RU2265244C2 - Method for modeling and predicting linking of ligand molecules with target molecules by quantum mechanics methods with consideration of solvent effect - Google Patents

Abstract

FIELD: pharmaceutics.

SUBSTANCE: method includes building models of inter-molecular complex and its components, using data concerning composition of target molecule and ligand molecule. Models for apparent and implicit flow count of solvent are introduced. Modeling of connection of ligand molecule and target molecule with consideration of solvent effect is performed either within limits of quantum-mechanical, or within limits of combined quantum-mechanical and classic approaches. Calculation of enthalpy of connection of target molecule and ligand molecule is performed, using full energies of molecular systems, calculated at minimal point or using average values of full energies, produced for a set of configurations of inter-molecular complex of target-ligands. In latter case, coordinates of atoms of target molecule, ligand molecule and their inter-molecular complex, appropriate for each of such configurations, are produced within limits of molecular-dynamic modeling. Calculation of entropy of connection of ligand molecule and target molecule is performed on basis of calculation of its oscillation, rotation and linear components. Free energy of connection of ligand molecule and target molecule is made on basis of enthalpy, entropy member and cavitation energy.

EFFECT: production at given precision level of energy values, characterizing intensiveness of connection of receptor and remedy, and, consecutively, are a criterion during predicting ligands as potential remedial substances.

3 cl, 9 dwg, 2 tbl

Description

The invention relates to the development of new compounds for medicine, biotechnology, condensed matter physics and various fields of material science in which intermolecular interactions are significant, and can be used to develop new drugs using in silico methods - that is, by numerically simulating a complex of a drug substance with a receptor or target protein. In the course of such modeling, values of energy quantities characterizing the intensity of the interaction of the protein and the drug substance can be obtained. Based on these values, it can be concluded that the complex of the drug substance with the receptor or target protein is stable. The stability of the complex is directly related to the possible effectiveness of the drug compound.

For this purpose, force field models are currently widely used (for example, such as AMBER2002, OPLS-AA, CHARMM, ab-initio force field MMFF), in which atoms in molecules are considered as classical particles interacting with each other using potentials interactions.

Despite the widespread use of force field models for numerically modeling the interaction of molecules with each other, this methodology often inadequately describes the behavior of molecular systems. This is due to the fact that the behavior of atoms in molecules and electrons in atoms obeys the laws of quantum rather than classical mechanics. At present, quantum mechanics is widely used to calculate the characteristics of relatively small molecules (tens of atoms) and their interactions. Recently, in connection with the rapid increase in the power of computers, quantum calculations of molecular systems containing hundreds and even thousands of atoms have become possible. The accuracy and time of such calculations depend on the applied calculation methods and the used computing power. Given the intensive development of the former and the rapid growth of the latter, it is clear that the use of quantum mechanics for the numerical simulation of molecular systems will increase. In particular, to calculate the intensity of binding of a ligand molecule to a target molecule, the methods of classical force fields will be replaced by methods based on equations of quantum mechanics.

However, the methods of quantum mechanics were previously extremely rarely used to describe biological molecules, which, as a rule, are macromolecules containing hundreds and thousands of atoms. Thus, the non-empirical Hartree-Fock method and the density functional method (DFT) were used in [1–3] to describe the quantum part of a system that is immersed in a molecular environment, described classically using a certain force field. This is the so-called QM / MM approximation, in which the part of the system is described by the laws of quantum mechanics (QM), and the other part of the system by the laws of classical molecular mechanics (MM). In particular, the interaction energy (or rather the interaction enthalpy) between two biological molecules was calculated in [2], in which an enzyme-substrate reaction was modeled.

The simpler and correspondingly faster quantum-chemical semi-empirical PM3 method was used in [4] to model the active center in the cytidine deaminase enzyme. The molecular system considered in the simulation contained an active center of 1330 atoms. To calculate such a large molecular system, the so-called Divide-and-Conquer (divide and conquer) method, or D&C or DAC for short, was used.

The semi-empirical quantum-mechanical method AM1 was used to study the electronic structure of biological macromolecules in solution [5], and a continuous model of the solvent was used. Protein – protein and protein – DNA binding enthalpies were obtained as the difference between the enthalpies of formation of the corresponding complexes and the enthalpies of formation of their individual components, however, the data obtained turned out to be quite unrealistic (about 5–20 eV).

Several organic macromolecules containing from 256 to 9378 atoms were calculated using the semiempirical PM3 method using the D&C method as part of the MOPAC package of quantum chemical programs [6]. In this case, the calculations were carried out both in vacuum and in an aqueous solution using the COSMO approximation, in which the solvent was modeled continually. At the same time, the energy characteristics of the studied chemical systems were not determined, and the main attention was paid to obtaining optimized structures of macromolecules and the time required for optimization.

Most of the known quantum-mechanical studies of biological macromolecules are devoted to calculating the energy characteristics of various enzymatic reactions. In this case, the mechanisms of various reactions involving water molecules, their transition complexes, and the corresponding energy barriers were studied. However, in all these works there are no estimates of the intensity of binding of proteins and ligands in their intermolecular complexes, and the influence of the solvent on the processes under consideration in macromolecules is not taken into account.

Thus, it is seen from the known literature that when applying the methods of quantum mechanics in the methods of modeling biological macromolecules, there is no single approach to determining the intensity of binding of ligand molecules to target molecules. In known methods using the methods of quantum mechanics, mainly structural and electronic characteristics of individual macromolecules are determined using the mechanisms and energy barriers of enzymatic reactions of peptide bond cleavage in proteins. Comparison of such calculated data with experimentally obtained data indicates unsatisfactory accuracy of the obtained values. The prior art methods for modeling based on quantum-mechanical calculations of the energy characteristics of the intermolecular interaction of ligand molecules and target molecules are not known. In addition, the existing methods of quantum-mechanical study of macromolecules do not correctly account for the influence of the solvent, which is very important in modeling the binding of biological target molecules to ligand molecules, where hydrogen bonds play an important role.

In this regard, the objective of the present invention is to provide a method for modeling intermolecular interaction in an aqueous solution based on quantum calculation methods, taking into account the influence of the solvent, both at the molecular level and in the form of a screening continuum, taking into account spatial relaxation of atoms and redistribution of electron density during the formation of intermolecular complex. This modeling method should be applicable to determining the intensity of binding of ligand molecules to target molecules, regardless of the composition and size of these molecules, and also regardless of the type of quantum calculation method used. This method should use the minimum number of adjustable parameters and rely, if possible, only on the basic principles of quantum mechanics. The technical result is the creation of a method for modeling and predicting the binding of ligand molecules to target molecules by quantum mechanics, taking into account the influence of the solvent.

This result is achieved by the fact that a method for modeling and predicting the binding of target molecules and ligand molecules is proposed, in which, based on the structure and composition of the intermolecular target-ligand complex, target molecule and ligand molecule, models of the intermolecular complex and its components are formed with explicit and implicit accounting for the solvent, which are used later in modeling the binding of the ligand molecule and the target molecule, taking into account the influence of the solvent by quantum mechanics with the selected mode parameters elite. Using the results of this simulation, the enthalpy, entropy, and free binding energy of the selected ligand molecule and target molecule are calculated, which characterize the intensity of binding of the ligand molecule to the target molecule, which is compared with known experimental data for known ligands. For new ligands, the calculated values for the selected modeling parameters are a criterion for the intensity of binding of a ligand molecule to a target molecule and, therefore, are a criterion for predicting ligands as potential drug substances.

In the claimed modeling method, the structure and composition of the target molecule and the ligand molecule are obtained using experimental measurements from the PDB database (Protein Data Bank) [7], in addition, the structure, composition and atomic coordinates of the new ligand molecule can be obtained using special programs - builders of new ligands. If the initial structures of target molecules and ligand molecules do not contain data on the Cartesian coordinates of hydrogen atoms, the coordinates of the missing atoms are added to the atomic coordinates of the target molecule and ligand molecule using various computer programs for constructing molecular structures. The positions in the space of the added hydrogen atoms are determined by molecular-mechanical or quantum-mechanical optimization from the condition under which the total energy of the target molecule and the ligand molecule reaches a minimum when the coordinates of the added hydrogen atoms are varied.

The structure of the intermolecular complex of the target molecule and the ligand molecule is obtained by docking the ligand molecule and the target molecule or, as is often called, docking, for which the coordinates of the atoms of these molecules are transformed so that the smallest distance between each of the ligand atoms and given atoms of the target molecule was in a given range.

In order to take into account the influence of a solvent on the binding of a target molecule and a ligand molecule in the course of explicit accounting of the solvent, the set of coordinates of the solvent molecules is added to the set of coordinates of the intermolecular complex of the target ligand and to the sets of coordinates of the ligand molecule and the target molecule separately. This is done so that the solvent molecules fill the entire space around these molecular systems without intersections and intersections with the atoms of the intermolecular complex, the target molecule and the ligand molecule. The position of the solvent molecules is optimized, as a rule, within the framework of packages of molecular mechanics or molecular dynamics near the intermolecular complex and its components taken individually.

Quantum-mechanical models of a target molecule, a ligand molecule, and their intermolecular complex are constructed on the basis of the obtained structures of this intermolecular complex and its components with an explicitly taken into account solvent. For this, the atoms of the intermolecular complex, the target molecule and the ligand molecule are sorted together with the solvent atoms into two groups. For an intermolecular complex, the first group should include all the atoms of the ligand molecule, as well as the atoms of the target molecule and the solvent molecule, the distances from which to each of the atoms of the ligand molecule do not exceed a specified value, and the second group includes all other atoms of the target molecule and all other solvent molecules. For the model of the target molecule, the same atoms of the target molecule that are included in the first group of atoms of the intermolecular complex must enter the first group of atoms. In addition, the first group should include solvent molecules that are located from the atoms of the target molecule included in the first group at a distance not exceeding a specified value, and the second group includes all other atoms of the target molecule and all other solvent molecules. To model a ligand molecule, the first group of atoms should include all atoms of the ligand molecule, as well as solvent molecules, which are located at a distance from the atoms of the ligand molecule not exceeding a specified value, and the second group includes all other solvent molecules.

As a rule, the atoms of the first group of all considered molecular systems are modeled by the methods of quantum mechanics, and the atoms of the second group are modeled by the methods of classical mechanics, or the atoms of the second group are excluded from the simulation. To simulate the joining of two groups of atoms, calculated in the framework of quantum and classical methods, additional atoms are introduced near the space region where the atoms of the first and second groups are at a distance from each other not exceeding a given value. In this case, additional boundary atoms are calculated simultaneously in the classical and quantum approximations. If only the atoms of the first group are calculated in the framework of the quantum method, and the atoms of the second group are excluded from the simulation, the added atoms are also calculated in the framework of the quantum approach. In this case, additional atoms are added so that they form new covalent bonds instead of dangling covalent bonds between the atoms of the first and second groups.

For the obtained models, the charge states of various molecular groups are determined and, according to this, additional atoms are added or removed in the corresponding places of these molecular groups. From these charge states, the total charge of the constructed models of the intermolecular target – ligand complex, target molecule, and ligand molecule is determined.

When the solvent is water, in order to better reproduce the formation and breaking of hydrogen bonds, when passing from the complex to its components, additional water molecules are introduced into the model. Water molecules are added to the intermolecular complex so that they are between the target molecule and the ligand molecule and form hydrogen bonds with them. Water molecules are added to the target molecule and to the ligand molecule so that, with their participation, the dangling hydrogen bonds that were present in the intermolecular complex between the target molecule and the ligand molecule and which were broken off when the ligand molecule was removed from the target molecule are restored.

However, in order to correctly take into account the influence of the solvent, as a rule, it is not enough to explicitly take into account a certain number of solvent molecules, and in this case, it is necessary to take into account the solvent in the implicit model, when its screening effect is taken into account by introducing into the model a continuous medium with the desired dielectric constant. In the proposed method for simulating target and ligand binding, three types of the model of implicit solvent accounting are used, namely, a model that implements the solution of the Poisson equation, a continuous conductor model, and a model that implements the solution of the Poisson-Boltzmann equation.

