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PAMPA—a drug absorption in vitro model
European Journal of Pharmaceutical Sciences 20 (2003) 393–402
PAMPA—a drug absorption in vitro model 5. Unstirred water layer in iso-pH mapping assays and pKaflux —optimized design (pOD-PAMPA)夽 Jeffrey A. Ruell, Konstantin L. Tsinman, Alex Avdeef∗ pION INC., 5 Constitution Way, Woburn, MA 01801 USA Received 10 March 2003; received in revised form 26 August 2003; accepted 26 August 2003
Abstract Iso-pH mapping unstirred parallel artificial membrane permeability assay (PAMPA) was used to measure the effective permeability, Pe , as a function of pH from 3 to 10, of five weak monoprotic acids (ibuprofen, naproxen, ketoprofen, salicylic acid, benzoic acid), an ampholyte (piroxicam), five monoprotic weak bases (imipramine, verapamil, propranolol, phenazopyridine, metoprolol), and a diprotic weak base (quinine). The intrinsic permeability, Po , the unstirred water layer (UWL) permeability, Pu , and the apparent pKa (pKaflux ) were determined from the pH dependence of log Pe . The underlying permeability-pH equations were derived for multiprotic weak acids, weak bases and ampholytes. The average thickness of the unstirred water layer on each side of the membrane was estimated to be nearly 2000 m, somewhat larger than that found in Caco-2 permeability assays (unstirred). Since the UWL thickness in the human intestine is believed to be about forty times smaller, it is critical to correct the in vitro permeability data for the effect of the UWL. Without such correction, the in vitro permeability coefficient of lipophilic molecules would be indicative only of the property of water. In single-pH PAMPA (e.g. pH 7.4), the uncertainty of the UWL contribution can be minimized if a specially-selected pH (possibly different from 7.4) were used in the assay. From the analysis of the shapes of the log Pe —pH plots, a method to improve the selection of the assay pH, called pKaflux —optimized design (pOD-PAMPA), was described and tested. From an optimally-selected assay pH, it is possible to estimate Po , as well as the entire membrane permeability—pH profile. © 2003 Elsevier B.V. All rights reserved. Keywords: PAMPA; Permeability; Unstirred water layer; pKaflux -optimized design; Oral absorption
1. Introduction Since its introduction in 1998, PAMPA (parallel artificial membrane permeability assay) has attracted considerable attention in the pharmaceutical industry (Kansy et al., 1998, 2001; Avdeef, 2001a,b; Avdeef et al., 2001; Faller and Wohnsland, 2001; Wohnsland and Faller, 2001; Sugano et al., 2001a,b, 2002; Zhu et al., 2002; Veber et al., 2002; Avdeef, 2003), and has been the focus of an international meeting (www.pampa2002.com). PAMPA can quickly provide information about passive-transport permeability, that is not complicated by other mechanisms. Due to its versa夽
Ref. Avdeef, et al., 2001, is part 2 of the series. Corresponding author. Tel.: +1-781-935-8939x22; fax: +1-781-935-8938. E-mail address: [email protected] (A. Avdeef). ∗
0928-0987/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2003.08.006
tility and relative low cost, the assay is an attractive model for high throughput screening. Presently, most PAMPA tests focus on obtaining binning results (high/low) for compounds based on their performance relative to internal standards used to predict human intestinal absorption. PAMPA implicitly is thought to correlate with the compound’s ability to traverse the model membrane barrier. However, this assumption may not be true in all cases, since compounds have to permeate not only through the artificial membrane barrier, but also the unstirred water layer (UWL), a domain of solvent adjacent to the membrane that is not subject to convective mixing of the bulk solution. For highly lipophilic molecules, the rate-limiting barrier to transport is the UWL. For example (Wohnsland and Faller, 2001), at pH 6.8, the effective permeability of propranolol, 40 × 10−6 cm/s, is about 40% less than that of metoprolol, 63 × 10−6 cm/s, even though propranolol is 40 times more
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Nomenclature All permeability coefficients are in units of cm/s Daq diffusivity of a solute in aqueous solution (cm2 /s) fu fraction of the total sample concentration in the uncharged form h thickness of the unstirred aqueous layer (cm) log Ki stepwise protonation constant of a multiprotic molecule, associated with the q + H+ = XHi , equilibrium reaction: XHq−1 i−1 q: charge KOW octanol–water partition coefficient for an uncharged species; pH-independent PAMPA parallel artificial membrane permeability assay Pe effective artificial-membrane permeability (measured), composed of the unstirred water layer and membrane permeability, and corrected for membrane retention Pm membrane permeability coefficient; can dependent on pH for ionizable molecules Po intrinsic artificial membrane permeability coefficient; pH-independent Pu unstirred water layer permeability coefficient pKa ionization constant (negative log form) pKaflux the apparent pKa derived from the Pe —pH profile, the pH at which the resistance to transport is 50% due to the membrane barrier and 50% due to the unstirred water layer pOD pKaflux -optimized design UWL unstirred water layer
lipophilic than metoprolol. The lingering problem with measuring water and not membrane permeability for lipophilic compounds is that structural differences in compounds, unless they are drastic, often will not affect permeability. The effect of the UWL in permeability measurement has been studied in black lipid membrane models (Gutknecht and Tosteson, 1973; Walter and Gutknecht, 1984), in vitro cellular models (Karlsson and Artursson, 1991; Ho et al., 2000), rat intestine (Winne et al., 1987; Anderson et al., 1988; Levitt et al., 1990), and human jejunum (Lennernäs, 1998). Wohnsland and Faller (2001) reported the thickness of the UWL in PAMPA to be 300 m (microtitre plate shaken at 50–100 rpm). In unstirred Caco-2 assays, the UWL was reported to be 1500 m (Wohnsland and Faller, 2001), while in the human intestine, the value is estimated to be 30–100 m (Lennernäs, 1998). This study is a detailed account of the UV-based iso-pH PAMPA method. Some preliminary results have been cited,
without data, in a review (Avdeef, 2001a). Since then, computational procedures in the treatment of the UV data have improved, additional molecules have been studied, and more data have been collected. In this study, the Pe -pH profiles of 12 well-known ionizable drugs (five acids, one ampholyte, and six bases) over the pH range of 3–10, have been evaluated, from which the UWL (Pu ), the intrinsic permeability (Po ), and the pKaflux values were determined. The analysis of the shapes of the log Pe -pH profiles has suggested a new computational procedure, called pKaflux -optimized design (pOD-PAMPA), for estimating the entire membrane permeability (Pm )-pH profile, including Po , from a single measured Pe value, at a conditionally selected pH, which may be quite different from pH 7.4.
