Application of singular value decomposition to the inter-fragment interaction energy analysis for ligand screening

We evaluated the binding affinity between p38 MAP kinase and various inhibitors through use of the fragment molecular orbital (FMO) method at MP2/6-31G^∗ level in comparison to experimental values of half maximal inhibitory concentration (IC₅₀). Initially, the calculated results of the FMO-IFIE (inter-fragment interaction energy) sums for 60 complex structures registered in the Protein Data Bank were not well correlated with the IC₅₀ activity data. Therefore, we performed the singular value decomposition (SVD) for the calculated results of the IFIE matrix (amino acid residues × various ligands) to improve the correlation and determine the cause of the initial poor results. In SVD, the original matrix is divided into multiple vectors that are orthogonal to each other. Through this method, we improved the correlation by removing some particular vectors that involved noise components and impaired the correlation. In addition, the correlation between the IC₅₀ and FMO-IFIE for 22 complex structures of estrogen receptor α (ERα) was also improved in this way. We analyzed the amino acid residues of receptors that were mainly involved in the removed vectors and found an overestimation of the strength of the hydrogen bond between glutamic acid and the ligand.