Use of Urea and Glycine Betaine to Quantify Coupled Folding and Probe the Burial of DNA Phosphates in Lac Repressor – Lac Operator Binding

Abstract

Thermodynamic analysis of urea-biopolymer interactions and urea effects on folding of proteins and α-helical peptides shows that urea interacts primarily with polar amide surface. Urea is therefore predicted to be a quantitative probe of coupled folding, remodeling and other large-scale changes in the amount of water-accessible polar amide surface in protein processes. A parallel analysis indicates that glycine betaine (N,N,N-trimethyl glycine; GB) can be used to detect burial or exposure of anionic (carboxylate, phosphate) biopolymer surface. To test these predictions, we have investigated the effects of these solutes (0 to 3 molal) on the formation of 1:1 complexes between lac repressor (LacI) and its symmetric operator site (SymL) at constant KCl molality. Urea reduces the binding constant K_TO (initial slope dln K_TO/dm_urea = −1.7 ± 0.2) and GB increases K_TO (initial slope dln K_TO/dm_GB = + 2.1 ± 0.2). For both solutes, this derivative decreases with increasing solute concentration.

Analysis of these initial slopes predicts that (1.5 ± 0.3) × 10³ Ų of polar amide surface and (4.5 ± 1.0) × 10² Ų of anionic surface are buried in the association process. Analysis of published structural data, together with modeling of unfolded regions of free LacI as extended chains, indicates that 1.5 × 10³ Ų of polar amide surface and 6.3 × 10² Ų of anionic surface are buried in complexation. Quantitative agreement between structural and thermodynamic results is obtained for amide surface (urea); for anionic surface (GB), the experimental value is ~70% of the structural value. For LacI-SymL binding, two thirds of the structurally-predicted change in amide surface (1.0 × 10³ Ų) occurs outside the protein-DNA interface in protein-protein interfaces formed by folding of the hinge helices and interactions of the DNA binding domain (DBD) with the core of repressor. Since urea interacts principally with amide surface, it is particularly well-suited to detect and quantify the extent of coupled folding and other large-scale remodeling events in the steps of protein-nucleic acid interactions and other protein associations.

One of the most intriguing results from analyses of the ever-expanding genome sequence data base has been the discovery of the prevalence of intrinsically disordered regions in proteins (1, 2). These unstructured domains (and sometimes entire protein chains) play key roles in transcription regulation, translation and cellular signal transduction, where folding is coupled to binding and recognition (see (3) for a review and references therein). Thus the very lack of structures in these systems determines function.

Prior to the explosion in sequence information, analysis of available thermodynamic data for protein-ligand, protein-protein and site-specific protein-DNA interactions for which structural information was available foreshadowed the generality of this functional design (4). Comparisons of the observed heat capacity and entropy changes of protein interactions with those predicted from model compound data for formation of a rigid-body interface indicated that large scale folding transitions are often coupled to binding and recognition (4). However, heat capacity changes can have contributions from other coupled processes (see Discussion). NMR, CD and other biophysical techniques provide powerful probes of the dynamic states of free proteins, but many systems are not suitable for such studies. Additionally, conformational changes may occur transiently as part of multi-step mechanisms such as DNA opening in transcription initiation. Thus a current challenge is to find alternative methods for detecting and quantifying these remodeling events in solution in order to relate them to function.

Analysis of the temperature dependence of interactions between lac repressor and various operator sequences (5, 6) led to the proposal that folding was coupled to binding (4) and that the extent of folding was a function of operator sequence (7). NMR and X-ray crystallographic studies confirmed these proposals and elegantly elucidated that the region connecting the DNA recognition element (helix-turn-helix domain) to the core domain of the protein is fundamentally the origin of the transitions detected by biophysical solution studies (8–13). Using this system, we test the hypothesis that urea at non-denaturing concentrations can be used as a quantitative probe of ordering of intrinsically disordered regions and other remodeling events in protein processes.

Precedent for this study is provided by the seminal work of Myers, Pace and Scholtz (14), who observed that the derivative of the protein unfolding free energy change with respect to urea molarity (dΔG^o_unfold/d[urea], defined as the urea m-value) is proportional to the calculated (disulfide-corrected) change in water-accessible surface area (ΔASA). Another important cornerstone for this study is provided by Baldwin and coworkers (15), who determined the per-residue m-value for unfolding of a series of α-helices (repeat unit AEAAKA). Using this per-residue α-helix m-value to estimate contributions from α-helical regions to observed m-values for unfolding of globular proteins, they concluded that the interaction of urea with peptide groups accounted for a major part of the destabilizing effect of urea on these systems. Significantly, ASA analysis reveals that the m-value/ΔASA_total ratio for unfolding the AEAAKA α-helices is more than three times as large as for unfolding globular proteins (16). Our quantitative analysis of these unfolding data for proteins and α-helical peptides, together with data for interactions of urea with native proteins and DNA, demonstrates that the only significant preferential interaction of urea is with polar amide (N, O) surface (16–18), and is the basis for the determination of its intrinsic interaction coefficient per unit of amide surface (in the Analysis section below).

Typically, as exemplified for lac repressor-lac operator binding (see Results), only a small fraction (5–15%) of the surface buried in the interface of a complex between a protein and duplex DNA is composed of polar amide groups. Therefore the effect of urea concentration on a rigid-body interaction of a protein with duplex DNA or RNA (in which no conformational changes in the protein occur) is predicted to be relatively small. However, polar amide surface constitutes a large fraction (40–60%) of the surface buried in α-helix formation, and a significant fraction (20–30%) of the surface buried in protein folding. Consequently urea is predicted to be particularly suitable as a quantitative probe of α-helix formation and other large-scale folding/remodeling processes coupled to protein-DNA binding or other protein associations.

In the present study, we also test the hypothesis that glycine betaine (GB), which interacts primarily with anionic oxygen surface of proteins and DNA (18, 19), can be used to quantify the amount of this surface buried or exposed in a biopolymer process. For reasons detailed below (see Analysis), GB is not expected to be as unambiguous a probe of changes in ASA of anionic surface as urea appears to be for amide surface, and the experimental value is ~70% of the structural value.

For urea and GB, we obtain and analyze both initial slopes and curvature at higher solute concentrations characterizing the dependence of the standard binding free energy (equivalently the logarithm of the observed binding constant) on solute molality at constant KCl molality. Using osmometric data, we correct these initial slopes from constant KCl molality to constant KCl activity. We summarize the current status of the thermodynamic characterization of interactions of urea and GB with a spectrum of biopolymer surfaces, and obtain values for the intrinsic interaction coefficients (per unit area of the specified type of biopolymer surface and per unit solute molality). Using these intrinsic interaction coefficients, we interpret the initial slopes and curvatures of plots of lnK_TO versus molality of urea and of GB to characterize coupled conformational changes and burial of polar amide and anionic surface respectively in the repressor-operator interaction. The agreement between predicted and experimental values of amide surface buried on forming the lac repressor-lac operator DNA interface indicates that urea will be a powerful tool for detecting coupled conformational changes in other protein associations.

MATERIALS AND METHODS

Chemicals

Glycine betaine monohydrate (>99% pure, FW 135.2) was obtained from Sigma (St. Louis, MO). Ultrapure urea (> 99.5% pure, FW 60.06) was obtained from Life Technologies. Glycerol (>99.5% pure, FW 92.09) was obtained from Aldrich (Milwaukee, WI). All other chemicals and enzymes are reagent or molecular biology grade.

Preparation and operator binding activity of lac repressor

Tetrameric lac repressor was purified from the E. coli strain HB101/lac pIQ by the method of (20) and (21) as modified (22, 23). Aliquots of purified repressor were stored at a total protein concentration of 27.1 μM (tetramer) at −70°C in 10 mM HEPES (pH 7.5), 0.1M KCl, 0.1 mM DTT and 30% (v/v) glycerol. Molar concentrations of repressor tetramer were determined from absorbance at 280 nm using the extinction coefficient ε = 9.2 × 10⁴ M⁻¹ cm⁻¹ (24). Working stocks of repressor were prepared by dilution from the −70°C stock to the μM range and stored for up to 10 days at −20° C in10 mM KH₂PO₄ (pH 7.5), 0.075 M KCl, 0.1 mM DTT and 30% (v/v) glycerol. Activities of these samples, defined as the fraction of active repressor tetramers, were determined from filter binding titrations in the CBLR (complete binding of limiting reagent) regime (25). Activities ranged from 36% to 44%; repressor activity was not significantly affected by urea or GB (tested up to 0.6 m urea and 1.1 m GB (data not shown)), nor by storage at −20°C during use for titrations of a labeled DNA sample (up to 10 days). All concentrations specified in the text are total (active plus inactive) molar concentrations of repressor tetramer.

Preparation of ³²P-labeled SymL plasmid DNA

pAS 8-1 (6) plasmid DNA (2514bp), carrying the symmetric 20 base pair SymL (formerly designated O^sym) operator (26) and no other operator sites, was isolated from E. coli HB101 using the QIAGEN plasmid purification method and linearized with restriction endonuclease PstI to obtain a centrally-located SymL operator. Linear plasmid DNA was replacement labeled (27) with [³²P]dATP and [³²P]dCTP (>6000 Ci/mmol), purified as previously described (25), and stored at a concentration of approximately 6 μM at −20°C in TE buffer (10 mM Tris pH 8.0, 1 mM Na₂EDTA).

The concentration of ³²P -labeled DNA was determined by a novel quantitative fluorescence assay using Gel-Star (Cambrex BioScience RockLand Inc.) stain to detect DNA; this reagent gives lower background, higher sensitivity and broader range of linearity than ethidium bromide. In this assay, fluorescence at 545 nm was measured with excitation at 310 nm in an SLM 8000 spectro-fluorimeter. A standard curve was prepared using DNA standards in the concentration range 0.035 to 0.18 μg/ml (0.11 to 0.53 μM in nucleotide monomer). These standards were prepared by accurate dilutions of a stock solution of known concentration of purified linearized plasmid DNA (3824bp pKO^c (28)), first with TE buffer, followed by a 1:20 dilution with a Gel Star solution prepared by 1:5000 dilution of the proprietary Gel Star stock. The concentration of the DNA stock solution was determined from absorbance at 260 nm by UV spectroscopy using ε = 0.02 (μg/ml)⁻¹ cm⁻¹ (27). Concentration determinations for one DNA sample using independently prepared standard curves are reproducible to approximately 5%.