All data obtained at the stage of constructing models of the target molecule, ligand molecule, and intermolecular complex are used to form input files for quantum-mechanical modeling. These input files contain information on the coordinates and types of all atoms of the considered molecular systems, their total charge and multiplicity, the coordinates and type of atoms of the solvent molecules added in the explicit model to the intermolecular complex and its components, the parameters of the solvent in the implicit model. In addition, the input files contain information about the parameters of the optimization process, namely the method and parameters of the modeling method, the type of optimization procedure, the limits of self-consistency and minimization.

The input files are used to use the appropriate program to simulate the total energy of the molecular system, based either on a combination of the quantum-mechanical and classical approximations, or only on the quantum-mechanical approximation, to find the minimum total energy of the three molecular systems under consideration when varying the positions of all or some of the additional certain atoms. The obtained values of the total energies of the target molecule, the ligand molecule and their intermolecular complex are used to calculate the enthalpy of binding of the components in the complex. The binding enthalpy is calculated as the difference between the total energy of the target-ligand intermolecular complex in the solvent, on the one hand, and the sum of the total energies of the target molecule in the solvent and the ligand molecule in the solvent, on the other hand, while observing and not observing the balance of solvent molecules.

In accordance with the present invention, the enthalpy of binding of the target molecule and the ligand molecule can be calculated using another method, in which the total energies of the target molecule, ligand molecule and their intermolecular complex are calculated not at the minimum point, but as average values of the total energies, obtained for a number of configurations of the intermolecular target-ligand complex. In this case, the atomic coordinates of the target molecule, ligand molecule, and their intermolecular complex, corresponding to each of these configurations, can be obtained in the framework of molecular dynamics modeling. The structure of the target molecule and the ligand molecule and their intermolecular complex obtained by joining the coordinates of its components are also used as input data for this type of modeling. In molecular dynamics modeling, both the explicit and implicit solvent models can be used, which are introduced by the methods described previously.

For an intermolecular complex, regardless of the solvent model, modeling is carried out by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the target molecule and the ligand molecule taking into account the presence of solvent molecules, and the state of the molecular system is determined in which it reaches thermal equilibrium. Then, the motion paths of all atoms of the system are determined after their thermal equilibrium is reached, and the coordinates of all atoms of the interacting target molecule, ligand molecule, and solvent molecules are determined at predetermined time intervals for a given number of times for a given set of configurations of the intermolecular target-ligand complex. Similarly, a set of configurations of the target molecule and the ligand molecule is obtained.

For each coordinate set of the intermolecular target-ligand complex, target molecule, ligand molecule, in an explicit or implicit solvent model, all atoms are sorted into groups in the same way as before. For each configuration of the intermolecular target-ligand complex, target molecules, ligand molecules, an input file is generated for quantum-mechanical modeling of the target-ligand intermolecular complex in a solvent, as described above. For each input file, that is, for each configuration of the target-ligand intermolecular complex, target molecule, ligand molecule, the total energy of these molecular systems in a solvent is calculated using the selected modeling method without optimizing the spatial structure of the complex. Then, the average values of the total energy of the target-ligand intermolecular complex, the target molecule, and the ligand molecule in the solvent are calculated over the entire selected set of configurations of this molecular system. Using the obtained average values of the total energies of the target-ligand intermolecular complex in the solvent, the target molecules in the solvent, and the ligand molecules in the solvent, the enthalpy of binding of the ligand molecule to the target molecule in the solvent is calculated as the difference between the total energy of the target-ligand intermolecular complex in the solvent on the one hand, and the sum of the total energies of the target molecule in the solvent and the ligand molecule in the solvent, on the other hand.

The calculation of the entropy of binding of a ligand molecule to a target molecule in a binding solvent can be divided into the calculation of its three components, namely, the vibrational, translational, and rotational components.

Entropy associated with the loss of vibrational degrees of freedom during the transition from free states of a target molecule and a ligand molecule in a solvent to their intermolecular complex is determined by the vibrational frequencies of the molecules involved in the process under consideration. To obtain the vibrational frequencies of the considered molecular systems, the force constant or second derivatives of the total energies related to the intermolecular complex, the target molecule, and the ligand molecule are calculated for all atomic coordinates at the points of the corresponding minima within the framework of the quantum-mechanical modeling method used.

The entropy change upon binding of the ligand molecule to the target molecule is also contributed by the fact that these molecules lose both the translational and rotational degrees of freedom that they possessed in the free state upon binding. To calculate this part of the entropy, only the coordinates and atomic weights of the atoms of the target molecule, the ligand molecule, and their intermolecular complex are used, and this calculation, as a rule, is outside the scope of quantum-mechanical modeling. The total change in entropy upon binding of the ligand molecule to the target molecule is calculated as the sum of the changes in its various components.

The process of binding a ligand molecule to a target molecule occurs in a solvent. Each of these molecules creates a cavity in the solvent, pushing apart the solvent molecules. This process requires the expenditure of a certain free energy, which is called cavitation energy, and it depends only on the properties of the solvent and the form of the molecule placed in the solvent. The change in cavitation energy upon binding of the target molecule and the ligand molecule is additionally calculated and taken into account when calculating the free binding energy in the complex. The latter is calculated as the sum of the enthalpy, entropy terms and the term characterizing the change in cavitation energy.

The calculated enthalpy, entropy, and free binding energy are energy characteristics of the binding intensity of the target molecule and the ligand molecule and are used to predict the binding of new ligands to target molecules.

The invention is illustrated in the embodiments illustrated by the drawings, which represent the following:

Figure 1 is a flowchart of a method of quantum mechanical modeling and prediction of the binding of a ligand molecule to a target molecule;

Figure 2 is a flow diagram of a method for selecting a target molecule and a ligand molecule and constructing an intermolecular complex consisting of a ligand and a target;

Figure 3 is a flowchart of a method for constructing quantum mechanical models of an intermolecular complex of a ligand-target and its components with explicit and implicit consideration of a solvent;

Figure 4 is a flowchart of a method for quantum-mechanical modeling of intermolecular interaction between a ligand molecule and a target molecule, taking into account a solvent, including calculation of enthalpy, entropy, free binding energy of a ligand and a target.

5 is a flowchart of a molecular dynamics method for quantum mechanical modeling of the binding of ligand molecules to target molecules in a solvent.

6 - structural formulas (left column) and quantum-mechanically optimized structures (right column) of ligands corresponding to protein-ligand complexes that were selected as test systems for modeling binding in a protein-ligand system by quantum mechanics.

7 is a model of the active center of the complex 1AJ6 (system 5 according to table 1). Protein is represented by thin rods, water molecules are represented by thick rods, the ligand molecule is represented by balls and rods. Dotted lines indicate hydrogen bonds in the protein-ligand complex.

Fig. 8 is a flow diagram of a method W1 for adding water molecules to components of a protein-ligand complex.

Fig.9 is a diagram of a method W2 adding water molecules to the components of the protein-ligand complex.

Figure 1 shows a General diagram of the claimed method for modeling and predicting the binding of a ligand molecule to a target molecule. In step 1, a target molecule and a ligand molecule are selected and their structure is obtained. From the selected target molecules and ligand molecules, at stage 2, their intermolecular complex is formed. Based on the structure and composition of this intermolecular complex, in step 3, models of the target-ligand intermolecular complex and its components are formed with explicit and implicit solvent considerations, which are used later in step 4 to model the binding of the ligand molecule and target molecule taking into account the influence of the solvent by methods quantum mechanics with selected simulation parameters. Using the results of this simulation, at step 5, numerical data characterizing the intensity of binding of the ligand molecule to the target molecule, namely the enthalpy, entropy, and free binding energy of the selected ligand molecule and target molecule, are calculated, and these values are written in the form of numerical data on storage medium. At step 6, similar values are experimentally measured that characterize the binding rate of a given ligand molecule with a given target molecule. Then, the values calculated during the simulation, characterizing the intensity of binding of the ligand molecule to the target molecule, are compared in step 7 with the corresponding values measured in step 6. In case of discrepancy above the predetermined limit of the calculated and measured values, at step 8, the model for constructing the intermolecular complex and the parameters of quantum-mechanical modeling of the interaction of the target molecule and the ligand molecule are corrected, in particular, the model for taking into account the influence of the solvent on binding is adjusted. Then, the simulation is again carried out in step 4 and the values characterizing the binding intensity of the ligand molecule with the target molecule are calculated in step 5. This process of developing the optimal model and modeling parameters continues until the discrepancy between the calculated and measured values characterizing the binding of molecules to each other is less than a given value. After that, the process of fitting modeling parameters for a given pair of target molecules and ligand molecules is considered complete.

Next, another pair of the ligand molecule and the target molecule is selected, and the steps described above for the formation of the model of the intermolecular complex (3), quantum-mechanical modeling (4), and the calculation of the quantities characterizing the binding of the ligand molecule to the target molecule are repeated for it (5 ), measuring these values (6), comparing the calculated and measured values (7) and adjusting the parameters (8). As the initial parameters, the values of the simulation parameters obtained for the previous pair of the target molecule and the ligand molecule are used. Then the next pair of target molecules and ligand molecules, etc., is selected.

As a result of such a self-consistent procedure, modeling parameters are determined that allow one to obtain, with a given accuracy, the values characterizing the intensity of binding of a ligand molecule to a target molecule, namely, enthalpy, entropy, and free binding energy, for a certain set of pairs of target molecules and ligand molecules . This process of expansion of many pairs of target molecules and ligand molecules and self-consistent fitting of the modeling parameters continues until, for the next pair of target molecules and the ligand molecule, characterizing the binding intensity, the values calculated using the modeling parameters obtained for other pairs molecules will not coincide with a given accuracy with the values measured for a given pair of molecules characterizing the binding intensity. After that, the final values of the simulation parameters are recorded at step 7 (Fig. 1) on a storage medium, and then they are used for forecasting.

At stage 9, the correctness of the chosen methods for the formation of quantum-mechanical models and methods for modeling intermolecular interactions in the complex is demonstrated by demonstrating the coincidence with a given accuracy (which should be on the order of accuracy of the quantum calculations themselves 0.1-2.0 kcal / mol) experimental and calculated in within the framework of the developed model of quantities characterizing the binding intensity for the next pairs of target molecules and ligand molecules that were not used in the iterative procedure ki modeling method. In the future, the procedure for constructing a quantum-mechanical model and modeling intermolecular interactions in a complex consisting of a ligand molecule and a target molecule is used to determine, at step 10, a group of new ligands that have better binding to a given target molecule.

Prediction at stage 11 of the ligand molecules, which are quite strongly associated with a given target molecule and may be new potential drug substances, is as follows. For a given target molecule, a lot of ligand molecules are formed, candidates for prediction based on various databases and fragment libraries using programs that use certain rules for constructing ligands in the active center of the target molecule. The source databases contain information about the structure of molecules or the structure of fragments of molecules obtained in various experiments, or contain the coordinates of the atoms of molecules or fragments of molecules constructed using various computer programs. The number of molecules in so many ligand molecules that are candidates for prediction can be huge, up to several million, and each of these molecules exists in reality or can be synthesized. It is important that for the molecules of this set there is information about their chemical composition, three-dimensional structure and the coordinates of all atoms. For each ligand molecule from the selected set, modeling is carried out at step 5 (Fig. 1) of the binding process and calculation at step 6 of the values characterizing the binding, taking into account the influence of a solvent, a ligand molecule with a given target molecule, namely, enthalpy, entropy and free binding energy using the final values of the simulation parameters obtained in the previous step. As a result of such modeling, values are obtained that characterize the intensity of binding of all ligand molecules from the selected set to a given target molecule. Based on the simulation results, a number of the most promising ligand molecules are selected that have the best values of the values characterizing the binding intensity. Those ligand molecules for which good binding is predicted can be used in real-world chemical experiments to bind to a given target molecule. Obviously, with this approach, the number of ligand molecules for which experimental testing is necessary is significantly reduced. Thus, the proposed method for computer-aided prediction of ligand molecules, which may be new potential drug substances, avoids significant time and material costs for the synthesis of new substances and experiments to measure values characterizing the intensity of binding of ligand molecules to target molecules.

