Thermodynamics protein solutions

Eigure 3.5 presents the dependence of A.S ° on temperature for chymotryp-sinogen denaturation at pH 3. A positive A.S ° indicates that the protein solution has become more disordered as the protein unfolds. Comparison of the value of 1.62 kj/mol K with the values of A.S ° in Table 3.1 shows that the present value (for chymotrypsinogen at 54.5°C) is quite large. The physical significance of the thermodynamic parameters for the unfolding of chymotrypsinogen becomes clear in the next section. 

The qualitative thermodynamic explanation of the shielding effect produced by the bound neutral water-soluble polymers was summarized by Andrade et al. [2] who studied the interaction of blood with polyethylene oxide (PEO) attached to the surfaces of solids. According to their concept, one possible component of the passivity may be the low interfacial free energy (ysl) of water-soluble polymers and their gels. As estimated by Matsunaga and Ikada [3], it is 3.7 and 3.1 mJ/m2 for cellulose and polyvinylalcohol whereas 52.6 and 41.9 mJ/m2 for polyethylene and Nylon 11, respectively. Ikada et al. [4] also found that adsorption of serum albumin increases dramatically with the increase of interfacial free energy of the polymer contacting the protein solution. 

We present a molecular theory of hydration that now makes possible a unification of these diverse views of the role of water in protein stabilization. The central element in our development is the potential distribution theorem. We discuss both its physical basis and statistical thermodynamic framework with applications to protein solution thermodynamics and protein folding in mind. To this end, we also derive an extension of the potential distribution theorem, the quasi-chemical theory, and propose its implementation to the hydration of folded and unfolded proteins. Our perspective and current optimism are justified by the understanding we have gained from successful applications of the potential distribution theorem to the hydration of simple solutes. A few examples are given to illustrate this point. 

With applications to protein solution thermodynamics in mind, we now present an alternative derivation of the potential distribution theorem. Consider a macroscopic solution consisting of the solute of interest and the solvent. We describe a macroscopic subsystem of this solution based on the grand canonical ensemble of statistical thermodynamics, accordingly specified by a temperature, a volume, and chemical potentials for all solution species including the solute of interest, which is identified with a subscript index 1. The average number of solute molecules in this subsystem is... 

Figure 7.10 Effect of the thermodynamic incompatibility of otsi/p-casein + high-methoxy pectin (pH = 7.0, / = 0.01 M) on phase diagram of the mixed solutions and elastic modulus of corresponding casein-stabilized emulsions (40 vol% oil, 2 wt% protein), (a) (O) Binodal line for p-casein + pectin solution with critical point ( ) ( ) binodal line for asi-casein + pectin solution with critical point ( ). (b) Complex shear modulus G (1 Hz) is plotted against the pectin concentration (O) p-casein ( ) o i -casein. Dotted lines indicate the range of pectin concentration for phase separation in the mixed solutions. The pectin was added to the protein solution before emulsion preparation. Data are taken front Semenova et al. (1999a).

Scott, R.L. "Phase equilibria in solutions of liquid sulfur. I Theory". J. Phys. Chem. 69,261-270 (1965). Sear, R. "Interactions in protein solutions". Curr. Opin. Colloid Interface Sci. 11, 35-39 (2006). Sept, D., and McCammon, J.A. "Thermodynamics and kinetics of actin filament nucleation". Biophys.. 81, 667-674 (2001). 

Shortcomings in current understanding of the thermodynamics of protein solutions can be illustrated by considering one of the oldest protein concentration methods, precipitation, and one of the newest and most technologically interesting methods for protein separation and purification, aqueous... 

As noted, the retention of a polypeptide or protein with HP-IEX sorbents primarily arises from electrostatic interactions between the ionized surface of the polypeptide or protein and the charged surface of the HPLC sorbent. Various theoretical models based on empirical relationships or thermodynamic considerations have been used to describe polypeptide and protein retention, and the involvement of the different ions, in HP-IEC under isocratic and gradient elution conditions (cf. Refs.6,19 33 40,78-90). Over a limited range of ionic strength conditions, the following empirical dependencies derived from the stoichiometric retention model can be used to describe the isocratic and gradient elution relationships between the capacity factor In and the corresponding salt concentration [C,] or the median capacity factor In k ex, and the median salt concentration [C,] of a polypeptide or protein solute, namely,... 