2. Materials and methods 2.1. Materials All drug compounds used in this study were purchased from Sigma–Aldrich (St. Louis, MO, USA), and used as received. 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) was purchased as a high-purity powder from Avanti Polar-Lipids Inc. (Alabaster, AL, USA), and was stored at −20 ◦ C when not used. Spectroscopic grade dodecane and dimethylsulphoxide were used. The pH of the assayed solutions was adjusted with a universal buffer (pION, PN 100621). 2.2. PAMPA method The PAMPA Evolution instrument from pION INC. (Woburn, MA, USA) was used in this study. In PAMPA, a “sandwich” is formed from a 96-well microtitre plate (pION, PN 100611) and a 96-well filter plate (Millipore, IPVH), such that each composite well is divided into two chambers: donor at the top and acceptor at the bottom, separated by a 125 m microfilter disc, coated with a 2% (w/v) dodecane solution of DOPC, based on the black lipid membrane formulations used in the past (Thompson et al., 1982). Initially, the buffered donor solutions were 10–50 M in test compounds and contained <1% (v/v) DMSO; the acceptor solutions contained just the buffer. The sandwich was formed and allowed to incubate for 6–15 h in a sealed box containing constant humidity and an oxygen and a carbon dioxide scrubber. The sandwich was then separated, and both the donor and acceptor compartments were assayed for the amount of material present, by comparison with the UV spectrum (235–500 nm) obtained from a pure reference standard. Mass balance was used to determine the amount of material remaining in the membrane barrier at the end of the assay. The buffers used in the assay were automatically prepared by the robotic system. The quality controls of the buffers were performed by alkalimetric titration, incorporating
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the Avdeef-Bucher procedure (Avdeef and Bucher, 1978). Following the completion of the UV assays, the pH in each microtitre plate well was measured to confirm correct value. Permeability (Pe ) was calculated as described previously (Avdeef et al., 2001). The Pe values were further divided by the apparent filter porosity, 0.76, so that the subsequently calculated UWL permeability values could be compared to values determined using filters with a different porosity, such as those used by Wohnsland and Faller (2001). 2.3. Equilibrium equations and permeability-pH profiles The basic relationships between permeability and pH can be derived for any given equilibrium model. The “model” refers to a set of equilibrium equations and the associated equilibrium quotients. As an example of derivation, consider the a diprotic ampholyte, such as piroxicam. The equilibrium equations and quotients are: H+ + X− = HX, H+ + HX = H2 X+ ,
K1 =
[HX] [H+ ][X− ]
K2 =
(1)
[H2 X+ ] [H+ ][HX]
(2)
With the aid of Eqs. (1) and (2), the total concentration of the ampholyte may be expressed in terms of the neutral
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species, HX, [HX]TOT = [X− ] + [HX] + [H2 X+ ] [HX] = + + [HX] + K2 [H+ ][HX] [H ]K1 1 + = [HX] + 1 + K [H ] 2 [H+ ]K1 or [HX]TOT = 1 + 10+pH−log K1 + 10−pH+log K2 [HX]
(3)
(4)
The fraction of the uncharged species, fu , is the inverse of the expression on the right side of Eq. (4). Other situations (mono-, di-, and triprotic) are summarized in Table 1, as equilibrium equations and the associated inverse-fu expressions. Their derivations followed similar steps as those indicated above. 2.4. Unstirred water layer permeability In a permeation cell, both sides of the membrane are in contact with a layer of water which is not stirred by convection. However, the thickness of this unstirred water layer does depend on the extent of stirring of the bulk solution, the layer becoming thinner with increased stirring (Karlsson and Artursson, 1991). The unstirred water layer contributes a resistance to the movement of permeating species. In the bulk solution, the concentration of the solute is uniformly distributed, as a result of convective mixing. However, in
Table 1 Permeability-pH equations: mono-, di-, and triprotic ionizable molecules Type
Equilibrium expressions
Equilibrium constanta
Permeability equations for Po /Pm b
1 acid
H+ + A− HA
K1
10−log K1 +pH + 1
2 acid
H+ + A2− HA− H+ + HA− H2 A
K1 K2
10−log K1 −log K2 +2pH + 10−log K2 +pH + 1
3 acid
H+ + A3− HA2− H+ + HA2− H2 A− H+ + H2 A− H3 A
K1 K2 K3
10−log K1 −log K2 −log K3 +3pH + 10−log K2 −log K3 +2pH + 10−log K3 +pH + 1
4 base
H+ + BBH+
K1
10+log K1 −pH + 1
5 base
H+ + BBH+ H+ + BH+ BH2 2+
K1 K2
10+log K1 +log K2 −2pH + 10+log K1 −pH + 1
6 base
H+ + BBH+ H+ + BH+ BH2 2+ H+ + BH2 2+ BH3 3+
K1 K2 K3
10+log K1 +log K2 +log K3 −3pH + 10+log K1 +log K2 −2pH + 10+log K1 −pH + 1
7 ampholyte
H+ + X− HX H+ + HXH2 HX+
K1 K2
10+log K2 −pH + 10−log K1 +pH + 1
8 ampholyte
H+ + X− HX H+ + HXH2 HX+ H+ + H2 X+ H3 HX2+
K1 K2 K3
10+log K2 +log K3 −2pH + 10+log K2 −pH + 10−log K1 +pH + 1
9 ampholyte
H+ + X2− HX− H+ + HX− H2 X H+ + H2 XH3 X+
K1 K2 K3
10−log K1 −log K2 +2pH + 10−log K2 +pH + 10+log K3 −pH +1
a b
log K1 = pKa for monoprotic molecules; log K1 = pKa2 , log K2 = pKa1 for diprotic molecules, etc. Note that Po /Pm = fu−1 , the inverse of the uncharged species fraction.
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the UWL, the concentration of molecules is not uniform, as they move from the region of higher concentration to the region of lower concentration by passive diffusion. For hydrophilic molecules, which permeate across phospholipid artificial membranes poorly, the membrane constitutes the rate-limiting barrier in the transport process. On the other hand, for lipophilic molecules, it is the UWL which constitutes the rate-limiting barrier. The calculations addressing this situation take into account that resistances in a series are additive. Since permeability is the inverse of resistance, 1 1 1 1 1 1 = D+ + A = + Pe Pu Pm Pu Pm Pu
(5)
where Pm is the permeability of the membrane, PuD and PuA are the UWL permeability coefficients on the donor and acceptor sides, respectively. If the permeation cell has equal agitation on both sides of the membrane, then Pu may be taken as the overall UWL permeability across the two aqueous layers, being equal to half of PuA or PuD . From Fick’s first law of diffusion, the UWL permeability may be related to the aqueous diffusivity, Daq , by the relation Pu =
Daq h
(6)
where h is the total thickness of the UWL, taken as the sum of the UWL thickness on each side of the membrane barrier. According to the Stokes-Einstein equation, aqueous diffusivity is expected to depend on the inverse square root of the molecular weight of the solute (Weiss, 1996). An
empirical equation (based on the analysis of 55 literature values of Daq ) describing the relationship has been proposed (Avdeef, 2003), log Daq = −4.14 − 0.417 log MW
(7)
The value of h may be calculated from the intercept in the plot of log Pu versus log MW, where the slope factor is kept fixed at −0.417 (cf. Eqs. (6) and (7)). 2.5. Membrane permeability For ionizable molecules, the membrane permeability, Pm , in Eq. (5) depends on pH of the bulk aqueous solution. The maximum possible value of Pm is realized at the pH where the solute is in its uncharged form. This limiting Pm is designated Po , the permeability of the uncharged species. The relationship between Pm and Po may be stated in terms of the fraction of the uncharged species, Pm = fu Po
(8)
Table 1 lists expressions of inverse-fu for nine types of ionizations of mono-, di- and triprotic molecules. For example, if one considers a monoprotic weak acid (log K1 = pKa ), the following permeability-pH relation holds 1 (10−pKa +pH + 1) 1 = + Pe Pu Po
(9)
The Pu and Po parameters were determined by weighted least-squares analysis, using 1/Pe as dependent variables and 1/fu as independent variables.
Fig. 1. The logarithm of permeability vs. pH for six weak acids, arranged in the order of decreasing intrinsic permeability. The solid curves refer to the effective permeability, the dashed curves refer to the membrane permeability (effective values corrected for the unstirred water layer), and the dotted lines refer to the unstirred water layer permeability.
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2.6. KOW and pKa The fragment-based program, Algorithm Builder v1.5 (Pharma Algorithms, Toronto, Canada) was used to calculate KOW and pKa required in the pOD-PAMPA method. Measured values were taken from published compilations (Avdeef, 2001a, 2003).
3. Results Fig. 1 displays the logarithm of measured Pe values as a function of pH for five of the acids and the ampholyte used in this study. Fig. 2 shows the same for the bases studied. The error bars were determined from replicate measurements. The solid hyperbolic curves in the figures were deduced from least square analysis of the Pe -pH data, using Eq. (9) and other similar equations derived from Table 1. The analysis deduces three parameters: Pu , Po , and pKaflux . These are listed in Table 2. The value of the unstirred water layer permeability, Pu , is indicated by the dotted horizontal lines in the figures. The apparent flux-pKa corresponds to the pH value at the point of intersection of the projected diagonal and horizontal portions of the solid curves. When the true pKa values are used in Eq. (9), the dashed hyperbolic curves in Figs. 1 and 2 result. The true pKa is indicated by the pH value at the point of intersection of the projected diagonal and horizontal portions of the dashed curves in the figures. Fig. 3 shows the relationship between log Pu and log MW. The average thickness of the UWL, h, is calculated from the
Fig. 3. The logarithm of unstirred water layer permeability as a function of the logarithm of the molecular weight.
regression analysis to be 0.384 cm. Assuming a symmetrical UWL on the two sides of the PAMPA membrane, the thickness of the individual UWL may be estimated as 1920 m. 4. Discussion 4.1. Permeability-pH in the Absence of the UWL For an ionizable molecule, the pH-partition hypothesis is predicated on the assumption that only the nonionized form of the molecule is able to cross lipid membranes. Consider weak acids (Fig. 1) for the discussion. If the UWL were absent, the measured membrane permeability as a function
Fig. 2. The logarithm of permeability vs. pH for six weak bases, arranged in the order of decreasing intrinsic permeability. The solid curves refer to the effective permeability, the dashed curves refer to the membrane permeability (effective values corrected for the unstirred water layer), and the dotted lines refer to the unstirred water layer permeability.
