The Partition Coefficient (?)

Lipophilicity is often referred to as the preference of a drug to dissolve in a lipid phase, such as a cell membrane in relation to an aqueous phase. Therefore polar substituents such as alcohols, amides, ketones, ethers or various ionised groups reduce lipophilicity, moving equilibrium concentrations towards the aqueous phase, and vice-versa for non-polar groups such as aryl, alkyl, chloro and bromo etc. In ideal experim ental conditions lipophilicity would be measured directly as a "partition coefficient, P " (see below) betw een the m embrane phospholipid bilayer and water. U nfortunately this is not experimentally possible, due to the fragile nature of the phospholipid bilayers making them very difficult to handle. The lipid phase is replaced by an organic solvent, which is not

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however, as accurate since bulk phase organic solvents do not posses the structure and order that cell membranes consist of. Many different solvent systems have been used, including those o f octanol/water, hexane/water, cyclohexane/w ater and various other alkane/water systems, chloroform/water, 6\-n -butylether/water and many more.^83 The most popular solvent system used is the octanol/water system since octanol is reported to closely mimic the properties of membrane lipids, since it consists o f a long hydrocarbon chain that contains a functional group with H-bond accepting and donating characteristics. The proposition of other solvent systems, such as those mentioned above, are of use when diffusion is particularly difficult, e.g. into the central nervous system (CNS). This difficulty of penetrating the CNS, which is often referred to as the blood-brain barrier, uses a combined figure from octanol/water and cyclohexane/water.284-285 However, the octanol/water solvent system, despite the system's popularity, is clearly a very poor representation o f a reality where the lipid bilayer has ordered hydrocarbon chains (mentioned above), charged head groups and contains cholesterol, protein, and some water. The hydrophobic character (see section 2.3.2 for further explanation) has been measured experimentally by testing the drug's relative distribution in the octanol/water mixture. Lipophilic compounds tend to dissolve in the octanol layer of this two phase system and in contrast, the hydrophilic drugs prefer the aqueous layer.

The relative distribution of the drug is referred to as the partition coefficient (P) and is obtained from the following equation:

Concentration of drug in octanol P = _____________________________

Concentration of drug in aqueous solution g q j

The partition coefficient P , thus simply expresses the ratio o f monomeric, neutral solute concentrations in the organic and aqueous phase o f the two com ponent system under equilibrium conditions. Since P is a quantity w ith no dim ensions, any units of concentration are appropriate. Lipophilic compounds, will tend to have a high P value in comparison to hydrophilic compounds, thus by convention, the organic phase is given as the numerator, so that a positive value for log P reflects a preference for a lipid phase, and

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a negative value reflects a relative affinity for water. The determination of P , quite often poses practical problems, particularly in the case of polar or highly lipophilic solutes. Impurity and instability of the solute can also produce unreliable data. Thus precautions are taken in order to provide an acccurate measurement (as much as possible) of P, which include presaturation of the phases, the use of low solute concentrations, centrifugation for a proper separation of the phases, and the determination of solute concentration in both phases.^83’ 286 ^ should also be noted that the partition coefficient is not very sensitive to changes in temperature if the phases employed are quite immiscible in each other. In this sense, octanol-water makes a good reference system. Various workers have indicated that in the tem perature range 0-25 ^C, log P varies about 0.005 to 0.01 units/degree.286 Therefore, partitioning at room temperature without temperature control is believed to be sufficient for most purposes.

SAR carried out by varying substituents based on the lead compound, cetiedil, resulted in the synthesis and submission for pharmacological testing, a series o f analogues with different P values. Plotting P values against biological activity o f these compounds, clarifies whether or not a relationship between these two properties exist. P values usually cover several factors of ten, so the use of logarithms (logio) enabling the use of more manageable numbers is incorporated, and hence lipophilicity is often expressed in terms of log P and by the same token, biological activity when plotted in this thesis, has been expressed as -log IC50 (where IC5 0, (as mentioned above) is the concentration of a drug (in |iM ) that causes 50% inhibition of a defined level of activity), and negative logarithmic values are used since the logarithmic values when calculated in molar concentrations are negative, thus the negative values are incorporated for convenience.

It should be noted that the distribution function D, is a useful parameter related to the partition coefficient, P, and the two parameters are unfortunately sometimes interchanged in the literature. The partition coefficient, P as mentioned above is a constant and refers to

a single molecular species partitioning between two phases. By contrast, the distribution

coefficient, D, can be thought of as an effective (or apparent) partition coefficient which varies with pH when ionisation of basic or acidic drugs are considered. Experimentally, the distribution coefficient D, mathematically converted to log D for the same reasons as

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those for conversion of P to log P above, may be measured with a buffered aqueous phase, usually at pH 7.4, the pH of many biological fluids, e.g. plasma. Log D and log P

can be related by pKg using the following formula:

log D = log P - log (l+lOPK^a PH)

Eq. 2

One limitation to this mathematical approach is that it assumes that ionized drug does not enter the organic phase. This assumption is considered an approximation since counter-ion effects from the buffer can be observed with log D m easurements. In addition, the synthetic technique o f phase transfer catalysis is capable o f taking ion pairs from an aqueous phase into a nonpolar organic solvent. As a consequence, the lipophilicity of drugs may behave non-ideally with respect to pH. However, on a quantitative scale, this effect would be small, since the partitioning ability of an un-ionised drug will be much more than for an ionised one, unless the drug happens to be very highly ionised or lipophilic. In the pH region where a substance is unionised, D = P, and the substance is usually maximally partitioning in the organic phase. However, as pH is changed (increased for weak acids or decreased for weak bases), the substance ionises causing redistribution between the two phases, resulting in more substance shifting to the aqueous phase.^^^’^^^ To conclude, log P refers to the neutral species and log D refers to the ratio o f total concentrations of ionised and unionised species across both phases.