WHAT IS A PARTITION COEFFICIENT?
The ability of a drug to reach a specific target in the body depends in part on its ability to cross cell membranes. These are comprised of bilayers of lipid molecules, which have a long nonpolar chain of carbon atoms at one end and a polar group at the other end. Lipid bilayers are arranged with the polar groups (head) projecting outward toward the aqueous environment with the nonpo- lar regions (tail) pointing toward each other (Figure 5.1). Drugs need to have some polar characteristics that impart a degree of water solubility so as to be transported throughout the body. Those polar properties also allow the drug to be attracted to and pass through the polar head groups of lipid bilayers.
Once a drug manages to traverse the head groups, however, it is confronted with a highly nonpolar domain that is composed of the hydrocarbon chains of the lipid molecules. A drug that is too polar will have little or no affinity for this region and will not be able to cross. Envision a container of oil and then imagine adding to it a drop of water. The water will bead up and not become dispersed in the oil. Thus compounds such as those containing quaternary ammonium groups have difficulty crossing lipid bilayers because of their high polarity, even though they will often have good water solubility. Most drugs require a balance of polar and nonpolar characteristics so as to ensure that they can readily pass from one bodily compartment to another. The ratio of polar to nonpolar characteristics of a drug is therefore a critical physico- chemical property and is known as the partition coefficient (P) of the drug.
5
Nonpolar chains Polar head groups
H2O
H2O
Drug A
B
Figure 5.1 This drawing depicts a lipid bilayer. The polar head groups face toward the aqueous environments of compartments A and B, while the hydrocarbon chains associ- ate to form a nonpolar interior region. For a drug to pass from A to B, it must possess some polar characteristics to ensure passage through the polar domains and some non- polar properties to navigate through the interior portion of the bilayer.
The partition coefficient (P) is defined as follows:
P=[Drug]lipid phase/[Drug]water
Theoretically, one can disperse a drug between equal amounts of a lipid layer and water and then determine the concentration of drug in each layer. The ratio is the partition coefficient. In practice, however, this is not done because the term lipid refers not to a single well-defined com- pound but to an entire class of molecules. Mixing lipids and water also tends to form emulsions which complicates such determinations. Instead, a well-behaved organic compound is often chosen as a model for the lipid layer. Most commonly this is 1-octanol, a compound with a polar OH group at one end, and a long nonpolar n-octyl chain at the other. Thus experimentally it is often octanol–water partition coefficients that are deter- mined (Figure 5.2).
Octanol–water partition coefficients may be obtained by distributing a drug between n-octanol and water in a separatory funnel and, after equili- bration, determining the concentration of drug in each layer.
P=[Drug]octanol/[Drug]water
The values that are obtained are usually exponential numbers and it is therefore common to express partition coefficients as the logarithm of the partition coefficient, log P. An alternative method employs reverse-phase high-performance liquid chromatography. The chromatographic retention time can be correlated to the log P.
Consider that drug molecules consist of core structures to which a vari- ety of substituents are attached. Each substituent has polar or nonpolar properties that will have an effect on the partition coefficient of the struc- ture onto which it is attached. The quantitative measure of the effect of a substituent on the partition coefficient of the molecule as a whole is called the Hansch partition coefficients (πx) of the substituent.
OH Nonpolar region
Polar head group n-Octanol
Figure 5.2 The compound n-octanol often serves as a model for a lipid molecule in determining partition coefficients.
πx=log(Px/PH) =logPx−logPH
where PH and Px are the partition coefficients of the unsubstituted and substituted molecules, respectively.
The values of πx can be either positive, which means that group x will increase the lipid solubility (hydrophobicity) of the compound, or negative, in which case group x will make the compound more water soluble (hydrophilic).
The above equation can be rewritten as: log Px = log PH + πx.
Thus the log P of a compound is equal to the log P of the parent com- pound plus the Hansch partition coefficient of the substituent. Alternatively, the partition coefficient can be viewed as being equivalent to the sum of the contributions from all of the various groups from which it is comprised.
Therefore,
logPcompound= Σ πx
EFFECT OF STRUCTURE ON PARTITION COEFFICIENTS
Consider the compounds benzene and anisole (methoxybenzene). Anisole can be derived from benzene by replacing one of the hydrogen atoms with a methoxy group. It has been reported that the log P of anisole is 2.11 and that of benzene is 2.13 [1]. Using the equation above, we can calculate a π value for a methoxy group (Figure 5.3).
