## Calculations Based on Surface Area

In 1949, Collander [42] showed that for solutes of a similar structure (homologous series, similar hydrogen bond donating, or accepting properties) logP for a solute in one solvent, e.g., octanol, could be related to its logP in another solvent, e.g., chloroform, by a linear equation as shown in Eq. (11).

logPoctanoi = a + b logFchloroform (11)

Collander relationships have often been invoked to estimate logP values in one system from values measured in another.

In 1978, Dunn and Wold [43] analyzed data for 26 solutes in 6 different solvent systems by principal components analysis, and established that there are two fundamental components which contribute to the partition coefficient. They suggested that one component is associated with the chain length in homologous series and may be a mo lar volume or surface area effect, while the second is clearly the result of a polar interaction between solute and solvent.

In discussing the concept of "hydrophobic bonding", Hermann in 1972 suggested and later found a linear relationship between solubility of hydrocarbons in water, and the surface area of the cavity they form [44]. Earlier, in 1971, Lee and Richards had introduced the concept and showed how to calculate "solvent accessible surface area" (SASA) to describe quantitatively the relationship of proteins to solvent [45], The SASA was defined as the area of the surface traced out by the center of a probe sphere, representing a water molecule, as it moves around the solute molecule, just touching its van der Waals surface. In 1974, Chothia [46] found linear relationships between SASA and free energy changes for the solvent transfer of protein residue side chains. In 1976, Yalkowsky and Valvani calculated SASA to estimate partition coefficients of hydrocarbons [47].

Following on from these studies, Moriguchi and coworkers [48] in 1985 made use of SASA (SA) together with empirical correction terms for polar moieties (SH), to core-late with logP for 138 miscellaneous compounds with a correlation coefficient of 0.995! In Eq. (12), note that since SA is the total surface area (but not including hydrogen atoms) and not the hydrophobic area, the 5„ parameter implies both a correction for hydrophilic surface area, and the effect of specific hydration of the polar moiety. The method was able to reproduce differences of logP between geometrical isomers, not calculable by other means. It therefore opened the way to the calculation of a logP for different conformations.

In 1987, Dunn and coworkers [49, 50] made a highly significant contribution by defining the possible structure of hydrated complexes of solute molecules containing polar groups. They then measured an isotropic surface area, ISA, as the SASA associated with the nonpolar portion of the hydrated solute, and as a separate parameter, the SASA associated with the hydrated surface area was calculated and expressed as a fraction, f(HSA) being the ratio of hydrated surface area and total surface area of the hydrated solute molecule. Principal component analysis on the logP values of 69 solutes in 6 solvent systems extracted two factors explaining almost all variance in partitioning, and these factors were proposed to be ISA and f(HSA). Linear regression equations were then developed to estimate logP in each solvent system. Interestingly, the coefficient in the ISA term was the same for each solvent system, the coefficient in the f(HSA) term differed considerably for each system, but was not statistically significant in predicting octanol/water or ether/water logP! This led to the suggestion that in these particular solvents, the solute may partition as the hydrated molecule. This suggestion is most reasonable, in the light of recent studies on the so-called "water-dragging" effect of many solutes, which can increase the concentration of water in the nonpolar phase at equilibrium [51].

Camilleri and coworkers in 1988 [52] explored the possibility of using surface area to predict partition, and considered over 200 benzene derivatives containing a variety of substituents and functional groups, such as alkyl, hydroxyl, alkoxyl, amino, ester, ketone, etc. They chose to use the Connolly surface of the molecule [53], which is also obtained by rolling a sphere over the solute surface, but which is defined as the sum of contact and re-entrant surfaces, the re-entrant surface being the inner surface of the solvent probe as it comes in contact with two or more atoms of the solute. Each molecule was considered as a combination of fragments defined as, e.g., aromatic hydrocarbon, saturated hydrocarbon chain, OH group, NH2 or NH group, carbonyl group, etc. The regression Eq. (13) was solved, to find coefficients a„ where An values are the measured surface areas of the various components of the molecule:

For interpolative prediction of logP, Eq. (13) was deemed as accurate as the CLOGP program. Moreover, it is clearly applicable to different conformations, especially those involving a shielding of certain parts of a molecule from solvent interaction. When applied to predict logP for paracyclophane (Fig. 2), for example, CLOGP gives a value of 5.79, whereas a value of 4.83 was calculated by the Camilleri method, compared with experimental measurements of 4.33 by "shake-flask" and 4.61 by HPLC. Whereas the Camilleri method is clearly applicable to different conformations, it was parameterized using conformationally rigid compounds, to avoid any problem of having to estimate conformation, and to avoid making the invalid assumption that structures do not change their conformation on passing from one phase to another.

In 1991, Kantola and coworkers presented an atom-based parameterization, using atomic contributions to surface area, Sh atomic numbers, N, and net charges Aqh associated with each atom and with the molecule in a defined conformation [54]. They thereby computed a conformationally dependent lipophilic quantity, p, which is only equal to the macroscopic property, logP, if only one conformer (or a rigid compound) is involved in each phase. For Eq. (14), parameters, a,/?,y were obtained by regression analysis on a set of 90 rigid compounds:

Considering all compounds, containing carbon, nitrogen, oxygen, halogen, and hydrogen atoms and by using AMl-computed geometries and charges, a quite reasonable correlation coefficient of 0.92 was achieved.

CHo-CHq

CHo-CHq

### CH2-CH2 Figure 2. Paracyclophane

The next advance to be made in computing conformationally dependent lipophilic-ities will involve a determination of thepopulation of each conformation in both phases. Partition coefficients will then need to be computed by summation over all conformations. Some progress towards this goal has been made by Richards and coworkers who in 1992 developed the HYDRO program [55]. This program is intended to compute logP for conformationally flexible molecules, but has so far been tested on only a few uncharged linear dipeptides. The method is the first to consider explicitly the effects of the population of accessible conformational minima in both phases. The partition coefficient for each dipeptide was calculated from the energy change on moving the relevant gas phase conformations into water and into octanol. These energies were calculated by using solvation contributions based upon solvent accessible surface area, and two sets of empirical parameters, the initial gas phase conformations being generated by systematic search, molecular mechanics.

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