Does Flory–Huggins theory help in interpreting solute partitioning experiments?

The development of Flory–Huggins (FH) theory is reviewed, particularly with regard to the molecular significance of the interaction parameter that scales the contact interaction of solute and solvent. The chemical potential given by FH theory for an “idealute” solute is then compared with that provided by a more general, statistical thermodynamic approach. It is found that the FH contact term does not directly correspond to the solvation free energy. The significance of this result for the interpretation of free energies of transfer of a solute from one solvent to another is examined. It is shown that neither the earlier recommended standard free energy change for the process (using the infinitely dilute reference state, mole fraction units) nor the recently recommended FH-corrected standard free energy change provides the solvation energy desired. Instead, the standard free energy using the infinitely dilute reference state and molarity units, as long advocated by Ben-Naim, provides the desired solvation free energy. Correction of extant values, based on mole fraction units, is easily made. However, application of such results to problems of protein folding is not straightforward. © 1994 John Wiley & Sons, Inc.     

Analytical ultracentrifugation in a Gibbsian perspective

The analytical ultracentrifuge has come into new intensive use following complete instrumental redesign and the use of advanced computer technologies for the analysis and interpretation of experimental results. Major attention is now devoted to the evaluation of interactions between similar and dissimilar biological macromolecules in dilute and concentrated systems. Electrostatically charged biological solute systems additionally comprise low molecular weight charged and non-charged cosolvents. Solvent/cosolvent interactions, insufficiently considered in most current analytical ultracentrifugation analyses, may quantitatively affect solute/solute interactions. For comprehensive analysis the Svedberg derivation considering a buoyant molar mass (1 - rho0 partial specific volume)M2 and valid at vanishing solute concentration for strictly two component systems only, should be replaced, following classical thermodynamic analysis, by the ratio (delta rho/delta c2)(mu)/d pi/dc2 of the density increment at constant chemical potential of diffusible cosolvents, to the derivative of the osmotic pressure with solute concentration. Disregard of the solvent/cosolvent and solute/cosolvent interactions should be avoided.     

Effect of temperature on viscosity properties of some alpha-amino acids in aqueous urea solutions

Viscosities for solutions of glycine, DL-alpha-alanine, DL-alpha-amino-n-butyric acid, DL-valine, DL-leucine and L-serine in 5 mol kg(-1) aqueous urea have been determined at 278.15, 288.15, 298.15 and 308.15 K. The viscosity B-coefficients for the amino acids in the aqueous urea solution have been calculated at different temperatures. The effect of temperature on the B-coefficients is discussed on the basis of the Feakins equation. The contribution of solute to the activation parameters (delta mu0*2, deltaH0*2, deltaS0*2) for viscous flow of the solution have been calculated, together with the Gibbs energy, enthalpy and entropy of transfer for the amino acids from the ground-state solvent to the hypothetical viscous transition state solvent. The contributions of the charged end group (NH3+, COO-) and CH2 groups of the amino acids to B-coefficient and delta mu0*2 have been also estimated using the linear correlations between B-coefficient or delta mu0*2 and the number of carbon atoms in the alkyl chains of the amino acids. All the activation parameters are discussed in terms of the solute-solvent interactions in the ground and transition states.     

Implicit solvent models

Implicit solvent models for biomolecular simulations are reviewed and their underlying statistical mechanical basis is discussed. The fundamental quantity that implicit models seek to approximate is the solute potential of mean force, which determines the statistical weight of solute conformations, and which is obtained by averaging over the solvent degrees of freedom. It is possible to express the total free energy as the reversible work performed in two successive steps. First, the solute is inserted in the solvent with zero atomic partial charges; second, the atomic partial charges of the solute are switched from zero to their full values. Consequently, the total solvation free energy corresponds to a sum of non-polar and electrostatic contributions. These two contributions are often approximated by simple geometrical models (such as solvent exposed area models) and by macroscopic continuum electrostatics, respectively. One powerful route is to approximate the average solvent density distribution around the solute, i.e. the solute-solvent density correlation functions, as in statistical mechanical integral equations. Recent progress with semi-analytical approximations makes continuum electrostatics treatments very efficient. Still more efficient are fully empirical, knowledge-based models, whose relation to explicit solvent treatments is not fully resolved, however. Continuum models that treat both solute and solvent as dielectric continua are also discussed, and the relation between the solute fluctuations and its macroscopic dielectric constant(s) clarified.     

