Figure 7. Prediction accuracy of several global aqueous solubility models. ACD. QikProp, Cerius2 and a Pharmacia developed model were used to predict solubility of several collections of homologous structures from Pharmacia discovery programs (Data sets 1, 3,4 and 6) and diverse structures from both the Pharmacia collection and structures taken from the literature (Data sets 2 and 5). It can be clearly seen that the prediction error depends both upon the model and characteristics of the query structures.
The residual plots for data set 5 are shown in Figure 8, differentiated by solubility range. Residual is the difference between experimental value and predicted value for each of the models and shows any bias to under or overpredict in the model. ACD and QikProp appear to be unbiased over all solubility ranges while the in-house model is over-predicting at all solubilities and Cerius2 over-predicts for low solubility compounds and under-predicts high solubility structures. Biases were observed in all the data sets, with no consistent trends with respect to the different models. Again, from the objective of using these models prospectively in making synthetic decisions, such biases should be acknowledged and taken into consideration.
With respect to lead optimization programs to overcome potential pharmacokinetic problems, accuracy in predicting the impact of subtle structural changes in a fairly homogenous structural space is desired. The results of this analysis clearly show that the performance of the different models is dependent upon the chemistry space and solubility range within that space, both with respect to accuracy and bias. While bias itself does not necessarily preclude the utility of a model, recognition that it exists and in what direction can help the user make more informed decisions with the predictions. At the least, these considerations suggest that the user of any model should characterize and validate the model in an intended application before general use.
As shown in Figure 6, permeability is an important determinant of absorption and a number of other ADME processes dictating the in vivo performance of a drug. However, permeability itself is a complex process containing contributions
0 2 Experimental
Figure 8. Comparison of prediction bias for ACD, QikProp, Cerius2 and Pharmacia aqueous solubility models. Structures are grouped into low (triangles, solubility S 100 |M), moderate (diamonds, solubility between 100 and 10,000 |M) and high (inverted triangles, solubility 5 10,000 |M) solubility ranges. Residual (y-axis) is the difference between experimental value and predicted value for each of the models. The experimental solubility (log S in | M ) is on the x-axis. Considerable bias is seen both in the computational model employed and solubility range for the structural series. Similar, unpredictable biases were observed for the other data sets summarized in Figure 7 (Crimin, et al., 2005).
from a number of different transport mechanisms, the relative contributions of which depend upon the structural features of the drug. After oral administration, a drug must move from the intestinal lumen through an unstirred water layer and mucus coat adjacent to the epithelial cell surface. Movement across the epithelial layer takes place by two independent routes-transcellular flux, i.e. movement across the cell, and paracellular flux, or movement between adjacent epithelial cells, restricted by the presence of tight junctions between the cells (Diamond, 1977; Gumbiner, 1987; Jackson, 1987). The solute then encounters a number of microenvironments including a basement membrane, interstitial space and capillary wall in accessing the mesenteric circulation. Any and all of these microenvironments can be considered a resistance to solute movement with an associated permeability coefficient. Further, the influence of drug structure with permeability in these different domains will be different. For example, unstirred water layer permeability is inversely related to solute size while paracellular permeability is dependent upon both size and charge. In the latter case, the characteristics of the paracellular "pore" result in size restricted diffusion as the size of the solute approaches that of the paracellular space. Further, cations are more permeable than neutral species, which in turn are more permeable than anions, consistent with the negative charge characteristics of the paracellular space (Adson et al., 1995; Kottra and Fromter, 1983).
With respect to transcellular permeability, the relationship of solute structure with permeability again depends upon the mechanism involved. Historically, a passive diffusion pathway has been assumed for most solutes. However, an increasing number of active absorptive and secretory processes in intestinal epithelial cells are being identified for which many common drugs are substrates (Tsuji and Tamai, 1996). These same considerations apply to tissue distribution and excretion (Figure 6), both of which are also dependent upon passive and active transport mechanism. With respect to structure/ transport or permeability relationships, while active transport involves specific interactions between solute and transporter, passive diffusion is dependent upon solute partitioning into the cellular plasma membrane and diffusion coefficient within the membrane (Jackson, 1987).