The main steps presented in FIG. 1 are described in detail below, of the claimed quantum mechanical method for simulating the binding of a ligand molecule to a target molecule, taking into account the influence of a solvent.

FIG. 2 is a flowchart illustrating a method for forming an intermolecular complex of a target molecule and a ligand molecule (step 2 in FIG. 1) in accordance with the invention.

Based on the set of 12 known ligand molecules, in step 13, a target molecule is selected for which it is necessary to model and predict the binding of various ligand molecules to it. The structure and composition of this target molecule is obtained in step 14 using experimental measurements, for example, using X-ray diffraction analysis, neutron scattering or nuclear magnetic resonance methods. The structure and composition of the target molecule can also be obtained in the form of a set of Cartesian coordinates of the corresponding atoms obtained during molecular-mechanical or molecular-dynamic modeling carried out after reading previously stored data extracted from various databases on the structure of the target molecule from the corresponding information carriers . In the case when the target molecule is a protein, its structure and composition are obtained from the PDB database (Protein Data Bank) [7], available via the Internet.

As a rule, the initial structures of target molecules do not contain data on the Cartesian coordinates of hydrogen atoms. The coordinates of the missing hydrogen atoms are added in step 15, where necessary, to the coordinates of the heavy atoms of the target molecule using various computer programs for constructing molecular structures. The optimized values of the Cartesian coordinates of the added hydrogen atoms are determined at step 16 from the condition under which the total energy of the target molecule reaches a minimum (with molecular-mechanical or quantum-mechanical optimization) with varying coordinates of the added hydrogen atoms.

Information on the structure and composition, as well as the coordinates of all atoms, including the coordinates of the added hydrogen atoms of the target molecule, is recorded at step 17 on the information carrier in the appropriate format.

Based on a plurality of 18 known ligand molecules, a ligand molecule is selected in step 19, for which it will then be modeled to bind to the selected target molecule. In addition, one can construct many 20 new ligands based on various kinds of databases or libraries of ligand fragments, and select at the stage 19 a ligand molecule from this set, for which it will be further predicted to bind to the selected target molecule. The structure, composition, and atomic coordinates of a known ligand molecule are obtained in step 21 in the same way as for a target molecule, namely, using experimental measurements, in the framework of molecular-mechanical or molecular-dynamic modeling, or based on the PDB database. The structure, composition and coordinates of atoms of a new ligand molecule can be obtained using special programs - builders of new ligands.

If the experimentally known or newly formed structure of the ligand molecule does not contain hydrogen atoms, then at step 22, coordinates of the missing hydrogen atoms are added to the coordinates of the heavy ligand atoms, using various computer programs for the formation of molecular structures. The coordinates of these hydrogen atoms are determined at step 23 by minimizing (either within the framework of molecular mechanics or within the framework of quantum mechanics) the total energy of the ligand molecule while varying the coordinates of the added hydrogen atoms. The coordinates of all atoms of the ligand molecule, including the coordinates of the added hydrogen atoms, are recorded at step 24 on the information carrier in the appropriate format.

Then, at step 25, by joining the ligand molecule and the target molecule, the structure of the intermolecular complex of the target molecule and ligand molecule (2 in FIG. 1) is obtained, which is subsequently used in quantum mechanical modeling. For this, the coordinates of all atoms of the target molecule and the ligand molecule, including the coordinates of the added hydrogen atoms, are read from the information carrier in the computer memory. After that, the coordinates of the atoms of these molecules are transformed so that the smallest distance between each of the ligand atoms and the given atoms of the target molecule is in the specified range. Such a docking procedure, or, as it is more commonly called, docking, is necessary for combining two molecules in space, since usually the coordinates of their atoms are obtained from various sources of information. The atomic coordinates of the intermolecular complex of the target molecule and the ligand molecule obtained in this way are written to computer memory at step 26 and used to construct a quantum-mechanical model of the corresponding intermolecular complex.

Further, the intermolecular complex and its components are transformed in such a way as to take into account, when modeling, the influence of the solvent on the binding of the target molecule and the ligand molecule based on the model of explicit accounting of the solvent. For this, at step 27, the multiple coordinates of the solvent molecules are added to the multiple coordinates of the intermolecular target-ligand complex. At steps 28 and 29, the multiple coordinates of the solvent molecules are added to the multiple coordinates of the components of this complex, taken individually, namely, the multiple coordinates of the target molecule (at step 28) and the multiple coordinates of the ligand molecule (at step 29). For the intermolecular complex, this is done at step 27 by computer calculation of the coordinates corresponding to the positions in the space of many solvent molecules, so that their average density corresponds to the experimentally observed density of the solvent. Solvent molecules must fill the space between the target molecule and the ligand molecule, and around them, without intersections and intersections with the atoms of the intermolecular complex of the target molecule and the ligand molecule. Similarly, the coordinates of many solvent molecules are added only to the set of coordinates of the target molecule at step 28, so that their average density corresponds to the experimentally observed density of the solvent, and they fill the space around it without intersections and intersections with the atoms of the target molecule. Also, the coordinates of the multiple solvent molecules are added only to the multiple coordinates of the ligand molecule at step 29, so that their average density corresponds to the experimentally observed density of the solvent, and they fill the space around it without intersections and intersections with the atoms of the ligand molecule. The position of the solvent molecules is optimized, as a rule, within the framework of packages of molecular mechanics or molecular dynamics near the intermolecular complex at step 30, as well as near its individual components, namely, near the target molecule in step 31 and the ligand molecule in step 32. At step 33, the coordinates of the atoms of the intermolecular target-ligand complex are recorded on the information carrier in an appropriate format together with the coordinates of the atoms of the solvent molecules located near the surface of the complex. In addition, at step 33, the coordinates of the atoms of the target molecule together with the coordinates of the atoms of the solvent molecules located near its surface and the coordinates of the atoms of the ligand molecule along with the coordinates of the atoms of the solvent molecules located near its surface are recorded separately on a carrier in the appropriate format.

Based on the structure of the obtained intermolecular complex, consisting of a target molecule and a ligand molecule, as well as solvent molecules, quantum mechanical models of this intermolecular complex and its components are then formed (step 3 in FIG. 1) with explicit and implicit solvents used in quantum mechanical modeling. Figure 3 is a flowchart illustrating a method according to the invention for generating such quantum-mechanical models and, accordingly, generating input files, which are then used to model binding in a target-ligand intermolecular complex.

Using a computer program, at step 34, the coordinates of the atoms of the target-ligand intermolecular complex together with the added solvent molecules are read from computer memory, and the coordinates of the atoms of the target molecule, together with the molecules added to it, and the coordinates of the atoms of the ligand molecule, along with those added to her solvent molecules. Then, the distances from the atoms of the ligand molecule in the intermolecular complex to each atom of the target molecule and solvent are calculated. To form a model of the intermolecular target – ligand complex, at stage 35, atoms of this complex are sorted into two groups. This is done so that the first group includes all the atoms of the ligand molecule, as well as the atoms of the target molecule and the solvent molecule, the distances from which to each of the atoms of the ligand molecule do not exceed a predetermined value, and the second group includes all other atoms of the molecule - targets and all other solvent molecules. Moreover, if at least one atom of a solvent molecule is within a specified distance from the atoms of a ligand molecule, then all atoms of this solvent molecule are included in the first group of atoms. After that, at the same stage 35, they begin to form, using the coordinates of the atoms of the first and second groups, an input file for calculating the intermolecular target-ligand complex in the solvent using the corresponding simulation program so that the atoms of the first group are modeled by quantum mechanics and the atoms of the second group are modeled methods of classical mechanics. In this case, the total energy operator is constructed as the sum of the following operators: the total energy operator for the quantum part, consisting of atoms of the first group, the total energy operator for the classical part, consisting of atoms of the second group, and the interaction operator between the classical and quantum parts.

To form the model of the target molecule, at stage 36, the atoms of the target molecule and the solvent molecules related to it are sorted so that the same atoms of the target molecule are included in the first group of atoms, which are included in the first group of atoms formed in stage 35. In addition to Moreover, the first group also includes solvent molecules that are located from the atoms of the target molecule included in the first group at a distance not exceeding a specified value, and the second group includes all other atoms of the target molecule and everything remains nye solvent molecules. After that, at the same stage 36, they begin to form, using the coordinates of the atoms of the first and second groups, an input file for calculating the target molecule in the solvent using the corresponding simulation program in such a way that the atoms of the first group are modeled by quantum mechanics, and the atoms of the second group are modeled by classical mechanics.

To form a model of a ligand molecule, at stage 37, the atoms of the ligand molecule and solvent molecules are sorted in such a way that all atoms of the ligand molecule, as well as solvent molecules that are located at a distance from the atoms of the ligand molecule, are not included in the first group of atoms a given value, and the second group includes all other solvent molecules. After that, at the same stage 37, they begin to form, using the coordinates of the atoms of the first and second groups, an input file for calculating the ligand molecule in the solvent using the appropriate simulation program so that the atoms of the first group are modeled by quantum mechanics, and the atoms of the second group are modeled by classical mechanics.

In the case where the target molecule is a protein, the atoms are sorted into two groups (at step 35) in the intermolecular complex as follows. The first group of atoms includes atoms of the ligand molecule, atoms of the solvent molecules located at a distance not exceeding the specified value from the atoms of the ligand molecule, and the atoms of the target molecule, which make up the whole amino acid residues, at least one atom of which is at a distance, not exceeding the set value from each atom of the ligand molecule. The second group includes all other atoms of the target molecule and solvent molecules. When constructing a model of the target molecule, which is a protein, the atoms of the target molecule, which comprise the whole amino acid residues assigned to the first group of atoms for the intermolecular complex, are included in the first group of atoms (at step 36).

For a more correct simulation of the joining of two groups of atoms, for which the data are processed within the framework of the quantum and classical methods, add the coordinates of additional atoms to the input files for the corresponding simulation program of the intermolecular target – ligand complex, target molecule, and molecule at steps 38, 39, and 40 ligand, respectively. These additional atoms are located near the region of space, where the atoms of the first and second groups are at a distance from each other, not exceeding a given value.

The binding of components in the target-ligand intermolecular complex can also be modeled in another way so that the coordinates of the atoms of the second group are not included in the input files of the corresponding program for modeling the intermolecular complex of the target-ligand, target molecules and ligand molecules, and the atoms of the first group are modeled by quantum mechanics. In this case, the coordinates of the additional atoms added are included in the input files of the corresponding simulation program so that they, together with the atoms of the first group, are modeled by the methods of quantum mechanics. With this modeling method, when atoms of the first group that have covalent bonds with atoms of the second group have unsaturated dangling bonds, it is necessary to restore or compensate for the loss of these covalent bonds. In this case, when forming the model of the intermolecular target – ligand complex in step 41 and the model of the target molecule in step 42, additional atoms are added to the atoms of the first group so that they form new covalent bonds instead of dangling covalent bonds between the atoms of the first and second groups.

In the case where the target molecule is a protein, the dangling covalent bonds of the N-ends of the main chain of the protein are closed by the groups -C (O) - (CH ₃ ), and the dangling covalent bonds of the C-ends of the main chain of the protein are closed by the groups -N (H) - (CH ₃ ).

During the formation of input files for modeling binding in the protein-ligand complex, steps 43, 44, and 45 determine the charge states of various molecular groups of the intermolecular target-ligand complex, target molecules, and ligand molecules in a solvent (as a rule, this is determined by physicochemical properties of these molecular groups in a solvent or directly in experiments). Accordingly, additional atoms are added or removed at appropriate locations in the target ligand intermolecular complex in step 46, the target molecule in step 47, and the ligand molecule in step 48. When the solvent is water, the required charge states of the various molecular groups of the components of the target ligand intermolecular complex , the target molecules and ligand molecules in the solvent are obtained by adding or removing additional hydrogen atoms in the corresponding places of the target molecule and ligand molecule.