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Table 2 Intrinsic and unstirred water layer permeability determined from iso-pH dependence of effective permeability in PAMPA, based on 2% DOPC in dodecane Compound
Po cm/s (S.D.)a
log KOW b
Pu (10−6 cm/s)c
MW
pKa d (I = 0.01 M)
pKaflux
Imipramine Verapamil Propranolol Ibuprofen Phenazopyridine Piroxicam Naproxen Ketoprofen Metoprolol Quinine Salicylic acid Benzoic acid
5.1 (0.6) 0.19 (0.03) 7.3 (0.9) × 4.4 (1.0) × 2.0 (0.3) × 1.5 (0.2) × 6.3 (0.6) × 2.0 (0.2) × 1.1 (0.1) × 7.7 (0.7) × 4.4 (0.3) × 3.1 (0.2) ×
4.39 4.33 3.48 4.13 3.31 1.98 3.24 3.16 1.95 3.50 2.19 1.96
23.3 14.1 13.1 14.5 23.0 21.3 16.2 28.1 7.4 15.4 31.5 47.7
280.4 454.6 259.3 206.3 213.2 331.4 230.3 254.3 267.4 324.4 138.1 122.1
9.51 9.07 9.53 4.59 5.15 5.22, 2.3 4.32 4.12 9.56 8.55, 4.09 3.02 4.2
4.1 5.0 6.8 7.1 3.2 6.9 5.9 4.9 8.5 7.9 3.3 4.4
10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−5 10−5 10−5
(1.3) (0.9) (0.9) (1.9) (0.7) (1.5) (0.9) (2.5) (0.7) (1.3) (6.0) (9.4)
a
P0 : intrinsic permeability; S.D.: estimated standard deviation. KOW : octanol-water partition coefficient. c P : unstirred water layer permeability. u d Ionization constants; I: ionic strength. b
of pH would take the form of the dashed curves in Fig. 1. The measured membrane permeability would be the intrinsic value, Po , for pH pKa . For pH pKa , the concentration of the uncharged form of the molecule decreases by an order of magnitude for every increased unit of pH. Concomitantly, in alkaline solutions, the observed membrane permeability of weak acids decreases by an order of magnitude for every increased unit of pH. This is clearly evident in Fig. 1. As the permeability decreases, the concentration of the weak acid appearing in the acceptor compartment decreases as well, and the uncertainty of the measured Pe values rises, as indicated by the error bars in Fig. 1d for ketoprofen and Fig. 1f for benzoic acid permeability above pH 7. The extent of the uncertainty is dependent on the molar absorptivity of a particular molecule. If there were no UWL effects, then PAMPA could be used to determine the pKa values of molecules at high-throughput speeds. These would be indicated by the pH values at the point where the first derivative of the dashed curves is at the value of −0.5 for acids and +0.5 for bases, the points of intersection of the projected diagonal and horizontal portions of the dashed curves. 4.2. Permeability-pH and the effect of the UWL The UWL resistance is rate-limiting for highly permeable molecules. Ionizable molecules are most permeable when they are uncharged, as indicated by the pH regions where the hyperbolic curves are nearly horizontal in Figs. 1 and 2. The effect of the UWL is to lower the effective permeability in the horizontal regions from the values indicated by the dashed curves. The extent of the lowering between the dashed curve and the solid curve in that region is precisely equal to the difference between the true pKa and the measured apparent pKa , which we call pKaflux (Avdeef, 2001a), log Po − log Pu = |pKaflux − pKa |. For acids, the pKa appears to shift to higher values, and for bases, the shift is in
the opposite direction. The latter equation is only defined for molecules with Po > Pu . 4.3. In vitro–in vivo UWL As can be seen in Figs. 1 and 2, all the dotted lines, corresponding to log Pu and representing an upper limit of log Pe values, intersect the vertical axes in a narrow range, −4.7 ± 0.2 (mean Pu 21 × 10−6 cm/s), even though the lipophilicity (KOW ) of the molecules range from 89 (metoprolol) to 24,550 (imipramine). If the permeability of imipramine, verapamil, propranolol, and phenazopyridine were measured at pH 7.4, no information about the in vivo membrane transport characteristics could be obtained. This is because of the UWL effect. In unstirred Caco-2 and PAMPA assays, the UWL thickness is estimated to be between 1500 m (Wohnsland and Faller, 2001) and 2000 m (this study). These dimensions are nearly the heights of the aqueous solutions in the microtitre plates used. However, the UWL is estimated to be about 30–100 m in the human small intestine (Lennernäs, 1998). In vitro permeability assays of lipophilic molecules (PAMPA or Caco-2), if uncorrected for the UWL effect, are more indicative of the properties of water than of the membrane modeled. 4.4. The pOD-PAMPA method It is a common practice to do PAMPA at pH 7.4 only. For lipophilic molecules, the result may only indicate the resistance of the UWL, which may not be of interest to the investigator. If only a single pH measurement is done, then there may be better choices of pH than 7.4. The pKaflux — optimized design (pOD-PAMPA) method attempts to define the optimum pH value to use in a single-pH PAMPA experiment. The valuable outcome of the pOD-PAMPA procedure is that Po can be determined from a single Pe measurement. Implicitly, the whole Pm -pH profile can be derived.
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Fig. 4. Four cases of pOD-PAMPA simulation for a weak acid with pKa 4 and MW 300. The objective is to determine the optimum design pH, pHOD , based on a given octanol–water partition coefficient, log KOW .
A ‘generic’ weak acid with pKa 4 and MW 300 is used to describe the new method. Fig. 4 illustrates four cases of hyperbolic log Pe -pH plots for weak acids of varying degrees of lipophilicity. The Pu , Po , and pKa constants of the weak acid uniquely define the dashed, solid, and dotted curves in Fig. 4 (cf. Table 1 equations). For a weak acid, the steps in the pOD-PAMPA procedure are: (a) predict the KOW and pKa of a new compound, using commercial computer programs; (b) use KOW to predict the ‘seed’ Po ; (c) use the MW to predict Pu ; (d) use the pKa , the Po and Pu from above to predict pKaflux ; (e) pHOD = pKaflux + 1.7 if Po ≥ Pu or pHOD = pKa − 1.7 if Po < Pu ; (f) perform a single-pH PAMPA at pHOD to obtain the measured Pe . Finally, calculate the intrinsic permeability from the measured effective permeability according to the situations: (1) if ‘seed’ Po ≥
Pu , log Po = log Pe + pHOD − pKa , else, (2) if ‘seed’ log Po > log Pu − 1.7, then log Po = log Pe + log(1 − Pe /Pu ), else (3) Po = Pe . (The rationale for ‘1.7’ is described below.) Details of this procedure are summarized in Table 3, and specific examples with hypothetical log KOW 3.6, 1.9, 1.4, and −0.4 are illustrated in Fig. 4. For a lipophilic molecule (Cases I and II in Table 3), the optimum pH needs to be selected from the diagonal region of the Pe -pH (solid) curve, because data in that region are not affected by the UWL. According to the analysis of hyperbolic log D-pH profiles (Avdeef, 1996), the diagonal segment is separated from the horizontal segment by the curved region, which is 3.4 pH units wide by 1.7 log units in height. So, for the weak acid, the optimally-designed pH, pHOD , would be 1.7 units greater than the pKaflux , and the
Table 3 Weak acid simulation to illustrate the pOD-PAMPA method
‘Seed’ log Po log Pe at pH pKa log KOW log Po (‘seed’), cm/s unitsa log Pu (calibration), cm/s unitsb pKaflux pHOD log Po (calculated from measured Pe at pHOD )
Case I
Case II
Case III
Case IV
>log Pu + 1.7 =log Pu 3.6 −2.20 −4.75 6.6 pKaflux + 1.7 = 8.3 log Pe + pHOD − pKa = log Pe + 4.3
>log Pu < log Pu + 1.7
log Pu − 1.7
MW = 300 in the simulated example. a log P (‘seed’) = −6.84 + 1.28 log K o OW . b log P (calibration) = −3.72 − 0.417 log MW. u
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Table 4 pOD-PAMPA method validation Compound
log KOW calculateda
pKa calculateda
Po (‘seed’)
Pu (calib.) 10−6 cm/s units
pHOD
Pe measured at pH 10−6 cm/s
pH nearest to pHOD
Po pODPAMPA
Po normal multi-pH
Imipramine Verapamil Propranolol Ibuprofen Phenazopyridine Piroxicam Naproxen Ketoprofen Metoprolol Quinine Salicylic acid Benzoic acid
4.12 4.68 2.95 3.44 1.86 2.39 2.75 2.46 1.80 2.29 1.93 1.80
9.4 9.1 9.6 4.3 4.9 5.8 4.3 4.3 9.6 8.6 3.0 4.1
2.7e−2 1.4e−1 8.6e−4 3.7e−3 3.5e−5 1.7e−4 4.8e−4 2.0e−4 2.9e−5 1.2e−4 4.3e−5 2.9e−5
18 15 19 21 20 17 20 19 19 17 24 26
4.5 3.4 6.2 8.2 3.0 8.5 7.4 7.0 7.7 6.0 4.9 5.9
15 0.79 2.6 1.0 9.2 0.79 0.46 0.38 1.2 1.2 0.32 0.62
4.5 3.5 6.2 8.1 3.0 8.5 7.4 7.0 7.7 6.8 5.0 5.9
5.9 0.33 7.6e−3 6.8e−3 1.4e−3 4.2e−4 6.0e−4 1.7e−4 1.1e−4 8.5e−5 3.2e−5 4.1e−5
5.1 0.19 7.3e−3 4.4e−3 2.0e−3 1.5e−3 6.3e−4 2.0e−4 1.1e−4 7.7e−5 4.4e−5 3.1e−5
a
Pharma Algorithms, Toronto, Canada.
