Contributions of the Histidine Side Chain and the N-terminal α-Amino Group to the Binding Thermodynamics of Oligopeptides to Nucleic Acids as a Function of pH

Abstract

Interactions of histidine with nucleic acid phosphates and histidine pK_a shifts make important contributions to many protein-nucleic acid binding processes. To characterize these phenomena in simplified systems, we quantified binding of a histidine-containing model peptide HWKK (⁺NH₃-His-Trp-Lys-Lys-NH₂) and its lysine analog KWKK (⁺NH₃-Lys-Trp-Lys-Lys-NH₂) to a single-stranded RNA model, polyuridylate (polyU), by changes in tryptophan fluorescence as a function of salt concentration and pH. For both HWKK and KWKK, equilibrium binding constants, K_obs, and magnitudes of log-log salt derivatives SK_obs ≡ (∂logK_obs/∂log[Na⁺]), decreased with increasing pH in the manner expected for a titration curve model in which deprotonation of the histidine and α-amino groups weakens binding and reduces its salt-dependence. Fully protonated HWKK and KWKK exhibit the same K_obs and SK_obs within uncertainty, and these SK_obs values are consistent with limiting-law polyelectrolyte theory for +4 cationic oligopeptides binding to single-stranded nucleic acids. The pH-dependence of HWKK binding to polyU provides no evidence for pK_a shifts nor any requirement for histidine protonation, in stark contrast to the thermodynamics of coupled protonation often seen for these cationic residues in the context of native protein structure where histidine protonation satisfies specific interactions (e.g., salt-bridge formation) within highly complementary binding interfaces. The absence of pK_a shifts in our studies indicates that additional Coulombic interactions across the nonspecific-binding interface between RNA and protonated histidine or the α-amino group are not sufficient to promote proton uptake for these oligopeptides. We present our findings in the context of hydration models for specific versus nonspecific nucleic acid binding.

Nucleic acid binding proteins typically possess a higher density of positively charged amino acids in the DNA or RNA binding interface relative to elsewhere on the protein surface (1,2). In a comparison of 75 protein-nucleic acid crystal structures, DNA phosphates participated in 60% of all protein-DNA hydrogen bonds (including salt bridges), of which 41% were salt bridges with lysine or arginine (1). A recent survey of 45 protein-RNA co-structures found that 68% of hydrogen bond interactions to the phosphodiester backbone were through lysine and arginine residues, with donor-acceptor distances strongly clustered within 2.5 – 3.1 Å to make the most favorable (i.e., dehydrated) hydrogen-bonds (3). The contributions of lysine (4-11) and arginine (11-13) to peptide-nucleic acid binding have been extensively characterized and demonstrate that Coulombic interactions between cationic protein residues and the polyanionic nucleic acid backbone significantly stabilize the protein-nucleic acid complex and cause binding affinity to increase strongly with decreasing salt concentration.

Histidine can also be cationic and often makes important contacts in the protein-nucleic acid interface, many of which are essential or conserved across species. For example, direct phosphate-histidine interactions are observed for E. coli CAP via the minor groove adjacent to the site of DNA bending (14,15), in the NF-κB-DNA complex at the −1 position of the DNA recognition sequence (16) and for T7 DNA polymerase with the primer phosphate backbone (17). Figure 1 shows the conserved histidine-phosphodiester interactions in the co-crystal structures of rat glucocorticoid receptor (GR) with DNA (18) and of Vts1 (a homologue of Smaug in animals) with RNA (19). Mutational studies disrupting histidine-phosphate interactions impact binding and catalytic activity for T7 polymerase with DNA (20) and ribonuclease A with RNA (21). Overall, histidine is the seventh most prevalent natural amino acid at the protein-DNA interface (1). In amino acid distribution surveys of protein-DNA (1) and protein-RNA co-structures (22), histidine exhibits respectively the sixth and fifth highest ratio of binding interface versus surface distributions. Analysis of 129 protein-DNA structures revealed that 65% of direct histidine-DNA hydrogen bonds were to the phosphate backbone (23).

Figure 1.

Representative crystal structures of conserved histidine-phosphodiester interactions. (A) The co-crystal of the rat glucocorticoid receptor DNA binding domain complexed with a glucocorticoid recognition element (pdb:1R4R) (18). (B) A co-crystal of the SAM domain of the Saccharomyces cerevisiae post-transcriptional regulator Vts1p recognizing an RNA hairpin SAM recognition element (pdb:2F8K) (19). (C) CLUSTALW analysis of a region within the glucocorticoid receptor DNA binding domain, highlighted in yellow. Database sequences were extracted from the following accession numbers: rat (Rattus norvegicus), NP_036708; human (Homo sapiens), CAJ65924; orangutan (Pongo abelii), NP_001126305; sheep (Ovis aries), NP_001107658; dog (Canis familiaris), ABA40754; mouse (Mus musculus), NP_032199; frog, NP_001081531; zebrafish (Danio rerio), NP_032199. (D) CLUSTALW analysis of the SAM RNA binding domain. Species highlighted in grey possess Smaug, a homologue of Vts1, which contains a conserved SAM domain highlighted yellow for the human sequence. Accession numbers used were Saccharomyces cerevisiae, NP_015004; Candida albicans, Q5AI80; human (Homo sapiens), NP_056404; mouse (Mus musculus), NP_083242; fruit fly (Drosophila melanogaster), NP_523987. In (C) and (D), the respective conserved histidines shown in panels (A) and (B) are highlighted in pink. The symbols below the sequence data in (C) and (D) denote CLUSTALW-defined sequence conservation: “*” indicates a fully conserved residue; “:”, strongly conserved; “.”, weakly conserved.

To our knowledge, no binding studies have been reported on histidine-nucleic acid model systems. Thermodynamic effects of histidine and other cationic residues on the thermal denaturation of DNA-oligopeptide conjugates have been reported (24), but data of this type only detect differences in interactions of the cationic residues with the native and denatured states of the nucleic acids. The frequency with which histidine is found in protein-nucleic acid interfaces suggests that histidine plays an important role in these binding processes. How does the behavior of histidine in a nonspecific ligand-nucleic acid complex compare to that seen for specific binding interactions such as those described above? What do these similarities and differences tell us? This study compares the nonspecific binding contributions of histidine versus lysine in model systems to address these questions.

The current work monitors tryptophan fluorescence as a function of pH and salt concentration to quantify the nonspecific binding of cationic peptides to single-stranded RNA in response to protonation changes of histidine and the α-amino group. Since histidine and the α-amino group are the only two basic amino acid residues which titrate near physiological pH, they are also the most likely to show any potential linkage effects between protonation and nucleic acid binding sometimes observed in native protein-nucleic acid binding processes (25-29). We examine whether protonation of histidine and the α-amino group is coupled to or independent of nonspecific RNA binding and discuss coupled protonation events within the protein-nucleic acid binding interface in the context of recent hydration studies.

BACKGROUND

McGhee-von Hippel Analysis of the Oligopeptide-DNA Binding Isotherm

The nonspecific, primarily Coulombic interactions between polyanionic nucleic acids and a variety of oligocations and proteins, including polyamines and oligopeptides similar to those studied here (4-6,8,30-36) are well described by the non-cooperative McGhee-von Hippel (30) binding isotherm,

$${\mathrm{K}}_{\mathrm{obs}}=\frac{\nu }{L_F(1-n\nu )}{\left(\frac{1-(n-1)\nu }{1-n\nu }\right)}^{n-1}.$$ (1)

This form of the McGhee-von Hippel equation assumes non-cooperative site binding of a linear ligand of arbitrary length to a linear, homogeneous infinite lattice with overlapping potential binding sites. In this case, the lattice is polyU and the ligand is the XWKK oligopeptide. L_F is the free ligand concentration. The site size (n) represents the number of adjacent phosphates (i.e., lattice residues) occluded by the binding of a single oligopeptide to the RNA. The ligand binding density (ν) represents the fraction of a ligand bound per lattice residue.

