Molecular shape analysis

Hopfinger et al. [53, 54] have constructed 3D-QSAR models with the 4D-QSAR analysis formahsm. This formalism allows both conformational flexibility and freedom of alignment by ensemble averaging, i.e., the fourth dimension is the dimension of ensemble sampling. The 4D-QSAR analysis can be seen as the evolution of Molecular Shape Analysis [55, 56]. 

Rhyn K-B, H C Patel and A J Hopfinger 1995. A 3D-QSAR Study of Anticoccidal Triazlnes Usir Molecular Shape Analysis. Journal of Chemical Information and Computer Science 35 771-778. 

With the development of accurate computational methods for generating 3D conformations of chemical structures, QSAR approaches that employ 3D descriptors have been developed to address the problems of 2D QSAR techniques, e.g., their inability to distinguish stereoisomers. The examples of 3D QSAR include molecular shape analysis (MSA) [34], distance geometry [35,36], and Voronoi techniques [37]. 

AJ Hopfinger. A QSAR investigation of dihydrofolate reductase inhibition by Baker triazmes based upon molecular shape analysis. I Am Chem Soc 102 7196-7206, 1980. 

Molecular Shape Analysis. Once a set of shapes or conformations are generated for a chemical or series of analogs, the usual question is which are similar. Similarity in three dimensions of collections of atoms is very difficult and often subjective. Molecular shape analysis is an attempt to provide a similarity index for molecular structures. The basic approach is to compute the maximum overlap volume of the two molecules by superimposing one onto the other. This is done for all pairs of molecules being considered and this measure, in cubic angstroms, can be used as a parameter for mathematical procedures such as correlation analysis. 

Hopfinger et al. (5) developed 4D-QSAR analysis which incorporates conformational and alignment freedom into the development of a 3D-QSAR model and can be viewed as the evolution of molecular shape analysis, also developed by Hopfinger (26,102) in the early 1980s. 

Hopfinger, A. J. (1981) Inhibition of dihydrofolate reductase structure-activity correlations of 2,4-diamino-5-benzylpyrimidines based upon molecular shape analysis. J. Med. Chem. 24, 818-822. 

Jokic, A., Zimpel, Z., Huang, P. M, and Mezey, P. G. (2001c). Molecular shape analysis of a Maillard reaction intermediate. SAR and QSAR Environ. Res. 12, 297-307. 

An important concern is the efficient detection of local shape changes introduced by chemical changes in remote locations of a molecule. One simple approach [20] applied a truncation method, compatible with the truncation process already used within the shape group methods for molecular shape analysis [41-44]. 

Additional advantages have been pointed out in the Introduction. Since density domains play a major role in molecular shape analysis and in the construction of various molecular similarity measures [5], shape analysis and molecular similarity can be formulated in terms of quantum-chemically defined functional groups. This model is also compatible with a rather general, algebraic-geometrical framework discussed in ref. [6]. 

S. N. Mohammad, A. J. Hopfinger, and D. R. Bickers, ]. Theor. Biol., 102, 323 (1983). Intrinsic Mutagenicity of Polycyclic Aromatic Hydrocarbons A Quantitative Structure-Activity Study Based on Molecular Shape Analysis. 

The adenosine A3 receptor antagonistic activity of these compounds have been further analyzed [104] in 3D-QSAR using molecular shape analysis (MSA) and molecular field analysis (MFA) techniques in Cerius2 (version 4.8) software [50]. hi this, Jurs atomic charge descriptors were used for the MSA study and H+ point charges and CH3 derived steric fields were used for the MFA study. In this 3D-QSAR study, MSA resulted in Eqs. 12 and 13 and MFA led to Eq. 14. 

Two important questions of molecular shape analysis are as follows ... 

Figure 2.2 Selected families (DDj(aj)) of density domains of the water molecule, as calculated with the GAUSSIAN 90 ab initio program [253] and the GSHAPE 90 molecular shape analysis program [254], using a 6-3IG basis set. There are only two topologically different types of families of density domains either a single density domain, or a family of three density domains. The sequence of topologically distinct cases provides a topological description of chemical bonding.

Figure 2.3 Some of the high density threshold density domains of the ethanol molecule, CH3CH2OH, as calculated with a 6-31G basis set, using the GAUSSIAN 90 [253] ab initio and the GSHAPE 90 [254] molecular shape analysis programs.

Within integer homology theory, sufficiently versatile for our purposes of molecular shape analysis, we consider only integers as coefficients and multiplying factors of cells and chains. 

In more general, "folded" cases, incidence numbers of higher absolute values can occur, however, these cases are irrelevant to the molecular shape analysis techniques... 

Molecular bodies of quantum mechanical electron distributions or some other molecular functions such as electrostatic potentials can be represented on various levels of approximation. These representations have two main components the physical property or model used to define a formal molecular body, and the geometrical or topological method used to describe and analyze the model. If a representation of the molecular body is selected, then the boundaries of these approximate molecular bodies can be regarded as formal molecular surfaces. Hence, the molecular shape analysis problem can be formulated as the shape analysis problem of formal molecular surfaces. 

This observation of Parr and Berk provides the basis for a simple approach to molecular shape analysis and molecular similarity analysis, described below. Although the molecular shapes, as defined by the electronic density, differ somewhat from the shapes of the nuclear potentials, their similarity can be exploited the nuclear potential contour surfaces provide a simple approximation of the shape of molecules. We shall refer to the isopotential surfaces of the nuclear potential contours as NUPCO surfaces. These surfaces have a major advantage the computation of NUPCO s is a trivially simple task as compared to the calculation of electronic densities. Furthermore, nuclear potential is a useful molecular property in its own right, without any reference to electronic density a comparison of NUPCO s of various molecules can provide a valid tool for evaluating molecular similarity. The superposition of potentials of different sets of nuclei can result in similar composite potentials, consequently, the comparison of NUPCO s is better... 

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