Application of a novel graph-theoretic folding degree index to the study of steroid-DB3 antibody binding affinity

Linear solvent structure-polymer solubility and solvation energy relationships to study conductive polymer/carbon nanotube composite solutions

Prediction of the solvation and solvent selectivity of polymer composites in different solvents is an important subject in colloid and polymer chemistry.

Enzymes/non-enzymes classification model complexity based on composition, sequence, 3D and topological indices

The huge amount of new proteins that need a fast enzymatic activity characterization creates demands of protein QSAR theoretical models. The protein parameters that can be used for an enzyme/non-enzyme classification includes the simpler indices such as composition, sequence and connectivity, also called topological indices (TIs) and the computationally expensive 3D descriptors. A comparison of the 3D versus lower dimension indices has not been reported with respect to the power of discrimination of proteins according to enzyme action. A set of 966 proteins (enzymes and non-enzymes) whose structural characteristics are provided by PDB/DSSP files was analyzed with Python/Biopython scripts, STATISTICA and Weka. The list of indices includes, but it is not restricted to pure composition indices (residue fractions), DSSP secondary structure protein composition and 3D indices (surface and access). We also used mixed indices such as composition-sequence indices (Chou's pseudo-amino acid compositions or coupling numbers), 3D-composition (surface fractions) and DSSP secondary structure amino acid composition/propensities (obtained with our Prot-2S Web tool). In addition, we extend and test for the first time several classic TIs for the Randic's protein sequence Star graphs using our Sequence to Star Graph (S2SG) Python application. All the indices were processed with general discriminant analysis models (GDA), neural networks (NN) and machine learning (ML) methods and the results are presented versus complexity, average of Shannon's information entropy (Sh) and data/method type. This study compares for the first time all these classes of indices to assess the ratios between model accuracy and indices/model complexity in enzyme/non-enzyme discrimination. The use of different methods and complexity of data shows that one cannot establish a direct relation between the complexity and the accuracy of the model.

Tight-binding "dihedral orbitals" approach to the degree of folding of macromolecular chains

We develop a tight-binding molecular approach to quantify the degree of folding of a macromolecular chain. This approach is based on the linear combination of "dihedral" orbitals to give molecular orbitals (LCDO-MO). The dihedral orbitals are a set of orbitals situated in each dihedral angle of the chain. The LCDO-MO approach remains basically topological, and we display its direct relation to known graph theoretical concepts. Using this approach, we define the dihedral electronic energy and the dihedral electronic partition function of a linear macromolecular chain. We show that the partition function per dihedral angle quantifies the degree of folding of the dihedral graph. We analyze the empirical relationship between these two functions by using a series of 100 proteins. We also study the relation between these two functions and the percentages of secondary structure for these proteins. Finally, we illustrate the use of the dihedral energy and the partition function in structure-property studies of proteins by analyzing the binding of steroids to DB3 antibody.

Computational chemistry comparison of stable/nonstable protein mutants classification models based on 3D and topological indices

In principle, there are different protein structural parameters that can be used in computational chemistry studies to classify protein mutants according to thermal stability including: sequence, connectivity, and 3D descriptors. Connectivity parameters (called topological indices, TIs) are simpler than 3D parameters being then less computationally expensive. However, TIs ignore important aspects of protein structure and hence are expected to be inaccurate. In any case, a comparison of 3D and TIs has not been reported with respect to the power of discrimination of proteins according to stability. In this study, we compare both classes of indices in this sense by the first time. The best model found, based on 3D spectral moments correctly classified 507 out of 525 (96.6%) proteins while TIs model correctly classified 404 out of 525 (77.0%) proteins. We have shown that, in fact, 3D descriptor models gave more accurate results than TIs but interestingly, TIs give acceptable results in a timely way in spite of their simplicity.

Effect of Protein Backbone Folding on the Stability of Protein−Ligand Complexes

The role played by the degree of folding of protein backbones in explaining the binding energetics of protein-ligand interactions has been studied. We analyzed the protein/peptide interactions in the RNase-S system in which amino acids at two positions of the peptide S have been mutated. The global degree of folding of the protein S correlates in a significant way with the free energy and enthalpy of the protein-peptide interactions. A much better correlation is found with the local contribution to the degree of folding of one amino acid residue: Thr36. This residue is shown to have a destabilizing interaction with Lys41, which interacts directly with peptide S. Another system, consisting of the interactions of small organic molecules with HIV-1 protease was also studied. In this case, the global change in the degree of folding of the protease backbone does not explain the binding energetics of protein-ligand interactions. However, a significant correlation is observed between the free energy of binding and the contribution of two amino acid residues in the HVI-1 protease: Gly49 and Ile66. In general, it was observed that the changes in the degree of folding are not restricted to the binding site of the protein chain but are distributed along the whole protein backbone. This study provides a basis for further consideration of the degree of folding as a parameter for empirical structural parametrizations of the binding energetics of protein folding and binding.

A protein folding degree measure and its dependence on crystal packing, protein size, secondary structure, and domain structural class

Comparing two or more protein structures with respect to their degree of folding is common practice in structural biology despite the fact that there is no scale for a folding degree. Here we introduce a formal definition of a folding degree, capable of quantitative characterization. This enables ordering among protein chains based on their degree of folding. The folding degree of a data set of 152 representative nonhomologous proteins is then studied. We demonstrate that the variation in the folding degree seen for this data set is not due to crystallization artifacts or experimental conditions, such as resolution, refinement protocol, pH, or temperature. A good linear relationship is observed between the folding degree and the percentages of secondary structures in the protein. The folding degree is able to account for the small changes produced in the structure due to crystal packing and temperature. Automating the classification of proteins into their respective structural domain classes, namely mainly-alpha, mainly-beta, and alpha-beta, is also possible.

Folding degrees of azurins and pseudoazurins

A quantitative measure of the degree of folding of azurins and pseudoazurins has been made. We have found that the reduction potential of azurins and pseudoazurins is a function of the contribution to the degree of folding of His117, a key amino acid in electron transfer which is directly bonded to copper in these proteins. The folding degree of His117 explains 95% of the variance in the experimental values of the reduction potential of azurins and pseudoazurins. The change in the folding degree of this amino acid influences several geometric parameters of the main backbones of these proteins. Among them, the angle formed between N(His117)...Cu...S(Cys112), which plays an important role in electron transport, but not the N(His117)...Cu distance, shows some non-linear correlation with the reduction potential of azurins and pseudoazurins. However, it is only able to explain less than 75% in the variance of the reduction potential of these proteins instead of the 95% explained by the folding degree of His117.

Characterization of the amino acid contribution to the folding degree of proteins

The folding degree index (Estrada, Bioinformatics 2002;18:697-704) is extended to account for the contribution of amino acids to folding. First, the mathematical formalism for extending the folding degree index is presented. Then, the amino acid contributions to folding degree of several proteins are used to analyze its relation to secondary structure. The possibilities of using these contributions in helping or checking the assignation of secondary structure to amino acids are also introduced. The influence of external factors to the amino acids contribution to folding degree is studied through the temperature effect on ribonuclease A. Finally, the analysis of 3D protein similarity through the use of amino acid contributions to folding degree is studied by selecting a series of lysozymes. These results are compared to that obtained by sequence alignment (2D similarity) and 3D superposition of the structures, showing the uniqueness of the current approach.