**1. Introduction**

90 Toxicity and Drug Testing

Ott, H.C.; Matthiesen, T. S.; Goh, S. K.; Black, L. D.; Kren, S. M.; Netoff, T. I. & Taylor, D. A.

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Redfern, W. S.; Carlsson, L.; Davis, A. S.; Lynch, W. G.; MacKenzie I.;Palethorpe, S.; Siegl, P.

Regan, C. P.; Cresswell, H. K.; Zhang, R. & Lynch J. J. (2005). Novel method to assess cardiac electrophysiology in the rat. *Journal of Cardiovascular Pharmacology*; 46(1):68-75. Shimizu, T.; Yamato, M.; Isoi, Y.; Akutsu, T.; Setomaru, T.; Abe, K.; Kikuchi, A.; Umezu, M.

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Vaughan-Williams E., M. (1975). Classificationof antidysrhythmic drugs. Pharmacology &

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Zimmermann, W. H.; Schneiderbanger, K.; Schubert, P.; Didie, M.; Munzel, F.; Heubach, J.

Zimmermann, W. H. & Eschenhagen, T. (2007). Embryonic stem cells for cardiac muscle

differentiated cardiac muscle construct. *Circulation Research*; 90:223–230 Zimmermann, W. H.; Melnychenko, I.; Wasmeier, G.; Didié, M.; Naito, H.; Nixdorff, U.;

diastolic function in infarcted rat hearts. *Nature Medicine*; 12:452-8

engineering. *Trends in Cardiovascular Medicine*; 17:134-40

bioartificial heart. *Nature Medicine*; 14:213–221

*England Journal of Medicine*; 351(11):1089-96

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therapeutics; 1(1):115-38.

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(2008). Perfusion-decellularized matrix: using nature's platform to engineer a

Novakovic, G. (2004). Functional assembly of engineered myocardium by electrical stimulation of cardiac myocytes cultured on scaffolds. *PNAS*; 101:18129–18134 Ray, W. A.; Murray, K. T.; Meredith, S.; Narasimhulu, S. S.; Hall K. & Stein C. M. (2004).

Oral erythromycin and the risk of sudden death from cardiac causes. *The New* 

K.; Strang, I.; Sullivan, A. T.; Wallis, R.; Camm, A. J. & Hammond, T. G. (2003). Relationship between preclinical cardiac electrophysiology, clinical QT interval prolongation and torsade de pointes for a broad range of drugs: evidence for a provisional safety margin in drug development. *Cardiovascular Research*; 58(1):32-45.

& Okano, T. (2002). Fabrication of pulsatile cardiac tissue grafts using a novel 3 dimensional cell sheet manipulation technique and temperature-responsive cell

& Crawford, G. (2008). Drug-screening platform based on the contractility of

Kamp, T. J. (2009). Functional cardiomyocytes derived from human induced

F.; Kostin, S.; Neuhuber, W. L. & Eschenhagen, T. (2002). Tissue engineering of a

Hess, A.; Budinsky, L.; Brune, K.; Michaelis, B.; Dhein, S.; Schwoerer, A.; Ehmke, H. & Eschenhagen, T. (2006). Engineered heart tissue grafts improve systolic and Modern drug testing and design includes experimental *in vivo* and *in vitro* measurements, combined with *in silico* computations that enable prediction of the drug candidate's ADMET (adsorption, distribution, metabolism, elimination and toxicity) properties in the early stages of drug discovery. Recent estimates place the discovery and development cost of a small drug molecule close to US \$1.3 billion, from the time of inception to the time when the drug finally reaches the market place. Only 20 % of conceived drug candidates proceed to clinical trial stage testing, and of the compounds that enter clinical development less than 10 % receive government approval. Reasons for the low success rate include unsatisfactory efficacy, poor solubility, poor bioavailability, unfavorable pharmacokinetic properties, toxicity concerns and drug-drug interactions, degradation and poor shelf-life stability. Unfavorable pharmacokinetic and ADME properties, toxicity and adverse side effects account for up to two-thirds of drug failures. Traditional ADME analyses relied heavily on whole animal assays and the more labor intensive biochemical studies. High throughput screening methods, fast ADMET profiling assays, and computational approaches have allowed the pharmaceutical industry to identify quickly the less promising drug candidates in the very early development stage so that time and valuable resources are not spent pursuing compounds that have little probability of reaching the general population.

Of the fore-mentioned properties, the drug's aqueous solubility will likely be one of the first properties measured. Aqueous solubility is a major indicator of the drug's solubility in physiological gastrointestinal fluids and is a major indicator of the drug's oral bioavailability. Approximately 40 % of the proposed new pharmaceutical candidates are rejected in the very early stages of drug discovery because of their poor aqueous solubility resulting in bioavailability problems (Lukyanov and Torchilin, 2004; Keck *et al.*, 2008). The

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

Solubility

**Class II**  Low Solubility High Permeability

**Class IV**  Low Solubility Low Permeability

Fig. 1. Properties used in the Biopharmaceutical Classification Scheme (a) and

lipophilicity of drug candidates and for quantifying drug-membrane interactions.

