Collander equation

An overview of permeability assays is presented in Table 2.2. As discussed earlier in this chapter, these permeability scales are correlated to each other as well as the various hpophilicity scales via extended Collander equations. 

Further reduction is possible. To a good approximation, partition coefficients from different organic solvents may be interrelated by the so-called Collander equation [364,587] logKp3 = a log Kp2 + c, or Kp3 = 10CK 2, where a and c are constants. Equations (7.38)-(7.40) can be expressed in log forms as a function of just one partition coefficient (i.e., Kp = Kpl) ... 

The 20% soy lecithin (Table 7.17) and the 2% DOPC (Table 7.15) intrinsic permeabilities may be compared in a Collander equation, as shown in Fig. 7.44. The slope of the regression line, soy versus DOPC, is greater than unity. This indicates that the soy membrane is more lipophilic than the DOPC membrane. Intrinsic permeabilities are generally higher in the soy system. Three molecules were significant outliers in the regression metoprolol, quinine, and piroxicam. Metoprolol and quinine are less permeable in the DOPC system than expected, based on their apparent relative lipophilicities and in vivo absorptions [593]. In contrast, piroxicam is more permeable in DOPC than expected based on its relative lipophilicity. With these outliers removed from the regression calculation, the statistics were impressive at r2 0.97. 

Only 66% of the variance in the data is explained by this equation. However, a separation of the various solutes into OH bond donors, acceptors, and neutrals helped account for 94%of the variance in the data. These restrictions led Seiler to extend the Collander equation by incorporating a corrective term for H-bondingin the cyclohexane system (119). Fujita generalized this approach and formulated Equation 1.43 as shown below (120). 

The use of a single standard system for drug partitioning is justified by the Collander equation (eq. 20) [183], which relates partition coefficients from different solvent systems. 

The presumed relationships between partitioning in different solvent/water systems (organic phases A and B) according to the Collander equation (1951)... 

It is known that the RPLC retention parameters are often strongly correlated to the analyte s distribution coefficient in organic solvent/ water. Generally, the relationship between liquid/liquid (LL) distribution and RPLC retention are of the form of the dimensionless Collander-type equations, e.g., see Eq. (15.21)... 

Combining the equation for the diffusion coefficient with a Collander-type expression for the lipid-water partition coefficient resulted in an expression for calculating the permeability across the stratum corneum ... 

Coffander-iype Relationships Collander has studied partition coefficients in different alcohol-water systems [16]. He found that these partition coefficients are mutually correlated. For certain compounds containing one hydrophilic group, such as alkanols, alkanoic acids, alkanoates, dialkyl ethers, and alkylamines and selected compounds containing two, three, or four such groups, he reports the following equation ... 

The less polar a solute is, the stronger will be its interaction with the stationary phase, which is expressed by decreasing Rf values and increasing Rm values in RP-TLC and by increasing retention times and log fe values in HPLC. Thus Rm and log fe values are directly correlated to octanol-water log P via Collander-type equations ... 

Further analysis of equation 39 reveals a reason for the validity of Collander s equation that correlates partition coefficients in different solvent systems (111). Thus, in equation 39 the terms (IW-IQ) and (Jy-JQ) both reflect a variable characteristic of the solvents. For small changes in this variable they should be proportional to each other... 

Thus, Collander s equation 42, which was established from empirical studies (111), is theoretically derived from the extrathermo-dynamic treatment of solvent effects and is obtained as a result of the second approximation which takes into account the effects of solvation on the interaction term between R and x> x S we now regard the interaction of drugs (in water) with tfie bio-phase as a partitioning phenomenon, equation 42 becomes the basis for the use of the partition coefficient in octanol/water, P, as a model for the partition coefficient between biophase and water,... 

The analysis of the parameters representing the effect of the medium in terms of extrathermodynamical relations has shown (see above, section A.2) that the hydrophobic substituent constant it depends on the molecules from which it is derived. For example, hydrophobic constants derived from the octanol/water partition coefficients of aromatic molecules differ from those obtained from aliphatic molecules (112). Collander s equation (111) provides the empirical basis for the evaluation of logP values for the same molecule in different solvents. However, solvents with markedly different solvation properties (e.g., hydrogen bonding ability) do not conform to Collander s equation (see below, section C.3). 

In the case of parameters related to the effects of the medium Collander s relation (equation 42) has been shown to hold for many different compounds in many solvent systems (112-118). For example, partition coefficients between water and oleyl alcohol, isobutyl alcohol, and xylene correlate well with partition... 

Deviations from equation 42 are not attributed solely to solvent effects. Applying Collander s equation to many partition coefficients for various compounds in various solvent systems, Hansch (112, 121) found that deviations from the correlation can be classified on the basis of known chemical properties as hydrogen bond donors for those that were below the regression line and as hydrogen bond acceptors for those above the line. 

Overton and Meyer both used olive oil as a partitioning system to model the physicochemical properties of the putative membrane lipoid site of action. Although Overton attempted to use melted cholesterol and other substances he thought might serve as a better reference phase, he abandoned this approach due to problems with the formation of inseparable emulsions (31). Collander in Finland (65) experimented with a variety of aqueous organic solvent systems and found that for many simple nonelectrolytes, the values were well-correlated according to the following equation ... 

Collander [51] determined the distribution coefficieiits of 50 organic solutes in five different solvent systems. He noted that for a given solute, the distribution coefficient in one solvent system (ui) was related to that in another (02) by Equation (41). a and b are constants characteristic of the two solvent systems. 

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