Charles F. Anderson

Thermodynamic analysis of ion effects on the binding and conformational equilibria of proteins and nucleic acids: the roles of ion association or release, screening, and ion effects on water activity

The purpose of this review is to examine the various effects of low- molecular-weight electrolytes on the associations and interactions of proteins and nucleic acids. Our primary interest is in general electrostatic effects, rather than chemical effects (specific interactions) of particular ions (e.g. transition metals, protons). We consider those interactions in which a variation in salt concentration has a significant effect on the macromolecular equilibrium, and analyse the effects of salt in these situations in terms of (i) direct participation of ions in the biopolymer reaction, (ii) Debye—Huckel screening by salt ions of the charge interactions on the biopolymers, and (iii) the reduction in water activity brought about at high salt concentrations.

Sodium-23 NMR studies of cation-DNA interactions

Abstract Sodium-23 NMR has been used to study the extent to which monovalent cations associate with double stranded DNA in aqueous solution (28°C, pH = 7.5). On the basis of the two site model for rapid exchange the 23 Na linewidth can be related to the fraction of sodium ions associated with DNA. To test the applicability to this system of the condensation model for the association of small counterions with polyelectrolytes, the concentration dependence of the sodium linewidth has been determined by making additions of NaCl to solutions of tetraethyl or tetrabutylammonium DNA. ([P], the DNA phosphate concentration was about 0.02M). The resulting titration curves extend over a wide range of the ratio [Na]/[P] (0.3–30). When [Na]/[P] ≳ 3 only sodium is associated, and the extent to which it compensates the charges on DNA does not vary with the addition of salt, at least until [Na]/[P] ≈ 30, the highest concentration examined. When [Na]/[P] ≲ 3 the tetraalkylammonium species is also associated with DNA; an equation has been derived to account for the effect on the 23 Na linewidth of the competition between sodium and another monovalent cation. Based on the assumption that the fraction of uncompensated charge remaining on DNA after the condensation of both species is constant, this equation fits all the linewidth data if the charge fraction is in the range 0.25 ± 0.10. The value required by the condensation model for DNA in the presence of monovalent counterions is ξ −1 = 0.24. The reasonable agreement between experimental and theoretical values of the charge fraction and its invariance with respect to large variations in the concentration of added salt indicate that even in moderately concentrated solutions of DNA, the association of sodium can usefully be described in terms of the condensation model. If the theoretical value of the charge fraction is assumed, it follows from fitting the titration curves that the approximate relative affinities for DNA of Na + , Et 4 N + , and Bu 4 N + are in the ratio 20:5:1, and the transverse relaxation rate of condensed sodium is 180 ± 10 s −1 .

Interpretation of preferential interaction coefficients of nonelectrolytes and of electrolyte ions in terms of a two-domain model.

For a three-component system consisting of solvent (1), polymer or polyelectrolyte (2J), and a nonelectrolyte or electrolyte solute (3), a two-domain description is developed to describe thermodynamic effects of interactions between solute components (2J) and (3). Equilibrium dialysis, which for an electrolyte solute produces the Donnan distribution of ions across a semipermeable membrane, provides a fundamental basis for this two-domain description whose applicability is not restricted, however, to systems where dialysis equilibrium is established. Explicit expressions are obtained for the solute-polymer preferential interaction coefficient gamma 3,2J (nonelectrolyte case) and for gamma +,2J and gamma -,2J, which are corresponding coefficients defined for single (univalent) cations and anions, respectively: gamma +,2J = magnitude of ZJ + gamma -,2J = 0.5(magnitude of ZJ + B-,2J + B+,2J) - B1,2Jm3/m1 Here B+,2J, B-,2J, and B1,2J are defined per mole of species J, respectively, as the number of moles of cation, anion, and water included within the local domains that surround isolated molecules of J; ZJ is the charge on J; m3 is the molal concentration of uniunivalent electrolyte, and m1 = 55.5 mol/kg for water. Incorporating this result into a general thermodynamic description(derived by us elsewhere) of the effects of the activity a+ of excess uniunivalent salt on an equilibrium involving two or more charged species J (each of which is dilute in comparison with the salt) yields:SaKobs bS/d a+ A(r+2J r 2j) A(B+2J B-2 2B12Jm3/m1)where KObS is an equilibrium quotient defined in terms of the molar concentrations of the participants, J, and A denotes astoichio metrically weighted combination of terms pertaining to the reactant(s) and product(s). The derivation presented here does not depend on any particular molecular model for salt-polyelectrolyte (or solute-polymer) interactions; it therefore generalizes our earlier (1978) derivation.

