Molecular connectivity derivatives

Once the 3D strucmre of a molecule and all the parameters required for the atomic and molecular connectivities are known, the energy of the system can be calculated via Eqs. (l)-(3). First derivatives of the energy with respect to position allow for determination of the forces acting on the atoms, information that is used in the energy minimization (see Chapter 4) or MD simulations (see Chapter 3). Second derivatives of the energy with respect to position can be used to calculate force constants acting on atoms, allowing the determination of vibrational spectra via nonnal mode analysis (see Chapter 8). 

On the basis of simple considerations of connected motifs, Michael Leviff and Cyrus Chothia of the MRC Laboratory of Molecular Biology derived a taxonomy of protein structures and have classified domain structures into three main groups a domains, p domains, and a/p domains. In ct structures the core is built up exclusively from a helices (see Figure 2.9) in p structures the core comprises antiparallel p sheets and are usually two P sheets packed... 

Therefore, for estimates of Kioc s it is more feasible to use compound class-specific LFERs. These include correlations of log Kioc with molecular connectivity indices (or topological indices for an overview see Gawlik et al., 1997), with log Cf (L) (analogous to Eq. 7-11), and with log Kiow. Although molecular connectivity indices or topological indices have the advantage that they can be derived directly from the structure of a chemical, they are more complicated to use and do not really yield much better results than simpler one-parameter LFERs using C (L) or Kmv/ as compound descriptors. 

Molecular Connectivity-AHvb Relationship Kier and Hall [14] derived the following relationship for alkanes (C2-C16) ... 

The correlation between aqueous solubility and molar volume discussed by McAuliffe [5] for hydrocarbons, and the importance of the cavity term in the solvatochromic approach, indicates a significant solubility dependence on the molecular size and shape of solutes. Molecular size and shape parameters frequently used in quantitative structure-water solubility relationships (QSWSRs) are molecular volume and molecular connectivity indices. Moriguchi et al. [33] evaluated the following relationship to estimate Cw of apolar compounds and a variety of derivatives with hydrophilic groups ... 

Meylan et al. (1992) described another attempt to extend MCI-Koc relationships to polar compounds. This method uses the first order molecular connectivity index (Jy) and a series of statistically derived fragment contribution factors for polar compounds. To develop the model, they performed two separate regression analyses. The first related log Koc to for... 

To derive these equations, log P (hydrophobic parameter), MR (molar refrac-tivity index), and MV (molar volume) were calculated using software freely available on the internet (wwwlogP.com, www.daylight.com). The first-order valence molecular connectivity index of substituents was calculated as suggested by Kier and Hall [46,47]. In these equations, is cross-vahdated obtained by the leave-one-out jackknife procedure. Its value higher than 0.6 defines the good predictive ability of the equation. The different indicator variables in these equations were defined as follows. 

These are truly structural descriptors because they are based only on the two-dimensional representation of a chemical structure. The most widely known descriptors are those that were originally proposed by Randic (173) and extensively developed by Kier and Hall (27). The strength of this approach is that the required information is embedded in the hydrogen-suppressed framework and thus no experimental measurements are needed to define molecular connectivity indices. For each bond the Ck term is calculated. The summation of these terms then leads to the derivation of X, the molecular connectivity index for the molecule. 

Molecular connectivity indices were first proposed by Randic in 1975 (16) as a means of estimating physical properties of alkanes. This formalism was quickly extended to other types of molecules (17) and, since then, a wide range of indices has been proposed, as reviewed by Hall and Kier (18) and Randic (19). The indices are derived from a graph theoret-... 

Molecular Connectivity. A class of molecular descriptors derived from the connection table of a structure. For increasing path lengths (1-, 2-, 3-bonds, etc.), the molecular connectivity values are computed as the sum of functions of the connectivity values (number of attachments) of the atoms in the path. Molecular connectivity descriptors can be used to distinguish structures. As such, they can be correlated with physicochemical properties that are functions of structure size, linearity, and degree of branching. 

A convenient point of departure is that of the increasingly popular quantitative structure activity relationships (QSAR) mentioned above [696,699,11], which derive adsorbate-adsorbent interaction indices from, for example, water solubility data, molecular connectivities [697], n-octanol-water partition coefficients, reversed-phase liquid chromatography capacity factors [723], or linear solvation energy relationships (LSER). 

The relationship between the retention behavior of benzodiazepine, sulfamides, substituted anilines, barbiturates, a group of natural phenolic derivatives, diethanolamine isomers, amino acids, sulfoether, thio-alcohol, 2,4-dinitrophenylhydrazones, and their molecular connectivity indices were studied. All of the results indicate that the Rf or values are highly correlated with molecular connectivity indices. 

Wells et al. investigated a series of twenty-three 5,5-dialkylbarbituric acid derivatives by RP-HPLC on Partisil ODS and Partisil ODS-2 columns using mixtures of methanol and water in volume compositions 30 70 and 50 50. The same three molecular connectivity indices were selected d Xp in the chromatographic... 

The two-dimensional representation of a molecule considers how the atoms are connected, i.e. it defines the connectivity of atoms in the molecule in terms of the presence and nature of chemical bonds. Approaches based on the -+ molecular graph allow a two-dimensional representation of a molecule, usually known as the topological representation. Molecular descriptors derived from the algorithms applied to a topological representation are called 2D-descriptors, i.e. they are the so-called - graph invariants. 

The three-dimensional representation views a molecule as a rigid geometrical object in space and allows a representation not only of the nature and connectivity of the atoms, but also the overall spatial configuration of the molecule. This representation of a molecule is called geometrical representation, and molecular descriptors derived from this representation are called 3D-descriptors. Examples of 3D-descrip-tors are -> geometrical descriptors, several -> steric descriptors, and -+ size descriptors. 

Kier, L.B. and Hall, L.H. (1981). Derivation and Significance of Valence Molecular Connectivity. 

Melkova, Z. (1984). Utilization of the Index of Molecular Connectivity in the Study of Antitumor Activity of a Group of Benzo(c)fluorene Derivatives. Cesk.Farm., 33,107. 

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