The heat capacity of proteins

The heat capacity plays a major role in the determination of the energetics of protein folding and molecular recognition. As such, a better understanding of this thermodynamic parameter and its structural origin will provide new insights for the development of better molecular design strategies. In this paper we have analyzed the absolute heat capacity of proteins in different conformations. The results of these studies indicate that three major terms account for the absolute heat capacity of a protein: (1) one term that depends only on the primary or covalent structure of a protein and contains contributions from vibrational frequencies arising from the stretching and bending modes of each valence bond and internal rotations; (2) a term that contains the contributions of noncovalent interactions arising from secondary and tertiary structure; and (3) a term that contains the contributions of hydration. For a typical globular protein in solution the bulk of the heat capacity at 25°C is given by the covalent structure term (close to 85% of the total). The hydration term contributes about 15 and 40% to the total heat capacity of the native and unfolded states, respectively. The contribution of non-covalent structure to the total heat capacity of the native state is positive but very small and does not amount to more than 3% at 25°C. The change in heat capacity upon unfolding is primarily given by the increase in the hydration term (about 95%) and to a much lesser extent by the loss of noncovalent interactions (up to ～5%). It is demonstrated that a single universal mathematical function can be used to represent the partial molar heat capacity of the native and unfolded states of proteins in solution. This function can be experimentally written in terms of the molecular weight, the polar and apolar solvent accessible surface areas, and the total area buried from the solvent. This unique function accurately predicts the different magnitude and temperature dependences of the heat capacity of both the native and unfolded states, and therefore of the heat capacity changes associated with folding/unfolding transitions. © 1995 Wiley-Liss, Inc.     

Reversible association processes of globular proteins. I. Insulin

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1. The dissociation of insulin is favored by (a) an increase in charge, (b) a decrease in ionic strength, and (c) an increase in temperature.     

Numerical investigations of transient heat transfer characteristics and vitrification tendencies in ultra-fast cell cooling processes

During freezing, cells are often damaged directly or indirectly by ice formation. Vitrification is an alternative approach to cryopreservation that avoids ice formation. The common method to achieve vitrification is to use relatively high concentrations of cryoprotectant agents (CPA) in combination with a relatively slow cooling rate. However, high concentrations of CPAs have potentially damaging toxic and/or osmotic effects on cells. Therefore, establishing methods to achieve vitrification with lower concentrations of CPAs through ultra-fast cooling rates would be advantageous in these aspects. These ultra-fast cooling rates can be realized by a cooling system with an ultra-high heat transfer coefficient (h) between the sample and coolant. The oscillating motion heat pipe (OHP), a novel cooling device utilizing the pressure change to excite the oscillation motion of the liquid plugs and vapor bubbles, can significantly increase h and may fulfill this aim. The current investigation was designed to numerically study the effects of different values of h on the transient heat transfer characteristics and vitrification tendencies of the cell suspension during the cooling processes in an ultra-thin straw (100 microm in diameter). The transient temperature distribution, the cooling rate and the volume ratio (x) of the ice quantity to the maximum crystallizable ice of the suspension were calculated. From these numerical results, it is concluded that the ultra-high h (>10(4) W/m2 K) obtained by OHPs could facilitate vitrification by efficiently decreasing x as well as the time to pass through the dangerous temperature region where the maximum ice formation happens. For comparison, OHPs can decrease both of the parameters to less than 20% of those from the widely used open pulled straw methods. Therefore, the OHP method will be a promising approach to improving vitrification tendencies of CPA solutions and could also decrease the required concentration of CPAs for vitrification, both of which are of great importance for the successful cryopreservation of cells by vitrification.     

Size and folding in globular proteins

We have modeled protein folding by packing a unified length of regular structural elements (alpha-helices and beta-sheets) into a 'cube'. In a globular protein with m alpha-helices and n beta-strands, this unified length is expressed in units of heptapeptides in alpha-helices, and in units of tripeptides in beta-strands. Calculations using published data show that a 4-helix bundle (m = 4, n = 0) has at least 2 x 2 x 2 helical heptapeptides; the 16-strand beta-barrel of porin (m = 0, n = 16) is at most 4 x 4 x 4 tripeptides in beta-strands. Compact, recurring protein modules with mixed helices and beta-strands are the ones that actually acquire a geometrically quasi-spherical, or cubic, shape.     

The low-temperature heat capacity of solid proteins.

Several harmonic models of protein fluctuations are used to calculate the heat capacity. They get the spectral density of conformational modes from inelastic neutron scattering, normal mode calculations, or macroscopic elasticity (Debye model). It is assumed that the low-frequency spectral density depends only weakly on temperature and protein species. The Debye model predicts temperatures below which modes are primarily in their ground states: 10 and 80 K for the lattice and conformational modes, respectively. The models differ most below 100 K. The mode calculations yield the most accurate predictions, though all three models are within twofold of the data. The heat capacity has the power law form aTb for T less than 30 K. The experimental b's of proteins are 1.6-1.8, and the theoretical, 1.1-1.3. One possible explanation for the discrepancy is the occurrence of transitions between discrete conformations. All of the models approach the measured data in the range 100-200 K. They are very similar above 200 K, where the heat capacity includes significant contributions from bond stretching and bending. This masks the possible anharmonic behavior of the conformational modes. Hydration substantially increases the heat capacity above 200 K. This effect seems to be a consequence of conformational transitions that have higher energy than the ones seen with low hydration. The analysis also predicts that denaturation with constant hydration produces a negligible increase of heat capacity. The larger increment in solution arises from the different hydration of the folded and unfolded states, and is responsible for the existence of cold denaturation. This phenomenon is thus predicted not to occur when the hydration is constant.     

