Modeling of the relationship between biological activity of delta-selective enkephalin analogues and docking results by polynomials

One of the areas of bioinformatics is the development of fast and reliable methods for predicting the biological activity of compounds. This will facilitate the design of new compounds and reduce costs. The process of creating selective ligands of a delta opioid receptor (DOR) was directed towards the synthesis of enkephalin analogues. Their biological activity was determined by using in vivo and in vitro methods, which allows establishing the relationship between structure and biological activity. The relationship between the values of the ChemScore scoring function from the docking procedure in GOLD 5.2 and the values of the total energy of the ligand-receptor complex in Molegro was modeled with first-to third-degree polynomials and a surface fitted method. The polynomial surface of third degree displayed the best fit, assessed by the least squares method. In our previous study with the theoretical model of DOR (PDBid: 1ozc) the relationship between the values of efficacy of the compound, the values of the GoldScore scoring function from the docking procedure in GOLD 5.2 and the values of the total energy of the ligand-receptor complex in Mollegro was established. This relationship was modeled with a third-degree polynomial in software MATLAB. The aim of the present work was to find an optimal fitting polynomial function modeling the relationship between the quantitative parameters of in vitro bioassay and the values of the scoring functions from molecular docking with crystal structure of DOR (PDBid: 4ej4) and delta-opioid ligands using the least squares method. The third-degree polynomial was successfully used for modeling the relationship between the efficacy of delta-selective enkephalin analogues and docking results. It was described by a polynomial surface of third degree.