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Potassium glutamate (KGlu) is the primary Escherichia coli cytoplasmic salt. After sudden osmotic upshift, cytoplasmic KGlu concentration increases, initially because of water efflux and subsequently by K + transport and Glu - synthesis, allowing water uptake and resumption of growth at high osmolality. In vitro, KGlu ranks with Hofmeister salts KF and K 2 SO 4 in driving protein folding and assembly. Replacement of KCl by KGlu stabilizes protein-nucleic acid complexes. To interpret and predict KGlu effects on protein processes, preferential interactions of KGlu with 15 model compounds displaying six protein functional groups-sp 3 (aliphatic) C; sp 2 (aromatic, amide, carboxylate) C; amide and anionic (carboxylate) O; and amide and cationic N-were determined by osmometry or solubility assays. Analysis of these data yields interaction potentials (α-values) quantifying non-Coulombic chemical interactions of KGlu with unit area of these six groups. Interactions of KGlu with the 15 model compounds predicted from these six α-values agree well with experimental data. KGlu interactions with all carbon groups and with anionic (carboxylate) and amide oxygen are unfavorable, while KGlu interactions with cationic and amide nitrogen are favorable. These α-values, together with surface area information, provide quantitative predictions of why KGlu is an effective E. coli cytoplasmic osmolyte (because of the dominant effect of unfavorable interactions of KGlu with anionic and amide oxygens and hydrocarbon groups on the water-accessible surface of cytoplasmic biopolymers) and why KGlu is a strong stabilizer of folded proteins (because of the dominant effect of unfavorable interactions of KGlu with hydrocarbon groups and amide oxygens exposed in unfolding)., (Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

Many studies of specific protein-nucleic acid binding use short oligonucleotides or restriction fragments, in part to minimize the potential for nonspecific binding of the protein. However, when the specificity ratio is low, multiple nonspecifically bound proteins may occupy the region of DNA corresponding to one specific site; this situation was encountered in our recent calorimetric study of binding of integration host factor (IHF) protein to its specific 34-bp H' DNA site. Here, beginning from the analytical McGhee and von Hippel infinite-lattice nonspecific binding isotherm, we derive a novel analytic isotherm for nonspecific binding of a ligand to a finite lattice. This isotherm is an excellent approximation to the exact factorial-based Epstein finite lattice isotherm even for short lattices and therefore is of great practical significance for analysis of experimental data and for analytic theory. Using this isotherm, we develop an analytic treatment of the competition between specific and nonspecific binding of a large ligand to the same finite lattice (i.e., DNA oligomer) containing one specific and multiple overlapping nonspecific binding sites. Analysis of calorimetric data for IHF-H' DNA binding using this treatment yields enthalpies and binding constants for both specific and nonspecific binding and the nonspecific site size. This novel analysis demonstrates the potential contribution of nonspecific binding to the observed thermodynamics of specific binding, even with very short DNA oligomers, and the need for reverse (constant protein) titrations or titrations with nonspecific DNA to resolve specific and nonspecific contributions. The competition treatment is useful in analyzing low-specificity systems, including those where specificity is weakened by mutations or the absence of specificity factors.

To obtain turgor pressure, intracellular osmolalities, and cytoplasmic water activity of Escherichia coli as a function of osmolality of growth, we have quantified and analyzed amounts of cell, cytoplasmic, and periplasmic water as functions of osmolality of growth and osmolality of plasmolysis of nongrowing cells with NaCl. The effects are large; NaCl (plasmolysis) titrations of cells grown in minimal medium at 0.03 Osm reduce cytoplasmic and cell water to approximately 20% and approximately 50% of their original values, and increase periplasmic water by approximately 300%. Independent analysis of amounts of cytoplasmic and cell water demonstrate that turgor pressure decreases with increasing osmolality of growth, from approximately 3.1 atm at 0.03 Osm to approximately 1.5 at 0.1 Osm and to less than 0.5 atm above 0.5 Osm. Analysis of periplasmic membrane-derived oligosaccharide (MDO) concentrations as a function of osmolality, calculated from literature analytical data and measured periplasmic volumes, provides independent evidence that turgor pressure decreases with increasing osmolality, and verifies that cytoplasmic and periplasmic osmolalities are equal. We propose that MDO play a key role in periplasmic volume regulation at low-to-moderate osmolality. At high growth osmolalities, where only a small amount of cytoplasmic water is observed, the small turgor pressure of E. coli demonstrates that cytoplasmic water activity is only slightly less than extracellular water activity. From these findings, we deduce that the activity of cytoplasmic water exceeds its mole fraction at high osmolality, and, therefore, conclude that the activity coefficient of cytoplasmic water increases with increasing growth osmolality and exceeds unity at high osmolality, presumably as a consequence of macromolecular crowding. These novel findings are significant for thermodynamic analyses of effects of changes in growth osmolality on biopolymer processes in general and osmoregulatory processes in particular in the E. coli cytoplasm.