Excluded volume in solvation: sensitivity of scaled-particle theory to solvent size and density

Changes in solvent environment greatly affect macromolecular structure and stability. To investigate the role of excluded volume in solvation, scaled-particle theory is often used to calculate delta G(tr)(ev), the excluded-volume portion of the solute transfer free energy, delta G(tr). The inputs to SPT are the solvent radii and molarities. Real molecules are not spheres. Hence, molecular radii are not uniquely defined and vary for any given species. Since delta G(tr)(ev) is extremely sensitive to solvent radii, uncertainty in these radii causes a large uncertainty in delta G(tr)(ev)-several kcal/mol for amino acid solutes transferring from water to aqueous mixtures. This uncertainty is larger than the experimental delta G(tr) values. Also, delta G(tr)(ev) can be either positive or negative. Adding neutral crowding molecules may not necessarily reduce solubility. Lastly, delta G(tr)(ev) is very sensitive to solvent density, rho. A few percent error in rho may even cause qualitative deviations in delta G(tr)(ev). For example, if rho is calculated by assuming the hard-sphere pressure to be constant, then delta G(tr)(ev) values and uncertainties are now only tenths of a kcal/mol and are positive. Because delta G(tr)(ev) values calculated by scaled-particle theory are strongly sensitive to solvent radii and densities, determining the excluded-volume contribution to transfer free energies using SPT may be problematic.     

Size effects in nonpolar solvation: lessons from two simple models

Size dependence of the solute chemical potential mu(u) is examined using the Ornstein-Zernike equation for two models of the nonpolar solute-solvent interactions. Simple Lennard-Jones interactions are assumed in the first model while the Lennard-Jones potential is distributed over the solute volume in the second model similar to the Hamaker theory for the colloid dispersion forces. In both models, while mu(u) rises asymptotically as the third power of the solute size in agreement with asymptotic solution of the scaled particle theory, it increases faster at smaller sizes. Deviations from the cubic law are more pronounced at higher solvent densities and stronger molecular interactions. Within a relatively narrow size range typical for small organic molecules, mu(u) can be approximated with a polynomial of the third or even the second power. However, the latter approximation is less accurate and cannot be employed for extrapolation to the larger size region.     

Theory of preferential solvation of nonelectrolytes

The concepts of local compositions around a solute and preferential solvation of a solute are defined in terms of the Kirkwood-Buff integrals. The difference between the local and the bulk composition is a measure of the preferential solvation of a solute with respect to the various components of the solvent. A statistical mechanical theory is developed that leads to simple relationships between local compositions and experimentally measurable quantities. Some preliminary results on preferential solvation of methane in mixtures of water-ethanol and water-p-dioxane are presented.     

Complementary addressed modification of a hairpin-shaped model oligodeoxyribonucleotide

A hairpin-shaped oligodeoxyribonucleotide d(pTTGGCACGAGCAGCCAA) (I) was alkylated with the reagent d(TTGGG) greater than UCHRCl (RCl = -C6H5-N(CH3)-CH2-CH2Cl) complementary to the hairpin's stem. Thermodynamic parameters for the hairpin structure estimated from melting curves were: delta Hh = -125 +/- 17 kJ/mol, delta Sh = -380 +/- 84 J/mol.K; and for the reagent - target complex delta Hpx = -155 +/- 8 kJ/mol, delta Spx = -427 +/- 21 J/mol.K. Effective constants of association Kx of the oligonucleotide with the reagent were determined at 30 and 50 degrees from the concentration dependence of the reaction yield and were 1988 +/- 83 and 1239 +/- 58 M-1, respectively. Experimental values of Kx agreed with the values of Kx = Kpx/(1 + Kh), calculated with the use of the thermodynamic parameters.     

