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Log PC

emphasized previously, the drug will go through a series of partitioning steps: (a) leaving the aqueous extracellular fluids, (b) passing through lipid membranes, and (c) entering other aqueous environments before reaching the receptor (Fig. 2.1). In this sense, a drug is undergoing the same partitioning phenomenon that happens to any chemical in a sep-aratory funnel containing water and a nonpolar solvent such as hexane, chloroform, or ether. The partition coefficient (P) is the ratio of the molar concentration of chemical in the nonaqueous phase (usually 1-octanol) versus that in the aqueous phase (Eq. 2.10). For reasons already discussed, it is more common to use the logarithmic expression (Eq. 2.11). The difference between the separatory funnel model and what actually occurs in the body is that the partitioning in the funnel will reach an equilibrium at which the rate of chemical leaving the aqueous phase and entering the organic phase will equal the rate of the chemical moving from the organic phase to the aqueous phase. This is not the physiological situation. Refer to Figure 2.1 and note that dynamic changes are occurring to the drug, such as it being metabolized, bound to serum albumin, excreted from the body, and bound to receptors. The environment for the drug is not static. Upon administration, the drug will be pushed through the membranes because of the high concentration of drug in the extracellular fluids relative to the concentration in the intracellular compartments. In an attempt to maintain equilibrium ratios, the flow of the drug will be from systemic circulation through the membranes onto the receptors. As the drug is metabolized and excreted from the body, it will be pulled back across the membranes, and the concentration of drug at the receptors will decrease.

[chemical]o [chemical]

Equations 2.10 and 2.11 assume that the drug is in the nonpolar state. A large percentage of drugs are amines whose pKa is such that at physiological pH 7.4, a significant percentage of the drug will be in its protonated, ionized form. A similar statement can be made for the HA acids (carboxyl, sulfon-amide, imide) in that at physiological pH, a significant percentage will be in their anionic forms. An assumption is made that the ionic form is water-soluble and will remain in the water phase of an octanol/water system. This reality has led to the use of log D, which is defined as the equilibrium ratio of both the ionized and un-ionized species of the molecule in an octanol/water system (Eq. 2.12). The percent ionization of ionized HA acids and BH protonated amines and acids can be estimated from Equations 2.3 and 2.4 and the log D from Equations 2.13 and 2.14, respectively.

[solute]o

[solute]aqnized + [solute]nq°nionized log Dacids = log P = log log Dbases = log P = log log Dacids = log P = log log Dbases = log P = log

Because much of the time the drug's movement across membranes is a partitioning process, the partition coefficient has become the most common physicochemical property. The question that now must be asked is what immiscible nonpolar solvent system best mimics the water/lipid membrane barriers found in the body? It is now realized that the n-octanol/water system is an excellent estimator of drug partitioning in biological systems. One could argue that it was fortuitous that n-octanol was available in reasonable purity for the early partition coefficient determinations. To appreciate why this is so, one must understand the chemical nature of the lipid membranes.

These membranes are not exclusively anhydrous fatty or oily structures. As a first approximation, they can be considered bilayers composed of lipids consisting of a polar cap and large hydrophobic tail. Phosphoglycerides are major components of lipid bilayers (Fig. 2.10). Other groups of bi-functional lipids include the sphingomyelins, galactocere-brosides, and plasmalogens. The hydrophobic portion is composed largely of unsaturated fatty acids, mostly with cis double bonds. In addition, there are considerable amounts of cholesterol esters, protein, and charged mucopolysaccharides in the lipid membranes. The final result is that these membranes are highly organized structures composed of channels for transport of important molecules such as metabolites, chemical regulators (hormones), amino acids, glucose, and fatty acids into the cell and removal of waste products and biochemically produced products out of the

Figure 2.10 • General structure of a bifunctional phospholipid. Many of the fatty acid esters will be cis unsaturated.
Figure 2.11 • Schematic representation of the cell membrane.

cell. The cellular membranes are dynamic, with the channels forming and disappearing depending on the cell's and body's needs (Fig. 2.11). So complex is this system that it is not uncommon to have situations where there is poor correlation between the partition coefficient of a series of molecules and the biological response.2