Filter binding assays

The nitrocellulose filter assay for repressor - operator DNA binding (25, 29–33) was used to determine binding isotherms and binding constants (equilibrium concentration quotients) K_TO for formation of 1:1 repressor tetramer-operator complexes (TO) as a function of urea or GB molality in binding buffer (BB: 0.010 m K₂HPO₄, 0.001 m K₂EDTA, 0.001 m dithiothreitol (DTT), 0.752 m glycerol, 50 μg/ml bovine serum albumin (BSA); and either 0.189 m or 0.404 m KCl; pH adjusted to 7.3 with concentrated HCl). The K⁺ concentration of BB (0.212 m or 0.427 m) is the sum of contributions from K₂HPO₄, K₂EDTA and KCl.

For binding studies in the presence of urea or GB, a series of binding buffers with varying molal concentrations (m₃) of urea or GB were prepared by adding accurately weighed amounts of solid urea or GB to BB. In the case of urea, this procedure kept the molality of all other solutes constant. For GB, added as the monohydrate, this procedure reduced the molality of K⁺, glycerol and other constituents in BB by approximately 5% at 3 molal GB. Experimentally-determined values of K_TO at each m_GB were corrected for the small and opposing effects of the changes in molality of K⁺ and glycerol. To determine the glycerol correction, complete titrations of operator DNA with repressor at 0.212 m K⁺ and zero or 1.59 m urea were performed at least twice at zero and 0.752 m glycerol. These data provide an estimate of ∂ ln K_TO/∂m_glycerol = 1.5 ± 0.5 (23), used here to correct K_TO to a constant glycerol concentration (0.752 molal). The log-log [salt] derivative of the LacI-SymL binding constant in the vicinity of 0.4 M KCl (SK_TO = −6.3; 30) was used to correct K_TO to a constant K⁺ concentration (0.427 m) as shown in the tabulated values of K_TO in supporting information. The calculated (opposing) effects on K_TO of the small reductions in K⁺ and glycerol molality with addition of hydrated GB increase the initial slope dlnK_TO/dm_GB by only 3%, which is substantially less than the uncertainty in this slope (10%). Repressor and ³²P SymL plasmid DNA stocks were serially diluted into BB at the desired solute concentration; dilution factors exceeded 10³ except for activity assays, where they exceeded 60, so that solutes in the storage buffer make no significant contribution to the composition of the binding buffer.

In urea, binding isotherms were determined at 0.212 m and 0.427 m K⁺ (corresponding to KCl concentrations (m₄) of 0.189 m and 0.404 m, respectively); in GB, binding isotherms were determined only at ~0.43m K⁺ because K_TO is too large to measure at high m_GB in 0.2 m K⁺. Ranges of solute concentration investigated were 0–3.2 m urea at 0.212 m K⁺, 0–1.3 m urea at 0.427 m K⁺ and 0–3.0 m GB at 0.43 m K⁺. All protein DNA binding experiments were performed at 24°C.

For each forward titration of SymL operator DNA with repressor, 15 sample tubes with the same concentration of ³²P labeled SymL operator DNA and increasing concentrations of repressor were equilibrated in binding buffer at a specified concentration of urea or GB for 0.8–2 hr at 24°C. Duplicate aliquots from each sample were then filtered under 250–350 mmHg vacuum through Schleicher & Schuell BA-85 nitrocellulose filters, pretreated as described (25). After filtration, filters were washed once and dried. Cerenkov radiation of each filter was measured in a Beckman LS 1801 scintillation counter. The total radioactivity filtered in each aliquot was measured by counting multiple aliquots of unfiltered reaction mixture. Experiments were carefully designed, based on preliminary results, to obtain data characterizing the entire binding isotherm. At least two independent determinations of the binding isotherm were performed for each solute and salt concentration investigated, with one exception (one isotherm at 1.06 m urea, 0.212 m K⁺).

The experimentally observed fraction of operator DNA retained on the filter by repressor (θ_obs) was calculated by eq 1 from the counts per minute (C) retained on the filter for each sample in a repressor titration experiment:

$${\theta }_{\text{obs}}=(\text{C}-{\text{C}}_{\text{b}})/({\text{C}}_{\text{t}}-{\text{C}}_{\text{b}})$$ (1)

where C_b and C_t are the background and total values of C for a sample. Values of θ_obs are related to θ, the fractional saturation of operator DNA with repressor by the efficiency E of retention of operator DNA on the filter at saturation with lac repressor:

$$\theta ={\theta }_{\text{obs}}/\text{E}$$ (2)

The efficiency E is invariably less than 1.0 because of DNA damage and/or incomplete retention of preexisting complexes; values of E in the range 0.55 to 0.65 were obtained in this study, and no solute effect on E was observed.

Titrations of a fixed operator DNA concentration with increasing repressor concentration were performed over a range of [SymL]_total (0.69–2.5 pM) chosen to be low enough so that even in the initial stages of the titration only 1:1 TO complexes formed (25). Lac repressor tetramer is stable to dissociation in the concentration range investigated (25, 34). The two-site binding model of the repressor tetramer (25, 30) was used to analyze binding isotherms, with the constraint that the two sites are identical at the salt concentrations investigated (equal site binding constants; ks₁ = ks₂, 30). Using the independently determined protein activity, values of θ_obs as a function of the total (active plus inactive) molar concentration of lac repressor for each isotherm (15 points) were fitted to the two-site binding model to determine binding constants K_TO (=2 ks₁) and filter efficiency E for each protein titration experiment. The activity of repressor tetramer was determined by fitting values of the observed fractional saturation of SymL operator DNA (θ_obs) for a protein titration in the CBLR regime (30) to the two-site model and fixing ks₁ ≫ [SymL]_total⁻¹.

Data fitting

The fitting program to determine the binding constant K_TO from the binding isotherm (25) uses the Newton-Raphson algorithm (35) linked to the non-linear least-squares parameter minimization program NONLIN (36). Multiple linear regression (37) was used to fit the dependences of ln K_TO on solute concentration (m₃) to second order polynomials and in analysis of thermodynamic data for urea-biopolymer interactions and urea effects on proteins and α helix folding (see Analysis).

Modeling and calculation of changes in water-accessible surface areas

All water-accessible surface areas (ASA) were calculated using ANAREA (38) as previously described (39).

a) Lac Repressor-SymL Operator

For the LacI-SymL interaction, the file 1EFA (40) from the Protein Data Bank (41) was used to calculate rigid-body changes in ASA on forming the LacI-SymL operator complex. This file contains the coordinates for the repressor dimer (lacking only the C-terminal helix required for tetramerization) bound to SymL operator DNA and the anti-inducer orthonitrophenyl fucoside (40). The resolution of the crystal structure is 2.6 Å. No water molecules are bound in the relevant protein-DNA or protein-protein interfaces in 1EFA. Although chemically both the repressor and this DNA site are two-fold symmetric, the degree of resolution in each half site differs. In the protein-DNA interface, side chains of residues 2 and 26-37 in monomer A and 2, 31, 36, and 37 in monomer B are missing. In the half site contacted by the A “headpiece” domain (residues 1-49), the terminal 5′ end is missing density for nucleic acid bases and backbone assigned as D1-D4 and E19-E21. In the “B” half site, only the terminal base E1 is missing. We chose a model that utilizes the B half site where more atoms are resolved. In 1EFA, SymL is bent by ~40°. InsightII (Accelyrs Software Inc.) was used to build a B-form DNA corresponding to the sequences E2-E11 and D12-D21 as a model of the free DNA half site. Values of ΔASA for forming the rigid body LacI-SymL interface were then calculated as the difference in ASA between the bound half site (B chain, DNA bases D12-D21, E2-E11 in 1EFA) and the “free” B chain (1EFA) and free DNA model. This difference was then multiplied by two.

In the free repressor, residues connecting headpiece to the core are unfolded (12), but fold upon binding SymL operator (8–13). To calculate the ΔASA of this folding process, Insight II was used to put the conformation of residues 50–60 from 1EFA in an extended conformation, a reproducible representation of unfolded regions used to calculate ΔASA of unfolding (14, 39, 42). However, under conditions where secondary structures or tertiary interactions (e.g. hydrophobic collapse) are stable, this model presumably overestimates the ASA of these regions (see (c) below). Since the side chains missing in chain A are not involved in this coupled folding transition, chains A and B were used in this calculation. The difference between ASA in this extended state model of the LacI dimer and in the bound conformation in1EFA was calculated. Values of ΔASA for this calculation include the folding transition in residues 50-58 as well as the surface changes arising from “docking” the DBD on the core domain. The change in ASA in residues 50-58 was subtracted from the total to obtain the amount buried in docking.

b) α-helical and unfolded states of alanine-containing peptides

Scholtz et al. (15) reported and analyzed the urea denaturation at 273 K of a series of α-helical peptides with sequence Ac-Tyr-(Ala-Glu-Ala-Ala-Lys-Ala)_k-Phe-NH₂, with values of k of 2, 3, 4, 5, and 8. To calculate the changes in total and amide surface area in the unfolding of these peptides, a representative α-helical peptide with k=3 was built using the standard parameters from the Insight II Biopolymer library (Accelrys). The denatured state was modeled as an extended chain. The difference in ASA calculated for the central six-residue internal repeat for conversion from the α-helix to the unfolded state was divided by six to obtain the ΔASA of unfolding per average residue. Three different conformations of the lysine and glutamate side chains in the α-helix were used and the results were averaged to obtain the values reported in Table 3. The first was the conformation modeled by Insight II and reported previously (16). In the second model, these side chains were rotated to be maximally extended from the helix backbone. In the third model, glutamate and lysine were rotated to make the best possible salt bridge consistent with the α-helical geometry (the side chain rotamer library in Insight II allows the carbonyl oxygens of glutamate to be positioned 3.4 Å from the terminal nitrogen in the side chain of lysine). Although the change in total ASA varies, the change in polar amide ASA upon unfolding is the same (±0.5 Ų) for all three models of the α-helix.

Table 3.