Next, at step 49, the total charge of the intermolecular target-ligand complex, the target molecule and the ligand molecule are determined. The total charge of the intermolecular complex and its components separately, i.e. target molecules and ligand molecules are obtained by simple addition of all charges that have been determined for individual molecular groups that make up the molecular systems under consideration. The obtained data on the total charges of the models of the intermolecular target – ligand complex, target molecules, and ligand molecules are used further to form three input files for the corresponding binding simulation program in the complex along with data on the multiplicity of the considered molecular systems, coordinates and types of their atoms.

In the case when the solvent is water, in order to more accurately take into account the explicit effect of the solvent on the binding of the target molecule and the ligand molecule, atom coordinates must be added to each of the three input files of the target molecule, ligand molecule, and their intermolecular complex additional water molecules. These additional water molecules are introduced into the modeling process in order to better reproduce the formation and breaking of hydrogen bonds, which play an essential role in the intermolecular complex of the target ligand, target molecule and ligand molecule.

At step 50, additional water molecules are added to the intermolecular complex so that they are between the target molecule and the ligand molecule and form hydrogen bonds with them.

The addition of water molecules to the target molecule in step 51 and to the ligand molecule in step 52 is carried out in such a way that, with their participation, the dangling hydrogen bonds that were present in the intermolecular complex between the target molecule and the ligand molecule and which were disconnected when the molecule was removed were restored. ligand from a target molecule. In addition, if water molecules were located between the target molecule and the ligand molecule and were connected by both hydrogen bonds, these water molecules were added twice each to the input file for calculating the target molecule at step 51 and to the input file for calculating the molecule ligand at step 52 when modeling the components of the intermolecular complex separately.

Typically, the solvent has a dielectric constant different from the dielectric constant of the vacuum and the dielectric constant of the target macromolecule. For example, the dielectric constant of water is approximately 80 at room temperature and normal pressure, while the dielectric constant of the protein dissolved in it does not exceed several units, and the dielectric constant of vacuum is 1. In this case, the presence of a solvent around the molecules in question significantly changes the electric potential and field that are created by charges of atoms around molecules. In order to take into account this screening effect of the solvent, as a rule, it is not enough to explicitly take into account a certain number of solvent molecules, and in this case, it is necessary to take into account the solvent in the implicit model, when its screening effect is taken into account by introducing into the model a continuous medium with the desired dielectric constant.

In the framework of the implicit solvent model, at step 53, the parameters of the solvent in the implicit model are included in the input files for calculating the intermolecular complex, the target molecule, and the ligand molecule using the appropriate program for modeling molecular systems in the solvent. For this, using the coordinates of the atoms of the target molecule, ligand molecule and solvent molecules, the coordinates of which are included in the corresponding input files, form the coordinates of points located on the surface accessible to the solvent. This surface covers the target molecule, ligand molecule and solvent molecules, in the case of calculating the intermolecular complex in the solvent, or covers only the target molecule and solvent molecules, in the case of calculating the target molecule in the solvent, or covers only the ligand molecule and solvent molecules , in the case of calculating a ligand molecule in a solvent. Using points located on these surfaces, a mathematical model of implicit solvent accounting is formed.

In the present invention, three types of implicit solvent accounting model are considered.

In the first of them, as a mathematical model of the implicit accounting of the solvent, a set of software tools is used that implement the solution of the Poisson equation and describe the interaction of the target molecule and the ligand molecule with a continuous medium that fills the entire space outside the surface accessible to the solvent and having a dielectric constant equal to dielectric constant solvent.

When using a solvent with a high dielectric constant of the solvent (for example, water has a dielectric constant of about 80 at room temperature), a set of software tools that implement the solution of equations describing the interaction of a target molecule and a ligand molecule with a continuous conductor are used as a mathematical model of implicit solvent accounting filling all the space outside the surface accessible to the solvent.

When using a solvent characterized by non-zero permittivity and conductivity, a set of software tools that implement the solution of the Poisson-Boltzmann equation is used as a mathematical model for implicit accounting of the solvent. This equation describes the interaction of a target molecule and a ligand molecule with a continuous medium having a non-zero dielectric constant and non-zero conductivity and filling the entire space outside the surface accessible to the solvent.

The generation of files describing the models for the quantum-mechanical calculation of the target-ligand intermolecular complex, the target molecule, and the ligand molecule in the solvent is completed at step 54, and the corresponding input files for the quantum-mechanical calculation are recorded on the information carrier.

These files are used, as a rule, depending on the chosen calculation method in two versions of quantum-mechanical modeling. In the first version of the simulation, the calculation of the intermolecular complex, the target molecule, the ligand molecule in the solvent is carried out so that the first group of atoms of the complex, target molecule and ligand molecule (described above) is calculated by quantum mechanics, and the second by classical mechanics. In the second version of the simulation, the calculation of the intermolecular complex, the target molecule, the ligand molecule in the solvent is carried out so that the first group of atoms is calculated by quantum mechanics, and the second is not included in the simulation.

The following describes the process of quantum-mechanical modeling of the interaction of a ligand molecule and a target molecule, taking into account the solvent (step 4 in FIG. 1) and calculation of energy quantities characterizing the binding of the target molecule and the ligand molecule (step 5 in figure 1). 4 is a flowchart illustrating a method according to the invention for quantum-mechanical modeling of intermolecular interaction between a ligand molecule and a target molecule, taking into account a solvent, including calculation of enthalpy, entropy and free binding energy of a ligand and a target.

The input files, which contain information on the structure and properties of the intermolecular complex, target molecules, and ligand molecules, are read from the storage medium at step 55. These input files contain information on the coordinates and types of all atoms of the considered molecular systems, their total charge and multiplicity, coordinates and type of atoms of solvent molecules added in the explicit model to the intermolecular complex and its components, solvent parameters in the implicit model. In addition, the input files contain information about the parameters of the optimization process, namely the method and parameters of quantum-mechanical modeling, the type of optimization procedure, the limits of self-consistency and minimization.

At step 56, various methods of quantum mechanical modeling of the total energy of molecular systems can be selected. When approaching, when part of the atoms of the intermolecular complex, the target molecule and the ligand molecule is calculated in the framework of the quantum-mechanical approximation, and the other part of the atoms is calculated in the framework of the classical approximation, various combinations of classical molecular-mechanical and molecular-dynamic methods are used, on the one hand , and quantum mechanical methods, on the other hand. The latter can vary from rigorous non-empirical methods and density functional methods [1-3] to faster, however, less accurate semi-empirical methods [4-7]. This approach, widely known as QM / MM, is currently implemented as a series of application software packages [8].

In addition, another approach is possible in which a part of the atoms of the intermolecular complex, the target molecule and the ligand molecule is calculated in the framework of the quantum-mechanical approximation, and the other part of the atoms is completely excluded from the modeling process. In order to more accurately reproduce the energy characteristics of binding in the intermolecular complex, with this approach it is necessary to take for quantum mechanical modeling as large sections of the target molecule as possible that describe the binding site with the ligand molecule with minimal influence of edge effects. In this case, the most promising methods of quantum-mechanical modeling are relatively quick calculations of semi-empirical methods, which have recently been implemented in a number of applied software packages with accelerated counting [9]. However, the use of more accurate, but slower non-empirical methods and density functional methods for this type of modeling is also possible.

At the beginning of the optimization procedure, at steps 57, 58, and 59, the variable parameters of the intermolecular target – ligand complex, the target molecule, the ligand molecule, and solvent molecules belonging to these systems are determined, namely, the variable coordinates of the atoms are determined, with a change in which there will be a minimum the total energy of each of the molecular systems.

Then, at step 60, using the appropriate program for modeling the total energy of the molecular system, based either on a combination of the quantum-mechanical and classical approximations or based only on the quantum-mechanical approximation, a minimum of the total energy of the intermolecular target-ligand and solvent complex is found with varying positions of all or some certain atoms of the complex and solvent. After this, the found new atomic coordinates and the total energy of the system, consisting of the intermolecular target-ligand complex and the solvent, and the corresponding atomic coordinates are recorded on the information carrier.

Similarly, at step 61, the minimum of the total energy of the target molecule and the solvent is found by varying the positions of all or part of the atoms of the target molecule and the solvent, and the new atom coordinates and the total energy of the system consisting of the target molecule and the solvent are recorded on the information carrier, and corresponding atomic coordinates.

Finally, at step 62, a minimum of the total energy of the ligand molecule and solvent is found by varying the positions of all or part of the atoms of the target molecule and the solvent, and the new atom coordinates and the total energy of the system consisting of the ligand molecule and solvent are found on the information carrier and corresponding atomic coordinates.

Using the obtained total energies of the intermolecular complex of the target ligand and solvent, the target molecule and solvent, as well as the ligand molecule and solvent, the enthalpy of binding of the ligand molecule to the target molecule in the solvent is calculated in step 63. In this case, two cases of calculating the enthalpy are possible.

The first case is realized when, in the process of binding a ligand molecule to a target molecule, the balance of solvent molecules is observed, that is, if the sum of the solvent molecules included in the calculation of the target molecule and the solvent molecules included in the calculation of the ligand molecule is equal to the number of solvent molecules, included in the calculation of the intermolecular complex of the target ligand. In this case, at step 63, the binding enthalpy ΔH bond _. target molecules and ligand molecules is calculated as the difference between the total energy of the intermolecular target ligand complex in the solvent, on the one hand, and the sum of the total energies of the target molecule in the solvent and the ligand molecule in the solvent, on the other hand, according to the formula:

ΔH _bond = E _{complex_Nmol.} - (E _{target_Lmol.} + E _{ligand_Mmol.} ),

where E _{complex_Nmol.rast.} is the total energy of the target ligand complex bound to N solvent molecules, E of the _{target_Lmol.} is the total energy of the target ligand complex bound to L solvent molecules, E _{ligand_Mol. solutions} is the total energy of the target ligand complex bound to M solvent molecules. If the balance of solvent molecules is N = L + M.

The second case is realized when, during the binding of the ligand molecule to the target molecule, the balance of the solvent molecules is not observed, that is, if the sum of the solvent molecules included in the calculation of the target molecule and the solvent molecules included in the calculation of the ligand molecule is not equal to the number of solvent molecules included in the calculation of the intermolecular target-ligand complex. In this case, at step 63, the binding enthalpy ΔH bond _. target molecules and ligand molecules is also calculated as the difference between the total energy of the intermolecular target ligand complex in the solvent, on the one hand, and the sum of the total energies of the target molecule in the solvent and the ligand molecule in the solvent, on the other hand. However, in calculating the enthalpy of binding, ΔH bond _. at this stage, it is necessary to take into account the energy that must be expended in order to remove from the solvent the number of solvent molecules that must be added to the system under consideration in order to maintain a balance in the number of solvent molecules in the process of binding the ligand molecule to the target molecule, according to the formula

ΔH _bond = E _{complex_Nmol . +} K * E _{mol. ---} (E _{target_Lmol.} + E _{ligand_Mmol.} ),

where E _{complex_Nmol.rast.} is the total energy of the target ligand complex bound to N solvent molecules, E of the _{target_Lmol.} is the total energy of the target ligand complex bound to L solvent molecules, E _{ligand_Mol. solutions} is the total energy of the target ligand complex bound to M solvent molecules, E _mol solution is the energy of removal of one water molecule from the solvent calculated in the same quantum -mechanical approximation as the full energies of the intermolecular complex, the target molecule and the ligand molecule. If the balance of solvent molecules is not observed, that is, when N = L + MK, in order to maintain the energy balance in the formula by which the enthalpy of binding of the target molecule and the ligand molecule is calculated, it is also necessary to take into account the K * E _{molar solution energy} .

