CONCEPTS

Clin Pharmacokinet 2002; 41 (11): 877-899 0312-5963/02/0011-0877/$25.00/0 © Adis International Limited. All rights reserved.

Theoretical Predictions of Drug Absorption in Drug Discovery and Development Patric Stenberg,1 Christel A.S. Bergström,1 Kristina Luthman2 and Per Artursson1 1 Department of Pharmaceutics, Uppsala Biomedical Center, Uppsala University, Uppsala, Sweden 2 Department of Chemistry, Medicinal Chemistry, Göteborg University, Göteborg, Sweden

Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Role of Predictive Models of Permeability and Solubility in Drug Discovery and Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Mechanisms of Intestinal Membrane Permeation . . . . . . . . . . . . . . . . . 2.1 Passive Transcellular Transport . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Paracellular Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Carrier-Mediated Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Active Drug Transport via the Oligopeptide Transporter PepT1 . . . 2.4 Efflux Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Computational Approaches for the Prediction of Intestinal Drug Permeability 3.1 Generation of Calculated Descriptors . . . . . . . . . . . . . . . . . . . . . 3.1.1 Descriptors Based on a Two-Dimensional Representation . . . . . . 3.1.2 Descriptors Based on a Three-Dimensional Representation . . . . . . 3.1.3 Descriptors Based on Wave Functions . . . . . . . . . . . . . . . . . . 3.2 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Qualitative Models of Drug-Likeness . . . . . . . . . . . . . . . . . . . 3.2.2 Quantitative Models of Intestinal Membrane Permeability . . . . . . 4. Computational Approaches for the Prediction of Drug Solubility . . . . . . . . 4.1 Influence of Physiological Factors on Drug Solubility . . . . . . . . . . . . . 4.2 Drug Dissolution After Oral Administration . . . . . . . . . . . . . . . . . . . 4.3 Prediction of Drug Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Development of Predictive Models for Aqueous Drug Solubility . . . 4.3.2 In Silico Models for Aqueous Drug Solubility . . . . . . . . . . . . . . . 4.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The clinical development of new drugs is often terminated because of unfavourable pharmacokinetic properties such as poor intestinal absorption after oral administration. Intestinal permeability and solubility are two of the most important factors that determine the absorption properties of a compound. Efficient and reliable computational models that predict these properties as early as possible in drug discovery and development are therefore desirable.

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In this review, we first discuss the implementation of predictive models of intestinal drug permeability and solubility in drug discovery and development. Secondly, we discuss the mechanisms of intestinal drug permeability and computational methods that can be used to predict it. We then discuss factors influencing drug solubility and models for predicting it. We finally speculate that once these and other predictive computational models are implemented in drug discovery and development, these processes will become much more effective. Further, an increased fraction of drug candidates that are less likely to fail during clinical development will be selected.

It is often desired that drugs are given orally because of the convenience of this administration route. However, not all compounds possess properties that are compatible with oral administration. In fact, the clinical development of a high proportion of new drugs is terminated because of unfavourable pharmacokinetic characteristics, such as poor bioavailability of the drug after oral administration (figure 1),[1-3] leading to significant costs for pharmaceutical companies.[4] The research costs for a compound increase dramatically as it enters clinical development, and so there is an economic incentive to identify and discontinue the development of poor drug candidates as soon as possible. Ideally, poor pharmacokinetic properties that would result in low oral bioavailability should be discovered even before the compound is synthesised. The introduction of modern technologies, such as combinatorial chemistry and high-throughput pharmacological screening in drug discovery, has resulted in a vast increase in the number of lead compounds identified. The compounds generated in high-throughput drug discovery programmes are generally more lipophilic, less water soluble and of higher molecular weight than conventional drugs.[5] These physicochemical properties often entail unfavourable pharmacokinetic properties, which keeps the success rate of such drug candidates in clinical development at a low level.[6] Therefore, research aimed at developing simple experimental and theoretical methods to predict these biopharmaceutical properties earlier is a growing field. Oral bioavailability is the result of a rather complex series of events. Stability issues introduced by © Adis International Limited. All rights reserved.

chemical and enzymatic degradation are one aspect, and the solubility of the drug must be such that the dissolution in the gastrointestinal fluids and the permeation of the intestinal wall keeps pace with the intestinal transit. Only if this is the case will the ingested drug reach the systemic circulation and, subsequently its site of action, in significant amounts.[7] While the term oral bioavailability refers to the entire process of bringing the unchanged drug molecule from its dosage form into the systemic circulation, we have adopted the term oral absorption to mean the transport of an intact drug molecule from its dosage form across the mucosal membrane.[8] The intestinal permeability and solubility of a drug are considered to be two of the most important properties that determine absorption after oral administration, and the influence of these two properties on the extent of absorption from the intestinal tract has received considerable attention.[9-11] Several software packages enable the calculation

Animal toxicity Miscellaneous Adverse effects in humans

Pharmacokinetics

Commercial

Lack of efficacy

Fig. 1. Reasons for failure of new chemical entities in clinical development. The pie chart indicates a strong negative effect of poor pharmacokinetic properties on the development of drug candidates (reproduced from Kennedy,[2] with permission).

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of pharmacokinetic properties such as oral absorption once the permeability and solubility are determined.[12,13] However, the interplay between the permeability and the solubility of a drug compound can also be roughly assessed by calculating the maximum absorbable dose (MAD) [equation 1]:[10,14] MAD = S ´ k a ´ SIWV ´ SIT

where S is the solubility, ka is the first-order rate constant, SIWV is the small intestinal water volume (250 ml) and SIT is the small intestinal transit time (270 min).[14] The required permeability of the intestinal mucosa to a drug compound can be approximated for a given dose provided that the solubility at pH 6.5 is known, while assuming that complicating factors such as presystemic metabolism and degradation are negligible (figure 2). For instance, for a high-dose drug such as amoxicillin (given in doses up to 3g) to be orally available, it must be readily soluble in the intestinal fluids and sufficiently permeable. In this review, we first discuss some key features of predictive models of intestinal transport

1

Required dose

0.1

100mg 5mg 0.1mg

ka (s−1)

0.01 0.001 0.0001 0.00001 0.000001 0.0000001 0.00000001 0.01

0.1

1

Solubility at pH 6.5 (g/L)

Fig. 2. Relationship between drug permeability (expressed as the first-order rate constant, ka) and solubility for a drug administered at three different doses. For a drug that is required in a high dose (e.g. 100mg), a high solubility in the intestinal fluid as well as a rapid permeation of the mucosa are needed. In contrast, the demands for high permeability and high solubility are less strict for a more potent drug that is given in a lower dose. These approximations assume that the drug is only absorbed from the small intestine and that presystemic metabolism and degradation are negligible (equation 1).[10,14]