Quantifying Urea Accumulation at Polar Amide Surface^a

Process	Example(s)	$\frac{\text{m}-\text{value}}{\mathrm{\Delta }{\text{ASA}}_{\text{total}}}$ (cal mol−1 M−1 Å−2)	% polar amide ΔASA	Urea accumulation per Å2 polar amide ΔASA Γμ3/m3ASAamide (m−1 Å−2)	Footnote
Protein unfolding	Set of 40 Globular proteins (without S-S or heme groups)	0.15 ± 0.03	17 ± 2%	(1.4 ± 0.3) ×10−3	b
α-helix melting	AcY(AEAAKA)kFNH2 ΔASAtotal = 42 ± 6 Å2 per residue	0.52 ± 0.07	49 ± 7%	(1.8±0.1) × 10−3	c
System:	ASAtotal (Å2)	$\frac{\text{RT}({\mathrm{\Gamma }}_{{\mu }_3}/{\text{m}}_3)}{{\text{ASA}}_{\text{total}}}$	% polar amide ASA	Urea accumulation per Å2 polar amide ASA Γμ3/m3ASAamide(m−1 Å−2)
BSA	2.78 × 104	0.12 ± 0.03	14.6%	(1.3± 0.4) × 10−3	d
ds DNA	171 per nucleotide monomer	−0.07 ± 0.07	2.5%	negligible	e

^aValues of ΔASA calculated as described in Methods.

^bSee Supporting information.

^cm-value is from (15) and corrected to 298K using temperature effect (48).

^dValue of Γ_μ3/m₃ is from Cannon et al., in preparation, and agrees within uncertainty with ref (17).

^eASA analysis assumes that preferential interactions of urea with K⁺ counterions are negligible (interaction of urea with KCl is weakly favorable (44)); (18).

c) Folded and Unfolded States of Monomeric and Dimeric Globular Proteins

Criteria for selection of monomeric and dimeric proteins for the analysis of change in surface area and m-value were: high resolution native structures containing no disulfide crosslinks or heme groups, reversible and two-state unfolding in urea, spectroscopically-determined m-values in the range pH 5–8 and 0–40°C. The data set in Supporting Information includes all proteins analyzed by Myers et al. (14) and all more recent systems which meet these criteria. Surface areas of the folded states of proteins were calculated using the appropriate PDB file and unfolded states were modeled as extended chains in which side chains were rotated to avoid steric clash using InsightII (see Supporting Information). Various models have been used to quantify the ASA of the unfolded state. We and others have proposed that, in the absence of evidence for secondary structure or tertiary interactions, the extended polypeptide chain provides the most reasonable estimate of the ASA (14, 39, 42). Tripeptide models overestimate ASA (39, 42) and models that include secondary structure should only be used where evidence of secondary structure exists. In unfolding studies at high urea concentration, no stable secondary structure is detected by circular dichroism of the unfolded state.

RESULTS

Surface Area Analysis of LacI-SymL Interactions

The high resolution structure of a LacI dimer-SymL complex (40), together with NMR structural data on the DNA binding domain (8), provide the data to predict the amount and composition of the surface buried in complexation. These results are summarized in Table 1. Of the 6882 Ų of total surface of LacI and SymL operator buried in complexation, 1526 Ų is polar amide surface, and 632 Ų is anionic oxygen surface. All anionic oxygen surface buried upon binding is from DNA phosphate oxygens buried in the protein-DNA interface. Since amide-like functional groups comprise only 2.5% of the ASA of duplex DNA, almost all of the change in polar amide surface (95%) arises from burial of carbonyl oxygen and nitrogen of amide groups of peptide backbone and of Q, N side chains of the repressor. Polar amide surface makes up only 13% of the surface buried in the protein-DNA binding interface, but constitutes 25% of the DBD-core interface and 45% of the surface buried in folding the hinge helices. Consequently less than one-third of the polar amide surface buried in the binding process (491 Ų/1526 Ų) is in the repressor-operator binding interface; the majority is buried in folding the two hinge helices (515 Ų) and forming protein-protein interfaces between the folded DNA binding domain and the core of lac repressor (520 Ų).

Table 1.

Changes in accessible surface area (ΔASA) in LacI - SymL complexation ^a.

Process:	Total (Å2)	Polar amide (O, N) (Å2) (% in total)	Anionic oxygen (Å2)
Form LacI-SymL interface (docking 2 DBD on SymL site)	3689	491 (13%)	632
Fold 2 hinge helices (residues 50-58)	1144	515 (45%)	0
Form 2 DBD-core interfaces	2049	520 (25%)	0
TOTAL	6882	1526	632

^aΔASA values calculated using ANAREA (38), PDB file 1EFA (40) and models of the free states of SymL and LacI as described in Methods.

Opposite Effects of Urea (Destabilizing) and Glycine Betaine (Stabilizing) on Binding of Lac Repressor to lac Operator DNA

Since the structural data predict that substantial amounts of amide and anionic oxygen surface are buried in forming the LacI-SymL complex, binding studies as a function of urea and glycine betaine (GB) concentration were performed to test the following hypotheses (18, 19): 1) urea is a quantitative thermodynamic probe of large-scale changes in the amount of water-accessible polar amide surface; and 2) GB can be used to detect burial or exposure of anionic (carboxylate, phosphate) biopolymer surface in biopolymer processes. Figures 1 and 2 show representative binding isotherms over the ranges of urea and GB concentrations investigated. Nitrocellulose filter binding data at 24 °C at each solute concentration are plotted as the fraction (θ) of total SymL operator DNA complexed with LacI as a function of the logarithm of the total molar concentration of repressor tetramer.

Figure 1. Effect of Urea Concentration on Specific Binding of Lac Repressor to Lac Operator DNA.

Representative binding isotherms determined by the nitrocellulose filter assay in binding buffer (BB) at 24 °C in the absence and presence of urea are plotted as the fractional occupancy (θ) of the SymL operator site by LacI protein as a function of the logarithm of the total (bound and free, uncorrected for activity) molar concentration of LacI tetramer.

A). Lower [Salt] Titrations (0.212 m K+). Isotherms at 6.9 pM DNA in the absence of urea (closed circles) and at 1.8 pM DNA in 0.796 m urea (open squares), in 1.59 m urea (crosses); and 2.39 m urea (closed squares). LacI activity is 0.39. B). Higher [Salt] Titrations (0.427 m K⁺). Isotherms at 1.0 pM DNA in the absence of urea (closed circles) and at 1.28 m urea (closed squares), and at 1.25 pM DNA at 0.427 m urea (crosses). LacI activity is 0.49. In both panels, the curves are nonlinear least square fits to a noncooperative model with two equivalent sites for operator DNA on a repressor tetramer (see Methods), assuming that only 1:1 LacI- operator complexes (TO) form under the conditions investigated. Table S1 summarizes the fitted values of the binding constants K_TO.

Figure 2. Effect of Glycine Betaine Concentration on Specific Binding of Lac Repressor to Lac Operator DNA.

Representative binding isotherms determined by the nitrocellulose filter assay in binding buffer (BB) at 24 °C in the absence and presence of GB are plotted as the fractional occupancy (θ) of the SymL operator site by LacI protein as a function of the logarithm of the total molar concentration of LacI tetramer. Isotherms at 1.0 pM DNA in the absence of GB (0.427 m K⁺; closed circles) and in 2.06 m GB (0.411 m K⁺; closed squares), at 1.25 pM DNA in 0.63 m GB (0.422 m K⁺; open squares), and at 1.50 pM DNA in 1.25 m GB (0.418 m K⁺; crosses). LacI activity is 0.36. The curves are nonlinear least square fits to a noncooperative model with two equivalent sites for operator DNA on a repressor tetramer (see Methods), assuming that only 1:1 LacI operator complexes (TO) form under the conditions investigated. Table S1 summarizes the fitted values of the binding constants K_TO.

For urea, Figure 1A compares binding isotherms at 0.212 m K⁺ for urea molalities of 0, 0.796, 1.59, and 2.39 m. Figure 1B compares binding isotherms at 0.427 m K⁺ for urea molalities of 0, 0.43 and 1.28 m. At both salt concentrations, the binding curve shifts to higher repressor concentrations with increasing urea concentration, demonstrating that urea shifts the binding equilibrium toward reactants.

For GB, Figure 2 compares isotherms at ~0.43 m K⁺ for GB molalities of 0, 0.634, 1.25 and 2.06 m. Figure 2 shows that the binding curve shifts to lower protein concentration with increasing GB concentration, in accordance with the previous finding that GB and other osmolytes increase the stability of the repressor-O₁ operator complex (43). The shape of these isotherms, typical of noncooperative binding, is independent of solute and salt concentration. Fitted curves are nonlinear least squares fits to a noncooperative isotherm involving only 1:1 (TO) LacI-SymL operator complexes (cf. 25). No significant contribution from 1:2 (TO₂) repressor-operator complexes is expected for the conditions of these experiments (25, 30).

Binding constants K_TO obtained from these fits are tabulated together with results at these and other urea or GB molalities in Table S1 (in Supporting Information). K_TO decreases with increasing urea concentration and increases with increasing GB concentration at constant K⁺ molality. At 0.427 m K⁺, where K_TO is ~4× 10⁹ M⁻¹ in the absence of perturbing solute (cf. Table S1), addition of 1.28 m urea reduces K_TO by somewhat more than an order of magnitude (to ~3 × 10⁸ M⁻1), while addition of 1.25 m GB increases K_TO by somewhat less than an order of magnitude (to ~3 × 10¹⁰ M⁻¹). Reduction in the K⁺ concentration from 0.427 m to 0.212 m increases K_TO more than two orders of magnitude (to ~6 × 10¹¹ M⁻¹) in the absence of perturbing solute (cf. Table S1). This strong dependence of K_TO on salt concentration above 0.2 molal (log-log [salt] derivative SK_obs = −7 ± 1 near 0.3M salt; 30) arises primarily from formation of the specific interface with operator. (A smaller, variable contribution to SK_obs is attributed to local wrapping of flanking nonoperator DNA on the repressor core (30).) Because both urea and GB at concentrations in the molal range significantly reduce the thermodynamic activity of KCl (18, 44) and because K_TO depends so strongly on salt activity, it is necessary to correct the observed derivatives of K_TO with respect to solute (urea, GB) concentration to constant salt activity, by the method developed in Appendix I and summarized below.

