xMaPAn Interpretable Alignment-Free Four-Dimensional Quantitative Structure–Activity Relationship Technique Based on Molecular Surface Properties and Conformer Ensembles

A novel alignment-free molecular descriptor called xMaP (flexible MaP descriptor) is introduced. The descriptor is the advancement of the previously published translationally and rotationally invariant three-dimensional (3D) descriptor MaP (mapping property distributions onto the molecular surface) to the fourth dimension (4D). In addition to MaP, xMaP is independent of the chosen starting conformation of the encoded molecules and is therefore entirely alignment-free. This is achieved by using ensembles of conformers, which are generated by conformational searches. This step of the procedure is similar to Hopfinger’s 4D quantitative structure–activity relationship (QSAR). A five-step procedure is used to compute the xMaP descriptor. First, a conformational search for each molecule is carried out. Next, for each of the conformers an approximation to the molecular surface with equally distributed surface points is computed. Third, molecular properties are projected onto this surface. Fourth, areas of identical properties are clustered to so-called patches. Fifth, the spatial distribution of the patches is converted into an alignment-free descriptor that is based on the entire conformer ensemble. The resulting descriptor can be interpreted by superimposing the most important descriptor variables and the molecules of the data set. The most important descriptor variables are identified with chemometric regression tools. The novel descriptor was applied to several benchmark data sets and was compared to other descriptors and QSAR techniques comprising a binary fingerprint, a topological pharmacophore descriptor (Cats2D), and the field-based 3D-QSAR technique GRID/PLS which is alignment-dependent. The use of conformer ensembles renders xMaP very robust. It turns out that xMaP performs very well on (almost) all data sets and that the statistical results are comparable to GRID/PLS. In addition to that, xMaP can also be used to efficiently visualize the derived quantitative structure–activity relationships

MOESM4 of Efficiency of different measures for defining the applicability domain of classification models

Additional file 4. Source of the data

Operator theory and its applications: in memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems

A Diverse Benchmark Based on 3D Matched Molecular Pairs for Validating Scoring Functions

The prediction of protein–ligand interactions and their corresponding binding free energy is a challenging task in structure-based drug design and related applications. Docking and scoring is broadly used to propose the binding mode and underlying interactions as well as to provide a measure for ligand affinity or differentiate between active and inactive ligands. Various studies have revealed that most docking software packages reliably predict the binding mode, although scoring remains a challenge. Here, a diverse benchmark data set of 99 matched molecular pairs (3D-MMPs) with experimentally determined X-ray structures and corresponding binding affinities is introduced. This data set was used to study the predictive power of 13 commonly used scoring functions to demonstrate the applicability of the 3D-MMP data set as a valuable tool for benchmarking scoring functions

10-Iodo-11<i>H</i>‑indolo[3,2‑<i>c</i>]quinoline-6-carboxylic Acids Are Selective Inhibitors of DYRK1A

The protein kinase DYRK1A has been suggested to act as one of the intracellular regulators contributing to neurological alterations found in individuals with Down syndrome. For an assessment of the role of DYRK1A, selective synthetic inhibitors are valuable pharmacological tools. However, the DYRK1A inhibitors described in the literature so far either are not sufficiently selective or have not been tested against closely related kinases from the DYRK and the CLK protein kinase families. The aim of this study was the identification of DYRK1A inhibitors exhibiting selectivity versus the structurally and functionally closely related DYRK and CLK isoforms. Structure modification of the screening hit 11<i>H</i>-indolo­[3,2-<i>c</i>]­quinoline-6-carboxylic acid revealed structure–activity relationships for kinase inhibition and enabled the design of 10-iodo-substituted derivatives as very potent DYRK1A inhibitors with considerable selectivity against CLKs. X-ray structure determination of three 11<i>H</i>-indolo­[3,2-<i>c</i>]­quinoline-6-carboxylic acids cocrystallized with DYRK1A confirmed the predicted binding mode within the ATP binding site