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and solubility. Secondly, we discuss the mechanisms of intestinal drug permeability and solubility and computational methods that can be used to predict these properties. Factors other than intestinal permeability and solubility, such as presystemic metabolism, that may also affect the extent of absorption after oral administration will not be dealt with in this review. 1. Role of Predictive Models of Permeability and Solubility in Drug Discovery and Development To be applicable in a drug discovery or development setting, any model for permeability and solubility predictions has to be accurate, since a high level of false negative predictions would lead to compounds with the potential of becoming good drugs being discarded, whereas a high level of false positive predictions would lead to significant investment of time and money into compounds that subsequently turned out to be useless. The number of compounds under consideration during drug discovery and development processes decreases rapidly as these processes proceed.[15] Therefore, experimental and computational models of different complexity can be applied at different stages of the discovery and development processes. At an early stage in drug discovery many compounds are being considered, and the applied model must have a high throughput. One possible scheme of permeability and solubility screening is presented in figure 3. The width of the shaded areas in the figure represents the number of compounds dealt with during the discovery process. Initially (at the top of the diagram) many compounds are considered. The number then decreases as the investigation proceeds (down the diagram). The pharmacological screening activities corresponding to the various stages are also shown. Quantitative structure-property relationships (QSPR) derived from fast computational methods can be used to guide the early stages of the design of a library that contains the highest possible number of wellabsorbed compounds.[5,16] The compounds are Clin Pharmacokinet 2002; 41 (11)

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Identification and validation of target

QSAR

Compound library design

QSPR

Library optimised with regard to both pharmacological activity and permeability

Synthesis Pharmacological HTS

Permeability HTS/MTS

Lead identification QSAR

Compound redesign

QSPR

Lead optimisation

Lead optimisation

Training of QSAR model

Synthesis

Training of QSPR model

Thorough pharmacological/permeability characterisation

Candidate selection

Drug development Fig. 3. Flow chart illustrating possible applications of computational and experimental screening for permeability and solubility in drug discovery. The width of the shaded areas represents the number of compounds dealt with during the discovery process. Initially (at the top of the diagram) many compounds are considered. The number then decreases as the investigation proceeds (down the diagram). The right side illustrates application of permeability and solubility models. The left side shows efforts aimed at optimisation of pharmacological properties. In the early discovery phase, simple and fast QSPR models are used as guides to optimise the library and obtain a high proportion of well-absorbed compounds for synthesis. Although not currently available, high-throughput (HTS) in vitro permeability/solubility screens would increase the ratio of well-absorbed compounds among the identified leads. Instead, a medium-throughput (MTS) permeability/solubility screen can be used for selected compounds. During the lead optimisation phase, results from the in vitro permeability/solubility characterisation are used to aid the candidate selection and to construct more complex (and possibly more accurate) QSPR models that can be used for compound redesign. By updating the QSPR models with data from the in vitro characterisation, these models will be tailored for the particular class of compounds investigated in the discovery phase. QSAR = quantitative structure-activity relationships; QSPR = quantitative structure-property relationships.

synthesised, and then rapid in vitro screening gives a rough estimate of the permeability and the solubility, and provides information to help in the lead selection. Although no simple in vitro methods are currently available for determining these properties at a rate that can match their pharmacological counterparts, significant progress towards the development of fast methods has been made.[5,17,18] During lead optimisation, the experimental data can be used to construct improved QSPR models. © Adis International Limited. All rights reserved.

At this stage, the number of compounds is lower, and more sophisticated and computationally demanding QSPR models can be applied. Finally, thorough in vitro and in vivo animal studies can be performed to obtain more reliable measurements and information about transport mechanisms.[19,20] It should be noted that, while separated in figure 3 for clarity, design and optimisation of pharmacological properties and calculations and determination of permeability/solubility are ideally perClin Pharmacokinet 2002; 41 (11)

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formed simultaneously. This review deals with computational models of a wide range of complexity for the prediction of human intestinal drug permeability and solubility. These models can therefore be applied at the different stages of the drug discovery process outlined above, and also be applied in drug development. 2. Mechanisms of Intestinal Membrane Permeation Once dissolved, a drug molecule encounters several sequential barriers (such as the mucus layer, the unstirred water layer, the epithelial cell layer and its underlying tissues) during the transport from the intestinal lumen into the blood. It is generally believed that permeation of the epithelium lining the intestine is the rate-limiting step.[21,22] There are two pathways by which a drug molecule can cross the epithelial membrane: the transcellular pathway, which requires the drug to penetrate the intestinal cell membranes; and the paracellular pathway, in which diffusion occurs through water-filled pores of the tight junctions between the cells. Both passive and active processes may contribute to the permeability of drugs transported by the transcellular pathway. These pathways and processes are distinctly different, and the molecular properties that influence drug transport by these routes are also different, as will be discussed in the following sections. It is therefore crucial to investigate which of these pathways and processes is the most important when developing experimental and theoretical models of drug permeability. 2.1 Passive Transcellular Transport

A drug compound must penetrate the membrane surrounding an epithelial cell in order to transverse the cell. The cell membrane consists of an interrupted double layer of phospholipids[23] and has traditionally been described by the fluid mosaic model,[24] and more recently, by the more complex superlattice model.[25] Different cell membranes throughout the body contain different lipids and different embedded proteins, which © Adis International Limited. All rights reserved.

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means that they have unique properties. Epithelial cells are polarised, and there are appreciable differences in membrane properties even within one epithelial cell. For example, the part of the cell membrane that faces the intestinal lumen (the apical side) and the part of the membrane facing the subepithelial tissues (the basolateral side) have different protein and lipid compositions, and thus different permeability properties. The lipoid nature of the cell membranes restricts the transport of ions and hydrophilic molecules.[26] The ordered structure of the membrane also slows the diffusion of drug molecules in the membrane as the size of the drug molecule is increased.[27] The first step of passive transcellular transport is the penetration by the drug of the apical membrane, which is followed by diffusion through the cytoplasm of the cell interior. If the drug molecule is very lipophilic, the transport across the cell interior may also involve lateral diffusion in the exterior and interior lipid bilayers of the cell. Finally, the drug molecule exits through the basolateral membrane. The diffusion of small molecules in the cytoplasm is normally a rapid process, and thus the rate of passive transcellular permeability is mainly determined by the rate of transport across the apical cell membrane.[28] Even though transport by this pathway requires a reasonably lipophilic molecule of moderate size, numerous studies indicate that the vast majority of well-absorbed drugs are predominantly transported passively across the cell membranes.[29] Thus, the rather complex process of intestinal drug permeation can often be satisfactorily described by considering passive transport across the apical cell membranes only, and the development of theoretical models describing transport by this mechanism is particularly important. Passive transport across the cell membrane was initially thought to occur according to the solubilitydiffusion model.[30] The cell membrane is treated in this model as a homogenous barrier, and the transport proceeds by distribution into and subsequent diffusion across the membrane. The pHpartition theory predicts that only the uncharged Clin Pharmacokinet 2002; 41 (11)

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be identified (figure 4).[33] These simulations suggested that partitioning of polar drug molecules into the dense apolar region of the membrane interior is often the main barrier in the transport process.[33,35,38] It should be emphasised that the interactions of drugs with real membranes containing multiple components is considerably more complex than simulated drug-membrane interactions.[39] In conclusion, regardless of whether the solubilitydiffusion model or the four-region membrane model is adopted to describe passive membrane permeation, the rate of the passive transcellular transport process is largely determined by the hydrogen bonding capacity, lipophilicity, size and charge of the solute. This is why experimental and theoretical models describing transport using these properties have received particular attention.[40,41] However, an increasing number of active transporters and efflux mechanisms that may influence drug permeability are being discovered, although the contributions of these active mechanisms to the in vivo absorption of drugs remain to be determined in most cases.