Solute Concentration Dependences of the LacI-SymL Binding Constant K_TO

Binding constants K_TO for the entire range of urea and GB concentrations investigated are summarized in Figure 3, which plots the natural logarithm of the ratio of K_TO to a binding constant, ${\text{K}}_{\text{TO}}^{\text{o}}$, as a function of solute molality. ( ${\text{K}}_{\text{TO}}^{\text{o}}$ is the binding constant in the absence of the solute (urea or GB) at the same KCl concentration.) The effect of urea concentration on lnK_TO is linear within the uncertainty at low urea concentrations (< 1.6 m) at both 0.212 m and 0.427 m K⁺. Data at higher urea concentrations (obtained only at 0.212 m K⁺) reveals detectable downward curvature. The fit of all values of $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})$ at both 0.212 m and 0.427 m K⁺ to a second order polynomial in m_urea (0 to 3.2 m urea) is shown in Figure 3:

$$ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})=-1.7(\pm 0.2){\text{m}}_{\text{urea}}-0.12(\pm 0.06){\text{m}}_{\text{urea}}^2$$ (3)

Figure 3. Effects of Urea and GB Molality on the Repressor-Operator Binding Constant.

K_TO. The quantity $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})$, the natural logarithm of the ratio of the repressor-operator binding constant to that in the absence of added solute, is plotted against solute (GB or urea) molality. Binding constants K_TO and ${\text{K}}_{\text{TO}}^{\text{o}}$ at the corresponding salt concentration are obtained from Table S1. For GB, all binding constants are at 0.427 m K⁺ (circles); for urea, binding data at 0.212 m K⁺ (squares) and at 0.427 m K⁺ (triangles) are plotted. Equations for the fitted curves are: for urea (combining data at both K⁺ molalities), $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})=-1.7(\pm 0.2){\text{m}}_3-0.12(\pm 0.06){\text{m}}_3^2$; for GB, $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})=2.1(\pm 0.2){\text{m}}_3-0.31(\pm 0.07){\text{m}}_3^2$.

The initial slope (∂ ln K_TO/∂m_urea)_murea→0 = −1.7± 0.2 is most directly interpretable in terms of the ASA buried upon binding repressor to operator (see Discussion, also 16, 45). The significant downward curvature (quadratic term) at higher molal concentrations of urea is opposite in direction to that expected if urea were only perturbing the intrinsic strength of the interaction and not affecting the structure of the DNA-binding domain of the unbound lac repressor. Possible origins of this effect are discussed below (see Discussion).

For GB, the plot of $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})$ vs. m_GB in Figure 3 is fitted as a quadratic function of m_GB (shown below in eq 4). The initial slope is opposite in sign but comparable in magnitude to that obtained with urea. Although the effects of the two solutes on $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})$ are in opposite directions, both solute plots exhibit the same direction of curvature at higher solute concentrations. Stronger downward curvature is exhibited in GB than in urea, and indeed K_TO approaches a GB independent plateau value or maximum at high GB concentration; the predicted maximum from the fit (given below) is at ~3.5 m GB. The fit of all values of $ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})$ at 0.427 m K⁺ to a second order polynomial in m_GB (0 to 3.03 molal GB) is shown in Figure 3:

$$ln({\text{K}}_{\text{TO}}/{\text{K}}_{\text{TO}}^{\text{o}})=2.1(\pm 0.2){\text{m}}_{\text{GB}}-0.31(\pm 0.07){\text{m}}_{\text{GB}}^2$$ (4)

As for urea, the initial slope (∂ ln K_TO/∂m_GB)_mGB→0 = 2.1± 0.2 is most directly interpretable in terms of the ASA buried upon binding repressor to operator (see Discussion, also 16, 45). Possible origins of the strong curvature (quadratic term) at higher GB concentrations are discussed below (see Discussion Section). Both the direction and magnitude of this curvature are consistent with that observed in studies of protein thermal stability as a function of GB concentration (45, 46).

Calculation of the Solute Concentration Dependence of the Repressor-Operator Binding Constant at Constant Salt Activity and In the Limit of Low Solute Concentration

Effects of denaturants (urea, guanidinium chloride) on the standard free energy change for protein unfolding have traditionally been reported as “m-values” (47). We (16, 17, 48) applied a thermodynamic analysis to interpret these m-values in terms of differences in preferential interactions of denaturant with denatured and native states of the protein, using the solute partitioning model of preferential interaction coefficient (16). For such an analysis, the molal scale of solute concentrations is more fundamental. Hence we analyze the dependence of lnK_obs = −ΔG^o/RT for the process of interest (here repressor-operator binding) as a function of molal concentration of solute (urea or GB).

Protein-nucleic acid interactions are very strongly dependent upon the type and thermodynamic activity of salt. In the determinations of the effects of urea and GB on repressor-operator binding constants reported here, the total K⁺ molal concentration and individual anion molal concentrations (primarily Cl⁻, also phosphate and EDTA) were maintained constant in each series of experiments. Because the osmolalities of three component aqueous solutions of KCl and urea (or GB) are always less than the sum of the osmolalities of the individual two component solutions, the KCl activity in experiments at constant KCl molality decreases with increasing concentration of urea or GB. The strong dependence of the repressor-operator binding constant on salt activity makes it necessary to correct the experimental data from constant salt molality to constant salt activity to isolate the effect of urea or GB on the LacI-SymL binding constant. This is most conveniently done at the level of the derivative ∂ ln K_obs/ ∂m₃, using experimental thermodynamic data obtained by VPO (vapor pressure osmometry) for the interaction of urea and GB with KCl. Appendix 1 provides the derivation of the relationship between the derivative (∂ ln K_obs/ ∂m₃)_m4 and the corresponding erivative at constant a₄, where component 4 is the salt and component 3 is the perturbing solute (urea, GB). The result is

$${\left(\frac{\partial ln{K}_{\mathit{obs}}}{\partial m_3}\right)}_{a_4}={\left(\frac{\partial ln{K}_{\mathit{obs}}}{\partial m_3}\right)}_{m_4}+\frac{{\text{SK}}_{\text{obs}}\mathrm{\Delta }{\text{Osm}}_{34}}{2{\text{m}}_3{\text{m}}_4(1+{\epsilon }_{\pm }){\text{m}}_3}$$ (5)

In eq 5, the quantity ΔOsm₃₄ is the difference in osmolality between the three component solute (urea, GB)-salt solution and the sum of its constituent two-component solutions at the same molalities (m₃ and m₄). (Because the quantity RTΔOsm₃₄/m₃m₄ is approximately equal to the derivative of chemical potential of urea or GB with respect to salt molality, it is expected to be relatively independent of m₃ over the range of molalities of interest here, including the situation m₃ → 0 (cf. Appendix 1).) Thermodynamic consequences of any interactions of urea or GB with glycerol or other components of the binding buffer are expected to be insignificant and are therefore neglected. For three component solutions containing KCl and either urea or GB, osmolality fitting functions to evaluate ΔOsm₃₄ have been published (18).

In applications of eq 5 to the initial value of the derivative (∂ ln K_obs/ ∂ m₃)_{m4,m3 →0,} values of the electrolyte nonideality term (1+ ε_±)_m3=0 and of the salt derivative of the protein-DNA binding constant (SK_obs) in the absence of perturbing solute were used. For lac repressor binding to plasmid operator DNA in the vicinity of 0.3 M salt, −SK_obs = 7± 1 (30). For KCl solutions in the range 0.2–0.43 m the nonideality term (1+ ε _±)_m3=0 =0.893 ± 0.001 (49). Table A1 in Appendix 1 provides numerical values for the second term on the right hand side of eq 5 for urea and GB at the KCl concentrations used in this study. Solute concentration derivatives (∂ lnK_obs/∂ m_{3 a4,m3→0}) at constant salt activity for both urea and GB are calculated using eq 5 and tabulated in Table 2. For the salt concentration range of our experiments (0.21–0.43 m KCl), the KCl correction terms for urea and GB have the same sign and similar magnitude. Thus for urea (GB) the derivative (∂ lnK_obs/∂m_{3) a4,m3→0} is larger (smaller) in magnitude than (∂ ln K_obs/∂m₃)_m4,m3→0.

Table 2.

Calculation of (∂ln K_obs /∂m₃ )_m3→0,a4 from (∂ln K_obs/∂m₃ ) _{m4, m3 →0}

	(∂ln Kobs/∂m3)m4, m3→0	Correction to constant KCl activity	(∂lnKobs/∂m3)a4,m3 →0
Urea effect	−1.7 ± 0.2	−0.34 ± 0.09 a	−2.1 ± 0.2
GB effect	2.1 ± 0.2	−0.37 ± 0.10 b	1.8± 0.2

^aFor KCl concentrations in range 0.212–0.427m.

^bFor a KCl concentration of approximately 0.43m.

Analysis of initial slopes (∂ lnK_obs/∂ m₃)_{a4, m3→0} is not only convenient from the point of view of the correction to constant salt activity (eq 5), but also provides the most direct information regarding changes in ASA in the absence of solute. Possible origins of the changes in slope observed at higher concentrations of both urea and GB are discussed below.

ANALYSIS

The Intrinsic Interaction Coefficient for Urea and Polar Amide Surface

To obtain intrinsic interaction coefficients for urea and different types of biopolymer surface, we analyze the preferential interactions of urea with a wide range of biopolymer surfaces, differing in composition and in total surface area (18). Our approach is based on dissection of urea-biopolymer interactions and urea effects on well-defined biopolymer processes to obtain intrinsic interaction coefficients for the solute and various types of biopolymer surface. This contrasts with analyses that obtain analogous quantities (transfer free energies) from the effect of the solute on the solubility of model compounds (50). To date the two approaches have not been systematically compared. A limited comparison of free energies and enthalpies of transfer of two model peptides (di- and triglycine) from water to urea (51, 52) calculated from isopiestic distillation and solubility data revealed significant systematic differences that were attributed to the treatment of activity coefficients in the analysis of the solubility data.