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.     

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.     

Structural mobility and transformations in globular proteins

Journal of Biosciences - Although globular proteins are endowed with well defined three-dimensional structures, they exhibit substantial mobility within the framework of the given three-dimensional...     

Hydrophobicity and residue-residue contacts in globular proteins

A comprehensive statistical analysis of residue-residue contacts and residue environment in protein 3-D structures is presented. In the present work the range of interresidue interactions (effective radius of influence) in tertiary structures of proteins is examined and found to be 10 Å. This result is obtained by correlating the average number of residues within a spherical volume of different radii (contact numbers) with hydrophobicity. Best correlations are obtained with a radius of 10 Å. The same result is obtained when (i) only long-range interactions are considered and (ii) representative side chain atoms are used to indicate the tertiary structure instead of the usual representation of C^α atoms. Residue environment has been investigated using similar methods. Environmental hydrophobicity varies within only a small range of all residue types. Other physicochemical properties also exhibit similar trends of variation, and only five hydrophobic residues (Leu, Val, Met, Phe and Ile) produce a decrement of around 10% from the expected mean of the physicochemical distance between a residue type and its average environment. An information theory approach is proposed to compare domains, which takes into account the effective radius of influence of residues and sequence similarity.     

Stability and stabilization of globular proteins in solution

Proteins are multifunctional: their amino acid sequences simultaneously determine folding, function and turnover. Correspondingly, evolution selected for compromises between rigidity (stability) and flexibility (folding/function/degradation), to the result that generally the free energy of stabilization of globular proteins in solution is the equivalent to only a few weak intermolecular interactions. Additional increments may come from extrinsic factors such as ligands or specific compatible solutes. Apart from the enthalpic effects, entropy may play a role by reducing the flexibility (cystine bridges, increased proline content), or by water release from residues buried upon folding and association. Additional quaternary interactions and closer packing are typical characteristics of proteins from thermophiles. In halophiles, protein stability and function are maintained by increased ion binding and glutamic acid content, both allowing the protein inventory to compete for water at high salt. Acidophiles and alkalophiles show neutral intracellular pH; proteins facing the outside extremes of pH possess anomalously high contents in ionizable amino acids. Global comparisons of the amino acid compositions and sequences of proteins from mesophiles and extremophiles did not result in general rules of protein stabilization, even after including complete genome sequences into the search. Obviously, proteins are individuals that optimize internal packing and external solvent interactions by very different mechanisms, each protein in its own way. Strategies deduced from specific ultrastable proteins allow stabilizing point mutations to be predicted.     

Structure of alpha-spiral hairpins with short connections in globular proteins

The analysis of conformations of more than 100 alpha-alpha-hairpins with closely packed helical segments and connections up to four amino acid residues in length was carried out. Five types of the connections were revealed and their phi and psi values on the Ramachandran map were found. Each type of alpha-alpha-hairpins was shown to have a unique sequence pattern for hydrophobic and hydrophilic residues.     

Solvent denaturation and stabilization 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 effects of solvents on protein stability. Folding is assumed to be driven by solvophobic interactions and opposed by conformational entropy. The solvent dependence of the solvophobic interactions is taken from transfer experiments of Nozaki and Tanford on amino acids into aqueous solutions of urea or guanidine hydrochloride (GuHCl). On the basis of the assumption of two pathways involving collapse and formation of a core, the theory predicts that increasing denaturant should lead to a two-state denaturation transition (i.e., there is a stable state along each path separated by a free energy barrier). The denaturation midpoint is predicted to occur at higher concentrations of urea than of GuHCl. At neutral pH, the radius of the solvent-denatured state should be much smaller than for a random-flight chain and increase with either denaturant concentration or number of polar residues in the chain. A question of interest is whether free energies of folding should depend linearly on denaturant, as is often assumed. The free energy is predicted to be linear for urea but to have some small curvature for GuHCl. Predicted slopes and exposed areas of the unfolded states are found to be in generally good agreement with experiments. We also discuss stabilizing solvents and compare thermal with solvent denaturation.     

Conformation of glycyl residues in globular proteins

Glycine is unique among the amino acids in view of its symmetric nature. While the overall distribution of glycyl residues in the (phi, psi) plane is near-symmetric, there can be certain preferences for the individual conformations. An analysis of the observed glycyl conformations in 70 proteins has been carried out to find the influence of residues adjoining the glycyl residues. For this purpose, the (phi, psi) plane has been divided into two regions: the region in which phi is negative and the region in which phi is positive. The analysis is done in terms of the number of conformations occurring in these regions. It has been found that while the overall percentage distribution of glycyl residues between the positive and the negative phi regions is 54:46, the distribution shows asymmetry when the examples are sorted out in terms of X-Gly and Gly-Y doublets. The asymmetry becomes more prominent when the data are sorted out into triplets X-Gly-Y. Using the available information, it has been possible to designate 25 triplets as P-predominant and 19 as N-predominant. An examination of P-predominant triplets for possible occurrence in beta-bends having one of the conformations in the positive phi region shows that only 25% are of this nature. Thus, the P-preference of P-predominant triplets is not an outcome of the bend formation alone and must be an inherent property of these triplets.