Passive Diffusion

Passive diffusion is the transport of a molecule across a lipid bilayer membrane according to its electrochemical potential gradient without the assistance of additional transporter molecules. This process can be studied in pure lipid membranes, although it is acknowledged that the properties of even relatively pure lipid patches in native membranes are altered by the high density of neighboring protein molecules. The physical and functional properties of membranes can be modeled with varying levels of detail and mathematical complexity. The simplest model represents the membrane as a single semipermeable barrier separating two uniform aqueous compartments. Transport is characterized by a single reversible rate constant. A more complex model represents the membrane as an intervening third compartment of 25-30 A thickness with properties equivalent to a bulk organic solvent. Transport is modeled as a reversible partition of molecules from the donor aqueous phase into the membrane compartment and rate-limiting release of the solute from the organic membrane phase into the receiving compartment. This model yields a rate equation of the same form as the Michaelis-Menten equation in enzyme kinetics. Although such kinetics are observed for mediated membrane transport, they are not typically observed for simple diffusive transport. A more sophisticated model adds barriers of high charge density and high dielectric constant on either side of the organic compartment to represent the phospholipid head groups. Still other models may incorporate unstirred diffusion layers extending into the aqueous compartments. These models reveal different points of view about what constitutes the most important rate-determining barrier to bulk transport.

Molecular dynamics simulations (12, 13) have provided a provocative image of passive diffusion of solute molecules within the membrane bilayer (Figure 14.2). These simulations illustrate the rapid but restricted mobility of the lipid side chains, and demonstrate that the membrane hydrophobic region is not particularly well modeled by bulk solvent properties. They suggest the spontaneous formation of voids and transient channels within the membrane and the ability of small molecules and ions to diffuse within the membrane by hopping among these voids (~8-A jumps on a 5-psec time scale).

FIGURE 14.2 Molecular dynamics simulation of the diffusion of benzene within a hydrated lipid bilayer membrane. Benzene molecules are shown as Corey-Pauling-Koltun (CPK) models; atoms in the phospholipid head groups are shown as ball and stick models; and hydrocarbon chains and water molecules as dark and light stick models, respectively. (Reproduced with permission from Bassolino-Klimas D, Alper HE, Stouch TR. Biochemistry 1993;32:12624-37.)

FIGURE 14.2 Molecular dynamics simulation of the diffusion of benzene within a hydrated lipid bilayer membrane. Benzene molecules are shown as Corey-Pauling-Koltun (CPK) models; atoms in the phospholipid head groups are shown as ball and stick models; and hydrocarbon chains and water molecules as dark and light stick models, respectively. (Reproduced with permission from Bassolino-Klimas D, Alper HE, Stouch TR. Biochemistry 1993;32:12624-37.)

They highlight the importance of concerted large con-formational motions, occurring with relatively low frequency compared to the continual small motions (~1.5 Á occurring on the 100-fsec time scale). Thus far, these methods have been used to successfully model the diffusion of water, hydrogen ions, small organic molecules, and various drugs within the bilayer. They have provided reasonably good agreement with experimental data on intramembrane diffusion. The types of motion available to small molecules such as benzene differ qualitatively from those available to a fairly large organic drug such as nifedipine.

Thus far, no one has successfully modeled the full process of transport of druglike molecules from one aqueous compartment into the membrane and into the other aqueous compartment. The problem has been that the feasible time scale for molecular dynamics simulations is presently in the nanosecond range, whereas the rates of drug transport are typically in the millisecond range. The process has been approximated for several small compounds by constraining solute molecules to different specific depths in a simulated membrane. Both the free energy of partitioning from an aqueous to a lipid environment and the local diffusion coefficients at each depth can be calculated. These can be used to calculate an overall permeability coefficient. The relative values (but not the absolute values) agree with experimental data (14, 15).

