Partition coefficient

In the physical sciences, a partition coefficient or distribution coefficient is the ratio of concentrations of a compound in a mixture of two immiscible solvents at equilibrium. This ratio is therefore a comparison of the solubilities of the solute in these two liquids. The partition coefficient generally refers to the concentration ratio of un-ionized species of compound, whereas the distribution coefficient refers to the concentration ratio of all species of the compound.
In the chemical and pharmaceutical sciences, both phases usually are solvents. Most commonly, one of the solvents is water, while the second is hydrophobic, such as 1-octanol. Hence the partition coefficient measures how hydrophilic or hydrophobic a chemical substance is. Partition coefficients are useful in estimating the distribution of drugs within the body. Hydrophobic drugs with high octanol-water partition coefficients are mainly distributed to hydrophobic areas such as lipid bilayers of cells. Conversely, hydrophilic drugs are found primarily in aqueous regions such as blood serum.
If one of the solvents is a gas and the other a liquid, a gas/liquid partition coefficient can be determined. For example, the blood/gas partition coefficient of a general anesthetic measures how easily the anesthetic passes from gas to blood. Partition coefficients can also be defined when one of the phases is solid, for instance, when one phase is a molten metal and the second is a solid metal, or when both phases are solids. The partitioning of a substance into a solid results in a solid solution.
Partition coefficients can be measured experimentally in various ways or estimated by calculation based on a variety of methods.
If a substance is present as several chemical species in the partition system due to association or dissociation, each species is assigned its own K_ow value. A related value, D, does not distinguish between different species, only indicating the concentration ratio of the substance between the two phases.

Nomenclature

Despite formal recommendation to the contrary, the term partition coefficient remains the predominantly used term in the scientific literature.
In contrast, the IUPAC recommends that the title term no longer be used, rather, that it be replaced with more specific terms. For example, partition constant, defined as
where K_D is the process equilibrium constant, represents the concentration of solute A being tested, and "org" and "aq" refer to the organic and aqueous phases respectively. The IUPAC further recommends "partition ratio" for cases where transfer activity coefficients can be determined, and "distribution ratio" for the ratio of total analytical concentrations of a solute between phases, regardless of chemical form.

Partition coefficient and log ''P''

The partition coefficient, abbreviated P, is defined as a particular ratio of the concentrations of a solute between the two solvents, specifically for un-ionized solutes, and the logarithm of the ratio is thus log P. When one of the solvents is water and the other is a non-polar solvent, then the log P value is a measure of lipophilicity or hydrophobicity. The defined precedent is for the lipophilic and hydrophilic phase types to always be in the numerator and denominator respectively; for example, in a biphasic system of n-octanol and water:
To a first approximation, the non-polar phase in such experiments is usually dominated by the un-ionized form of the solute, which is electrically neutral, though this may not be true for the aqueous phase. To measure the partition coefficient of ionizable solutes, the pH of the aqueous phase is adjusted such that the predominant form of the compound in solution is the un-ionized, or its measurement at another pH of interest requires consideration of all species, un-ionized and ionized.
A corresponding partition coefficient for ionizable compounds, abbreviated log P ^I, is derived for cases where there are dominant ionized forms of the molecule, such that one must consider partition of all forms, ionized and un-ionized, between the two phases. M is used to indicate the number of ionized forms; for the -th form the logarithm of the corresponding partition coefficient,, is defined in the same manner as for the un-ionized form. For instance, for an octanol–water partition, it is
To distinguish between this and the standard, un-ionized, partition coefficient, the un-ionized is often assigned the symbol log P⁰, such that the indexed expression for ionized solutes becomes simply an extension of this, into the range of values.

