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 IUPAC has deemed the term partition coefficient is to be "obsolete," and recommends use of the most appropriate rigourous term —e.g., partition constant, defined as (K_D)_A = [A]_org / [A]_aq, where K_D is the process equilibrium constant, [A] represents the concentration of solute A being tested, and "org" and "aq" refer to the organic and aqueous phases, respectively; also recommended is "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 and log P ^I

Separatory funnel, an example of a two-phase system. A hydrophobic layer (often at top) and a hydrophilic (often at bottom) are established in special glassware (flasks or tubes) that allows shaking and sampling, from which the log P is determined. A separatory funnel is a related example of such a two-phase system, used in organic synthesis. Here such a funnel contains a yellow/golden hydrophobic layer above a clear green-tinted aqueous, hydrophilic phase; the funnel is capped, and has a valve at bottom, here partially open, for draining the lower phase.

The partition coefficient, abbreviated P, is defined as a particular ratio of the concentrations of a solute between the two solvents (a biphase of liquid phases), 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 (hereafter simply "octanol") and water:

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

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 (see following).

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 (as well as the interaction of the two equilibria, partition and ionization). M is used to indicate the number of ionized forms; for the ${\rm {I}}$-th form (${\rm {I}}$ = 1, 2, ...M) the logarithm of the corresponding partition coefficient, $\log \ P_{\rm {oct/wat}}^{\rm {I}}$, is defined in the same manner as for the un-ionized form. For instance, for an octanol-water partition, it is:

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

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 $\log \ P_{\rm {oct/wat}}^{\rm {I}}$ expression for ionized solutes becomes simply an extension of this, into the range of values ${\rm {I}}$ > 0.

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 (ionized plus un-ionized) 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:

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

In the above formula, 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 (which includes P ⁰ as state ${\rm {I}}$ = 0), thus covering both un-ionized and ionized species. For example, in octanol-water:

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

which sums the individual partition coefficients (not their logarithms), and where $f^{\rm {I}}$ indicates the pH-dependent mole fraction of the ${\rm {I}}$-th form (of the solute) in the aqueous phase, and other variables are defined as previously.

Example partition coefficient data

The values in the following table are from the Dortmund Data Bank. They are sorted by the partition coefficient, smallest to largest (acetamide being hydrophilic, and 2,2',4,4',5-pentachlorobiphenyl lipophilic), and are presented with the temperature at which they were measured (which impacts the values).

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 a variety of available reviews and monographs. Critical discussions of the challenges of measurement of log P, and related computation of its estimated values (see below), appear in several reviews.

Measurement

A number of methods of measuring distribution coefficients have been developed, including the shake-flask, reverse phase HPLC, and pH-metric techniques.

Shake flask-type methods

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.

HPLC-based methods

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.

An advantage of this method is that it is fast (5-20 minutes per sample); a disadvantage is that the solute's chemical structure must be known beforehand. Moreover, since the value of log P is determined by linear regression, several compounds with similar structures must have known log P values, and extrapolation from one chemical class to another—applying a regression equation derived from one chemical class to a second one—may not be reliable, since each chemical classes will have its characteristic regression parameters.

pH-metric techniques

The pH-metric set of techniques determine lipophilicity pH profiles directly from a single acid-base titration in a two-phase water-organic solvent system. Hence the distribution coefficients (logD) over a pH range (typically between 2 and 12) and partition coefficient (logP) (the distribution coefficient where the molecule is primarily neutrally charged) can be measured in a single experiment. This method does however require the separate determination of the pK_a value(s) of the substance.

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. The first is ITIES, Interfaces between two immiscible electrolyte ssolutions. The second is droplet experiments. 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.

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

Drug/compound permeability in brain capillaries, as a function of compound partition coefficient. Measured or computed partition coefficients correlate with behaviour important to understanding and predicting the disposition of exogenous molecules in biological systems. Plot, from Bodor and Buchwald, of a group of chemical compounds, including solvents and drugs, presenting the permeability coefficient (as log P_C) of compounds in rat brain capillaries (ordinate, units, centimeters per second), as a function of the measured octanol-water partition coefficient, (as log P, abscissa, dimensionless). The insets in the upper left and lower right quadrants represent Transport and Efflux, active processes that move compounds off the diagonal line of high correlation. (Labels are in German, but English terms are either identical or readily understandable cognates, e.g., oktanol and octanol, caffein and caffeine, wasser and water, vincristin and vincristine, etc.)

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. For cases where a drug reaches its target locations through passive mechanisms (i.e., diffusion through membranes), the ideal distribution coefficient for the drug is typically intermediate in value (neither too lipophilic, nor too hydrophilic); 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 used to predict the mobility of radionuclides in groundwater. 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.

Agrochemical research

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.

Consumer product development

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.

Computation of coefficients

In many cases of new molecules, or molecules that are experimentally challenging to handle (e.g., for their availability, properties, or toxicity), it can be useful to estimate physicochemical parameters before or instead of measuring them. Estimation can be based on a variety of methods that fall into such categories as fragment-based, atom-based, and so on (see below). In the estimation of partition coefficients, some methods rely on critical component parameters (measured or computed) such as log S and pK_a, while others are independent of all other component measurements. A further distinction between methods can be made on the degree to which they rely on empirical measurements, directly or indirectly, versus being computed de novo (or otherwise independently of empirical studies). The methods also differ in accuracy (based on comparison of computed versus experimentally measured values), and on the scope of their applicability (e.g., whether they can be applied to all molecules, or only ones similar to molecules already studied). Important computational approaches are gathered in following.

