Complex machine learning model needs complex testing: Examining predictability of molecular binding affinity by a graph neural network.

Drug discovery pipelines typically involve high-throughput screening of large amounts of compounds in a search of potential drugs candidates. As a chemical space of small organic molecules is huge, a "navigation" over it urges for fast and lightweight computational methods, thus promoting machine-learning approaches for processing huge pools of candidates. In this contribution, we present a graph-based deep neural network for prediction of protein-drug binding affinity and assess its predictive power under thorough testing conditions. Within the suggested approach, both protein and drug molecules are represented as graphs and passed to separate graph sub-networks, then concatenated and regressed towards a binding affinity. The neural network is trained on two binding affinity datasets-PDBbind and data imported from RCSB Protein Data Bank. In order to explore the generalization capabilities of the model we go beyond traditional random or leave-cluster-out techniques and demonstrate the need for more elaborate model performance assessment - six different strategies for test/train data partitioning (random, time- and property-arranged, protein- and ligand-clustered) with a k-fold cross-validation are engaged. Finally, we discuss the model performance in terms of a set of metrics for different split strategies and fold arrangement. Our code is available at https://github.com/SoftServeInc/affinity-by-GNN.

Ensembling machine learning models to boost molecular affinity prediction.

This study unites six popular machine learning approaches to enhance the prediction of a molecular binding affinity between receptors (large protein molecules) and ligands (small organic molecules). Here we examine a scheme where affinity of ligands is predicted against a single receptor - human thrombin, thus, the models consider ligand features only. However, the suggested approach can be repurposed for other receptors. The methods include Support Vector Machine, Random Forest, CatBoost, feed-forward neural network, graph neural network, and Bidirectional Encoder Representations from Transformers. The first five methods use input features based on physico-chemical properties of molecules, while the last one is based on textual molecular representations. All approaches do not rely on atomic spatial coordinates, avoiding a potential bias from known structures, and are capable of generalizing for compounds with unknown conformations. Within each of the methods, we have trained two models that solve classification and regression tasks. Then, all models are grouped into a pipeline of two subsequent ensembles. The first ensemble aggregates six classification models which vote whether a ligand binds to a receptor or not. If a ligand is classified as active (i.e., binds), the second ensemble predicts its binding affinity in terms of the inhibition constant Ki.

The maximum occupancy condition for the localized property-optimized orbitals.

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

Atomic charges for conformationally rich molecules obtained through a modified principal component regression.

A modification of the principal component regression model is proposed for obtaining a fixed set of atomic charges (referred to as dipole-derived charges) optimized for reproducing the dipole moment of a conformationally rich molecule, i.e., a molecule with multiple local minima on the potential energy surface. The method does not require any adjustable parameters and requires the geometries of conformers, their dipole moments and atomic polar tensor (APT) charges as the only input data. The fixed atomic charges generated by the method not only reproduce the molecular dipole moment in all the conformers accurately, but are also numerically close to the APT charges, thereby ensuring accurate reproduction of the dipole moment variations caused by small geometrical distortions (e.g., by vibrations) of the conformers. The proposed method has been applied to canonical 2'-deoxyribonucleotides, the model DNA monomers, and the dipole-derived charges have been shown to outperform both the averaged APT and RESP charges in reproducing the dipole moments of large sets of conformers, thus demonstrating a potential usefulness of the dipole-derived charges as a 'reference point' for modeling polarization effects in conformationally rich molecules.

On the Existence of HeHe Bond in the Endohedral Fullerene Hе2 @C60.

