Thermodynamics of globular proteins

The analysis of temperature-induced unfolding of proteins in aqueous solutions was performed. Based on the data of thermodynamic parameters of protein unfolding and using the method of semi-empirical calculations of hydration parameters at reference temperature 298 K, we obtained numerical values of enthalpy, free energy, and entropy which characterize the unfolding of proteins in the ‘gas phase’. It was shown that specific values of the energy of weak intramolecular bonds (?H^int), conformational free energy (?G^conf) and entropy (?S^conf) are the same for proteins with molecular weight 7–25 kDa. Using the energy value (?H^int) and the proposed approach for estimation of the conformational entropy of native protein (S^NC), numerical values of the absolute free energy (G^NC) were obtained.     

Topology of globular proteins

This paper inquires whether it is reasonable to expect the native structure of proteins to be “knotted”. To this end, some topological properties of polypeptides containing disulfide bridges are discussed using notions from mathematical knot theory and graph theory. The probability of occurrence of knots in random cyclic polymers is calculated as a function of chain length by elementary Monte Carlo methods. The implications of this for protein renaturation and for determining the tertiary structure of proteins are discussed.     

The adsorption of globular proteins

A series of experiments is suggested to elucidate further the nature of the adsorption of globular proteins on polar solid surfaces. Two ratios of surface energies and the total protein volume are used to characterize the expected form of the adsorbed species. A simple model calculation illustrates the approach.     

Compressibility-structure relationship of globular proteins

The adiabatic compressibility, -beta s, of 11 globular proteins in water was determined by means of sound velocity measurements at 25 degrees C. All the proteins studied except for subtilisin showed positive -beta s values, indicating the large internal compressibility of the protein molecules. The intrinsic compressibility of proteins free from the hydration effect appeared to be comparable to that of normal ice. The compressibility data for 25 proteins, including 14 reported previously [Gekko, K., & Noguchi, H. (1979) J. Phys. Chem. 83, 2706-2714], were statistically analyzed to examine the correlation of the compressibility with some structural parameters and the amino acid compositions of proteins. It was found that -beta s increases with increasing partial specific volume and hydrophobicity of proteins. The helix element also seemed to be a dynamic domain to increase -beta s. Four amino acid residues (Leu, Glu, Phe, and His) greatly increased -beta s, and another four (Asn, Gly, Ser, and Thr) decreased it. Some empirical equations were derived for the estimation of the -beta s values of unknown proteins on the basis of their amino acid compositions. The volume fluctuations of proteins revealed by the compressibility data were in the range of 30-200 mL/mol, which corresponded to about 0.3% of the total protein volume. The conformational fluctuation seemed to enhance the thermal stability of proteins.     

Foam fractionation of globular proteins

Foam fractionation of bovine serum albumin (BSA) was studied as a model system for potato wastewater. The effects of feed concentration, superficial gas velocity, feed flow rate, bubble size, pH, and ionic strength on the enrichment and recovery of BSA were investigated in a single-stage continuous foam fractionation column. Enrichments ranged from 1.5 to 6.0 and recoveries from 5 to 85%. The feed concentrations were varied from 0.01 to 0.2 wt %, and enrichments were found to increase with lower feed concentrations. Enrichments also increased with lower superficial gas velocities and larger bubble sizes. At sufficiently low feed flow rates, enrichment was found to increase with an increase in the flow rate, eventually becoming insensitive to the feed flow rate at higher values. The pH was varied from 3.5 to 7.0 and ionic strength from 0.001M to 0.2M. The effects of pH and ionic strength were found to be coupled with bubble size. A minimum bubble size was found at pH 4.8, the isoelectric point of BSA, resulting in a minimum in the enrichment. Bubble size, and thus enrichment, was found to increase as the ionic strength decreased from 0.2M to 0.01M. Previous models(1,2) for the hydrodynamics of foam column were extended for a singlestage continuous foam fractionation column for the prediction of enrichment and recovery. The model assumed adsorption equilibrium, infinite surface viscosity, and bubbles of the same size. Though coalescence was formally accounted for in the model by considering bubble size as a function of foam height, calculations for the experimental runs were performed only for the case of no coalescence. Quantitative predictions of enrichment and recovery could not be made with a single representative bubble size because of the broad inlet bubble size distribution as well as broadening of the distribution as a result of coalescence. The experimental enrichments were higher and recoveries were lower than the model predictions, the discrepancy being more pronounced at lower feed concentrations because of increased coalescence. The higher enrichments are due to the predominant effect of internal reflux as a result of coalescence whereas the lower recoveries are a result of detrimental effects of broadening bubble size distributions.     

Salting-in characteristics of globular proteins

Protein solubility, and the formation of various solid phases, is of interest in both bioprocessing and the study of protein condensation diseases. Here we examine the the phase behavior of three proteins (chymosin B, β-lactoglobulin B, and pumpkin seed globulin) previously known to display salting-in behavior, and measure their solubility as a function of pH, ionic strength, and salt type. Although the phase behavior of the three proteins is quantitatively different, general trends emerge. Stable crystal nucleation does not occur within the salting-in region for the proteins examined, despite the crystal being observed as the most stable solid phase. Instead, two types of amorphous phases were found within the salting-in region; additionally, an analog to the instantaneous clouding curve was observed within the salting-in region for chymosin B. Also, protein solutions containing sulfate salts resulted in different crystal morphologies depending on whether Li₂SO₄ or (NH₄)₂SO₄ was used.     

