Annotation of the results obtained in 2023
1. The second stage of developing a three-dimensional version of the RSDFT method for calculating the structural and thermodynamic parameters of solvation and complex formation of molecules of arbitrary shape and size, including complex biomolecules containing hundreds and thousands of atoms, was performed, namely, the methodology developed on the basis of molecular-atomic formalism was expanded to systems with a large number of particles. The methodology uses a dual representation of free energy functionals - through atomic density and solvent-induced intermolecular interaction potential, as well as a special procedure for renormalization to the intramolecular structure factor. The corresponding software package has been modified. 2. The algorithms developed during the first year of the project for calculating the constant and binding energy of the protein-ligand complex in a limited region of the hydration shell and the parameterized functional of the free energy of solvation (hydration) were implemented to the software package. 3. The developed method was tested using the example of a target protein, drug ligand compounds, protein-ligand complexes in an aqueous solution (protein is tyrosine phosphatase PTP1B; ligand compounds are 2HB1 and 2QBP). The following features of the biomolecule hydration and the formation of protein-ligand complexes have been established: 3.1. It was shown that the ligands and PTP1B protein in the unbound and bound states are well hydrated. Upon binding, ligands undergo significant dehydration compared to the protein. At the same time, the first hydration shell of the complex contains almost the same number of water molecules as the bound protein, which is due to the partial “collectivization” of water molecules by the protein and ligand in the complex. The fact of insignificant dehydration of the protein during its transition to the bound state is confirmed by a slight decrease in the solvent-accessible surface area. It has been established that the domain of the protein binding site, when the protein in complex with the ligand, is also well hydrated. When a protein binds to a ligand, the domain is partially dehydrated, which is caused by the displacement of some water molecules from the active site region by the ligand. 3.2. It was found that both ligands are completely “immersed” in the active site domain of the protein. In this case, most of the amino acid residues of the domain, near which the ligand is located, belong to the active site loops (P-loop, pTyr-loop, WPD-loop and Q-loop). In the studied complexes in the active site region of PTP1B, possible H-bonds between the active site and water, the ligand and water, the active site and the ligand were determined, including, in the latter case, with the participation of “bridging” water molecules. Using the parameterized solvation free energy functional, the binding free energy for the complexes was calculated, the values of which are in satisfactory agreement with the experimental ones. From the data obtained, it follows that the 2QBP ligand has a greater affinity for PTP1B compared to 2HB1, and, therefore, is more preferable as an inhibitor for this protein. 4. The verification assessment of the results obtained showed that the proposed method makes it possible to successfully describe in detail and at the same time holistically the structure of the biomolecule hydration shell. The method gives the possibilities for spatial representation of their nearest environment with the determination of the solvent localization near their polar and non-polar regions, as well as the quantitative estimation of their hydration using hydration numbers and the number of H-bonds. The method makes it possible to find the location of “internal” water molecules that provide stabilization of the structure of the protein and protein complexes and to describe the features of protein hydration and its binding to ligands in its active site region. The use of a parameterized solvation free energy functional allows one to increase significantly the accuracy of calculating the binding free energy of protein to ligands. The above allows us to assert the effectiveness of the new proposed approach for studying the solvation and complex formation of molecules with arbitrary shape and size, including complex biomolecules containing hundreds and thousands of atoms. The results of the project for the 2nd year of its implementation were presented in three oral reports at the following conferences: VII Congress of Russian Biophysicists, Krasnodar, Russia, April 17-23, 2023 (http://rusbiophysics.ru/db/conf.pl?cid=1&lang=ru&div=9); 38th International Conference on Solution Chemistry (38ICSC), Belgrade, Serbia, July 9-14, 2023 (https://icsc2023.pmf.uns.ac.rs/); XXXV Symposium “Modern Chemical Physics”, Tuapse, Russia, September 18-28, 2023 (https://www.chemicalphysics.ru/) and published in articles: S.E. Kruchinin, G.N. Chuev, M.V. Fedotova, Journal of Molecular Liquids 384 (2023) 122281; https://doi.org/10.1016/j.molliq.2023.122281, Q1, IF = 6.0; 2) S.E. Kruchinin, M.V. Fedotova, E.E. Kislinskaya, G.N. Chuev, Biophysics, 2003, V. 68, N 5, P. 837-849. DOI: 10.31857/S0006302923050010, Q4, K3, IF = 0.205; G.N. Chuev, S.E. Kruchinin, M.V. Fedotova, Investigation of biomolecular solvation by classical site density functional theory (The 7th Congress of Biophysicists of Russia - conference proceedings). Biophys Rev (2023) V. 15, N 5. P. 169 (S5.310). https://doi.org/10.1007/s12551- 023-01150-w, Q1, IF = 9.8 (Scopus)

 

