Diffusion of ionizable solutes across planar lipid bilayer membranes: boundary-layer pH gradients and the effect of buffers

Mechanistic study of the cellular interplay of transport and metabolism using the synthetic modeling method

PURPOSE

The aims of this study were 1) to demonstrate a new modeling strategy that uses experimental computational models built by the synthetic method and 2) to study the consequences of spatial alignment, or lack thereof, of P-glycoprotein (Pgp) and CYP3A4 on the transport and metabolism of drug-like compounds and the influence of competitive inhibition by metabolites on the transport and metabolism of those compounds.

METHODS

The synthetic method of modeling and simulation was used to construct discrete-event, discrete-space models. Within a framework designed for experimentation, object-oriented software components were assembled into devices representing the efflux transport and metabolism mechanisms within cell monolayers in Caco-2 transwell systems.

RESULTS

Conditions for transport and metabolism synergism (and lack thereof) were identified. Simulations showed how spatial alignment altered the coordinated influences of Pgp and CYP3A4 on absorption of a series of drug-like compounds. Within those experiments, when the metabolites were also substrates of Pgp, the metabolite levels produced were insufficient to give evidence of a competitive inhibitory effect on either transport or metabolism.

CONCLUSIONS

The results provide evidence of the potential value of using this class of models to improve our understanding of how complex cellular processes influence the transport and absorption of compounds, and the consequences of interventions.

Studies of intestinal drug transport using an in silico epithelio-mimetic device

We report the development and use of a synthetic, discrete event, discrete space model that functions as an epithelio-mimetic device (EMD). It is intended to facilitate the study of intestinal transport of drug-like compounds. We represent passive paracellular and transcellular transport, carrier-mediated transport and active efflux using stand-alone components. Systematic verification of the EMD over a wide physiologically realistic range is essential before we can use it to address questions regarding the details of the interacting mechanisms that are believed to influence absorption. We report details of key verification experiments. We demonstrate that this device can generate behaviors similar to those observed in the in vitro Caco-2 transwell system. To do that we used a series of hypothetical drugs and we simulated behaviors for two clinically used drugs, alfentanil and digoxin. The results support the feasibility and practicability of the EMD as a tool to expand the experimental options for better understanding the biological processes involved in intestinal transport and absorption of compounds of interest.

The rise of PAMPA

The parallel artificial membrane permeability assay (PAMPA), as a passive-permeability screen, is a possible low-cost alternative to cellular models for the earliest ADME primary screening of research compounds. Its popularity in the industry has risen rapidly. This review examines state-of-the-art PAMPA methods. The various covered topics include: different lipid formulations, the quantitative relationships between hexadecane, dioyleyoylphosphatidycholine and Double-Sink PAMPA measurements, the use of individual-well stirring, issues of ultraviolet sensitivity, timing strategies, reproducibility of measurements, the correct pH to perform the measurement to avoid aqueous boundary layer problems, the pKa(flux) method for determining intrinsic permeability coefficients and the cosolvent method for very insoluble molecules. Examples of the determination of permeability of very difficult molecules, but molecules that are well absorbed, are given. Carefully gathered evidence in support of the use of the Double-Sink PAMPA model is presented. The review concludes with a binning strategy to predict human intestinal absorption, based on the use of the sum of permeability coefficients, measured at gradient pH 5.0, 6.2 and 7.4. Opinions regarding the future of PAMPA are offered.

Chemotaxis of Amoeba proteus in the developing pH gradient within a pocket-like chamber studied with the computer assisted method

A new "U" shaped, pocket-like chamber was used to observe the chemotactic responses of individual cells. This method permits monitoring of both the development of the concentration gradient of a tested substance and cell locomotion. We investigated the chemotactic responses of Amoeba proteus and observed that the amoebae moved in positively and negatively developing [H+] gradients towards the solution of lower pH in a pH range 5.75-7.75. The chemotactic response of amoebae to [H+] gradients required the presence of extracellular calcium ions. It was blocked and random locomotion was restored by the replacement of calcium with magnesium in the cell medium. Time-lapse video recording and data processing were accomplished with computer-assisted methods. This made it possible to compare selected methods of data presentation and analysis for cells locomoting in isotropic and anisotropic conditions. The cell trajectories were determined and displayed in circular diagrams, lengths of cell tracks and final cell displacements were estimated and a few parameters characterizing cell locomotion were computed.