π(OCH3)=logPanisole−logPbenzene
π(OCH3)=2.11−2.13 π(OCH3)= −0.02
H OCH3
Benzene log P = 2.13
Anisole log P = 2.11
Figure 5.3 The Hansch partition coefficient (πx) of the methoxy group can be derived using partition coefficients of a compound having a methoxy group (such as anisole) and one identical in all respects except for the absence of such a group (benzene).
The replacement of hydrogen with a methoxy group will result in the compound becoming very slightly more water soluble. Once the Hansch partition coefficient of a methoxy group is known, it can be used to calcu- late the partition coefficients of other compounds. For example, the log P value of 1,3,5-trimethoxybenzene can be calculated as shown below:
OCH3
1,3,5-Trimethoxybenzene H3CO
OCH3
logPx=logPbenzene+3π(OCH3)
logPx=2.13+3(−0.02)
logPx=2.07
Examine the structures of acetic acid and methoxyacetic acid (Figure 5.4).
Here again we see that the difference between the compounds is replace- ment of a hydrogen by a methoxy group. But in this case, when the Hansch partition coefficient of the methoxy group is determined, it is seen that the value obtained is considerably more negative (π(OCH3) = −0.24) than that derived using anisole. One of the differences between methoxyacetic acid and anisole is that in the former the methoxy group is attached to an
O
CH2 OH
H
O
CH2 OH
CH3O Acetic acid
log P = –0.31 Methoxyacetic acid log P = –0.55 π(OCH3) = –0.55 – (–0.31)
π(OCH3) = –0.24
Figure 5.4 Using known partition coefficients for methoxyacetic acid and acetic acid, the Hansch partition coefficient of an aliphatic methoxy group can be derived. The val- ues are obtained from Ref. [1].
aliphatic carbon while in anisole it is an aromatic carbon to which it is joined. Water solubility depends in part on the ability to form hydrogen bonds between a compound and water (Figure 5.5). A lone pair on the ether oxy- gen supplies the electron density needed to bond with a hydrogen atom of water. An aromatic ring serves as an electron-withdrawing group exerting a pull on the lone pair electrons, effectively decreasing their ability to form hydrogen bonds. There is no such withdrawing effect for an ether group attached to an aliphatic carbon. Therefore, such a compound will more readily form hydrogen bonds with water. This will be reflected in a more negative Hansch partition coefficient for an aliphatic ether as opposed to an aromatic ether. Similar effects are observed with many other functional groups.
Consider now the series of compounds shown in Figure 5.6: acetic acid, propionic acid, and butyric acid. These represent what is known as a homolo- gous series, each differs from the preceding compound by one methylene (CH2) group. Log P values of −0.31, 0.33, and 0.79 respectively have been reported for these compounds [1]. We see that on average, each additional aliphatic carbon adds +0.5 to the log P value. It has been established that when all other factors are equivalent, log P values increase with the number of carbon atoms.
O
CH2 OH
CH3O OCH3
H O
H H
O H
Figure 5.5 The negative values for the Hansch partition coefficients of an aromatic and aliphatic methoxy group are a reflection of the group’s ability to hydrogen bond with water. An aromatic ring will withdraw electron density from oxygen reducing its πx
value relative to an aliphatic methoxy group.
CH3 CO2H CH3CH2 CO2H CH3CH2CH2 CO2H
log P = –0.31 log P = 0.33 log P = 0.79
∆log P = 0.64
∆log P = 0.46
Figure 5.6 Partition coefficients for the homologous series acetic acid, propionic acid, and butyric acid. On average, each additional aliphatic carbon adds 0.5 to the partition coefficient. Values are from Ref. [1].
The compounds n-butanol and i-butanol are positional isomers (C4H10O) that differ only by the presence of a branch in i-butanol (Figure 5.7). If one subtracts the log P value of n-butanol from that of i-butanol, the difference is the Hansch partition coefficient for the branch. On average, this value is −0.2, meaning that branching tends to increase water solubility to a small extent.
To understand why branching lowers the partition coefficient, consider what happens when a more extended compound such as n-butanol and a branched compound (i-butanol) partition from an organic solvent such as octanol into water. Figure 5.8 shows that the critical volume (the volume occupied by 1 mol of a compound) calculated for i-butanol is smaller than that of n-butanol.
OH OH
n-Butanol
log P = 0.88 i-Butanol log P = 0.65
Branch
πbranch = log Pi-BuOH – log Pn-BuOH
πbranch = 0.65 – 0.88 πbranch = –0.23
Figure 5.7 The structures of n-butanol and i-butanol showing that the latter has a branch in the alkyl chain. A Hansch partition coefficient is derived here for a branch. The values are from Ref. [1].
