Partition coefficient

Not to be confused with distribution constant.

In the physical sciences, a partition-coefficient (P) or distribution-coefficient (D) is the ratio of concentrations of a compound in a mixture of two immiscible phases at equilibrium. These coefficients are a measure of the difference in solubility of the compound in these two phases.

In the chemical and pharmaceutical sciences, the two phases are often restricted to mean two immiscible solvents. In this context, a partition coefficient is the ratio of concentrations of a compound in the two phases of a mixture of two immiscible liquids at equilibrium. Normally one of the solvents chosen is aqueous while the second is hydrophobic such as 1-octanol. Hence both the partition and distribution coefficient are measures of how hydrophilic ("water-loving") or hydrophobic ("water-fearing") 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 preferentially distributed to hydrophobic compartments such as the lipid bilayers of cells while hydrophilic drugs (low octanol/water partition coefficients) preferentially are found in aqueous compartments such as blood serum.

If one of the solvents is a gas and the other a liquid, the "gas/liquid partition coefficient" is the same as the dimensionless form of the Henry's law constant. 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 used when one or both solvents is a solid (see solid solution).

The term "partition coefficient" is now considered obsolete by IUPAC, and "partition constant", "partition ratio", or "distribution ratio" are all more appropriate terms that should be used.

Partition coefficient and log P (logP)

The partition coefficient is a ratio of concentrations of un-ionized compound between the two liquid phases. The logarithm of the ratio of the concentrations of the un-ionized solute in the solvents is called log P: When one of the solvents is water and the other is a non-polar solvent, then the log P value is also known as a measure of lipophilicity. For example, in an octanol-water system:

• $\log \ P_{\rm {oct/wat}}=\log {\Bigg (}{\frac {{\big [}{\rm {{solute}{\big ]}_{\rm {octanol}}^{\rm {un-ionized}}}}}{{\big [}{\rm {{solute}{\big ]}_{\rm {water}}^{\rm {un-ionized}}}}}}{\Bigg )}$

In the first approximation, the non-polar phase is usually dominated by the electrically neutral un-ionized form of the solute. 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 is also un-ionized.

Generalization to ionized forms of the solute

In cases where the strong dominance of un-ionized form in the non-polar phase is no longer ensured, or where greater precision is required, one must also consider partition of all ionized forms between the two phases. Let M indicate the number of ionized forms. For the I-th form (I = 1,...,M) the logarithm of the corresponding partition coefficient log P^I is defined in the same manner as for the un-ionized form; e.g., in octanol-water:

• $\log \ P_{\rm {oct/wat}}^{\rm {I}}=\log {\Bigg (}{\frac {{\big [}{\rm {{solute}{\big ]}_{\rm {octanol}}^{\rm {I}}}}}{{\big [}{\rm {{solute}{\big ]}_{\rm {water}}^{\rm {I}}}}}}{\Bigg )}$

For consistency, the "ordinary" (i.e., un-ionized) partition coefficient is often assigned the symbol log P⁰ and the index I is extended to span the 0,...,M range.

Distribution coefficient and log D (logD)

The distribution coefficient is the ratio of the sum of the concentrations of all forms of the compound (ionized plus un-ionized) in each of the two phases. As such, it depends on pH. For measurements of distribution coefficient, 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 logarithm of the ratio of the sum of concentrations of the solute's various forms in one solvent, to the sum of the concentrations of its forms in the other solvent is called log D:

• $\log \ D_{\rm {oct/wat}}=\log {\Bigg (}{\frac {{\big [}{\rm {{solute}{\big ]}_{\rm {octanol}}^{\rm {ionized}}+{\big [}{\rm {{solute}{\big ]}_{\rm {octanol}}^{\rm {un-ionized}}}}}}}{{\big [}{\rm {{solute}{\big ]}_{\rm {water}}^{\rm {ionized}}+{\big [}{\rm {{solute}{\big ]}_{\rm {water}}^{\rm {un-ionized}}}}}}}}{\Bigg )}$

In the above formula, superscript "ionized" indicates the sum of concentrations of all ionized species in a respective solvent. In addition, since log D is pH dependent one must specify the pH at which the log D was measured. Of particular interest is the log D at pH = 7.4 (the physiological pH of blood serum).