Computed component parameters

pK_a

Main article: Acid_dissociation_constant § Computational_estimation

Hammett-type approaches

Approaches based on the use of Hammett-type equations have frequently been applied to the estimation of pK_a.

log S

There are a variety of modern approaches to compute solubilities, and so log S, with varying degrees of success in relation to their predictive value.

Computed partition coefficients

Atom-based methods

A standard approach of this type, using atomic contributions, is 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 methods

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).

Knowledged-based methods

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 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.

Derivative methods

Log P from log S

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

Log D from log P and pK_a

As noted above, at $\log D\cong \log P$ for cases where the molecule is un-ionized under the conditions of interest. For other cases, estimation of log D at a given pH, from log P and the 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, can be formulated as $\log D\cong \log P+\log \left(f^{0}\right)$.

• Approximate expressions valid only for monoprotic acids and bases:
• $\log D_{\text{acids}}\cong \log P+\log \left[{\frac {1}{(1+10^{pH-pK_{a}})}}\right]$ , and $\log D_{\text{bases}}\cong \log P+\log \left[{\frac {1}{(1+10^{pK_{a}-pH})}}\right]$ .
• Further approximations for when the compound is largely ionized:
• ${\text{for acids with }}{\big (}pH-pK_{a}{\big )}>1,\log D_{\text{acids}}\cong \log P+pK_{a}-pH$, and
• ${\text{for bases with }}{\big (}pK_{a}-pH{\big )}>1,\log D_{\text{bases}}\cong \log P-pK_{a}+pH$.

See also

• Blood–gas partition coefficient
• Cheminformatics
  • ADME
  • Lipinski Rule of 5
  • Druglikeness
  • Lipophilic Efficiency
  • QSAR
• Distribution law
• ITIES
• Ionic partition diagram

Further reading

• Berthod A, Carda-Broch S (2004). "Determination of liquid-liquid partition coefficients by separation methods" (PDF). (secondary). Journal of Chromatography. a. 1037 (1–2): 3–14. doi:10.1016/j.chroma.2004.01.001. PMID 15214657.
• Comer, John; Tam, Kin (2001). "Lipophilicity Profiles: Theory and Measurement". In Testa, Bernard; van de Waterbed, Han; Folkers, Gerd; Guy, Richard (eds.). Pharmacokinetic Optimization in Drug Research: Biological, Physicochemical, and Computational Strategies. (secondary). Weinheim: Wiley-VCH. pp. 275–304. doi:10.1002/9783906390437.ch17. ISBN 978-3-906390-22-2. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)
• Hansch, Corwin; Leo A (1979). Substituent Constants for Correlation Analysis in Chemistry and Biology. (secondary). New York: John Wiley & Sons Ltd. ISBN 978-0-471-05062-9. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)
• Hill AP, Young RJ (2010). "Getting physical in drug discovery: a contemporary perspective on solubility and hydrophobicity". (secondary). Drug Discovery Today. 15 (15–16): 648–55. doi:10.1016/j.drudis.2010.05.016. PMID 20570751.
• Kah M, Brown CD (2008). "LogD: lipophilicity for ionisable compounds". (secondary). Chemosphere. 72 (10): 1401–8. doi:10.1016/j.chemosphere.2008.04.074. PMID 18565570.
• Klopman G, Zhu H (2005). "Recent methodologies for the estimation of n-octanol/water partition coefficients and their use in the prediction of membrane transport properties of drugs". (secondary). Mini Reviews in Medicinal Chemistry. 5 (2): 127–33. doi:10.2174/1389557053402765. PMID 15720283.
• Leo A, Hansch C, and Elkins D (1971). "Partition coefficients and their uses". (secondary). Chem Rev. 71 (6): 525–616. doi:10.1021/cr60274a001.
• Leo, Albert; Hoekman, DH; Hansch, C (1995). Exploring QSAR, Hydrophobic, Electronic, and Steric Constants. (secondary). Washington, DC: American Chemical Society. ISBN 978-0-8412-3060-6. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)
• Mannhold R, Poda GI, Ostermann C, Tetko IV (Mar 2009). "Calculation of molecular lipophilicity: State-of-the-art and comparison of log P methods on more than 96,000 compounds". (secondary). Journal of Pharmaceutical Sciences. 98 (3): 861–93. doi:10.1002/jps.21494. PMID 18683876.
• Martin, Yvonne Connolly (2010). "Chapter 4: The Hydrophobic Properties of Molecules". Quantitative Drug Design: A critical introduction. (secondary) (2nd ed.). Boca Raton: CRC Press/Taylor & Francis. pp. 66–73. ISBN 978-1-4200-7099-6. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)
• Pandit, Nita K. (2007). "Chapter 3: Solubility and Lipophilicity". Introduction to the Pharmaceutical Sciences. (secondary) (1st ed.). Baltimore, MD: Lippincott Williams & Wilkins. pp. 34−37. ISBN 978-0-7817-4478-2. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)
• Pearlman, Robert S.; Dunn III, William J.; Block, John H. (1986). Partition Coefficient: Determination and Estimation. (secondary) (1st ed.). New York: Pergamon Press. ISBN 978-0-08-033649-7. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)
• Rutkowska E, Pajak K, Jóźwiak K (2013). "Lipophilicity—methods of determination and its role in medicinal chemistry" (PDF). (secondary). Acta Poloniae Pharmaceutica. 70 (1): 3–18. PMID 23610954.
• Sangster, James (1997). Octanol-Water Partition Coefficients: Fundamentals and Physical Chemistry. (secondary). Wiley Series in Solution Chemistry. Vol. 2. Chichester: John Wiley & Sons Ltd. ISBN 978-0-471-97397-3. {{cite book}}: Unknown parameter |name-list-format= ignored (|name-list-style= suggested) (help)

External links

• vcclab.org. Overview of the many logP and other physical property calculators available commercally and on-line.