The McGhee-von Hippel isotherm and its finite lattice analog (37) have been extensively used to interpret fluorescence data (local accumulation of ligand) and equilibrium dialysis (global accumulation of ligand) for oligocation-nucleic acid interactions. Specific examples include fluorescence studies with oligolysines (4,6,34,35) and oligoarginines (13), and equilibrium dialysis studies with oligolysines (9,10), polyamines, Mg²⁺ (32), and Co(NH₃)₆³⁺ (31). Monte Carlo and Poisson-Boltzmann calculations modeling the nonspecific Coulombic accumulation of a divalent cation (Mg²⁺) in the vicinity of polynucleotides over a range of univalent salt concentration from 10 – 100 mM are well described by a McGhee-von Hippel isotherm with a site size between 2 – 3 (38). Although the McGhee-von Hippel isotherm was derived for site binding of a ligand and does not explicitly consider Coulombic or polyelectrolyte effects, its application to oligocation-polyanion data yield physically reasonable site sizes and binding constants. A comparison of the McGhee-von Hippel isotherm with alternative polyelectrolyte-based expressions for an oligocation-polyanion binding isotherm (39-41) is provided by Ni et al. (38).

Lohman and coworkers developed a quantitative fluorescence titration protocol that has been used extensively to obtain thermodynamic binding parameters of protein-nucleic acid interactions and is readily applied to oligopeptide-DNA/RNA binding (4-6,13,34,42,43). For ligands including E. coli SSB protein and various small oligopeptides, Lohman and coworkers found that the fractional fluorescence quenching (Q_obs/Q_max), where Q_max is defined as the maximum quenching of the oligopeptide obtained at saturation, was equal to the fraction of ligand bound (L_B/L_T),

$$\frac{Q_{\mathit{obs}}}{Q_{\max }}=\frac{L_B}{L_T}.$$ (2)

From eq.2, ν and L_F of the McGhee-von Hippel equation (eq.1) can be expressed in terms of experimentally accessible variables,

$$\nu \equiv \frac{L_B}{R_T}=\left(\frac{Q_{\mathit{obs}}}{Q_{\mathit{max}}}\right)\left(\frac{L_T}{R_T}\right),$$ (3)

$$L_F=\left(1-\frac{Q_{\mathit{obs}}}{Q_{\mathit{max}}}\right)\left(L_T\right).$$ (4)

L_T and R_T are the total concentrations of ligand and RNA phosphate, and L_B is the concentration of bound ligand (4,6).

Effects of 1:1 Salt Concentration on K_obs

Binding interactions of nucleic acids with charged ligands are highly sensitive to salt concentration. At low to moderate salt concentrations ([NaCl] < 0.5 M), DNA and RNA binding constants of oligocations and proteins typically exhibit a power-law dependence on the activity (concentration) of univalent salt which can be expressed as the log-log derivative

$${\mathrm{SK}}_{\mathrm{obs}}\equiv \left(\frac{\partial {\log K}_{\mathrm{obs}}}{\partial \log \left[{\mathrm{Na}}^{+}\right]}\right)\cong \Delta {\Gamma }_{+}+\Delta {\Gamma }_{-},$$ (5),

where the ΔΓ terms are differences in preferential interaction coefficients for the interaction of the Na⁺ cation (ΔΓ₊) and the Cl⁻ anion (ΔΓ₋) with the complex vs. the uncomplexed reactants in the oligocation-nucleic acid binding process. SK_obs quantifies the thermodynamic consequences of the differences in preferential interactions of the monovalent salt ions (i.e., Na⁺ and Cl⁻) with the complex and with the reactants (36,44,45). Below 0.25 M salt, the nature of the monovalent salt ions do not significantly impact SK_obs for Z_L < 10 ligands binding to polyU (4,6), allowing comparisons of SK_obs across experimental systems even when obtained using different monovalent salts.

For the binding of a homologous series of cationic oligopeptides and polyamines to polyanionic DNA or RNA, logK_obs varies linearly as a function of [Na⁺]

$${\log K}_{\mathrm{obs}}={\log K}_0+\left({\mathrm{SK}}_{\mathrm{obs}}\right)\log \left[{\mathrm{Na}}^{+}\right],$$ (6)

where K₀ is the extrapolated value of K_obs at 1 M salt (4,8,32). Experimentally, SK_obs is independent of [Na⁺] and proportional to Z_L, the charge on the binding surface of the oligopeptide. The large magnitude of SK_obs and the independence of SK_obs versus salt concentration result primarily from the polyelectrolyte character of nucleic acids (35,46). Record et al. (8) predicted a thermodynamic limiting law (low [salt]) expression for SK_obs for oligocation-polyanion binding

$${\mathrm{SK}}_{\mathrm{obs}}\cong -Z_L\psi ,$$ (7)

where Z_L is the valence of the oligocation ligand and ψ represents the net thermodynamic extent of salt ion accumulation per phosphate of uncomplexed DNA (7,8,47,48). Experimentally, ψ ≈ 0.88 for double stranded DNA (47) and ψ ≈ 0.74 for single stranded nucleic acids (4,6). Equation 7 is a special case of the general expression for SK_obs in eq. 5. Although derived as a limiting law, equation 7 is found to describe oligocation-polyanion binding data at higher salt concentration, possibly because of compensating salt concentration dependences of preferential interaction coefficients for the ligand and macromolecule (36,49).

Cylindrical Poisson-Boltzmann theory (50) and counterion condensation theory (8,51) predict that at low salt (limiting law) conditions,

$$\psi =1-\frac{1}{2\xi },$$ (8)

where the reduced axial charge density, ξ, is

$$\xi =\frac{e^2}{\epsilon kTb}.$$ (9)

Here, e is the electronic charge, ε is the bulk dielectric constant of water, k is the Boltzmann constant, T is the absolute temperature, and b is the axial charge spacing of the polyelectrolyte. In water at 25 °C, ξ = 7.14/b, where b is in units of Angstroms (Å). We use equations 6 - 9 as the basis for analyzing the effects of pH on K_obs and SK_obs, as described below.

The Effects of pH on logK_obs and SK_obs

1) Titration curve model

The effects of pH on the interactions of pentalysine with double stranded DNA were shown to fit a “titration” curve model (7) where at fixed salt concentration, the dependence of K_obs on pH is determined by the pH-dependence of free ligand valence (Z_L). In this model, Z_L does not increase upon binding to nucleic acids, i.e., the pK_a of the titratable groups on the oligopeptide are not affected by binding to DNA. For the simple case of independent titratable functional groups on the oligopeptide, the dependence of Z_L on [H⁺] is given by

$$Z_L=Z_L^{\max }-\sum _{i=1}^g\frac{1}{1+k_{i,L}\left[{\mathrm{H}}^{+}\right]},$$ (10)

where Z_L is the valence at a given pH, $Z_L^{\mathit{max}}$ is the maximum valence at low pH ($Z_L^{\mathit{max}}=4$ in the present study), k_i,L is the equilibrium protonation constant of the i-th titratable group on the oligopeptide, and g is the number of groups titrating in the pH range of interest (6,7,47). Assuming that the two lysines at the C-terminal end of XWKK are always protonated at the pH and salt concentrations studied here, Z_L can be expressed as

$$Z_L=Z_L^{\max }-\frac{1}{1+k_{{\mathit{NH}}_3^{+}}\left[{\mathrm{H}}^{+}\right]}-\frac{1}{1+k_X\left[{\mathrm{H}}^{+}\right]},$$ (11)

where k_x is the protonation constant for the side chain of residue X (lysine or histidine) in XWKK and $k_{{\mathit{NH}}_3^{+}}$ is the protonation constant for the N-terminal α-amino group. The uridylate moieties in polyU are also expected to deprotonate at sufficiently high pH, which in turn will reduce the axial charge spacing b. Taking the assumption of Mascotti and Lohman (6), we model the pH-dependence of b as

$$\frac{b_0}{b}=1+\frac{1}{1+k_U\left[H^{+}\right]},$$ (12)

where b₀ is the average charge spacing of polyU at neutral pH and k_U is the protonation constant of uridylate.