expected log Pe at this pH would be 1.7 log units lower than log Pu . The required unstirred water layer permeability may be estimated from the MW of a compound, according to the equation: log Pu = −3.72 − 0.417 log MW (Fig. 3). From the analysis of measured Po and KOW values (Table 2), we estimate log Po (‘seed’) = −6.84 + 1.28 log KOW (r2 0.59). By using a calculated KOW , the latter equation may be used to estimate the log Po (‘seed’) of new compounds. Then, a calculated pKa (e.g. Pharma Algorithms computer program), along with a ‘seed’ Po and an estimated Pu , may be used to predict the solid, dashed, and dotted curves in Fig. 4. The pHOD value is on the solid curve, right below the end of the curved zone (point 1 in Fig. 4a). For a hydrophilic weak acid (Cases III and IV in Table 3), where the ‘seed’ Po value is less than the estimated Pu value,
the pHOD value is selected to be 1.7 pH units less than the pKa value of the molecule. For these cases, the permeability data are not greatly affected by the UWL. (Note that pKaflux cannot be defined, since transport is always more than 50% membrane controlled.) For such cases, Po can be determined without accurate knowledge of pKa , since the latter values are not explicitly used in the calculation of Po (Table 3). 4.5. Interpretation of the pOD-PAMPA permeability Point 1 in Fig. 4a is expected, but because the ‘seed’ Po and the calculated pKa may be in error, measured Pe may take on values indicated by open-symbol points 2, 3, or 4. If it can be assumed that pKa values are not the source of error (e.g. reliably measured pKa values were used), then
Fig. 5. Correlation plots comparing one-point pOD-PAMPA to the multiple-pH PAMPA. Inset is a similar correlation, relating measured pKa values to calculated values (Pharma Algorithm).
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log KOW overestimated the true Po in the case of 2 and underestimated the true Po in the cases of 3 and 4. Since 4 lies on the Pu line, only the lower limit of the true value of Po may be determined, i.e. log Po ≥ log Pu + pHOD − pKa (Table 3), or Po ≥ 0.35 cm/s in this example, about 56 times higher than the seed value used to predict the Pe at point 1. 4.6. Testing the pOD-PAMPA method The computational procedure illustrated in Fig. 4 and summarized in Table 3 was applied to the experimental measurements. Most of the compounds in our study belong to Case II (propranolol, phenazopyridine, piroxicam, naproxen, ketoprofen, metoprolol, quinine, salicylic and benzoic acids) and some belong to Case I (imipramine, verapamil, and ibuprofen). There are no examples of Cases III and IV from the twelve molecules characterized here. Octanol-water partition coefficients and ionization constants for the twelve molecules were calculated using the computer program from Pharma Algorithms, and the results are summarized in Table 4. The pHOD values derived by the pOD-PAMPA method are listed in Table 4. From the set of measurements performed for each molecule, the Pe corresponding to the pH closest to the pHOD value was selected and processed as a single-pH Pe value to determine the intrinsic permeability, Po (Table 4). The correlation plot of the Po values based on all pH-data and the Po values determined from a single Pe value is shown in Fig. 5. The fit is robust, with r2 0.985 and s 0.20. The inset in Fig. 5, calculated pKa versus measured pKa , indicates comparable statistics.
5. Conclusion In high-throughput applications, PAMPA is usually performed at a single pH (7.4 or 6.5). But measured Pe at that pH may not be indicative of membrane permeability, due to the UWL effect. The pOD-PAMPA method was devised to overcome this problem. It was shown that single-pH PAMPA, done at the optimum value of pH, pHOD , can be used to generate permeability profiles corrected for the UWL. The novel procedure was effectively tested with twelve lipophilic compounds studied here.
References Anderson, B.W., Levine, A.S., Levitt, D.G., Kneip, J.M., Levitt, M.D., 1988. Physiological measurement of luminal stirring in perfused rat jejunum. Am. J. Physiol. 254, G843–G848. Avdeef, A., Bucher, J.J., 1978. Accurate measurements of the concentration of hydrogen ions with a glass electrode: calibrations using the Prideaux and other universal buffer solutions and a computer-controlled automatic titrator. Anal. Chem. 50, 2137– 2142.
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Avdeef, A., 1996. Assessment of Distribution-pH profiles. In: Pliska, V., Testa, B., van de Waterbeemd, H. (Eds.), Methods and Principles in Medicinal Chemistry, vol. 4. VCH, Weinheim, Germany, 1996, pp. 109–139. Avdeef, A., 2001a. Physicochemical profiling (solubility, permeability, and charge state). Curr. Topics Med. Chem. 1, 277–351. Avdeef, A., 2001b. High-throughput measurements of solubility profiles. In: Testa, B., van de Waterbeemd, H., Folkers, G., Guy, R. (Eds.), Pharmacokinetic Optimization in Drug Research, Verlag Helvetica Chimica Acta, Zürich. Wiley/VCH, Weinheim, pp. 305–326. Avdeef, A., Strafford, M., Block, E., Balogh, M.P., Chambliss, W., Khan, I., 2001. Drug absorption in vitro model: filter-immobilized artificial membranes. 2. Studies of the permeability properties of lactones in piper methysticum forst. Eur. J. Pharm. Sci. 14, 271–280. Avdeef, A., 2003. Absorption and Drug Development—Solubility, Permeability, and Charge State. Wiley, New York, pp. 116–246. Faller, B., Wohnsland, F., 2001. Physicochemical parameters as tools in drug discovery and lead optimization. In: Testa, B., van de Waterbeemd, H., Folkers, G., Guy, R. (Eds.), Pharmacokinetic Optimization in Drug Research, Verlag Helvetica Chimica Acta, Zürich. Wiley/VCH, Weinheim, pp. 257–274. Gutknecht, J., Tosteson, F.C., 1973. Diffusion of weak acids across lipid membranes: effects of chemical reactions in the unstirred layers. Science 182, 1258–1261. Ho, N.F.H., Raub, T.J., Burton, P.S., Barsuhn, C.L., Adson, A., Audus, K.L., Borchardt, R.T., 2000. Quantitative approaches to delineate passive transport mechanisms in cell culture monolayers. In: Amidon, G.L., Lee, P.I., Topp, E.M. (Eds.), Transport Processes in Pharmaceutical Systems. Marcel Dekker, New York, pp. 219–317. Kansy, M., Senner, F., Gubernator, K., 1998. Physicochemical high throughput screening: parallel artificial membrane permeability assay in the description of passive absorption processes. J. Med. Chem. 41, 1007–1010. Kansy, M., Fischer, H., Kratzat, K., Senner, F., Wagner, B., Parrilla, I., 2001. High-throughput aritificial membrane permeability studies in early lead discovery and development. In: Testa, B., van de Waterbeemd, H., Folkers, G., Guy, R. (Eds.). Pharmacokinetic Optimization in Drug Research, Verlag Helvetica Chimica Acta, Zürich. Wiley/VCH, Weinheim, pp. 447–464. Karlsson, J.P., Artursson, P., 1991. A method for the determination of cellular permeability coefficients and aqueous boundary layer thickness in monolayers of intestinal epithelial (Caco-2) cells grown in permeable filter chambers. Int. J. Pharm. 7, 55–64. Lennernäs, H., 1998. Human intestinal permeability. J. Pharm. Sci. 87, 403–410. Levitt, M.D., Furne, J.K., Strocchi, A., Anderson, B.W., Levitt, D.G., 1990. Physiological measurements of luminal stirring in the dog and human small bowl. J. Clin. Invest. 86, 1540–1547. Sugano, K., Hamada, H., Machida, M., Ushio, H., Saitoh, K., Terada, K., 2001a. Optimized conditions of bio-mimetic artificial membrane permeability assay. Int. J. Pharm. 228, 181–188. Sugano, K., Hamada, H., Machida, M., Ushio, H., 2001b. High throughput prediction of oral absorption: improvement of the composition of the lipid solution used in parallel artificial membrane permeability assay. J. Biomolec. Screen 6, 189–196. Sugano, K., Takata, N., Machida, M., Saitoh, K., Terada, K., 2002. Prediction of passive intestinal absorption using bio-mimetic artificial membrane permeation assay and the paracellular pathway model. Int. J. Pharm. 241, 241–251. Thompson, M., Lennox, R.B., McClelland, R.A., 1982. Structure and electrochemical properties of microfiltration filter-lipid membrane systems. Anal. Chem. 54, 76–81. Veber, D.F., Johnson, S.R., Cheng, H.-Y., Smith, B.R., Ward, K.W., Kopple, K.D., 2002. Molecular properties that influence the oral bioavailability of drug candidates. J. Med. Chem. 45, 2615–2623. Walter, A., Gutknecht, J., 1984. Monocarboxylic acid permeation through lipid bilayer membranes. J. Membr. Biol. 77, 255–264.