Thermal stabilities of globular proteins

Statistical thermodynamic theory has recently been developed to account for the stabilities of globular proteins. Here we extend that work to predict the dependence on temperature. Folding is assumed to be driven by solvophobic interactions and opposed by the conformational entropy. The temperature dependence of the solvophobic interaction is taken from the transfer experiments on amino acids by Tanford and Nozaki and on model solutes by Gill and Wads?. One long-standing puzzle has been why proteins denature upon heating, since the solvophobic force to fold strengthens with increasing temperature. This is resolved by the theory, which predicts two first-order phase transitions. "Cold denaturation" is driven principally by the weakening of the solvophobic interaction, but normal denaturation is driven principally by the gain of conformational entropy of the chain. Predictions of the thermodynamic state functions are in reasonable agreement with the calorimetric experiments of Privalov and Khechinashvili. Comparison of the theory with experiments suggests that there may be an additional enthalpic driving force toward folding which is not due to the solvophobic interactions.     

Conformational stability of globular proteins

The conformational stability of ribonuclease T1 has been measured as a function of the variables of most interest to biochemists: temperature, pH, salt concentration, disulfide-bond content and amino acid sequence. The results provide insight into the forces that stabilize globular proteins.     

Disulphide bridges in globular proteins

Disulphide bridges in proteins of known sequence, connectivity and structure were studied to search for common features. Their distribution, topology, conformation and conservation were analysed in detail. Several general patterns emerge which to some extent dictate disulphide bridge formation. For example, there is a strong preference for shorter connections, with half-cystines separated by less than 24 residues in 49% of all disulphides. Right- and left-handed disulphides occur equally; the left-handed structures adopt one predominant conformation (symmetric χ₁ = ?60 °, χ₂ = ?80 °, χ₃ = t-90 °). Cystines are generally very well conserved, in contrast to cysteines, with a free —SH group, which mutate rapidly. If a disulphide is not conserved, both cystines are mutated. The role of disulphide bridges in globular proteins is discussed.     

Origins of globular structure in proteins

Thermodynamic incompatibility of polymers in a common solvent is possibly a driving force for formation and evolution of globular protein structures. Folding of polypeptide chains leads to a decrease in both excluded volume of molecules and chemical differences between surfaces of globular molecules with chemical information hidden in the hydrophobic interior. Folding of polypeptide chains results in 'molecular or thermodynamic mimicry' of globular proteins and in at least more than 10-fold higher phase separation threshold values of mixed protein solutions compared to those of classical polymers. Unusually high co-solubility might be necessary for efficient biological functioning of proteins, e.g. enzymes, enzyme inhibitors, etc.     

Origins of globular structure in proteins

Since natural proteins are the products of a long evolutionary process, the structural properties of present-day proteins should depend not only on physico-chemical constraints, but also on evolutionary constraints. Here we propose a model for protein evolution, in which membranes play a key role as a scaffold for supporting the gradual evolution from flexible polypeptides to well-folded proteins. We suggest that the folding process of present-day globular proteins is a relic of this putative evolutionary process. To test the hypothesis that membranes once acted as a cradle for the folding of globular proteins, extensive research on membrane proteins and the interactions of globular proteins with membranes will be required.     

Far-infrared spectra of some globular proteins

The far-infrared absorption spectrum (40–400 cm^?1) of solid pellets and films of several globular proteins (lysozyme, myoglobin, hemoglobin, serum albumin, ribonuclease, chymotrypsinogen, subtilisin) and of some representative polypeptides [nylon 66, poly (γ-benzyl L -glutamate)] have been investigated by using a Michelson interferometer. While polypeptides are known to present several peaks which can be assigned mostly to hydrogen-bond modes, all the investigated globular proteins display only one broad, intense baud in the 100–200 cm^?1 region. The origin of this band, which persists even after denaturation or partial digestion, is discussed.     

Directional structural features of globular proteins

We describe a novel presentation of the conformation of the backbone atoms for proteins of known structure. Given the C^α atom cartesian co-ordinates from X-ray crystallography, a matrix is calculated, where the ijth element of the matrix is the cosine of the angle between the direction of the chain at residue i and the direction of the chain at residue j. These “direction matrices” have distinctive patterns which correspond to α-helix, extended structure, straight or bent segments, “superhelix”, and many other important structural features. We discuss the direction matrices for a number of proteins, and make some generalizations on the basic principles of protein folding.     

Study of beta-turns in globular proteins

The formation of beta-turns in globular proteins has been studied by the method of molecular mechanics. Statistical method of discriminant analysis was applied to calculate energy components and sequences of oligopeptide segments, and after this prediction of I type beta-turns has been drawn. The accuracy of true positive prediction is 65%. Components of conformational energy considerably affecting beta-turn formation were delineated. There are torsional energy, energy of hydrogen bonds, and van der Waals energy.     

Dynamic polyhedral models of globular proteins

We have devised several mechanical models of globular proteins by approximating them to various polyhedra (dodecahedron, truncated octahedron, icosahedron, truncated icosahedron). The models comprise hollow blocks linked together in a flexible chain. Between blocks there is a set of several reversible, weak magnetic interactions such that when the chain is agitated, it will fold into a stable polyhedral structure about the size of a hand. Folding may be followed in real time with a video camera. Key to the success of the folding process is the lightness of the chain. Several side chains may also be added to the blocks such that they come together to create a polyhedral core when the chain folds. The models have a number of similarities to globular proteins: each chain folds into a unique, but dynamic, three-dimensional structure; the instructions that determine this structure are built into the configuration of blocks; and it is difficult to predict this structure given the unfolded block configuration. Furthermore, the chains fold quickly, generally in less than a minute, several pathways are involved, and these pathways progress through elements of "native" structure. In particular, the models emphasize the importance of restricted conformational mobility in assisting the chain to fold, and also in eliminating undesirable interactions. Because of these similarities to globular proteins, we believe that the polyhedral models will, with continued development, be helpful in understanding the protein folding process, while at the same time acting as valuable educational visual aids. They might also inspire the construction of new types of microscopic, self-assembling devices.