Publications

---

Annotation of the results obtained in 2022
1. A new method for calculating the parameters of hydration (hydration free energy) and binding (binding constant and binding free energy) of a protein-ligand complex has been developed, which makes it possible to perform calculations in a limited region of the hydration shell of the complex (near the binding site of the ligand to the protein). The technique ensures the implementation of the task of increasing the speed of calculations. On the basis of the developed technique, a numerical algorithm was created and implemented in our own 3D-RISM program. 2. The developed method was tested on the example of protein-ligand complexes in an aqueous solution (protein is tyrosine phosphatase PTP1B; ligand compounds are 2HB1 and 2QBP). Additional testing was also carried out on a large protein complex such as hACE2 protein - S-protein of the SARS-CoV-2 virus. For of these complexes, the binding free energies were obtained both in the framework of the traditional method of calculation over the entire hydration shell, and in the framework of the new method of calculation in a limited region of the hydration shell. It is shown that, in comparison with the traditional method, the use of the new method reduces the speed of calculations and the amount of RAM several times, which confirms its effectiveness. 3. Using the developed method, the following features of the formation of protein-ligand complexes were established. 3.1. It has been shown that the formation of PTP1B-2HB1 / 2QBP complexes occurs directly, without the participation of binding, "bridging" water molecules. The protein amino acid residues responsible for its binding to ligands have been established. 3.2. For the hACE2–S protein complex of SARS-CoV-2, it was found that interfacial water molecules strongly interact with the RBD domain of the S protein, as well as with subunits of the N-terminal peptidase domain of hACE2. It has been shown that the formation of the complex occurs with the participation of binding, “bridging” water molecules, which distinguishes the (hACE2–S-protein)aq system from the (PTP1B–2HB1)aq and (PTP1B–2QBP)aq systems. It has been established that strong H-bonds are formed between SARS-CoV-2 and hACE2, which suggests that “bridging” water molecules play a significant role in stabilizing the hACE2–SARS-CoV-2 S-protein complex. The results are published in the article: https://doi.org/10.3390/molecules27030799 Q1, IF = 4.927 4. Comparison of the results on the hydration and binding free energies with the literature data showed that, despite the effectiveness of the developed technique, which makes it possible to multiply the calculation speed, the accuracy of the obtained characteristics is still low. Therefore, to improve the accuracy of calculations, the parametrization of the solvation (hydration) free energy functional was performed. 5. The first stage has been performed as part of the development of a three-dimensional version of the RSDFT method for calculating the structural and thermodynamic parameters of solvation and complex formation of molecules of arbitrary shape and size, including complex biomolecules. Based on the molecular-atomic formalism, a calculation methodology for low molecular weight compounds is constructed. The methodology uses a double representation of the free energy functionals i.e. through the atomic density and the intermolecular interaction potential induced by the solvent, as well as a special renormalization procedure to the intramolecular structural factor. The latter made it possible to reduce the formalism of integral RSDFT equations to integral equations of the Ornstein-Zernike type, and the mathematical task of their solution to an iterative process of solution. 6. Approbation of the 3D-RSDFT method was carried out on the example of low-molecular compounds with the number of atoms from tens to several hundreds. Structural and thermodynamic parameters of hydration of the amino acids glycine (Gly), threonine (Thr), leucine (Leu), and bovine pancreatic trypsin inhibitor protein (BPTI) were obtained. The results of the 3D-RSDFT method were verified by comparison with the results of the MD and 3D-RISM methods and literature data. The following features of hydration of biomolecules have been established. 6.1. It was determined that amino acids have a well-defined hydration layer, in which there are 17.2 water molecules in the case of Gly, 26.4 molecules in the case of Leu, 27.8 molecules in the case of Thr with their predominant location near the amino and carboxyl groups, and in the case of Thr - more and near the hydroxyl group. All amino acids are capable of H-bonding with water through hydrophilic groups. The data obtained are in good agreement with modern ideas about the structure of the hydration shell of amino acids. Estimation of the free energies of hydration of amino acids showed that methods based on the formalism of integral equations give underestimated values of ΔGhydr for Gly, Leu, Thr (on average, 2-2.5 times) compared with the MD data and literature data. 6.2. It is shown that the methods used in the study successfully reproduce the BPTI crystal structure with 4 internal water molecules in an aqueous solution. The results obtained are in good agreement with each other, as well as with the experimental X-ray diffraction data. The parameters of the 3D hydration structure (hydration shell thickness and hydration numbers) of BPTI were determined both for the entire protein and for its polar and nonpolar parts. An analysis of the results using the traditional method of determining the layer thickness from the position of the 1st minimum, rcut, of the corresponding radial distribution functions showed that an inappropriate choice of rcut can give an incorrect estimate of the layer thickness, and as a result, lead to a significant discrepancy in the hydration numbers and, thus, to an incorrect description of protein hydration. A new procedure for determining the thickness of the hydration layer of an arbitrary molecule is proposed, which is based on the idea of taking into account the properties of the hydration layer (increased relative density of the solvent in the layer and decreased at its boundaries). The proposed methodology is simple, effective, and has shown its efficiency both in methods based on the integral equations formalism and in the MD method. The procedure was successfully tested on Gly, Leu, Thr and then applied to BPTI. Using the proposed methodology, the BPTI hydration layer thickness was determined to be 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in methods based on the integral equations formalism. The proposed procedure was also applied to a more detailed description of the BPTI integral equations structure in the vicinity of positively and negatively charged radicals, as well as in the vicinity of uncharged radicals. The results are published in the article: https://doi.org/10.3390/ijms232314785; Q1, IF = 6.208. From the estimation of the hydration free energy for BPTI, it follows that the value of this value differs from the literature data by almost 3 times. 6.3. The results of 3D-RSDFT data verification show that the method gives the correct parameters of hydration structure for low molecular weight compounds, and an accurate estimation of the thermodynamic parameters of hydration requires parameterization of the solvation (hydration) free energy functional. 7. The parametrization of the solvation free energy functional was performed, based on the introduction of semi-empirical corrections into the functional, which depend on the charge and the partial molar volume of the solute molecule.

 

Publications

---