA, and NaCl concentration in the range 0.038 M – 0.128 M, pH 7.5) using Spectra/Pore membrane tubing (3500 Da cutoff for HU and 500 Da cutoff for DNA). Forward ITC titrations, where HU was injected into the cell containing DNA, were performed with VP-ITC (MicroCal, LLC, Northhampton, MA). Detailed procedures for centrifuging/degassing the samples, measurements of protein/DNA concentrations, choosing the running parameters of ITC, and determination of dilution/mechanical heats were described previously ¹⁰

For formation of a single type of complex (designated S) from two reactants, the standard ITC equation ⁹⁵ for the heat q_p,i of the ith injection, which takes into account the volume displacement in the reaction cell, is:

$$q_{p,i}=\frac{\Delta {\text{H}}_{\text{S}}°{\text{V}}_{\text{cell}}}{{[\text{HU}]}_{\text{inj}}{\text{V}}_{\text{inj}}}\{{[\text{S}]}_{\text{i}}-{[\text{S}]}_{\text{i}-1}+\frac{{\text{V}}_{\text{inj}}}{{\text{V}}_{\text{cell}}}(\frac{{[\text{S}]}_{\text{i}}+{[\text{S}]}_{\text{i}-1}}{2})\}$$ (Eq. 2)

In Eq. 2, ΔH_s° is the standard enthalpy change for formation of any complex S, V_cell is the volume of the reaction cell, [HU]_inj is the molar concentration of HU in the injection syringe, V_inj is the injection volume, and [S]_i and [S]_i-1 are the equilibrium molar concentrations of the complex in the cell after ith and i-1th injection, respectively. To analyze ITC isotherms for binding of HU to DNA oligomers, a sum of heat contributions from the different types of complexes formed (each contribution given by Eq. 2) was used in the nonlinear regression program NONLIN ⁹⁶ and Igor Pro 5/6. Concentrations [S]_i used in fitting or simulation of binding isotherms and population distributions were obtained by numerically solving the appropriate system of equations involving total concentrations of HU and DNA (mass balance equation) and the partition function for each length of DNA as given in the following sections.

Fittings and simulations of 8 bp and 15 bp DNA binding isotherms

In the salt concentration ([Na⁺]) range from 0.06 M to 0.125 M, forward titrations of 8 bp DNA with HU were fit to eq. 2 where the general concentration term [S] is the concentration of HU bound in the 6 bp mode ([HU]_b,6). For each iteration of the fitting procedure, trial values of k₆ and Δh₆ are used to solve the mass balance equation for the total concentration of HU and the partition function for 8 bp DNA (Z_{8 bp}) ¹⁰ to obtain the concentration of free HU ([HU]_free) and [HU]_b,6:

$${\left[\text{HU}\right]}_{\text{total}}={\left[\text{HU}\right]}_{\text{free}}+{\left[\text{HU}\right]}_{\text{b},6}={\left[\text{HU}\right]}_{\text{free}}+{\left[\text{DNA}\right]}_{\text{total}}\frac{\partial ln{\text{Z}}_{8\text{bp}}}{\partial ln{\left[\text{HU}\right]}_{\text{free}}}$$ (Eq. 3a)

$${\text{Z}}_{8\text{bp}}=1+3{\text{k}}_6{\left[\text{HU}\right]}_{\text{free}}$$ (Eq. 3b)

The 15 bp DNA binding isotherms of HU were analyzed as a sum of heat contributions (q_{p, i} in Eq. 2) from binding of HU to 15 bp DNA in the 10 bp mode ([S] = [HU]_{b, 10}) and the 6 bp mode ([S] = [HU]_{b, 6}) and from formation of a “contact point” between nearest neighbor HU molecules bound in the 6 bp mode ([S] = [contact point]). For each iteration of the fitting procedure (or for final simulation), trial (or best fit) values of k₁₀, Δh₁₀, k₆, Δh₆, ω₆, and Δh_ω6 are used to solve the mass balance equation for the total concentration of HU and the partition function for 15 bp DNA (Z_{15 bp}) ¹⁰ to obtain [HU]_free, [HU]_b,10, [HU]_{b, 6}, and [contact point]:

$$\begin{array}{ll}{\left[\text{HU}\right]}_{\text{total}}\hfill & ={\left[\text{HU}\right]}_{\text{free}}+{\left[\text{HU}\right]}_{\text{b},10}+{\left[\text{HU}\right]}_{\text{b},6}\hfill \\ & ={\left[\text{HU}\right]}_{\text{free}}+{\left[\text{DNA}\right]}_{\text{total}}(\frac{\partial {ln\text{Z}}_{15\text{bp}}}{\partial {ln\text{k}}_{10}{\left[\text{HU}\right]}_{\text{free}}}+\frac{\partial {ln\text{Z}}_{15\text{bp}}}{\partial {ln\text{k}}_6{\left[\text{HU}\right]}_{\text{free}}})\hfill \end{array}$$ (Eq. 4a)

$${\text{Z}}_{15\text{bp}}=1+(6{\text{k}}_{10}+10{\text{k}}_6){\left[\text{HU}\right]}_{\text{free}}+(6+4{\omega }_6){({\text{k}}_6{\left[\text{HU}\right]}_{\text{free}})}^2$$ (Eq. 4b)

$$\left[\text{contact point}\right]={\left[\text{DNA}\right]}_{\text{total}}\frac{\partial {ln\text{Z}}_{15\text{bp}}}{\partial ln{\omega }_6}$$ (Eq. 4c)

Fitting and simulation of 34 bp DNA binding isotherms

The 34 bp DNA binding isotherms of HU were analyzed as a sum of heat contributions (q_{p, i} in Eq. 2) from binding of HU to 34 bp DNA in the 34 bp, the 10 bp, and the 6 bp modes ([S] = [HU]_{b, 34}, [HU]_{b, 10}, and [HU]_{b, 6}) and from formation of three types of contact points between nearest neighbor HU molecules bound in the 10 bp or the 6 bp mode ([S] = [contact point]_10-10, [contact point]_6-6, and [contact point]_10-6). Based on the modified sequence generating function method that we previously developed to describe the competition between the 34 bp, the 10 bp, and the 6 bp modes on 34 bp DNA ¹⁰, the mass balance equation for the total concentration of HU is given by:

$$\begin{array}{c}\\ {\left[\text{HU}\right]}_{\text{total}}={\left[\text{HU}\right]}_{\text{free}}+{\left[\text{HU}\right]}_{\text{b},6}+{\left[\text{HU}\right]}_{\text{b},10}+{\left[\text{HU}\right]}_{\text{b},34}\\ ={\left[\text{HU}\right]}_{\text{free}}+\frac{{\left[\text{DNA}\right]}_{\text{total}}{{\text{x}}_1}^{34}}{{{\text{x}}_1}^{34}+{\text{k}}_{34}{\left[\text{HU}\right]}_{\text{free}}}{[\frac{\partial {ln\text{x}}^{34}}{\partial \text{ln}({\text{k}}_6{\left[\text{HU}\right]}_{\text{free}})}+\frac{\partial {ln\text{x}}^{34}}{\partial \text{ln}({\text{k}}_{10}{\left[\text{HU}\right]}_{\text{free}})}+\frac{{\text{k}}_{34}{\left[\text{HU}\right]}_{\text{free}}}{1+{\text{k}}_{34}{\left[\text{HU}\right]}_{\text{free}}/{\text{x}}^{34}}]}_{\text{x}=\text{x}1}\end{array}$$ (Eq. 5)

In Eq. 5, x₁³⁴ is the partition function for 34 bp DNA including the free state and bound states in the 10 bp and the 6 bp modes and x₁ is the largest root of the secular equation f(x):

$$\text{f}(\text{x})={{[\text{HU}]}_{\text{free}}}^2\{{\text{k}}_{10}{\text{k}}_6[({\omega }_{10}{\omega }_6-{{\omega }_{10/6}}^2)\text{x}+({\omega }_{10}+{\omega }_6-2{\omega }_{10/6}-{\omega }_{10}{\omega }_6+{{\omega }_{10/6}}^2)]\}+{[\text{HU}]}_{\text{free}}\{{\text{k}}_6[({\omega }_6-1){\text{x}}^{10}{-\omega }_6{\text{x}}^{11}]+{\text{k}}_{10}[({\omega }_{10}-1){\text{x}}^6-{\omega }_{10}{\text{x}}^7]\}+{\text{x}}^{17}-{\text{x}}^{16}=0$$ (Eq. 6)