For non-ionizable compounds, log D = log P at any pH.

Relationship to log P (logP)

For aqueous - non-polar solvent systems it is often convenient to express the logarithm of the distribution coefficient in terms of the partition coefficients of un-ionized (P⁰) and ionized (P^I) forms rather than individual concentrations; see the definitions above. For example, in octanol-water:

$\log \ D_{\rm {oct/wat}}=\log {\Bigg (}\sum _{I=0}^{M}f^{I}P_{\rm {oct/wat}}^{I}{\Bigg )}$

where $f^{I}$ indicates the pH-dependent molar fraction of the I-th form (of the solute) in the aqueous phase. Please note that individual partition coefficients, not their logarithms appear under the summation!

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.

LogP is one criterion used in medicinal chemistry to assess the druglikeness of a given molecule, and used to calculate lipophilic efficiency, a function of potency and LogP that evaluate the quality of research compounds. For a given compound lipophilic efficiency is defined as the pIC₅₀ (or pEC₅₀) of interest minus the LogP of the compound.

Pharmacokinetics

In the context of pharmacokinetics (what the body does to a drug), the distribution coefficient has a strong influence on ADME properties of the drug. Hence the hydrophobicity of a compound (as measured by its distribution coefficient) 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 (a process known as transcellular transport). 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 (what a drug does to the body), 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 (e.g., intracellular), 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. Therefore the ideal distribution coefficient for a drug is usually intermediate (not too hydrophobic nor too hydrophilic).

Consumer products

Many other industries take into account distribution coefficients for example in the formulation of make-up, topical ointments, dyes, hair colors and many other consumer products.

Agrochemicals

Hydrophobic insecticides and herbicides tend to be more active. Hydrophobic agrochemicals in general have longer half lives and therefore display increased risk of adverse environmental impact.

Metallurgy

In metallurgy, the partition coefficient is an important factor in determining how different impurities are distributed between molten and solidified metal. It is a critical parameter for purification using zone melting, and determines how effectively an impurity can be removed using directional solidification, described by the Scheil equation.

Environmental

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 used to predict the mobility of radionuclides in groundwater.

Distribution coefficients may be measured or predicted for compounds currently causing problems or with foresight to gauge the structural modifications necessary to make a compound environmentally more friendly in the research phase.

In the field of hydrogeology, the octanol-water partition coefficient, or K_ow, is used to predict and model the migration of dissolved hydrophobic organic compounds in soil and groundwater.

Measurement

Shake flask (or tube) method

Two phase system, hydrophobic (top) and hydrophilic (bottom) for measuring the partition coefficient of compounds.

The classical and most reliable method of log P determination is the shake-flask method, which consists of dissolving some of the solute in question in a volume of octanol and water, then measuring the concentration of the solute in each solvent. The most common method of measuring the distribution of the solute is by UV/VIS spectroscopy. There are a number of pros and cons to this method:

Pros:

• Most accurate method
• Accurate for broadest range of solutes (neutral and charged compounds applicable)
• Chemical structure does not have to be known beforehand.

Cons:

• Time-consuming (>30 minutes per sample)
• Octanol and water must be premixed and equilibrated (takes at least 24 hours to equilibrate)
• Complete solubility must be attained, and it can be difficult to detect small amounts of undissolved material.
• The concentration vs. UV-Vis response must be linear over the solute's concentration range. (See Beer-Lambert law)
• If the compound is extremely lipophilic or hydrophilic, the concentration in one of the phases will be exceedingly small, and thus difficult to quantify.
• Relative to chromatographic methods, large amounts of material are required.