Distribution coefficient and log ''D''

The distribution coefficient, log D, is the ratio of the sum of the concentrations of all forms of the compound in each of the two phases, one essentially always aqueous; as such, it depends on the pH of the aqueous phase, and log D'' = log P for non-ionizable compounds at any pH. For measurements of distribution coefficients, the pH of the aqueous phase is buffered to a specific value such that the pH is not significantly perturbed by the introduction of the compound. The value of each log D is then determined as the logarithm of a ratio—of the sum of the experimentally measured concentrations of the solute's various forms in one solvent, to the sum of such concentrations of its forms in the other solvent; it can be expressed as
In the above formula, the superscripts "ionized" each indicate the sum of concentrations of all ionized species in their respective phases. In addition, since log D'' is pH-dependent, the pH at which the log D was measured must be specified. In areas such as drug discovery—areas involving partition phenomena in biological systems such as the human body—the log D at the physiologic pH = 7.4 is of particular interest.
It is often convenient to express the log D in terms of P^I, defined above, thus covering both un-ionized and ionized species. For example, in octanol–water:
which sums the individual partition coefficients, and where indicates the pH-dependent mole fraction of the -th form in the aqueous phase, and other variables are defined as previously.

Example partition coefficient data

The values for the octanol-water system in the following table are from the Dortmund Data Bank. They are sorted by the partition coefficient, smallest to largest, and are presented with the temperature at which they were measured.

Component	log P_OW	T
Acetamide	−1.16	25
Methanol	−0.81	19
Formic acid	−0.41	25
Diethyl ether	0.83	20
p-Dichlorobenzene	3.37	25
Hexamethylbenzene	4.61	25
2,2',4,4',5-Pentachlorobiphenyl	6.41	Ambient

Values for other compounds may be found in a variety of available reviews and monographs. Critical discussions of the challenges of measurement of log P and related computation of its estimated values appear in several reviews.

Applications

Pharmacology

A drug's distribution coefficient strongly affects how easily the drug can reach its intended target in the body, how strong an effect it will have once it reaches its target, and how long it will remain in the body in an active form. Hence, the log P of a molecule is one criterion used in decision-making by medicinal chemists in pre-clinical drug discovery, for example, in the assessment of druglikeness of drug candidates. Likewise, it is used to calculate lipophilic efficiency in evaluating the quality of research compounds, where the efficiency for a compound is defined as its potency, via measured values of pIC₅₀ or pEC₅₀, minus its value of log P.

Pharmacokinetics

In the context of pharmacokinetics, the distribution coefficient has a strong influence on ADME properties of the drug. Hence the hydrophobicity of a compound is a major determinant of how drug-like it is. More specifically, for a drug to be orally absorbed, it normally must first pass through lipid bilayers in the intestinal epithelium. For efficient transport, the drug must be hydrophobic enough to partition into the lipid bilayer, but not so hydrophobic, that once it is in the bilayer, it will not partition out again. Likewise, hydrophobicity plays a major role in determining where drugs are distributed within the body after absorption and, as a consequence, in how rapidly they are metabolized and excreted.

Pharmacodynamics

In the context of pharmacodynamics, the hydrophobic effect is the major driving force for the binding of drugs to their receptor targets. On the other hand, hydrophobic drugs tend to be more toxic because they, in general, are retained longer, have a wider distribution within the body, are somewhat less selective in their binding to proteins, and finally are often extensively metabolized. In some cases the metabolites may be chemically reactive. Hence it is advisable to make the drug as hydrophilic as possible while it still retains adequate binding affinity to the therapeutic protein target. For cases where a drug reaches its target locations through passive mechanisms, the ideal distribution coefficient for the drug is typically intermediate in value ; in cases where molecules reach their targets otherwise, no such generalization applies.

Environmental science

The hydrophobicity of a compound can give scientists an indication of how easily a compound might be taken up in groundwater to pollute waterways, and its toxicity to animals and aquatic life. Partition coefficient can also be used to predict the mobility of radionuclides in groundwater. In the field of hydrogeology, the octanol–water partition coefficient K_ow is used to predict and model the migration of dissolved hydrophobic organic compounds in soil and groundwater.