Empirical atomic hydrophobicities

Evaluating Docked Complexes with the HINT Exponential Function and Empirical Atomic Hydrophobicities. 

E. C. Meng, I. D. Kuntz, D. J. Abraham, and G. E. Kellogg. Evaluating docked complexes with the HINT exponential function and empirical atomic hydrophobicities. Journal of Computer-Aided Molecular Design, 8 299-306, 1994. 

Fig. 5.3 Comparison of the theoretical and experimental 3D structure (ribbon representation) of the putative nitroreductase, one of the targets of CASP6 competition. The energy expression which was used in theoretical calculations takes into account the physical interactions (such as hydrogen bonds, hydrophobic interactions, etc.) as well as an empirical potential deduced from representative proteins experimental structures deposited in the Brookhaven Protein Data Bank (no bias towards the target protein), (a) Predicted by Kolinski and Bujnicki [11] by the Monte Carlo method, and (b) determined experimentally by X-ray diffraction [12]. Both structures in atomic resolution differ (r.m.s.) by 2.9A. Reproduced by courtesy of Professor Andrzej Kolinski...

The primary supposition of any toxicological QSAR is that the potency of a compound is dependent upon its molecular structure, which is typically quantified by chemical properties (Schultz et al., 2002). Chemical descriptors include a variety of types, including atom, substituent, and molecular parameters. The most transparent of these are the molecular-based empirical and quantum chemical descriptors. Empirical descriptors are measured descriptors and include physicochemical properties such as hydrophobicity (Dearden, 1990). Quantum chemical properties are theoretical descriptors and include charge and energy values (Karelson et al., 1996). Physicochemical and quantum chemical descriptors are for the most part easily interpretable with regard to how that property may be related to toxicity. The classic example of this, the partitioning of a toxicant between aqueous and lipid phases, has been used as a measure of hydrophobicity for over a century (Livingstone, 2000). 

In simulations with explicit water molecules, the hydrophobic interactions must result from a complicated interplay of Leimard-Jones and electrostatic interactions between the atoms of the proteins and the surrounding water molecules. In the case that the water is represented implicitly, the hydrophobic interactions are usually modeled by an empirical term that depends on the surface area buried on binding ... 

In most empirical scoring functions, a hydrophobic character is attributed to several atom types, with equivalent weight for all hydrophobic contributions. In a more sophisticated approach, the propensity of particular atom types to be solvent-exposed or embedded in the interior of a protein can be assessed by so-called atomic solvation parameters. These have been derived, for example, from experimental octanol/water partition coefficients (303, 304) or from protein crystal structures (305, 306). Atomic solvation parameters are used in the VALIDATE scoring function (307) and have been tested in DOCK (308). 

Examples of empirical descriptors can be considered to be the -+ Taillander index (restricted to substituted benzenes), - second-grade structural parameters (restricted to alkenes), - polar hydrogen factor (restricted to halogenated hydrocarbons), - hydrophobic fragmental constants, - six-position number, Idoux steric constant, -> hydrophilicity index, - adsorbability index, -> bond flexibility index, and -+ atomic solvation parameter. 

Empirical Equations Many investigators have developed empirical equations relating the CMC to the various structural units in surface-active agents. Thus, for homologous straight-chain ionic surfactants (soaps, alkanesulfonates, alkyl sulfates, alkylammonium chlorides, alkyltrimethylammonium bromides) in aqueous medium, a relation between the CMC and the number of carbon atoms N in the hydrophobic chain was found (Klevens, 1953) in the form... 

Many empirical equations have been developed relating CMC of surfactants to structural units in them. For homologous straight-chain ionic surfactants (soaps, alkylsul-fonates, alkylsulfates, alkylammonium chlorides and alkyltrimethyl-ammonium bromides) in aqueous medium, the following relationship between CMC and the number of carbon atoms (n) in the hydrophobic chain has been obtained (Somasundaran, 1964 Lin, 1971 Somasundaran and Fuerstenau, 1968 Bolden et al., 1983) ... 

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