On characterization of molecular surfaces

Abstract

We consider the problem of quantitative characterization of the molecular surface. We start with a set of matrices, the elements of which give interatomic separation and higher powers of the separations. Averaged row sums of individual matrices suitably normalized give molecular profiles. The problem that we consider is how to generalize this approach to 2-dimensional and 3-dimensional objects. By using a large number of random points distributed over the molecular surface or molecular volume, respectively, we arrive at matrices from which one can extract invariants that offer a good characterization of the molecular surface and the molecular volume. It is suggested that the ratio VrS, where V and S are components of the volume and surface profile for a molecule, respectively, represents a novel shape index.* Some may think that size is a well understood concept but how is one to decide on the relative size of two molecules, one which has more atoms of smaller size and the other fewer atoms of larger size. Is molecular volume rather than the number of atoms to be a measure of size?† This avenue has not yet been much investigated.

A novel numerical model for protein sequences analysis based on spherical coordinates and multiple physicochemical properties of amino acids

“…Other properties can be employed for other purposes. [11,12] Next, we define two relative indices d ij (=PK 2ij /PK 1ij ) and h ij (=ASA ij /Hy ij ), where i and j represent the four types of amino acids (i = 1, 2, 3,4) and the index for amino acid residues within each type, respectively.…”

“…In particular, how to represent protein or DNA sequences mathematically to capture their intrinsic features is an active area of research, with statistical methods and graphical representations as two main approaches. [1][2][3][4] Compared to statistical methods, graphical representations are more intuitive and simpler to calculate. Recent studies indicate that they are useful for identification of essential genes and characterization of protein properties.…”

On representation of proteins by star-like graphs

“…Because matrix elements of D/D matrix are smaller than one, or at most equal to one, when considering higher powers of their elements there is no need to introduce appropriate normalizing factor to ensure convergence of its eigenvalues. The k D/ k D matrices were also applied to non-chain structures, such as smaller molecules, ring systems, polyhedra and molecular surfaces [53][54][55]. In these systems, the leading eigenvalue can be interpreted as a measure of the compactness of a system, because in more compact systems the Euclidean distances will be relatively small and consequently the bounds on the leading eigenvalue will be decreased, implying thus that smaller magnitudes for the leading eigenvalue will characterize more compact systems.…”

Investigation of the molecular surface area and volume: Defined and calculated by the molecular face theory

“…The research until 1996, including Connolly's dot surface,35, 36 the overlapped multiple spheres method of Gibson and Scheraga,30 the parametric representations of Duncan and Olson,37 etc., have been generally reviewed by Connolly 38. Afterward, many new approaches have also been proposed 19–26, 39–61. Pomelli et al19–21 presented the DefPOL program, which is more efficient than GEPOL62–64 to describe the solvent effects on molecular system of large size.…”