Source: Refs. 52 and 70.

Source: Refs. 52 and 70.

7.4.3 Role of Serum Proteins

Sawada et al. [574-576] characterized the iso-pH 7.4 MDCK permeabilities of very lipophilic molecules, including chlorpromazine (CPZ) [574]. They included 3% wt/vol bovine serum albumin (BSA) on the apical (donor) side, and 0.1-3% BSA on the basolateral (acceptor) side, and found that plasma protein binding greatly affected the ability of molecules to permeate cellular barriers. They observed cell tissue retention of CPZ ranging within 65-85%, depending on the amount of BSA present in the receiving compartment. They concluded that the rapid rate of disappearance of lipophilic compounds from the donor compartment was controlled by the unstirred water layer (UWL; see Section 7.7.6), a rate that was about the same for most lipophilic compounds; however, the very slow appearance of the compounds in the receiving compartment depended on the rate of desorption from the basolateral side of the membranes, which was strongly influenced by the presence of serum proteins in the receiving compartment. They recommended the use of serum proteins in the receiving compartment, so as to better mimic the in vivo conditions when using cultured cells as in vitro assays.

Yamashita et al. [82] also studied the effect of BSA on transport properties in Caco-2 assays. They observed that the permeability of highly lipophilic molecules could be rate limited by the process of desorption off the cell surface into the receiving solution, due to high membrane retention and very low water solubility. They recommended using serum proteins in the acceptor compartment when lipophilic molecules are assayed (which is a common circumstance in discovery settings).

7.4.4 Effects of Cosolvents, Bile Acids, and Other Surfactants

Figure 7.13 shows some of the structures of common bile acids. In low ionic strength solutions, sodium taurocholate forms tetrameric aggregates, with critical taurocholic acid glycocholic acid taurocholic acid glycocholic acid

Figure 7.13 Examples of bile salts and aggregate structures formed in aqueous solutions.

Figure 7.13 Examples of bile salts and aggregate structures formed in aqueous solutions.

micelle concentration (CMC) 10-15 mM. Sodium deoxycholate can have higher levels of aggregation, with lower cmc (4-6 mM) [577]. Mixed micelles form in the GIT, where the edges of small sections of planar bilayer fragments are surrounded by a layer of bile salts (Fig. 7.13).

Yamashita et al. [82] added up to 10 mM taurocholic acid, cholic acid (cmc 2.5 mM), or sodium laurel sulfate (SLS; low ionic strength cmc 8.2 mM) to the donating solutions in Caco-2 assays. The two bile acids did not interfere in the transport of dexamethasone. However, SLS caused the Caco-2 cell junctions to become leakier, even at the sub-CMC 1 mM level. Also, the permeability of dexa-methasone decreased at 10 mM SLS.

These general observations have been confirmed in PAMPA measurements in our laboratory, using the 2% DOPC-dodecane lipid. With very lipophilic molecules, glycocholic acid added to the donor solution slightly reduced permeabilities, taurocholic acid increased permeabilities, but SLS arrested membrane transport altogether in several cases (especially cationic, surface-active drugs such as CPZ).

Yamashita et al. [82] tested the effect of PEG400, DMSO, and ethanol, with up to 10% added to solutions in Caco-2 assays. PEG400 caused a dramatic decrease (75%) in the permeability of dexamethasone at 10% cosolvent concentration; DMSO caused a 50% decrease, but ethanol had only a slight decreasing effect.

Sugano et al. [562] also studied the effect of PEG400, DMSO, and ethanol, up to 30%, in their PAMPA assays. In general, water-miscible cosolvents are expected to decrease the membrane-water partition coefficients. In addition, the decreased dielectric constants of the cosolvent-water solutions should give rise to a higher proportion of the ionizable molecule in the uncharged state [25]. These two effects oppose each other. Mostly, increasing levels of cosolvents were observed to lead to decreasing permeabilities. However, ethanol made the weak-acid ketoprofen (pKa 4.12) more permeable with increasing cosolvent levels, an effect consistent with the increasing pKa with the decreasing dielectric constant of the cosolvent mixtures (leading to a higher proportion of uncharged species at a given pH). But the same reasoning cannot be used to explain why the weak-base propranolol (pKa 9.5) decreased in permeability with increasing amounts of ethanol. This may be due to the increased solubility of propranolol in water with the added ethanol in relation to the solubility in the membrane phase. This leads to a lowered membrane/ mixed-solvent partition coefficient, hence lowering flux due to a diminished sample concentration gradient in the membrane (Fick's law) [25]. DMSO and PEG400 dramatically reduced permeabilities for several of the molecules studied. Cosolvent use is discussed further in Section 7.7.9.