1

2

3

4

3

2

1

Resistance to water permeation

species of protolytic drugs will be partitioned into the membrane.[31] Thus, according to the solubilitydiffusion model and the pH-partition theory, three properties describe the transport process: membrane-water partitioning, charge and solute size (assuming that diffusion rate in the membrane is reflected by the solute size). The transport of a molecule across a cell membrane is impaired when the molecule is ionised, but it does not completely cease.[32] The solubility-diffusion model also implies that membrane partitioning is a one-step process. This is why drug partitioning in isotropic solvent systems, such as the octanol/water system, has frequently been used to predict passive membrane transport, with some success (see below). However, the simplistic model in which membrane partitioning is considered to be a one-step process fails to account for the anisotropic nature of the cell membrane.[33] Two significant facts that arise from the anisotropic nature of the membrane must be considered: that the diffusion rate of a drug molecule is different in various regions of the membrane[34] and, perhaps more importantly, the forces that govern partitioning into the membrane are different in various regions of the membrane.[35] The anisotropic nature of the membrane has been included in a model in which membrane partitioning is considered to be a two-step process,[36] and this model has been successfully applied to describe drug transport.[37] The two-step partitioning process can be rationalised by considering the insertion of a polar, but lipophilic, molecule into a phospholipid membrane. Lipophilicity is the major driving force for solute accommodation into the region of the phospholipid head groups. Subsequent transfer of the solute into the interior of the phospholipid bilayer, on the other hand, depends mainly on energetically unfavourable interactions between the bilayer and the polar parts of the solute. This process depends to a lesser extent on lipophilicity, and can be largely accounted for by hydrogen bonding and polarity.[35] Evidence that this mechanism is likely to occur comes from molecular dynamics simulations in which four separate regions in the membrane could

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Fig. 4. Schematic representation of the four-region membrane model. In the perturbed water layer (1) an approaching solute starts to experience the polar head groups. The membrane reaches its highest density in the interphase (2), and the charges presented by the polar head groups restrict the movement of water molecules. In the soft polymer region (3), a high tail density restricts solute diffusion. The apolar nature of this region will not allow the incorporation of water molecules. The tail density decreases in the middle of the bilayer. The decane region (4) does not contain any water, and has a high percentage of free volume. This region allows for the incorporation of hydrophobic solutes.[33] The curve represents the resistance that a water molecule experiences during its passage through the membrane.

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2.2 Paracellular Transport

Transport across the epithelial cell layer can also occur via water-filled pores between the cells, a process known as paracellular transport. Some investigators have reported that a saturable and substrate-specific mechanism operates during the transport of some H2 antagonists by this pathway,[42,43] but paracellular transport is generally considered to be a passive process that follows Fick’s law (i.e. the transport rate is proportional to the drug concentration at the surface of the apical membrane).[44] The paracellular pathway offers a route for the transport of hydrophilic compounds, which do not penetrate the cell membranes of the epithelial cells, but the surface area presented by the pores constitutes only a small fraction (0.01 to 0.1%) of the total intestinal membrane surface area.[45,46] In addition, tight junctions provide a seal between adjacent epithelial cells, which restricts solute transport via this route.[47,48] The tight junctions further limit transport by the paracellular pathway in the distal parts of the intestine.[49,50] It is therefore unlikely that this pathway contributes significantly to the overall transport of most drugs in vivo, although small molecules (with molecular weight less than approximately 200) may be exceptions to this statement.[51,52] 2.3 Carrier-Mediated Transport

Solutes can also be transported in the apical to basolateral direction by proteins embedded in the cell membrane. These proteins extract nutrients and other compounds essential for the organism from the luminal contents by various carriermediated mechanisms. The most notable features of carrier-mediated transport are its substrate specificity, saturability and regional variability.[53] Substrate specificity is crucial to preventing the entry of unwanted compounds into the body, but the substrate specificity is not absolute and this transport route is available to a limited number of drugs. These include β-lactam antibiotics and ACE inhibitors, which are transported by the oligopeptide carrier as discussed in section 2.3.1, and nucleoside © Adis International Limited. All rights reserved.

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and phosphate analogues, all of which are structurally similar to the native substrates of transport proteins.[54-56] Saturability will become apparent when the carrier protein is faced with a high substrate concentration. From a pharmacokinetic perspective, saturation manifests itself as nonlinearity in the dose-response relationship. Another characteristic that must be considered is the regional variability of the expression of carrier proteins. These are expressed to different degrees in different regions of the intestinal tract, and the substrate will be absorbed better in areas of the intestine where expression of the carrier protein is high (usually upper intestine). The perhaps most widely targeted active transport system for orally administered drugs is the oligopeptide transporter. 2.3.1 Active Drug Transport via the Oligopeptide Transporter PepT1

Extensive research has recently been performed into the use of active transport mechanisms for improving the oral bioavailability of drugs. This research has paid special attention to the use of the oligopeptide transporter PepT1[54,57,58] (and references therein). PepT1 is located in the apical membrane of enterocytes and mediates transport of dipeptides and tripeptides. Human PepT1 has been cloned and expressed in HeLa cells and Xenopus laevis oocytes.[59] PepT1 has been classified as a low-affinity [its Michaelis constant (Km) is in the mmol/L range], high-capacity transporter belonging to the proton oligopeptide transporter (POT) superfamily. It is driven by a transmembrane proton gradient that catalyses the cotransport of the substrates with protons. This 708-amino-acid protein contains 12 putative membrane-spanning regions[60] that form a channel through which substrates are transported.[61] Site-directed mutagenesis has identified several amino acids, including histidine and tyrosine, as important for recognition, binding and transport.[62,63] The importance of histidine, in particular His-57, has been inferred from studies showing a complete inhibition of transport after treatment with the histidine-modifying agent diethylpyrocarbonate. In addition, the pH activaClin Pharmacokinet 2002; 41 (11)