Michael E. Paulaitis is Professor of Chemical and Biomolecular Engineering and Ohio Eminent Scholar at Ohio State University. He is also Director of the Institute of Multiscale Modeling of Biological Interactions at Johns Hopkins University. His research focuses on molecular thermodynamics of hydration, protein solution thermodynamics, and molecular simulations of biological macromolecules. 

If a titratable group on a protein molecule can combine with substances, other than hydrogen ions, which may be present in a protein solution, then its titration properties will be altered. If the combining substance is present at a thermodynamic activity an, and if it combines with the basic form of the titratable group only, the equilibrium constant for association being ku, then the apparent hydrogen ion dissociation constant Xapp of the group becomes... 

C.R. Middaugh, W.A. Tisel, R.N. Haire, A. Rosenberg, Determination of the apparent thermodynamic activities of saturated protein solution, J. Biol. 

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water—protein—cosolvent mixtures is developed. The Kirkwood—Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water—protein—cosolvent mixtures. These properties can be divided into two groups (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water—cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions (1) one due to the protein—solvent interactions which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B p ), and (3) a third one representing an ideal mixture contribution The cosolvent composition dependencies of these three contributions... 

For more than 60 years it is known that B2, the osmotic second virial coefficient (OSVC), constitutes an important thermodynamic characteristic of protein—protein interactions in protein solutions. " In a binary mixture solvent (1)—protein (2), B2 is connected to the osmotic pressure (n) via the virial equation... 

Middaugh CR, Tisel WA, Haire RN, and Rosenberg A. Determination of the Apparent Thermodynamic Activities of Saturated Protein Solutions./Bio/ Chem 1997 254 367-370. 

In a dilute protein solution, the nano length scale or the molecular structure of protein molecules determines the thermodynamic equilibrium between protein-protein and protein-water interactions. The consequent surface and hydrodynamic properties of proteins are resulted from the proportion of hydrophobic, hydrophilic, and charged amino acid residues. For example, caseins could adopt a random coil structure due to their flexible structure as a result of phosphorylated serine residues caseins indeed lack the ordered structures of a-helix, 3-sheet, and 3-turn found in globular proteins. This gives rise to better multifunctionality of caseins over globular proteins. 

The consequences of cooperative folding can be illustrated by considering the contents of a protein solution under conditions corresponding to the middle of the transition between the folded and unfolded forms. Under these conditions, the protein is half folded. Yet the solution will contain no half-folded molecules but, instead, will be a 50/50 mixture of fully folded and fully unfolded molecules (Figure 3.57). Structures that are partly intact and partly disrupted are not thermodynamically stable and exist only transiently. Cooperative folding ensures that partly folded structures that might interfere with processes within cells do not accumulate. 

A frequently used approach to study the thermal stability of proteins is to incubate a protein solution at an elevated constant temperature and to observe the change of certain physical parameters (e.g., CD, IR absorbance, enzyme activity) over periods of minutes or hours. Such measurements deliver precious information for the practical application of the protein in question. On the other hand, it is impossible to extract thermodynamic or structural parameters firom such measurements, as they reflect the loss of native protein caused by a variety of processes. Irreversible thermal denaturation involves complex mechanisms and can lead to precipitation. The rates of such reactions depend on the concentration the rate constants depend on temperature and solution conditions. The order of such reactions can vary from 1 to FTIR has the advantage that it at least allows clear identification of -aggregation in the changes in the amide I band (1600-1700 cm ) of the infrared spectrum. The band component at around 1618 cm reliably reflects the progress of P-aggregation. ... 

Ruckenstein, E. and I. L. Shulgin, eds. 2009. Thermodynamics of Solutions From Gases to Pharmaceutics to Proteins. Dordrecht Springer. 

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