Research area

Voronoi-Delaunay method

 

    Geometrical ideas of G.F.Voronoi and B.N.Delaunay proved to be extremely helpful for analysis of structure and intermolecular voids. They present a method to define regions of space “assigned” to atoms (Voronoi regions) and enable to divide a system of atoms into the simplest groups (Delaunay simplexes). The base of the method was described in book N.N. Medvedev, "Voronoi-Delaunay method for non-crystalline structures". SB of Russian Academy of Science, Novosibirsk, 2000 (in Russian). Generalization of the method to atoms of different size was made in articleMedvedev et al. J. of Comput. Chem. Vol. 27, 1676, 2006. Application to the analysis of intermolecular voids can be found in :  M.G. Alinchenko et al.  Morphology of Voids in Molecular Systems. A Voronoi-Delaunay Analysis of a Simulated DMPC Membrane.  J. Phys. Chem. B, 108 (49), 19056 -19067, 2004.  The possibilities for studying the volumetric characteristics of proteins are discussed in Voloshin, V.P., et al. J. Phys. Chem. B, 2015, 119, 1881-1890. The application to the study of lipid membranes, see V. P. Voloshin, et al., Journal of Structural Chemistry 2018, 59 (1), P. 96-105. For a study of the global structure of solutions, see A.V.Anikeenko, et al. // Journal of Molecular Liquids, 2017, 245, 35-41. Some computer programs realizing the method are accessible on our website.

The method of molecular dynamics

      The Gromacs package for molecular dynamics simulation is used. The models of aqueous solutions of amphiphilic molecules, proteins, DNA, as well as lipid bilayers are studied. We use our workstations with graphics accelerators, as well as the NSU computing cluster. [можете дать ссылку на него, если есть]. The microsecond trajectories of a DNA oligomer with the attached spin labels were calculated, and the fraying of DNA oligomer chains was studied [E.D. Kadtsyn, et al. A.V. Journal of Molecular Liquids, 2016, 221, 489-496.]. 

A training course for students of the Novosibirsk State University was developed on the basis of the laboratory: A.V. Kim, N.N. Medvedev. "Molecular dynamics, practical exercises", Textbook NSU, RIC NSU, 109str. 2015, Electronic version http://str.phys.nsu.ru/md/

Packing of spheres

The model of hard spheres reflects the basic structural features of the liquid, glassy and crystalline phase, helps to understand the essence of phase transitions, crystallization, melting and amorphysation. However, the laws of the non-crystalline filling of space by balls are still not understood. We investigated the packing of hard spheres in a wide range of densities, both loose and dense, including in the vicinity of the Bernal density (64.5% of the volume occupied by balls), which is the limiting for the existence of non-crystalline packing. The results of our research are discussed in publications:  Phys. Rev. Focus (2007),  A.V. Anikeenko et al. PRE 77, 031101 (2008),   А.В.  А.В. Аникеенко, Н.Н. Медведев, ЖСХ, 2009, Том 50, №4, с. 787-794

It was shown that for dense, disordered packages, the "polytetrahedral" principle of structure organization is characteristic. However, its possibilities are exhausted when the Bernal limit is reached. Further increase in density is possible only due to a change in the principle of packaging, namely, allowing the emergence of the crystalline arrangement of spheres.

 

Cavities and intermolecular voids

 

    Analysis of empty intermolecular space gives complementary information to atom-atom structure. Some structural features of complex molecular systems can be understood easier if we study the motifs of voids in addition to the atom-atom correlation. In particular, instead of traditional atom-atom pair correlation function one can calculate a similar function for intermolecular voids: M.G. Alinchenko, et al. Journal of Structural Chemistry, Vol. 47, Supplement, pp. S119-S125, 2006. The analysis of the voids themselves is an independent task. It is convenient to use Delaunay simplices, each of which represents an elementary interatomic cavity, and any large cavity is composed of them. Delaunay simplices define interstitial spheres, through which it is possible to represent the voids in the system. In particular, G. Hantal et al. J. Chem. Phys. 133, 144702, 2010 shows the voids formed in the model particles of high-atmospheric soot.

Calculation of the partial molar volume and its components for biomacromolecules in aqueous solution

      To understand the conformational transformations of a protein occurring under the temperature or pressure influence, it is important to know how its components behave: the intrinsic, molecular volume of the protein in the solution, and the contribution from the change in the density of the hydration shell. These characteristics can now be reliably extracted from the molecular dynamics simulation. With the help of the Voronoi-Delaunay method, the solution is decomposed into regions related to the protein, to the boundary between the protein and water (solvation shell), and to pure water  [Voloshin, V. P. et al. Biophys. Chem. 2014, 192, 1–9].

For a rapid calculation of the volume of voids between molecules, a new original algorithm has been developed using a special geometric construction:  the Voronoi-Delaunay subsimplex [V.P. Voloshin, et al Trans. on Comput. Sci. XXII, LNCS 8360, pp. 156--172. Springer, Heidelberg (2014)]. As a result, it became possible to obtain reliable values of the unknown quantities, to average over a large number (thousands) of independent configurations of the molecular dynamics trajectory. Models of protein solutions are obtained and processed at different temperatures and pressures e.g. in [Voloshin, V.P. et al  J. Phys. Chem. B, 2015, 119, 1881-1890; Smolin N, at al // Phys Chem Chem Phys. 2017, 19(9):6345-6357].

Small clusters of amphiphilic molecules

      The formation of small clusters of glycyrrhizic acid (GA) molecules with the participation of cholesterol in water and in methanol, as well as dimers of the molecules of polyethylene glycols of fatty acids CnEm was studied. It was found that GA in water forms stable small clusters, while a molecule of cholesterol joins the surfaces of such a cluster. This means that GA can promote the solubility and transport of hydrophobic molecules in water according to the so-called guest-host mechanism. It is noted that the mechanism of transport of hydrophobic molecules, realized for GA, is not universal for amphiphilic molecules capable of micelle formation, it is not realized for CnEm molecules [M.V. Zelikman, et al.  // Journal of Structural Chemistry. 2016, 57 (5), pp. 940-946].

Investigation of voids and permeability of lipid membranes

      The boundary between the lipid membrane and the surrounding water (as well as between any immiscible liquids) is not a plane at the micro level. It is proposed to use, as such a boundary, the Voronoi boundary surface V. P. Voloshin, et al.// Journal of Structural Chemistry  2018, 59 (1), P. 96-105. 

It is determined by the set of Voronoi faces between the atoms of the lipids and water. Thus, profiles of various membrane characteristics, which are traditionally constructed with respect to the central plane of the membrane, can also be calculated from the boundary surface. Such profiles give new information about the distribution of atoms or voids inside the membrane, since the membranes have waves and different thicknesses.