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tion of PepT1 coincides with the pKa of His, which indicates that it is also important in the proton transport. It has been suggested that residues from the length of the protein construct the binding site for peptide substrates; however, a crystal structure is needed to get a detailed picture of the binding site. Recently, X-ray structures were published of complexes between tripeptides and a peptide transporter (OppA) in Gram-negative bacteria.[64] However, the relevance of the structural information obtained from these studies for PepT1 binding has not yet been established. The natural substrates for PepT1 are di- and tripeptides. Therefore it was initially believed that at least one peptide bond together with free aminoand carboxy-termini were needed for binding and transport. However, recent structure-transport studies on ω-amino fatty acids revealed that a peptide bond is not necessary for binding and transport via PepT1.[65] It was shown that the chain between the amino and carboxylic acid group should contain at least four methylene groups. Interestingly, δaminolaevulinic acid (5-amino-4-oxo-pentanoic acid) showed enhanced affinity compared with 5aminopentanoic acid, suggesting a beneficial hydrogen bonding interaction in a position corresponding to the first peptide bond in a di- or tripeptide. Studies by Börner et al.[66] suggest that a free carboxylic acid group is not necessary to obtain efficient binding and transport by PepT1, as it could transport amino acid aryl amides. In fact, Ala-4-nitroanilide, Phe-4-nitroanilide and Ala-4phenylanilide were accepted as substrates with higher affinity than the corresponding natural dipeptides. It seems as electron-withdrawing substituents on the aromatic rings improve the binding of the ligand to the C-terminal site, probably by increasing the acidity of the amide bond. However, a free amino group appears to be important for efficient binding of substrates to PepT1, although this statement has also been challenged in some studies.[66] The peptide transporter PepT1 has been shown to act as an efficient drug delivery pathway. For example, it has been known for many years that © Adis International Limited. All rights reserved.

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orally active β-lactam antibacterials (both cephalosporins and penicillins) have structural features similar to tripeptides and that they therefore can serve as substrates for oligopeptide transporters. The structure-transport properties for β-lactam antibiotics have been studied extensively,[67,68] and a set of key structural features has been proposed. The compounds should preferentially contain: (i) both an N- and a C-terminal amide or lactam group to mimic a tripeptide backbone; (ii) a free carboxylic acid group in the sulphur-containing ring; and (iii) a free α-amino group, to ensure efficient binding to PepT1. Other types of drugs whose structures are based on a di- or tripeptide skeleton, such as ACE inhibitors, have also been established as PepT1 substrates. These compounds have at least one peptide bond and a free terminal carboxylic acid group as key elements for binding. The antineoplastic agent bestatin, a dipeptide containing an unusual amino acid, is also a substrate for PepT1.[69] It has been used clinically as an orally available anticancer agent. Targeting of the intestinal peptide transport system by prodrug approaches has received considerable attention. Prodrugs designed to mimic di- or tripeptides can be efficiently transported. For example the nucleoside antiviral drugs acyclovir and ganciclovir,[70] widely used in the treatment of cytomegalovirus infections, are polar compounds with low oral bioavailability. When L-valine was connected to acyclovir and ganciclovir via an ester linkage to produce valacyclovir and valgancyclovir, respectively, a significantly improvement of the bioavailability of the two drugs was observed. The same concept has been used to improve the oral bioavailability of the anti-HIV drug zidovudine.[71] When zidovudine was coupled to L-valine to form L-valyl-zidovudine, its bioavailability increased as a result of PepT1 transport. Thus, the addition of a valyl ester residue to otherwise nontransported compounds appears to make them transportable substrates for PepT1.[72] Interestingly, there was also observed a stereospecific preference for the L-valine ester over the D-valine ester in the transport. However, the transport of Clin Pharmacokinet 2002; 41 (11)

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these nucleoside-based drugs has recently been shown to involve multiple transporters.[73] The transport of amino acid drugs such as Ldopa and L-α-methyldopa has been improved by converting them into dipeptidic prodrug derivatives. L-Dopa has, for example, been modified into the dipeptide derivatives L-dopa-L-Phe and Ldopa-D-Phe,[74] whereas L-α-methyldopa was converted into L-α-methyldopa-L-Phe and D-Phe-Lα-methyldopa. Again, a clear stereochemical effect was shown, with the L-isomers being more efficiently transported. Recently, a systematic investigation of the importance of free amino and/or carboxylic acid groups for interaction with rabbit PepT1 was published.[75] A series of blocked amino acids and dipeptide derivatives were tested for their ability to inhibit the uptake of D-Phe-L-Gln, a well known PepT1 substrate. The results from this study were used for the development of a two-dimensional model that could be useful in design of substrates with high affinity for PepT1. The model is based on the following assumptions (figure 5): (a) the N-terminal amino group is anchored to Glu-595 via an ionic interaction; (b) a hydrogen bond stabilises the first peptide bond; (c) the side chain of the second amino acid appears to occupy a critical binding region, and therefore the stereochemistry is most important at this site; and (d) the Cterminus of a dipeptide binds to His-57 via an ionic interaction, whereas tripeptidic substrates or dipeptide amides probably interact with His-57 via hydrogen bonding. To further improve the generality of this model, a three-dimensional substrate template was developed using molecular modeling. This new model explains the binding and transport properties of all PepT1 substrates published so far,[76] and can also discriminate between substrates that will be transported with high, medium or low efficiency (figure 5). The same key binding sites as in the twodimensional model have been identified, but a second carboxylate-binding site with the correct stereochemistry at the adjacent stereogenic centre appears also to be required. The distance between © Adis International Limited. All rights reserved.

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H Glu −

H2N R1

H N

R2

O

X

(d)

O (a)

His

H Y

R3

CO2

_

+

(c)

(b)

Fig. 5. Substrate recognition pattern for the oligopeptide transporter PepT1. The model is based on four key binding sites: (a)

an ionic interaction between the N-terminus of the dipeptide or tripeptide and Glu-595; (b) a hydrogen bond that stabilises the first peptide bond; (c) an ionic or hydrogen bond interaction between the C-terminus of the peptide and His-57; and (d) an interaction between the side chain of the second amino acid in the peptide and a hydrophobic pocket in PepT1.[76]

the amino and carboxylate groups should preferably be 0.6nm. As this model also takes the threedimensional features into account, it assigns the high affinity substrates as those that easily adopt the correct conformation for efficient binding. Thus, if using these models correctly, interesting drug candidates can be designed that exhibit high oral bioavailability through PepT1 transport. In summary, carrier-mediated mechanisms, such as that provided by PepT1, enhance the transcellular permeability to a limited number of drugs. The extent of this enhancement depends not only on the structural similarity between the drug and the natural substrate of the transporter, but also on drug concentration and physiological factors. 2.4 Efflux Mechanisms

In contrast to the carrier-mediated mechanisms that promote drug permeability, efflux proteins localised in the apical or basolateral cell membranes have the potential to influence overall permeability by pumping drugs out from the cell into the apical or basolateral extracellular fluids. Drug efflux into the intestine is often attributed to apically located proteins of the ABC-transporter family, such as P-glycoprotein and multidrug resistance–associated protein 2 (MRP2).[77-79] Recently, the breast cancer resistance protein (BCRP) was shown to limit the intestinal absorption of Clin Pharmacokinet 2002; 41 (11)

