Eectiveness of modern rational new drugs development is connected with accurate modelling of binding between target-proteins responsible for the disease and small molecules (ligands) candidates to become drugs. The main modeling tools are docking programs for positioning of the ligands in the target proteins. Ligand positioning is realized in the frame of the docking paradigm: the ligand binds to the protein in the pose corresponding to the global energy minimum on the complicated multidimensional energy surface of the protein-ligand system. Docking algorithm on the base of the novel method of tensor train global optimization is presented. The respective novel docking program SOL-T is validated on the set of 30 protein-ligand complexes with known 3D structures. The energy of the protein-ligand system is calculated in the frame of MMFF94 force eld. SOL-T performance is compared with the results of exhaustive low energy minima search carried out by parallel FLM docking program on the base of Monte Carlo method using large supercomputer resources. It is shown that SOL-T docking program is about 100 times faster than FLM program, and SOL-T is able to nd the global minimum (found by FLM docking program) for 50% of investigated protein-ligand complexes. Dependence of SOL-T performance on the rank of tensor train decomposition is investigated, and it is shown that SOL-T with rank 16 has almost the same performance as SOL-T with rank 64. It is shown that the docking paradigm is true not for all investigated complexes in the frame of MMFF94 force eld.

We present the novel docking algorithm based on the Tensor Train decomposition and the TT-Cross global optimization. The algorithm is applied to the docking problem with flexible ligand and moveable protein atoms. The energy of the protein-ligand complex is calculated in the frame of the MMFF94 force field in vacuum. The grid of precalculated energy potentials of probe ligand atoms in the field of the target protein atoms is not used. The energy of the protein-ligand complex for any given configuration is computed directly with the MMFF94 force field without any fitting parameters. The conformation space of the system coordinates is formed by translations and rotations of the ligand as a whole, by the ligand torsions and also by Cartesian coordinates of the selected target protein atoms. Mobility of protein and ligand atoms is taken into account in the docking process simultaneously and equally. The algorithm is realized in the novel parallel docking SOL-P program and results of its performance for a set of 30 protein-ligand complexes are presented. Dependence of the docking positioning accuracy is investigated as a function of parameters of the docking algorithm and the number of protein moveable atoms. It is shown that mobility of the protein atoms improves docking positioning accuracy. The SOL-P program is able to perform docking of a flexible ligand into the active site of the target protein with several dozens of protein moveable atoms: the native crystallized ligand pose is correctly found as the global energy minimum in the search space with 157 dimensions using 4700 CPU ∗ h at the Lomonosov supercomputer.

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