The calculation of the entropy of binding of a ligand molecule to a target molecule in a solvent is carried out within the framework of the used quantum-mechanical approximation for the same models of the intermolecular complex, target molecule, and ligand molecule using the same input files that were used in calculating the total energies of these molecular systems. This binding entropy is determined by the vibrational frequencies of the molecules involved in the process under consideration. To calculate the vibrational frequencies at steps 64, 65, and 66 for the intermolecular complex, the target molecule, and the ligand molecule, the force constants or second derivatives of the total energies of these molecular systems are calculated for all atomic coordinates at the points of the corresponding minima (global or local). A matrix (Hessian matrix) is composed of these quantities, and the vibrational frequencies are then found by solving the eigenvalue problem of the Hessian matrix. At values of these frequencies, at step 67, the entropy component is calculated (using formulas, for example, in [10]), which is associated with the loss of vibrational degrees of freedom during the transition from free states of a target molecule and a ligand molecule in a solvent to their intermolecular complex. The entropy of binding due to the loss of vibrational degrees of freedom ΔS _bond. calculated by the formula

ΔS _{bond_oscillation} = S _{complex_Nmol .} - (S _{target_Lmol.} + S _{ligand_Mmol.} ),

subject to the balance of solvent molecules, and according to the formula

ΔS _{bond_oscillation} = S _{complex_N molar solution +} K * S _{molar solution-} (S _{target_L molar solution} + S _{ligand_M molar solution} ), without observing the balance of solvent molecules.

The change in entropy upon binding of a ligand molecule to a target molecule also contributes to the fact that, upon binding, these molecules lose each of the three translational and three rotational degrees of freedom that they possess in a free state. This part of the entropy is calculated at step 68 using the Sakura-Titroda formula, and for this, only the coordinates and atomic weights of atoms of the target molecule, ligand molecule, and their intermolecular complex are used (see, for example, [11]). In this case, the atomic weights of atoms are uniquely determined by their type (i.e., position in the Table of D.I. Mendeleev), which is recorded in the source files read from the information carrier at step 55 (Fig. 4). When relatively small ligand molecules (usually molecules with an atomic weight not exceeding 500 daltons) are bound to target macromolecules, such as proteins, the target molecule can be considered immobile, and the change in entropy calculated in step 68 will be determined only by the characteristics of the molecule ligand.

In step 69, using the values calculated in steps 67 and 68, the total change in entropy upon binding of the ligand molecule to the target molecule is calculated as the sum of the changes in entropy obtained in steps 67 and 68.

The process of binding a ligand molecule to a target molecule occurs in a solvent. Each of these molecules, when placed in a solvent, creates a cavity in it, pushing apart the solvent molecules. This process requires the cost of a certain free energy, which depends on the properties of the solvent. This free energy is called cavitation energy, and it depends only on the properties of the solvent and the form of the molecule placed in the solvent. Currently, several methods are known for calculating the cavitation energy of dissolution (see, for example, [12] and the references therein). Since when the ligand molecule is bound to the target molecule and the formation of the intermolecular complex, the shape of the cavities in which the molecules are located changes, the cavitation free energy will also change. _Kav its change ΔG is calculated in step 70 and the result, being folded at step 71 with the results of calculations of binding enthalpy ΔH _bond derived at step 63 and the entropy contribution -TΔS _binder, calculated in step 69, it gives the value of the total free energy of binding the ligand molecule with a target molecule in a solvent according to the formula

ΔG _bond = ΔH _bond -TΔS _{the connected} + ΔG _Kav

In accordance with the present invention, the enthalpy of binding of the target molecule and the ligand molecule (step 63 in FIG. 4) can be calculated using another method in which the total energies of the target molecule, ligand molecule and their intermolecular complex are calculated not at the minimum point as average values of the total energies obtained for a number of configurations of the intermolecular target-ligand complex. In this case, the atomic coordinates of the target molecule, ligand molecule, and their intermolecular complex, corresponding to each of these configurations, can be obtained in the framework of molecular dynamics modeling. 5 is a flowchart illustrating a method for molecularly dynamically generating atomic coordinates of a target molecule, a ligand molecule and a target-ligand intermolecular complex for a set of intermolecular complex configurations, as well as a method for calculating the enthalpy of binding of a target molecule to a ligand molecule, based on the average values of the total energies obtained for a set of these configurations.

The initial data for the formation of input files for a set of configurations of the intermolecular complex, target molecule, and ligand molecule are the coordinates of atoms of the target molecule, ligand molecule, and their intermolecular complex, which can be obtained from the PDB database or from using various molecular structure builders. In addition, if an explicit solvent model is used, the initial data are the atomic coordinates of the solvent molecules that are entered in step 73, similar to what was done earlier in steps 27, 28 and 29. If you use the implicit solvent model that is entered in step 74, similar to the above step 53, the coordinates of the atoms of the solvent molecules are not explicitly included in the simulation.

The procedure for molecular-dynamic formation of input files with the coordinates of the atoms of the target molecule, the ligand molecule and the intermolecular target-ligand complex for a number of configurations with an explicit solvent model includes the following steps.

Using the coordinates of the atoms of the intermolecular complex, the target molecule and the ligand molecule, as well as the solvent molecules (steps 26, 27 and 30 in FIG. 2) and, if necessary, introducing additional atoms to establish the desired charge of the intermolecular target-ligand complex (steps 46, 49 in FIG. 3), a molecular dynamics simulation of the target ligand complex is performed in step 75 as part of an explicit solvent model. In this case, by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the target molecule and the ligand molecule interacting with each other, taking into account the presence of solvent molecules, determine the state of the molecular system at which it reaches thermal equilibrium. Then, the motion paths of all atoms of the system are determined after they reach thermal equilibrium, when the average values of the observed values (for example, the interaction energy of the ligand molecule with the target molecule) cease to change with time (usually these are the lengths of the paths in time of about one nanosecond), and are recorded on step 76, on the information carrier, the coordinates of all atoms of the interacting target molecule, ligand molecule, and solvent molecules at predetermined intervals a predetermined number of times for a given set of configurations of the intermolecular target – ligand complex.

Using the coordinates of the atoms of the target molecule, as well as the solvent molecules (steps 17, 28 and 31 in FIG. 2) and, if necessary, introducing additional atoms to establish the desired charge of the target molecule (steps 47, 49 in FIG. 3), at step 77, a molecular dynamics simulation of the target molecule is performed as part of an explicit solvent model. In this case, by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the target molecule interacting with each other, taking into account the presence of solvent molecules, determine the state of the molecular system at which it reaches thermal equilibrium. Then, the motion paths of all atoms of the system are determined after their thermal equilibrium is reached, and at step 78, the coordinates of all atoms of the interacting target molecules and solvent molecules are recorded on the information carrier at specified intervals for a specified number of times for a given set of configurations of the target molecule.

Using the coordinates of the atoms of the ligand molecule, as well as solvent molecules (steps 24, 29 and 32 in FIG. 2) and, if necessary, introducing additional atoms to establish the desired charge of the ligand molecule (steps 48, 49 in FIG. 3), at step 79, molecular dynamics simulation is performed as part of an explicit solvent model. In this case, by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the ligand molecule interacting with each other, taking into account the presence of solvent molecules, the state of the molecular system at which it reaches thermal equilibrium is determined at step 79. Then, the motion paths of all atoms of the system are determined after their thermal equilibrium is reached, and at step 80, the coordinates of all atoms of the interacting ligand molecule and solvent molecules are recorded on the information carrier at specified intervals for a specified number of times for a given set of ligand molecule configurations.

The molecular dynamics procedure for generating input files with atomic coordinates of a target molecule, a ligand molecule, and an intermolecular target-ligand complex for a number of configurations with an implicit solvent model includes the following steps.

Using the coordinates of the atoms of the intermolecular complex of the target molecule and the ligand molecule (step 26 in figure 2) and, if necessary, introducing additional atoms to establish the desired charge of the intermolecular complex of the target ligand (steps 46, 49 in figure 3), carry out molecular dynamics modeling in the framework of the implicit solvent model. The solvent in this case is taken into account using the implicit model, as described above (step 53 in FIG. 3), in the framework of solving the Poisson, Poisson-Boltzmann equations, the equations for a continuous conductor, or in another way that takes into account the influence of the solvent without using the coordinates of the solvent molecules. Then, in the same way as in the framework of the explicit solvent model, by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the target molecule and the ligand molecule interacting with each other, determine the state of the molecular system at which it reaches the thermal equilibrium. Then, the motion paths of all atoms of the system are determined after their thermal equilibrium is reached, and at step 76, the coordinates of all atoms of the interacting target molecules, ligand molecules, and solvent molecules are recorded on a data carrier at specified intervals for a given number of times for a given set of configurations of the target-ligand intermolecular complex .

Using the coordinates of the atoms of the target molecule and, if necessary, introducing additional atoms to establish the desired charge of the target molecule (steps 47, 49 in FIG. 2), molecular dynamics modeling is performed within the implicit solvent model. The solvent in this case is taken into account using the implicit model (step 53 in FIG. 3) in the framework of solving the Poisson, Poisson-Boltzmann equations, the equation for a continuous conductor, or in another way that takes into account the influence of the solvent without using the coordinates of the solvent molecules. Then, in the same way as in the framework of the explicit solvent model, by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the target molecule interacting with each other, taking into account the presence of solvent molecules, determine the state of the molecular system at step 77, at which it reaches thermal equilibrium. Then, the motion paths of all atoms of the system are determined after their thermal equilibrium is reached, and at step 78, the coordinates of all atoms of the interacting target molecules and solvent molecules are recorded on the information carrier at specified intervals for a specified number of times for a given set of configurations of the target molecule.

Using the coordinates of the atoms of the ligand molecule and, if necessary, introducing additional atoms to establish the desired charge of the ligand molecule (steps 47, 49 in FIG. 3), molecular dynamics modeling is performed within the framework of an implicit solvent model. The solvent in this case is taken into account using the implicit model (step 53 in FIG. 3) in the framework of solving the Poisson, Poisson-Boltzmann equations, the equation for a continuous conductor, or in another way that takes into account the influence of the solvent without using the coordinates of the solvent molecules. Then, similarly to how this was done in the framework of the explicit solvent model, by solving the Newton or Lagrange equations, taking into account the thermal motion of all atoms of the ligand molecule interacting with each other, taking into account the presence of solvent molecules, determine the state of the molecular system at step 79, at which it reaches thermal equilibrium. Then, the motion paths of all atoms of the system are determined after their thermal equilibrium is reached, and at step 80, the coordinates of all atoms of the interacting ligand molecule and solvent molecules are recorded on the information carrier at specified intervals for a specified number of times for a given set of ligand molecule configurations.

Next, for each coordinate set of the intermolecular target – ligand complex in the explicit or implicit model of the solvent obtained in step 76, in step 81, all atoms are divided into groups in the same way as before (step 35 in FIG. 3).

For each coordinate set of the target molecule in the solvent obtained in step 78, all atoms are divided into groups according to method 82, similar to method 36.

For each set of coordinates of the ligand molecule in the solvent obtained by method 80, at step 83, all atoms are divided into groups in the same way as before (step 37 in FIG. 3).

For each configuration of the target-ligand intermolecular complex, that is, for each set of its coordinates obtained in molecular dynamics modeling, an input file is generated at step 84 for quantum-mechanical simulation of the target-ligand intermolecular complex in a solvent, as described above (step 4 in FIG. .1 and step 56 in FIG. 4).

Similarly, for each configuration of the target molecule, that is, for each set of its coordinates obtained in molecular dynamics modeling, an input file is generated in step 85 for quantum-mechanical modeling of the target molecule in a solvent, as described above (step 4 in FIG. 1 and step 56 of FIG. 4).

For each configuration of the ligand molecule, that is, for each set of its coordinates obtained in molecular dynamics modeling, an input file is generated at step 86 for quantum-mechanical modeling of the ligand molecule in a solvent, as described above (step 4 in FIG. 1 and step 56 in FIG. 4).

For each input file generated in step 84, that is, for each configuration of the target-ligand intermolecular complex, using the modeling method selected in step 87, at step 88, the total energy of the target-ligand intermolecular complex in the solvent is calculated without optimizing the spatial structure of the complex. Then, at step 89, the average total energy of the target-ligand intermolecular complex in the solvent is calculated over the entire selected set of configurations of this molecular system.

For each input file generated in step 85, that is, for each configuration of the target molecule, using the simulation method selected in step 87, in step 90, the total energy of the target molecule in the solvent is calculated without optimizing its spatial structure. Then, at step 91, the average total energy of the target molecule in the solvent is calculated over the entire selected set of configurations of this molecular system.