Provided that any salt concentration dependences of $k_{{\mathit{NH}}_3^{+}}$ , k_x, and k_U are negligible and that eq.7 for SK_obs is valid in the range of salt concentration of interest, the dependence of logK_obs on pH from eq. 6 - 9 is

$${\log K}_{\mathrm{obs}}-{\log K}_0=-\psi \left(Z_L^{\max }-\frac{1}{1+k_{{\mathit{NH}}_3^{+}}\left[{\mathrm{H}}^{+}\right]}-\frac{1}{1+k_X\left[{\mathrm{H}}^{+}\right]}\right)\log \left[{\mathrm{Na}}^{+}\right],$$ (13)

where ψ is

$$\psi =1-\frac{b_0}{14.28}\left(1+\frac{1}{1+k_U\left[H^{+}\right]}\right)$$ (14)

and K₀ is the extrapolated binding constant in the 1 M Na⁺ reference state. From eq. 7 and 11,

$${\mathrm{SK}}_{\mathrm{obs}}=-\psi \left(Z_L^{\max }-\frac{1}{1+k_{{\mathit{NH}}_3^{+}}\left[{\mathrm{H}}^{+}\right]}-\frac{1}{1+k_X\left[{\mathrm{H}}^{+}\right]}\right)$$ (15)

withψ as defined in eq. 14. In this model, any protonation state of the unbound oligopeptide can bind to RNA, with K_obs and the magnitude of SK_obs increasing with increasing protonation (i.e., greater Z_L). At sufficiently low pH where all of the sites are protonated (i.e., $Z_L=Z_L^{\max }$), both K_obs and SK_obs will become insensitive to pH.

2) Coupled Protonation Model

As an extreme alternative model, if protonation of the peptide were driven by complex formation so that the bound state of the peptide was the fully protonated state, then

$${\mathrm{SK}}_{\mathrm{obs}}=-\psi \left(Z_L^{\max }\right),$$ (16)

predicting that SK_obs would be to be independent of pH. However, logK_obs should still decrease with an increase in pH because of the increasing thermodynamic cost of protonating groups on the oligopeptide as the pH increases. This effect should give rise to a pH-dependence of K₀ and hence of K_obs:

$${\mathrm{K}}_0=K_0^0\sum _{i=1}^g\frac{k_{i,L}\left[{\mathrm{H}}^{+}\right]}{1+k_{i,L}\left[{\mathrm{H}}^{+}\right]},$$ (17)

where in the pH range of our experiments (5.2 – 8.7), g = 1 or 2 for KWKK and g = 2 for HWKK. $K_0^0$ is the 1 M Na⁺ extrapolated binding constant in the limiting case when all titratable sites on the ligand are protonated. As the pH increases, K₀ decreases, thus reducing K_obs. Although the pH dependence of K_obs cannot be used to distinguish between the coupled protonation model and the titration curve model within an experimentally accessible range, the pH dependence of SK_obs can be so used. The titration model predicts that SK_obs should decrease in magnitude with increasing pH. In contrast, if protonation is coupled to binding, SK_obs is expected to be independent of pH.

EXPERIMENTAL PROCEDURES

Buffers and Reagents

Reagents used were reagent grade, purchased from either Sigma Chemical Company (St. Louis, MO) or Fisher Scientific (Pittsburgh, PA). All solutions were prepared with 18 Mohm/cm deionized water. All buffers contained 0.2 mM Na₂EDTA and were titrated to the indicated pH with concentrated HCl. The pH 5.2 buffer was 3 mM sodium acetate, the pH 6 buffer was sodium cacodylate, pH 7 – 8 buffers were 3 mM sodium HEPES, and the pH 8.7 buffer was 2.5 mM sodium borate. “High salt” and “low salt” solutions were prepared with 0.2 mM Na₂EDTA and the specified buffer, with and without 1 M NaCl, respectively. Intermediate salt concentrations at a given pH were obtained using linear combinations of the low salt and high salt buffers.

Peptides

Oligopeptides of the general form XWKK, where the α-amino terminus is positively charged, the C-terminus is capped as an amide, and “X” is lysine or histidine, were synthesized, purified, lyophilized, and validated by matrix-assisted laser desorption ionization mass spectroscopy by the University of Maryland Biopolymer Core Facility. Stock peptide concentrations were determined spectrophotometrically from the 280 nm absorbance of the tryptophan in 6 M guanidinium chloride using ${\epsilon }_{280}^{\mathrm{Trp}}=5690{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$ (52). The extinction coefficients of the oligopeptides dissolved in the buffers described above (3 – 5 mM Na⁺) were then experimentally measured for use in determining the inner-filter corrections (see above) for the fluorescence titrations performed (${\epsilon }_{292}^{\mathrm{HWKK}}=3380\pm 50{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$, ${\epsilon }_{292}^{\mathrm{KWKK}}=3140\pm 110{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$, ${\epsilon }_{350}^{\mathrm{XWKK}}<5{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$). The resulting inner-filter correction is small relative to the corresponding correction due to the RNA concentration (see below).

polyU single-stranded RNA

The potassium salt of polyuridylic acid (polyU) was manufactured (lot # 011805) by the Midland Certified Reagent Company (Midland, TX). After synthesis, phenol/chloroform/isoamyl alcohol extraction and extensive dialysis against potassium chloride, the polyU was exhaustively dialyzed against deionized water to remove excess salt and then lyophilized by the manufacturer. Analytical polyacrylamide gel electrophoretic analysis indicated that the polyU substrates ranged between 40 – 200 bases in length. Studies of the transition between oligomeric versus polymeric binding for oligopeptides associating with single stranded nucleic acids found that a ligand with Z_L ≤ 4 binds the central site of a nucleic acid with 22 or more charges with the same affinity as the central site of a polymeric nucleic acid (53,54). As such, XWKK is predicted to bind this distribution of polyU lengths equivalently in the low binding density limit reported by the McGhee-von Hippel isotherm (23). Extinction coefficients of the RNA were determined for use with the inner-filter corrections (${\epsilon }_{292}^{\mathrm{RNA}}=160\pm 40{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$, ${\epsilon }_{350}^{\mathrm{RNA}}\sim 0{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$). The inner-filter correction (42) due to the RNA concentration in the cuvette can result in as much as a 17% change in fluorescence intensity.

Bioinformatics

Sequence alignments were prepared using the CLUSTALW Version 3.2 software package available via the World Wide Web at the San Diego Supercomputing Center Workbench (http://www.workbench.sdsc.edu).

Fluorescence Quenching Studies of Oligopeptide Binding

Oligopeptide binding to polyU was monitored by tryptophan fluorescence quenching with a Cary Eclipse spectrofluorometer (Varian Instruments) equipped with a Peltier temperature controller maintaining solution at 25 °C. The excitation wavelength was 292 nm with a bandpass of 2.5 nm, and the emission wavelength was 350 nm with a bandpass of 10 nm. These wavelengths were chosen to minimize the inner-filter corrections and RNA absorbance (42). Solutions of the oligopeptides and RNA used in the fluorescent titrations were prepared from freezer stocks and diluted to identical buffer and salt concentration conditions. All titrations were performed in 1×1 cm square quartz cuvettes to allow for “crown” stir-bar mixing during titration and measurement. After addition of titrant (either with polyU during the “reverse titration” or with “high salt” buffer during “saltbacks”) to the oligopeptide solution, samples were incubated with stirring for at least one minute before measurement. Photobleaching of tryptophan in XWKK was minimized by illuminating the sample only during measurement. For comparison, unbound KWKK and HWKK exhibited less than 3% loss in fluorescence after an hour of continuous irradiation (data not shown). To correct for Raman light scattering from the water and any background fluorescent emission, the fluorescence of a buffer solution (no oligopeptide present) that was at the equivalent RNA and salt concentration in the titration was subtracted from the fluorescent signal of the sample. The extent of tryptophan fluorescence quenching is thus defined as

$$Q_{\mathit{obs}}\equiv \frac{F_0-F_{\mathit{obs}}}{F_0},$$ (18)

where F_obs is the observed fluorescence intensity at a given point in the titration and F₀ is the initial fluorescence intensity of the free ligand (i.e., oligopeptide). All fluorescence intensities were corrected for background fluorescence, dilution, inner-filter contributions, and photobleaching effects as described previously (35,42).