Permeation of dicarboxylic acids with different terminal position of two carboxylic groups through planar bilayer lipid membranes

Electrically silent hydrogen ion fluxes across a planar bilayer lipid membrane (BLM) induced by an addition of dicarboxylic (DC) acids at one side of BLM are monitored by measuring pH changes in the unstirred layers near the BLM surface via recording protonophore-dependent potentials. Two groups of DC acids are studied: (1) 2-n-alkylmalonic acids with an alkyl chain of different length which carry both carboxylic groups at one terminus of the hydrocarbon chain (alpha,alpha-DC acids); and (2) dicarboxylic acids of different linear chain length having carboxylic groups at the opposite ends of the hydrocarbon chain (alpha,omega-DC acids). It is shown that the pH optimum of hydrogen ion fluxes for the DC acids is shifted considerably to acidic pH values compared to monocarboxylic acids and is located near pH 5. For both types of DC acids at pH&z. Lt;5, the total transport is limited by diffusion of the anionic forms of the acids across the unstirred layers, while at pH&z.Gt;5 the transport is limited by diffusion of the neutral form across the membrane. The fluxes of alpha,alpha-DC acids are similar to those of alpha,omega-DC acids provided that the acids have the similar number of carbon atoms, the fluxes grow with the increase in the chain length of the alkyl radical.

The size of the unstirred layer as a function of the solute diffusion coefficient

By monitoring the concentration distribution of several solutes that are diffusing at the same time under given mixing conditions, it was established that the unstirred layer (USL) has no clearly defined boundary. For the cases of solute permeation and water movement across planar bilayer lipid membranes, respectively, experiments carried out with double-barreled microelectrodes have shown that the thickness of the USL depends on which species is diffusing. Small molecules with a larger diffusion coefficient encounter an apparently thicker USL than larger molecules with a smaller diffusion coefficient. The ratio of the USL thicknesses of two different substances is equal to the third root of the ratio of the respective diffusion coefficients. This experimental finding is in good agreement with theoretical predictions from the theory of physicochemical hydrodynamics.

Permeation of ammonia across bilayer lipid membranes studied by ammonium ion selective microelectrodes

Ammonium ion and proton concentration profiles near the surface of a planar bilayer lipid membrane (BLM) generated by an ammonium ion gradient across the BLM are studied by means of microelectrodes. If the concentration of the weak base is small compared with the buffer capacity of the medium, the experimental results are well described by the standard physiological model in which the transmembrane transport is assumed to be limited by diffusion across unstirred layers (USLs) adjacent to the membrane at basic pH values (pH > pKa) and by the permeation across the membrane itself at acidic pH values. In a poorly buffered medium, however, these predictions are not fulfilled. A pH gradient that develops within the USL must be taken into account under these conditions. From the concentration distribution of ammonium ions recorded at both sides of the BLM, the membrane permeability for ammonia is determined for BLMs of different lipid composition (48 x 10(-3) cm/s in the case of diphytanoyl phosphatidylcholine). A theoretical model of weak electrolyte transport that is based on the knowledge of reaction and diffusion rates is found to describe well the experimental profiles under any conditions. The microelectrode technique can be applied for the study of the membrane permeability of other weak acids or bases, even if no microsensor for the substance under study is available, because with the help of the theoretical model the membrane permeability values can be estimated from pH profiles alone. The accuracy of such measurements is limited, however, because small changes in the equilibrium constants, diffusion coefficients, or concentrations used for computations create a systematic error.

Effect of some environmental factors on the content and composition of microbial membrane lipids

Lipids are known as a part of an effective adaptation mechanism reflecting the changes in the extracellular environment. The fluidity of biological membranes is influenced by the lipid structure and the portion of saturated, unsaturated, branched, or cyclic fatty acids in individual phospholipids. For all living organisms undergoing environmental adaptation, the fluidity can be changed only to a relatively small extent. This range is genetically determined and it is specific for every microorganism. This article presents recent knowledge about the influence of some environmental parameters (temperature, osmotic pressure, pH, the presence of salt or ethanol in medium) on a microbial membrane with the emphasis on regulation aspect in fatty acid biosynthesis. The main tools for regulation of membrane fluidity, for example, fatty acid desaturation or incorporation of branched and cyclic fatty acids into phospholipids, are discussed in more detail.