7.4.5 Ideal Model Summary

The literature survey in this section suggests that the ideal in vitro permeability assay would have pH 6.0 and 7.4 in the donor wells, with pH 7.4 in the acceptor wells. (Such a two-pH combination could differentiate acids from bases and nonionizables by the differences between the two Pe values.) Furthermore, the acceptor side would have 3% wt/vol BSA to maintain a sink condition (or some sink-forming equivalent). The donor side may benefit from having a bile acid (i.e., taurocholic or glycocholic, 5-15 mM), to solubilize the most lipophilic sample molecules. The ideal lipid barrier would have a composition similar to those in Table 7.1, with the membrane possessing substantial negative charge (mainly from PI and PS). Excessive DMSO or other cosolvents use requires further research, due to their multimechanistic effects. In vitro assays where permeabilities of lipophilic molecules are diffusion-limited [574-576], the role of the unstirred water layer (UWL; see Section 7.7.6) needs to be accounted, since under in vivo conditions, the UWL is nearly absent, especially in the BBB.


The equations used to calculate permeability coefficients depend on the design of the in vitro assay to measure the transport of molecules across membrane barriers. It is important to take into account factors such as pH conditions (e.g., pH gradients), buffer capacity, acceptor sink conditions (physical or chemical), any precipitate of the solute in the donor well, presence of cosolvent in the donor compartment, geometry of the compartments, stirring speeds, filter thickness, porosity, pore size, and tortuosity.

In PAMPA measurements each well is usually a one-point-in-time (singletimepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a "physically maintained" sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase; see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements.

The extra timepoint measurements make the traditional Caco-2 assay too slow for high-throughput applications. Since the PAMPA assay was originally developed for high-throughout uses, there is no continuous replacement of the acceptor compartment solution. Some technical compromises are necessary in order to make the PAMPA method fast. Consequently, care must be exercised, in order for the singletimepoint method to work reliably. If the PAMPA assay is conducted over a long period of time (e.g., >20 h), the system reaches a state of equilibrium, where the sample concentration becomes the same in both the donor and acceptor compartments (assuming no pH gradients are used) and it becomes impossible to determine the permeability coefficient. Under such conditions, the membrane will also accumulate some (but sometimes nearly all) of the sample, according to the membranebuffer partition coefficient. In the commonly practiced PAMPA assays it is best to take the single timepoint at 3-12 h, before the system reaches a state of equilibrium. Since the acceptor compartment is not assumed to be in a sink state, the permeability coefficient equation takes on a more complicated form [Eq. (7.20) or (7.21)] than that used in traditional Caco-2 assays.

For ionizable sample molecules, it is possible to create an effective sink condition in PAMPA by selecting buffers of different pH in the donor and acceptor compartments. For example, consider salicylic acid (pKa 2.88; see Table 3.1). According to the pH partition hypothesis, only the free acid is expected to permeate lipophilic membranes. If the donor pH < 2 and the acceptor pH is 7.4, then as soon as the free acid reaches the acceptor compartment, the molecule ionizes, and the concentration of the free acid becomes effectively zero, even though the total concentration of the species in the acceptor compartment may be relatively high. This situation may be called an 'ionization-maintained' sink.

Another type of nonphysical sink may be created in a PAMPA assay, when serum protein is placed in the acceptor compartment and the sample molecule that passes across the membrane then binds strongly to the serum protein. Consider phenazopyridine (pKa 5.15; see Table 3.1) in a pH 7.4 PAMPA assay, where the acceptor solution contains 3% wt/vol BSA (bovine serum albumin). As soon as the free base reaches the acceptor compartment, it binds to the BSA. The unbound fraction becomes very low, even though the total concentration of the base in the acceptor compartment may be relatively high. This may be called a binding-maintained sink.