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Wohnsland, F., Faller, B., 2001. High-throughput permeability pH profile and high-throughput alkane/water log P with artificial membranes. J. Med. Chem. 44, 923–930. Zhu, C., Jiang, L., Chen, T.-M., Hwang, K.-K., 2002. A comparative study of artificial membrane permeability assay for high-throughput profiling of drug absorption potential. Eur. J. Med. Chem. 37, 399–407.
PAMPA—a drug absorption in vitro model 5. Unstirred water layer in iso-pH mapping assays and pKaflux —optimized design (pOD-PAMPA)夽 Jeffrey A. Ruell, Konstantin L. Tsinman, Alex Avdeef∗ pION INC., 5 Constitution Way, Woburn, MA 01801 USA Received 10 March 2003; received in revised form 26 August 2003; accepted 26 August 2003
Abstract Iso-pH mapping unstirred parallel artificial membrane permeability assay (PAMPA) was used to measure the effective permeability, Pe , as a function of pH from 3 to 10, of five weak monoprotic acids (ibuprofen, naproxen, ketoprofen, salicylic acid, benzoic acid), an ampholyte (piroxicam), five monoprotic weak bases (imipramine, verapamil, propranolol, phenazopyridine, metoprolol), and a diprotic weak base (quinine). The intrinsic permeability, Po , the unstirred water layer (UWL) permeability, Pu , and the apparent pKa (pKaflux ) were determined from the pH dependence of log Pe . The underlying permeability-pH equations were derived for multiprotic weak acids, weak bases and ampholytes. The average thickness of the unstirred water layer on each side of the membrane was estimated to be nearly 2000 m, somewhat larger than that found in Caco-2 permeability assays (unstirred). Since the UWL thickness in the human intestine is believed to be about forty times smaller, it is critical to correct the in vitro permeability data for the effect of the UWL. Without such correction, the in vitro permeability coefficient of lipophilic molecules would be indicative only of the property of water. In single-pH PAMPA (e.g. pH 7.4), the uncertainty of the UWL contribution can be minimized if a specially-selected pH (possibly different from 7.4) were used in the assay. From the analysis of the shapes of the log Pe —pH plots, a method to improve the selection of the assay pH, called pKaflux —optimized design (pOD-PAMPA), was described and tested. From an optimally-selected assay pH, it is possible to estimate Po , as well as the entire membrane permeability—pH profile. © 2003 Elsevier B.V. All rights reserved. Keywords: PAMPA; Permeability; Unstirred water layer; pKaflux -optimized design; Oral absorption
1. Introduction Since its introduction in 1998, PAMPA (parallel artificial membrane permeability assay) has attracted considerable attention in the pharmaceutical industry (Kansy et al., 1998, 2001; Avdeef, 2001a,b; Avdeef et al., 2001; Faller and Wohnsland, 2001; Wohnsland and Faller, 2001; Sugano et al., 2001a,b, 2002; Zhu et al., 2002; Veber et al., 2002; Avdeef, 2003), and has been the focus of an international meeting (www.pampa2002.com). PAMPA can quickly provide information about passive-transport permeability, that is not complicated by other mechanisms. Due to its versa夽
Ref. Avdeef, et al., 2001, is part 2 of the series. Corresponding author. Tel.: +1-781-935-8939x22; fax: +1-781-935-8938. E-mail address: [email protected] (A. Avdeef). ∗
0928-0987/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.ejps.2003.08.006
tility and relative low cost, the assay is an attractive model for high throughput screening. Presently, most PAMPA tests focus on obtaining binning results (high/low) for compounds based on their performance relative to internal standards used to predict human intestinal absorption. PAMPA implicitly is thought to correlate with the compound’s ability to traverse the model membrane barrier. However, this assumption may not be true in all cases, since compounds have to permeate not only through the artificial membrane barrier, but also the unstirred water layer (UWL), a domain of solvent adjacent to the membrane that is not subject to convective mixing of the bulk solution. For highly lipophilic molecules, the rate-limiting barrier to transport is the UWL. For example (Wohnsland and Faller, 2001), at pH 6.8, the effective permeability of propranolol, 40 × 10−6 cm/s, is about 40% less than that of metoprolol, 63 × 10−6 cm/s, even though propranolol is 40 times more
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Nomenclature All permeability coefficients are in units of cm/s Daq diffusivity of a solute in aqueous solution (cm2 /s) fu fraction of the total sample concentration in the uncharged form h thickness of the unstirred aqueous layer (cm) log Ki stepwise protonation constant of a multiprotic molecule, associated with the q + H+ = XHi , equilibrium reaction: XHq−1 i−1 q: charge KOW octanol–water partition coefficient for an uncharged species; pH-independent PAMPA parallel artificial membrane permeability assay Pe effective artificial-membrane permeability (measured), composed of the unstirred water layer and membrane permeability, and corrected for membrane retention Pm membrane permeability coefficient; can dependent on pH for ionizable molecules Po intrinsic artificial membrane permeability coefficient; pH-independent Pu unstirred water layer permeability coefficient pKa ionization constant (negative log form) pKaflux the apparent pKa derived from the Pe —pH profile, the pH at which the resistance to transport is 50% due to the membrane barrier and 50% due to the unstirred water layer pOD pKaflux -optimized design UWL unstirred water layer
lipophilic than metoprolol. The lingering problem with measuring water and not membrane permeability for lipophilic compounds is that structural differences in compounds, unless they are drastic, often will not affect permeability. The effect of the UWL in permeability measurement has been studied in black lipid membrane models (Gutknecht and Tosteson, 1973; Walter and Gutknecht, 1984), in vitro cellular models (Karlsson and Artursson, 1991; Ho et al., 2000), rat intestine (Winne et al., 1987; Anderson et al., 1988; Levitt et al., 1990), and human jejunum (Lennernäs, 1998). Wohnsland and Faller (2001) reported the thickness of the UWL in PAMPA to be 300 m (microtitre plate shaken at 50–100 rpm). In unstirred Caco-2 assays, the UWL was reported to be 1500 m (Wohnsland and Faller, 2001), while in the human intestine, the value is estimated to be 30–100 m (Lennernäs, 1998). This study is a detailed account of the UV-based iso-pH PAMPA method. Some preliminary results have been cited,
without data, in a review (Avdeef, 2001a). Since then, computational procedures in the treatment of the UV data have improved, additional molecules have been studied, and more data have been collected. In this study, the Pe -pH profiles of 12 well-known ionizable drugs (five acids, one ampholyte, and six bases) over the pH range of 3–10, have been evaluated, from which the UWL (Pu ), the intrinsic permeability (Po ), and the pKaflux values were determined. The analysis of the shapes of the log Pe -pH profiles has suggested a new computational procedure, called pKaflux -optimized design (pOD-PAMPA), for estimating the entire membrane permeability (Pm )-pH profile, including Po , from a single measured Pe value, at a conditionally selected pH, which may be quite different from pH 7.4.