For each iteration of the fitting procedure (or for final simulation), trial (or best fit) values of k₃₄, Δh₃₄, k₁₀, Δh₁₀, k₆, Δh₆, ω₁₀, Δh_ω10, ω₆, Δh_ω6, ω_10/6, and Δh_ω10/6 are used to simultaneously solve these two equations to obtain x₁, [HU]_free, [HU]_b,34, [HU]_{b, 10}, and [HU]_{b, 6}. All three types of [contact point] can be also calculated using the following equations:

$${[\text{contact point}]}_{\text{i}}=\frac{{[\text{DNA}]}_{\text{total}}{{\text{x}}_1}^{34}}{{{\text{x}}_1}^{34}+{\text{k}}_{34}{[\text{HU}]}_{\text{free}}}{(\frac{\partial {ln\text{x}}^{34}}{\partial ln{\omega }_{\text{i}}})}_{\text{x}={\text{x}}_1}\text{i}=10-10,6-6,\text{or}10-6$$ (Eq. 7a)

$${(\frac{\partial ln\text{x}}{\partial ln{\omega }_{\text{i}}})}_{\text{x}={\text{x}}_1}=-\frac{{\omega }_{\text{i}}}{{\text{x}}_1}[{(\frac{\partial \text{f}(\text{x})}{\partial {\omega }_{\text{i}}})}_{\text{x}={\text{x}}_1}/{(\frac{\partial \text{f}(\text{x})}{\partial \text{x}})}_{\text{x}={\text{x}}_1}]$$ (Eq. 7b)

Structural modeling and calculations

The crystal structures of the Anabaena HU – TR3 DNA (PDB code 1P71) ²¹ and the IHF – H′ DNA complexes (PDB code 1IHF) ⁷² were used as templates to model the structures of the complexes between E. coli HU and duplex 34 bp DNA in the 34 bp, the 10 bp, and the 6 bp modes. In modeling the 34 bp mode, the 17 bp DNA in the Anabaena HU – TR3 DNA structure was replaced by the 34 bp DNA in the IHF – H′ DNA structure after aligning these two structures using Pymol ⁹⁷ Then, the overall bend angle of the 34 bp DNA (163°) was reduced to that of the 17 bp DNA (143°) by rotating and aligning the flanking regions of the 34 bp DNA to the corresponding flanking regions of the 17 bp DNA. In modeling the 10 bp mode, the bent 34 bp DNA in the model structure of the 34 bp mode was replaced by a linear duplex 34 bp DNA (obtained from the make-na web server and the nucleic acid builder program developed by Case and co-workers: http://structure.usc.edu/make-na/) after aligning the central 10 bp regions of these two DNA molecules. Then, the flexible arm regions of HU (residues 57 – 73) were moved out of the DNA minor grooves to obtain a binding site size of approximately 10 bp and to minimize steric clash of these regions with DNA phosphate backbone/bases. Subsequently, this structure was used to model the 6 bp mode by rotating the HU molecule around the axis perpendicular to the DNA helical axis by 50° to reduce the binding site size from 10 bp to 6 bp.

A homology model of E. coli HU_αβ was calculated using Swiss Model (http://swissmodel.expasy.org/) ^{98; 99}. Models of EHU_α and EHU_β were calculated using the A and B chains from 1P71 ²¹ as templates, respectively. These models were then assembled to form the E. coli HU_αβ dimer by superposing the alpha carbon backbone residues 2–88 on those in the dimer from 1P71 using InsightII. The 34 bp mode complex was then modeled by superposing the E. coli HU_αβ model dimer on the structure modeled above with a DNA bend angle of 143°. For the 10 bp and the 6 bp modes, the core residues (2–50) were superposed on the respective DNA models above. Because the arms are modeled out of the minor groves, the arms (57–73) were superposed independently. These independent superpositions were then assembled into a HU dimer bound in either the 10 bp or 6 bp mode using InsightII. Steric clash was removed using the side chain rotamer library in InsightII.

Using these models, the number of cationic and anionic residues of HU within 3 Ǻ -10 Ǻ from DNA phosphate oxygens were calculated using Pymol ⁹⁷ Water (solvent) accessible surface areas (ASA) of the model structures were calculated for both HU – DNA complexes and unbound HU and DNA (obtained by removing DNA or HU coordinates in the PDB codes) using Surface Racer ¹⁰⁰ with a probe radius of 1.4 Ǻ and accepted values of the van der Waals radii ¹⁰¹.

