In thephysical sciences, apartition coefficient (P) ordistribution coefficient (D) is the ratio ofconcentrations of acompound in a mixture of twoimmiscible solvents atequilibrium. 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 ofun-ionized species of compound, whereas the distribution coefficient refers to the concentration ratio of all species of the compound (ionized plus un-ionized).[1]
In thechemical andpharmaceutical sciences, both phases usually aresolvents.[2] Most commonly, one of the solvents is water, while the second ishydrophobic, such as1-octanol.[3] Hence the partition coefficient measures howhydrophilic ("water-loving") orhydrophobic ("water-fearing") a chemical substance is. Partition coefficients are useful in estimating thedistribution of drugs within the body. Hydrophobic drugs with highoctanol-water partition coefficients are mainly distributed to hydrophobic areas such aslipid bilayers of cells. Conversely, hydrophilic drugs (low octanol/water partition coefficients) are found primarily in aqueous regions such asblood serum.[4]
If one of the solvents is a gas and the other a liquid, a gas/liquid partition coefficient can be determined. For example, theblood/gas partition coefficient of ageneral anesthetic measures how easily the anesthetic passes from gas to blood.[5] Partition coefficients can also be defined when one of the phases issolid, for instance, when one phase is a moltenmetal and the second is a solid metal,[6] or when both phases are solids.[7] The partitioning of a substance into a solid results in asolid solution.
Partition coefficients can be measured experimentally in various ways (by shake-flask,HPLC, etc.) or estimated by calculation based on a variety of methods (fragment-based, atom-based, etc.).
If a substance is present as severalchemical species in the partition system due toassociation ordissociation, each species is assigned its ownKow value. A related value, D, does not distinguish between different species, only indicating the concentration ratio of the substance between the two phases.[citation needed]
Despite formal recommendation to the contrary, the termpartition coefficient remains the predominantly used term in the scientific literature.[8][additional citation(s) needed]
In contrast, theIUPAC recommends that the title term no longer be used, rather, that it be replaced with more specific terms.[9] For example,partition constant, defined as
(KD)A =[A]org/ [A]aq,
1
whereKD is the processequilibrium constant, [A] 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 wheretransfer activity coefficients can be determined, and "distribution ratio" for the ratio of total analytical concentrations of a solute between phases, regardless of chemical form.[9]
An equilibrium of dissolved substance distributed between a hydrophobic phase and a hydrophilic phase is established in special glassware such as thisseparatory funnel that allows shaking and sampling, from which the logP is determined. Here, the green substance has a greater solubility in the lower layer than in the upper layer.
Thepartition coefficient, abbreviatedP, is defined as a particular ratio of theconcentrations of asolute between the two solvents (a biphase of liquid phases), specifically for un-ionized solutes, and thelogarithm of the ratio is thuslogP.[10]: 275ff When one of the solvents is water and the other is anon-polar solvent, then the logP value is a measure oflipophilicity orhydrophobicity.[10]: 275ff [11]: 6 The defined precedent is for the lipophilic andhydrophilic phase types to always be in thenumerator anddenominator respectively; for example, in a biphasic system ofn-octanol (hereafter simply "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 thepartition coefficient of ionizable solutes, thepH 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 correspondingpartition coefficient for ionizable compounds, abbreviatedlogPI, is derived for cases where there are dominantionized 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).[11]: 57ff, 69f [12]M is used to indicate the number of ionized forms; for theI-th form (I = 1, 2, ... ,M) 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 symbollogP0, such that the indexed expression for ionized solutes becomes simply an extension of this, into the range of valuesI > 0.[citation needed]
Thedistribution coefficient,logD, 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 thepH of the aqueous phase, and logD = logP for non-ionizable compounds at any pH.[13][14] For measurements of distribution coefficients, the pH of the aqueous phase isbuffered to a specific value such that the pH is not significantly perturbed by the introduction of the compound. The value of eachlogD 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[10]: 275–8
In the above formula, the superscripts "ionized" each indicate the sum of concentrations of all ionized species in their respective phases. In addition, since logD is pH-dependent, the pH at which the logD was measured must be specified. In areas such as drug discovery—areas involving partition phenomena in biological systems such as the human body—the logD at the physiologic pH = 7.4 is of particular interest.[citation needed]
It is often convenient to express the logD in terms ofPI, defined above (which includesP0 as stateI = 0), thus covering both un-ionized and ionized species.[12] For example, in octanol–water:
which sums the individual partition coefficients (not their logarithms), and where indicates the pH-dependentmole fraction of theI-th form (of the solute) in the aqueous phase, and other variables are defined as previously.[12][verification needed]
The values for the octanol-water system in the following table are from theDortmund Data Bank.[15][better source needed] 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).[citation needed]
Values for other compounds may be found in a variety of available reviews and monographs.[2]: 551ff [21][page needed][22]: 1121ff [23][page needed][24] Critical discussions of the challenges of measurement of log P and related computation of its estimated values (see below) appear in several reviews.[11][24]
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.[25] Hence, the logP of a molecule is one criterion used in decision-making bymedicinal chemists in pre-clinical drug discovery, for example, in the assessment ofdruglikeness of drug candidates.[26] Likewise, it is used to calculatelipophilic efficiency in evaluating the quality of research compounds, where the efficiency for a compound is defined as itspotency, via measured values ofpIC50 orpEC50, minus its value of logP.[27]
Drug permeability in brain capillaries (y axis) as a function of partition coefficient (x axis)[28]
In the context ofpharmacokinetics (how the body absorbs, metabolizes, and excretes a drug), the distribution coefficient has a strong influence onADME properties of the drug. Hence the hydrophobicity of a compound (as measured by its distribution coefficient) is a major determinant of howdrug-like it is. More specifically, for a drug to be orally absorbed, it normally must first pass throughlipid bilayers in the intestinalepithelium (a process known astranscellular 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.[29][30] 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.