Reverse Titrations

Isotherms of either HWKK or KWKK binding to polyU were generated by “reverse titration”: 1 – 10 mM stock solutions of RNA were titrated into cuvettes containing 1 – 8 μM of XWKK. Titrations continued until binding saturation was observed or a maximum concentration of 0.3 mM RNA phosphate was achieved, a limit dictated by the approximations used for inner-filter correction. Values of Q_obs (eq. 18) as a function of XWKK and polyU concentrations were then used to calculate binding affinity (see below).

HWKK deprotonates to a greater extent relative to KWKK within the range of pH considered, resulting in decreased binding affinity at moderate and high pH values. To maintain oligopeptide-RNA binding affinity within measurable limits yet allow for direct comparison of binding affinities across the full pH range, titrations were performed at the common salt concentrations of 24.4 mM Na⁺ for KWKK and 9.8 mM Na⁺ for HWKK (Table 1).

Table 1.

pH dependence of McGhee-von Hippel logK_obs and SK_obs as a function of amino acid composition

pH	logKobsa	SKobsb	logK0b (1 M Na+)	Qmaxc (%)
	KWKK (24.4 mM Na+)
5.2	5.06 ± 0.02	−3.06 ± 0.09	0.10 ± 0.12	0.91 ± 0.01
6.0	4.88 ± 0.01	−3.05 ± 0.06	0.01 ± 0.09	0.91 ± 0.01
7.0	4.69 ± 0.02	−2.94 ± 0.06	−0.06 ± 0.08	0.91 ± 0.02
8.0	4.16 ± 0.01	−2.59 ± 0.06	−0.01 ± 0.09	0.91 ± 0.02
8.7	3.77 ± 0.02	−2.45 ± 0.11	−0.13 ± 0.17	0.87 ± 0.01d
	HWKK (9.8 mM Na+)
5.2	5.98 ± 0.02	−2.84 ± 0.10	0.25 ± 0.15	0.92 ± 0.02
6.0	5.23 ± 0.02	−2.55 ± 0.09	0.09 ± 0.12	0.93 ± 0.01
7.0	4.59 ± 0.02	−2.21 ± 0.06	0.11 ± 0.11	0.93 ± 0.01
8.0	3.83 ± 0.02	−1.93 ± 0.07	−0.01 ± 0.12	0.88 ± 0.01e
8.7	3.38 ± 0.02	−1.64 ± 0.13	0.14 ± 0.24	0.81 ± 0.02e

^aDetermined by global nonlinear least squares analysis of data collected at 25 °C across multiple oligopeptide concentrations at the specified salt concentration using the noncooperative McGhee-von Hippel equation (eq. 1) with the indicated Q_max and n = 5. Errors represent 95% confidence intervals.

^bSK_obs and logK₀ values were calculated by nonlinear least squares analysis of aggregate logK_obs versus [Na⁺] data from reverse titrations and saltbacks. Saltback logK_obs data were obtained using the indicated Q_max and n = 5 via eq. 1 – 4.

^cCalculated via model-independent ligand binding density analysis (42) of reverse titration data at the specified salt concentration.

^dWhen binding was weaker than K_obs ≲ 10⁴ M⁻¹, Q_max was found by ligand binding density analysis using data collected at the same pH but lower salt concentration to improve the accuracy of the determination (cf. Figure S1). At high pH, Q_max is reported at 12.4 mM Na⁺ for KWKK

^eWhen binding was weaker than K_obs ≲ 10⁴ M⁻¹, Q_max was found by ligand binding density analysis using data collected at the same pH but lower salt concentration to improve the accuracy of the determination (cf. Figure S1). At high pH, Q_max is reported at 5.4 mM Na⁺ for HWKK.

Salt Back Titrations

Salt concentration dependences of the oligopeptide-RNA binding equilibrium were determined in part via “saltback” titrations, where the pre-equilibrated XWKK-RNA complex was titrated with the “high salt” buffer with the appropriate pH (see Buffers and Reagents section above), monitoring the increase in fluorescence and therefore the decrease in quenching Q_obs, as the salt concentration of the solution increases. After all corrections were applied (i.e., background fluorescence, dilution, inner-filter, photobleaching), more than 90% of the original fluorescence of the free oligopeptide is recovered, indicative of the reversibility of oligopeptide-RNA complex formation. SK_obs and logK₀ values determined by saltback titrations were supported by at least three independent reverse titration determinations of K_obs at various salt concentrations, with each K_obs derived from at least three isotherms (see below and Figure 5).

Figure 5.

Dependence of logK_obs on [Na⁺] and pH. logK_obs, determined directly by global analysis of multiple reverse titrations (black symbols) or via calculation using eq. 1, 2 and 4 and saltback data (red symbols) are plotted as a function of pH and salt concentration. Black solid lines represent linear least squares fits of combined reverse titration and saltback data (reported in Table 1). Green solid lines indicate the predicted dependence of logK_obs on [Na⁺] and pH using eq. 13 - 14 and parameters found by global nonlinear least squares analysis of all logK_obs vs [Na⁺] data (Table 2).

Analysis of Oligopeptide-RNA Binding Isotherms

The binding constant K_obs was determined from reverse titration data by fitting to the non-cooperative McGhee-von Hippel (30) binding isotherm (eq. 1). The parameters ν and L_F were determined via eq. 2 - 4. Q_max was calculated by global analysis of 3 – 7 isotherms for XWKK concentrations ranging between 1 – 8 μM using the model-independent method of ligand binding density (LBD) analysis (42). The nonlinear least squares program NONLIN (55) was used to fit logK_obs and n to eq.1 - 5 using a fixed Q_max obtained by LBD analysis. Q_max converged to the LBD-determined value when allowed to float for titrations where K_obs ≳ 10⁵ M⁻¹ and in global analysis of multiple reverse titrations across 4 – 6 salt concentrations (data not shown). The site size parameter, n, was typically not integral when allowed to float during nonlinear fitting. Any Coulombic or other source of negative or positive cooperativity that may exist has effectively been absorbed by n and these factors may be responsible for the nonintegral n. Nevertheless, no dependence of n on the values of ν or L_F has been found in this or previous studies. Site size was indistinguishable from or near n = 5 in global analysis of reverse titration data obtained at a common pH (Table SI). The n ≈ 5 site size was also determined using a model-independent approach (see Results). Unless otherwise indicated, binding constants and their salt dependence are reported using a site size fixed at n = 5.

logK_obs as a function of salt concentration was directly calculated for saltback data via eq. 1 using a constant Q_obs determined by LBD analysis and site size n = 5. To facilitate comparison of HWKK versus KWKK binding to polyU in Figure 6, logK_obs data for HWKK at 24.4 mM Na⁺ was linearly interpolated via eq.6 and the SK_obs and logK₀ parameters listed in Table 1. All K_obs data (Figure 5) were globally fit to eq.13 as a function of salt concentration and pH, with parameters listed in Table 2.

Figure 6.

Model description of XWKK-polyU logK_obs and SK_obs as a function of pH. (A) LogK_obs for XWKK binding to polyU at 25 °C and 24.4 mM Na⁺ are plotted as a function of pH. KWKK logK_obs was directly determined from reverse titration data (●), whereas HWKK logK_obs (○) was interpolated via eq. 6 using the parameters in Table 1. Curves represent the global nonlinear least squares fit of the combined logK_obs vs [salt] and pH data in Figure 6 to eq. 9 (Table 2). (B) SK_obs, as reported in Table 1, is plotted as a function of pH for KWKK and HWKK. Curves represent the fits to eq. 13 - 14 using the parameters in Table 2.

Table 2.