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topotecan in mice.[80] This protein, and several other efflux proteins of the ABC-transporter family, is also present in human small intestine.[81] Several researchers have attempted to define the substrate specificity of the various efflux proteins, but the exact structural requirements remain uncertain.[78,82-84] However, distinct patterns of electrondonating groups seem to characterise P-glycoprotein substrates and inducers, respectively.[83] For instance, the P-glycoprotein substrate verapamil carries two pairs of electron-donating oxygen atoms, and the distance between the oxygen atoms in each pair is approximately 0.25nm. The P-glycoprotein inducer vincristine carries an additional group of three oxygen atoms, the maximum distance between the oxygen atoms in this group being approximately 0.46nm.[85] These patterns were consistent when a set of 100 P-glycoprotein substrates, inducers and non-substrates were analysed, although the electron-donating groups may also contain nitrogen atoms.[85] The function of the efflux system may be to prevent uptake of toxic substrates or to facilitate the excretion of such substrates across the mucosa of the intestinal tract.[86] This would explain the broad and sometimes overlapping substrate specificity of the efflux proteins. For example, the chemotherapeutic agent etoposide is transported across the intestinal wall not only by P-glycoprotein, but also by other efflux systems.[87] Understanding the behaviour of the substrates in vivo is complicated not only by the intra- and interindividual differences in expression levels of efflux proteins, but also by functional polymorphism.[88] Studies of efflux proteins, such as P-glycoprotein, may also be complicated by simultaneous metabolism of the substrates by intestinal cytochrome P450s, such as 3A4, as their substrate specificity often overlaps. The interplay between these efflux and metabolic systems have been discussed elsewhere.[89-91] Furthermore, differences between in vitro and in vivo systems sometimes give rise to contradictory results.[29,92-94] © Adis International Limited. All rights reserved.

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2.5 Overview

In summary, a high passive transcellular permeability is important for the satisfactory absorption of most drugs. Other transport processes contribute significantly to the transport in certain cases, but the contribution of these processes varies widely between different regions of the intestinal tract, making knowledge of passive transcellular permeability important also in these cases. We may conclude that the development of models that predict passive transcellular permeability is essential, and such models are the focus of the remaining part of this review. 3. Computational Approaches for the Prediction of Intestinal Drug Permeability

3.1 Generation of Calculated Descriptors

The first step in the development of a model that predicts membrane permeability is to construct a description of the drug molecule. In its simplest form, this description may be the number of atoms in the drug molecule (the general trend would show that the lower the atom count, the higher the permeability). Such a simple descriptor, however, would generate a scattered relationship with membrane permeability, and more fine-tuned descriptions are often used. 3.1.1 Descriptors Based on a Two-Dimensional Representation

Molecules can be represented by their twodimensional structure or by their Simplified Molecular Input Line Entry Specification (SMILES) line notation code.[95] Such representations identify atom types and functional groups, and this information can be used to rapidly calculate physicochemical properties such as hydrogen bonding capacity,[96] lipophilicity[97,98] and charge. A number of topological descriptors can also be derived from the two-dimensional structure.[99] Clin Pharmacokinet 2002; 41 (11)

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3.1.2 Descriptors Based on a Three-Dimensional Representation

Two-dimensional representations provide incomplete information about a molecule, and threedimensional structures may be required. Further, using the three-dimensional structure of the molecule allows several different spatial arrangements that are not accounted for in the two-dimensional representation to be distinguished. Three-dimensional structures depend on the environment of the molecule and can be obtained by performing molecular mechanics calculations. Descriptors generated from three-dimensional structures are therefore unique for a particular molecular conformation and are considered to better reflect the intramolecular interactions. A single three-dimensional conformation can be generated in a fraction of a second, but a full search of the conformational space may require several days or weeks when using molecular mechanics calculations based on the Monte Carlo algorithm or when carrying out molecular dynamics simulation. Descriptors such as molecular surface areas,[100] molecular volume and conformationally dependent lipophilicity (MLP) [101] can then be derived from the threedimensional structures that are generated. 3.1.3 Descriptors Based on Wave Functions

The two-dimensional and three-dimensional structures do not generally provide an accurate description of the electron distribution of the molecules. The electron distribution determines the valence properties of the molecules, and the molecules must be represented by wave functions in order to obtain information about the electron distribution. Wave functions are generated by quantum mechanics calculations. These representations contain a massive amount of information and allow virtually every known computational descriptor to be calculated. However, quantum mechanics calculations are very time-consuming even if only one conformation of each compound is considered, and these calculations are not practical for application in larger compound libraries. The two-dimensional structure is the basis for molecular mechanics or molecular dynamics cal© Adis International Limited. All rights reserved.

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culations, and an appropriate three-dimensional structure is used as input for the quantum mechanics calculations. These methods thus correspond to different levels of complexity of the representation of a molecule (figure 6). Descriptors of a particular level of complexity (or a lower level) can be derived from the corresponding level of complexity of the representation. However, complex descriptors have been successfully predicted from less complex ones.[102-105] Whether simple or complex, the descriptors outlined in figure 6 may be related to membrane permeability by appropriate statistical methods, and in this way provide predictive models of intestinal membrane permeability. 3.2 Model Development

Several computational models have been developed in recent years for the prediction of passive intestinal membrane permeability. The models described in this section are primarily aimed at predicting passive transport. Note that in large diverse data sets, where several transport mechanisms contribute significantly to membrane permeability, the correlations between permeability and calculated descriptors are likely to become weaker.[106] These models are either qualitative or quantitative. These two types of model are often constructed using different approaches and they allow different types of predictions to be made. The models will therefore be treated separately in the following sections. 3.2.1 Qualitative Models of Drug-Likeness

It is assumed that a drug or a compound that has reached phase II in the development process is sufficiently well absorbed to meet clinical demands (since oral administration is preferred for most drugs) and that it possesses other properties that are associated with drugs. Such a compound may be defined as drug-like.[107] Qualitative models have been developed by examining groups of drug-like compounds and looking for systematic patterns in the structures of these compounds. Several investigators have used this method to compare a set of drug-like compounds with a set of Clin Pharmacokinet 2002; 41 (11)

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Representation

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I

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IIa

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Wave function

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Atom counts, fragment counts, topological indexes

Molecular surface properties and volume

Dynamic molecular surface properties and volume

Molecular valence properties

Fig. 6. The three levels of complexity for molecular structure representation discussed in the text are shown on the left. Some of the descriptors that can be derived from these representations are shown on the right. 2D = two-dimensional; 3D = three-dimensional.