For our dissection of observed urea-biopolymer interactions, quantitative information about the interactions of urea with the protein surface exposed in unfolding (which is typically relatively uncharged (< 5% charged ASA), largely nonpolar (65–75%), with 15–20% polar amide ASA), is obtained from the characterization of urea effects on the stability of globular proteins. Myers et al. (14) compiled urea m-values for the set of 45 globular proteins for which structural data were available, and found a linear relationship (with a small positive intercept) between the m-value and the ΔASA of unfolding. Correction for the effect of disulfide bonds on the ASA of the unfolded state eliminated the intercept and yielded a proportionality between the m-value and the total ΔASA.

In general the proteins in the Myers et al. (14) data set have stable folds, and exhibit midpoint unfolding concentrations of urea in excess of 4 M. Given the relatively high concentrations of urea used to denature proteins, the m-value only describes the initial slope if ΔG^o is a linear function of [urea]. (Initial slopes characterizing solute dependence on molal and molar concentration scales are the same.) Evidence for the validity of the linear extrapolation method (LEM) for urea is provided by detailed studies of the urea-induced helix-coil transitions of a series of marginally-stable α-helical peptides at 273 K (15) and unfolding studies of marginally-stable proteins as functions of temperature and urea concentration (e.g., 48, 53). For these marginally-stable systems, effects of urea on stability are observable over the concentration range from 0 up to 4–6 M; in all cases the m-value is independent of urea concentration within experimental uncertainty, justifying the LEM. Theoretical justification for the validity of the LEM for urea is provided by the two-domain, solute partitioning model of the preferential interaction, which should be valid for noncoulombic interactions of solutes with biopolymers (16, 45). For solutes other than urea, especially in cases where the solute-concentration-dependence of bulk solute nonideality (i.e. in 2-component solution) is larger in magnitude than that observed for urea, the LEM may be less successful (45).

We selected from the Myers et al. (14) data set the 14 proteins which lack both disulfide crosslinks and heme groups, and added to this set an additional 26 proteins (with high resolution folded structures and lacking disulfides and hemes) for which urea m-values have been recently reported at or near neutral pH (pH 5–8; in this range, typically no significant effect of pH on the m-value is observed (54)). Determinations at temperatures other than 298 K were corrected to 298 K using the small temperature dependence of the m-value determined previously for lac HTH (48), weighted by the relative amounts of polar amide surface exposed in the two processes. In Figure 4A, these 40 m-values are plotted as a function of the total ΔASA of unfolding. (All protein m-values, conditions, PDB files, and ΔASA calculations are reported in Table S2 in Supporting Information.) An excellent correlation is observed; the intercept is zero within the uncertainty of the best-fit line, indicating proportionality of the m-value to ΔASA_total. The error weighted average and standard deviation of the ratio m-value/ΔASA_total for the 40 protein data set is 0.15 ± 0.03. This result is plotted as the line in Figure 4A. (For the disulfide-corrected, 45 protein set of Myers et al. (14), the proportionality constant is 0.14, within error of the current result.) The largest deviation from this proportionality of urea m-value to ΔASA_total is observed for the largest protein in the data set, human glutathione transferase A1-1 (hGSTA1-1) (55). Unfolding of hGSTA1-1 is two-state (folded dimer _→ 2 unfolded monomer) and reversible. The surface exposed in unfolding hGSTA1-1 is only 13% amide (one of the two lowest values in the data set); for this protein the m-value/ΔASA_total ratio is smaller than the average by almost 3 standard deviations.

Figure 4. ASA Analysis of Urea m-Values for Unfolding of Monomeric and Dimeric Globular Proteins.

A). Literature determinations of urea m-values (converted to 25°C) are plotted vs. calculated values of the total ΔASA of unfolding for 40 monomeric and dimeric proteins (cf. Table S2 in Supporting Information). The line plotted corresponds to the error-weighted average value of the quantity m-value/ΔASA_total =0.15± 0.03.

B). The same set of urea m-values at 25°C as in Figure 4A are plotted vs. calculated values of the polar amide ΔASA of unfolding. The line plotted corresponds to the error-weighted average value of the quantity m-value/ΔASA_amide = 0.83±0.18, from which an intrinsic urea-amide ASA interaction coefficient Γ_μ3/m₃ASA_amide = (1.4±0.3) × 10⁻³ m⁻¹ Å⁻² is calculated.

C). Distribution of values of the intrinsic urea-amide ASA interaction coefficient (equal to m-value/RTΔASA_amide) for the set of 40 monomeric and dimeric proteins.

The m-value is related by fundamental three-component thermodynamics to the difference in urea preferential interaction coefficients for unfolded and folded states of the protein (16, 56–58). Assuming that interactions of urea with the protein surface which is solvent-accessible in both folded and unfolded forms are not affected by unfolding, the m-value is a direct measure of the preferential interaction coefficient Γ_μ3 characterizing the net interaction of urea with the entire protein surface exposed in unfolding. The ratio m-value/RTΔASA_total is interpreted as the intrinsic preferential interaction coefficient Γ_μ3/m₃ASAtotal (per unit of urea concentration and per unit area of protein surfaces exposed in unfolding) in the limit of low urea concentration (16). To determine whether the favorable preferential interaction with urea is specific for some subset of the surface exposed in unfolding (e.g. amide, nonpolar, etc.), we determined thermodynamic coefficients characterizing the interactions of urea with native DNA and protein (BSA) surfaces (17, 18; Cannon et al., in preparation) and analyzed literature data (15) for effects of urea on α-helix melting (16).

For α-helix melting, Table 3 shows that the ratio m-value/ΔASA_total is more than three times larger than for protein unfolding at 25°C, and that the fraction of total surface exposed upon unfolding which is polar amide surface (backbone and side chain ASA attributable to amide N and O) is also more than three times larger for α-helix melting than for protein unfolding (0.52 vs. 0.17; 16). The per residue ΔASA_total varies from 36 Ų to 47 Ų for various plausible models of the conformations of the K and E side chains in the helix (16, 18), which introduces substantial uncertainty in the ratio m-value/ΔASA_total. However, the average amount of polar amide ASA exposed per residue of (AEAAKA)_k α-helix unfolded is the same (20.6 ± 0.3 Ų), for all three structural models assumed for the α-helix.

We proposed (16, 18) that interaction coefficients of urea with protein and other biopolymer surfaces should be interpreted as primarily due to a favorable preferential interaction with polar amide surface. Since the m-value is independent of [urea], the intrinsic interaction coefficient for urea and polar amide surface exposed in unfolding proteins and α-helices at low [urea] Γ_μ3/m₃ASA_amide is equal to the ratio m-value/RTΔASA_amide. Calculated from the α-helix unfolding m-value, the intrinsic interaction coefficient for urea and polar amide surface is (1.8 ± 0.1) × 10⁻³ m⁻¹ Å⁻². Figure 4B shows the corresponding analysis for the protein unfolding data set of Figure 4A; in Figure 4B, 25 °C m-values are plotted as a function of the amount of polar amidesurface exposed in unfolding. Comparison of Figure 4A and 4B shows that in general the m-values correlate equally well with either total ΔASA or polar amide ΔASA, which is the expected result because most of the proteins in the data set form a homologous series in which 17 ± 2% of the surface exposed in unfolding is polar amide surface. The line in Figure 4B represents the error-weighted average value of the intrinsic urea-amide interaction coefficient m-value/RTΔASA_amide = (1.4 ± 0.3) × 10⁻³ m⁻¹ Å⁻² for all 40 proteins (cf. Supporting Information). The protein hGSTA1-1, which deviates by the largest amount from the average in Figure 4A, agrees with the average in Figure 4B.

The intrinsic interaction coefficient for urea and polar amide surface obtained from the protein unfolding data ((1.4 ± 0.3) × 10⁻³) is the same within uncertainty as that obtained from analysis of α-helix unfolding m-value (1.8 ± 0.1) × 10⁻³, which supports the hypothesis that a favorable interaction of urea with polar amide surface is the dominant factor contributing to urea denaturation of proteins and of α-helices. Figure 4C plots the distribution of the protein folding data set around this error-weighted average. It will be important to ascertain whether the breadth of this distribution indicates the existence of a secondary interaction of urea with other types of protein surface, or whether it arises from experimental factors (e.g., deviations from two-state, reversible transitions or differences in baseline assignments used to calculate m-values) or from the choice of structural models for the folded and unfolded states of these proteins in solution used for calculation of ΔASA.

Native biopolymer surfaces, such as those of BSA and duplex DNA, differ profoundly in composition from the surfaces exposed in the processes of unfolding proteins and melting α-helices. These native surfaces are much more highly charged and much less nonpolar than are the surfaces exposed in unfolding/melting. As shown in Table 3, the intrinsic interaction of urea with BSA surface (2.78 × 10⁴ Ų), which is 14.6% polar amide but 29% charged and 53% nonpolar, expressed per Ų of polar amide surface, is the same within error as that obtained for the surfaces exposed in unfolding proteins and α-helices. No significant effect of the large percentage of charged surface on this ratio is detected. For duplex DNA, the surface of which is 44% charged (anionic) but only 2.5% polar amide, no significant preferential interaction with urea is observed, indicating that urea is not significantly accumulated nor excluded from anionic or other types of DNA surface. (Because we do not detect the predicted slight accumulation of urea at the 2.5% of the surface of duplex DNA which is amide-like, it is possible that there is a compensating slight exclusion from anionic or other DNA surface, which we are unable to dissect.)

Since protein unfolding comprises the most extensive data set in Table 3, we select the intrinsic urea-polar amide surface preferential interaction coefficient and uncertainty specified by these data for use in analysis of the effects of urea on binding of LacI to SymL. All other data in Table 3 are consistent with this result within the uncertainty. We therefore propose that, for any biopolymer process with equilibrium concentration quotient K_obs, the derivative (∂ lnK_obs/∂ m₃)_{a4,m3→ 0} at low urea concentration is, to a good approximation, proportional to the change in the amount of water accessible polar amide surface (ΔASA_amide) in the process.

$${(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_3)}_{a_4,{\text{m}}_3\to 0}=(1.4\pm 0.3)\times {10}^{-3}\mathrm{\Delta }{\text{ASA}}_{\text{amide}}$$ (6)

When the data of Table 3 are analyzed as a linear combination of contribution from polar amide, nonpolar and anionic surface (by the method of Appendix 2), fitted coefficients for nonpolar and anionic surface are an order of magnitude smaller than for polar amide surface, and comparable to their uncertainties; the coefficient for polar amide surface agrees within uncertainty with eq 6 above.

