A novel and simple interpretation of the three-dimensional structure of globular proteins based on quantum mechanical computations on small model molecules. II. The clusters of myoglobin

We show that the bridges and clusters of the kind found earlier in rubredoxin also occur in myoglobin. The familiar acid–base(salt) bridges are at the heart of many of the clusters. The data reported by Takano [(1977) J. Mol. Biol., 110 , 537–508] on sperm whale metmyoglobin reveals ten clusters together with the heme structure and some unidentified fragments. The data reported by Hanson and Schoenborn [(1981) J. Mol. Biol. 153 , 117–146] on carbonmonoxymyoglobin shows numerous bridges that generally fit into the cluster picture derived from Takano's data. The data reported by S. E. V. Phillips (personal communication) on oxymyoglobin also fits into the same pattern of cluster. All but one of the myoglobin clusters are formed from two pieces of local structure each of which covers up to fifteen consecutive aminoacid residues. A “long-range” union joins the two pieces of local structure. The clusters are generally involved with the nonhelical structure and with the junctions of the two helices. Two applications of the theory are suggested. First, the clusters offer an explanation for the formation of the α-helices and second the unfolding of the myoglobin molecule at pH 3.8 to 5.3 is readily interpreted as the protonation at this pH of the carboxylate ions that generate the clusters that in turn support the α-helices.     

A novel supersecondary structure in globular proteins comprising the collagen-like helix and beta-turn

A structure consisting of the polyproline-II or collagen-like helix immediately succeeded by a beta-turn is seen in several synthetic peptides and has been suggested to be the conformational requirement for proline hydroxylation in nascent procollagen. Using a simple algorithm for detecting secondary structures, we have analysed crystal structure data on 40 globular proteins and have found eight examples of the collagen-helix + beta-turn supersecondary structure in 15 proteins that contain the collagen-like helical segments.     

A simple method for predicting the secondary structure of globular proteins: implications and accuracy

A method is presented for predicting the secondary structureof globular proteins from their amino acid sequence. It is basedon a rigorous statistical exploitation of the well-known biologicalfact that the amino acid compositions of each secondary structureare different. We also propose an evaluation process that allowsus to estimate the capacity of a method to predict the secondarystructure of a new protein which does not have any homologousproteins whose structure is already known. This evaluation processshows that our method has a prediction accuracy of 58.7% overthree states for the 62 proteins of the Kabsch and Sander (1983a)data bank. This result is better than that obtained by the mostwidely used methods—Lim (1974), Chou and Fasman (1978)and Garnier et al. (1978)—and also than that obtainedby a recent method based on local homologies (Levin et al.,1986). Our prediction method is very simple and may be implementedon any microcomputer and even on programmable pocket calculators.A simple Pascal implementation of the method prediction algorithmis given. The interpretation of our results in terms of proteinfolding and directions for further work are discussed. Received on December 15, 1987; accepted on April 12, 1988     

A theoretical approach to the binding of amphipathic molecules to globular proteins.

1. A theory based on a multiple equilibrium model with stoicheiometric binding constants has been formulated. It is applicable to the interaction of amphipathic molecules with charged macromolecules. 2. The theory has been applied to the binding of sodium n-dodecyl sulphate to ribonuclease A, beta-lactoglobulin and bovine serum albumin. 3. Over the ranges of surfactant concentration where binding is non-co-operative and co-operative, the experimental data can be satisfactorily fitted with energy and co-operatively parameters which are of comparable magnitude for the three globular proteins. 4. The results imply that the energy of interaction of sodium n-dodecyl sulphate with the proteins is equivalent to the formation of approximately four CH2 hydrophobic bonds.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation

A statistical-mechanical model (a noninteracting local structure model) of folding and unfolding transition in globular proteins is described and a formulation is given to calculate the partition function. The process of transition is discussed in this model within the framework of equilibrium statistical mechanics. In order to clarify the range of applicability of such an approach, the characteristics of the folding and unfolding transition in globular proteins are analyzed from the statistical-physical point of view. A theoretical advantage is pointed out in studying folding and unfolding processes taking place as conformational fluctuations in individual protein molecules under macroscopic equilibrium at the melting temperature. In this case, paths of folding and unfolding are shown to be identical in the statistical sense. A key to the noninteracting local structure model lies in the concept of local structures and the assumption of the absence of interactions between local structures. A local structure is defined as a continuous section of the chain which takes the same or similar local conformation as in the native conformation. The assumption of the absence of inter-actions between local structures endows the model with the remarkable character that its partition function can be calculated exactly; thereby the equilibrium population of various conformations along the folding and unfolding paths can be discussed only by a knowledge of the folded native conformation.     