compounds that are not drug-like,[107-111] or to analyse molecular descriptors in a set of drug-like compounds.[5,112-117] One advantage of these qualitative models is that they do not require the conduct of additional experiments, and this allows the study of a large number of compounds (provided that the databases have been validated to actually consist of drugs and, when applicable, nondrugs, respectively). The way in which the model treats the difference between drugs and nondrugs may be too simple, however, since a drug may differ from a nondrug in many respects. The reason that a compound is not a drug may be poor permeability, but it may also be a lack of efficacy, lack of pharmacological activity, toxicity, extensive metabolism or poor solubility. These factors need to be considered when interpreting the results from such models. The qualitative model that is probably the best known is the ‘rule of five’.[5] This model was developed by Lipinski and coworkers, who analysed 2245 phase II compounds and identified four easily © Adis International Limited. All rights reserved.

calculated descriptors that did not exceed certain limits for most of the compounds. The descriptors, with the limits given in parentheses were: the number of hydrogen bond donors (more than five), the number of hydrogen bond acceptors (more than ten), molecular weight (greater than 500) and calculated octanol/water partition coefficient (greater than five). The rule of five states that if two or more of these limits are exceeded, the compound in question is not likely to be (or become) a drug. The rule of five is only applicable to compounds that are absorbed by passive mechanisms (see section 2).[5] The merit of this model is the ease with which the descriptors can be determined and interpreted. This is probably also the major reason for its widespread use. However, the relevance of the rule of five has recently been questioned.[117] 3.2.2 Quantitative Models of Intestinal Membrane Permeability

Quantitative models have been developed by relating experimental permeability to one or more calculated molecular descriptors. The relationClin Pharmacokinet 2002; 41 (11)

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ships can be derived using several statistical methods, ranging from simple linear regression[118] to complex methods involving neural networks.[119] In general, simple models that contain few descriptors are easier to interpret than models that contain many descriptors related to permeability in a complex way. Calculated lipophilicity, hydrogen bonding capacity and molecular size derived from fragment and atom counts (figure 6, level I) were among the first descriptors to be used for the description of passive membrane permeability.[120,121] These descriptors have subsequently been correlated to passive membrane permeability, with some success.[118,122-125] Other descriptors based on fragment and atom counts that have been employed for the description of membrane transport include solubility parameters,[126] electrotopological state indexes[105,127] and a composite ensemble of physicochemical properties.[128] The results obtained using these simple methods were generally comparable to the results obtained using more computationally demanding methods,[105,129,130] which suggests that the computational procedures can be simplified with little effect on the correlations with membrane permeability. Molecular surface properties derived from molecular mechanics calculations (figure 6, level II) have been used to describe various physicochemical properties such as lipophilicity,[101,131] solvation energy[132] and solubility.[133] Molecular surface properties, and in particular the polar molecular surface area (PSA), have recently received a great deal of attention as potential predictors of the rate of membrane transport.[37,102,112,118,122,134-140] PSA, which is generally assumed to be related to hydrogen bonding capacity, was introduced as a descriptor for passive membrane transport by van de Waterbeemd and Kansy.[141] PSA provides an accurate description of permeability for most series of compounds that have been investigated. The method has been modified to consider the PSA not only of a single molecular conformation, but of all low-energy conformations.[118] The dy© Adis International Limited. All rights reserved.

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namic PSA (PSAd) obtained by this procedure was considered to better reflect the conformational flexibility of the molecule (figure 6, level IIb). PSAd was closely related to intestinal absorption after oral administration to humans of a series of 20 structurally diverse conventional drugs for which calculated lipophilicity had proved to be a poor descriptor (figure 7).[134] PSAd is computationally more demanding than the easily calculated PSA, and the significance of the improvement of the molecular representation introduced by using PSAd has been addressed in some studies.[105,112,139] These studies showed only small differences between the results obtained using PSA and those obtained using PSAd, although flexible compounds with larger PSA are expected to show a larger variability between PSA and PSAd.[102,135] Conformational effects resulting in such variability in PSA are believed to play an important role for the membrane permeation of the immunosuppressive agent cyclosporin.[142] Krarup et al.[136] found that PSAd calculated from atomic van der Waals’ radii did not account for the enhanced Caco-2 cell monolayer permeability that was observed as a series of β-receptor antagonists was esterified. Although the problem was circumvented by increasing the atomic radii to shield the polar surface contributed by the ester group, this study shows one fundamental drawback of PSAd: alone, it cannot account for hydrophobic effects introduced by the addition of nonpolar substituents. We have therefore tested whether the dynamic nonpolar surface area (NPSAd) should also be considered in the prediction of membrane permeability.[37] We found that the relationship between a combination of polar and nonpolar surface areas and in vitro intestinal epithelial permeability to a series of oligopeptide derivatives was much stronger than that of single surface properties. Similarly, the relationship between surface properties and in vitro colonic permeability to a series of endothelin receptor antagonists was stronger for a combination of polar and nonpolar surface areas than for PSAd alone.[138] Clin Pharmacokinet 2002; 41 (11)

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a 100

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0 0

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200

250

PSAd (Å2) b 100

80

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60

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0 −8

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Fig. 7. Prediction of intestinal absorption from dynamic polar molecular surface area (PSAd). (a) Sigmoidal relationship between PSAd of 20 structurally diverse model drugs and their fraction absorbed (fa) after oral administration to humans (reproduced from Palm et al.,[134]with permission). The relationship suggests that drugs with a PSAd < 63Å2 will be completely absorbed (fa > 90%) whereas drugs with PSAd > 139Å2 will be absorbed to less than 10%. (b) Lack of relationship between calculated lipophilicity (C log P) and fa. The compounds represent common drugs and model compounds, as detailed in Palm et al.[134]

© Adis International Limited. All rights reserved.

PSA, lipophilicity and hydrogen bonding properties have been used to construct models of human intestinal permeability based on partial least squares projections to latent structures (PLS).[137] The study included 22 drug compounds. Wessel et al.[119] used the descriptors derived from the surface area of hydrogen bond acceptor atoms as input parameters for a neural network that described human intestinal absorption of 86 drugs and related compounds. This data set includes most drugs recommended by the Food and Drug Administration as standards for the biopharmaceutical classification system.[143] A number of other methods have been developed for predicting permeability from descriptors derived from three-dimensional structures.[103,144-146] Molecular descriptors generated by complex quantum mechanics calculations (figure 6, level III) have also been used to describe membrane permeability. Several descriptors related to physicochemical properties have been calculated using such methods and then correlated to Caco-2 cell monolayer permeability,[105,130] to human intestinal absorption,[129] and to in vitro rabbit colonic permeability[138] by a PLS methodology. Reasonably accurate descriptions of intestinal membrane permeability were obtained by these calculations, but computational requirements generally limit the applicability of such models to a small number of compounds. However, these descriptors are regarded as relatively accurate,[147] and quantum mechanics calculations can be useful when mechanistic structure-permeability relationships rather than screening methods are sought. Thus, a large number of computational models spanning a wide range of computational requirements have been developed to predict intestinal membrane permeability and absorption. Methods based on quantum mechanics calculations often provide predictions that are comparable to those obtained from faster methods involving molecular mechanics or atom or fragment counts.[104,105,128] However, simple methods do not always perform as well as the more computationally demanding methods.[138] Therefore, the choice of method will Clin Pharmacokinet 2002; 41 (11)

