The X / System of Rekker

Nys and Rekker jn 1973 (as mentioned above), were the first to publish the hydrophobic fragmental system as a method of calculating log Poet and is still to this day , applied as a manual procedure. A data set of more than 1000 experimentally derived log Poet values of simple organic molecules was used in order to derive a list of approximately 160 fragmental values by means of regression analysis, and as a consequence this approach was labelled as "reductionistic." Nys and R ekker used f to denote the hydrophobic fragm ental constant (as mentioned before), which is the lipophilicity contribution of a constituent part of a structure to the total lipophilicity, hence this method of calculating log Poet is known as the X / system o f Rekker, and has been used in this thesis as the method of calculating log Poet values manually.

Later in 1977, Rekker ^93 further reported several calculated lipophilicities by measuring the lipophilicity of a compound from a related series of compounds, and provided means o f calculating the lipophilicity of others using fragm ental values. The use o f these fragm ental values simply involves an arithm etical subtraction or addition for each functionality that has been introduced or deleted from the molecule, with the introduction of correction factors if the altered functional groups happen to be in close proximity. The Rekker method had soon appeared to be remarkably well suitable for calculating in general, with reasonable accuracy, lipophilicities of a large range o f organic structures in the

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octanol/water system; and increase in knowledge the general principles o f the lipophilic behaviour o f functional groups as influenced by their composition, their location in a given structure, and in addition, the nature of the organic partner in the partitioning system chosen. Generally, the calculated Rekker fragmental values can be used for any structure without the necessity for measured values. Log P is thus the sum of the calculated Rekker fragmental values. However, it should be noted that these calculations do not account for the overall three-dimentional shape of a molecule. Shape may have large effects on lipophilicity since polar/lipophilic groups can bury away from the solvent or be subjected to intramolecular hydrogen bonding, which reduces polarity (see below).

Rekker and colleagues, 2 9 2 - 2 9 3 from a comprehensive library of measured values, used

statistical methods to determine the average contribution of simple fragments, such as C, CH, CH2, CH3, OH, NH2, etc. Although the atomic values for carbon and hydrogen were determined (0.15 and 0.175 respectively), the combined fragments shown above were actually used, since this eliminated the need for a branching factor. By the same token, for aromatic hydrocarbons, only combined fragments are listed; i.e. C^H^ = 1.8 6 6; C6H4 = 1.688; C^Hg = 1.431. Rekker and colleagues had very early in their work recognised the need for assigning different values for a polar fragment depending whether the carbon atom to which it was attatched was aliphatic or aromatic. "Proximity" corrections were also introduced for cases in which, for example, two polar fragments were separated by only one or two aliphatic carbons.^^^'293

Thus, Rekker based his calculation method according to equation 4 below:

n m

log P = X / = E ai/i + X kj C

i=l i=l Eq. 4

where / denotes the hydrophobic fragmental constant, and a is a num erical factor indicating the incidence o f a given fragment in that structure. Rekker reasoned that all constitutive factors could be directly attributed to a fundamental property of the structured water in the solvation shell in the aqueous phase. His method attempts to allow for both corrections (aliphatic versus aromatic and polar proximity) as a product o f a "magic constant". Cm (where Cm = 0.289) times a key number, kj, which is simply the number

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of structured water molecules involved in the structure under consideration. Rekker's "magic constant" has indeed proven to be related to a fundamental property o f structured w a te r ,293 and has been counted as a significant advance for other workers in the understanding of the solvation p r o c e s s . 2 9 6 it is important to note that a revised version of

the Rekker system became available in 1 9 9 2 and 1 9 9 5 , 2 9 4 , 3 0 3 which covers an increased

number of fragmental values and provides a better founded concept for the constant Cm; with the value now fixed at 0 . 2 1 9 . This constant has proven to be o f great importance

when concerned with restoring imbalances that occur between experimentally derived log P

values and calculations done by addition of fragmental values. It is however important to realise that the Rekker methodology gives no clear indication as to what constitutes a valid fragment, and if it could be evaluated, it would indeed be of ideal use.

It is of interest to note that computer programs based on the Rekker approach are also available. However, by the nature of the Rekker method, it cannot be fully computerised, because the breakdown of solute structure into fragments is left to human decision.