Protein shape descriptors

Geometry-based approach from a geometrical point of view, a cavity is a concave empty space that can be described using 2D (surface) or 3D shape descriptors (19-21). We consider three regions in the protein environment the protein bulk, the bulk solvent and the cavity space. The protein bulk is the space filled by the protein atoms. The bulk solvent is the space outside the protein which differentiates from the space inside the protein which defines the cavity where the drug-like molecule is supposed to bind. The identification of protein pockets by numerical methods suppose the capacity to discriminate first the protein bulk from the rest... 

Morris RRJ, Najmanovich RRJ, Kahraman A et al (2005) Real spherical harmonic expansion coefficients as 3D shape descriptors for protein binding pocket and ligand comparisons. Bioinformatics (Oxford, England) 21 2347-2355... 

Leicester, S.E., Finney, J.L. and Bywater, R.P. (1994b). A Quantitative Representation of Molecular Surface Shape. 11 Protein Classification Using Fourier Shape Descriptors and Classical Scaling. J.Math.Chem., 16,343-365. 

Goldman BB, Wipke WT. QSD quadratic shape descriptors. 2. Molecular docking using quadratic shape descriptors (QSDock). Proteins Struct Funct Genet 2000 38 79-94. 

Spherical harmonics provide a parameterization of three-dimensional shape which is especially useful for protein structure description (4). Overlap volume comparisons are the basis for the Molecular Shape Analysis (MSA) method of Hopfinger (5,6). TTiis technique has been extended to include a quantification of the steric and electrostatic fields surrounding a molecule (7). A further refinement of field analysis, which merges statistical and molecular modeling techniques, is the COMparative Molecular Field Analysis method (COMFA) of Cramer (8). These latter approaches seek to encode information about more than just steric bulk or form. They express multivariate information about the structure, so they might be considered multidimensional shape descriptors. 

Using differential geometry, a curve can be reconstructed from the knowledge of its curvature and torsional functions (the Frenet-Serret formulas). Therefore, these two functions give a concise shape description, provided one associates an everywhere-differentiable curve to the molecular skeleton. This approach has been employed in the analysis of protein shape. Moreover, this technique allows one to represent the dynamics of molecular chains or loops in terms of the deformation of elastic bodies. We return to this point when we discuss a number of purely topological descriptors of molecular curves. 

Figure 4 Comparison of backbones and overcrossing spectra for ribonuclease inhibitor (IBNH) and yeast hexokinase B (2YHX). These two proteins are similar in number of amino acid residues but radically different in their folding patterns. The difference is well reflected by the shape descriptor A, . The spectra are the superposition of five randomizations of projections. See Table 1.

Figures 4 and 5 illustrate the use of these shape descriptors. As a first example, we have considered two proteins with a similar number of amino acid residues but radically different folding patterns. Figure 4 contrasts the backbone of ribonudease inhibitor ( = 456) and yeast hexokinase ( = 457). These structures are found in the Brookhaven Protein Data Bank (PDB) with the codes IBNH and 2YHX, respectively. Ribonudease inhibitor is a very unusual horseshoe-shaped protein, the first known 3D structure of a protein with a highly repetitive amino acid sequence. Table 1 gives their size and entanglement characterization in terms of Rq, A, N, andN. Protem IBNH is less compact and less entangled than 2YHX (note the smaller N and N values).

Their different folding features become more evident upon comparison of the two overcrossing spectra (i.e., the histograms of An( ) ) in the lower part of Figure 4. [These spectra superimpose five computations with various numbers of randomized projections.] Without resorting to visual inspection, the shape descriptor indicates immediately that these two proteins have no 3D folding homology. 

G. A. Arteca, Phys. Rev. E, 49, 2417 (1994). Scaling Behavior of Some Molecular Shape Descriptors of Polymer Chains and Protein Backbones. 

Also in the field of biomacromolecules, several powerful methods for conformational analysis and shape descriptors of nucleic acids and proteins have been recently developed by Lavery, who maintains the tradition of the theoretical biochemistry laboratory in Paris. 

Visual inspection on a computer screen is a widespread approach to recognizing the occurrence of systematic structural patterns in proteins [1,2]. However, there is an unavoidable bias in this rather subjective approach to assess molecular shape. On the other hand, numerical or algebraic descriptors provide an alternative description, which is more objective, since the computation of the shape descriptors can be done, in principle, in an automated way. 

In Figure 1 we present an example, which illustrates the results obtained by our procedure. The example chosen is one view of a small protein, the pancreatic Uypsin inhibitor [21,22]. The image in the left-hand side of Fig. 1 represents schematically the protein backbone, as it appears in the crystal structure. The protein has only 58 aminoacid residues. In this projection, the protein shows 12 overcrossings a simple analysis [14] gives the following shape descriptor. 

Goldman, B.B. Wipke, W.T. QSD Quadratic Shape Descriptors. 2. Molecular Docking Using Quadratic Shape Descriptors (QSDock). Proteins 2000, 3S (1), 79-94. 

D-QSAR. Since compounds are active in three dimensions and their shape and surface properties are major determinants of their activity, the attractiveness of 3D-QSAR methods is intuitively clear. Here conformations of active molecules must be generated and their features captured by use of conformation-dependent descriptors. Despite its conceptual attractiveness, 3D-QSAR faces two major challenges. First, since bioactive conformations are in many cases not known from experiment, they must be predicted. This is often done by systematic conformational analysis and identification of preferred low energy conformations, which presents one of the major uncertainties in 3D-QSAR analysis. In fact, to date there is no computational method available to reliably and routinely predict bioactive molecular conformations. Thus, conformational analysis often only generates a crude approximation of active conformations. In order to at least partly compensate for these difficulties, information from active sites in target proteins is taken into account, if available (receptor-dependent QSAR). Second, once conformations are modeled, they must be correctly aligned in three dimensions, which is another major source of errors in the system set-up for 3D-QSAR studies. 

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