Fragmental constant

The obvious drawback of this method is that the parent solute, at least, has to be available or must be synthesized, and its log P value has to be determined experimentally. Nys and Rekker therefore developed a method known as the fragmental constant approach, which is based on the additivity of fragment contributions to the molecular lipophilidty [7] (see Eq. (9), where a( is the inddence of fragment i, fi the lipophilic fragment constant, Ci a corredion factor, and the frequency of Cm). 

In order to obtain the fragmental constants, sets of molecules for which experimental log P values are available are cut into the predefined fragments and the numerical contribution of each fragment is determined by multiple hnear regression analysis. 

The correction term in Eq. (9) shows that the basic assumption of additivity of the fragmental constants obviously does not hold true here. Correction has to be appHed, e.g., for structural features such as resonance interactions, condensation in aromatics or even hydrogen atoms bound to electronegative groups. Astonishingly, the correction applied for each feature is always a multiple of the constant Cu, which is therefore often called the magic constant . For example, the correction for a resonance interaction is +2 Cj, or per triple bond it is -1 A detailed treatment of the Ef system approach is given by Mannhold and Rekker [5]. 

Rekker, R. E. The Hydrophobic Fragmental Constant Its Derivation and Application with a Means of Characterizing Membrane Systems, Elsevier, Amsterdam, 1977. 

With only few exceptions, most log P programs refer to the octanol-water system. Based on Rekker s fragmental constant approach, a log P calculation for aliphatic hydrocarbon-water partitioning has been reported [96]. Another more recent approach to alkane-water log P and log D is based on the program VolSurf [97]. It is believed that these values may offer a better predictor for uptake in the brain. 

Mannhold, R., Rekker, R. F. The hydrophobic fragmental constant approach for calculating log P in octanol/ water and aliphatic hydrocarbon/water systems. Perspect. Drug Discov. Des. 2000, 18,1-18. 

Nys, G. G., Rekker, R. F. Statistical analysis of a series of partition coefficients with special reference to the predictability of folding of drug molecules. Introduction of hydrophobic fragmental constants (/-values). Chim. Therap. 1973, 8, 521-535. 

Rekker, R. F., Mannhold, R. Calculation of Drug Lipophilicity. The Hydrophobic Fragmental Constant Approach, VCH, Weinheim, 1992. 

The HINT method [49-51] refers to the idea of Abraham and Leo [52] that hydro-phobic fragment constants, reduced to atomic values, could be used to evaluate interactions between small and large molecules. The interaction energy term by scores atom-atom interactions ij) within or between the molecules using the following equation ... 

As mentioned before, the hydrophobicity and the partition coefficient can be related to the solubility of the solutes in water (also see Section 15.8.4). The partition coefficient (P) between octanol and water can be described as the 7r-constant of Hansch or the logP values of Rekker. The logP values calculated from the fragmental constant are then used for the optimization of RPLC. However, this method is not adequate to develop an optimization system for the mixtures of different types of compounds [71]. 

Various methods by which the Kow of PAHs could be calculated are based on their molecular structures, i. e., a quantitative structure-property relationship (QSPR) approach [ 1,199,200]. One of the most famous techniques involves summation of hydrophobic fragmental constants (or f-values) for all groups in a molecule of a specific compound. On the other hand, Aboul-Kassim [1] and Aboul-Kassim et al. [202, 203] introduced a modeling technique based on the molecular connectivity indices of various PAHs, ranging from low- to high-molecular weight compounds. More details are given in Chap. 4 of this volume. 

Fragment constant The partition coefficient is expressed as the sum of its component fragments log P=([jj an-fn where (a) is the number of fragment (f) of type (n) in the molecule Adjustment for steric effects, bond type and different interactions gives a complex calculation usually accomplished with computer software... 

Lipophilicity in particular, as reflected in partition coefficients between aqueous and non-aqueous media most commonly water (or aqueous buffer) and Z-octanol,has received much attention [105,141,152,153,176,199,232,233]. Logic )W for the octanol-water system has been shown to be approximately additive and constitutive, and hence, schemes for its a priori calculation from molecular structure have been devised using either substituent tt values or substructural fragment constants [289, 299]. The approximate nature of any partition coefficient has been frequently emphasized and, indeed, some of the structural features that cause unreliability have been identified and accommodated. Other complications such as steric effects, conformational effects, and substitution at the active positions of hetero-aromatic rings have been observed but cannot as yet be accounted for completely and systematically. Theoretical statistical and topological methods to approach some of these problems have been reported [116-119,175,289,300]. The observations of linear relationships among partition coefficients between water and various organic solvents have been extended and qualified to include other dose-response relationships [120-122,160,161,299-302]. 

Rekker RF (1977) The hydrophobic fragmental constant. Elsevier, Amsterdam/New York, NY, 220 pp... 

The measurement of the solubility of drugs in polar and non-polar media is very important in the pharmaceutical field. One method proposed to describe this solubility is the partition coefficient between octanol and water. The mathematical calculation of an octanol-water partition coefficient from values for functional groups was first proposed by Hansch et al. as Hansch s n constants,1 and was later developed by Rekker as hydrophobic fragmental constants (logP).2 This method was further improved by the use of molecular connectivities.17 The prediction of logP values can be performed by either a computer program or by manual calculation. For example, approximate partition coefficients (log P) have been calculated by Rekker s method ... 

A part of his fragmental constant tables is given in Table 6.1. (The predicted log P values are summarized in Table 6.4.)... 

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