A novel analytical method based on the exact solution of equations of kinetics of unbranched first- and pseudofirst-order mechanisms is developed for application to the process of Esigma70 RNA polymerase (R)-lambdaPR promoter (P) open complex formation, which is described by the minimal three-step mechanism with two kinetically significant intermediates (I1, I2), [equation: see text], where the final product is an open complex RPo. The kinetics of reversible and irreversible association (pseudofirst order, [R] >> [P]) to form long-lived complexes (RPo and I2) and the kinetics of dissociation of long-lived complexes both exhibit single exponential behavior. In this situation, the analytical method provides explicit expressions relating observed rate constants to the microscopic rate constants of mechanism steps without use of rapid equilibrium or steady-state approximations, and thereby provides a basis for interpreting the composite rate constants of association (ka), isomerization (ki), and dissociation (kd) obtained from experiment for this or any other sequential mechanism of any number of steps. In subsequent papers, we apply this formalism to analyze kinetic data obtained in the reversible and irreversible binding regimes of Esigma70 RNA polymerase (R)-lambdaP(R) promoter (P) open complex formation.

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.

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.

The local cation concentration at the surface of oligomeric or polymeric B-DNA is expected, on the basis of MC simulations (Olmsted, M. C., C. F. Anderson, and M. T. Record, Jr. 1989. Proc. Natl. Acad. Sci. USA. 86:7766-7770), to decrease sharply as either end of the molecule is approached. In this paper we report 23Na NMR measurements indicating the importance of this "coulombic" end effect on the average extent of association of Na+ with oligomeric duplex DNA. In solutions containing either 20-bp synthetic DNA or 160-bp mononucleosomal calf thymus DNA at phosphate monomer concentrations [P] of 4-10 mM, measurements were made over the range of ratios 1 < or = [Na]/[LP] < or = 20, corresponding to Na+ concentrations of 4-200 nM. The longitudinal 23Na NMR relaxation rates measured in these NaDNA solutions, Robs, are interpreted as population-weighted averages of contributions from "bound" (RB) and "free" (RF) 23Na relaxation rates. The observed enhancements of Robs indicate that RB significantly exceeds RF, which is approximately equal to the 23Na relaxation rate in an aqueous solution containing only NaCl. Under salt-fre-tconditions ([Na]/[P] = 1), where the enhancement in Robs is maximal, we find that Robs--RF in the solution containing 160-bp DNA is approximately 1.8 times that observed for the 20-bp DNA. For the 160-bp oligomer (which theoretical calculations predict to be effectively polyion-like), we find that a plot of Robs v. [P]/[Na] is linear, as observed previously for sonicated (approximately 700 bp) DNA samples. For the 20-bp oligonucleotide this plot exhibits a marked departure from linearity that can be fitted to a quadratic function of [P]/[Na]. Monte Carlo simulations based on a simplified model are capable of reproducing the qualitative trends in the 23Na NMR measurements analyzed here. In particular, the dependences of Robs--RF on DNA charge magnitude of Z(320 vs. 38 phosphates) and (for the 20-bp oligomer) on [Na]/[P] are well correlated with the calculated average surface concentration of Na+. Thus, effects of sodium concentration on RB appear to be of secondary importance. We conclude that 23Na NMR relaxation measurements are a sensitive probe of the effects of oligomer charge on the extent of ion accumulation near B-DNA oligonucleotides, as a function of [Na] and [P].

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.

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.

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.