Dissociation Mode of the O-H Bond in Betanidin, pKa-Clusterization Prediction, and Molecular Interactions via Shape Theory and DFT Methods.

Betanidin (Bd) is a nitrogenous metabolite with significant bioactive potential influenced by pH. Its free radical scavenging activity and deprotonation pathway are crucial to studying its physicochemical properties. Motivated by the published discrepancies about the best deprotonation routes in Bd, this work explores all possible pathways for proton extractions on that molecule, by using the direct approach method based on pKa. The complete space of exploration is supported by a linear relation with constant slope, where the pKa is written in terms of the associated deprotonated molecule energy. The deprotonation rounds 1, …, 6 define groups of parallel linear models with constant slope. The intercepts of the models just depend on the protonated energy for each round, and then the pKa can be trivially ordered and explained by the energy. We use the direct approximation method to obtain the value of pKa. We predict all possible outcomes based on a linear model of the energy and some related verified assumptions. We also include a new measure of similarity or dissimilarity between the protonated and deprotonated molecules, via a geometric-chemical descriptor called the Riemann-Mulliken distance (RMD). The RMD considers the cartesian coordinates of the atoms, the atomic mass, and the Mulliken charges. After exploring the complete set of permutations, we show that the successive deprotonation process does not inherit the local energy minimum and that the commutativity of the paths does not hold either. The resulting clusterization of pKa can be explained by the local acid and basic groups of the BD, and the successive deprotonation can be predicted by using the chemical explained linear models, which can avoid unnecessary optimizations. Another part of the research uses our own algorithm based on shape theory to determine the protein's active site automatically, and molecular dynamics confirmed the results of the molecular docking of Bd in protonated and anionic form with the enzyme aldose reductase (AR). Also, we calculate the descriptors associated with the SET and SPLET mechanisms.

Shape Theory Applied to Molecular Docking and Automatic Localization of Ligand Binding Pockets in Large Proteins.

Automatic search of cavities and binding mode analysis between a ligand and a 3D protein receptor are challenging problems in drug design or repositioning. We propose a solution based on a shape theory theorem for an invariant coupled system of ligand-protein. The theorem provides a matrix representation with the exact formulas to be implemented in an algorithm. The method involves the following results: (1) exact formulae for the shape coordinates of a located-rotated invariant coupled system; (2) a parameterized search based on a suitable domain of van der Waals radii; (3) a scoring function for the discrimination of sites by measuring the distance between two invariant coupled systems including the atomic mass; (4) a matrix representation of the Lennard-Jones potential type 6-12 and 6-10 as the punctuation function of the algorithm for a molecular docking; and (5) the optimal molecular docking as a solution of an optimization problem based on the exploration of an exhaustive set of rotations. We apply the method in the xanthine oxidase protein with the following ligands: hypoxanthine, febuxostat, and chlorogenic acid. The results show automatic cavity detection and molecular docking not assisted by experts with meaningful amino acid interactions. The method finds better affinities than the expert software for known published cavities.