In addition, the membranes on the surface of nucleated cells have specific antigenic markers, major histocompatibility complex (MHC), by which the immune system monitors the cell's status. There are receptors on the cell surface where hormones such as epinephrine and insulin bind, setting off a series of biochemical events within the cell. Some of these receptors are used by viruses to gain entrance into the cells, where the virus reproduces. As newer instrumental techniques are developed, and genetic cloning permits isolation of the genetic material responsible for forming and regulating the structures on the cell surface, the image of a passive lipid membrane has disappeared to be replaced by a very complex, highly organized, dynamically functioning structure.

For purposes of the partitioning phenomenon, picture the cellular membranes as two layers of lipids (Fig. 2.9). The two outer layers, one facing the interior and the other facing the exterior of the cell, consist of the polar ends of the bifunc-tional lipids. Keep in mind that these surfaces are exposed to an aqueous polar environment. The polar ends of the charged phospholipids and other bifunctional lipids are solvated by the water molecules. There are also considerable amounts of charged proteins and mucopolysaccharides present on the surface. In contrast, the interior of the membrane is populated by the hydrophobic aliphatic chains from the fatty acid esters.

With this representation in mind, a partial explanation can be presented as to why the n-octanol/water partitioning system seems to mimic the lipid membranes/water systems found in the body. It turns out that n-octanol is not as nonpolar as initially might be predicted. Water-saturated octanol contains 2.3 M water because the small water molecule easily clusters around octanol's hydroxy moiety. n-Octanol-saturated water contains little of the organic phase because of the large hydrophobic 8-carbon chain of octanol. The water in the n-octanol phase apparently approximates the polar properties of the lipid bilayer, whereas the lack of octanol in the water phase mimics the physiological aqueous compartments, which are relatively free of nonpolar components. In contrast, partitioning systems such as hexane/water and chloroform/water contain so little water in the organic phase that they are poor models for the lipid bilayer/water system found in the body. At the same time, remember that the n-octanol/water system is only an approximation of the actual environment found in the interface between the cellular membranes and the extracellular/intracellular fluids.

Experimental determination of octanol/water partition coefficients is tedious and time consuming. Today, most are calculated. The accuracy of these calculations is only as good as the assumptions made by the writers of the software. These include atomic fragment values, correction factors, spatial properties, effects of resonance and induction, internal secondary bonding forces, etc. There are over 30 different software packages for calculating a molecules partition coefficient, and their accuracy varies widely.3,4

Other Physicochemical and Descriptor Parameters

There is a series of other descriptors that measure the contribution by substituents to the molecule's total physicochemical properties. These include Hammett's $ constant; Taft's steric parameter, Es; Charton's steric parameter, v; Verloop's multidimensional steric parameters, L, Bi, B5; and molar re-fractivity, MR, number of hydrogen bond donors and acceptors, pKa, polar surface area, number of rotatable bonds, connectivity indices, and the list goes into the thousands. Although directories of these have been published, it is common to calculate them. Table 2.6 lists a very small set and illustrates several items that must be kept in mind when selecting substituents to be evaluated in terms of the type of factors that influence a biological response. For electronic parameters such as the location on an aromatic ring is important because of resonance versus inductive effects. Notice the twofold differences seen between $meta and $para for the three aliphatic substituents and iodo, and severalfold difference for methoxy, amino, fluoro, and phenolic hydroxyl.

Selection of substituents from a certain chemical class may not really test the influence of a parameter on biological activity. There is little numerical difference among the $meta or $para values for the four aliphatic groups or the four halogens. It is not uncommon to go to the tables and find missing parameters such as the Es values for acetyl and N-acyl.

TABLE 2.6 Sampling of Physicochemical Parameters Used in Quantitative Structure-Activity Relationships Investigations

Substituent

TABLE 2.6 Sampling of Physicochemical Parameters Used in Quantitative Structure-Activity Relationships Investigations

Substituent

Group

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