Considerable structure-property relationship (SPR) work has been published over the years to describe the passive transport mechanism, still believed in many cases to be the most significant pathway responsible for intestinal permeability and oral drug absorption. A very successful model for predicting passive permeability is the so called passive/diffusion model in which the cellular barrier is reduced conceptually to a homogenous, single biomembrane. Both partitioning and diffusion are influenced by the physicochemical and structural characteristics of the drug. Factors influencing plasma membrane partitioning are solute size, lipophilicity, hydrogen bonding potential and charge characteristics, while diffusion is dependent upon size or total molecular surface area properties (Conradi et al., 1996). In general, non-polar surface area favors partitioning while polar, hydrogen bonding functionality opposes partitioning. With respect to diffusion, an inverse relationship with size is found, similar to the situation with paracellular permeability.
These multiple influences on permeability are manifested in a number of different ways. If intestinal permeability of a number of homologous, non-actively transported solutes is measured as a function of membrane partitioning, or more commonly, an organic solvent partition coefficient such as octanol as a surrogate, a sigmoidal relationship is frequently observed (Ho et al., 1977; Camenisch et al., 1996). For solutes with little or no membrane affinity, permeability is low, resulting primarily from paracellular diffusion of the solute between cells. As the propensity of the solute to partition into the cell membrane increases, permeability also increases as a result of the significant increase in surface area of the transcellular pathway relative to the paracellular route. This increase in permeability will approach a plateau value beyond which further increases in partition coefficient do not result in increased permeability. This is the so-called aqueous boundary layer limited situation where diffusion across the cell is very rapid relative to diffusion of the solute through the unstirred water/mucus layer adjacent to the cell (Westergaard and Dietschy, 1974). The dimensions, and resistance, of this layer can be modified by perturbing hydrodynamics which shift the plateau to a new, limiting permeability.
In the case of ionizable solutes, permeability is also pH dependent. The neutral, uncharged species is capable of transcellular, passive diffusion while the charged species is restricted to the paracellular pathway. Thus the observed permeability of such molecules is dependent upon the relative concentrations of charged and neutral species. In the case of a weak acid such as salicylic acid for example, at pH less than about 5.5, rat intestinal permeability is aqueous boundary controlled. Increasing pH results in progressively lower permeability coefficients until at pH greater than 9, a limiting, small permeability is achieved which is independent of further pH increases. This limiting permeability represents the paracellular diffusion of the charged anion (Ho et al., 1983). For such ionizable solutes a correlation with permeability and logD, defined as the apparent octanol-water partition coefficient at a specific pH, frequently 6.5 or 7.4, is used to predict permeability. Both ClogP and ClogD algorithms are available to help optimize permeability characteristics of lead structures where this property is not found to be in a favorable range to effect the desired in vivo performance.
However, octanol-water partition coefficients are not always useful for predicting permeability of all solutes. In the case of highly functionalized solutes such as peptides, permeability has been found to be better correlated with structural and physicochemical measures of hydrogen bond potential (Conradi et al., 1991, 1992). One such system is the AlogP model where AlogP is the difference between octanol-water partition coefficient and hydrocarbon-water partition coefficient of the solute (Seiler, 1974; El Tayer et al., 1991). At the present time, no reliable computational models are available for predicting AlogP, although recent work in this direction has appeared in the literature (Ruelle, 2000).
Polar surface area (PSA) of a solute, which can be computed from structure, has been proposed as an alternative to octanol-water and/or ClogP for predicting intestinal permeability (Palm et al., 1996,1997). Recent examples of successful correlations using this simple metric have been published (Ertl et al., 2000; Papageorgiou et al., 2001) suggesting this as a useful general tool for optimizing permeability characteristics of a solute. However, failure of PSA to correlate cellular permeability of a series of peptidomimetics has also been reported. In this case, a reasonable correlation could be obtained by taking a weighted average of PSA and NPSA (non-polar surface area) of the solutes (Stenberg et al., 1999). The conclusion from these examples is that, as in the case of computational solubility modeling, application of a specific tool for predicting permeability must be validated by the user as appropriate for the molecular structure of interest.