A coulombic hypothesis of mitochondrial oxidative phosphorylation

A coulombic hypothesis of mitochondrial oxidative phosphorylation is presented, founded upon the evidence for negative fixed charge formation during electron transport chain activity. The intermediary force is electrostatic (psi H) and not electrochemical (delta mu H). The electrochemical potential of the chemiosmotic hypothesis is identified as a "phantom" parameter which owes its delusive existence to the procedures by which it is measured. The connection between psi H and the conditional delta mu H values is examined; it entails the use of a variable conversion factor, f, where delta mu H (mV) = f psi H, and the concept of the "protonic status" of the diffuse double layer. A number of problems which beset the chemiosmotic view are reappraised in the light of the new interpretation, and find authentic solutions.     

Solution nonideality related to solute molecular characteristics of amino acids.

By measuring the freezing-point depression for dilute, aqueous solutions of all water-soluble amino acids, we test the hypothesis that nonideality in aqueous solutions is due to solute-induced water structuring near hydrophobic surfaces and solute-induced water destructuring in the dipolar electric fields generated by the solute. Nonideality is expressed with a single solute/solvent interaction parameter I, calculated from experimental measure of delta T. A related parameter, I(n), gives a method of directly relating solute characteristics to solute-induced water structuring or destructuring. I(n)-values correlate directly with hydrophobic surface area and inversely with dipolar strength. By comparing the nonideality of amino acids with progressively larger hydrophobic side chains, structuring is shown to increase with hydrophobic surface area at a rate of one perturbed water molecule per 8.8 square angstroms, implying monolayer coverage. Destructuring is attributed to dielectric realignment as described by the Debye-Hückel theory, but with a constant separation of charges in the amino-carboxyl dipole. By using dimers and trimers of glycine and alanine, this destructuring is shown to increase with increasing dipole strength using increased separation of fixed dipolar charges. The capacity to predict nonideal solution behavior on the basis of amino acid characteristics will permit prediction of free energy of transfer to water, which may help predict the energetics of folding and unfolding of proteins based on the characteristics of constituent amino acids.     

Molecular dynamics simulation study of the static and dynamic properties of a model colloidal suspension with explicit solvent

Molecular dynamics simulation was used to study a colloidal suspension with explicit solvent to determine how inclusion of the solvent affects the structure and dynamics of the system. The solute was modelled as a hard-core particle enclosed in a Weeks–Chandler–Andersen (WCA) potential shell, while the solvent was modelled as a simple WCA fluid. We found that when the solute–solvent interaction included a hard core equal to half of the solute hard-core diameter, large depletion effects arose, leading to an effective attraction and large deviations from hard-sphere structure for the colloidal component. It was found that these effects could be eliminated by reducing the hard-core distance parameter in the solute–solvent interaction, thus allowing the solvent to penetrate closer to the colloidal particles. Three different values for the solute–solvent hard-core parameter were systematically studied by comparing the static structure factor and radial distribution function to the predictions of the Percus–Yevick theory for hard spheres. When the optimal value of the solute–solvent hard-core interaction parameter was found, this model was then used to study the dynamical behaviour of the colloidal suspension. This was done by first measuring the velocity autocorrelation function (VACF) over a large range of packing fractions. We found that this model predicted the sign of the long-time tail in the VACF in agreement with experimental values, something that single component hard-sphere systems have failed to do. The intermediate scattering functions at low wavevector were briefly studied to determine their behaviour in a dilute system. It was found that they could be modelled using a simple diffusion equation with a wavevector independent diffusion coefficient, making this model an excellent analogue of experimentally studied hard-sphere colloids.     