Biopharmaceutics Drug Disposition Classification System (b)

Solubility Low

**Class I**  High Solubility High Permeability

**Class III**  High Solubility Low Permeability

**High Permeability**

**Low Permeability**

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 93

**Extensive Metabolism**

**Poor Metabolism** 

a) b)

Lipophilicity is another of the physical properties that is measured in the early stages of drug testing to predict the transport of molecules from the gastrointestinal track into the epithelial cells that line the inner and outer surfaces of the body. Most common drugs cross cellular barriers by transcellular pathways (across epithelial cells) that require the drug to enter the outer portion of the lipid bilayer of the cell membrane. The drug then diffuses to the inner lipid layer and travels across the cell before crossing the cell membrane once again to exit. Lipophilicity was introduced to describe a compound's affinity to be in lipid-like environment. Several solvent systems have been suggested as a surrogate to represent the lipid membrane against water. For convenience and economical reasons, the partition coefficient of the drug candidate between 1-octanol and a series of aqueous buffers has become the standard measure of lipophilicity. The *intrinsic lipophilicity* (logarithm of the water-to-octanol partition coefficient, log Po/w) describes the equilibrium distribution of molecular drug candidate (unionized form of the molecule) between water and the aqueous buffer, and is independent of pH. The *effective lipophilicity* (logarithm of the water-to-octanol distribution coefficient) reflects the concentration ratio of the neutral drug molecule plus all ionized forms that may be present in the aqueous buffered solution at the given pH. The effective lipophilicity is often quoted at the physiological pH of 7.4. The intrinsic and effective lipophilicities are equivalent if the drug candidate contains no ionizable or protonatable functional groups. Experimental techniques employed to measure water-tooctanol partition coefficients include the traditional shake-flask method, as well as several methods based on reversed-phase liquid chromatography (hplc), counter-current chromatography and centrifugal partition chromatography (Sangster, 1989; Berthod *et al*., 1992; Menges *et al*., 1990; Berthod *et al*., 1988; McDuffie, 1981; Veith *et al*., 1979). Ribeiro and coworkers (2010) recently discussed the advantages and limitations associated with using the water-to-octanol partitioning system as a surrogate for biological membranes. The authors noted that there is a considerable difference between the homogeneous macroscopic 1-octanol solvent system and the highly-ordered microscopic structure of a lipid layer. Chromatographic retention data determined using an immobilized artificial membrane (IAM) stationary phase was suggested as a more appropriate method for measuring the

High Solubility

**Class I**  High solubility Highly Metabolized

**Class III**  High solubility Poorly Metabolized

Low Solubility

**Class II**  Low solubility Highly Metabolized

**Class IV**  Low solubility Poorly Metabolized

number of failures due to poor solubility is likely to increase in future years because the new drug candidates generally have higher molecular weights and more complicated molecular structures than their predecessors. Moreover, drug molecules that are insoluble in water are difficult to study with existing *in vitro* biological assays, often give unreliable biological test results, and may precipitate from solution during storage or upon dilution. The importance of aqueous solubility in drug design is further evidenced by the fact that the editors of one prominent computational journal (Llinàs *et al*., 2008) challenged readers to develop *in silico* methods to predict the intrinsic solubilities of 32 crystalline drug like molecules in water from an experimental data set of accurately measured solubilities of 100 compounds. Only a few of the more successful approaches were actually published (Wang, *et al.* 2009; Hewitt *et al*., 2009). Similar challenges have been published regarding the prediction and measurement of the hydration free energies of functionally diverse neutral drug-like molecules (Nicholls *et al*., 2008; Guthrie, 2009). Aqueous solubility is the reference media to predict the absorption and bioavailability of orally administered drugs. More than 85 % of the drugs sold in the US and in Europe are administered orally.