Conformational transitions of duplex and triplex nucleic acid helices: thermodynamic analysis of effects of salt concentration on stability using preferential interaction coefficients.

For order-disorder transitions of double- and triple-stranded nucleic acid helices, the midpoint temperatures Tm depend strongly on a +/-, the mean ionic activity of uniunivalent salt. Experimental determinations of dTm/d ln a +/- and of the enthalpy change (delta H(o)) accompanying the transition in excess salt permit evaluation of delta gamma, the stoichiometrically weighted combination of preferential interaction coefficients, each of which reflects thermodynamic effects of interactions of salt ions with a reactant or product of the conformational transition (formula; see text) Here delta H(o) is defined per mole of nucleotide by analogy to delta gamma. Application of Eq. 1 to experimental values of delta H(o) and Tm yields values of delta gamma for the denaturation of B-DNA over the range of NaCl concentrations 0.01-0.20 M (Privalov et al. (1969), Biopolymers 8,559) and for each of four order-disorder transitions of poly rA.(poly rU)n, n = 1, 2 over the range of NaCl concentrations 0.01-1.0 M (Krakauer and Sturtevant (1968), Biopolymers 6, 491). For denaturation of duplexes and triplexes, delta gamma is negative and not significantly dependent on a +/-, but delta gamma is positive and dependent on a +/- for the disproportionation transition of poly rA.poly rU duplexes. Quantitative interpretations of these trends and magnitudes of delta gamma in terms of coulombic and excluded volume effects are obtained by fitting separately each of the two sets of thermodynamic data using Eq. 1 with delta gamma PB evaluated from the cylindrically symmetric Poisson-Boltzmann (PB) equation for a standard model of salt-polyelectrolyte solutions. The only structural parameters required by this model are: b, the mean axial distance between the projections of adjacent polyion charges onto the cylindrical axis; and a, the mean distance of closest approach between a salt ion center and the cylindrical axis. Fixing bMS and aMS for the multi-stranded (ordered) conformations, we determined the corresponding best fitted values of bSS and aSS for single-stranded RNA and DNA. The resulting best fitted values of aSS are systematically less than aDS by 2-4 A. Uncertainty in the best-fitted values of bSS is significantly lower than in the aSS, because bMS is known with relatively high precision and because the larger uncertainty in aMS has a relatively small effect on the best-fitted values of bSS:bSS = 3.2 +/- 0.6 A for single-stranded poly rA and poly rU; and bSS = 3.4 +/- 0.2 A for single-stranded DNA. These values are approximately one-halt of those expected for a fully extended single-stranded conformation. With the best fitted values of ass and bss, our calculations of delta gamma PB are in close quantitative agreement with experimental observations on each of five nucleic acid order-disorder transitions.

Grand canonical Monte Carlo molecular and thermodynamic predictions of ion effects on binding of an oligocation (L8+) to the center of DNA oligomers

Grand canonical Monte Carlo (GCMC) simulations are reported for aqueous solutions containing excess univalent salt (activities a +/- = 1.76-12.3 mM) and one of the following species: an octacationic rod-like ligand, L8+; a B-DNA oligomer with N phosphate charges (8 < or = N < or = 100); or a complex resulting from the binding of L8+ at the center of an N-mer (24 < or = N < or = 250). Simplified models of these multiply charged species are used in the GCMC simulations to predict the fundamental coulombic contributions to the following experimentally relevant properties: 1) the axial distance over which ligand binding affects local counterion concentrations at the surface of the N-mer; 2) the dependence on N of GCMC preferential interaction coefficients, gamma 32MC identical to delta C3/delta C2l a +/-, T, where C3 and C2 are, respectively, the molar concentrations of salt and the multiply charged species (ligand, N-mer or complex); and 3) the dependence on N of SaKobs identical to d in Kobs/d in a +/- = delta (magnitude of ZJ + 2 gamma 32J), where Kobs is the equilibrium concentration quotient for the binding of L8+ to the center of an N-mer and delta denotes the stoichiometric combination of terms, each of which pertains to a reactant or product J having magnitude of ZJ charges. The participation of electrolyte ions in the ligand binding interaction is quantified by the magnitude of SaKobs, which reflects the net (stoichiometrically weighted) difference in the extent of thermodynamic binding of salt ions to the products and reactants. Results obtained here from GCMC simulations yield a picture of the salient molecular consequences of binding a cationic ligand, as well as thermodynamic predictions whose applicability can be tested experimentally. Formation of the central complex is predicted to cause a dramatic reduction in the surface counterion (e.g., Na+) concentration over a region including but extending well beyond the location of the ligand binding site. For binding a cationic ligand, SaKobs is predicted to be negative, indicating net electrolyte ion release in the binding process. At small enough N, -SaKobs is predicted to decrease strongly toward zero with decreasing N. At intermediate N, -SaKobs appears to exceed its limiting value as N-->infinity.