Twenty years have already been passed since the endohedral fullerene's void ceaselessly attracts attention of both, experimentalists and theoreticians, computational chemists and physicists in particular, who direct their efforts on computer simulations of encapsulating atoms and molecules into fullerene void and on unraveling the arising bonding patterns. We review recent developments on the endohedral He2 @C60 fullerene, on its experimental observation and on related computational works. The two latter are the main concerns in the present work: on the one hand, there experimentally exists the He dimer embedded into C60 void. On the other, computational side, each He atom exhibits a negligible charge transfer to C60 resulting in that altogether, the He dimer exists as a fractionally charged (He+δ )2 . Whether there exists a bond between these two helium atoms is the key question of the present work. Since a bond is a two-body creature, we assert that it suffices to define the bond on the basis of Löwdin's postulate of a molecule which we invoke to investigate such formation of the He dimer in a given C60 void in terms of the HeHe potential energy well. It is analytically demonstrated that this well enables to maintain at least one bound (ground) state, and therefore, according to Löwdin's postulate which is naturally anticipated within quantum theory, we infer that (He+δ )2 is a molecule, a diatomic, where two heliums are bonded to each other. Using these arguments, we also propose to extend the concept of stability of endohedral fullerenes. © 2017 Wiley Periodicals, Inc.

Nucleotides containing variously modified sugars: energetics, structure, and mechanical properties.

The influence of various sugar residue modifications on intrinsic energetic, conformational, and mechanical properties of 2'-deoxyribonucleotide-5'-monophosphates (dNs) was comprehensively investigated using modern quantum chemical approaches. In total, fourteen sugar modifications, including double bonds and heteroatoms (S and N) inside the sugar ring, as well as fluorination in various positions, were analyzed. Among hundreds of possible conformational states of dNs, only two - AI and BI, corresponding to the most biologically significant forms of a double-helical DNA, were considered for each dN. It was established that the most of the studied modifications tend to strongly stabilize either AI or BI conformation of dNs both in the gas phase and in aqueous solution (modelled by implicit solvent models). Therefore, some of these modifications can be used as a tool for reducing structural polymorphism of nucleic acids in solution as well as for designing oligonucleotides with specific structural features. The evaluation of relaxed force constants (RFC) for glycosidic bonds suggests that the majority of the studied modifications of the sugar residue yield increased strengths of glycosidic bonds in dNs, and can therefore be used for designing modified nucleic acids with an increased resistance to abasic lesions. The most significant reinforcement of the glycosidic bond occurs in dNs containing the CF2 group instead of the O4' oxygen and the fluorine atom at the 2'-α-position. The calculation of the RFC and vibrational root-mean-square (VRMS) deviations for conformational degrees of freedom revealed a strong dependence between mechanical properties of dNs and their energetic characteristics. In particular, electronic energies of AI and BI conformers of dNs calculated in vacuo are closely connected with the values of relaxed force constants (RFC) for the δ angle: the higher RFC(δ) values correspond to more energetically favorable conformers.

Formation of dimers of light noble atoms under encapsulation within fullerene's voids.

Van der Waals (vdW) He2 diatomic trapped inside buckminsterfullerene's void and preserving its diatomic bonding is itself a controversial phenomenon due to the smallness of the void diameter comparing to the He-He equilibrium distance. We propound a computational approach, including smaller fullerenes, C20 and C28, to demonstrate that encapsulation of He2 inside the studied fullerenes exhibits an interesting quantum behavior resulting in a binding at shorter, non-vdW internuclear distances, and we develop a computational model to interpret these He-He bonding patterns in terms of Bader's atom-in-molecule theory. We also conjecture a computational existence of He2@C60 on a solid basis of its theoretical UV absorption spectrum and a comparison with that of C60.

The Complexation of the Anticancer Drug ThioTEPA with Methylated DNA Base Guanine: Combined Ab Initio and QTAIM Investigation.

Non-covalent complexes of methylated nitrogenous DNA base guanine (m(9) Gua) with 1 to 6 molecules of anticancer drug ThioTEPA (1,1',1''-phosphorothioyltriaziridine) have been investigated by molecular modeling techniques (molecular docking and DFT geometry optimization), ab initio wavefunction calculations and the quantum theory of atoms in molecules (QTAIM). The accuracy of complex structures predicted by standard molecular docking techniques have been assessed by comparing them with ab initio calculations, and the most important differences have been discussed. Obtained stabilization enthalpies (kcal/mol) for the m(9) Gua⋅⋅⋅(ThioTEPA)n complexes with n=1…6 have been found to be -15.6, -26.5, -38.4, -49.6, -60.5 and -69.3 respectively. The non-covalent interactions revealed by the QTAIM method have been shown to be a dominating factor responsible for the complex stability, with hydrogen bonds of NH⋅⋅⋅N type being the most important interactions in small (n=1 to 4) and CH⋅⋅⋅N bonds - in large (n=5, 6) complexes. The obtained results may help to understand ThioTEPA-DNA interactions and clarify the mechanism of the drug action.