These homology models were compared to the crystal structures of the HU_αβheterodimer (2O97)¹⁰² and the HU_αsubunit (1MUL)⁵⁹ from E.coli without DNA and DNA binding arms. Superposition of the homology model (34 bp mode) on the heterodimer (2O97) and on the HU_α subunit (1MUL) yields rms deviations of 0.58 Å and 0.52 Å, respectively, indicating equivalent overall folding for these three structures. Side chain conformations of charged amino acid residues of these two published structures were also examined to identify any charged residue interacting with DNA phosphates but not detected in our homology model. For 2O97, αK51, αK83, αK86, βK53, βR55, βR58, and βK86 are within 8 Ǻ of DNA phosphates and all these residues are also detected in the homology model. βR80 and βK83 are detected only in the homology model. For 1 MUL, only αK86 is within 8 Ǻ of a DNA phosphate, and αK51 and αR55 are resolved only to the C delta atoms of the side chains. In summary, the homology model built in this study captures the correct overall folding and all possible charge-charge interaction pairs for the HU-DNA complex.

Numerical NLPB calculations of Coulombic free energy changes for formations of model structures for the three HU-DNA binding modes as a function of salt concentration

The change in Coulombic standard free energy (ΔG^Coul) for formation of a small site size mode (10 bp or 6 bp) complex of HU on 34 bp DNA is estimated from the Coulombic free energy change for rigid-body docking $(\Delta G_{\mathit{\text{dock}}}^{\mathit{\text{Coul}}})$, assuming that conformational changes in HU coupled to binding are not significant.

$$\Delta G^{\mathit{\text{Coul}}}=\Delta G_{\mathit{\text{dock}}}^{\mathit{\text{Coul}}}=G_C^{\mathit{\text{Coul}}}-G_P^{\mathit{\text{Coul}}}-G_D^{\mathit{\text{Coul}}}$$ (Eq. 8)

where $G_C^{\mathit{\text{Coul}}}$, $G_D^{\mathit{\text{Coul}}}$, and $G_P^{\mathit{\text{Coul}}}$ are Coulombic standard free energies of the model complex (C), of free DNA (D: obtained by removing HU coordinates from C), and of free protein (P: obtained by removing DNA coordinates from C). For the 34 bp binding mode, ΔG^Coul is calculated using $G_C^{\mathit{\text{Coul}}}$ and $G_P^{\mathit{\text{Coul}}}$ from the model for the 34 bp mode complex, and $G_D^{\mathit{\text{Coul}}}$ from the linear 34 bp DNA structure used in models of the 10 bp and 6 bp mode complexes, in order to include the Coulombic free energy change for DNA bending. (No other DNA conformational changes are invoked.)

The Coulombic free energies are calculated by Adaptive Poisson-Boltzmann Solver (APBS) ⁷⁹ with the Amber force field. PDB files were converted to format required for APBS input with online converter ¹⁰³. APBS solves the nonlinear Poisson-Boltzmann (NLPB) equation numerically for an all-atom molecular model of a biopolymer and calculates its standard free energy (standard chemical potential), which differs from G^Coul (Eq. 8) by a salt concentration independent contribution that we determine from the high salt limit of the NLPB-calculated free energy ¹⁰⁴. Structural models of the three binding modes (Fig. 9) were used for these calculations. Cell sizes and grid point spacings were chosen as described previously in detail ¹⁰⁴ and an initial focusing procedure was applied, in order to obtain accurate and efficient calculations. Small ion radii were set at 2 Ǻ; the external dielectric constant was set at 78.5 (water, 25 °C) and a value of 2 was chosen for the internal dielectric constant. NLPB values of $G_C^{\mathit{\text{Coul}}}$, $G_D^{\mathit{\text{Coul}}}$, and $G_P^{\mathit{\text{Coul}}}$ calculated at univalent salt concentrations of 0.06 M, 0.082 M, 0.1 M, 0.125 M, 0.15 M, 0.175 M and 0.2 M were used to calculate ΔG^Coul. The Coulombic contribution to the salt concentration dependence of the binding free energy $(S{K}^{\mathit{\text{Coul}}}=-\frac{\partial \Delta G^{\mathit{\text{Coul}}}/\mathit{\text{RT}}}{\partial ln[M^{+}]})$ is then determined from the slope of the plot of Δ G^Coul vs. ln[M⁺].