In this chapter we use the term ''sink'' to mean any process that can significantly lower the concentration of the neutral form of the sample molecule in the acceptor compartment. Under the right conditions, the ionization and the binding sinks serve the same purpose as the physically maintained sink often used in Caco-2 measurements. We will develop several transport models to cover these ''chemical'' sink conditions. When both of the chemical sink conditions (ionization and binding) are imposed, we will use the term ''double sink'' in this chapter.

The chemical sink may be thought of as a method used to increase the volume of distribution of species in the acceptor solution beyond the geometric volume of the receiving compartment. As such, this extension of terminology should be clear to traditional Caco-2 users. The use of the chemical sinks in PAMPA is well suited to automation, and allows the assay to be conducted at high-throughput speeds. As mentioned above, the one-point-in-time (single-timepoint) sampling can lead to errors if not properly executed. We will show that when multitimepoint PAMPA is done (see Fig. 7.15), the equations developed in this chapter for high-speed single-timepoint applications are acceptably good approximations.

7.5.1 Thin-Membrane Model (without Retention)

Perhaps the simplest Fick's law permeation model consists of two aqueous compartments, separated by a very thin, pore-free, oily membrane, where the unstirred water layer may be disregarded and the solute is assumed to be negligibly retained in the membrane. At the start (t = 0 s), the sample of concentration CD(0), in mol/cm3 units, is placed into the donor compartment, containing a volume (VD, in cm3 units) of a buffer solution. The membrane (area A, in cm2 units) separates the donor compartment from the acceptor compartment. The acceptor compartment also contains a volume of buffer (VA, in cm3 units). After a permeation time, t (in seconds), the experiment is stopped. The concentrations in the acceptor and donor compartments, CA(t) and CD(t), respectively, are determined.

Two equivalent flux expressions define such a steady-state transport model [41]

where P denotes either the effective or the apparent permeability, Pe or Pa, depending on the context (see later), in units of cm/s. These expressions may be equated to get the differential equation

It is useful to factor out CA (t) and solve the differential equation in terms of just CD(t). This can be done by taking into account the mass balance, which requires that the total amount of sample be preserved, and be distributed between the donor and the acceptor compartments (disregarding the membrane for now). At t = 0, all the solute is in the donor compartment, which amounts to VDCD(0) moles. At time t, the sample distributes between two compartments:

This equation may be used to replace CA (t) in Eq. (7.3) with donor-based terms, to get the simplified differential equation dC() + aCD(t)+b = 0 (7.5)

dt where a = AP/[(VAVD)/(V* + VD)] = t-1, teq is the time constant, and b = APCd(0) /V*. Sometimes, t— is called the first-order rate constant, k [in s—1 units (reciprocal seconds)]. The ordinary differential equation may be solved by standard techniques, using integration limits from 0 to t, to obtain an exponential solution, describing the disappearance of solute from the donor compartment as a function of time

where mD(t) refers to the moles of solute remaining in the donor compartment at time t. Note that when VA ^ VD, Eq. (7.6) approximately equals exp(-t/teq). Furthermore, exp(-t/teq)« 1 — t/teq when t is near zero. Using the mole balance relation [Eq. (7.4)], the exponential expression above [Eq. (7.6)] may be converted into another one, describing the appearance of solute in the acceptor compartment.

In mole fraction units, this is

Note that when VA ^ VD, Eq. (7.8) approximately equals 1 — exp(—t/teq). Furthermore, 1 — exp(—t/teq) « t/teq when t is near zero. Figure 7.14 shows the forms of Eqs. (7.6) and (7.8) under several conditions. When less than ~10% of the compound has been transported, the reverse flux due to CA(t) term in Eq. (7.1) is nil. This is effectively equivalent to a sink state, as though VA ^ VD. Under these conditions, Eq. (7.8) can be simplified to

mD(0) teq Vd and the apparent permeability coefficient can be deduced from this ''one-way flux'' equation,

0 0

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