Machine learning to predict the specific optical rotations of chiral fluorinated molecules.

A chemoinformatics method was applied to the assignment of absolute configurations and to the quantitative prediction of specific optical rotations using a data set of 88 chiral fluorinated molecules (44 pairs of enantiomers). Counterpropagation neural networks were explored for the classification of enantiomers as dextrorotatory or levorotatory. Regression models were trained using multilayer perceptrons (MLP), random forests (RF) or multilinear regressions (MLR), on the basis of physicochemical atomic stereo (PAS) descriptors. New descriptors were also derived considering the common structural features of the data set (cPAS descriptors), which enabled RF models to predict the whole data set with R = 0.964, mean absolute error (MAE) of 9.8° and root mean square error (RMSE) of 12.5° in leave-one-pair-out cross-validation experiments. The predictions for the 30 compounds measured in chloroform were obtained with R = 0.971, MAE = 9.1° and RMSE = 12.5°, which compares favorably with quantum chemistry calculations reported in the literature.

The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations.

Free-energy calculations in multiple dimensions constitute a challenging problem, owing to the significant computational cost incurred to achieve ergodic sampling. The generalized adaptive biasing force (gABF) algorithm calculates n one-dimensional lists of biasing forces to approximate the n-dimensional matrix by ignoring the coupling terms ordinarily taken into account in classical ABF simulations, thereby greatly accelerating sampling in the multidimensional space. This approximation may however occasionally lead to poor, incomplete exploration of the conformational space compared to classical ABF, especially when the selected coarse variables are strongly coupled. It has been found that introducing extended potentials coupled to the coarse variables of interest can virtually eliminate this shortcoming, and, thus, improve the efficiency of gABF simulations. In the present contribution, we propose a new free-energy method, coined extended generalized ABF (egABF), combining gABF with an extended Lagrangian strategy. The results for three illustrative examples indicate that (i) egABF can explore the transition coordinate much more efficiently compared with classical ABF, eABF, and gABF, in both simple and complex cases and (ii) egABF can achieve a higher accuracy than gABF, with a root mean-squared deviation between egABF and eABF free-energy profiles on the order of kBT. Furthermore, the new egABF algorithm outruns the previous ABF-based algorithms in high-dimensional free-energy calculations and, hence, represents a powerful importance-sampling alternative for the investigation of complex chemical and biological processes.

Machine Learning Estimation of Atom Condensed Fukui Functions.

To enable the fast estimation of atom condensed Fukui functions, machine learning algorithms were trained with databases of DFT pre-calculated values for ca. 23,000 atoms in organic molecules. The problem was approached as the ranking of atom types with the Bradley-Terry (BT) model, and as the regression of the Fukui function. Random Forests (RF) were trained to predict the condensed Fukui function, to rank atoms in a molecule, and to classify atoms as high/low Fukui function. Atomic descriptors were based on counts of atom types in spheres around the kernel atom. The BT coefficients assigned to atom types enabled the identification (93-94 % accuracy) of the atom with the highest Fukui function in pairs of atoms in the same molecule with differences ≥0.1. In whole molecules, the atom with the top Fukui function could be recognized in ca. 50 % of the cases and, on the average, about 3 of the top 4 atoms could be recognized in a shortlist of 4. Regression RF yielded predictions for test sets with R(2) =0.68-0.69, improving the ability of BT coefficients to rank atoms in a molecule. Atom classification (as high/low Fukui function) was obtained with RF with sensitivity of 55-61 % and specificity of 94-95 %.

Extension of a Highly Discriminating Topological Index.

A highly discriminating topological index, EAID, is generated in our laboratory. A systematic search for degeneracy was performed on a total of over 14 million structures, and no duplicate occurred. These structures are as follows: over 3.8 million alkane trees with 1-22 carbon atoms; over 0.38 million structures containing heteroatoms; over 4 million benzenoids with 1-13 benzene rings; and over 5.9 million compounds from three reality databases. However, in a search of over 20 million alkane trees with 23 and 24 carbon atoms, five and 13 duplicates occurred, respectively, and for over 20 million compounds from the ZINC database, 10 duplicates occurred. To increase the discriminating power of the index, EAID has been extended, and the resulting index is termed 2-EAID. All of the over 55 million structures mentioned above were uniquely identified by 2-EAID except for two duplicates that occurred for the ZINC database. EAID and 2-EAID are the most highly discriminating indices examined to date. Thus, the two indices possess not only theoretical significance but also potential applications. For example, they could possibly be used as a supplementary reference for CAS Registry Numbers for structure documentation.

Graph theoretical representation of atomic asymmetry and molecular chirality of benzenoids in two-dimensional space.

In order to explore atomic asymmetry and molecular chirality in 2D space, benzenoids composed of 3 to 11 hexagons in 2D space were enumerated in our laboratory. These benzenoids are regarded as planar connected polyhexes and have no internal holes; that is, their internal regions are filled with hexagons. The produced dataset was composed of 357,968 benzenoids, including more than 14 million atoms. Rather than simply labeling the huge number of atoms as being either symmetric or asymmetric, this investigation aims at exploring a quantitative graph theoretical descriptor of atomic asymmetry. Based on the particular characteristics in the 2D plane, we suggested the weighted atomic sum as the descriptor of atomic asymmetry. This descriptor is measured by circulating around the molecule going in opposite directions. The investigation demonstrates that the weighted atomic sums are superior to the previously reported quantitative descriptor, atomic sums. The investigation of quantitative descriptors also reveals that the most asymmetric atom is in a structure with a spiral ring with the convex shape going in clockwise direction and concave shape going in anticlockwise direction from the atom. Based on weighted atomic sums, a weighted F index is introduced to quantitatively represent molecular chirality in the plane, rather than merely regarding benzenoids as being either chiral or achiral. By validating with enumerated benzenoids, the results indicate that the weighted F indexes were in accordance with their chiral classification (achiral or chiral) over the whole benzenoids dataset. Furthermore, weighted F indexes were superior to previously available descriptors. Benzenoids possess a variety of shapes and can be extended to practically represent any shape in 2D space-our proposed descriptor has thus the potential to be a general method to represent 2D molecular chirality based on the difference between clockwise and anticlockwise sums around a molecule.