Global fit parameters describing the pH dependence of logK_obs and SK_obs versus amino acid composition^a

peptide		logK0 (1 M Na+)	pKa
	ψ		Histidine	αNH3+
KWKK	0.77 ± 0.01	0.02 ± 0.07	---	7.57 ± 0.08
HWKK	0.76 ± 0.03	0.12 ± 0.10	5.75 ± 0.18	7.86 ± 0.13

^aValues reported are the globally fitted values to eq. 13 for all reverse titration and salt back data in Figure 5 (N ≈ 70 – 71 data points each). Errors represent 95% confidence intervals for the global fit.

Statistical comparison of fitting parameters and thermodynamic models

Several times in this study, we assess whether adding complexity to our models dramatically improves the description of the data. The F-test is a common means to determine the statistical significance of adding terms to nested models (i.e., a series of models where fixing parameters to some value such as 0 or 1 generates a simpler expression from a more complex one). However, both the McGhee-von Hippel isotherm (eq.1) and the titration binding model (eq.13 - 15) are nonlinear equations where terms cannot be eliminated by setting a parameter to a constant value. The second-order Akaike Information Criterion (AIC_c) (56,57) is a well accepted alternative to the F-test which does not have the nested-model restriction:

$${\mathrm{AIC}}_{\mathrm{c}}=N\ln \left(\frac{S{S}_{\mathit{res}}}{N}\right)+2(p+1)+\frac{2(p+1)(p+2)}{N-p-2}$$ (19),

In eq.19, N is the number of data points, SS_res is the residual sum of squares of the fit, and p is the number of parameters in the model. The AIC_c is calculated for each model considered. For two models “A” versus “B”, the better model has a smaller (or more negative) AIC_c. When AIC_c scores are close in value, the probability that one model is favored over the other is defined by

$$\text{probability}=\frac{e^{-\Delta {\mathrm{AIC}}_{\mathrm{c}}}}{1+e^{-\Delta {\mathrm{AIC}}_{\mathrm{c}}}}$$ (20),

where ΔAIC_c = AIC_c,B – AIC_c,A. The evidence ratio (also called the relative likelihood) is the ratio of the probability (eq. 20) favoring model “A” versus the probability favoring “B.” The evidence ratio can be calculated directly by e^0.5ΔAIC_c since the ΔAIC_c values for these two cases are related by a sign inversion. As an example, if “A” is favored over “B” with a ΔAIC_c = 6.0, model “A” has a ~95% probability of being a better description of the data in comparison to “B” (with a ~5% chance). The evidence ratio of A/B states that “A” is 20-fold more likely than “B” to be the correct model (56). Model comparisons are reported using ΔAIC_c or evidence ratios if ΔAIC is small. We arbitrarily define that a model is convincingly preferred when ΔAIC_c has a magnitude of 6.0 or greater (evidence ratio ≥ 20).

RESULTS

The work presented here compares polyU binding by HWKK, which has not been studied before, with the previously characterized KWKK (4-6,13) to determine how the change from lysine to histidine affects binding affinity K_obs (eq. 1), its salt dependence SK_obs, and site size over a range of pH in which histidine and the α-amino group deprotonate. Titrations under stoichiometric binding conditions were used to determine a model-independent site size of XWKK on polyU (Figure 2). The titrations were performed at low salt (3.4 mM Na⁺) and low pH (pH 5.2) to maximize binding affinity (logK_obs ≥ 7.3). The site size is indicated by the intersection of the polyU concentration-dependent regime with the polyU concentration-independent plateau. The invariance of the intersection point across three titrations over a two-fold concentration range suggests that n ≈ 5 is a true site size for KWKK and HWKK binding to polyU at pH 5.2.

Figure 2.

Determination of XWKK site size on polyU by stoichiometric binding. Titrations of (A) KWKK or (B) HWKK as a function of initial oligopeptide concentration (see legend above) at 3.4 mM Na⁺ and 25 °C (i.e., high affinity conditions). Intersection of the linear least square fits of the two regimes (dashed purple lines) is indicated by a light purple dotted line for clarity. The intersections for indicate a site size n = 5.3 ± 0.1 for KWKK and n = 5.4 ± 0.1 for HWKK.

Figure 3 shows a typical series of reverse titration binding isotherms. As the initial oligopeptide concentration is increased, increasing amounts of polyU are required to achieve an equivalent level of binding saturation. The HWKK isotherms are well described by the noncooperative McGhee-von Hippel model, as has been shown for KWKK (4-6,13). Mg²⁺ (8) and model peptides (34,46) bind to nucleic acids with McGhee-von Hippel site sizes approximately equal to the net charge of the ligand. However, constraining the site size to n = 4, the number of ligand charges neutralized in the XWKK-polyU complex, results in a statistically poorer fit relative to n = 5 (Figure 3, dashed versus solid lines; Table SI). Site size converges to n ≈ 5 when allowed to float as a parameter (Table SI; Figure 3, solid lines), consistent with the model-independent determination of site size in Figure 2. At pH 6, increasing n from 4 to 5 increases K_obs 35% and decreases ΔG^o by about 3%; this site size effect on K_obs decreases at higher pH.

Figure 3.

Titrations of the oligopeptide HWKK with polyU. Titrations at three HWKK concentrations (2 μM (○), 4 μM (●), and 6 μM (□)) observed as function of tryptophan fluorescence quenching (eq. 14) at 9.8 mM Na⁺, pH 6.0, and 25 °C. The concentration of polyU is given in moles of nucleotides per liter. Solid and dashed lines are the nonlinear least squares global fits across all three titrations using eq. 1, 3, and 4, with Q_max = 0.93 as determined by ligand binding density analysis (35). The dashed line reports the McGhee-von Hippel isotherm with logK_obs = 5.11 ± 0.02 with a site size fixed at n = 4. The solid line isotherm shows the fit with the site size allowed to float (logK_obs = 5.22 ± 0.02, n = 4.96 ± 0.11). If all parameters are allowed to float, logK_obs = 5.23 ± 0.03, Q_max = 0.929 ± 0.007, and n = 4.97 ± 0.13 (data not shown in plot above).

Calculation of binding affinity requires knowledge of how binding density ν varies as a function of free oligopeptide concentration L_F. Q_obs can be directly related to ν and L_F through Q_max (eq. 3 - 4). The upper asymptote, and thus Q_max, is easily defined when binding is saturable (e.g., at low pH and/or low [Na⁺]; cf. HWKK at pH 5.2 in Figure 4). However, with weaker binding, uncertainty in the estimation of Q_max from a single isotherm dramatically increases as the upper asymptote becomes more difficult to reach. Ligand binding density (LBD) analysis provides a model-independent means of determining Q_max and other thermodynamic parameters (42,58). Mascotti and Lohman applied LBD analysis to nucleic acid binding studies of a series of oligopeptides KWK_x (x = 1 – 8), including KWKK. Figure S1 presents the results of LBD analysis of KWKK and HWKK, plotting Q_obs as a function of L_B/L_T. Because Q_obs is a linear function of the fraction of peptide bound (L_B/L_T), eq. 3 shows that binding density ν is also a linear function of Q_obs, and by extension, L_F can be calculated using eq. 4. Extrapolation of L_B/L_T to 1 allows calculation of Q_max without requiring XWKK binding saturation. Q_max was insensitive to salt concentration in the range considered (data not shown). Q_max was relatively constant over pH 5.2 – 7, decreasing at pH 8 for HWKK and pH 8.7 for KWKK (Table 1 and Figure S1). The pH dependence of XWKK Q_max is consistent with previous reports showing that Q_max was proportional to net oligopeptide charge for a series of oligolysines (Z_L ≤ 4) binding to polyU (6), suggesting that tryptophan fluorescence quenching is modulated by net differences in adjacent charge, whether by deprotonation in the case of XWKK, or by the presence of additional lysines at the C-terminus, in the work of Mascotti and Lohman (6).

Figure 4.

XWKK binding isotherms as a function of pH. Titrations of (A) KWKK at 24.4 mM Na⁺ or (B) HWKK at 9.8 mM Na⁺ as a function of polyU. Data from titrations peformed at 25 °C with 4 μM oligopeptide are presented for each pH with the following symbols: (●), pH 5.2; (○), pH 6.0; (■), pH 7.0; (□), pH 8.0; (◆), pH 8.7. Curves represent fits determined by global nonlinear least squares analysis across all oligopeptide concentrations (2 – 6 μM) at the specified pH and salt concentration (cf. Figure 3). Lines represent the best global fits to the data when the site size is constrained to n = 4 (dashed lines) or n = 5 (solid lines; Table 1).