Solute clearance as a PB-PK parameter includes both metabolism and excretion mechanisms. As shown in Figure 6, metabolism and excretion rates are dependent upon biopharmaceutical processes such as active and passive permeability, and physicochemical properties of the solute which influence these processes. With regards to SPR models of these pathways, considerable work has been focused on models for predicting metabolism of potential drug candidates, primarily identifying sites of reactivity in the solute (Jones et al., 2002; Zamora et al., 2003; Harris, 2004; Crivori et al., 2004). These include models for most of the major cytochrome P450 (CYP450) isoforms. Octanol-water partition coefficients have been correlated with CYP450 binding for both substrates and inhibitors and may be considered as a design strategy to decrease association with the enzymes (Lewis et al., 2004). Further, given that lipophilicity also plays a role in passive diffusion, decreasing logP may both decrease binding to CYP's and solute permeability in the liver to the site of metabolism.
Along with passive permeability, a major contribution from active, frequently vectorial transport both to metabolism and excretion pathways is increasingly being recognized (Faber et al., 2003; Hirano et al., 2004). SPR models for these processes is of considerable current interest and some progress has been made towards identifying substrates and/or inhibitors for some of them, most notably P-glycoprotein (Seelig, 1998; Stouch and Gudmundsson, 2002; Gombar et al., 2004). As in the case of metabolism, these models focus on recognition events such as binding and do not generally predict rates of reaction. However, at least in one case, a structure-based predictive model for hepatic clearance rates has been reported, derived from an internal training set of such data (www.lionbiosciences.com). Until such kinetic models are more generally available, in vitro data will likely continue to be required for use in PB-PK modeling.
As is the situation with permeability, metabolism and clearance, both biophar-maceutical processes and physicochemical solute properties define tissue distribution. Reasonably accurate predictions of blood-level time profiles can be obtained in PB-PK models considering only plasma-tissue partition coefficients derived from unbound plasma solute concentrations and octanol-water partition coefficients, as shown earlier in this review and in other, similar models (Poulin and Theil, 2002). Alternatively, a distribution parameter utilizing octanol-water partition coefficients and fraction unionized at pH 7.4, has been shown to provide good estimates of volume of distribution in humans for neutral and basic compounds (Lombardo et al., 2004). At the present time, these are experimentally determined inputs in contrast to exclusively computed values.
Again, complicating the issue is the role of active transport processes on distribution especially in tissues such as brain and lung. In the case of brain for example, P-glycoprotein plays a significant role in limiting distribution of solutes which are substrates into the brain (Raub, this volume). This can be clearly seen in cases where P-glycoprotein inhibitors were administered with the therapeutic agent and significantly greater CNS toxicities were noted which were not observed in the absence of inhibitor (Tsujikawa et al., 2003). The ability to predict these processes from structure alone presently remains an unsolved challenge.
Plasma protein binding
Fraction unbound is an important determinant of both tissue distribution and clearance in the PB-PK model. Computational SPR models of protein binding are focused almost entirely on serum albumin, primarily human serum albumin (Colmenarejo, 2003; Ermondi et al., 2004). Generally, these models use lipophilicity and charge of the solute to estimate association between the solute and protein. A recent review challenged these models and proposed an alternative approach employing a pharmacophore similarity concept and partial least squares as a more generally accurate strategy (Kratochwil et al., 2002). While this and other approaches are useful as a starting point for consideration of protein binding issues, a major weakness is the limitation to albumin as the only relevant potential binding component in blood. Other blood components important for binding certain classes of drugs are lipoprotein particles and a-1-acid glycoprotein (Boffito et al., 2003; Akhlaghi and Trull, 2002; Chung and Wasan, 2004).
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