In the context ofpharmacodynamics (how the drug affects the body), thehydrophobic effect is the major driving force for the binding of drugs to theirreceptor targets.[31][32] 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.[33] 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.[citation needed]
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.[34] Partition coefficient can also be used to predict the mobility ofradionuclides in groundwater.[35] In the field ofhydrogeology, theoctanol–water partition coefficientKow is used to predict and model the migration of dissolved hydrophobic organic compounds in soil and groundwater.
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.[36]
Inmetallurgy, 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 usingzone melting, and determines how effectively an impurity can be removed usingdirectional solidification, described by theScheil equation.[6]
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.[37]
A number of methods of measuring distribution coefficients have been developed, including the shake-flask, separating funnel method, reverse-phase HPLC, and pH-metric techniques.[10]: 280
In this method the solid particles present into the two immiscible liquids can be easily separated by suspending those solid particles directly into these immiscible or somewhat miscible liquids.
The classical and most reliable method of logP determination is theshake-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.[38][39] The most common method of measuring the distribution of the solute is byUV/VIS spectroscopy.[38]
An advantage of this method is that it is fast (5–20 minutes per sample). However, since the value of logP is determined bylinear regression, several compounds with similar structures must have known logP 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 characteristicregression parameters.[citation needed]
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.[10]: 280–4 Hence, a single experiment can be used to measure the logarithms of the partition coefficient (logP) giving the distribution of molecules that are primarily neutral in charge, as well as the distribution coefficient (logD) of all forms of the molecule over a pH range, e.g., between 2 and 12. The method does, however, require the separate determination of the pKa value(s) of the substance.
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 isITIES, "interfaces between two immiscible electrolyte solutions".[41] The second is droplet experiments.[42] Here a reaction at a triple interface between a conductive solid, droplets of a redox active liquid phase and anelectrolyte solution have been used to determine the energy required to transfer a charged species across the interface.[43]
There are attempts to provide partition coefficients for drugs at a single-cell level.[44][45] This strategy requires methods for the determination of concentrations in individual cells, i.e., withFluorescence correlation spectroscopy or quantitativeImage analysis. Partition coefficient at a single-cell level provides information on cellular uptake mechanism.[45]
There are many situations where prediction of partition coefficients prior to experimental measurement is useful. For example, tens of thousands of industrially manufactured chemicals are in common use, but only a small fraction have undergone rigoroustoxicological evaluation. Hence there is a need to prioritize the remainder for testing.QSAR equations, which in turn are based on calculated partition coefficients, can be used to provide toxicity estimates.[46][47] Calculated partition coefficients are also widely used in drug discovery to optimizescreening libraries[48][49] and to predictdruglikeness of designed drug candidates before they are synthesized.[50] As discussed in more detail below, estimates of partition coefficients can be made using a variety of methods, including fragment-based, atom-based, and knowledge-based that rely solely on knowledge of the structure of the chemical. Other prediction methods rely on other experimental measurements such as solubility. The methods also differ in accuracy and whether they can be applied to all molecules, or only ones similar to molecules already studied.
Standard approaches of this type, using atomic contributions, have been named by those formulating them with a prefix letter: AlogP,[51] XlogP,[52] MlogP,[53] etc. A conventional method for predicting logP through this type of method is to parameterize the distribution coefficient contributions of various atoms to the overall molecular partition coefficient, which produces aparametric model. This parametric model can be estimated using constrainedleast-squaresestimation, using atraining set of compounds with experimentally measured partition coefficients.[51][53][54] 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.[53]
The most common of these uses agroup contribution method and is termed cLogP. It has been shown that the logP 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 logP 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 ofelectronic andsteric 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).[21]: 125ff [23]: 1–193
For cases where the molecule is un-ionized:[13][14]
For other cases, estimation of logD at a given pH, from logP and the knownmole fraction of the un-ionized form,, in the case where partition ofionized forms into non-polar phase can be neglected, can be formulated as[13][14]
The partition coefficient betweenn-Octanol andwater is known as then-octanol-water partition coefficient, orKow.[62] It is also frequently referred to by the symbol P, especially in the English literature. It is also known asn-octanol-water partition ratio.[63][64][65]
Kow, being a type of partition coefficient, serves as a measure of the relationship betweenlipophilicity (fat solubility) andhydrophilicity (water solubility) of a substance. The value is greater than one if a substance is more soluble in fat-like solvents such as n-octanol, and less than one if it is more soluble in water.[citation needed]
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