Solute partitioning into lipid bilayer membranes

We have measured the membrane/water partition coefficients of benzene into lipid bilayers as a function of the surface density of the phospholipid chains. A simple 2H NMR method was used for the measurement of surface densities; it is shown to give results similar to those obtained from more demanding X-ray diffraction measurements. We observe that benzene partitioning into the bilayer is dependent not only on the partitioning chemistry, characterized by the oil/water partition coefficient, but also on the surface density of the bilayer chains. Increasing surface density leads to solute exclusion: benzene partitioning decreases by an order of magnitude as the surface density increases from 50% to 90% of its maximum value, a range readily accessible in bilayers and biomembranes under physiological conditions. This effect is independent of the nature of the agent used to alter surface density: temperature, cholesterol, and phospholipid chain length were tested here. These observations support the recent statistical thermodynamic theory of solute partitioning into chain molecule interphases, which predicts that the expulsion of solute is due to entropic effects of the orientational ordering among the phospholipid chains. We conclude that the partitioning of solutes into bilayer membranes, which are interfacial phases, is of a fundamentally different nature than partitioning into bulk oil and octanol phases.     

A novel thermodynamic relationship based on Kramers Theory for studying enzyme kinetics under high viscosity

In most studies of enzyme kinetics it has been found sufficient to use the classical Transition State Theory (TST) of Eyring and others. This theory was based on the solvent being an ideal dilute substance treated as a heat bath. However, enzymes found in organisms adapted to very low (psychrophiles) and very high (thermophiles) temperatures are also subjected to variable solute concentrations and viscosities. Therefore, the TST may not always be applicable to enzyme reactions carried out in various solvents with viscosities ranging from moderate to very high. There have been numerous advances in the theory of chemical reactions in realistic non-ideal solvents such as Kramers Theory. In this paper we wish to propose a modified thermodynamic equation, which have contributions from kcat, Km and the viscosity of the medium in which the enzyme reaction is occurring. These could be very useful for determining the thermodynamics of enzymes catalyzing reactions at temperature extremes in the presence of substrate solutions of different compositions and viscosities.     

Alcohol binding to liposomes by 2H NMR and radiolabel binding assays: does partitioning describe binding?

Implicit within the concept of membrane-buffer partition coefficients of solutes is a nonspecific solvation mechanism of solute binding. However, (2)H NMR studies of the binding of (2)H(6)-ethanol and [1-(2)H(2)] n-hexanol to phosphatidylcholine vesicles have been interpreted as evidence for two distinct alcohol binding modes. One binding mode was reported to be at the membrane surface. The second mode was reported to be within the bilayer interior. An examination of the (2)H NMR binding studies, together with direct radiolabel binding assays, shows that other interpretations of the data are more plausible. The results are entirely consistent with partitioning (nonspecific binding) as the sole mode of alcohol binding to liposomes, in accord with our previous thermodynamic interpretation of alcohol action in phosphatidylcholine liposomes.     

Homeostasis of the protonmotive force in phosphorylating mitochondria

The relationship between the respiration rate and the magnitude of the electrochemical proton potential (delta mu H+) in rat liver mitochondria was investigated. (1) Under the active-state conditions, the action of inhibitors of either phosphorylation (oligomycin) or respiration (rotenone, malonate) on the respiration and delta mu H+ was measured. Both inhibitors diminished the respiration, whereas rotenone resulted in a decrease of delta mu H+, and oligomycin produced an increase of this potential. The effect of the inhibitors was much more pronounced on the respiration rate than on delta mu H+; for example, the excess of oligomycin produced a 90% inhibition of the respiration while delta mu H+ was changed only by 9%. (2) Under the resting-state conditions, small concentrations of the uncoupler stimulated the respiration while changing delta mu H+ to a relatively small extent. The uncoupler concentrations which doubled and tripled the respiration rate produced only 5 and 9% decrease of delta mu H+, respectively. (3) The present results enabled us to propose a model describing the interrelationship between respiration and delta mu H+.     

A statistical mechanical theory of unfolding of globular proteins induced by preferential binding of solvent components in water-organic solvent systems

A statistical mechanical model was developed for use in connection with the problem of preferential binding of solvent components to proteins and of conformational transition in water-organic solvent systems. The model is a statistical one for the conformational transition of globular proteins induced by the adsorption of solutes in the solution, considered as a nearest-neighbor problem in statistical mechanics. Although a few illustrative examples are given, the actual interpretations of the experimental data using this theory are reserved for a later paper.     

Biphasic competition between opiates and enkephalins: does it indicate the existence of a common high affinity ("mu-1") binding site?