In order to obtain average values of SK^Coul for the ensemble of all potential binding sites on 34 bp DNA for the 10 bp mode (25 sites) and the 6 bp mode (29 sites), the DNA in each structural model (Fig. 9) was shifted along its helical axis by j base pairs (j = ±1, ±2…). Values of ΔG^Coul and SK^Coul were calculated as outlined above for each position (j) of the complex. Then, an ensemble-average SK^Coul was obtained from a sum of SK^Coul for all positions weighted by exp $(-\Delta G_j^{\mathit{\text{Coul}}}/\text{RT})/{\sum }_{j}exp(-\Delta G_j^{\mathit{\text{Coul}}}/\text{RT})$. Parallel calculations were performed for all positions of the 10 bp and the 6 bp mode complexes on 15 bp DNA, and of the 6 bp mode complex on 8 bp DNA.

Prediction of Coulombic end effects (CEE) on the binding constants of the 10 bp (k₁₀) and the 6 bp (k₆) modes as a function of DNA length using the analytical CEE model

The fold-increases in k₁₀ and k₆ from 8 bp to 15 bp DNA and from 15 bp to 34 bp DNA (i.e., k_{6, 15bp}/k_{6, 8bp}, k_{6, 34bp}/k_{6, 15bp}, and k_{10, 34bp}/k_{10, 15bp}) caused by CEEs were estimated using the so-called CEE model ⁵⁶ for binding of an oligocation ligand to a DNA oligomer. The model predicts the binding free energy Δg_ij° and corresponding log-log salt concentration derivative Sk_ij for a complex involving binding mode i where the ligand position is described by index j, the number of phosphate charges in the unoccupied region between the nearer end and the bound region. Then, the position-averaged binding constant for a given mode and DNA length is the average of e^-Δgi,^j°^/RT over all potential binding sites (j) on DNA. The position-averaged Sk_i is a sum of Sk_i,_j weighted by e^-Δgi,^j°^/RT / Σ _j e^-Δgi,^j°^/RT In applying the oligocation binding model, DNA length is expressed as the number of phosphate charges (Z_D: for N bp DNA like those oligomers studied here, without terminal phosphates, Z_D = 2N – 2). Other input quantities for the oligocation model include the effective net charge on the DNA binding interface of HU (Z_L), the length of the “end” region of DNA expressed as a number of phosphate charges (N_e), and the coefficients describing a CEE for the chemical potential (G₁) and salt ion association (J₁) of a short DNA oligomer. Detailed discussions of these quantities are provided in Shkel et al. (2006). Values of Z_D are 14, 28, and 66 for 8 bp, 15 bp, and 34 bp DNA oligomers, respectively. Values of Z_L are +8 and +9 for the 10 bp and the 6 bp modes, respectively, based on the values of polymeric Sk_i (= Sk _{i, ∞} = -0.89Z_L) which are estimated from the all-atom NLPB calculations of Sk_i for these modes on 34 bp DNA (-8.2 and -7.3 for the 10 bp and the 6 bp modes, respectively). Values of N_e, G₁, and J₁ are 12 phosphates at each end, 0.015 kcal/mol (for 0.15 M Na⁺), and 0.019, respectively ⁵⁶.

The position index j was assigned to potential binding sites for a given mode, starting from the most central complex with j=Q/2 where Q is the number of phosphate charges unoccupied after binding of HU. Then, j changes by ± 2 as HU moves along DNA with a step of one base pair to each end of DNA until the total number of the complexes considered reaches N − n_i + 1.

From comparison of Sk_ij from the quadratic model to all-atom NLPB results, we found that Q = Z_D − Z_L for the 10 bp mode and Q = Z_D − Z_L + 5 for the 6 bp mode. At 0.15 Na⁺, Δg_i,_j° and Sk_i,_j are given by eqs. 28, 29, 20, and 21 of Shkel et al. (2006) for the 6 bp mode on 8 bp DNA, by eqs. 30, 31, 22, and 23 for the 6 bp mode on 15 bp and 34 bp DNA and the 10 bp mode on 34 bp DNA, and by eqs. 28, 29, 22, and 23 for the 10 bp mode on 15 bp DNA. Therefore, the fold-increases in the binding constants for the 10 bp and the 6 bp modes between different DNA lengths can be calculated at 0.15 M Na⁺, and the difference in Sk_i between different DNA lengths allows calculations of the fold-increases in the binding constants at other salt concentrations.