It is shown that the free energy of a volume V of an isotropic system of nonuniform composition or density is given by : NV∫V [f 0(c)+κ(▿c)2]dV, where NV is the number of molecules per unit volume, ▿c the composition or density gradient, f 0 the free energy per molecule of a homogeneous system, and κ a parameter which, in general, may be dependent on c and temperature, but for a regular solution is a constant which can be evaluated. This expression is used to determine the properties of a flat interface between two coexisting phases. In particular, we find that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc , and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2 . The predicted interfacial free energy and its temperature dependence are found to be in agreement with existing experimental data. The possibility of using optical measurements of the interface thickness to provide an additional check of our treatment is briefly discussed.

Free Energy of a Nonuniform System. I. Interfacial Free Energy

T e purpose of this review is to assess the nature and magnitudes of the dominant forces in protein folding. Since proteins are only marginally stable at room temperature,’ no type of molecular interaction is unimportant, and even small interactions can contribute significantly (positively or negatively) to stability (Alber, 1989a,b; Matthews, 1987a,b). However, the present review aims to identify only the largest forces that lead to the structural features of globular proteins: their extraordinary compactness, their core of nonpolar residues, and their considerable amounts of internal architecture. This review explores contributions to the free energy of folding arising from electrostatics (classical charge repulsions and ion pairing), hydrogen-bonding and van der Waals interactions, intrinsic propensities, and hydrophobic interactions. An earlier review by Kauzmann (1959) introduced the importance of hydrophobic interactions. His insights were particularly remarkable considering that he did not have the benefit of known protein structures, model studies, high-resolution calorimetry, mutational methods, or force-field or statistical mechanical results. The present review aims to provide a reassessment of the factors important for folding in light of current knowledge. Also considered here are the opposing forces, conformational entropy and electrostatics. The process of protein folding has been known for about 60 years. In 1902, Emil Fischer and Franz Hofmeister independently concluded that proteins were chains of covalently linked amino acids (Haschemeyer & Haschemeyer, 1973) but deeper understanding of protein structure and conformational change was hindered because of the difficulty in finding conditions for solubilization. Chick and Martin (191 1) were the first to discover the process of denaturation and to distinguish it from the process of aggregation. By 1925, the denaturation process was considered to be either hydrolysis of the peptide bond (Wu & Wu, 1925; Anson & Mirsky, 1925) or dehydration of the protein (Robertson, 1918). The view that protein denaturation was an unfolding process was

/pdf/dominant-forces-in-protein-folding-42bjzlldw4.pdf

Dominant forces in protein folding

A statistical mechanical treatment of high polymer solutions has been carried out on the basis of an idealized model, originally proposed by Meyer, which is analogous to the one ordinarily assumed in the derivation of the ``ideal'' solution laws for molecules of equal size. There is obtained for the entropy of mixing of n solvent and N linear polymer molecules (originally disoriented), ΔS=−k[(n/β) ln v1+N ln v2] where v1 and v2 are volume fractions and β is the number of solvent molecules replaceable by a freely orienting segment of the polymer chain. This expression is similar in form to the classical expression for equal‐sized molecules, mole fractions having been replaced by volume fractions. When the disparity between the sizes of the two components is great, this expression gives entropies differing widely from the classical values, which accounts for the large deviations of high polymer solutions from ``ideal'' behavior. The entropy of disorientation of a perfectly arranged linear polymer is found t...

Thermodynamics of High Polymer Solutions

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrat...

/pdf/evolution-of-networks-27h4ny8xbi.pdf

Evolution of networks

We have derived, by using simple considerations, a relation between the diffusion constant D in a liquid of hard spheres and the ``free volume'' vf. This derivation is based on the concept that statistical redistribution of the free volume occasionally opens up voids large enough for diffusive displacement. The relation is D=A exp[−γv*/vf], where v* is the minimum required volume of the void and A and γ are constants. This equation is of the same form as Doolittle's [J. Appl. Phys. 22, 1471 (1951)] empirical relation between the fluidity φ of simple hydrocarbons and their free volume. It has been shown [Williams, Landel, and Ferry, J. Am. Chem. Soc. 77, 3701 (1955)] that the Doolittle equation also can be adapted to describe the abrupt decrease in molecular kinetic constants with decreasing temperature that accompanies the glass transition in certain liquids. Our result predicts that even the simplest liquids would go through this glass transition if sufficiently undercooled and crystallization did not oc...

Molecular Transport in Liquids and Glasses

Introduction The various colors of iodine in different solvents have attracted the attention of investigators for over half a century. Beckmann’ showed that the differences are not due to any change in the molecular weight of iodine and suggested solvation as the cause of brown color. Lachman2 supported this explanation, pointing out that the solvents which give a violet color are saturated, those which give brown colors are unsaturated. He stated that small additions of alcohol to a solution of iodine in chloroform suffice to shift the color stepwise from violet to brown. Hildebrand and Glascock3 found that when iodine and an alcohol were both added to a “violet” solvent, bromoform or ethylene bromide, the molal lowering of the freezing point was considerably less than additive, indicating combination of iodine with alcohol. Furthermore, they investigated colorimetrically the equilibria of iodine with ethyl alcohol, ethyl acetate and nitrobenzene dissolved together in a “violet” solvent such as carbon tetrachloride, chloroform or carbon disulfide, and found in each case an equilibrium constant corresponding to a 1 : 1 compound. They calculated the heat of combination in one case. There followed a long series of investigations of the general problem, well summarized by Gmelin4 and in a recent review by Kleinberg and Davidson.6 But the original division of iodine solutions into two or more distinct color classes became untenable with the work of Waentig, Groh’ and \\X7alkers which showed that the position of the absorption bands of iodine solutions in the visible region moved gradually from violet to brown, the shift being only small in the case of benzene in which the color of iodine is a red-violet. We have long been curious about the chemical basis for iodine solvates. It is not a question of dipole moment, as Walkers concluded, for we have recently shown rather conclusively that the iodine solubility, which would be altered by solvation effects, bears little or no relation to the dipole moment of the solvent mole~ule .~ The alcohols are extraordinary dipoles, and their effect is readily understandable, but the case of benzene seemed

A Spectrophotometric Investigation of the Interaction of Iodine with Aromatic Hydrocarbons

The solubility of nonelectrolytes

AbstractIT is not often that a reviewer, who has read through the first edition of a book, finds it worth while to do more than glance through a second edition, in order to discover and review the new sections that have been introduced. Prof. Hildebrand's book is an exception, since the reviewer has taken the opportunity to renew his acquaintance with the earlier as well as the later text, and has found this to be a most interesting experience, since the book is full of matter which is not dealt with adequately (and indeed appears to have been largely overlooked) in the ordinary text-books of physical chemistry.Solubility of Non-Electrolytes
 By Prof. Joel H. Hildebrand. (American Chemical Society Monograph Series, No. 17.) Second edition. Pp. 203. (New York: Reinhold Publishing Corporation; London: Chapman and Hall, Ltd., 1936.) 22s. 6d. net.

Joel H. Hildebrand

Papers

A Spectrophotometric Investigation of the Interaction of Iodine with Aromatic Hydrocarbons

The solubility of nonelectrolytes

The solubility of non-electrolytes

The theory of emulsification1

Solubility. xii. regular solutions1