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.     

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.     

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.     

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.     

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.     

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...     

Outlining folding nuclei in globular proteins

Our theoretical approach for prediction of folding/unfolding nuclei in three-dimensional protein structures is based on a search for free energy saddle points on networks of protein unfolding pathways. Under some approximations, this search is performed rapidly by dynamic programming and results in prediction of Phi values, which can be compared with those found experimentally. In this study, we optimize some details of the model (specifically, hydrogen atoms are taken into account in addition to heavy atoms), and compare the theoretically obtained and experimental Phi values (which characterize involvement of residues in folding nuclei) for all 17 proteins, where Phi values are now known for many residues. We show that the model provides good Phi value predictions for proteins whose structures have been determined by X-ray analysis (the average correlation coefficient is 0.65), with a more limited success for proteins whose structures have been determined by NMR techniques only (the average correlation coefficient is 0.34), and that the transition state free energies computed from the same model are in a good anticorrelation with logarithms of experimentally measured folding rates at mid-transition (the correlation coefficient is -0.73).     

Hydrogen bonding in globular proteins.

A global census of the hydrogen bonds in 42 X-ray-elucidated proteins was taken and the following demographic trends identified: (1) Most hydrogen bonds are local, i.e. between partners that are close in sequence, the primary exception being hydrogen-bonded ion pairs. (2) Most hydrogen bonds are between backbone atoms in the protein, an average of 68%. (3) All proteins studied have extensive hydrogen-bonded secondary structure, an average of 82%. (4) Almost all backbone hydrogen bonds are within single elements of secondary structure. An approximate rule of thirds applies: slightly more than one-third (37%) form i----i--3 hydrogen bonds, almost one-third (32%) form i----i--4 hydrogen bonds, and slightly less than one-third (26%) reside in paired strands of beta-sheet. The remaining 5% are not wholly within an individual helix, turn or sheet. (5) Side-chain to backbone hydrogen bonds are clustered at helix-capping positions. (6) An extensive network of hydrogen bonds is present in helices. (7) To a close approximation, the total number of hydrogen bonds is a simple function of a protein's helix and sheet content. (8) A unique quantity, termed the reduced number of hydrogen bonds, is defined as the maximum number of hydrogen bonds possible when every donor:acceptor pair is constrained to be 1:1. This quantity scales linearly with chain length, with 0.71 reduced hydrogen bond per residue. Implications of these results for pathways of protein folding are 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.     

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.     

Nanofibers made of globular proteins

Strong nanofibers composed entirely of a model globular protein, namely, bovine serum albumin (BSA), were produced by electrospinning directly from a BSA solution without the use of chemical cross-linkers. Control of the spinnability and the mechanical properties of the produced nanofibers was achieved by manipulating the protein conformation, protein aggregation, and intra/intermolecular disulfide bonds exchange. In this manner, a low-viscosity globular protein solution could be modified into a polymer-like spinnable solution and easily spun into fibers whose mechanical properties were as good as those of natural fibers made of fibrous protein. We demonstrate here that newly formed disulfide bonds (intra/intermolecular) have a dominant role in both the formation of the nanofibers and in providing them with superior mechanical properties. Our approach to engineer proteins into biocompatible fibrous structures may be used in a wide range of biomedical applications such as suturing, wound dressing, and wound closure.     

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.     

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.