The Intrinsic Interaction Coefficient for Glycine Betaine and Anionic Surface

GB is strongly excluded from the surfaces of native BSA and DNA, and modestly excluded from native hen egg white lysozyme (19). GB modestly increases the thermal stability of RNase and lysozyme (46), and more significantly stabilizes the lac HTH (19). One interpretation of the stabilizing effects of GB is that it is modestly excluded from the surface exposed in unfolding these proteins (19). Unpublished experiments from our laboratory show that GB at concentrations up to 2M has no significant effect on the stability of an (AEAAKA)₆ α-helix and therefore is neither excluded from nor accumulated at the surface exposed in melting this α-helix (Cannon, Heitkamp et al, unpublished). We also find that GB is significantly excluded from the dicarboxylic acid salt potassium glutamate (Cannon, unpublished), although it is slightly accumulated in the vicinity of potassium chloride (18), indicating that the exclusion is probably attributed to the glutamate anion.

From these data, we are able to refine our previous analysis (19, 59) to conclude that GB is detectably excluded only from anionic surface (phosphate, carboxylate) and that it exhibits no detectable preferential interaction with amide and nonpolar surface. The observed exclusion from anionic surface may be explained by the fact that GB, unlike water, has no hydrogen bond donor groups and so no ability to hydrogen bond to anionic groups of proteins or nucleic acids. Analysis of the published data for interactions of GB with BSA and duplex DNA as an interaction only with anionic surface yields an intrinsic interaction coefficient (per unit molality of GB and per unit anionic surface) of − 4.0 × 10⁻³ m⁻¹ Å⁻², as previously reported (19). In addition to this exclusion from anionic surface, GB has been observed to interact favorably with (i.e., accumulated at) some aromatic surfaces, forming a cation-π complex in the co-crystal structure of its transporter protein (60), and to selectively destabilizing GC (but not AT) DNA at molar concentrations, presumably by a weak favorable interaction with G or C bases in the single-stranded state (18, 61). A weak cation-π interaction of GB with tyrosines on the surface of the folded HTH which are buried in the protein-DNA interface could explain the greater-than-expected stabilization of the lac HTH against thermal unfolding by GB, as discussed below.

For biopolymer processes where the interaction of GB with aromatic surface is not significant, the semilogarithmic derivative (∂ lnK_obs/∂ m₃)_a4,m3→0 at low GB concentration is expected to be proportional to the change in the amount of water accessible anionic surface (ΔASA_anionic).

$${(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_3)}_{{\text{a}}_4,{\text{m}}_3\to 0}=-4.0\times {10}^{-3}\mathrm{\Delta }{\text{ASA}}_{\text{anionic}}$$ (7)

We estimated an uncertainty in this value of ~ 20% based on the standard deviation of the much larger data set sed to establish the corresponding proportionality for urea and polar amide surface (cf. eq 6).

DISCUSSION

Use of urea to quantify burial of polar amide surface in repressor-operator binding: Contributions from the interface and from coupled folding

Previously we used heat capacity changes upon binding to quantify changes in nonpolar and polar water-accessible surface area in protein-ligand and protein-protein interactions (62); this analysis has successfully predicted the occurrence and often the amount of coupled folding in these protein associations (4). However, other large-scale temperature-dependent coupled processes also can contribute to the heat capacity change in reactions involving biopolymers (e.g., 63–66). These coupled equilibria (e. g. protonation, changes in base stacking, salt bridge disruption) are not generally related to overall structural changes, necessitating the development of more direct probes of coupled folding. Here we propose that the study of the urea concentration dependence of the binding constant provides one such method.

The initial slope describing the urea dependence of the logarithm of the LacI-SymL binding constant at low urea molality and at constant KCl activity is (cf. Table 2)

$${(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_3)}_{{\text{a}}_4,{\text{m}}_3\to 0}=-2.1\pm 0.2$$ (8)

Interpretation of the initial effect of urea on the binding constant of the LacI-SymL interaction (eq 8) using the intrinsic urea-polar amide interaction coefficient (eq 6) predicts that (1.5 ± 0.3) × 10³ Ų of polar amide surface is buried upon specific binding of a SymL operator to the lac repressor tetramer. This thermodynamics-based structural prediction greatly exceeds the amount of amide surface buried in the rigid body LacI-SymL interface (491 Ų, see Table 1 and Figure 5). However, this apparent discrepancy ((1.0 ± 0.3) × 10³ Ų) is fully explained by inclusion of the coupled conformational changes inferred from the structure. The DNA binding domains (DBD), composed of helix-turn-helix (HTH) residues 1-49 and flexible tethers (“hinges”) connecting the HTH to core repressor (residues 50-58), are not observed in the crystal structure of the intact (DBD-containing) free repressor (12). Hence in the free (unbound) form of repressor the DBD are not assembled on the repressor core, whereas they are visualized in the structure of the complex in an ordered and docked state (See Figure 5). Indeed solution NMR experiments reveal that the hinge residues are unstructured in the free state and fold upon binding to the SymL operator (8, 10).

Figure 5. Structural Model Showing Lac Repressor Surfaces Buried in Binding Operator DNA.

Binding of LacI to SymL involves the formation of the protein-DNA interface, folding of the hinge helices and docking of the DNA binding domains on the core domains of repressor. In this cartoon, residues buried in forming the rigid body interface are shown in yellow, residues buried in folding the hinge helices are red, and residues buried in the core-DBD interface are blue. This model is based on PDB file 1EFA (40), and was created using MolScript (76) and Raster3D (77).

Coupled folding of the two hinge helices is predicted (see Table 1) to bury 515 Ų of polar amide surface (258 Ų for folding of each hinge helix). As shown in Figure 5, the folded hinge helices not only participate in the interface with SymL operator DNA, but also participate in an interface between the LacI DBD and the LacI core in the operator complex (40). Docking of the pairs of DNA-bound hinge helices and HTH domains on the repressor core buries 2 × 260 Ų = 520 Ų of polar amide surface. Therefore the total amount of polar amide surface deduced to be buried in coupled folding of the hinge helices and in forming an interface between the folded headpieces/hinge helices and core is 1035 Ų of polar amide surface. This value calculated from structural data is the same as that obtained by urea analysis within uncertainty.

The structural data of Table 1 reveal why urea is a sensitive probe of the existence and amount of folding that is coupled to binding in protein interactions. Only 1144 Ų of total surface are buried in folding the two 9-residue hinge helices, but 45% of this is polar amide surface (515 Ų). Therefore the contribution of folding 18 residues and burying a total of only 1144 Ų of surface to the observed effect of urea on the binding constant is just as large as the contribution from the burial of 2049 Ų of surface in the interface between the folded DBD and core repressor (which is only 25% polar amide), and from the burial of 3689 Ų of surface in the repressor-operator (protein-DNA) interface (which is only 13% polar amide surface because of the lack of these functional groups on the accessible surface of duplex DNA).

If the hinge helices are completely unfolded in the free state of repressor and completely folded and docked in the complex with SymL, and if no other coupled processes contribute to the thermodynamics, the heat capacity change predicted (4) from the ASA data in Table 1 and Figure 5 is approximately −0.80 kcal K⁻¹. By contrast, the experimental value is approximately −1.5 kcal K⁻¹. Calorimetric studies with a crosslinked dimer of the DNA binding domain (residues 1-62) are in progress in an attempt to determine the other factor(s) contributing to the heat capacity change of LacI-SymL binding.

It is instructive to compare the structural prediction of the polar amide ASA analysis of the urea effect with that which would be obtained using the original Myers et al. (14) expression in terms of total ASA, applicable only to analysis of unfolding data for the homologous series of globular proteins. Analysis of the urea dependence of the repressor-operator binding constant (eq 8), using the original protein folding expression (m-value/ΔASA_total = 0.14 (14)) yields a predicted ΔASA_total = 8.9× 10³ Ų, which exceeds the structural value by 74% (cf. Table 1: 5.1× 10³ Ų of repressor ASA buried in complexation). Even if the ASA of DNA buried in complexation were included, which is not justifiable given the observation of no significant preferential interaction of urea with duplex DNA (18; see Table 3), the protein-folding correlation overpredicts ΔASA_total by 29%. The over-prediction occurs because the m-value/ΔASA_total ratio obtained from analysis of globular protein folding data is only applicable to processes which expose or bury surface with the same polar amide percentage (17%) as that characteristic of folding globular proteins. However, the percentage of total surface buried in LacI-SymL complexation which is polar amide surface is 22% (including DNA surface) or 30% (including only repressor surface).

Interpreting the Urea Concentration Dependence of dlnK_obs/dm₃ for Repressor-Operator Binding

Figure 3 and eq 3 indicate that the magnitude of the derivative dlnK_obs/dm₃ increases with increasing urea concentration in the range examined (up to 3.19 molal). This urea concentration dependence of dlnK_obs/dm₃ is in the opposite direction from that expected from the solute partitioning model, in which three factors make contributions to the concentration dependence of dlnK_obs/dm₃: 1) urea nonideality (1+ ε₃); 2) attenuation of the urea local-bulk partition coefficient (45), and 3) the effect of replacement of local water by urea when it accumulates at biopolymer surfaces (16). These three factors, predicted to be of approximately equal significance, together are expected to reduce the magnitude of dlnK_obs/dm₃ by approximately 25% at 1.59 molal urea and 43% at 3.19 molal urea. However, we observe that the magnitude of dlnK_obs/dm₃ increases by approximately 18% at 1.59 molal urea and 35% at 3.19 molal urea.

A plausible origin of these effects is urea-driven unfolding of either the HTH or the core of lac repressor. At 298 K and salt conditions which differ from those investigated here, the core of lac repressor unfolds in a very narrow transition at approximately 3 M urea (34, 67). At 298 K, the HTH unfolds in a very broad transition starting in the absence of urea at low salt (25 mM K₂HPO₄; 48) and near 1 M urea at 0.2 M K₂HPO₄ (67), which is probably a more stabilizing salt than our binding buffer. Therefore urea-induced unfolding of the DNA-binding HTH appears to be the most likely explanation of the direction and magnitude of curvature in Figure 3. Calculations of the curvature predicted as a result of a broad unfolding transition for the HTH are consistent with that observed (data not shown).