2. Materials and methods 2.1. Materials All drug compounds used in this study were purchased from Sigma–Aldrich (St. Louis, MO, USA), and used as received. 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC) was purchased as a high-purity powder from Avanti Polar-Lipids Inc. (Alabaster, AL, USA), and was stored at −20 ◦ C when not used. Spectroscopic grade dodecane and dimethylsulphoxide were used. The pH of the assayed solutions was adjusted with a universal buffer (pION, PN 100621). 2.2. PAMPA method The PAMPA Evolution instrument from pION INC. (Woburn, MA, USA) was used in this study. In PAMPA, a “sandwich” is formed from a 96-well microtitre plate (pION, PN 100611) and a 96-well filter plate (Millipore, IPVH), such that each composite well is divided into two chambers: donor at the top and acceptor at the bottom, separated by a 125 m microfilter disc, coated with a 2% (w/v) dodecane solution of DOPC, based on the black lipid membrane formulations used in the past (Thompson et al., 1982). Initially, the buffered donor solutions were 10–50 M in test compounds and contained <1% (v/v) DMSO; the acceptor solutions contained just the buffer. The sandwich was formed and allowed to incubate for 6–15 h in a sealed box containing constant humidity and an oxygen and a carbon dioxide scrubber. The sandwich was then separated, and both the donor and acceptor compartments were assayed for the amount of material present, by comparison with the UV spectrum (235–500 nm) obtained from a pure reference standard. Mass balance was used to determine the amount of material remaining in the membrane barrier at the end of the assay. The buffers used in the assay were automatically prepared by the robotic system. The quality controls of the buffers were performed by alkalimetric titration, incorporating
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the Avdeef-Bucher procedure (Avdeef and Bucher, 1978). Following the completion of the UV assays, the pH in each microtitre plate well was measured to confirm correct value. Permeability (Pe ) was calculated as described previously (Avdeef et al., 2001). The Pe values were further divided by the apparent filter porosity, 0.76, so that the subsequently calculated UWL permeability values could be compared to values determined using filters with a different porosity, such as those used by Wohnsland and Faller (2001). 2.3. Equilibrium equations and permeability-pH profiles The basic relationships between permeability and pH can be derived for any given equilibrium model. The “model” refers to a set of equilibrium equations and the associated equilibrium quotients. As an example of derivation, consider the a diprotic ampholyte, such as piroxicam. The equilibrium equations and quotients are: H+ + X− = HX, H+ + HX = H2 X+ ,
K1 =
[HX] [H+ ][X− ]
K2 =
(1)
[H2 X+ ] [H+ ][HX]
(2)
With the aid of Eqs. (1) and (2), the total concentration of the ampholyte may be expressed in terms of the neutral
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species, HX, [HX]TOT = [X− ] + [HX] + [H2 X+ ] [HX] = + + [HX] + K2 [H+ ][HX] [H ]K1 1 + = [HX] + 1 + K [H ] 2 [H+ ]K1 or [HX]TOT = 1 + 10+pH−log K1 + 10−pH+log K2 [HX]
(3)
(4)
The fraction of the uncharged species, fu , is the inverse of the expression on the right side of Eq. (4). Other situations (mono-, di-, and triprotic) are summarized in Table 1, as equilibrium equations and the associated inverse-fu expressions. Their derivations followed similar steps as those indicated above. 2.4. Unstirred water layer permeability In a permeation cell, both sides of the membrane are in contact with a layer of water which is not stirred by convection. However, the thickness of this unstirred water layer does depend on the extent of stirring of the bulk solution, the layer becoming thinner with increased stirring (Karlsson and Artursson, 1991). The unstirred water layer contributes a resistance to the movement of permeating species. In the bulk solution, the concentration of the solute is uniformly distributed, as a result of convective mixing. However, in
Table 1 Permeability-pH equations: mono-, di-, and triprotic ionizable molecules Type
Equilibrium expressions
Equilibrium constanta
Permeability equations for Po /Pm b
1 acid
H+ + A− HA
K1
10−log K1 +pH + 1
2 acid
H+ + A2− HA− H+ + HA− H2 A
K1 K2
10−log K1 −log K2 +2pH + 10−log K2 +pH + 1
3 acid
H+ + A3− HA2− H+ + HA2− H2 A− H+ + H2 A− H3 A
K1 K2 K3
10−log K1 −log K2 −log K3 +3pH + 10−log K2 −log K3 +2pH + 10−log K3 +pH + 1
4 base
H+ + BBH+
K1
10+log K1 −pH + 1
5 base
H+ + BBH+ H+ + BH+ BH2 2+
K1 K2
10+log K1 +log K2 −2pH + 10+log K1 −pH + 1
6 base
H+ + BBH+ H+ + BH+ BH2 2+ H+ + BH2 2+ BH3 3+
K1 K2 K3
10+log K1 +log K2 +log K3 −3pH + 10+log K1 +log K2 −2pH + 10+log K1 −pH + 1
7 ampholyte
H+ + X− HX H+ + HXH2 HX+
K1 K2
10+log K2 −pH + 10−log K1 +pH + 1
8 ampholyte
H+ + X− HX H+ + HXH2 HX+ H+ + H2 X+ H3 HX2+
K1 K2 K3
10+log K2 +log K3 −2pH + 10+log K2 −pH + 10−log K1 +pH + 1
9 ampholyte
H+ + X2− HX− H+ + HX− H2 X H+ + H2 XH3 X+
K1 K2 K3
10−log K1 −log K2 +2pH + 10−log K2 +pH + 10+log K3 −pH +1
a b
log K1 = pKa for monoprotic molecules; log K1 = pKa2 , log K2 = pKa1 for diprotic molecules, etc. Note that Po /Pm = fu−1 , the inverse of the uncharged species fraction.
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the UWL, the concentration of molecules is not uniform, as they move from the region of higher concentration to the region of lower concentration by passive diffusion. For hydrophilic molecules, which permeate across phospholipid artificial membranes poorly, the membrane constitutes the rate-limiting barrier in the transport process. On the other hand, for lipophilic molecules, it is the UWL which constitutes the rate-limiting barrier. The calculations addressing this situation take into account that resistances in a series are additive. Since permeability is the inverse of resistance, 1 1 1 1 1 1 = D+ + A = + Pe Pu Pm Pu Pm Pu
(5)
where Pm is the permeability of the membrane, PuD and PuA are the UWL permeability coefficients on the donor and acceptor sides, respectively. If the permeation cell has equal agitation on both sides of the membrane, then Pu may be taken as the overall UWL permeability across the two aqueous layers, being equal to half of PuA or PuD . From Fick’s first law of diffusion, the UWL permeability may be related to the aqueous diffusivity, Daq , by the relation Pu =
Daq h
(6)
where h is the total thickness of the UWL, taken as the sum of the UWL thickness on each side of the membrane barrier. According to the Stokes-Einstein equation, aqueous diffusivity is expected to depend on the inverse square root of the molecular weight of the solute (Weiss, 1996). An
empirical equation (based on the analysis of 55 literature values of Daq ) describing the relationship has been proposed (Avdeef, 2003), log Daq = −4.14 − 0.417 log MW
(7)
The value of h may be calculated from the intercept in the plot of log Pu versus log MW, where the slope factor is kept fixed at −0.417 (cf. Eqs. (6) and (7)). 2.5. Membrane permeability For ionizable molecules, the membrane permeability, Pm , in Eq. (5) depends on pH of the bulk aqueous solution. The maximum possible value of Pm is realized at the pH where the solute is in its uncharged form. This limiting Pm is designated Po , the permeability of the uncharged species. The relationship between Pm and Po may be stated in terms of the fraction of the uncharged species, Pm = fu Po
(8)
Table 1 lists expressions of inverse-fu for nine types of ionizations of mono-, di- and triprotic molecules. For example, if one considers a monoprotic weak acid (log K1 = pKa ), the following permeability-pH relation holds 1 (10−pKa +pH + 1) 1 = + Pe Pu Po
(9)
The Pu and Po parameters were determined by weighted least-squares analysis, using 1/Pe as dependent variables and 1/fu as independent variables.