Amidon and coworkers (1995) proposed a biopharmaceutical classification scheme (BCS) to categories drugs and drug candidates into four groups based on their combined solubility and permeability properties. The classification scheme is depicted in Figure 1a. Drug candidates in Class I exhibit high solubility and high permeability, which is preferred from both a bioavailability and drug delivery standpoint. A drug candidate is considered highly soluble when the highest dose strength is soluble in 250 ml water over a pH range 1 to 7.5. A drug candidate possesses high permeability when the extent of absorption in humans is determined to be 90% of an administered dose, based on the mass balance or in comparison to an intravenous dose. Drug candidates in Class II have low solubility and high permeability, hence, the dissolution rate becomes the governing parameter for bioavailability. These drugs exhibit variable bioavailability and need enhancement in the dissolution rate for improvement in bioavailability. Drug candidates in Class III have high solubility and low permeability. Permeation through the intestinal membrane represents the rate-determining step for Class III drug candidates, with the bioavailability being independent of drug release from the dosage form. Class IV drug candidates possess both low solubility and low permeability. Drugs in this category are generally not suitable for oral drug delivery unless one employs a special drug delivery technology (such as a nanosuspension). Wu and Benet (2005) examined the biopharmaceutical classification scheme as a predictive method for assessing drug disposition. The authors found that drugs in Classes I and II of BCS were metabolized and eliminated. Drugs in the latter two classes were eliminated unchanged from the body by renal and/or biliary elimination. On the basis of these findings the authors suggested the Biopharmaceutics Drug Disposition Classification System (BDDCS) where the extent of metabolism has replaced permeability as a classification criterion (see Figure 2b). Aqueous solubility is an important consideration in both drug classification systems. Adverse drug solubility can sometimes be overcome by structural modifications (e.g., prodrugs) or by adding an organic cosolvent, surfactant, hydrophilic macromolecular and/or an inclusion host compound (such as a modified cyclodextrin) to the drug formulation or application vehicle. Knowledge of the drug's solubility in different organic solvents aids in the selection of an appropriate organic cosolvent and provides valuable information regarding drug's molecular interactions with other organic molecules.

number of failures due to poor solubility is likely to increase in future years because the new drug candidates generally have higher molecular weights and more complicated molecular structures than their predecessors. Moreover, drug molecules that are insoluble in water are difficult to study with existing *in vitro* biological assays, often give unreliable biological test results, and may precipitate from solution during storage or upon dilution. The importance of aqueous solubility in drug design is further evidenced by the fact that the editors of one prominent computational journal (Llinàs *et al*., 2008) challenged readers to develop *in silico* methods to predict the intrinsic solubilities of 32 crystalline drug like molecules in water from an experimental data set of accurately measured solubilities of 100 compounds. Only a few of the more successful approaches were actually published (Wang, *et al.* 2009; Hewitt *et al*., 2009). Similar challenges have been published regarding the prediction and measurement of the hydration free energies of functionally diverse neutral drug-like molecules (Nicholls *et al*., 2008; Guthrie, 2009). Aqueous solubility is the reference media to predict the absorption and bioavailability of orally administered drugs. More than 85 % of

Amidon and coworkers (1995) proposed a biopharmaceutical classification scheme (BCS) to categories drugs and drug candidates into four groups based on their combined solubility and permeability properties. The classification scheme is depicted in Figure 1a. Drug candidates in Class I exhibit high solubility and high permeability, which is preferred from both a bioavailability and drug delivery standpoint. A drug candidate is considered highly soluble when the highest dose strength is soluble in 250 ml water over a pH range 1 to 7.5. A drug candidate possesses high permeability when the extent of absorption in humans is determined to be 90% of an administered dose, based on the mass balance or in comparison to an intravenous dose. Drug candidates in Class II have low solubility and high permeability, hence, the dissolution rate becomes the governing parameter for bioavailability. These drugs exhibit variable bioavailability and need enhancement in the dissolution rate for improvement in bioavailability. Drug candidates in Class III have high solubility and low permeability. Permeation through the intestinal membrane represents the rate-determining step for Class III drug candidates, with the bioavailability being independent of drug release from the dosage form. Class IV drug candidates possess both low solubility and low permeability. Drugs in this category are generally not suitable for oral drug delivery unless one employs a special drug delivery technology (such as a nanosuspension). Wu and Benet (2005) examined the biopharmaceutical classification scheme as a predictive method for assessing drug disposition. The authors found that drugs in Classes I and II of BCS were metabolized and eliminated. Drugs in the latter two classes were eliminated unchanged from the body by renal and/or biliary elimination. On the basis of these findings the authors suggested the Biopharmaceutics Drug Disposition Classification System (BDDCS) where the extent of metabolism has replaced permeability as a classification criterion (see Figure 2b). Aqueous solubility is an important consideration in both drug classification systems. Adverse drug solubility can sometimes be overcome by structural modifications (e.g., prodrugs) or by adding an organic cosolvent, surfactant, hydrophilic macromolecular and/or an inclusion host compound (such as a modified cyclodextrin) to the drug formulation or application vehicle. Knowledge of the drug's solubility in different organic solvents aids in the selection of an appropriate organic cosolvent and provides valuable information regarding drug's molecular interactions with

the drugs sold in the US and in Europe are administered orally.

other organic molecules.