For each input file generated in step 86, that is, for each configuration of the ligand molecule, using the modeling method selected in step 87, in step 92, the total energy of the ligand molecule in the solvent is calculated without optimizing its spatial structure. Then, at step 93, the average value of the total energy of the ligand molecule in the solvent is calculated over the entire selected set of configurations of this molecular system.

Using the obtained average values of the total energies of the target-ligand intermolecular complex in the solvent, the target molecules in the solvent, and the ligand molecules in the solvent obtained in steps 89, 91, and 93, respectively, the enthalpy of binding of the ligand molecule to the target molecule in solvent, as the difference between the average value of the total energy of the target-ligand intermolecular complex in the solvent, on the one hand, and the sum of the average values of the total energies of the target molecule in the solvent and the ligand molecule in solvent, on the other hand. Next, the entropy of binding of the ligand molecule to the target molecule in the solvent and the free binding energy of the ligand molecule to the target molecule in the solvent are calculated (steps 69 and 71 in FIG. 4).

The above method of modeling the binding of ligand molecules to target molecules by quantum mechanics, taking into account the influence of a solvent, was carried out by the authors of the present invention for a number of intermolecular complexes of proteins and ligands for which the binding energy characteristics, namely binding enthalpy, were experimentally known. In accordance with the claimed method, the protein-ligand binding enthalpy was calculated for these test complexes. By comparing the obtained results with the corresponding experimental values, an initial assessment of the accuracy of the claimed modeling method was given.

For test modeling, eight protein complexes with ligands were selected for which not only the experimental values of the binding enthalpy were known, but also the structures obtained by X-ray diffraction analysis and entered into the PDB database (Protein Data Bank) [7]. Table 1 presents a list of the studied complexes. This table shows the names of these complexes according to the PDB database, the Latin names of the corresponding proteins and ligands, the experimental values of the binding enthalpies for each complex, as well as links to the works from which these data were obtained. Figure 6 shows the structural formulas and the structures of the ligands of the corresponding complexes optimized within the framework of quantum mechanics.

Table 1
Protein-ligand complexes with experimentally known binding enthalpy values that were selected as test systems for modeling binding in the protein-ligand system by quantum mechanics Nn PDB system Protein Ligand ΔH _{St. (Exp.)} , Kcal / mol Link 1 1ABE L-Arabinose-binding protein of Escherichia coli L-arabinose -15.3 ± 0.5 [thirteen] 2 1A78 Galectin-1 Thiodigalactopyranoside -10.1 ± 0.8 [14] 3 1SWD Apo-core-streptavidin Biotin -28.6 ± 0.4 [fifteen] 4 1DF8 S45A Mutant of Streptavidin Biotin -21.1 ± 0.5 [fifteen] 5 1AJ6 R136H Mutant 24kDa fragment from the B subunit of DNA gyrase Novobiocin -17.5 ± 0.1 [16] 6 1I3H Concanavalin a Dimannoside -7.0 [17] 7 1CVN Concanavalin a Trimannoside -10.7 [17] 8 1SHA Phosphotyrosine recognition domain SH2 of the v-src Tyrosine-phosphorylated peptide (Tyr-Val-Pro-Met-Leu, Phosphorylated Tyr) -2.7 ± 0.8 [18]

As can be seen from the above table 1 and figure 6, the selected complexes contain ligands, which are organic compounds with different chemical composition and properties. Among them are carbohydrates (systems 1, 2, 6 and 7 according to the numbering of table 1), heterocyclic compounds (systems 3 and 4 according to the numbering of table 1), aromatic compound (system 5 by the numbering of table 1) and oligopeptide (system 8 according to the numbering of the table 1). Some of these ligands are negatively charged, some are neutral, the number of atoms in them ranges from 20 atoms to 94. The experimental values of the binding enthalpies in the selected series of complexes vary from -2.7 to -28.6 kcal / mol. Two selected complexes (systems 3 and 4 according to the numbering of table 1) contain the same ligands and different proteins, the other two complexes (systems 6 and 7 according to the numbering of table 1) contain different ligands and the same proteins. Thus, the selected series of protein-ligand intermolecular complexes was a fairly wide range of systems, which is of interest when testing the claimed modeling method.

The initial structures of the complexes, namely, the Cartesian coordinates of their atoms, were taken from the PDB database. Almost all of the initial structures of proteins and ligands contained only the coordinates of heavy (C, N, O, S) atoms. Hydrogen atoms were added to the protein structures of all complexes using the REDUCE program [19] at the first stage of building complex models. Hydrogen atoms were added to the ligand structures of all complexes using the Materials Studio Visualizer package provided by Accelrys [20].

In this case, the influence of the solvent was taken into account within the framework of an explicit water model; however, in the present simulation, no water molecules were added in molecular mechanics or in molecular dynamics. The positions of water molecules associated with the complex and its components were taken from experimental data (PDB data of X-ray diffraction analysis) on water molecules structured in the complex.

For each complex, atoms were sorted into two groups according to the method proposed in the claimed invention. This procedure was performed using the LigEnv program [21], developed by Algodine. For each complex, the first group of atoms included ligand atoms and protein atoms, which made up whole amino acid residues, at least one atom of which was at a distance not exceeding a specified value from each ligand atom. In addition, the first group included atoms of water molecules that were present in the input data obtained from the PDB database, each of which was at a distance not exceeding a specified value from the ligand atoms. The second group included all other atoms of the protein and water molecules. When constructing the protein model, the protein atoms included in the first group of atoms for the intermolecular complex were included in the first group of atoms. To model the enthalpy of binding in all selected complexes, an approach was chosen in which the atoms of the protein, ligand, and their complex, together with water molecules belonging to the first groups, were modeled by quantum mechanics, and the atoms of the second groups were excluded from the simulation. With this modeling method, as was already mentioned, firstly, it was necessary to select sufficiently large protein models that adequately describe the ligand binding site, and, therefore, the semiempirical quantum-mechanical method for calculating PM3 was chosen to speed up the counting [22]. This method, along with a sufficiently high counting rate, provides satisfactory accuracy in calculating the total energy of molecular systems with hydrogen bonds. Secondly, with this approach, it was necessary to introduce a number of additional atoms, which restored dangling covalent bonds of protein atoms when they were divided into groups. The dangling covalent bonds of the N-ends of the main chains of the proteins were closed by the groups -C (O) - (CH ₃ ), and the dangling covalent bonds of the C-ends of the main chains of the proteins were closed by the groups -N (H) - (CH ₃ ). The additionally added atoms were included along with the atoms of the first group in the simulation by quantum mechanics. The coordinates of ligand atoms, water molecules, and side chains of proteins were chosen as optimized parameters. To maintain the three-dimensional structure of the protein taken from the experiment, the coordinates of the heavy atoms (C, N, O) of the main chains of the proteins and the coordinates of the added atoms were considered as not optimized parameters.

During the formation of the input data for modeling, the charge states of various molecular groups of proteins and ligands in water were determined at known pH values. Accordingly, additional protons in the corresponding acidic or basic amino groups of the protein have been added or removed. By summing the charge states of acidic and basic amino groups, the total charge of protein models, ligands, and their intermolecular complexes was determined.

Figure 7 presents the optimized structure of the thus constructed model of one of the studied complexes. The structures of all other models, in the general case, look similar and are omitted to facilitate the perception of the material.

During the simulation, it was shown that special attention should be paid to modeling water as a solvent, which is explicitly taken into account. Two methods have been proposed for taking into account the breaking and formation of hydrogen bonds during the transition from the complex to its components and the participation of water molecules in this process. Accordingly, two methods for adding water molecules during the transition from the complex to its components were considered. Conventionally, these methods have been named as approaches W1 and W2.

According to the W1 approach, water molecules, the position of which was taken from the experiment from the PDB database, bound in a complex with a protein, were calculated by modeling individual components of the complex together with the protein. Water molecules, the position of which was taken from the experiment from the PDB database, linked in a complex with a ligand, were calculated by modeling the individual components of the complex together with the ligand. Water molecules bound in the complex simultaneously with the protein and the ligand and forming bridges with hydrogen bonds with them were taken into account when calculating the protein and ligand separately twice.

According to the W2 approach, water molecules, the position of which was taken from the experiment, were also taken into account in a way similar to W1. In addition, in this case, additional water molecules were added to both the protein and the ligand in those places where the complex had hydrogen bonds between the protein and the ligand, so as to replace the broken hydrogen bonds during the transition from the intermolecular complex to its components.

A schematic representation of these two methods of accounting for water molecules W1 and W2 is explicitly presented in FIGS. 8 and 9, respectively.

According to the above schemes, the calculation of the enthalpy of binding of protein and ligand in the complex according to method W1 was carried out according to the formula

ΔH _{bond (W1)} = ΔH _LP - (ΔH _{P [nW (P), kW (LP)]} + ΔH _{L [mW (L), kW (LP)]} ) + k · ΔH _W ,

Here ΔH _LP is the calculated energy of the protein-ligand (LP) complex, taken together with all water molecules interacting with the complex. ΔH _{P [nW (P), kW (LP)]} is the calculated energy of the protein (P) taken together with all (n + k) water molecules interacting with it (see Fig. 8), ΔH _{L [mW (L ), kW (LP)]} is the calculated energy of the ligand (L) taken together with all (m + k) water molecules interacting with it (see Fig. 8). k · ΔH _W is the calculated energy k of water molecules W (LP) (see Fig. 8), which must be added to the sum to maintain the energy balance. ΔH _W is the energy of a water molecule, which is calculated taking into account its removal from a drop of water. In this case, the calculated energy ΔH _W = -53.43 kcal / mol.

The calculation of the enthalpy of binding of protein and ligand in the complex according to method W2 was performed according to the formula

ΔH _{bind (W2)} = ΔH _LP - (ΔH _{P [nW (P), kW (LP), qW (PHB)]} + ΔH _{L [mW (L), kW (LP), tW (LHB)]} ) + ( k + q + t) ΔH _W.

Here ΔH _LP is the calculated energy of the protein-ligand (LP) complex, taken together with all water molecules interacting with the complex. ΔH _{P [nW (P), kW (LP), qW (PHB)]} is the calculated energy of the protein (P) taken together with all water molecules (n + k + q) interacting with it (see Fig. 9) , ΔH _{L [mW (L), kW (LP), tW (LHB)]} is the calculated energy of the ligand (L) taken together with all (m + k + t) water molecules interacting with it (see Fig. 9 ) (k + q + t) ΔH _W is the calculated energy (k + q + t) of the water molecules W (LP), W (PHB) and W (LHB) (see Fig. 9), which should be added to the sum for maintaining energy balance.

The enthalpies of binding of proteins and ligands obtained in approximations W1 and W2 according to the claimed invention for complexes taken as test systems (see table 1, systems 1-8) are shown in table 2 together with the corresponding experimental data and deviations calculated from the experimental values.

As can be seen from this table, for both methods of water accounting, quite reasonable agreement was obtained between the calculated and experimental data on the enthalpy of binding in protein-ligand complexes. The standard deviation (RMS) calculated for all complexes of binding enthalpies in the W1 approach was 7.0 kcal / mol, the similar standard deviation obtained for the W2 method was 1.85 kcal / mol. The latter accuracy in calculating the binding enthalpy is quite high and comparable with the accuracy of existing experimental methods for measuring the binding enthalpy in protein-ligand complexes.

table 2
The calculated enthalpies of binding of proteins and ligands for complexes 1-8 according to table 1 Nn PDB system Calculation of W1, ΔH _{bond (W1)} , kcal / mol Calculation of W1, error ¹⁾ , kcal / mol Calculation of W2, ΔH _{bond (W2),} kcal / mol Calculation of W2, error ¹⁾ , kcal / mol 1 1ABE -18.14 2,8 -12.72 -2.58 2 1A78 -14.42 4.32 -9.79 -0.31 3 1SWD -24.66 -3.94 -26.47 -2.13 4 1DF8 -17.01 -4.09 -18.06 -3.04 5 1AJ6 -13.22 -4.28 -18.91 1.41 6 1I3H -16.18 9.18 -7.65 0.65 7 1CVN -12.69 1.99 -11.58 0.88 8 1SHA -18.03 15.33 -4.66 1.96 ¹⁾ Deviations of the protein-ligand binding enthalpies calculated in the W1 and W2 approximations from experimental values.