Use of glycine betaine to quantify burial of DNA phosphate surface in repressor-operator binding

The initial slope describing the GB dependence of the logarithm of the LacI-SymL binding constant at low GB molality and at constant KCl activity is (cf. Table 2)

$${(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_3)}_{{\text{a}}_4,{\text{m}}_3\to 0}=1.8\pm 0.2$$ (9)

Comparison of eq 9 with eq 7 for the repressor-operator interaction yields the following structural prediction from the thermodynamic analysis: ΔASA_anionic = − (4.5 ± 1.0) × 10² Ų. By this analysis, approximately 450 Ų of anionic surface are predicted to be buried upon binding one SymL operator DNA to one pair of headpieces on a LacI tetramer. This prediction is ~ 70(± 16)% of the amount of anionic surface which we calculated as buried in the LacI-SymL (TO) interface (632 Ų, obtained by doubling the amount of anionic ASA buried in the more highly resolved half site).

One possible explanation of the discrepancy between the structural value and the GB-based prediction for the ΔASA of anionic surface, which, if correct, will limit the utility of GB as a quantitative probe for changes in exposure of anionic surface in biopolymer processes, involves the same proposal as that discussed above to rationalize the greater-than-expected stabilization of the folded state of the lac HTH by GB. Interaction of the cationic end of GB with the aligned tyrosines in the DNA binding site of the folded HTH would not only stabilize the folded state against unfolding but also compete with DNA binding, and hence reduce the otherwise stabilizing effect of GB on a process which buries anionic surface. A second possible explanation, developed in Appendix 2, is that residual water in the interface of the complex, not detected in the crystallization, reduce the magnitude of the GB effect. Even with the uncertainty regarding this effect, it appears that GB can be used as a semiquantitative probe of changes in exposure of anionic surface in processes involving proteins and double stranded DNA. For example, the rate-determining conformation change in open complex formation by E.coli RNA polymerase (Eσ⁷⁰) at the λ P_R promoter is significantly disfavored by GB, consistent with exposure of anionic surface in this step (68). Since DNA phosphates presumably are buried in this process, the GB result (68) may indicate exposure of carboxylates on RNA polymerase in this step. One possible candidate, shown to be exposed in open complex formation (69) is the negatively charged N terminal domain of σ⁷⁰, exposure of which would unmask the active site. Since GB is inferred to interact with guanine and/or cytosine bases in single-stranded DNA (18), perhaps also by a cation-π interaction involving stacked bases, it will probably not be a suitable probe of processes involving single-stranded DNA. If GB were also excluded from amide surface, as originally proposed (19, 50), the discrepancy between structural and thermodynamic analyses of the change in “GB-affected” surface area would be even greater.

Interpreting the Glycine Betaine Concentration Dependence of dlnK_obs/dm₃ for Repressor-Operator Binding

Figure 3 and eq 4 indicate that the magnitude of the derivative dlnK_obs/dm₃ decreases with increasing GB concentration in the range examined (up to 3.03 m). This GB concentration dependence of dlnK_obs/dm₃ is consistent with an attenuation model (45), in which the GB concentration dependence of its nonideality in the local domain is expected to be attenuated relative to that of the bulk domain due to GB-protein surface interaction in the local domain. The same amount of attenuation as that deduced for the GB effect on lac HTH unfolding (45) can be used to interpret the curvature of dlnK_obs/dm₃ in our LacI binding study. (Details of the calculation are given in Supporting Information.) Using the GB attenuation model (45), $ln({\text{K}}_{\text{obs}}/{\text{K}}_{\text{obs}}^{\text{o}})$ is expressed as a 4^th power polynomial in m₃. Fitting experimental values of $ln({\text{K}}_{\text{obs}}/{\text{K}}_{\text{obs}}^{\text{o}})$ to this polynomial yields the value of (∂ lnK_obs/∂m₃)_a4,m3→0 =1.6 ± 0.2 which is the same within uncertainty as determined above (see eq 9) from analyzing the initial slope (∂ ln K_obs/∂m₃)_m4,m3→0 of the quadratic fitting of $ln({\text{K}}_{\text{obs}}/{\text{K}}_{\text{obs}}^{\text{o}})$ vs. m₃.

CONCLUSION

This study provides the basis for, and an example of the use of, urea as a quantitative probe of coupled folding and other large scale coupled conformational changes in protein-DNA interactions and other protein associations. Urea selectively detects changes in exposure of polar amide surface, and consequently is a very sensitive probe of α-helix formation (or disruption) and other local folding or unfolding processes. Urea is also a sensitive probe of formation (or disruption) of protein-protein interfaces coupled to DNA binding, and is relatively insensitive to the formation of the protein-duplex DNA interface because of the virtual absence of water-accessible amide-like surface on the DNA double helix. Urea should be very useful to determine the order and the magnitude of coupled conformational changes that occur in a multistep protein-DNA binding process, such as formation of an open promoter complex, by observing urea-concentration-dependent effects on the rate and equilibrium constants of the individual steps of the mechanism. Studies of urea effects on open complex formation by RNA polymerase are in progress.

Supplementary Material

si20051007_043. Supporting Information Available.

In Supporting Information we tabulate the observed values of K_TO at the concentrations of urea, GB, and KCl investigated here, as well as the corrected values of K_TO in GB experiments in which KCl and glycerol molality varied slightly with GB molality. Individual values of surface area changes and corresponding m-values for the set of monomeric and dimeric proteins summarized in Table 3 are also reported. In addition, the details of the thermodynamic analysis using a solute partitioning model are presented. This analysis is used to interpret the curvature in ln Kobs as a function of GB concentration. The Supporting Information is available free of charge via the Internet at http://pubs.acs.org.

Abbreviations

ASA

water-accessible surface area

ASA_amide

the contribution to ASA from the polar atoms (N, O) of amide groups

GB

glycine betaine (N,N,N-trimethyl glycine)

LacI

lac repressor

SymL

symmetric lac operator, a palindrome of the left (upstream)-half site of the primary O₁ operator

m-value

the slope of plot of ΔG^o of protein unfolding versus the molar concentration of chemical denaturant or osmolyte

AEAAKA

Ala-Glu-Ala-Ala-Lys-Ala

DBD

DNA binding domain (residues 1-62) of LacI

LEM

linear extrapolation method of analysis of urea unfolding data

APPENDIX 1

Conversion of (∂ln K_obs/∂m₃)_m4 to (∂ ln K_obs/∂m₃)_a4

Here we obtain eq 5 in the text, which relates the experimentally-determined derivative (∂ ln K_obs/∂m₃)_m4 at constant temperature, pressure and molality of a 1-1 salt (4) to the derivative (∂ ln K_obs/∂m₃)_a4 at constant salt activity a₄ and thereby eliminates the effect on ln K_obs of changes in salt activity brought about by changing solute (urea or GB) concentration at constant salt molality. This analysis is accomplished using standard manipulations of partial derivatives. The basic mathematical relationship between (∂ ln K_obs/∂m₃)_m4 and (∂ ln K_obs/∂m₃)_a4 in an excess of solute components 3 and 4 (relative to biopolymer participants (70)) is

$${(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_3)}_{{\text{a}}_4}={(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_3)}_{{\text{m}}_4}+{(\partial ln{\text{K}}_{\text{obs}}/\partial {\text{m}}_4)}_{{\text{m}}_3}{(\partial {\text{m}}_4/\partial {\text{m}}_3)}_{{\text{a}}_4}$$ (A1)

The partial derivatives in the additive correction term in eq A1 are evaluated using experimental data:

$${\text{where SK}}_{\text{obs}}\equiv {(\partial ln{\text{K}}_{\text{obs}}/\partial ln{\text{C}}_4)}_{{\text{m}}_3}\cong {(\partial ln{\text{K}}_{\text{obs}}/ln{\text{m}}_4)}_{{\text{m}}_3}$$ (A2)

$$\text{and }{(\partial {\text{m}}_4/\partial {\text{m}}_3)}_{{\text{a}}_4}=-\frac{{\mu }_{43}}{{\mu }_{44}}=-\frac{{\mu }_{34}}{{\mu }_{44}}$$ (A3)

$$\text{where }{\mu }_{34}\equiv {(\partial {\mu }_3/\partial {\text{m}}_4)}_{{\text{m}}_3}\cong \text{RT}\mathrm{\Delta }{\text{Osm}}_{34}/{\text{m}}_3{\text{m}}_4$$ (A4)

$$\text{and }{\mu }_{44}\equiv {(\partial {\mu }_4/\partial m_4)}_{m_3}=2\text{RT}{(1+{\epsilon }_{\pm })}_{{\text{m}}_3}{/\text{m}}_4$$ (A5)

Euler reciprocity is used in the second equality of equation A3. In equation A4, ΔOsm₃₄ ≡ Osm(m₃,m₄) − Osm(m₃) − Osm(m₄) where Osm(m₃) and Osm(m₄) are osmolalities of two component solutions at the same molality as that of these solutes in the three component solution with osmolality Osm(m₃,m₄). The approximate relationship between μ₃₄ and ΔOsm₃₄, sufficiently accurate for this purpose, was originally presented by Robinson and Stokes (71) and was recently derived by Anderson and Record (72). In equation A5, ε_± symbolizes the derivative ∂ lnγ_±/∂ ln m₄ of the mean ionic activity coefficient of the 1-1 salt with respect to its concentration.