Prediction of the secondary structure content of globular proteins based on structural classes

The prediction of the secondary structure content (-helix and-strand content) of a globular protein may play an important complementary role in the prediction of the protein's structure. We propose a new prediction algorithm based on Chou's database [Chou (1995),Proteins Struct. Fund Genet. 21, 319]. The new algorithm is an improved multiple linear regression method, taking the nonlinear and coupling terms of the frequencies of different amino acids into account. The prediction is also based on the structural classes of proteins. A resubstitution examination for the algorithm shows that the average errors are 0.040 and 0.033 for the prediction of-helix content and-strand content, respectively. The examination of cross-validation, the jackknife analysis, shows that the average errors are 0.051 and 0.044 for the prediction of-helix content and-strand content, respectively. Both examinations indicate the self-consistency and the extrapolative effectiveness of the new algorithm. Compared with the other methods available currently, our method has the merits of simplicity and convenience for use, as well as a high prediction accuracy. By incorporating the prediction of the structural classes, the only input of our method is the amino acid composition of the protein to be predicted.     

Stereochemical theory of the 3-dimensional structure of globular proteins. I. Highly helical intermediate structures

The authors analyze the physical prerequisites on which the proposed stereochemical theory of the three-dimensional structure of globular proteins is based. The theory represents a stereochemical modelling of the mechanism of protein self-organization suggested earlier by one of the authors. According to this mechanism, a highly helical intermediate structure(s) is formed at first and then it passes into the native one. In the highly-helical intermediate structure the arrangement of the polypeptide chain in space is the same as in the native structure. These two structures differ mainly by the secondary structure of the chain. The transition into the native structure proceeds under the effect of long-range interactions which transform the excess alpha-helices into beta-structural and irregular conformations. The so-called s-helices are considered (the alpha-helix, whose hydrophobic groups form a separate cluster on its surface). s-Helices can be obtained on the greater part of the polypeptide chain of any globular protein. In the unfolded protein chain they are the most stable and rapidly formed structures. It has been shown that namely s-helices are the initial blocks for the formation of the highly-helical intermediate structure. Stereochemical principles of the s-helix packing that permit to predict the three-dimensional structure of highly helical proteins have been found. According to these principles the highly helical structure represents the packing of hydrophobic surfaces and s-helices. In their turn, hydrophobic surfaces are formed as a result of complementary interaction of borders of hydrophobic clusters of two s-helices according to the "knob-hole" principle.     

A view of the three dimensional structure of globular proteins

A view of the three dimensional structure of globular proteins based on continuous networks of hydrogen bonds is proposed. Active sites of enzymes and ion sites are prominent and, within the networks, there are islands of hydrophobic regions giving an overall piebald effect to the appearance of the molecule. This point of view was originally suggested by the results of quantum mechanical computations on the coupling between hydrogen bonds. A formalism for the total energy of a globular protein in water is also suggested.The study of five lines of experimental evidence supports this suggestion. The analysis of the experimental X-ray data for ten globular proteins, using the NETWORK program, revealed the existence of these hydrogen bond networks; X-ray data showed that water molecules tend to occupy fixed positions relative to the protein molecule; a survey has shown that water molecules tend to occupy specific positions relative to the hydrogen bonding side chains; experimental evidence on the bulk properties of lysozyme showed that there exist tightly bound water molecules; graphics studies of the ribonucleaseA molecule demonstrated the networks and the piebald effect. This point of view is pictorially simple and, to illustrate the use of such networks, we discuss the simple ion pairs which occur as substructures within the networks.     

Analysis of the accuracy and implications of simple methods for predicting the secondary structure of globular proteins