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Claims (30)

1. A method of quantum-mechanical modeling of the binding of ligand molecules to target molecules in a solvent, comprising the steps of a) receive the structure and composition of the target molecule in the form of a set of coordinates and types of atoms and write this data to the storage medium; b) receive the structure and composition of the ligand molecule in the form of a set of coordinates and the type of atoms and write this data to the storage medium; c) read the coordinates of the atoms of the target molecule and the ligand molecule from the storage medium into the computer memory and perform the conversion of the coordinates of the atoms of these molecules so that the smallest distance between each of the atoms of the ligand molecule and the given atoms of the target molecule is in a given range, and write the new coordinates of the atoms of the target molecule and the ligand molecule, forming the intermolecular complex of the target ligand, in computer memory, d) the solvent parameters are added to the set of coordinates of the intermolecular target-ligand complex based on the model of explicit accounting of the solvent and the coordinates of all atoms of the target-ligand intermolecular complex and the solvent are recorded in the computer memory as the first set of coordinates, e) the solvent parameters are added to the target coordinate set based on the explicit solvent accounting model and the coordinates of all atoms of the target molecule and the solvent are recorded in the computer memory as a second set of coordinates, f) the solvent parameters are added to the coordinate set of the ligand molecule based on the explicit solvent accounting model and the coordinates of all atoms of the ligand molecule and the solvent are recorded in the computer memory as a third coordinate set, g) using a computer program that reads from the computer’s memory the first set of coordinates of the atoms of the intermolecular complex and the solvent, calculate the distances from the atoms of the ligand molecule to each atom of the target molecule and solvent and sort all the atoms of the first set so that the first group includes all atoms of the ligand molecule, as well as atoms of the target molecule and solvent atoms, the distances from which to each of the atoms of the ligand molecule do not exceed a specified value, and include in the second group removed all the remaining atoms of the target molecule and solvent, h) sorting all the atoms of the second set so that the first group of atoms includes the same atoms of the target molecule that are in the first group of atoms formed in step (g), and the second group includes all the other atoms of the target molecule and all atoms of the solvent, and in the first and second groups of atoms include the same atoms of the solvent molecules that are included in the corresponding groups of atoms formed in step (g), i) they sort all the atoms of the third set so that the first group of atoms includes all the atoms of the ligand molecule and those atoms of the solvent molecules that are in the first group of atoms formed in step (g), and the remaining group includes all other atoms solvent molecules j) form using the coordinates of the atoms of the first and second groups formed in step (g), an input file for calculating the intermolecular target-ligand complex in a solvent using an appropriate simulation program so that the atoms of the first group with their nuclei and electrons are modeled by quantum mechanics, and the atoms of the second group mentioned are modeled by classical mechanics, k) form using the coordinates of the atoms of the first and second groups formed in step (h), an input file for calculating the target molecule in the solvent using the appropriate simulation program so that the atoms of the first group with their nuclei and electrons are modeled by quantum mechanics , and the atoms of the second group mentioned are modeled by methods of classical mechanics, m) form using the coordinates of the atoms of the first and second groups formed in step (s), an input file for calculating the ligand molecule in the solvent using the appropriate simulation program so that the atoms of the first group with their nuclei and electrons are modeled by quantum mechanics , and the atoms of the second group mentioned are modeled by methods of classical mechanics, m) on the basis of the physicochemical properties of the corresponding molecules, the charge states of various groups of atoms of the target molecule and the ligand molecule in the solvent are determined and, in accordance with this, additional atoms are added or removed in the corresponding places of the target molecule and the ligand molecule, o) determine the total charge of the target molecule, the total charge of the ligand molecule and the total charge of the intermolecular complex of the target ligand, o) modify the input files to calculate the intermolecular target-ligand complex, calculate the target molecule and calculate the ligand molecule, taking into account the coordinates of the corresponding atoms, their type, as well as the full charges and multiplicity of these molecules, p) the input parameters for calculating the intermolecular complex of the target ligand, target molecules and ligand molecules include the parameters of the solvent in an implicit model, in which, using the coordinates of the atoms of the target molecule, ligand molecule and solvent molecules, the coordinates of which are included in the corresponding input files modified in step (p) form the coordinates of points located on a surface accessible to the solvent, which encompasses the target molecule, ligand molecule, and solvent molecules, or encompasses only molecules -the target and solvent molecules in the case of calculating the target molecule in the solvent, or covers only the ligand and solvent molecules in the case of calculating the ligand molecule in the solvent, and using these points form a mathematical model of the implicit accounting of the solvent, and write these input files to the storage medium to calculate the intermolecular complex of the target ligand, the target molecule and the ligand molecule using the appropriate simulation program, c) using an appropriate simulation program, calculate the total energy of the target-ligand intermolecular complex and solvent using the corresponding input file generated in step (p), and find the minimum total energy of the target-ligand and solvent intermolecular complex with varying positions of at least some atoms intermolecular complex and solvent; write to the information carrier the value of the minimum total energy of the intermolecular complex of the target ligand and solvent, and the corresponding atomic coordinates, r) using the appropriate simulation program, calculate the total energy of the target molecule and solvent using the corresponding input file generated in step (p), and find the minimum total energy of the target molecule and solvent when varying the positions of at least part of the atoms of the target molecule and solvent; write to the information carrier the value of the minimum total energy of the target molecule and the solvent, and the corresponding atomic coordinates, s) using the appropriate simulation program, calculate the total energy of the ligand molecule and solvent using the input file generated in step (p), and find the minimum total energy of the ligand molecule and solvent by varying the positions of at least part of the atoms of the ligand molecule and solvent ; write to the information carrier the value of the minimum total energy of the ligand molecule and the solvent, and the corresponding atomic coordinates, f) using the values of the minima of the total energies of the target-ligand intermolecular complex, and the solvent, the target molecule and the solvent, and the ligand molecule and solvent obtained in steps (c), (t) and (y), respectively, the enthalpy of binding of the molecule is calculated a ligand with a target molecule in a solvent, as the difference between the minimum total energy of the target-ligand intermolecular complex in the solvent calculated on the one hand in step (c) and the sum of the minimum energies of the target molecule in the solvent and the molecules ligand in the solvent, calculated respectively in steps (r) and (y), on the other hand, x) provide, in the process of binding the ligand molecule to the target molecule, the balance of solvent molecules, when the sum of the solvent molecules included in the calculation of the target molecule and the solvent molecules included in the calculation of the ligand molecule is equal to the sum of the solvent molecules included in the calculation of the intermolecular complex the ligand target, in this case, when the balance of the solvent molecules during the binding process is impaired, when calculating the binding enthalpy in step (f), the energy that must be expended to remove from the solvent is taken into account the number of solvent molecules that must be added to the system under consideration in order to maintain a balance in the number of solvent molecules during the binding of the ligand molecule to the target molecule. 2. The method according to p. 1, characterized in that in the case when the target molecule is a protein, its structure and composition is obtained from the PDB database. 3. The method according to p. 1, characterized in that the structure and composition of the target molecule is obtained in the form of a set of Cartesian coordinates of the corresponding atoms. 4. The method according to claim 1, characterized in that the coordinates of the missing hydrogen atoms are added to the coordinates of the atoms of the target molecule, whereby the coordinates of the added hydrogen atoms are determined at which the total energy of the target molecule reaches a minimum when the coordinates are varied these hydrogen atoms, and the coordinates of all atoms of the target molecule, including the coordinates of the added hydrogen atoms, are recorded on the information carrier. 5. The method according to claim 1, characterized in that the coordinates of the missing hydrogen atoms are added to the coordinates of the atoms of the ligand molecule, whereby the coordinates of the added hydrogen atoms are determined at which the total energy of the ligand molecule reaches a minimum when the coordinates are varied these hydrogen atoms, and the coordinates of all atoms of the ligand molecule, including the coordinates of the added hydrogen atoms, are recorded on the information carrier. 6. The method according to p. 1, characterized in that adding the parameters of the solvent based on the model of explicit accounting for the solvent is carried out by computer calculation of the coordinates corresponding to the positions in the space of many solvent molecules, so that their average density corresponds to the experimentally observed density of the solvent and they filled without intersections and intersections with atoms of the target molecule and the ligand molecule, the space both between the target molecule and the ligand molecule, and around them. 7. The method according to p. 1, characterized in that the input files for calculating the intermolecular complex of the target ligand, the target molecule and the ligand molecule add the coordinates of additional atoms in the space where the atoms of the first and second groups are at a distance from each other not exceeding a predetermined value, and simulate the conjugation of two groups of atoms, calculated respectively by the methods of quantum and classical mechanics. 8. The method according to p. 7, characterized in that the coordinates of the atoms of the second group are not taken into account when generating the input files of the corresponding program for modeling the intermolecular complex of the target ligand, the target molecule and the ligand molecule, and the coordinates of the additional atoms added are included in the input files of the corresponding program simulation so that they, together with the atoms of the first group, are modeled by the methods of quantum mechanics. 9. The method according to p. 8, characterized in that, using additional atoms, compensate for dangling covalent bonds that the atoms of the first group had with the atoms of the second group. 10. The method according to p. 1, characterized in that in the case where the target molecule is a protein, the first group of atoms of the intermolecular complex of the target ligand include atoms of the ligand molecule, the atoms of the solvent molecules located at a distance not exceeding a predetermined value from atoms of the ligand molecule, and atoms of the target molecule, which make up whole amino acid residues, at least one atom of which is at a distance not exceeding the specified value from each atom of the ligand molecule, and the remaining group of m atoms are included in the second group target molecules and solvent molecules. 11. The method according to p. 1, characterized in that in the case where the target molecule is a protein, the atoms of the target molecule that comprise the whole amino acid residues are included in the first group of atoms formed in step (h). 12. The method according to p. 9, characterized in that in the case where the target molecule is a protein, additional atoms shorten the dangling covalent bonds of the protein chain so that the N-terminus of the dangling protein chain is closed by the C (O) - (CH ₃ ), and the C-terminus of the dangling chain of the protein is closed by the group -NH- (CH ₃ ). 13. The method according to p. 1, characterized in that in the case when the solvent is water, the required charge states of various groups of atoms of the target molecule and the ligand molecule in the solvent are obtained by adding or removing additional hydrogen atoms in the corresponding places of the target molecule and molecule ligand. 14. The method according to p. 13, characterized in that the atom coordinates of additional water molecules are added to each of the three input files of the target molecule, ligand molecule and intermolecular target-ligand complex. 15. The method according to p. 14, characterized in that the water molecules are added to the intermolecular target-ligand complex, so that they form hydrogen bonds with both the target molecule and the ligand molecule. 16. The method according to p. 14, characterized in that water molecules are added to the target molecule so that with their participation to restore hydrogen bonds that were present in the intermolecular complex of the target ligand and which were broken when the ligand molecule was removed from the target molecule . 17. The method according to p. 14, characterized in that the water molecules are added to the ligand molecule so that with their participation to restore hydrogen bonds that were present in the intermolecular complex of the target ligand and which were broken when the ligand molecule was removed from the target molecule . 18. The method according to p. 1, characterized in that as a mathematical model of implicit accounting for the solvent using a combination of software that implements the solution of the Poisson equation and describes the interaction of the target molecule and the ligand molecule with a continuous medium filling the entire space outside the surface accessible to the solvent and having a dielectric constant equal to the dielectric constant of the solvent. 19. The method according to p. 1, characterized in that when using a solvent with a high dielectric constant of the solvent as a mathematical model of the implicit accounting of the solvent using a set of software tools that implement the solution of the equations describing the interaction of the target molecule and the ligand molecule with a continuous conductor, filling all the space outside the surface accessible to the solvent. 20. The method according to p. 1, characterized in that when using a solvent characterized by non-zero dielectric constant and conductivity, a set of software tools that implement the solution of the Poisson-Boltzmann equation and describe the interaction of the target molecule is used as a mathematical model of implicit solvent accounting a ligand molecule with a continuous medium having a non-zero dielectric constant and non-zero conductivity and filling the entire space outside the surface is accessible full of solvent. 