Effect of the alkyl chain length of monocarboxylic acid on the permeation through bilayer lipid membranes

Electrically silent hydrogen ion fluxes across a planar bilayer lipid membrane (BLM) induced by an addition of monocarboxylic acid at one side of BLM were studied by measuring pH changes in the unstirred layers near the BLM surface. The pH changes were assayed by recording protonophore-dependent potentials as well as by direct measurements of pH shifts in he unstirred layers close to the membrane by the pH microelectrode. It was shown that the mechanism of the acid transport changed qualitatively upon the increase of the hydrophobic chain length of the acid. In the case of short-chain acids at pH < pKa, the total transport was limited by diffusion of the anionic form of the acid across the unstirred layers, while at the alkaline pH (pH>>pKa) the transport was limited by diffusion of the neutral form across the membrane. In the alkaline pH range the pH shifts induced by short-chain acids were sensitive to the presence of cholesterol in the BLM as well as to the stirring conditions in the cell. However, in the case of long chain acids (more than 8 carbonic atoms) the transport was limited by diffusion of the anionic form of the acid in the whole range of pH studied. In the latter case, pH changes in the unstirred layers did not depend on the presence of cholesterol in the membrane, and moreover pH shifts were not dependent on the thickness of the unstirred layer. It was proposed that the peculiarities of the long-chain acid-induced proton transport were associated with the formation of micelles of the acid in bathing solutions.

Development of a combined NMR paramagnetic ion-induced line-broadening/dynamic light scattering method for permeability measurements across lipid bilayer membranes

A combined method using NMR line-broadening for permeant lifetime determination and dynamic light scattering for vesicle size determination has been developed for the measurement of permeability coefficients of ionizable permeants across phospholipid:cholesterol large unilamellar vesicles. The method has been validated by examining its reproducibility and the influence of various factors that might affect the permeability measurements. The vesicle hydrodynamic diameter was varied between 0.1 and 0.2 micron by extruding multilamellar vesicles through polycarbonate membranes with different pore sizes (0.03-0.2 microns). For these large unilamellar vesicles, the normalized size distributions analyzed by the CONTIN method had standard deviations < 0.36, which led to errors in permeability coefficients < 10% as predicted from a theoretical model developed here. The permeability coefficient for acetic acid is independent of its concentration, vesicle hydrodynamic diameter, the concentration of Pr3+, and ionic strength over the ranges 0.01-0.2 M, 0.1-0.2 microns, 0.004-0.04 M, and 0.03-0.3, respectively. Membrane/water and decane/water partition coefficient measurements of acetic acid indicate that the effects of permeant binding onto the bilayer membrane and self-association are negligible within the permeant concentration range 0.01-0.2 M. The addition of Pr3+ ions induces vesicle fusion with rates increasing with temperature and decreasing with cholesterol concentration in the membranes. While the intravesicular resonance intensity for acetic acid decreases continuously with time due to vesicle fusion under certain conditions, the corresponding line width and chemical shift remain constant over the same period, highlighting an important advantage of this NMR method over those based on detecting net flux in response to a concentration gradient as there is no means in the latter experiments of discerning vesicle leakiness from passive diffusion rates. The effective chemical nature of a dimristoylphosphatidylcholine:cholesterol bilayer barrier microenvironment was explored by comparing the transport of two permeants, D-(-)-mandelic acid and phenylacetic acid, to their relative bulk solvent/water partition coefficients using three reference solvents (n-decane, 1,9-decadiene, and isoamyl alcohol). Using the NMR line-broadening method, the permeability coefficients for these two permeants were determined to be (2.9 +/- 0.4) x 10(-4) cm/s and (3.9 +/- 0.7) x 10(-2) cm/s, respectively, at 294 K and Xchol = 0.3. The incremental free energy of transport for the additional OH group in D-(-)-mandelic acid, delta delta G0 = +2.9 kcal/mol, resembles most closely that for the transfer of this group from water to 1,9-decadiene, suggesting that the barrier domain resides in the acyl chain region and is slightly more polar/polarizable than a saturated hydrocarbon, possibly due to the presence of a double bond in cholesterol and/or the proximity of the barrier domain to the hydrophilic interface.

