## Atom Based Methods

Log P calculations which have been given this heading have be proposed by Broto and his colleagues [30], by Ghose and Crippen [31] by Moriguchi and coworkers [32], by

Table 9.1. Methods of calculation of log Pncliinni/wllltl from structure

1. Substituent constants, Jt: Hansch and Fujita: log P (Ph-X) = log P (Ph-H) + Jt-X

A. Rekker and Nauta (by regression; i.e., "reductionist")

B. Pomona CLOGP ("constructionist"; i.e., greater weight give simplest analogs)

C. Moriguchi and Iwase: originally SASA + If (see 3G)

D. van de Waterbeemd (by regression; computerized)

E. Rekker and Mannhold (by regression; manual)

3. Atomic: (i.e., atoms and environment of atom-base clusters)

A. Broto and Moreau (regression, 222 variables)

B. Ghose and Crippen; later Viswanadhan (regression 120 variables)

C. Dubost and Croizet (computerized Broto and Moreau)

D. Klopman (regression 39 variables; computerized in CASE)

E. Suzuki and Kudo (groups: basic, extended an user defined)

F. King (using molecular transform index)

G. Moriguchi and Hirono: regression with 2a + HF + I

4. Molecular properties

A. Rogers and Cammarata

B. Hopfinger and Battershell (SCAP)

. C. Bodor (regression: /alk, 4th power ovality, 4th power atomic charges; total 15 parameters)

D. Kasai (regression: charge transfer + electrostatic energies)

F. Richards and Essex (log P difference by molecular dynamics)

G. Niemi and Basak (regression graph-theoretical invariant + molecular connectivity + H-bond)

H. Politzer and Brinck (SASA + electrostatic potential)

Viswanadhan et al. [33] and by many others (see Table 1). The atom in question is characterized by the "cluster" of which it is the center. Somewhere between 100 and 300 such atom-centered clusters are chosen by means of regression analysis to cover most of the structural variation encountered. As can be anticipated, the variation in the training set is crucial to the method's ability to predict entirely new structures. This method of defining "clusters" is unable to cover more than a four-bond pathway between electronically interactive pairings, and this can lead to difficulty at times. Intramolecular hydrogen bonding is also difficult to deal with [30]. Calculation by computer is available for most of these.

### 9.2.3 Methods Based on Molecular Properties

The ratio of the free energies of solvation in the two phases, water and wet octanol, ought to yield a dependable partition coefficient. An early attempt to calculate this value with quantum chemical methods was made by Rogers and Cammarata [34], fol-

progesterone log P = 3.87 CLOGP = 3.78

11 -a-hydroxyprogesterone log P = 2.36 CLOGP = 1.69

,ch3

Figure 1. Anomalies with sterically hindered hydroxyl fragments.

lowed by Hopfinger and Battershell using SCAP (solvent-dependent conformation analysis procedure) [35], It must be kept in mind that there is a demand for methods to cope with very large databases of complex structures such as antibiotics and peptides. The present calculation rate of 6000 structures per minute (CLOGP operating on an SGI INDY) is, perhaps, faster than necessary. In contrast, good quantum chemical calculations take time, and currently may be applied to only a few of the most interesting structures.

As might be expected, solvent-accessible-surface area (SASA) is a calculated molecular property which appears in most log P calculations of this type. There is good evidence that solute size is one of the primary determinants of log P [36]. Although it would seem logical to do so, there are serious pitfalls in attempting to separate SASA into two components - one hydrophobic and one hydrophilic [37]. One quite often finds a polar group in certain structural contexts in which it appears to be not as hydrophilic as usual. A prominent example is the 11-a or p substituents in steroids. When this position is unsubstituted, as in progesterone or estradiol, the calculations are normal, as seen in Fig. 1. With a hydroxyl group or carbonyl oxygen at this position, it appears that a correction of about +1.0 log units is required. Using the SASA as calculated by the SAVOL program [38], allowing for a water radius of 1.5 A, it was found that the oxygen of an ll-|3-hydroxyl group exposed only 6.46 square Angstroms (A2) to the solvent while in cyclohexanol 25.97 A2 was exposed. This lent support to the postulate that the decrease in hydrophilicity resulted from the shielding of the polar oxygen by surrounding hydrocarbon. However, this explanation fails to consider the partition equilibrium as a competing process. The oxygen in 2,6-di-sec-butylphenol exposes less than half the area to solvent, as does the oxygen in the parent phenol, but in this case the measured log P is one log units lower than calculated. It makes more sense to propose that octanol, as an H-donor, has more difficulty reaching a hindered H-acceptor than does water. Thus the decreased hydrophilicity of oxygens at the 11 position in steroids remains an anomaly.

### 9.2.4 Fragment-Based Methods

The first published fragment method of calculating log Poa was proposed in 1973 by Nys and Rekker [39-41], and is still widely applied as a manual procedure. A variation of it is available on computers. The Medchem method, developed at Pomona College and also based on the additivity of fragments, considers so many interaction factors that it is not recommended as a manual procedure but should be applied via the CLOGP program. The two methods fragment the solute structure in different ways, but each requires some knowledge of the fragment's attachment bonds before lookup in a table provided. CLOGP uses five bond types while the Rekker procedure utilizes only two. The fragment interaction factors are crucial to both, and until these are understood more fully, it is impossible to say which treatment of them can be judged superior. Therefore, the balance of this paper will focus on these common problems, which, in a different guise perhaps, are also the stumbling blocks to the proper application of atom-based procedures as well as quantum chemical methods.

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