Fig. 1. The logarithm of permeability vs. pH for six weak acids, arranged in the order of decreasing intrinsic permeability. The solid curves refer to the effective permeability, the dashed curves refer to the membrane permeability (effective values corrected for the unstirred water layer), and the dotted lines refer to the unstirred water layer permeability.
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2.6. KOW and pKa The fragment-based program, Algorithm Builder v1.5 (Pharma Algorithms, Toronto, Canada) was used to calculate KOW and pKa required in the pOD-PAMPA method. Measured values were taken from published compilations (Avdeef, 2001a, 2003).
3. Results Fig. 1 displays the logarithm of measured Pe values as a function of pH for five of the acids and the ampholyte used in this study. Fig. 2 shows the same for the bases studied. The error bars were determined from replicate measurements. The solid hyperbolic curves in the figures were deduced from least square analysis of the Pe -pH data, using Eq. (9) and other similar equations derived from Table 1. The analysis deduces three parameters: Pu , Po , and pKaflux . These are listed in Table 2. The value of the unstirred water layer permeability, Pu , is indicated by the dotted horizontal lines in the figures. The apparent flux-pKa corresponds to the pH value at the point of intersection of the projected diagonal and horizontal portions of the solid curves. When the true pKa values are used in Eq. (9), the dashed hyperbolic curves in Figs. 1 and 2 result. The true pKa is indicated by the pH value at the point of intersection of the projected diagonal and horizontal portions of the dashed curves in the figures. Fig. 3 shows the relationship between log Pu and log MW. The average thickness of the UWL, h, is calculated from the
Fig. 3. The logarithm of unstirred water layer permeability as a function of the logarithm of the molecular weight.
regression analysis to be 0.384 cm. Assuming a symmetrical UWL on the two sides of the PAMPA membrane, the thickness of the individual UWL may be estimated as 1920 m. 4. Discussion 4.1. Permeability-pH in the Absence of the UWL For an ionizable molecule, the pH-partition hypothesis is predicated on the assumption that only the nonionized form of the molecule is able to cross lipid membranes. Consider weak acids (Fig. 1) for the discussion. If the UWL were absent, the measured membrane permeability as a function
Fig. 2. The logarithm of permeability vs. pH for six weak bases, arranged in the order of decreasing intrinsic permeability. The solid curves refer to the effective permeability, the dashed curves refer to the membrane permeability (effective values corrected for the unstirred water layer), and the dotted lines refer to the unstirred water layer permeability.
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Table 2 Intrinsic and unstirred water layer permeability determined from iso-pH dependence of effective permeability in PAMPA, based on 2% DOPC in dodecane Compound
Po cm/s (S.D.)a
log KOW b
Pu (10−6 cm/s)c
MW
pKa d (I = 0.01 M)
pKaflux
Imipramine Verapamil Propranolol Ibuprofen Phenazopyridine Piroxicam Naproxen Ketoprofen Metoprolol Quinine Salicylic acid Benzoic acid
5.1 (0.6) 0.19 (0.03) 7.3 (0.9) × 4.4 (1.0) × 2.0 (0.3) × 1.5 (0.2) × 6.3 (0.6) × 2.0 (0.2) × 1.1 (0.1) × 7.7 (0.7) × 4.4 (0.3) × 3.1 (0.2) ×
4.39 4.33 3.48 4.13 3.31 1.98 3.24 3.16 1.95 3.50 2.19 1.96
23.3 14.1 13.1 14.5 23.0 21.3 16.2 28.1 7.4 15.4 31.5 47.7
280.4 454.6 259.3 206.3 213.2 331.4 230.3 254.3 267.4 324.4 138.1 122.1
9.51 9.07 9.53 4.59 5.15 5.22, 2.3 4.32 4.12 9.56 8.55, 4.09 3.02 4.2
4.1 5.0 6.8 7.1 3.2 6.9 5.9 4.9 8.5 7.9 3.3 4.4
10−3 10−3 10−3 10−3 10−4 10−4 10−4 10−5 10−5 10−5
(1.3) (0.9) (0.9) (1.9) (0.7) (1.5) (0.9) (2.5) (0.7) (1.3) (6.0) (9.4)
a
P0 : intrinsic permeability; S.D.: estimated standard deviation. KOW : octanol-water partition coefficient. c P : unstirred water layer permeability. u d Ionization constants; I: ionic strength. b
of pH would take the form of the dashed curves in Fig. 1. The measured membrane permeability would be the intrinsic value, Po , for pH pKa . For pH pKa , the concentration of the uncharged form of the molecule decreases by an order of magnitude for every increased unit of pH. Concomitantly, in alkaline solutions, the observed membrane permeability of weak acids decreases by an order of magnitude for every increased unit of pH. This is clearly evident in Fig. 1. As the permeability decreases, the concentration of the weak acid appearing in the acceptor compartment decreases as well, and the uncertainty of the measured Pe values rises, as indicated by the error bars in Fig. 1d for ketoprofen and Fig. 1f for benzoic acid permeability above pH 7. The extent of the uncertainty is dependent on the molar absorptivity of a particular molecule. If there were no UWL effects, then PAMPA could be used to determine the pKa values of molecules at high-throughput speeds. These would be indicated by the pH values at the point where the first derivative of the dashed curves is at the value of −0.5 for acids and +0.5 for bases, the points of intersection of the projected diagonal and horizontal portions of the dashed curves. 4.2. Permeability-pH and the effect of the UWL The UWL resistance is rate-limiting for highly permeable molecules. Ionizable molecules are most permeable when they are uncharged, as indicated by the pH regions where the hyperbolic curves are nearly horizontal in Figs. 1 and 2. The effect of the UWL is to lower the effective permeability in the horizontal regions from the values indicated by the dashed curves. The extent of the lowering between the dashed curve and the solid curve in that region is precisely equal to the difference between the true pKa and the measured apparent pKa , which we call pKaflux (Avdeef, 2001a), log Po − log Pu = |pKaflux − pKa |. For acids, the pKa appears to shift to higher values, and for bases, the shift is in
the opposite direction. The latter equation is only defined for molecules with Po > Pu . 4.3. In vitro–in vivo UWL As can be seen in Figs. 1 and 2, all the dotted lines, corresponding to log Pu and representing an upper limit of log Pe values, intersect the vertical axes in a narrow range, −4.7 ± 0.2 (mean Pu 21 × 10−6 cm/s), even though the lipophilicity (KOW ) of the molecules range from 89 (metoprolol) to 24,550 (imipramine). If the permeability of imipramine, verapamil, propranolol, and phenazopyridine were measured at pH 7.4, no information about the in vivo membrane transport characteristics could be obtained. This is because of the UWL effect. In unstirred Caco-2 and PAMPA assays, the UWL thickness is estimated to be between 1500 m (Wohnsland and Faller, 2001) and 2000 m (this study). These dimensions are nearly the heights of the aqueous solutions in the microtitre plates used. However, the UWL is estimated to be about 30–100 m in the human small intestine (Lennernäs, 1998). In vitro permeability assays of lipophilic molecules (PAMPA or Caco-2), if uncorrected for the UWL effect, are more indicative of the properties of water than of the membrane modeled. 4.4. The pOD-PAMPA method It is a common practice to do PAMPA at pH 7.4 only. For lipophilic molecules, the result may only indicate the resistance of the UWL, which may not be of interest to the investigator. If only a single pH measurement is done, then there may be better choices of pH than 7.4. The pKaflux — optimized design (pOD-PAMPA) method attempts to define the optimum pH value to use in a single-pH PAMPA experiment. The valuable outcome of the pOD-PAMPA procedure is that Po can be determined from a single Pe measurement. Implicitly, the whole Pm -pH profile can be derived.