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depend on the nature of the information that is required and the computational resources available. It is, however, concluded that several different approaches have been applied to predict intestinal membrane permeability, and the results are generally promising. Drug absorption following oral administration depends not only on the permeability of the membrane, but also on the solubility of the drug. Studies in silico of drug absorption must also deal with this aspect, and the next section describes the methods available. 4. Computational Approaches for the Prediction of Drug Solubility As for drug permeability, the solubility of a drug compound in the gastrointestinal tract depends on the physicochemical characteristics of the drug. Some simple rules of thumb can be extracted from the knowledge of molecular physicochemical properties such as lipophilicity, size and charge. First, the higher the lipophilicity of a compound, the lower the solubility.[148] Secondly, the larger the size of the compound, the lower the solubility.[149,150] Thirdly, for protolytic compounds, the higher the degree of the ionisation of the compound, the higher the solubility as described by the Henderson-Hasselbach equation. The degree of ionisation depends on the pKa of the drug and the pH of the intestinal fluid. Acids are more soluble at alkaline pH, where the acid loses its proton and receives a negative charge, whereas bases are more soluble at acidic pH, where the functional group attracts a proton and receives a positive charge. Thus, the solubility of a drug depends not only on its intrinsic physicochemical properties, but also on physiological factors, such as the intestinal pH. In the following sections, physiological factors that influence drug solubility will be briefly discussed before methods for predicting solubility are reviewed. 4.1 Influence of Physiological Factors on Drug Solubility

The pH of the gastrointestinal tract varies from approximately pH 1 in the stomach up to pH 8 in © Adis International Limited. All rights reserved.

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the colon. The solubility of protolytic drug compounds will therefore be dependent on the location in the gastrointestinal tract. Other factors that influence the solubility are the ionic strength of the intestinal fluid, the production of bile salt and the fed and nonfed state. The ionic strength of the intestinal fluid depends on the intake of food and fluid, and on intestinal absorption and secretion. In general, the solubility of a drug compound will decrease when the ionic strength of the solvent increases.[151-153] The decrease in solubility is a result of the common ion effect and/or the salting-out effect. The common ion effect occurs when a charged drug compound and its counter-ion associate to form an uncharged complex. This complex precipitates out and the solubility is thus lowered.[152,154] The salting-out effect arises when electrolytes in the solution compete with the drug compound for bonds to water molecules.[151,153] The more electrolytes that exist in the water, the more of the water molecules will be occupied, which means that the drug molecules can make fewer hydrogen bonds to the water. The solubility of the drug compound thus decreases. However, the addition of electrolytes/ions to the water can give rise to a higher solubility of some compounds.[151,153,155] This is the salting-in effect and occurs when the additives loosen up the tight water structure, making it easier for the compound to form hydrogen bonds with the water molecules. The production of bile salt usually increases the solubility of a compound.[156] Bile salts are surfactants that can adhere to the drug molecule and act as an intermediate phase between the lipophilic molecule and the hydrophilic water phase and thus act as a wetting agent. If secreted at high concentrations, simple micelles incorporating bile salts only, or mixed micelles incorporating bile salt and other surfactants such as food components, are formed. The micelles form a lipophilic interior and a hydrophilic exterior, since the outside is in contact with the aqueous fluid. The solubility of lipophilic drug compounds usually increases due to the wetting mechanism of the bile salt, but they can also be solubilised in the micelles. Hammad and Clin Pharmacokinet 2002; 41 (11)

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Müller[157,158] have shown that the solubilities of benzodiazepines (lorazepam, diazepam, clonazepam and tetrazepam) and steroids (prednisolone and progesterone) were increased 2- to 3-fold in the presence of mixed micelles of bile salt and phosphatidylcholine due to solubilisation. The secretion of bile salt increases as food is ingested. However, the food components compete with the drug compound for hydrogen bonds to water (in the same way as electrolytes and ions do), which may result in a lower solubility of the drug. Furthermore, the food increases the viscosity of the intestinal fluids, which may decrease the dissolution rate and the solubility. The effect of food on solubility, and thus bioavailability, should therefore be investigated for each compound individually.[156] In conclusion, the intestinal solubility of a drug compound depends on several factors associated with its physicochemical properties, and on physiological factors. Such factors include the site of dissolution (stomach, small or large intestine), the general physiology (pH fluctuations, absorption/secretion processes) and the presence of food in the gastrointestinal tract. 4.2 Drug Dissolution After Oral Administration

When a drug is ingested in a solid dosage form, for example in the form of a tablet, the dosage form first disintegrates and thereafter the drug dissolves in the gastric or intestinal fluids. The dissolved drug molecules can then diffuse through the fluid to the enterocyte membrane, pass through the cells and enter the systemic circulation. The dissolution process can be described quantitatively by the Noyes-Whitney equation (equation 2):[159] dm D ´ A = ´ ( Cs - C t ) dt h

where dm/dt is the dissolution rate, Cs is the maximum amount of drug that can be dissolved in the fluid, i.e. the solubility, Ct is the drug concentration at time t, A is the surface area of the undissolved dosage form, D is the diffusion coefficient of the drug in the intestinal fluid, and h is the height of the diffusion layer adjacent to the solid dosage © Adis International Limited. All rights reserved.

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form. The parameters in the Noyes-Whitney equation show how physiological properties influence the rate of dissolution. The higher the diffusion coefficient of a molecule, the higher the dissolution rate. The diffusion coefficient is inversely correlated to the viscosity of the intestinal fluid. Moreover, the particle surface area of the dosage form affect the dissolution rate. An example of this is HO-221, a poorly water-soluble oral anticancer drug, the solubility of which was significantly increased by introducing micronisation into the processing of the dosage form, resulting in increased bioavailability of the drug.[160,161] The surface area can be increased in vivo by diffusion of water into the dosage form, which forces the dosage form to burst into several smaller particles. Furthermore, the dissolution rate increases with increasing solubility. The solubility can be improved either by a salt formation of the compound or by synthesis of a prodrug of the compound. For example, phenytoin is a poorly soluble drug, whose solubility and thus bioavailability have been improved in different ways. By salt formation with sodium, the bioavailability of phenytoin has been considerably improved.[162] Prodrugs of phenytoin have shown higher solubility in the gastrointestinal fluid than phenytoin itself. This is probably because the more lipophilic prodrugs are solubilised by bile salt, resulting in increased bioavailability of phenytoin.[163] 4.3 Prediction of Drug Solubility