Ions as regulators of protein-nucleic acid interactions in vitro and in vivo.

The key feature of the kinetics and equilibria of both specific and non-specific noncovalent interactions of proteins with nucleic acids is their sensitivity to the details of the ionic environment. Investigation of the effects of ion concentrations provides detailed and otherwise unobtainable information about the thermodynamics and mechanisms of these interactions. We discuss the molecular and thermodynamic basis of the contribution to these ion effects from electrolyte-nucleic acid interactions, and demonstrate that a simple ion exchange formalism, involving the stoichiometric participation of individual ions, is the appropriate basis for interpreting these profound effects at a thermodynamic level. Since the in vivo ionic environment is both complex and variable, we propose that variations in intracellular concentrations of individual ions play both global and specific roles in the control of the protein-nucleic acid interactions responsible for nucleoprotein structure and gene expression.

The Importance of Coulombic End Effects: Experimental Characterization of the Effects of Oligonucleotide Flanking Charges on the Strength and Salt Dependence of Oligocation (L8+) Binding to Single-Stranded DNA Oligomers

Binding constants Kobs, expressed per site and evaluated in the limit of zero binding density, are quantified as functions of salt (sodium acetate) concentration for the interactions of the oligopeptide ligand KWK6NH2 (designated L8+, with ZL = 8 charges) with three single-stranded DNA oligomers (ss dT-mers, with |ZD| = 15, 39, and 69 charges). These results provide the first systematic experimental information about the effect of changing |ZD| on the strength and salt dependence of oligocation-oligonucleotide binding interactions. In a comparative study of L8+ binding to poly dT and to a short dT oligomer (|ZD| = 10),. Proc. Natl. Acad. Sci. USA. 93:2511-2516) demonstrated the profound thermodynamic effects of phosphate charges that flank isolated nonspecific L8+ binding sites on DNA. Here we find that both Kobs and the magnitude of its power dependence on salt activity (|SaKobs|) increase monotonically with increasing |ZD|. The dependences of Kobs and SaKobs on |ZD| are interpreted by introducing a simple two-state thermodynamic model for Coulombic end effects, which accounts for our finding that when L8+ binds to sufficiently long dT-mers, both DeltaGobso = -RT ln Kobs and SaKobs approach the values characteristic of binding to poly-dT as linear functions of the reciprocal of the number of potential oligocation binding sites on the DNA lattice. Analysis of our L8+-dT-mer binding data in terms of this model indicates that the axial range of the Coulombic end effect for ss DNA extends over approximately 10 phosphate charges. We conclude that Coulombic interactions cause an oligocation (with ZL < |ZD|) to bind preferentially to interior rather than terminal binding sites on oligoanionic or polyanionic DNA, and we quantify the strong increase of this preference with decreasing salt concentration. Coulombic end effects must be considered when oligonucleotides are used as models for polyanionic DNA in thermodynamic studies of the binding of charged ligands, including proteins.