J.A. Ruell et al. / European Journal of Pharmaceutical Sciences 20 (2003) 393–402
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Fig. 4. Four cases of pOD-PAMPA simulation for a weak acid with pKa 4 and MW 300. The objective is to determine the optimum design pH, pHOD , based on a given octanol–water partition coefficient, log KOW .
A ‘generic’ weak acid with pKa 4 and MW 300 is used to describe the new method. Fig. 4 illustrates four cases of hyperbolic log Pe -pH plots for weak acids of varying degrees of lipophilicity. The Pu , Po , and pKa constants of the weak acid uniquely define the dashed, solid, and dotted curves in Fig. 4 (cf. Table 1 equations). For a weak acid, the steps in the pOD-PAMPA procedure are: (a) predict the KOW and pKa of a new compound, using commercial computer programs; (b) use KOW to predict the ‘seed’ Po ; (c) use the MW to predict Pu ; (d) use the pKa , the Po and Pu from above to predict pKaflux ; (e) pHOD = pKaflux + 1.7 if Po ≥ Pu or pHOD = pKa − 1.7 if Po < Pu ; (f) perform a single-pH PAMPA at pHOD to obtain the measured Pe . Finally, calculate the intrinsic permeability from the measured effective permeability according to the situations: (1) if ‘seed’ Po ≥
Pu , log Po = log Pe + pHOD − pKa , else, (2) if ‘seed’ log Po > log Pu − 1.7, then log Po = log Pe + log(1 − Pe /Pu ), else (3) Po = Pe . (The rationale for ‘1.7’ is described below.) Details of this procedure are summarized in Table 3, and specific examples with hypothetical log KOW 3.6, 1.9, 1.4, and −0.4 are illustrated in Fig. 4. For a lipophilic molecule (Cases I and II in Table 3), the optimum pH needs to be selected from the diagonal region of the Pe -pH (solid) curve, because data in that region are not affected by the UWL. According to the analysis of hyperbolic log D-pH profiles (Avdeef, 1996), the diagonal segment is separated from the horizontal segment by the curved region, which is 3.4 pH units wide by 1.7 log units in height. So, for the weak acid, the optimally-designed pH, pHOD , would be 1.7 units greater than the pKaflux , and the
Table 3 Weak acid simulation to illustrate the pOD-PAMPA method
‘Seed’ log Po log Pe at pH pKa log KOW log Po (‘seed’), cm/s unitsa log Pu (calibration), cm/s unitsb pKaflux pHOD log Po (calculated from measured Pe at pHOD )
Case I
Case II
Case III
Case IV
>log Pu + 1.7 =log Pu 3.6 −2.20 −4.75 6.6 pKaflux + 1.7 = 8.3 log Pe + pHOD − pKa = log Pe + 4.3
>log Pu < log Pu + 1.7
MW = 300 in the simulated example. a log P (‘seed’) = −6.84 + 1.28 log K o OW . b log P (calibration) = −3.72 − 0.417 log MW. u
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Table 4 pOD-PAMPA method validation Compound
log KOW calculateda
pKa calculateda
Po (‘seed’)
Pu (calib.) 10−6 cm/s units
pHOD
Pe measured at pH 10−6 cm/s
pH nearest to pHOD
Po pODPAMPA
Po normal multi-pH
Imipramine Verapamil Propranolol Ibuprofen Phenazopyridine Piroxicam Naproxen Ketoprofen Metoprolol Quinine Salicylic acid Benzoic acid
4.12 4.68 2.95 3.44 1.86 2.39 2.75 2.46 1.80 2.29 1.93 1.80
9.4 9.1 9.6 4.3 4.9 5.8 4.3 4.3 9.6 8.6 3.0 4.1
2.7e−2 1.4e−1 8.6e−4 3.7e−3 3.5e−5 1.7e−4 4.8e−4 2.0e−4 2.9e−5 1.2e−4 4.3e−5 2.9e−5
18 15 19 21 20 17 20 19 19 17 24 26
4.5 3.4 6.2 8.2 3.0 8.5 7.4 7.0 7.7 6.0 4.9 5.9
15 0.79 2.6 1.0 9.2 0.79 0.46 0.38 1.2 1.2 0.32 0.62
4.5 3.5 6.2 8.1 3.0 8.5 7.4 7.0 7.7 6.8 5.0 5.9
5.9 0.33 7.6e−3 6.8e−3 1.4e−3 4.2e−4 6.0e−4 1.7e−4 1.1e−4 8.5e−5 3.2e−5 4.1e−5
5.1 0.19 7.3e−3 4.4e−3 2.0e−3 1.5e−3 6.3e−4 2.0e−4 1.1e−4 7.7e−5 4.4e−5 3.1e−5
a
Pharma Algorithms, Toronto, Canada.
expected log Pe at this pH would be 1.7 log units lower than log Pu . The required unstirred water layer permeability may be estimated from the MW of a compound, according to the equation: log Pu = −3.72 − 0.417 log MW (Fig. 3). From the analysis of measured Po and KOW values (Table 2), we estimate log Po (‘seed’) = −6.84 + 1.28 log KOW (r2 0.59). By using a calculated KOW , the latter equation may be used to estimate the log Po (‘seed’) of new compounds. Then, a calculated pKa (e.g. Pharma Algorithms computer program), along with a ‘seed’ Po and an estimated Pu , may be used to predict the solid, dashed, and dotted curves in Fig. 4. The pHOD value is on the solid curve, right below the end of the curved zone (point 1 in Fig. 4a). For a hydrophilic weak acid (Cases III and IV in Table 3), where the ‘seed’ Po value is less than the estimated Pu value,
the pHOD value is selected to be 1.7 pH units less than the pKa value of the molecule. For these cases, the permeability data are not greatly affected by the UWL. (Note that pKaflux cannot be defined, since transport is always more than 50% membrane controlled.) For such cases, Po can be determined without accurate knowledge of pKa , since the latter values are not explicitly used in the calculation of Po (Table 3). 4.5. Interpretation of the pOD-PAMPA permeability Point 1 in Fig. 4a is expected, but because the ‘seed’ Po and the calculated pKa may be in error, measured Pe may take on values indicated by open-symbol points 2, 3, or 4. If it can be assumed that pKa values are not the source of error (e.g. reliably measured pKa values were used), then
Fig. 5. Correlation plots comparing one-point pOD-PAMPA to the multiple-pH PAMPA. Inset is a similar correlation, relating measured pKa values to calculated values (Pharma Algorithm).
J.A. Ruell et al. / European Journal of Pharmaceutical Sciences 20 (2003) 393–402
log KOW overestimated the true Po in the case of 2 and underestimated the true Po in the cases of 3 and 4. Since 4 lies on the Pu line, only the lower limit of the true value of Po may be determined, i.e. log Po ≥ log Pu + pHOD − pKa (Table 3), or Po ≥ 0.35 cm/s in this example, about 56 times higher than the seed value used to predict the Pe at point 1. 4.6. Testing the pOD-PAMPA method The computational procedure illustrated in Fig. 4 and summarized in Table 3 was applied to the experimental measurements. Most of the compounds in our study belong to Case II (propranolol, phenazopyridine, piroxicam, naproxen, ketoprofen, metoprolol, quinine, salicylic and benzoic acids) and some belong to Case I (imipramine, verapamil, and ibuprofen). There are no examples of Cases III and IV from the twelve molecules characterized here. Octanol-water partition coefficients and ionization constants for the twelve molecules were calculated using the computer program from Pharma Algorithms, and the results are summarized in Table 4. The pHOD values derived by the pOD-PAMPA method are listed in Table 4. From the set of measurements performed for each molecule, the Pe corresponding to the pH closest to the pHOD value was selected and processed as a single-pH Pe value to determine the intrinsic permeability, Po (Table 4). The correlation plot of the Po values based on all pH-data and the Po values determined from a single Pe value is shown in Fig. 5. The fit is robust, with r2 0.985 and s 0.20. The inset in Fig. 5, calculated pKa versus measured pKa , indicates comparable statistics.
5. Conclusion In high-throughput applications, PAMPA is usually performed at a single pH (7.4 or 6.5). But measured Pe at that pH may not be indicative of membrane permeability, due to the UWL effect. The pOD-PAMPA method was devised to overcome this problem. It was shown that single-pH PAMPA, done at the optimum value of pH, pHOD , can be used to generate permeability profiles corrected for the UWL. The novel procedure was effectively tested with twelve lipophilic compounds studied here.
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