Using Q_max determined by LBD analysis and eq. 2 - 4 to calculate ν and L_F, we assessed the pH sensitivity of XWKK-polyU binding for HWKK relative to KWKK (Figure 4). KWKK binding is only moderately affected at low pH, with marked decreases at pH 8 and 8.7. In contrast, logK_obs for HWKK is a strong function of pH and is weaker than KWKK at neutral pH even at a relatively lower salt concentration which favors tighter binding (9.8 mM Na⁺ versus 24.4 mM Na⁺). With the exception of HWKK at pH 7.0 which has a fitted n = 4.36 ± 0.36, the McGhee-von Hippel site size is invariant at n = 5.0 within error across the full 5.2 – 8.7 pH range for both HWKK and KWKK (Table SI).

The linear dependence of Q_obs on binding density and the apparent invariance of site size across salt concentration and pH permits simple calculation of K_obs from eq. 1, 3, and 4 for a given Q_obs. In cases where NaCl titration of preformed XWKK-polyU complexes results in full recovery of the initial tryptophan fluorescence, “saltback” titrations provide a much more direct route to calculating the salt dependence of logK_obs via eq. 6. Figure 5 presents the logK_obs data as a function of salt concentration and pH for KWKK and HWKK. Black symbols represent reverse titration data measured and analyzed across 3 – 7 oligopeptide concentrations, while red symbols indicate logK_obs values determined via the saltback methodology (42). The colinearity of logK_obs vs. log[Na⁺] data observed by reverse titration versus saltback approaches suggests that saltback measurements accurately reflect the salt dependence of polyU-binding affinity for KWKK and HWKK. In light of this observation, the reverse titration and saltback data were analyzed as a whole. Black lines in Figure 5 represent linear least squares fits of logK_obs vs. log[Na⁺] for each peptide and pH. Green lines indicate the predicted salt dependence of binding affinity using eq.13 and parameters determined by global nonlinear least-squares analysis of the combined logK_obs data from reverse titrations and saltbacks across the full pH range (Figure 5). The SK_obs of HWKK-polyU shows a steep magnitude decrease as pH increases (Table 1), reflected in more shallow slopes in the salt dependence of logK_obs in Figure 5B. KWKK in Figure 5A also exhibits a decreased SK_obs magnitude at high pH, although to a lesser extent than HWKK. The small magnitude of logK₀ (the residual binding affinity at 1 M Na⁺ where polyelectrolyte contributions are considered to be negligible) indicates that the polyelectrolyte effect accounts for the majority of the ΔG^o of the binding interaction for XWKK (Table 1). This is consistent with previous oligocation-nucleic acid binding studies (4-8,11,32,35,46,53).

XWKK binding affinity K_obs and its salt dependence SK_obs are presented in Figure 6. To facilitate comparison to the KWKK logK_obs data, HWKK logK_obs values were interpolated to 24.4 mM Na⁺ by eq. 6 using the SK_obs and logK₀ parameters reported in Table 1. The same global analysis which generated the green logK_obs vs log[Na⁺] fits in Figure 5 are presented as a function of pH in Figure 6. At low pH, K_obs of HWKK approaches K_obs of KWKK, indicating that the nucleic acid binding free energy contribution of protonated histidine is similar to that of lysine. The titration model (eq. 13 - 15) is overwhelmingly favored over the proton-uptake model (eq. 16 - 17) to describe the pH dependence of polyU-binding for KWKK (evidence ratio = 2 × 10¹⁹) and HWKK (evidence ratio =2 × 10³⁹). In other words, the titration model which accounts for changes in the oligopeptide Z_L charge (eq.10), coupled to SK_obs through ψ (eq. 7) and thus to logK_obs by eq. 6, describes all of the observed binding phenomena for both HWKK and KWKK across changes in salt concentration and pH. The net thermodynamic ion accumulation around each polyU phosphate was equivalent for KWKK and HWKK withψ ^KWKK = 0.77 ± 0.01 and ψ ^HWKK = 0.76 ± 0.03 (Table 2), consistent with literature values for KWKK (ψ = 0.78 ± 0.05) and its KWK_x variants (compositeψ = 0.74 ± 0.04) at pH 6 (4,6).

With increasing pH, HWKK-polyU binding exhibits two observable deprotonation events with pK_a values of 5.75 ± 0.18 and 7.86 ± 0.13 for the histidine imidazole and the α-amino group, respectively. The fitted α-amino pK_a for KWKK was 7.57 ± 0.08 in agreement with previous results (6). Accounting for potential lysine ε-NH₃⁺ deprotonation at pH > 8 by adding a second titration term to the fixed-ψ model provides a minor improvement to the fit as judged by comparison of the second-order Akaike Information Criteria (AIC_c) with a only 78% probability favoring the two pK_a fixed-ψ model (evidence ratio = 3.5). Additional model complexity compensating for uracil deprotonation through eq.14 was not necessary for HWKK (99% probability favoring the fixed-ψ model; evidence ratio = 79.1) or the two-pK_a model for KWKK (37% favoring the 2-pK_a titrating-ψ model with ΔAIC_c= 1.05; evidence ratio = 1.7). However, fitting KWKK to the single-pK_a model was dramatically improved by using eq.14 in lieu of a fixed-ψ model (ΔAIC_c= 38.4). Including the potential deprotonation of uracil or of lysine by increasing g = 1 to g = 2 in eq.10 contributes another KWKK-polyU titration event with a pK_a ≥ 9.6 (Figure S2). Inspection of Figure S2 suggests that the KWKK preference for an additional alkaline pK_a is dictated predominantly by the pH 8.7 data. Indeed, all other KWKK-polyU fitted parameters (α-amino pK_a, logK₀, and ψ fitted directly or through eq.14 using the fitted b₀) were equivalent within error across the four model variants. Taking all of these factors in consideration, we chose the fixed-ψ mode using a single titratable group for KWKK and two titratable groups for HWKK to describe XWKK binding data in Figures 5 - 6 and Table 1.

DISCUSSION

Protonation of histidine and N-terminal α-amino residues on HWKK and KWKK is not required for binding to polyU

This study determines whether nonspecific nucleic acid-binding exhibits pK_a shifts of titratable amino acid moieties in histidine- and lysine-containing peptides. Three observations indicate that both KWKK and HWKK bind to polyU without pK_a shifts and coupled uptake of protons. First and foremost, the pK_a values found here for histidine, lysine, and the α-amino group are consistent with pK_a measurements for free oligopeptides. Second, the magnitude of SK_obs decreases with increasing pH (Figures 5 - 6), indicating that the number of positive charges and therefore the protonation state of HWKK and KWKK in the complex with polyU decreases with increasing pH, consistent with the titration model (eq.15) and not the coupled protonation model (eq.16). Finally, logK₀, which is small in magnitude and does not vary significantly with increasing pH, does not reflect the decrease in K₀ predicted by the coupled protonation model (eq.17) to account for the enthalpic cost of stabilizing the peptide-polyU complex by proton uptake. Our demonstration that histidine and α-amino group protonation is intrinsically uncoupled from nonspecific nucleic acid binding indicates that the histidine pK_a shifts observed for many specific protein-nucleic acid recognition processes require additional noncovalent interactions to stabilize the protonated state which are not available in generalized nonspecific binding interfaces.