Combining eqns A2-5 in eq A1 yields:

$${\left(\frac{\partial ln{K}_{\mathit{obs}}}{\partial m_3}\right)}_{a_4}={\left(\frac{\partial ln{K}_{\mathit{obs}}}{\partial m_3}\right)}_{m_4}+\frac{{\text{SK}}_{\text{obs}}\mathrm{\Delta }{\text{Osm}}_{34}}{2{\text{m}}_3{\text{m}}_4{(1+{\epsilon }_{\pm })}_{{\text{m}}_3}}$$ (A6)

In the limiting case where m₃ approaches zero, the log-log salt derivative SK_obs and the activity coefficient derivative ε_± may be approximated by their values in the absence of the perturbing solute (component 3). The quantityΔOsm₃₄/m₃m₄ = μ₃₄/RT does not vanish as the urea concentration is reduced because it represents the intrinsic effect of salt concentration on the chemical potential of urea. For lac repressor binding to plasmid operator DNA, SK_obs = −7.0 ± 1.0 in the vicinity of 0.3m KCl (30). For KCl solutions in the range 0.2–0.43m, (1+ ε_±) _m3=0 =0.893 ± 0.001 (49).

APPENDIX 2

Analysis of the Solute Concentration Dependence of ln K_obs using the Solute Partitioning Model: Initial Slope Method

Hong (23, thesis chapter 4 Appendix 1) generalized the basic thermodynamic relationship that expresses a concentration effect of a nonelectrolyte solute (3) on the observed equilibrium constant K_obs (or free energy change $\mathrm{\Delta }{\text{G}}_{\text{obs}}^{\text{o}}=-\text{RT}ln{\text{K}}_{\text{obs}}$) for a biopolymer process from a system containing one perturbing solute (58, 73) to the case where two perturbing solutes (e.g., GB and KCl) are present:

$${\left(\frac{\partial ln{\text{K}}_{\text{obs}}}{\partial {\text{m}}_3}\right)}_{{\text{a}}_4}\cong \frac{\mathrm{\Delta }{\mathrm{\Gamma }}_{{\mu }_3}}{{\text{m}}_3}{(1+{\epsilon }_3)}_{{\text{a}}_4}$$ (A7)

where Γ_μ3 is a solute-biopolymer preferential interaction coefficient, ΔΓ_μ3 is the stoichiometrically weighted difference in preferential interaction coefficients between products and reactants, and ε₃ ≡ (∂ ln γ₃/∂ ln m₃)_T,P,a4. Major approximations in eq A7 are discussed by Hong (23). In the limit m₃ → 0, but maintaining the excess of solute over any biopolymer reactant or product (denoted by numerical number 2) (m₃ ≫m₂), there is no significant difference between the bulk and the total solute concentration (74), and the initial slope of ln K_obs vs. m is given by

$${\left(\frac{\partial ln{\text{K}}_{\text{obs}}}{\partial {\text{m}}_3}\right)}_{{\text{a}}_4}^{{\text{m}}_3\to 0}\cong {\left(\frac{\mathrm{\Delta }{\mathrm{\Gamma }}_{{\mu }_3}}{{\text{m}}_3}\right)}^{{\text{m}}_3\to 0}$$ (A8)

For the interaction of a nonelectrolyte solute with a biopolymer, in the solute partitioning model (also called the local-bulk or two domain model) (16, 75), Γ_μ3/ m₃ is expressed in terms of molecular parameters:

$$\frac{{\mathrm{\Gamma }}_{{\mu }_3}}{{\text{m}}_3}=\frac{{\text{B}}_3}{{\text{m}}_3}-\frac{{\text{B}}_1}{{\text{m}}_1^{•}}=\frac{({\text{K}}_{\text{p}}-1){\text{b}}_1^{\text{o}}\text{ASA}}{{\text{m}}_1^{•}(1+{\text{K}}_{\text{p}}{\text{S}}_{1,3}{\text{m}}_3/{\text{m}}_1^{•})}$$ (A9)

In the first part of eq A9, B3 and B1 are the numbers of solute and water molecules in the local domain at the surface of a biopolymer and ${\text{m}}_1^{•}=55.5\text{mol}({\text{H}}_2\text{O})/\text{kg}({\text{H}}_2\text{O})$. In the second part of eq A9, the local-bulk solute partition coefficient K_p is defined as ${\text{K}}_{\text{p}}\equiv ({\text{B}}_3/{\text{B}}_1)/({\text{m}}_3^{\text{bulk}}{/\text{m}}_1^{•})$, the hydration of the biopolymer per unit area in the absence of solute ${\text{b}}_1^{\text{o}}={\text{B}}_1^{\text{o}}/\text{ASA}$, and S_1,3 is the cumulative exchange stoichiometry (the number of water molecules displaced from the local domain divided by the number of solute molecules accumulated) (16, 75). As m₃ → 0, using the superscript “o” to denote this limit,

$${\left(\frac{{\mathrm{\Gamma }}_{{\mu }_3}}{{\text{m}}_3}\right)}^{{\text{m}}_3\to 0}=\frac{{\text{B}}_3}{{\text{m}}_3}-\frac{{\text{B}}_1^{\text{o}}}{{\text{m}}_1^{•}}=\frac{({\text{K}}_{\text{p}}^{\text{o}}-1){\text{b}}_1^{\text{o}}\text{ASA}}{{\text{m}}_1^{•}}$$ (A10)

For the binding of a protein to a nucleic acid where the creation of the binding interface(s) is characterized by reductions in ASA of different types of biopolymer surface and where some water molecules (and, in principle, some solute molecules) are retained in these interface(s), eq A8 and eq A10 yield

$${\left(\frac{\partial ln{\text{K}}_{\text{obs}}}{\partial {\text{m}}_3}\right)}_{\text{T},\text{P},{\text{a}}_4}^{{\text{m}}_3\to 0}=[(\frac{{\text{B}}_{3,\text{I}}}{{\text{m}}_3}-\frac{{\text{B}}_{1,\text{I}}}{55.5})+\sum _{\text{i}}{\text{f}}_{\text{i}}{\left(\frac{{\mathrm{\Gamma }}_{{\mu }_3}}{{\text{m}}_3\text{ASA}}\right)}_{\text{i}}^{{\text{m}}_3\to 0}\mathrm{\Delta }{\text{ASA}}_{\text{i}}]$$ (A11)

In eq A11, B_3,I and B_1,I are the numbers of solute and water molecules retained in the interface of the complex. Eq A11 assumes that contributions to ΔΓ_μ3 from interactions of solute with different types of biopolymer surface are additive (16–19). In eq A11, f_i is the fraction of total surface of the i^th type and ΔASA_i is the change in the amount of water accessible biopolymer surface of this type in the process. The sum in eq A11 is over all types of biopolymer surface (i) for which ASA_i changes; types of surface considered at the current level of resolution include anionic, polar amide, other polar, cationic, and nonpolar (18, 19). For binding processes, these ΔASA_i are typically negative (as a result of forming the binding interfaces), although coupled conformational changes may expose some biopolymer surface (e.g., coupled unfolding). Each ΔASA_i in eq A11 should be calculated without regard for any buried water (or solute) within the interface (no such water is present in relevant interfaces of the lac repressor-operator complex in 1 EFA). Then the term ${({\mathrm{\Gamma }}_{{\mu }_3}/{\text{m}}_3\text{ASA})}_{\text{i}}^{{\text{m}}_3\to 0}\mathrm{\Delta }{\text{ASA}}_{\text{i}}$ represents the contribution to (∂ lnK_obs/∂ m₃) _{a4,m3→ 0} from the i^th type of surface for the situation where its interactions with water and solute are eliminated in formation of the complex.

For urea, the quantity ${({\mathrm{\Gamma }}_{{\mu }_3}/{\text{m}}_3\text{ASA})}_{\text{i}}^{{\text{m}}_3\to 0}$ is significantly different from zero only for interactions with polar amide surface (18). Interactions with cationic, anionic and nonpolar surface are an order of magnitude smaller and comparable to their uncertainties. The observation that GB has no significant effect on α-helix stability (Cannon, Heitkamp et al, unpublished), together with the data analyzed previously (19) indicates that ${({\mathrm{\Gamma }}_{{\mu }_3}/{\text{m}}_3\text{ASA})}_{\text{i}}^{{\text{m}}_3\to 0}$ is most significant for GB interaction with anionic surface, although interactions with other types of biopolymer surface may also contribute (see Discussion).

The term B_1,I (and B_3,I if relevant) in eq A11 accounts for the effect of any water (or solute) retained in the interface. No water is detected in the binding interface in crystal and NMR structures of repressor-operator complexes, though the 2.6 Å resolution of the crystal structure can not unambiguously allow one to conclude that water is totally absent from the interface. For every 10 waters remaining in the interface of the complex, the predicted value of the derivative (∂ lnK_obs/∂ m₃)_a4,m3→0 (for any solute) is reduced by the amount 10/55.5 = 0.18 from that calculated by considering the contributions of the different types of dehydrated surface in eq A11. Therefore, if the presence of 40 residual water molecules in the interface of the complex were the explanation for the deviation between predicted and observed effects of GB (Δ(∂lnK_obs/∂m₃) = 2.5–1.8 =0.7), 40 water molecules should also contribute to the effect of urea on K_obs according to eq A11. If 40 water molecules were retained in the interfaces of the repressor-operator complex, the contribution to ∂lnK_obs/∂m_urea ascribed to burial of polar amide surface would be changed from −2.1 to −1.4, a 33% reduction in the magnitude of the thermodynamic prediction for polar amide ΔASA, thereby introducing a 33% discrepancy between structural and thermodynamic predictions. Since such a discrepancy is well outside of experimental uncertainty, we interpret it to mean that substantially less than 40 water molecules are present in the interfaces of the repressor-operator complex, and that the discrepancy in the GB result is largely due to other factors, as discussed in the text.

Table A1

	KCl molality (m4)	SKobs for LacI-SymL	ΔOsm34/m3 m4 at m3→0	2 (1 + ε±)m3=0	$\frac{{\text{SK}}_{\text{obs}}\mathrm{\Delta }{\text{Osm}}_{34}}{2{\text{m}}_3{\text{m}}_4{(1+{\epsilon }_{\pm })}_{{\text{m}}_3}}$
Urea:
	0.212	−7.0	−0.09 ± 0.02	1.788	−0.35 ± 0.09
	0.427	−6.3	−0.09 ± 0.01	1.785	−0.33 ± 0.09
GB:
	0.212	−7.0	−0.12 ± 0.01	1.788	−0.43 ± 0.08
	0.404	−6.3	−0.10 ± 0.02	1.785	−0.34 ± 0.09
	0.427	−6.3	−0.12 ± 0.02	1.785	−0.42 ± 0.08