Fig. 1. Properties used in the Biopharmaceutical Classification Scheme (a) and Biopharmaceutics Drug Disposition Classification System (b)

Lipophilicity is another of the physical properties that is measured in the early stages of drug testing to predict the transport of molecules from the gastrointestinal track into the epithelial cells that line the inner and outer surfaces of the body. Most common drugs cross cellular barriers by transcellular pathways (across epithelial cells) that require the drug to enter the outer portion of the lipid bilayer of the cell membrane. The drug then diffuses to the inner lipid layer and travels across the cell before crossing the cell membrane once again to exit. Lipophilicity was introduced to describe a compound's affinity to be in lipid-like environment. Several solvent systems have been suggested as a surrogate to represent the lipid membrane against water. For convenience and economical reasons, the partition coefficient of the drug candidate between 1-octanol and a series of aqueous buffers has become the standard measure of lipophilicity. The *intrinsic lipophilicity* (logarithm of the water-to-octanol partition coefficient, log Po/w) describes the equilibrium distribution of molecular drug candidate (unionized form of the molecule) between water and the aqueous buffer, and is independent of pH. The *effective lipophilicity* (logarithm of the water-to-octanol distribution coefficient) reflects the concentration ratio of the neutral drug molecule plus all ionized forms that may be present in the aqueous buffered solution at the given pH. The effective lipophilicity is often quoted at the physiological pH of 7.4. The intrinsic and effective lipophilicities are equivalent if the drug candidate contains no ionizable or protonatable functional groups. Experimental techniques employed to measure water-tooctanol partition coefficients include the traditional shake-flask method, as well as several methods based on reversed-phase liquid chromatography (hplc), counter-current chromatography and centrifugal partition chromatography (Sangster, 1989; Berthod *et al*., 1992; Menges *et al*., 1990; Berthod *et al*., 1988; McDuffie, 1981; Veith *et al*., 1979). Ribeiro and coworkers (2010) recently discussed the advantages and limitations associated with using the water-to-octanol partitioning system as a surrogate for biological membranes. The authors noted that there is a considerable difference between the homogeneous macroscopic 1-octanol solvent system and the highly-ordered microscopic structure of a lipid layer. Chromatographic retention data determined using an immobilized artificial membrane (IAM) stationary phase was suggested as a more appropriate method for measuring the lipophilicity of drug candidates and for quantifying drug-membrane interactions.

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

for specific classes of solute: alkylpyridines, alkylanilines, and sulfoxides.

solute descriptors.

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 95

several of our published papers (Abraham *et al*., 2006a; Abraham *et al*., 2009a; Mintz *et al*., 2007). Solute descriptors can be obtained by regression analysis using various types of experimental data, including water-to-solvent partitions, gas-to-solvent partitions, solubility data and chromatographic retention data as discussed below and elsewhere (Abraham *et al*., 2010; Zissimos *et al*., 2002a,b). For a number of partitions into solvents that contain large amounts of water at saturation, an alternative hydrogen bond basicity parameter, **Bo**, is used

Equations 1 and 2 contain the following three quantities: (a) measured solute properties; (b) calculated solute descriptors; and (c) calculated equation coefficients. Knowledge of any two quantities permits calculation of the third quantity through the solving of simultaneous equations and regression analysis. Solute descriptors are calculated from measured partition coefficient (Psolute,system), chromatographic retention factor (k') and molar solubility (Csolute,solvent) data for the solutes dissolved in partitioning systems and in organic solvents having known equation coefficients. Generally partition coefficient, chromatographic retention factor and molar solubility measurements are fairly accurate, and it is good practice to base the solute descriptor computations on observed values having minimal experimental uncertainty. The computation is depicted graphically in Figure 1 by the unidirectional arrows that indicate the direction of the calculation using the known equation coefficients that connect the measured and solute descriptors. Measured Psolute,system and Csolute,solvent values yield solute descriptors. The unidirectional red arrows originating from the center solute descriptor circle represent the equation coefficients that have been reported for blood-to-brain partition coefficient, blood-to-tissue partition coefficients, percentage of human intenstinal absorption, Draize eye scores, and aquatic toxicity Abraham model linear free energy relationships. Plasma-to-milk partition ratio predictions are achieved (Abraham *et al*., 2009b) through an artificial neural network with five inputs, 14 nodes in the hidden layer and one node in the output layer. Linear analysis of the plasma-to-milk partition ratios for 179 drugs and hydrophobic environmental pollutants revealed that drug molecules preferentially partition into the aqueous and protein phases of milk. Hydrophobic environmental pollutants, on the other hand, partition into the fat phase. Prediction of the fore-mentioned ADMET and biological properties does require a prior knowledge of the Abraham solute descriptors for the drug candidate of interest. There are also commercial software packages (ADME Boxes, 2010) and several published estimation schemes (Mutelet and Rogalski, 2001; Arey *et al*., 2005; Platts *et al*., 1999; Abraham and McGowan, 1987) for calculating the numerical values of solute descriptors from molecular structural information if one is unable to find the necessary partition, chromatographic and/or solubility data. For any fully characterized system/process (those with calculated values for the equation coefficients) further values of SP can be estimated for solutes with known values for the