Histidine-polyU binding thermodynamics are well described by limiting law polyelectrolyte theory

Polyelectrolyte theory developed in the limit of low monovalent salt concentration and near-zero macromolecule binding density accurately describes XWKK-polyU binding between pH 5.2 – 8.7 and 5.4 – 200 mM Na⁺. The non-electrostatic binding constant K₀ at 1 M Na⁺ was indistinguishable from zero for both HWKK and KWKK as expected for a Coulombic interaction entropically driven by salt ion release, consistent with previous model studies (4-6,32,36,44). The contributions of protonated histidine and protonated lysine to binding free energy are indistinguishable. From the perspective of the nucleic acid, the polyU per-phosphate ion accumulation is equivalent within error for Z_L = 4 oligopeptides HWKK (ψ = 0.76 ± 0.03), KWKK (ψ = 0.77 ± 0.01) and the arginine-containing oligopeptide RWRR (ψ = 0.80 ± 0.05) (13). If ψ is expressed as a function of the polyU axial charge spacing through eq.14, values of b₀ = 3.2 ± 0.2 Å and 3.3 ± 0.3 Å obtained from the salt dependence of binding for KWKK and HWKK respectively (Figure S2), are consistent with a previous report of b₀ = 3.2 ± 0.6 Å for single-stranded polyU and poly(rA) obtained by analysis of nucleic acid folding-unfolding processes (59). The reproducibility of ψ and b₀ determined for differing processes (binding versus melting) and with ligands with varying amino acid composition (lysine, arginine, or histidine) indicate that ψ and b₀ are thermodynamic parameters entirely dictated by the polyelectrolyte character of polyU. With logK₀ ≈ 0 and ψ ≈ 0.78, HWKK-polyU binding and its dependence on salt concentration and pH are fully explained by changes in the protonation state of histidine and the N-terminal α-amino group.

Protonation states of amino acid moieties are tunable

Statistically validated differences in the α-amino pK_a for HWKK versus KWKK indicate that replacing the neighboring lysine moiety with histidine promotes a pK_a shift (Table 2). Fitting HWKK data with a pK_a held constant using the pK_a = 7.57 from KWKK is strongly disfavored (ΔAIC_c = 8.6; evidence ratio = 75.4), while the converse constraint of fitting KWKK data with the HWKK pK_a = 7.81 results in an even poorer fit (ΔAIC_c = 20.0; evidence ratio = 1.3 × 10⁵). The decreased acidity of the α-amino group in HWKK relative to KWKK likely reflects the reduced free energy cost of adjacent charge-charge repulsion due to prior histidine deprotonation.

Analogous to our findings that the α-amino group pK_a depends on adjacent sequence in XWKK, numerous reports show that histidine protonation equilibria are sensitive to local environment changes (28,60-63). The highly tunable nature of histidine protonation in native proteins is exemplified by sperm whale myoglobin which possesses seven histidines with pK_a values ranging between 5.13 – 8.08 (60). Histidine pK_a variations for a series of model peptides based on sequences from sperm whale myoglobin were assessed at 0.02 M NaCl and 25 °C by NMR spectroscopy (60). Flanking lysines in Phe-Lys-His-Leu-Lys (FKHLK) acidify the adjacent histidine by ΔpK_a = −0.52 relative to Gly-His-Gly (GHG) (^HispK_a = 6.16 ± 0.02 versus 6.68 ± 0.02, respectively). Proline isomerization from cis to trans in Lys-Ser-His-Pro-Glu (KSHPE) suppresses histidine deprotonation with a ΔpK_a = +0.46 from 6.23 ± 0.02 to 6.69 ± 0.02, likely due to the difference in relative orientation of glutamate and histidine residues. These findings demonstrate that simple electrostatic differences in the vicinity of histidine are sufficient to modulate its protonation pH dependence in either direction. However, the histidines in FKHLK and KSHPE exhibit further pK_a perturbations in the context of native protein structure. FKHLK and KSHPE are the respective oligopeptide models for His36 and His48 in sperm whale myoglobin (60). His36, only observed in the trans conformation in the wild-type protein, has a pK_a = 7.67 ± 0.02, which is ΔpK_a = +0.98 more basic than its corresponding model peptide, trans-KSHPE. Similarly, His48 is more acidic in sperm whale myoglobin (pK_a = 5.42 ± 0.02), reflecting a ΔpK_a = −0.74 relative to FKHLK. The potential to tune the histidine protonation equilibrium constant across three orders of magnitude suggests that the prevalence of histidine at nucleic acid-binding interfaces may serve as an exquisite means to regulate protein-nucleic acid processes by providing important noncovalent interactions through coupled protonation.

Many nucleic acid-binding proteins exhibit histidine protonation coupled to binding. The pK_a of highly conserved His318 in the DNA-binding interface of human papillomavirus type 16 E2 protein (E2C) increases upon DNA binding (from 6.7 to 7.8; ΔpK_a = +1.1) in a mechanism proposed to be critical for the transition from nonspecific to specific DNA recognition (28). The pK_a of His451 in rat glucocorticoid receptor increases from 5.9 to 7.9 after binding the phosphodiester backbone of its DNA recognition element (25). His203 of the origin-binding domain of SV40 T antigen (T-ag-obd) exhibits a pK_a shift from ~5 to >8 when it binds specifically to the middle phosphate of the GAGGC pentanucleotide (27). His49 of the thermophile Pyrococcus woesei TATA-binding protein (PwTBP) has a pK_a of 6.2 in the unbound state but increases to pK_a = 7.2 when PwTBP complexes with its recognition sequence in which His49 interacts directly with a DNA phosphate (29). In each of the structural studies described above, proton uptake is coupled to specific binding to generate salt-bridges or other interactions between the protonated histidine and complementary surfaces within the binding interface (25,27-29). In cases where nonspecific binding was considered, histidine did not show these interactions (18,27,28). For example, His451 which exhibits a ΔpK_a = +2 in the specific complex did not interact with a non-cognate element (18). The coupled protonation of His203 with specific binding of T-ag-obd to its recognition sequence was not observed for the binding a non-cognate sequence (27). In E2C, His322 and His326 reside in a flexible and fully solvent-exposed loop domain known to participate in long-range nonspecific electrostatic interactions with cognate DNA (64). However, the His322 and His326 pK_a values (6.3 and 6.2, respectively) do not change upon specific binding, whereas the nearby His318 protonates during the same process to make a hypothesized water-mediated contact to a DNA phosphate (28). Together, the unbound proteins highlighted above (25,27-29) have comparable histidine pK_a values (average pK_a = 6.0 ± 0.7) to those seen for nonspecific binding histidines in E2C (28) and to the pK_a = 5.75 ± 0.18 for HWKK nonspecific binding to single-stranded RNA seen here. We note that all of these pK_a values are nearly indistinguishable from that of free histidine (pK_a = 6.04 (65)). In addition to the proteins above which show coupled protonation upon specific binding, lac repressor (lacR) exhibits cooperative uptake of 2 protons during nonspecific binding between pH 7.7 – 8.4 (26), even though specific binding of lacR with lac operator DNA is well-described by the titration model for a single titratable group with no evidence of coupled protonation between pH 7.1 – 8.4 (66). deHaseth et al. did not identify which residues were protonated, but Kalidomos et al. observed that lacR His29 makes electrostatic contacts with a DNA phosphate in both specific and nonspecific complexes (67).

The striking pK_a shifts described above are likely independent of large changes in protein structure. For example, E2C does not significantly change its conformation upon specific binding of its recognition element (68). Several structural comparisons of protein-DNA complexes report that the distribution of protein residues interacting with DNA are overall quite similar for a given protein in specific versus nonspecific complexes, although the DNA targets of these interactions typically change (18,67,69-72). For ~80% of the 44 specific DNA-binding proteins considered in rigid-body docking simulations, the sites involved in specific DNA recognition were also predicted to be favorable interaction sites for nonspecific DNA-binding (72). These combined findings suggest that protonation events coupled to specific binding are principally due to many small changes in the local environment rather than large domain rearrangements within the protein.