21. The method according to p. 1, characterized in that the vibrational frequencies of the ligand molecule, the target molecule and the intermolecular target-ligand complex are calculated, and the entropy of binding of the ligand molecule to the target molecule in the solvent is calculated using these frequencies. 22. The method according to p. 1 or 21, characterized in that, using the atomic weights and atomic coordinates of the ligand molecule, the target molecule and the intermolecular target-ligand complex, the entropy of binding due to the loss of each of these three rotational and three translational molecules is calculated degrees of freedom when bundling them into a complex. 23. The method according to p. 1 or 22, characterized in that, using the properties of the solvent molecules and the coordinates of the atoms of the target molecule, the ligand molecule and the intermolecular target-ligand complex, the cavitation binding energy is calculated as the difference between the cavitation energy of solvation of the intermolecular target-complex ligand, on the one hand, and the sum of the cavitation energy of solvation of the target molecule and the ligand molecule separately, on the other hand, and the cavitation energy of solvation is calculated as free energy, which is necessary and creating an empty cavity in the solvent, the shape of which matches the shape of the molecule is dissolved. 24. The method according to p. 23, characterized in that, using the enthalpy and entropy of binding of the ligand molecule to the target molecule in the solvent, and the value of the cavitation binding energy, calculate the free binding energy of the ligand molecule with the target molecule in the solvent. 25. Molecular-dynamic method of quantum-mechanical modeling of the binding of ligand molecules to target molecules in a solvent, comprising the steps of a) receive the structure and composition of the target molecule in the form of a set of coordinates and types of atoms and write this data to the storage medium; b) receive the structure and composition of the ligand molecule in the form of a set of coordinates and the type of atoms and write this data to the storage medium; c) read the coordinates of the atoms of the target molecule and the ligand molecule from the storage medium into the computer memory and perform the conversion of the coordinates of the atoms of these molecules so that the smallest distance between each of the ligand atoms and the given atoms of the target molecule is in a given range, and record new the coordinates of the atoms of the target molecule and the ligand molecule, forming the intermolecular complex of the target ligand, in computer memory, d) the solvent parameters are added to the set of coordinates of the intermolecular target-ligand complex based on the model of explicit accounting of the solvent and the coordinates of all atoms of the target-ligand intermolecular complex and the solvent are recorded in the computer memory as the first set of coordinates, e) the solvent parameters are added to the target coordinate set based on the explicit solvent accounting model and the coordinates of all atoms of the target molecule and the solvent are recorded in the computer memory as a second set of coordinates, f) the solvent parameters are added to the coordinate set of the ligand molecule based on the explicit solvent accounting model and the coordinates of all atoms of the ligand molecule and the solvent are recorded in the computer memory as a third coordinate set, g) using the coordinates of the atoms of the intermolecular target-ligand complex and the solvent obtained in step (d), determine the motion paths of all atoms of the target molecule and the ligand molecule interacting with each other, taking into account the presence of solvent molecules by solving Newton or Lagrange equations taking them into account thermal movement; after reaching the thermal equilibrium atoms in the system under consideration, the coordinates of all atoms of the target molecule, ligand molecule and solvent molecules are recorded on the information carrier a specified number of times at certain intervals; h) using the coordinates of the atoms of the target molecule and the solvent obtained in step (e), determine the trajectories of all interacting atoms of the target molecule, taking into account the presence of solvent molecules by solving the Newton or Lagrange equations taking into account their thermal motion; after reaching the thermal equilibrium atoms in the system under consideration, the coordinates of all atoms of the target molecule and solvent molecules are recorded on the information carrier a specified number of times at certain intervals; i) using the coordinates of the atoms of the ligand molecule and the solvent obtained in stage (e), determine the trajectories of all interacting with each other atoms of the ligand molecule, taking into account the presence of solvent molecules by solving the Newton or Lagrange equations taking into account their thermal motion; after reaching the thermal equilibrium atoms in the system under consideration, the coordinates of all atoms of the ligand molecule and solvent molecules are recorded on the information carrier a specified number of times at certain intervals, j) for each coordinate set of the target-ligand intermolecular complex in the solvent recorded in step (g), all atoms are divided into groups, using a computer program that reads from the computer's memory the first set of atomic coordinates of the target-ligand intermolecular complex, including the coordinates of the atoms of the target molecule, ligand molecule and solvent, calculate the distance from the atoms of the ligand molecule to each atom of the target molecule and solvent and sort all the atoms of the first sets so that the first group includes all the atoms of the ligand molecule, as well as the atoms of the target molecule and solvent atoms, the distances from which to each of the atoms of the ligand molecule do not exceed a specified value, and the second group includes all other atoms of the molecule target and solvent k) for each set of coordinates of the target molecule in the solvent recorded in step (h), all atoms of the second set are sorted so that the same atoms of the target molecule are included in the first group of atoms, which are included in the first group of atoms formed on step (k), and the second group includes all the remaining atoms of the target molecule and all the atoms of the solvent, and the first and second groups of atoms include the same atoms of the solvent molecules that are included in the corresponding groups of atoms formed in step (k), m) for each set of coordinates of the ligand molecule — in the solvent recorded in step (s), all atoms of the third set are sorted so that the first group of atoms includes all atoms of the ligand molecule and those atoms of the solvent molecules that are in the first a group of atoms formed in step (k), and the second group includes all other atoms of the solvent molecules, m) using the sets of coordinates of the atoms of the first and second groups formed in step (k), sets of input files for calculating the intermolecular target-ligand complex in the solvent are formed using the appropriate simulation program so that the atoms of the first group with their nuclei and electrons are modeled by the methods of quantum mechanics, and the atoms of the second group mentioned are modeled by the methods of classical mechanics, o) form using sets of coordinates of atoms of the first and second groups formed in step (l), sets of input files for calculating a target molecule in a solvent using an appropriate simulation program so that the atoms of the first group with their nuclei and electrons are modeled by quantum mechanics, and the atoms of the second group mentioned are modeled by classical mechanics, o) form using sets of coordinates of atoms of the first and second groups formed in step (m), sets of input files for calculating a ligand molecule in a solvent using an appropriate simulation program so that the atoms of the first group with their nuclei and electrons are modeled by methods quantum mechanics, and the atoms of the second group mentioned are modeled by classical mechanics, p) on the basis of the physicochemical properties of the corresponding molecules, the charge states of various groups of atoms of the target molecule and the ligand molecule in the solvent are determined and, in accordance with this, additional atoms are added or removed in the corresponding places of the target molecule and the ligand molecule, C) determine the total charge of the target molecule, the total charge of the ligand molecule and the total charge of the intermolecular complex of the target ligand, r) modify the sets of input files for calculating the intermolecular target-ligand complex, calculating the target molecule and calculating the ligand molecule, taking into account the coordinates of the corresponding atoms, their type, as well as the full charges and multiplicity of these molecules, s) the solvent parameters in an implicit model, in which using the coordinates of the atoms of the target molecule, the ligand molecule and the solvent molecules, the coordinates of which are included in the corresponding input files modified in step (t) form the coordinates of points located on the surface accessible to the solvent, which covers the target molecule, the ligand molecule and solvent molecules, or covers only the target molecule and the sol in the case of calculating the target molecule in the solvent, or encompasses only the ligand molecule and solvent molecules in the case of calculating the ligand molecule in the solvent, and using these points, a mathematical model of the implicit accounting of the solvent is formed, and these sets of input files are written to the storage medium calculation of the intermolecular complex of the target ligand, the target molecule and the ligand molecule using the appropriate simulation program, f) for each file from the set of input files for calculating the intermolecular target-ligand complex formed in step (y), calculate the total energy of the target-ligand intermolecular complex in the solvent using the appropriate simulation program; calculate the average value of the total energy of the intermolecular target-ligand complex in the solvent according to the results of calculations using all input files from the set of input files for calculating the intermolecular target-ligand complex formed in step (y), x) for each file from the set of input files for calculating the target molecule formed in step (y), calculate the total energy of the target molecule in the solvent using the appropriate simulation program; calculate the average value of the total energy of the target molecule in the solvent according to the results of calculations using all the input files from the set of input files for calculating the target molecule formed in step (y), c) for each file from the set of input files for calculating the ligand molecule formed in step (y), calculate the total energy of the ligand molecule in the solvent using the appropriate simulation program; calculate the average value of the total energy of the ligand molecule in the solvent according to the results of calculations using all the input files from the set of input files for calculating the ligand molecule formed in step (y), h) using the average total energies of the target-ligand intermolecular complex in the solvent, the target molecules in the solvent and the ligand molecules in the solvent obtained in steps (f), (x) and (c), respectively, the enthalpy of binding of the ligand molecule is calculated with a target molecule in a solvent, as the difference between the average value of the total energy of the target-ligand intermolecular complex in the solvent, on the one hand, and the sum of the average values of the total energies of the target molecule in the solvent and the ligand molecule in the solvent, etc. goy side. 26. The method according to p. 25, characterized in that the vibrational frequencies of the ligand molecule, the target molecule and the intermolecular complex of the target ligand are calculated, and the entropy of binding of the ligand molecule to the target molecule in the solvent is calculated using these frequencies. 27. The method according to p. 25 or 26, characterized in that, using the atomic weights and atomic coordinates of the ligand molecule, the target molecule and the intermolecular target-ligand complex, the entropy of binding due to the loss of each of these three rotational and three translational molecules is calculated degrees of freedom when bundling them into a complex. 28. The method according to p. 25 or 27, characterized in that, using the properties of the solvent molecules and the coordinates of the atoms of the target molecule, the ligand molecule and the intermolecular target-ligand complex, the cavitation binding energy is calculated as the difference in the cavitation energy of solvation of the intermolecular target-complex ligand, on the one hand, and the sum of the cavitation energy of solvation of the target molecule and the ligand molecule separately, on the other hand, and the cavitation energy of solvation is calculated as free energy, which is necessary to create an empty cavity in the solvent, the shape of which coincides with the shape of the soluble molecule. 29. The method according to p. 28, characterized in that, using the enthalpy and entropy of binding of the ligand molecule to the target molecule in the solvent and the value of the cavitational binding energy, calculate the free binding energy of the ligand molecule with the target molecule in the solvent. 30. A method for predicting the binding of a ligand molecule to a target molecule, comprising the steps of: a) receive the structure and composition of the target molecule; b) receive the structure and composition of the ligand molecule; c) record data on the structure and composition of the target molecule and the ligand on the storage medium in the appropriate format; d) select simulation parameters for use in a program for simulating the interaction between a target molecule and a ligand, wherein said simulation program implements a method for quantum-mechanical modeling of binding of ligand molecules to target molecules in a solvent according to claim 1 or a molecular-dynamic method of quantum-mechanical modeling according to item 21; e) read said recorded data and process them with at least one processor using said program for modeling interaction between a target molecule and modeling, f) by means of the aforementioned quantum-mechanical simulation of the binding of ligand molecules to target molecules in a solvent, simulation results are obtained in the form of numerical data characterizing the intensity of binding of the ligand molecule to the target molecule and the obtained numerical data are recorded on the information carrier; g) carry out real chemical measurements of quantities characterizing the intensity of the binding of the said molecules to each other; h) compare the data obtained in the measurements in step (g) with the simulation results obtained in step (e); i) in the event of a discrepancy between the calculated and measured target and ligand exceeding the specified value, the modeling parameters used by the program simulating the interaction between the target molecule and the ligand are corrected; j) repeat steps (d) - (i) until the discrepancy between the values calculated in step (e) and measured in step (g), characterizing the binding of molecules to each other, becomes less than a predetermined value; k) repeat steps (a) - (k) for another pair of target molecules and a ligand; m) repeat steps (a) - (l) until, for each new pair of molecules, the difference between the measured and calculated values characterizing the binding of the molecules to each other is less than a predetermined value with the modeling parameters obtained in steps (a) - (l) for other pairs of molecules, and write the final values of the simulation parameters on the information carrier; m) use the modeling parameters of the binding of the ligand molecule to the target molecule created in steps (a) - (m) to predict, by computer simulation, the ligand molecules that bind in the best way to the target molecule.

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