Displacement from brain membranes of labeled opiates by low concentrations of enkephalins and of labeled enkephalins by low concentrations of opiates has been previously explained by the existence of a common high affinity site termed mu-1. An alternative interpretation of the same results is that the trough seen in the low concentration zone of the displacement curves represents cross binding of mu and delta opioid ligands to delta and mu receptors, respectively. In three sets of experiments with brain membranes, the size of the trough is shown to be dependent on the labeled ligand used: The ratio between the size of troughs seen with [3H]D-Ala, D-Leu enkephalin and with [3H]morphine varies with experimental conditions (storage of membranes at 4 degrees C for 72 h), with ratio of mu:delta receptors (e.g. in thalamus and cortex which are enriched in mu and delta sites, respectively) and with pretreatment of membranes with naloxonazine. These results can not be explained by a common high affinity site, but rather by binding of [3H]D-Ala, D-Leu enkephalin to mu and of [3H]morphine to delta opioid receptors.     

On the relationship between rate of ATP synthesis and H+ electrochemical gradient in rat-liver mitochondria

The relationship between rate of ATP synthesis, JATP, and value of the proton electrochemical gradient, delta mu H, has been analyzed in intact mitochondria. Onset of phosphorylation causes a depression of delta mu H of 1.5 kJ/mol. There is a close parallelism between inhibition of JATP and restoration of delta mu H to its state-4 value during titrations with oligomycin or atractyloside. Titrations with ionophores display the following features: (a) delta mu H can be depressed by 3-4 kJ/mol by valinomycin + K+ without affecting the rate of ATP synthesis; (b) uncouplers abolish JATP completely while depressing delta mu H by 3 kJ/mol; (c) complete abolition of ATP synthesis by inhibitors of electron transport is accompanied by a depression of delta mu H of only 1 kJ/mol. The results indicate that: (a) there is a close functional relationship between redox and ATPase H+ pumps, whereby inhibition of electron transfer is accompanied by simultaneous inhibition of the ATPase H+ pumps; and (b) uncoupling of oxidative phosphorylation is not due to depression of delta mu H per se. The consistence of the present data with either a chemiosmotic model where delta mu H is the sole and obligatory intermediate for energy coupling, or models where there is a direct transfer of energy between the two pumps is discussed.     

The indefinite self-association of lysozyme: consideration of composition-dependent activity coefficients

An improved iterative method for computing association constants from sedimentation equilibrium results obtained with self-interacting protein systems is presented which accounts for the composition-dependence of the activity coefficients of all oligomeric species. The method is based on the calculation of virial coefficients from covolume and charge considerations, the statistical mechanical basis of which is discussed in relation to the DLVO theory. The method is applied to results obtained with lysozyme in diethylbarbiturate buffer of pH 8.0 and ionic strength 0.15 at 15°C. It is shown that these results, encompassing a range of total solute concentration up to 19.7 g/liter are consistent with self-association patterns comprising either a monomer-dimer-trimer system or an isodesmic indefinite self-association of the monomer, the latter being favored. A firmer distinction between these possibilities is sought on the basis of the dependence of the weight-average partition coefficient, determined by frontal gel chromatography, on total solute concentration (up to 56.6 g/liter). This analysis accounts for the composition-dependence of the ratio of the activity coefficients of partitioning monomer in mobile and stationary phases. It is concluded that all results are consistent with an indefinite self-association of lysozyme governed by a single association constant of 4.61 × 10² liter/mole.     

The sodium cycle--a new type of bacterial energetics

The literature data and experimental results of the author's laboratory on the role of Na+ in bacterial energetics are reviewed. It was shown that certain bacterial species utilize the transmembrane difference of Na+ electrochemical potentials (delta mu Na+) as a convertible membrane-linked form of energy. The membranes of such bacteria were found to contain delta mu Na+ generators (e. g., decarboxylases of some carboxylic acids of NADH-menaquinone reductase). It was shown that delta mu Na+ formed by these generators may support all the three main types of work of the bacterial cell, i. e., chemical (ATP synthesis), osmotic (substrate accumulation) and mechanical (motility).