• 1.(1) Co-operation between a laboratory interested in developing the theory for protein secondary structure prediction methods and a laboratory interested in applying and comparing such methods has led to the development of a simple predictive algorithm.
• 2.(2) Four-state predictions, in which each residue is unambiguously assigned one conformational state of α-helix, extended chain, reverse turn or coil, predict 49% of residue states correctly (in a sample of 26 proteins) when the overall helix and extended-chain content is not taken into account.
• 3.(3) When the relative abundances of helix, extended chain, reverse turn and coil observed by X-ray crystallography are taken into account, a single constant for each protein and type of conformation can be used to bias the prediction. When predictions are optimized in this way, 63% of all residue states are unambiguously and correctly assigned.
• 4.(4) By analysing the nature of the bias required, proteins can be classified into helix-rich types, pleated-sheet-rich types, and so on. It is shown that, if the type of protein can be determined even approximately by circular dichroism, 57% of residue states can be correctly predicted without taking into account the X-ray structure. Further, comparable predictions can be obtained if, instead of circular dichroism, preliminary predictions are made to assess the protein type.
• 5.(5) It is emphasized that the numbers quoted here depend on the method used to assess accuracy, and the algorithm is shown to be at least as good as, and usually superior to, the reported prediction methods assessed in the same way.
• 6.(6) Ways of further enhancing predictions by the use of additional information from hydrophobic triplets and homologous sequences are also explored. Hydro-phobic triplet information does not significantly improve predictive power and it is concluded that this information is used by proteins in the next stage of folding. On the other hand, the use of homologous sequences appears to be very promising.
• 7.(7) The implication of these results in protein folding is discussed.

     

The ribbon of hydrogen bonds and the pseudomolecule in the three-dimensional structure of globular proteins. III. Bovine pancreatic ribonuclease A and bovine seminal ribonuclease

The model of the three-dimensional structure of globular proteins, which is based on a ribbon of hydrogen bonds along the whole of the backbone, is now applied to the comparison between monomeric bovine pancreatic ribonuclease A and dimeric bovine seminal ribonuclease. Some waters are involved in the hydrogen bonding of the ribbon, and the protein molecule plus these waters forms a pseudomolecule. The conformations of the three backbones are essentially identical and the three ribbons of hydrogen bonds are conserved with greater than 90% accuracy. We suggest that the conservation of the backbone conformations of the two molecules is a consequence of the conservation of the ribbons of hydrogen bonds. There are 16 simple mutations between the two molecules, of which 15 involve only side-chain groups with no more than one hydrogen bond to the backbone. Such mutations are not sufficient to change the ribbon of hydrogen bonds and hence there is no change in the backbone conformation. Generalizing this result, we suggest that the conservation of the ribbon is the reason why single point mutations rarely change the conformation of the backbone of the globular proteins.     

On the computation of the tertiary structure of globular proteins II.

The semi-empirical approach proposed earlier (Y?as et al., 1978) to compute the tertiary structures of globular proteins is here amplified and developed further. Using, as input, information on sequence and certain averages of interatomic distances which can be semi-empirically estimated, structures have been computed for pancreatic trypsin inhibitor, lysozyme and staphylococcal nuclease which resemble those determined by X-ray diffraction methods. The approach used is compared and contrasted with others proposed recently.     

A thermodynamic analysis of a family of small globular proteins: SH3 domains.

The stability and folding thermodynamics of two SH3-domains, belonging to Fyn and Abl proteins, have been studied by scanning calorimetry and urea-induced unfolding. They undergo an essentially two-state unfolding with parameters similar to those of the previously studied alpha-spectrin SH3 domain. The correlations between the thermodynamic parameters (heat capacity increment, delta Cp,U, the proportionality factor, m, and the Gibbs energy, delta Gw298) of unfolding and some integral structural parameters, such as polar and non-polar areas exposed upon domain denaturation, have been analyzed. The experimental data on delta Cp,U and the m-factor of the linear extrapolation model (LEM) obey the simple empirical correlations deduced elsewhere. The Gibbs energies calculated from the DSC data were compared with those found by fitting urea-unfolding curves to the LEM and the denaturant-binding model (DBM). The delta Gw298 values found with DBM correlate better with the DSC data, while those obtained with LEM are systematically smaller. The systematic difference between the parameters calculated with LEM and DBM are explained by an inherent imperfection of the LEM.     

A simple model for surface charge on ion channel proteins.

We present a simple two-parameter model for surface charge directly associated with ion channels. A spherically symmetric "charged shell" models a distribution of surface charge arrayed about the channel entrance, with a corresponding set of image charges behind the plane of the membrane. The transition between a regime of buffered conductance and a regime of rapidly falling conductance at very low ionic strength is found to depend on the magnitude of the surface charge as well as the separation between the charge and the channel entrance. This resolves an apparent discrepancy between the experimental findings of Naranjo and Latorre (1993. Biophys. J. 64:1038-1050) and previous theoretical computations. The charged-shell model is used in a comparative study of the toad skeletal muscle conductance data of Naranjo and Latorre, the rat skeletal muscle conductances of Ravindran et al. (1992. Biophys. J. 61:494-508), and a second set of rat muscle conductances presented in this paper.