As an alternative to UV/VIS spectroscopy other methods can be used to measure the distribution, one of the best is to use a carrier free radiotracer. In this method (which is well suited for the study of the extraction of metals) a known amount of a radioactive material is added to one of the phases. The two phases are then brought into contact and mixed until equilibrium has been reached. Then the two phases are separated before the radioactivity in each phase is measured. Using an energy dispersive detector (such as a high purity germanium detector) allows the use of several different radioactive metals at once, whereas the simpler gamma ray detectors only allow one radioactive element to be used in the sample.

If the volume of both of the phases are the same then the math is very simple.

For a hypothetical solute (S)

D or P = radioactivity of the organic phase / radioactivity of the aqueous phase

D or P = [S_organic]/[S_aqueous]

In such an experiment using a carrier free radioisotope the solvent loading is very small, hence the results are different from those obtained when the concentration of the solute is very high. A disadvantage of the carrier free radioisotope experiment is that the solute can adsorb to the surfaces of the glass (or plastic) equipment or at the interface between the two phases. To guard against this the mass balance should be calculated.

It should be the case that:

radioactivity of the organic phase + radioactivity of the aqueous phase = initial radioactivity of the phase bearing the radiotracer

For nonradioactive metals, it is possible in some cases to use ICP-MS or ICP-AES. Sadly ICP methods often suffer from many interferences that do not apply to gamma spectroscopy hence the use of radio-tracers (counted by gamma ray spectroscopy) is often more straightforward.

HPLC determination

A faster method of log P determination makes use of high-performance liquid chromatography. The log P of a solute can be determined by correlating its retention time with similar compounds with known log P values.

Pros:

• Fast method of determination (5-20 minutes per sample)

Cons:

• The solute's chemical structure must be known beforehand.
• Since the value of log P is determined by linear regression, several compounds with similar structures must have known log P values.
• Different chemical classes will have different regression parameters, hence extrapolations to other chemical classes (applying a regression equation derived from one chemical class to a second chemical class) are not reliable.

Electrochemical methods

In the recent past some experiments using polarized liquid interfaces have been used to examine the thermodynamics and kinetics of the transfer of charged species from one phase to another. Two main methods exist.

• ITIES, Interfaces between two immiscible electrolyte solutions, which, for example, has been used at Ecole Polytechnique Fédérale de Lausanne.
• Droplet experiments, which have been used by Alan Bond, Frank Marken, and the team at the Ecole Polytechnique Fédérale de Lausanne. Here a reaction at a triple interface between a conductive solid, droplets of a redox active liquid phase and an electrolyte solution have been used to determine the energy required to transfer a charged species across the interface.

Prediction

Quantitative structure-property relationship (QSPR) algorithms (many of which have been evaluated in a recent review) calculate log P in several different ways:

• Atomic based prediction (atomic contribution; AlogP, XlogP, MlogP, etc.)

A conventional method for predicting log P is to parameterize the distribution coefficient contributions of various atoms to the over-all molecular partition coefficient, which produces a parametric model. This parametric model can be estimated using constrained least-squares estimation, using a training set of compounds with experimentally measured partition coefficients. In order to get reasonable correlations, the most common elements contained in drugs (hydrogen, carbon, oxygen, sulfur, nitrogen, and halogens) are divided into several different atom types depending on the environment of the atom within the molecule. While this method is generally the least accurate, the advantage is that it is the most general, being able to provide at least a rough estimate for a wide variety of molecules.

• Fragment based prediction (group contribution; ClogP, etc.)

It has been shown that the log P of a compound can be determined by the sum of its non-overlapping molecular fragments (defined as one or more atoms covalently bound to each other within the molecule). Fragmentary log P values have been determined in a statistical method analogous to the atomic methods (least squares fitting to a training set). In addition, Hammett type corrections are included to account of electronic and steric effects. This method in general gives better results than atomic based methods, but cannot be used to predict partition coefficients for molecules containing unusual functional groups for which the method has not yet been parameterized (most likely because of the lack of experimental data for molecules containing such functional groups).

• Data mining prediction

A typical data mining based prediction uses support vector machines, decision trees, or neural networks. This method is usually very successful for calculating log P values when used with compounds that have similar chemical structures and known log P values.