Structural and thermodynamic studies provide evidence that the interfaces in specifically bound protein-DNA complexes are highly dehydrated, with specific interactions between protein and nucleic acid functional groups replacing the interactions of these functional groups otherwise provided by water (1,3,73). Analyses (1,3) of structures of protein-nucleic acid complexes illustrate that a large fraction of the hydrogen bonds spanning the binding interfaces of cognate complexes have donor-acceptor distances that are too short to accommodate bridging waters (< 3.5 Å). For example, Janin and coworkers reported that 98% of protein-nucleic acid donor-acceptor distances were shorter than 3.4 Å and 67% were shorter than 3.0 Å (3). Recently, the large stabilizing effect of glycine betaine on the equilibrium constant for specific binding of lac repressor to lac operator DNA has been quantitatively interpreted in terms of the loss of more than 1200 waters of hydration (and some glycine betaine) from almost 7000 Ų of repressor and operator surface buried in this interaction (74). (Burial of 630 Ų of DNA phosphate surface area, with release of approximately 170 waters of hydration from which glycine betaine was completely excluded in the uncomplexed DNA, was shown to contribute the majority of the stabilizing effect of glycine betaine.) More generally, effects of glycine betaine, urea and Hofmeister salts on protein-DNA interactions, on protein folding and other protein processes are explained in terms of the loss of approximately 2 layers of water from all surfaces buried in the interface (74-77). Conversely, interfaces of nonspecific complexes of oligocations like KWKK and HWKK with nucleic acids probably are fully hydrated, based on several lines of evidence. First, experimentally-determined K_obs and SK_obs values for oligocation-nucleic acid binding processes were accurately predicted by Poisson-Boltzmann calculations which only account for Coulombic interactions and not changes in surface hydration (78). Second, oligopeptide-polyU binding constants were essentially indistinguishable as a function of anion composition at constant salt concentration (4). If significant dehydration occurred in these interactions, specific effects of different Hofmeister anions on the binding constant would be expected (77). Finally, NMR studies (79,80) demonstrated that polyamines bound to DNA are highly mobile, which is consistent with a hydrated, Coulombic, “loose” polyamine-DNA complex. Therefore, XWKK-RNA complexes most likely have hydrated binding interfaces which are exclusively stabilized by long-range Coulombic interactions. Our studies show that an addition of 1 – 2 positive charges on XWKK to increase Coulombic interactions across the hydrated interface is not sufficiently favorable to promote protonation of histidine or the α-amino group at a pH above their respective typical pK_a values. However, in the dehydrated interfaces of specifically bound complexes, residues interact directly instead of through water. Protein-nucleic acid binding processes exhibiting coupled histidine protonation require that histidine interact via the proton that makes it positively charged to satisfy the salt-bridges or other necessary hydrogen bonds with the nucleic acid. In these cases, the free energy penalty of protonating histidine above its nominal pK_a is much less than the consequences of not fulfilling the interactions it provides. These findings provide a rationale explaining why the presence of histidine coupled protonation exhibited by some nucleic acid-binding proteins depends on the nucleic acid sequences to which they bind (18,26-28).

Site size of XWKK binding to polyU is invariant with pH and larger than predicted by charge neutralization alone

Nonspecific binding of many cationic ligands to nucleic acids exhibits a site size approximately equal to the number of charges neutralized in the ligand-nucleic acid complex. Examples include inorganic salts such as Mg²⁺ (6,47) and Co(NH₃)₆³⁺ (31), polyamines (32), and oligopeptides of varying lengths (4-6,13,34,35,46). A small ligand such as Mg²⁺ binding to polyU or poly(rA)-polyU has a site size n = 2.0 ± 0.1 and n = 2.2 ± 0.1, respectively (47), whereas KWK₆ bound to homopolymeric dT ssDNA with n ≈ 8 under stoichiometric binding conditions (35). The site sizes of KWKK and KWKK were larger than expected if a 1:1 correlation of charge to lattice occupation size is assumed. For both HWKK and KWKK, the site size was about 5 nucleotides both by nonlinear least squares analysis of binding isotherms and via independent measurement of stoichiometric binding at low pH. In addition, we saw no obvious dependence on site size with protonation state, even for HWKK whose charge (Z_L) decreases from ~4 to ~2 over pH 5.2 – 8.7 (Table S1).

Flexibility of the oligopeptide and/or nucleic acid may play a role in explaining these findings. Unstructured oligopeptides of intermediate length appear to have slightly larger site sizes when binding double stranded DNA (dsDNA) than would be expected from ligand charge alone. Spermine (a polyamine with Z_L = 4) has an average site size of n = 4.9 ± 0.3 phosphates at pH 6.5 between 71 – 132 mM Na⁺ (32) and WK₄ (Z_L = 4) binds at 6.4 mM Na⁺ pH 7.0 with n = 4.6 ± 0.5 (34). Larger ligands of the form ε-DNP-Lys-(Lys)_x, where x indicates the number of unmodified lysines and the total charge Z_L, bind poly(rA)-polyU with n = 6.6 when Z_L = 5 and with n = 7.1 when Z_L = 6 (9,30). These results suggest that ligand conformational constraints may require a larger nucleic acid site size than expected based on charge neutralization alone. The converse of this phenomenon, where ligand flexibility permits interstitial residue compaction upon nucleic acid binding, was observed for a series of 17-residue Z_L = 4 oligopeptides which each bound dsDNA with a comparable site size of n = 4.0 ± 0.7 and most exhibited a concomitant conformational transition from random-coil to α-helix by circular dichroism (34). The pH-invariant site size n ≈ 5 for XWKK may be due to inherent inflexibility which prohibits decreases in site size as Z_L decreases.

To determine the dependence of nucleic acid binding as a function of peptide charge, nucleic acid base composition and salt effects, Lohman et al. estimated site size either by linear extrapolation of ν/L_F to ν/L_F = 0 on a Scatchard plot (4) or assumed that site size was proportional to oligopeptide charge (5,6,13). Our results suggest that this assumption may not be justified for the shorter oligopeptides they considered. However, because the McGhee-von Hippel isotherm determines K_obs in the zero-binding density limit (i.e., as if a single ligand were binding at the center of an infinitely long lattice), site size effects are expected to be fairly inconsequential. Indeed, Mascotti and Lohman reported that increasing the site size ~20% resulted in only a 4% perturbation to logK_obs (6). Given the comparative approach of their studies and the relatively insensitive nature of the McGhee-von Hippel equilibrium binding constant to n, the discrepancy in site size does not impinge the major findings of these previous studies. Nevertheless, the larger site size has potential implications for complex formation with finite lattices at higher binding densities where ligands have to compete for overlapping sites.

In conclusion, our nonspecific binding studies of HWKK and KWKK to polyU reveal that protonated histidine and lysine have equivalent effects on the stability of these nucleic acid complexes and that reduction in the binding constant with increasing salt concentration is well-described by limiting-law polyelectrolyte theory. Both tetrapeptides, with a maximum of 4 positive charges, have a site size of ~5 nucleotides and do not vary significantly with pH or salt concentration. Binding constants for nonspecific interactions of HWKK and KWKK to polyU increase with protonation of histidine and the α-amino group, but pK_a shifts coupled to binding are not observed and there is no requirement for protonation. This contrasts with well-documented examples of histidine pK_a shifts and proton uptake in the binding of native proteins to nucleic acids. We propose that this disparity in histidine protonation behavior derives from differences in interface hydration. The interface in the nonspecific, Coulombically-driven complexes of HWKK and KWKK with polyU is almost certainly fully hydrated, in contrast to the largely dehydrated, complementary interfaces of many native protein-nucleic acid complexes. We find that the additional Coulombic stabilization of a nonspecific HWKK-polyU complex provided by protonation is insufficient to cause a histidine pK_a shift and proton uptake upon binding. Conversely, the pK_a shifts and coupled protonation observed in several protein-nucleic acid binding processes (presumably) reflect the requirement for a salt-bridge or other specific interaction with the protonated histidine in the significantly dehydrated binding interface.

Abbreviations used

ss

single-stranded

dsDNA

double stranded DNA

GR

glucocorticoid receptor

PNAI

protein-nucleic acid interactions

polyU

polyuridylic acid

AICc

second-order Akaike Information Criterion

EDTA

ethylenediaminetetraacetic acid

HEPES

4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid

LBD

ligand binding density

SAM

sterile alpha motif

lacR

lac repressor

PwTBP

Pyrococcus woesei TATA-binding protein

E2C

human papillomavirus type 16 E2 protein

T-ag-obd

origin-binding domain of SV40 T antigen.