Structural flexibility of DNA-like conformers of canonical 2'-deoxyribonucleosides.

Relaxed force constants (RFC) and vibrational root-mean-square (VRMS) deviations are used for comparative characterization of mechanical properties of canonical 2'-deoxyribonucleosides (2DRs) and 1,2-dideoxyribose molecule, their model sugar residue. It has been shown that RFC and VRMS should be preferred over traditional force constants when one needs to obtain the quantitative measure of the 'collective' parameter flexibility (furanose sugar pseudorotation phase P in particular) and compare it with classical torsion angles (ß, γ, ε, χ). It has been found that torsions ε and ß determining the 2DRs backbone hydroxyl orientations are as soft as the pseudorotation phase P with RFC values within 1-10 kcal mol(-1) rad(-2) depending on conformation. Torsion γ is the most rigid one with RFC 15-30 kcal mol(-1) rad(-2), while the glycosidic torsion χ is characterized by intermediate values of RFC (typically 5-10 kcal mol(-1) rad(-2)) and its RFC changes by 10 times, depending on the furanose sugar conformation (K(χ)≈ 3 kcal mol(-1) rad(-2) in B- vs. K(χ)≈ 21 kcal mol(-1) rad(-2) in A-DNA-like conformation of 2'-deoxycytidine). Quantum zero-point motion of the nuclei makes the dominant contribution to VRMS deviations of molecules structural parameters: 9-22° for ß, ε and P, 5-7° for γ and χ at the temperature of 0 K, and 15-38° for ß, ε and P, 9-26° for γ and χ at the room temperature (298.15 K). Obtained results can be used in constructing simple dynamical models of the DNA fragments.

Bridging QTAIM with vibrational spectroscopy: the energy of intramolecular hydrogen bonds in DNA-related biomolecules.

Physical properties of over 8000 intramolecular hydrogen bonds (iHBs), including 2901 ones of the types OH···O, OH···N, NH···O and OH···C, in 4244 conformers of the DNA-related molecules (four canonical 2'-deoxyribonucleotides, 1,2-dideoxyribose-5-phosphate, and 2-deoxy-D-ribose in its furanose, pyranose and linear forms) have been investigated using quantum theory of atoms in molecules (QTAIM) and vibrational analysis. It has been found that for all iHBs with positive red-shift of the proton donating group stretching frequency the shift value correlates with ρ(cp)-the electron charge density at the (3,-1)-type bond critical point. Combining QTAIM and spectroscopic data new relationships for estimation of OH···O, OH···N, NH···O and OH···C iHB enthalpy of formation (kcal mol(-1)) with RMS error below 0.8 kcal mol(-1) have been established: E(OH···O) = -3.09 + 239·ρ(cp), E(OH···N) = 1.72 + 142·ρ(cp), E(NH···O) = -2.03 + 225·ρ(cp), E(OH···C) = -0.29 + 288·ρ(cp), where ρ(cp) is in e a(0)(-3) (a(0)- the Bohr radius). It has been shown that XHY iHBs with red-shift values over 40 cm(-1) are characterized by the following minimal values of the XHY angle, ρ(cp) and nubla(2)ρ(cp): 112°, 0.005 e a(0)(-3) and 0.016 e a(0)(-5), respectively. New relationships have been used to reveal the strongest iHBs in canonical 2'-deoxy- and ribonucleosides and the O(5')H···N(3) H-bond in ribonucleoside guanosine was found to have the maximum energy (8.1 kcal mol(-1)).