Several computational and semi-empirical models have been devised to predict drug solubility. Unfortunately, these are often only valid for homologous series of compounds or for diverse series of compounds that do not include complex molecules.[164,165] However, more complex models have recently been developed that can predict solubility in more diverse series of compounds.[165-168] 4.3.1 Development of Predictive Models for Aqueous Drug Solubility

Both experimentally determined and calculated physicochemical descriptors can be used for prediction of solubility. In the late 1960s, Hansch and Clin Pharmacokinet 2002; 41 (11)

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coworkers found a correlation between lipophilicity and solubility.[148] In this study, the octanolwater partition coefficient was used to describe the lipophilicity and a fairly linear relationship was found between the lipophilicities and the aqueous solubilities for 156 organic liquids. Further work attempted to extend the applicability of this model to cover solids. Yalkowsky and coworkers investigated several series of solid compounds, and showed that lipophilicity, entropy of fusion and melting point can be used as descriptors for the solubility of solids.[169-172] However, these models require the experimental determination of melting point and are thus not pure computational models. Furthermore, the models may not be generally applied, as they depend on the dataset investigated. The cohesive energy of a solvent will determine how readily a molecule will be dissolved in a specific solvent and thus can be used to predict solubility. This approach was introduced by Hildebrand and Scott,[173] who derived what is known as the solubility parameter from the square root of the cohesive energy. The model has been further developed by including parameters that also describe polarisability and interactions due to hydrogen bonding.[174-176] An extension is the linear solvation energy relationship (LSER), which considers solubility as a function of volume, dipolarity and hydrogen bonding capacity.[177,178] The LSER theory has been successfully used to predict the solubilities of simple organic nonelectrolytes.[179] Some of the experimental descriptors used in these models can be readily calculated from the two-dimensional structure of the molecule. However, solubility models in early drug discovery settings require purely computational approaches. During the last few years, descriptors for electrotopology have been proved to be useful in predictions of drug solubility. These descriptors can be computationally generated from the two-dimensional structure of the compound by a SMILES line notation code (figure 6, level I).[164,166,168] Recently, descriptors associated with molecular surface area calculated from the three-dimensional structure of the drug molecule using molecular me© Adis International Limited. All rights reserved.

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chanics (figure 6, level IIb) have been correlated with solubility.[180] 4.3.2 In Silico Models for Aqueous Drug Solubility

Solubility has been predicted in silico using different types of descriptors and linear regression. An investigation of a large dataset of 1450 compounds, including solids, showed that size and lipophilicity alone could be used as solubility descriptors.[150] Unfortunately, this simple model is based mainly on compounds that are not drug-like, and its usefulness in drug discovery may therefore be restricted. Abraham and Lee recently published solubility predictions for 659 compounds using an amended LSER model with computationally calculated descriptors (figure 6, level I).[165] The model performed as well as models including the melting point, and has recently been developed as software.[181] Jorgensen and Duffy calculated descriptors associated with hydrogen bonding capacity and solvent-accessible surface area by molecular mechanics (figure 6, level IIb). These descriptors, together with correction values for carboxylic acids and amines, were successfully used to predict the solubilities for a dataset of 150 compounds, of which 80 were drug-like compounds.[180] In the last decade, computational models based on neural networks have been proved to be useful in solubility predictions.[164,166-168,182-185] Huuskonen and coworkers successfully predicted the solubilities of three homologous series of steroids, barbiturates and reverse transcriptase inhibitors using 12 descriptors of molecular connectivity and electrotopology (figure 6, level I).[164] Later, a dataset of drug-like compounds was predicted using 23 electrostatic and topological descriptors.[166] Similarly, Mitchell and Jurs predicted the solubilities of a large heterologous dataset by using nine topological, geometric and electrostatic descriptors.[167] Most of the data sets investigated contain a minority of complex drug-like molecules, which might be due to the limited amount of reliable solubility data that are available for such compounds. Furthermore, the models in general predict soluClin Pharmacokinet 2002; 41 (11)

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bilities with errors of 0.5 to 1 log units, which some authors argue is due to uncertainties in the experimental data that are used for the model.[165,172,180] Taken together, this means that the predictive models cannot yet be generally applied in a quantitative manner in drug discovery and development settings, even though they can be used to get an qualitative estimation of the solubility of a new compound. 4.4 Overview

In conclusion, there is no simple way to predict drug solubility. Several more or less complex models have been developed, but no easy, reliable and universal ‘hands on’ model is available. The in vivo situation is complicated by physiological factors that make the prediction of drug solubility even more difficult. However, research in this field has recently resulted in improved predictive models for drug solubility. Moreover, descriptors extracted from two-dimensional or three-dimensional structures have proved to be useful for the prediction of drug solubility. It is therefore possible that further improvements will be obtained in the near future, allowing the establishment of virtual screens also for drug solubility. 5. Conclusions The computational models presented in this review can be used to assess intestinal permeability and solubility at an early stage of the drug discovery process. These models are not yet perfect, but they can be further trained using experimental data generated in different projects during the discovery process. The development of computational models can be considered as an extension of the ongoing efforts to accelerate screening of compound libraries for pharmaceutical properties (figure 8). A knowledge-based approach utilising such fast computational and experimental screening methods will speed up the discovery process and produce drug candidates that are more drug-like and that are less likely to fail in clinical development. The challenge for the future is to integrate the results of the research efforts into universal compu© Adis International Limited. All rights reserved.

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b Near term (parallel)

a Traditional (serial)

c Future (knowledge based)

Library

Virtual library P/S

Library

Privileged library

P/S

P/S Development Development

P/S Development P/S = In vitro permeability and solubility studies P/S = In silico permeability and solubility studies

Fig. 8. Paradigms for the drug discovery process. (a) Traditional drug research is performed in a serial manner and is time-consuming. Pharmacokinetic models have a low capacity and are introduced late in the drug discovery process on a very limited number of lead compounds. (b) The introduction of efficient methods for screening of pharmacokinetic properties such as drug metabolism and absorption now makes it possible to develop a more time-efficient parallel strategy in which the pharmacokinetic properties of a large number of compounds are characterised. (c) In future drug research, the approach presented in the introductory part of this review (figure 3) has generated knowledge that enables computer-based modelling of structure-absorption relationships. Only drug compounds that are sufficiently well absorbed are synthesised and screened in vitro. New and better drugs are generated more rapidly.

tational models that describe whole organisms in the healthy and diseased states. Efforts along these lines are already under way in many laboratories. Acknowledgements This work was supported by Grant 9478 from the Swedish Medical Research Council, by Grant 95-58 from Centrala Försöksdjursnämnden and by AstraZeneca.

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Correspondence and offprints: Dr Per Artursson, Department of Pharmaceutics, Uppsala Biomedical Center, Uppsala University, PO Box 580, Uppsala, SE-751 23, Sweden. E-mail: [email protected]

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