• Molecule mining prediction

Molecule mining approaches apply a similarity matrix based prediction or an automatic fragmentation scheme into molecular substructures. Furthermore there exist also approaches using maximum common subgraph searches or molecule kernels.

• Predicting log P from log S

If the solubility of an organic compound is known or predicted in both water and 1-octanol, then you can estimate log P as $\log P=\log S_{o}-\log S_{w}$

• Approximate estimation of log D (at a given pH) from log P and known mole fraction of the un-ionized form, $f^{0}$, in the case where partition of ionized forms into non-polar phase can be neglected:

  $\log D\cong \log P+\log \left(f^{0}\right)$

  • approximate expressions valid for monoprotic acids and bases only:

  $\log D_{\text{acids}}\cong \log P+\log \left[{\frac {1}{(1+10^{pH-pK_{a}})}}\right]$

  $\log D_{\text{bases}}\cong \log P+\log \left[{\frac {1}{(1+10^{pK_{a}-pH})}}\right]$

  • further approximations for when the compound is largely ionized:

  ${\text{for acids with }}{\big (}pH-pK_{a}{\big )}>1,\log D_{\text{acids}}\cong \log P+pK_{a}-pH$

  ${\text{for bases with }}{\big (}pK_{a}-pH{\big )}>1,\log D_{\text{bases}}\cong \log P-pK_{a}+pH$

  • further approximation when the compound is largely un-ionized:

  $\log D\cong \log P$

• Prediction of pK_a

  For prediction of pK_a, which in turn can be used to estimate log D, Hammett type equations have frequently been applied. See for a recent review of newer methods.

Some octanol-water partition coefficient data

The given values are sorted by the partition coefficient. Acetamide is hydrophilic and 2,2',4,4',5-pentachlorobiphenyl is lipophilic.

• $\log \ P_{\rm {OW}}=\log \ P_{\rm {octanol/water}}$

Component	log POW	T (°C)
Acetamide	-1.16	25
Methanol	-0.82	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 Sangster Research Laboratories' 1989 publication

Limitations

Log P is not an accurate determinant of lipophilicity for ionizable compounds because it only correctly describes the partition coefficient of neutral (uncharged) molecules. Taking the example of drug discovery we see how the limitations of log P can affect research. Since the majority of drugs (approximately 80%) are ionizable, log P is not an appropriate predictor of a compound's behaviour in the changing pH environments of the body. The distribution coefficient (Log D) is the correct descriptor for ionizable systems. Alternatively, use may be made of the apparent partition coefficient, which is defined as follows: (true partition coefficient) x (fraction of the drug that is unionised). Clearly, if the drug is 100% un-ionized then P_apparent = P_true.

See also

• Blood–gas partition coefficient
• Cheminformatics
  • ADME
  • Lipinski Rule of 5
  • Druglikeness
  • Lipophilic Efficiency
  • QSAR
• Distribution law
• ITIES
• Ionic partition diagram
• Chemicalize.org:List of predicted structure based properties

External links

There are many logP calculators or predictors available both commercially and for free.

• Chemistry Development Kit
• JOELib
• BioByte ClogP/Bio-Loom
• ACD/LogP DB a commercial application that calculates LogP values and includes the largest commercially available database of experimental logP values with calculation of Rule-of-5 parameters
• ACD/LogP Freeware Download the free logP calculator
• Simulations Plus - S+logP an application for calculating logP with high accuracy
• ALOGPS Free online calculations and comparison of 10 logP methods
• Molecular Property Explorer
• Free online logP calculations using ChemAxon's Marvin and Calculator Plugins - requires Java
• miLogP free logP and Rule of Five calculator by Molinspiration
• an overview of on-line WWW resources for logP and other PhysProp calculations
• PreADMET Web-based logP/logS and ADME/Tox prediction program
• XLOGP3 an online and standalone logP calculator (including rule-of-5). Free for academy and available for PubChem Compound.