OH
OH
Octanol + n-Butanol
Critical vol: 278.5 cm3/mol Critical vol: 272.5 cm3/mol
Octanol + i-Butanol
Water + n-Butanol
Water + i-Butanol Klinear
Kbranch
Figure 5.8 Critical volumes for n-butanol and i-butanol as calculated using ChemBio- Draw Ultra 13.0, Perkin Elmer Informatics, Waltham, MA. Partitioning behavior can be viewed as an equilibrium between the substrate in dissolved in octanol and water.
An equilibrium can be established between n-butanol in octanol and n-butanol in water with a constant called Klinear. A similar equilibrium can be written for i-butanol with constant Kbranch. As the organic substrates begin to partition into water, the water molecules must organize around the organic molecules. The more extended compound n-butanol will require more water molecules to organize than i-butanol because it occupies a larger volume. A higher degree of organization means lower entropy (S) and so ΔSlinear < ΔSbranch. The change in entropy for a process is related to the equilibrium constant by two equations. The first of these states that as ΔS decreases, the free energy change (ΔG) for a process increases.
ΔG = ΔH − TΔS, where ΔH is the change in enthalpy, T is the tempera- ture in Kelvin (K) and ΔS is the entropy change
A second equation relates ΔG to the equilibrium constant.
ΔG = −RT log K, where R is the universal gas constant and T is the temperature (K)
Thus −ΔG is proportional to log K and as ΔG increases K decreases. The difference in ΔS for a linear vs a branched compound therefore translates into Kbranch being larger than Klinear. A branched compound will partition into water to a greater extent than a linear compound and will therefore have a smaller partition coefficient.
Another structural feature that has an effect on partition coefficient is unsaturation. Figure 5.9 shows the calculated log P values for cyclohexane, cyclohexene, and benzene. The difference between cyclohexene and cyclo- hexane is the replacement of two hydrogens by a π-bond leading to a sig- nificant decrease in the partition coefficient. Thus π-bonds can also be considered to have negative values for their Hansch partition coefficients.
Benzene, with three π-bonds, has an even lower partition coefficient than cyclohexene. Remember that electrons in π-bonds are not held as tightly by the nuclei as those in σ-bonds. They can be donated to a certain extent to form hydrogen bonds with water, which thereby increases water solubility.
log P = 2.13 log P = 3.35 log P = 2.87
Figure 5.9 Calculated log P values for cyclohexane, cyclohexene, and benzene showing that unsaturation lowers the partition coefficient. Values were calculated using Chem- BioDraw Ultra 13.0, Perkin Elmer Informatics, Waltham, MA.
A listing of some structural effects that decrease the partition coefficient (have negative values of πx) includes the following:
• Any functional group that can readily form hydrogen bonds with water.
This includes carbonyl-based groups and other oxygen and nitrogen- containing functionality such as alcohols, ethers, amines, nitro groups, nitriles, sulfonamides, etc.
• Charged groups such as carboxylate anion, alkoxide anion, and ammo- nium groups. Salts also fall into this category. Positive charges are attracted to the oxygen of water while negative charges are attracted to the hydrogens.
• Unsaturation • Branching
• Isolated aliphatic fluoro groups. Fluorine has three lone pairs of elec- trons and is a small element, which facilitates the formation of H bonds with water.
Groups that do not readily form hydrogen bonds with water will gener- ally increase the partition coefficient (have positive values for πx). Among these are the following:
• Carbons (CH3, CH2, CH, C). Unsaturated carbons (sp2 and sp) will have less of an effect than aliphatic carbons but will still increase the log P.
• Halogens: –I, –Br, –Cl, and –F if it is attached to an unsaturated carbon.
The electron-withdrawing effect of a multiple bond removes electron density from fluorine making the formation of hydrogen bonds more difficult. The other halogens are all much larger than water rendering hydrogen bond formation more difficult.
• Trifluoromethyl (CF3): Three strongly electronegative fluorines attached to one carbon exert a strong polar effect on each other’s lone pair elec- trons decreasing their ability to form hydrogen bonds. The CF3 group is one of the strongest +π groups.
• Thiols and sulfides: The larger size of sulfur as compared to water decreases its ability to hydrogen bond with water.
REFERENCE
[1] A. Leo, C. Hansch, D. Elkins, Partition coefficients and their uses, Chemical Reviews 71 (1971) 525–616.
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