The usefulness of Eqns. 1 and 2 in the characterization of solvent phases is that the coefficients *e, s, a, b, l* and *v* are not just curve-fitting constants. The coefficients reflect particular solute-solvent interactions that correspond to chemical properties of the solvent phase. The excess molar refraction, **E**, is defined from the solute refractive index, and hence the *e* coefficient gives a measure of general solute-solvent dispersion interactions. The **V** and **L** descriptors were set up as measures of the endoergic effect of disrupting solventsolvent bonds. However, solute volume is always well correlated with polarizability and so the *v* and *l* coefficients will include not only an endoergic cavity effect but also exoergic solute-

Solubility and water-to-organic solvent partition coefficients are fairly easy to measure as the equilibrated solutions contain only the dissolved drug candidate and the solubilizing solvent media. Blood-to-tissue partition coefficients, plasma-to-milk partition coefficient, percentage of human intestinal absorption and the steady-state volume of distribution are much harder to measure. The analytical methodology employed to measure these latter properties must be able to distinguish and quantify the drug from all of the many other molecules present in the biological sample. It is not easy, even with today's modern instrumentation, to design chemical analysis methods that are specific to a given molecule. Moreover, measurements involving human and/or animal tissues are expensive and are subject to larger experimental uncertainties. Replicate studies involving the same animal species have shown that the measured values can depend on gender, age and eating habits. This chapter will discuss the prediction of the blood-to-tissue partition coefficients, plasmato-milk partition coefficients, human intestinal absorption based on the Abraham solvation parameter model and solute descriptors calculated from measured solubilities and partition coefficients.

#### **2. Abraham solvation parameter model**

The Abraham general solvation model is one of the more useful approaches for the analysis and prediction of the adsorption, distribution and toxicological properties of potential drug candidates. The method relies on two linear free energy relationships (lfers), one for transfer processes occurring within condensed phases (Abraham, 1993a,b; Abraham *et al*., 2004):

$$\mathbf{SP} = \mathbf{c} + \mathbf{e} \cdot \mathbf{E} + \mathbf{s} \cdot \mathbf{S} + \mathbf{a} \cdot \mathbf{A} + \mathbf{b} \cdot \mathbf{B} + \mathbf{v} \cdot \mathbf{V} \tag{1}$$

and one for processes involving gas-to-condensed phase transfer

$$\mathbf{^c}\mathbf{S}\mathbf{P} = \mathbf{c} + \mathbf{e} \cdot \mathbf{E} + \mathbf{s} \cdot \mathbf{S} + \mathbf{a} \cdot \mathbf{A} + \mathbf{b} \cdot \mathbf{B} + \mathbf{l} \cdot \mathbf{L} \tag{2}$$

The dependent variable, SP, is some property of a series of solutes in a fixed phase, which in the present study will include the logarithm of drug's water-to-organic solvent and bloodto-tissue partition coefficients, the logarithm of the drug's molar solubility in an organic solvent divided by its aqueous molar solubility, the logarithm of the drug's plasma-to-milk partition coefficient, percent human intestinal absorption and the logarithm of the kinetic constant for human intestinal absorption, and the logarithm of the human skin permeability coefficient. The independent variables, or descriptors, are solute properties as follows: **E** and **S** refer to the excess molar refraction and dipolarity/polarizability descriptors of the solute, respectively, **A** and **B** are measures of the solute hydrogen-bond acidity and basicity, **V** is the McGowan volume of the solute and **L** is the logarithm of the solute gas phase dimensionless Ostwald partition coefficient into hexadecane at 298 K. The first four descriptors can be regarded as measures of the tendency of the given solute to undergo various solute-solvent interactions. The latter two descriptors, **V** and **L**, are both measures of solute size, and so will be measures of the solvent cavity term that will accommodate the dissolved solute. General dispersion interactions are also related to solute size, hence, both **V** and **L** will also describe the general solute-solvent interactions. Solute descriptors are available for more than 4,000 organic, organometallic and inorganic solutes. No single article lists all of the numerical values; however, a large compilation is available in one published review article (Abraham *et al*., 1993a), and in the supporting material that has accompanied

Solubility and water-to-organic solvent partition coefficients are fairly easy to measure as the equilibrated solutions contain only the dissolved drug candidate and the solubilizing solvent media. Blood-to-tissue partition coefficients, plasma-to-milk partition coefficient, percentage of human intestinal absorption and the steady-state volume of distribution are much harder to measure. The analytical methodology employed to measure these latter properties must be able to distinguish and quantify the drug from all of the many other molecules present in the biological sample. It is not easy, even with today's modern instrumentation, to design chemical analysis methods that are specific to a given molecule. Moreover, measurements involving human and/or animal tissues are expensive and are subject to larger experimental uncertainties. Replicate studies involving the same animal species have shown that the measured values can depend on gender, age and eating habits. This chapter will discuss the prediction of the blood-to-tissue partition coefficients, plasmato-milk partition coefficients, human intestinal absorption based on the Abraham solvation parameter model and solute descriptors calculated from measured solubilities and partition

