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5.8.2 Free energies of transfer

The standard free energy of transfer of a solute between two phases is given by

octanol phase and thus partitioning is more complex than with an anhydrous solvent, but perhaps its usefulness stems from the fact that biological membranes are also not simple anhydrous lipid phases. While octanol is favoured, other alcohols have also been used. For example, isobutanol has been used to show that the binding of many drugs to serum protein is determined by the hydrophobicity or lipophilicity of the drug, following the relationship log K = °.9 log Pisobutanol + constant (5.39)

where K is an equilibrium constant measuring the binding of solute to protein. Transfer of a hydrophobic drug from an aqueous phase to a protein is, of course, a type of partitioning.

The correlation of lipophilicity and biological activity usually involves equations of the type log c = A log P + constant

In a homologous series, P can be measured and the increase in its value observed for each substituent group (for example, —CH2—). As the chain length of nonpolar aliphatic compounds increases, it has been found that P increases by a factor of 2-4 per methylene group. The substituent contributions to P are additive, so a substituent constant, nX, may be defined as where PX is the partition coefficient of the derivative of the parent compound whose partition coefficient is PH and nX is the logarithm of the partition coefficient of the function X. For example, nCl can be obtained by subtracting log Pbenzene from log Pchlorobenzene.

5.8.3 Octanol as a nonaqueous phase

Octanol is often used as the nonaqueous phase in experiments to measure the partition coefficient of drugs. Its polarity means that water is solubilised to some extent in the where C is the concentration required to produce a given pharmacological response.

5.9 Biological activity and partition coefficients: thermodynamic activity and Ferguson's principle

As the site of action of many biologically active species is in lipid components such as membranes, correlations between partition coefficients and biological activity were found early on by investigators of structure-action relationships. For example, a wide range of simple organic compounds can exert qualitatively identical depressant actions (narcosis) on many simple organisms. Lack of any chemical specificity in the compounds tested led to the suggestion that physical, rather than chemical, properties governed the activity of the compounds. Early work by Meyer and Overton related narcotic potency to the oil/ water partition coefficient of the compounds concerned, and in a later re-interpretation of the data, it was concluded that narcosis n commences when any chemically nonspecific substance has attained a certain molar concentration in the lipids of the cells.

In 1939 Ferguson placed the OvertonMeyer theory on a more quantitative basis by applying thermodynamics to the problem of narcotic action. By expressing compound potency in terms of thermodynamic activity, rather than concentration, he avoided the problem of there being various distribution coefficients between the numerous different phases within the cell, any of which might be the phase in which the drug exerted its pharmacological effects (the biophase). The fact that the narcotic action of a drug remains at a constant level while a critical concentration of drug is applied, decreasing rapidly when administration of the drug is stopped, indicates that an equilibrium exists between some external phase and the biophase.

According to equation (3.49) the chemical potentials in two phases at equilibrium are equal. Thus, from equation (3.52),

If the standard states are identical, consequently the activities will be equal in the two phases. The activity of a substance in the biophase at equilibrium is thus identical to the readily determined value in an external phase.

For narcotic agents applied as a vapour, the standard state can be taken to be the saturated vapour, and thus activity a = pt/ps where pt is the partial pressure of the vapour and ps is the saturated vapour pressure at the same temperature. When the narcotic agent was applied in solution and was also of limited solubility, activity was equated with the ratio St/S0 where St is the molar concentration of the narcotic solution and S0 its limiting solubility; the ratio St /S0 therefore represents proportional saturation. This is in contrast to the normal procedure of taking the standard state as an infinitely dilute solution.

From recalculations of published data and also from measurements of the potency of many different compounds, Ferguson concluded that, within reasonable limits, substances present at approximately the same proportional saturation (that is with the same thermodynamic activity) in a given medium have the same biological potency. For example, Table 5.17 shows that while the bactericidal concentrations against Bacillus typhosus vary widely (0.0022-3.89 mol dm 3), the thermo-dynamic activities vary within a relatively restricted range (0.11-0.76).

As with most physicochemical theories there may be problems in applying the equations to real life. If an attempt is made to correlate hydrophobicity with the rate of

Table 5.17 Bactericidal concentrations and activities of organic

substances in solutiona

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