Extensive efforts have been made to develop quantitative structure/activity relationships (QSARs) that predict membrane transport (16, 17). Particularly extensive use has been made of log P (log solvent/water partition coefficient values) and the Hansch equation (Equation 14.3):

log (1/C) = -k (log P)2 + k'(log P) + pa + k" (14.3)

where C = substrate concentration or dose producing a given effect (ED50, IC50, rate of reaction or transport), log P = partition coefficient or lipophilicity factor p, a = Hammett electronic substituent effect constants, and k, k', k", p = regression coefficients. Derivation of this correlation originally was based on the expectation that passive diffusion across a lipid bilayer would be the limiting factor in drug action, but many other factors, such as enzyme inhibition and receptor binding data, often also correlate well. The octanol/water partition coefficient (log Poctanol/water) is most commonly used and is generally assumed unless otherwise noted. Reverse-phase HPLC and immobilized artificial membrane methods for estimating log P have largely replaced actual liquid/liquid extraction methods for determining these values (18, 19). The ability to correlate log P values with structure has become quite

TABLE 14.2 Sample of QSAR Studies on Transport"

Drug class

System

Physical parameters correlated with activity^

Absorption as log (% absorbed), log permeability, or log k

Barbiturates Sulfonamides Anilines Xanthines Cardiac glycosides

Gastric log pCHCl3/wat er, Rm

Gastric log pisoamyl/alcohol/water

Gastric pKa

Intestinal DpH 5.3

Intestmal log Poctanol/water, Rm

Excretion as log (% excreted), log CL, or log k

Barbiturates Sulfonamides Anilines Xanthines Cardiac glycosides

Gastric log pCHCl3/wat er, Rm

Gastric log pisoamyl/alcohol/water

Gastric pKa

Intestinal DpH 5.3

Intestmal log Poctanol/water, Rm

Excretion as log (% excreted), log CL, or log k

Penicillins

Biliary

log P

Sulfathiazoles

Biliary

log Poctanol/water, PK<

Sulfapyridines

Renal

Rm, pKa

Sulfonamides

Renal

P, pKa

Amphetamines

Renal

log Pheptane/buffer

a a Adapted from Table VI in Austel B, Kutter R. Absorption, distribution and metabolism of drugs. In: Toplis JG, ed. Quantitative structure activity relationships. Medicinal chemistry monographs, vol 19. New York: Academic Press; 1983. p. 437-96.

b Parameters: k = rate constant, CL = clearance, P = partition coefficient for indicated solvents, Rm = relative mobility under specific chromatographic conditions, DpH 5.3 = distribution coefficient (a partition coefficient corrected for fractional ionization at pH 5.3), p = substitutent lipophilicity values.

a Adapted from Table VI in Austel B, Kutter R. Absorption, distribution and metabolism of drugs. In: Toplis JG, ed. Quantitative structure activity relationships. Medicinal chemistry monographs, vol 19. New York: Academic Press; 1983. p. 437-96.

b Parameters: k = rate constant, CL = clearance, P = partition coefficient for indicated solvents, Rm = relative mobility under specific chromatographic conditions, DpH 5.3 = distribution coefficient (a partition coefficient corrected for fractional ionization at pH 5.3), p = substitutent lipophilicity values.

good, and calculated log P values (CLOGP) are now often used.

Table 14.2 presents a selection of drugs, transport sites, and parameters that have been studied in QSAR studies relevant to drug absorption and excretion measurements excerpted from a much larger table (17). Overall conclusions from this work are that transportability correlates with (1) lipophilicity (log P), (2) water solubility, (3) pKa, and (4) molecular weight. Correlations with lipophilicity are almost always good. Although different log P ranges are optimal for oral (log P = 0.5-2.0), buccal (log P = 4-4.5), and topical (log P > 2.0) delivery, there is much overlap. Unfortunately, increasing drug lipophilicity may increase delivery generally throughout the body and do little to improve selective delivery to target tissues. Water solubility bears on the total concentration available for transport (e.g., in GI absorption). Solubility is more difficult to predict from structure than is log P, although calculated estimates can be made from melting point data and calculated solvation energies. Molecular weight is related to diffusivity (D a 1/1VMW), in both the membrane and the aqueous phases. It has been found empirically that there is a cutoff molecular weight (< 500-650) above which passive diffusion across most biological membranes is excluded. An analysis of 2245 compounds from the World Drug Index database for which human clinical data are available led to the so-called Lipinsky's Rules of 5 (20). Poor absorption is predicted if two or more of the following occur: (1) H-bonding donor groups > 5, (2) H-bonding acceptor groups > 5, (3) (N + O atoms) > 10, (4) MW > 500, and (5) CLOGP > 5.0 (or measured log P > 4.15).

Apart from these basic rules of thumb, the ability to predict the relationship between molecular structure and transport across biological membranes is limited beyond narrow ranges of known compounds. Confounding factors include inaccurate, incomplete, and/or noncomparable data, and the potential existence of multiple drug transport mechanisms in real biological membranes. In particular, limited QSAR data are available for the specific drug transporters that are considered in the following sections.

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