The Abraham general solvation model is one of the more useful approaches for the analysis and prediction of the adsorption, distribution and toxicological properties of potential drug candidates. The method relies on two linear free energy relationships (lfers), one for transfer processes occurring within condensed phases (Abraham, 1993a,b; Abraham *et al*., 2004):

The dependent variable, SP, is some property of a series of solutes in a fixed phase, which in the present study will include the logarithm of drug's water-to-organic solvent and bloodto-tissue partition coefficients, the logarithm of the drug's molar solubility in an organic solvent divided by its aqueous molar solubility, the logarithm of the drug's plasma-to-milk partition coefficient, percent human intestinal absorption and the logarithm of the kinetic constant for human intestinal absorption, and the logarithm of the human skin permeability coefficient. The independent variables, or descriptors, are solute properties as follows: **E** and **S** refer to the excess molar refraction and dipolarity/polarizability descriptors of the solute, respectively, **A** and **B** are measures of the solute hydrogen-bond acidity and basicity, **V** is the McGowan volume of the solute and **L** is the logarithm of the solute gas phase dimensionless Ostwald partition coefficient into hexadecane at 298 K. The first four descriptors can be regarded as measures of the tendency of the given solute to undergo various solute-solvent interactions. The latter two descriptors, **V** and **L**, are both measures of solute size, and so will be measures of the solvent cavity term that will accommodate the dissolved solute. General dispersion interactions are also related to solute size, hence, both **V** and **L** will also describe the general solute-solvent interactions. Solute descriptors are available for more than 4,000 organic, organometallic and inorganic solutes. No single article lists all of the numerical values; however, a large compilation is available in one published review article (Abraham *et al*., 1993a), and in the supporting material that has accompanied

SP c e · s · a · b · v · **ESA B V** (1)

SP c e · s · a · b · l · **E S A BL** (2)

coefficients.

**2. Abraham solvation parameter model** 

and one for processes involving gas-to-condensed phase transfer

several of our published papers (Abraham *et al*., 2006a; Abraham *et al*., 2009a; Mintz *et al*., 2007). Solute descriptors can be obtained by regression analysis using various types of experimental data, including water-to-solvent partitions, gas-to-solvent partitions, solubility data and chromatographic retention data as discussed below and elsewhere (Abraham *et al*., 2010; Zissimos *et al*., 2002a,b). For a number of partitions into solvents that contain large amounts of water at saturation, an alternative hydrogen bond basicity parameter, **Bo**, is used for specific classes of solute: alkylpyridines, alkylanilines, and sulfoxides.

Equations 1 and 2 contain the following three quantities: (a) measured solute properties; (b) calculated solute descriptors; and (c) calculated equation coefficients. Knowledge of any two quantities permits calculation of the third quantity through the solving of simultaneous equations and regression analysis. Solute descriptors are calculated from measured partition coefficient (Psolute,system), chromatographic retention factor (k') and molar solubility (Csolute,solvent) data for the solutes dissolved in partitioning systems and in organic solvents having known equation coefficients. Generally partition coefficient, chromatographic retention factor and molar solubility measurements are fairly accurate, and it is good practice to base the solute descriptor computations on observed values having minimal experimental uncertainty. The computation is depicted graphically in Figure 1 by the unidirectional arrows that indicate the direction of the calculation using the known equation coefficients that connect the measured and solute descriptors. Measured Psolute,system and Csolute,solvent values yield solute descriptors. The unidirectional red arrows originating from the center solute descriptor circle represent the equation coefficients that have been reported for blood-to-brain partition coefficient, blood-to-tissue partition coefficients, percentage of human intenstinal absorption, Draize eye scores, and aquatic toxicity Abraham model linear free energy relationships. Plasma-to-milk partition ratio predictions are achieved (Abraham *et al*., 2009b) through an artificial neural network with five inputs, 14 nodes in the hidden layer and one node in the output layer. Linear analysis of the plasma-to-milk partition ratios for 179 drugs and hydrophobic environmental pollutants revealed that drug molecules preferentially partition into the aqueous and protein phases of milk. Hydrophobic environmental pollutants, on the other hand, partition into the fat phase. Prediction of the fore-mentioned ADMET and biological properties does require a prior knowledge of the Abraham solute descriptors for the drug candidate of interest. There are also commercial software packages (ADME Boxes, 2010) and several published estimation schemes (Mutelet and Rogalski, 2001; Arey *et al*., 2005; Platts *et al*., 1999; Abraham and McGowan, 1987) for calculating the numerical values of solute descriptors from molecular structural information if one is unable to find the necessary partition, chromatographic and/or solubility data. For any fully characterized system/process (those with calculated values for the equation coefficients) further values of SP can be estimated for solutes with known values for the solute descriptors.

