Membrane Permeability

4.3.1.1 Effective Permeability

Passive permeability (P) of molecules across a membrane can be expressed as

where K is the partition coefficient, D is the diffusion coefficient, and h is the thickness of the cell membrane. The diffusion coefficient (D) depends on the molecular weight or size of a molecule. K is a measure of the solubility of the substance in lipid. Therefore, the passive permeability is related to membrane and drug properties. For a specific drug, the passive membrane permeability should be a constant Pm and independent to drug concentration.

The permeability for active absorption can be presented by

where J is the drug flux, Jmax is the maximum drug flux, C is the drug concentration, and Km is the drug affinity to the carrier. Obviously, active permeability is dependent on drug concentration.

Therefore, the total effective permeability is dependent on drug concentration for drugs that absorbed through both passive diffusion and active transport, and it can be expressed as follows

However, at very low concentration, C ^ Km, drug permeability is independent to drug concentration

At high concentration, C ^ Km, drug permeability is dependent on drug concentration.

Therefore, the permeability vs. concentration plot can be generated as in Fig. 4.5.

4.3.1.2 Fraction of Drug Absorbed

Drug permeability through intestinal wall will determine the fraction of drug absorbed (Fa). Fa can be estimated by drug permeability through intestinal wall

Jabs Peff where, Tres is the small intestine transit time (~3h), Tabs is the absorptive time (h), R is the radius of small intestine (2 cm), and Peff is the drug permeability through intestinal wall.

CD CL

9.1 8.1 7.1 6.1 5.1 4.1 3.1 2.1 1.1 0.1

f

s

\

\ Pm = 0 for very hydrophilic drug

Jm/Km + Pm \ /

/

\

Active + passive \ /

y

Pm m

V

passive

Drug Concentration

High

Drug Concentration

Figure 4.5. Active and passive permeability at low and high drug concentration

Figure 4.6. Model for intestinal absorption compartment

4.3.1.3 Permeability and Absorption Rate Constant Absorption rate constant can be expressed as

2nRL tiR2L

where Ka is the absorption rate constant with unit 1 s , P is the permeability (cm s-1), A is the membrane surface area (cm2), and V is the volume of absorption compartment (cm3) (Fig. 4.6). However this equation tends to overestimate absorption by 12.5-fold, so Ka = P/(2nR) may be more realistic.

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