The relationship between the poisson-boltzmann model and the condensation hypothesis: an analysis based on the low salt form of the donnan coefficient

Two common models for the interaction of counterions with cylindrical polyions are considered in the context of the Donnan membrane equilibrium. General analytic expressions are obtained from the Poisson-Boltzmann equation for the Donnan coefficient in terms of the potential at the surface of the polyion or the local concentration of unbound ions at the surface. Analysis based on these expressions shows that if, and only if, the polyion charge density exceeds a certain critical value a large local concentration of ions will persist near the polyion surface at low ionic strengths. We therefore conclude that this principal hypothesis of the condensation model is consistent with the characteristics of the Poisson-Boltzmann potential at the surface of the polyion.

Analyses of thermodynamic data for concentrated hemoglobin solutions using scaled particle theory: implications for a simple two-state model of water in thermodynamic analyses of crowding in vitro and in vivo.

Quantitative description of the thermodynamic consequences of macromolecular crowding (excluded volume nonideality) is an important component of analyses of the thermodynamics and kinetics of noncovalent interactions of biopolymers in vivo and in concentrated polymer solutions in vitro. By analyzing previously published thermodynamic data, we have investigated extensively the comparative applicability of two forms of scaled particle theory (SPT). In both forms, macromolecules are treated as hard spheres, but MSPT, introduced by Ross and Minton, treats the solvent as a structureless continuum, whereas bulk water molecules are included explicitly as hard spheres in BSPT, an approach developed by Berg. Here we use both MSPT and BSPT to calculate the excluded volume component of the macromolecular activity coefficient of hemoglobin (Hb) at concentrations up to 509 mg/ml by fitting osmotic pressure data for Hb and sedimentation equilibrium data for Hb and sickle-cell Hb (HbS). Both forms of SPT also are used here to analyze the effects of other globular proteins (BSA and Hb) on the solubility of HbS. In applying MSPT and BSPT to analyze macromolecular crowding, the extent of hydration delta Hb (in gH2O/gprotein) is introduced as an adjustable parameter to specify the effective (hard sphere) radius of hydrated Hb. In our nonlinear least-squares fittings based on BSPT, the hard sphere radius of bulk water molecules is either fixed at 1.375 A or floated. Although both forms of SPT yield good fittings (with different values of delta Hb) at Hb concentrations up to 350 mg/ml, only BSPT gives good fittings of all available Hb osmotic pressure data as well as of the sedimentation equilibrium and solubility data. Only BSPT predicts values for delta Hb (approximately 0.5-0.6 g/g) in the range obtained for Hb from hydrodynamic measurements (approximately 0.36-0.78 g/g). These findings indicate the applicability, at least in the context of BSPT, of a simple two-state classification of water (bulk water and water of macromolecular hydration) as a basis for interpreting excluded volume nonideality in concentrated solutions of globular proteins.

Preferential interactions in aqueous solutions of urea and KCl.

A quantitative characterization of the thermodynamic effects due to interactions of salt ions and urea in aqueous solution is needed for rigorous analyses of the effects of changing urea concentration on biopolymer processes in solutions that also contain salt. Therefore, we investigate preferential interactions in aqueous solutions containing KCl and urea by using vapor pressure osmometry (VPO) to measure osmolality as a function of the molality of urea (component 3) over the range 0.09<or=m(3)<or=1.65 m at two fixed molalities of KCl (component 2) (m(2)=0.212 and 0.427 m). With this experimental input and corresponding VPO measurements on solutions that contain only urea or KCl, we evaluate approximately the chemical potential derivative micro(23)=( partial differential micro(KCl)/ partial differential m(urea))(T,P,m(KCl))=( partial differential micro(urea)/ partial differential m(KCl))(T,P,m(urea))= micro(32) and hence the preferential interaction coefficients Gammamicro(3) and Gammamicro(1),micro(3). These results show that for water-KCl-urea solutions neither of these coefficients is determined primarily by contributions from thermodynamic nonideality to micro(23). In aqueous solutions containing a biopolymer and a small solute, the contribution of ideal mixing entropy to micro(23) is negligible in comparison with the experimental uncertainty, whereas in KCl-urea solutions the contribution due to ideal mixing entropy accounts for at least half of the magnitude of micro(23). For comparison, we analyze literature data for NaCl-urea interactions and find again that nonideality makes a smaller contribution to micro(23) than does ideal mixing entropy. In contrast, for aqueous solutions of urea and the protein bovine serum albumin, the experimentally determined contribution of nonideality to micro(23) exceeds the contribution of ideal mixing by a factor of approximately 2 x 10(2).