The usefulness of Eqns. 1 and 2 in the characterization of solvent phases is that the coefficients *e, s, a, b, l* and *v* are not just curve-fitting constants. The coefficients reflect particular solute-solvent interactions that correspond to chemical properties of the solvent phase. The excess molar refraction, **E**, is defined from the solute refractive index, and hence the *e* coefficient gives a measure of general solute-solvent dispersion interactions. The **V** and **L** descriptors were set up as measures of the endoergic effect of disrupting solventsolvent bonds. However, solute volume is always well correlated with polarizability and so the *v* and *l* coefficients will include not only an endoergic cavity effect but also exoergic solute-

Prediction of Partition Coefficients and Permeability of Drug Molecules in Biological

*ij*

surprising given that fat is about 80 % lipid.

needs to measure the kinetic or thermodynamic solubility.

**solubilities** 

*Cos*

Systems with Abraham Model Solute Descriptors Derived from Measured Solubilities and… 97

which are now regarded as lines in five-dimensional space. The angle between the two lines, θij, yields information regarding how the two compared processes are in terms of their chemical similarity. As θij approaches zero (or alternatively as cos θij approaches unity) the two lines coincide, and the correlation between the two partitioning processes/systems approaches unity. Analysis of the Abraham model coefficients for the solubility of gases and vapors in biological phases (blood, brain, fat, heart, kidney, liver, lung and muscle) and organic solvents (alcohols, amides, olive oil, chloroform, diethyl ether, butanone), and equation coefficients for biological activity (nasal pungency thresholds, eye irritation thresholds, odor detection and anesthesia) using Eqns. 3 and 4 (along with Principal Component Analysis) found N-methylformamide to be an excellent model for both eye irritation thresholds in humans and nasal pungency thresholds in humans (Abraham *et al*., 2009a). The receptor site controlling both biological responses must be protein-like in character. The study further showed that no organic solvent is a suitable model (or surrogate) for blood, brain, heart, kidney, liver, lung and muscle. Two relatively nonpolar solvents (olive oil and chloroform) were found to be suitable models for fat, which is not too

**3. Experimental methods for measuring thermodynamic and kinetic** 

Recent advances in automated chemical synthesis and combinatorial chemistry have generated large numbers of new chemical compounds that need to be screened for possible biological activity and desired ADMET properties. The conventional experimental methods that were once used in the pharmaceutical industry to measure solubility and water-toorganic solvent partition coefficients are inadequate to handle large numbers of new compound because of low throughput capacity and the amount of compound required for the experimental determination. Large quantities of highly purified compounds are not usually available in the initial stages of drug discovery and drug testing. To meet the demands imposed by the increased compound numbers, the pharmaceutical industry has developed miniaturized and automated sample preparation platforms, combined with rapid chemical analysis methods based on nephelometric, uv/visible absorption and/or chromatographic measurements. The experimental protocol used depends on whether one

High throughput kinetic aqueous solubility assays are based on the detection of precipitation of compounds in aqueous or aqueous buffered solutions. Typically, small known aliquots of the stock solution are added incrementally to the aqueous (or aqueous buffered solution) at predetermined time intervals until the solubility limit is reached. The resulting precipitation can be detected optically by nephlometric or laser monitoring methods, and the kinetic solubility is defined as the solute concentration immediately preceding the point at which precipitation was first detected. Kinetic solubility thus represents the maximum solubility of the fastest precipitation species of the given compound into the desired solubilizing solvent media. Numerous modifications of kinetic assays have been suggested in recent years. The suggested modifications differ in the dilution and detection method. For example, Lipinski *et al*. (2001) added small aliquots of a

2222 2 22 2 2 2 *ij ij ij ij i j*

(4)

*iiii i jjjj j*

*esabv esabv* 

*ee ss aa bb vv*

solvent effects that arise through solute polarizability. The **S** descriptor is a measure of dipolarity and polarizability and hence the *s* coefficient will reflect the ability of a solvent to undergo dipole-dipole and dipole-induced dipole interactions with the solute. The **A** descriptor is a measure of solute hydrogen bond acidity, and hence the *a* coefficient will reflect the complementary solvent hydrogen bond basicity. Similarly the *b* coefficient will be a measure of solvent hydrogen bond acidity. All this is straightforward for gas-to-solvent partitions because there are no interactions to consider in the gas phase. For partition between solvents, the coefficients in Eqn. 1 then refer to differences between the properties of the two phases.

Fig. 2. Outline illustrating the calculation of Abraham model solute descriptors from experimental partition coefficient and solubility data, and then using the calculated values to estimate biological activities and partitioning, such as blood-to-tissue partition coefficients, Draize eye scores, aquatic toxicities and air-to-blood partition coefficients.

