Benchmarking of Linear and Nonlinear Approaches for Quantitative Structure−Property Relationship Studies of Metal Complexation with Ionophores

Abstract

A benchmark of several popular methods, Associative Neural Networks (ANN), Support Vector Machines (SVM), k Nearest Neighbors (kNN), Maximal Margin Linear Programming (MMLP), Radial Basis Function Neural Network (RBFNN), and Multiple Linear Regression (MLR), is reported for quantitative-structure property relationships (QSPR) of stability constants logK1 for the 1:1 (M:L) and logbeta2 for 1:2 complexes of metal cations Ag+ and Eu3+ with diverse sets of organic molecules in water at 298 K and ionic strength 0.1 M. The methods were tested on three types of descriptors: molecular descriptors including E-state values, counts of atoms determined for E-state atom types, and substructural molecular fragments (SMF). Comparison of the models was performed using a 5-fold external cross-validation procedure. Robust statistical tests (bootstrap and Kolmogorov-Smirnov statistics) were employed to evaluate the significance of calculated models. The Wilcoxon signed-rank test was used to compare the performance of methods. Individual structure-complexation property models obtained with nonlinear methods demonstrated a significantly better performance than the models built using multilinear regression analysis (MLRA). However, the averaging of several MLRA models based on SMF descriptors provided as good of a prediction as the most efficient nonlinear techniques. Support Vector Machines and Associative Neural Networks contributed in the largest number of significant models. Models based on fragments (SMF descriptors and E-state counts) had higher prediction ability than those based on E-state indices. The use of SMF descriptors and E-state counts provided similar results, whereas E-state indices lead to less significant models. The current study illustrates the difficulties of quantitative comparison of different methods: conclusions based only on one data set without appropriate statistical tests could be wrong.

New Approach for Accurate QSPR Modeling of Metal Complexation: Application to Stability Constants of Complexes of Lanthanide Ions Ln3+, Ag+, Zn2+, Cd2+ and Hg2+ with Organic Ligands in Water

“…). "Quorum Control" guided QSPR models perform better than previously reported models [23,39,40,52] for all studied metal ions. In whole, RMSE values of predictions obtained in this work are twice lower than those for the earlier reported models [23,39,40,52] (Figure 4) and they are close to experimental systematic errors (see Table 1).…”

“…[40,74] In this procedure, an entire dataset is divided in 5 non-overlapping pairs of training and test sets. Predictions are prepared for all molecules (n) of the initial dataset, since each of them belongs to one of the test sets.…”

“…[15][16][17][18][19][20][21] This opens an opportunity to develop quantitative structure -property relationships (QSPR) linking the stability constants with the structure of ligands which, in turn, can be used for computeraided design of new metal binders. [22,23] To date, QSPR modeling of stability constants of the metal -ligand complexation was performed for alkali, [24][25][26][27][28][29][30][31][32] alkaline-earth, [32][33][34][35][36][37][38] rare-earth [39][40][41][42] and transition metal [23,34,36,37,40,[43][44][45] ions. In many cases the practical application of the reported QSPR is complicated due to the lack of complete information about descriptors' calculations and details of machine-learning method implementation.…”

“…It has been demonstrated that prediction performance of the models built on SMF is, at least, as good as that for the models involving molecular descriptors of different types, [48][49][50] E-state counts and E-state indices [40] and pharmacophore descriptors. [51] In our studies for alkaline-earth [33] and some heavy metal ions, [43] the root-mean squared error (RMSE) of predictions is comparable with experimental systematic errors.…”

“…[51] In our studies for alkaline-earth [33] and some heavy metal ions, [43] the root-mean squared error (RMSE) of predictions is comparable with experimental systematic errors. [15] For lanthanide ions, [39,52] Ag + , [40] Zn 2+ , Cd…”