Steady-state nonmonotonic concentration profiles in the unstirred layers of bilayer lipid membranes

Catalytic reactions in the unstirred layers near bilayer lipid membranes can induce nonmonotonic concentration profiles near the membrane surface. In the case of transmembrane diffusion of a substrate immediately followed by its conversion due to the presence of an aqueous soluble enzyme the size of the unstirred layer defined in terms of the concentration gradient at the membrane surface does not correspond to the width of the aqueous layer adjacent to the membrane where the concentration differs from the bulk phase concentration. Deducing of flux values or convection parameters from the concentration gradient at zero distance from the membrane gives misleading results. An empirical equation for the estimation of the size of the concentration boundary layer is proposed. It was derived from pH profiles registered with the help of a microelectrode near a planar bilayer lipid membrane surrounded by a buffer solution containing at one side of the membrane acetaldehyde and sodium acetate and at the other side alcohol dehydrogenase. Since this parameter equals to the thickness of the unstirred layer in the case of exponential concentration profiles it may be applied to estimate both mass transfer restrictions and kinetic of diffusion limited reactions occurring in the immediate membrane vicinity regardless the complexity of the system under investigation.

Substituent contributions to the transport of substituted p-toluic acids across lipid bilayer membranes

The fluxes of p-toluic acid and seven alpha-methylene-substituted analogs have been determined as a function of pH across planar egg lecithin/decane bilayers to construct a set of well-isolated polar functional group contributions to the free energy of transfer from water to the bilayer transport barrier domain. Nonlinear regression analyses of flux-pH profiles using a model which accounts for unstirred layer effects yielded membrane permeability coefficients (PRX) that varied from 1.1 cm/s for p-toluic acid to 4.1 x 10(-5) cm/s for the alpha-carbamoyl-p-toluic acid. Bulk organic solvent/water partition coefficients (KRX) were obtained for the same set of permeants using four solvent systems to identify a bulk solvent which closely resembles the chemical nature of the bilayer barrier microenvironment for these permeants. The slopes of plots of log PRX vs log KRX were 0.85, 0.91, 0.99, and 2.4, respectively, for hexadecane/water, hexadecene/water, 1,9-decadiene/water, and octanol/water with the best model solvent being that which yielded a slope closest to unity. A significant deviation in the slope from 1, as observed in the correlation with octanol/water partition coefficients, reveals that this relatively polar, hydrogen-bonding solvent is a poor model solvent for describing the barrier microenvironment for these permeants. Thus, the polar interfacial regions occupied by phospholipid head groups are not the barrier domain for the transport of the series examined in this study. The incremental group contributions to the free energy of transfer to the barrier domain (cal/mol) for the functional groups, CI, OCH3, CN, OH, COOH, and CONH2, were found to be 325, 687, 2170, 3860, 5170, and 6060, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

The relationship between permeant size and permeability in lipid bilayer membranes

Permeability coefficients (Pm) across planar egg lecithin/decane bilayers and bulk hydrocarbon/water partition coefficients (Kw-->hc) have been measured for 24 solutes with molecular volumes, V, varying by a factor of 22 and Pm values varying by a factor of 10(7) to explore the chemical nature of the bilayer barrier and the effects of permeant size on permeability. A proper bulk solvent which correctly mimics the microenvironment of the barrier domain was sought. Changes in Pm/Kw-->hc were then ascribed to size-dependent partitioning and/or size-dependent diffusivity. The diffusion coefficient-size dependency was described by Dbarrier = Do/Vn. When n-decane was used as a reference solvent, the correlation between log Pm/Kw-->hc and log V was poor (r = 0.56) with most of the lipophilic (hydrophilic) permeants lying below (above) the regression line. Correlations improved significantly (r = 0.87 and 0.90, respectively) with more polarizable solvents, 1-hexadecene and 1,9-decadiene. Values of the size selectivity parameter n were sensitive to the reference solvent (n = 0.8 +/- 0.3, 1.2 +/- 0.1 and 1.4 +/- 0.2, respectively, for decane, hexadecene, and decadiene). Decadiene was selected as the most suitable reference solvent. The value for n in bilayer transport is higher than that for bulk diffusion in decane (n = 0.74 +/- 0.10), confirming the steep dependence of bilayer permeability on molecular size. Statistical mechanical theory recently developed by the authors suggests that a component of this steep size dependence may reside in size-dependent solute partitioning into the ordered chain region of bilayers. This theory, combined with the above diffusion model, yielded the relationship, Pm/Kw-->hc = D(o)exp(-alpha V)Vn. A fit of the experimental data to this model gave the best fit (r = 0.93) with alpha = 0.0053 +/- 0.0021 and n = 0.8 +/- 0.3, suggesting that both diffusion and partitioning mechanisms may play a role in determining the size dependence of lipid bilayer permeabilities.