The Abraham model equation coefficients encode chemical information, and several methods have been suggested to assess the chemical similarity between different partitioning processes/systems. Abraham and Martins (2004) calculated the fivedimensional distance between the coefficients as points in five-dimensional space by straightforward geometry

$$\text{Distance} = \sqrt{\left(\mathbf{e}\_i - e\_j\right)^2 + \left(s\_i - s\_j\right)^2 + \left(a\_i - a\_j\right)^2 + \left(b\_i - b\_j\right)^2 + \left(\upsilon\_i - \upsilon\_j\right)^2} \tag{3}$$

where the subscripts "i" and "j" denote the two partitioning processes being compared. For comparison purposes, the authors suggested that for a good chemical model the calculated distance should be less than about 0.5 – 0.8. The water-to-isobutanol and water-to-octanol partitioning systems were the two chemical systems that the authors found closest to human skin permeability, with calculated distances of 1.2 and 1.9, respectively. The chemical interactions that govern skin permeability were quite different from the chemical interactions governing solute partitioning between water and isobutanol, and between water and 1-octanol. Ishiharma and Asakawa (1999) suggested a different comparison method based on calculating the cosine of the angle (cos θij) between the coefficients

solvent effects that arise through solute polarizability. The **S** descriptor is a measure of dipolarity and polarizability and hence the *s* coefficient will reflect the ability of a solvent to undergo dipole-dipole and dipole-induced dipole interactions with the solute. The **A** descriptor is a measure of solute hydrogen bond acidity, and hence the *a* coefficient will reflect the complementary solvent hydrogen bond basicity. Similarly the *b* coefficient will be a measure of solvent hydrogen bond acidity. All this is straightforward for gas-to-solvent partitions because there are no interactions to consider in the gas phase. For partition between solvents, the coefficients in Eqn. 1 then refer to differences between the properties of the two

Fig. 2. Outline illustrating the calculation of Abraham model solute descriptors from experimental partition coefficient and solubility data, and then using the calculated values

The Abraham model equation coefficients encode chemical information, and several methods have been suggested to assess the chemical similarity between different partitioning processes/systems. Abraham and Martins (2004) calculated the fivedimensional distance between the coefficients as points in five-dimensional space by

where the subscripts "i" and "j" denote the two partitioning processes being compared. For comparison purposes, the authors suggested that for a good chemical model the calculated distance should be less than about 0.5 – 0.8. The water-to-isobutanol and water-to-octanol partitioning systems were the two chemical systems that the authors found closest to human skin permeability, with calculated distances of 1.2 and 1.9, respectively. The chemical interactions that govern skin permeability were quite different from the chemical interactions governing solute partitioning between water and isobutanol, and between water and 1-octanol. Ishiharma and Asakawa (1999) suggested a different comparison

method based on calculating the cosine of the angle (cos θij) between the coefficients

22 2 2 2 Distance (e ) ( ) ( ) ( ) ( ) <sup>i</sup> *j ij ij ij i j e ss aa bb vv* (3)

to estimate biological activities and partitioning, such as blood-to-tissue partition coefficients, Draize eye scores, aquatic toxicities and air-to-blood partition coefficients.

phases.

straightforward geometry

$$\text{Cost } \Theta\_{ij} = \frac{e\_i e\_j + s\_i s\_j + a\_i a\_j + b\_i b\_j + v\_i v\_j}{\sqrt{e\_i^2 + s\_i^2 + a\_i^2 + b\_i^2 + v\_i^2} \sqrt{e\_j^2 + s\_j^2 + a\_j^2 + b\_j^2 + v\_j^2}} \tag{4}$$

which are now regarded as lines in five-dimensional space. The angle between the two lines, θij, yields information regarding how the two compared processes are in terms of their chemical similarity. As θij approaches zero (or alternatively as cos θij approaches unity) the two lines coincide, and the correlation between the two partitioning processes/systems approaches unity. Analysis of the Abraham model coefficients for the solubility of gases and vapors in biological phases (blood, brain, fat, heart, kidney, liver, lung and muscle) and organic solvents (alcohols, amides, olive oil, chloroform, diethyl ether, butanone), and equation coefficients for biological activity (nasal pungency thresholds, eye irritation thresholds, odor detection and anesthesia) using Eqns. 3 and 4 (along with Principal Component Analysis) found N-methylformamide to be an excellent model for both eye irritation thresholds in humans and nasal pungency thresholds in humans (Abraham *et al*., 2009a). The receptor site controlling both biological responses must be protein-like in character. The study further showed that no organic solvent is a suitable model (or surrogate) for blood, brain, heart, kidney, liver, lung and muscle. Two relatively nonpolar solvents (olive oil and chloroform) were found to be suitable models for fat, which is not too surprising given that fat is about 80 % lipid.
