Imaging Molecular Transport across Lipid Bilayers

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Biophysical Journal

Volume 101

August 2011

700–708

Imaging Molecular Transport across Lipid Bilayers Su Li, Peichi C. Hu, and Noah Malmstadt* Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California

ABSTRACT Low-molecular-weight carboxylic acids have many properties common to small molecule drugs. The transport of these acids across cell membranes has been widely studied, but these studies have produced wildly varying permeability values. Recent reports have even claimed that the transport behavior of these drugs is contrary to the rule of thumb called Overton’s rule, which holds that more lipophilic molecules transport across lipid membranes more quickly. We used confocal microscopy to image the transport of carboxylic acids with different lipophilicities into a giant unilamellar lipid vesicle (GUV). Fluorescein-dextran, which acts as a pH-sensitive dye, was encapsulated in the GUV to trace the transport of acid. The GUV was immobilized on the surface of a microfluidic channel by biotin-avidin binding. This microchannel allows the rapid and uniform exchange of the solution surrounding the GUV. Using a spinning-disk confocal microscope, the entire concentration field is captured in a short (<100 ms) exposure. Results show that more lipophilic acids cross the bilayer more quickly. A finite difference model was developed to simulate the experimental process and derive permeabilities. The permeabilities change with the same trend as literature oil-water partition coefficients, demonstrating that Overton’s rule applies to this class of molecules.

INTRODUCTION Overton’s rule broadly states that more lipophilic drug molecules cross cell membranes more readily, increasing their oral bioavailabilty and pharmaceutical activity (1). This empirical rule of thumb has traditionally been interpreted in the context of the membrane partition/diffusion transport theory, in which the transport process across the membrane is dominated by partitioning of the drug molecule between the membrane and the aqueous phase external to the membrane. Oil/water partition coefficients can predict membrane permeability in many cases (2–4), and these partition coefficients have subsequently been widely used to estimate membrane permeability (5–7). Oil/water partition has become an important criterion for determining which molecules might make good drugs. However, recent studies have suggested that some carboxylic acids fail to obey Overton’s rule. Grime and co-workers (8) found that permeability decreased with acyl tail length in a manner contrary to that expected from the trend of partition coefficients. Xiang and co-workers (9) found that the permeability initially decreased as acyl tails got longer (from formic acid to propionic acid) and then increased with tail length from propionic acid to valeric acid. They suggested that besides partition coefficient, molecular shape and size must be taken into consideration and that Overton’s rule needs to be reevaluated. In fact, the multifactorial nature of the relationship between molecular structure and drug activity has long been recognized by the medicinal chemistry community. Structure-based drug design takes into account several molecular factors, such as molecular weight, oil/water partition coefficient, hydrogen bonding, dipolarity, and polarizSubmitted November 15, 2010, and accepted for publication June 24, 2011. *Correspondence: [email protected] Editor: Heiko H. Heerklotz. Ó 2011 by the Biophysical Society 0006-3495/11/08/0700/9 $2.00

ability. In 1997, Lipinski proposed the rule of five—based on studies of over 2500 drugs in the World Drug Index— which states that a molecule that has a molecular weight <500, log (partition coefficient) <5, and no more than 5 hydrogen bond donors is more likely to be a good drug (10). Quantitative structure-activity relationship studies have related drug activity to molecular weight, molecular refractivity, substructure such as rings and rotatable bonds, lone-pair electrons, and hydrogen bonding (11–14). Some work has gone toward understanding specifically how structural considerations might modulate membrane interactions (15), but in general overall drug activity is the focus of these studies. Clarifying how molecular structure specifically relates to permeability could be of great value in the rational design of novel drugs and in the design of drugs targeted to cells with specific membrane structure and composition. Establishing this relationship, however, requires accurate measurements of permeability. The measurement of the permeability of lipid bilayers to small molecules has been a surprisingly challenging problem, and published results for even simple systems have been inconsistent. The study of low-molecular-weight carboxylic acid permeability is an example of these inconsistencies. Studies of carboxylic acid permeability have produced wildly varying results, spanning orders of magnitude, some agreeing with (4,16,17) and some contradicting (8,9) Overton’s rule. Table 1 summarizes these differences. Steady-state measurements of membrane permeability have been made with planar lipid bilayers. These measurements involve forming a bilayer between two aqueous chambers and allowing a small-molecule species to diffuse to steady state between these chambers (8,18–21). The gradient established across the membrane consists of both the immediate concentration difference across the membrane and a diffusive unstirred layer adjacent to the doi: 10.1016/j.bpj.2011.06.044

Imaging Molecular Transport across Lipid

membrane on either side (22–27). If this unstirred layer is well characterized and properly modeled, steady-state measurements in a planar bilayer format can produce accurate membrane permeabilities (18–21). In addition to these steady-state measurements, kinetic measurements of molecular permeation across lipid membranes have been made with liposome-based systems (28,29). In an attempt to clarify the discrepancies in reported values of membrane permeability, we have developed a complementary measurement technique. This technique is based on directly imaging the evolution of the concentration gradient of a molecule permeating a cell-sized membrane structure. We first demonstrated the basic principle by using confocal microscopy to observe the transport of fluorescently labeled molecules into giant unilamellar lipid vesicles (GUVs) (30). Here, we adapt this technique to transport measurements of unlabeled, relatively fasttransporting species. Fluorescein-dextran (40 kDa), which is a pH sensitive dye, is encapsulated in the GUV to visualize the transport of weak carboxylic acids. The GUV is immobilized on the surface of a microfluidic channel to allow the rapid exchange of the surrounding solution. The pH gradient on either side of the membrane is optically tracked as acid molecules in the exterior space permeate the membrane and enter the GUV interior. The high speed of spinning-disc confocal microscopy (SDCM) allows us to characterize the rapidly changing acid concentration profile and to obtain a temporal record of acid permeation. The use of a single vesicle over all experiments eliminates any artifacts arising from vesicle polydispersity or variations in preparation. Imaging of the entire concentration field allows for mixing and diffusion kinetics to be handled explicitly during data analysis. Here, we apply this technique to analyze the permeation of carboxylic acids containing between one (formic acid) and six (hexanoic acid) carbon atoms. Our results show that acid permeability clearly and monotonically increases with chain length and, therefore, lipophilicity. MATERIALS AND METHODS Reagents Dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), cholesterol, and biotinylated dipalmitoylphosphatidylethanolamine (biotin-DPPE) were obtained from Avanti Polar Lipids (Alabaster, AL). Texas Red-modified DPPE (TR-DPPE) and avidin were obtained from Invitrogen (Carlsbad, CA). Indium-tin oxide (ITO)-coated glass was obtained from Delta Technologies (Stillwater, MN). Poly(dimethylsiloxane) (PDMS) was obtained from Dow Chemical (Midland, MI). NoChromix was obtained from Godax Laboratories (Cabin John, MD). All other chemicals were used as provided by Sigma-Aldrich (St. Louis, MO).

701 TABLE 1 Permeabilities (P) from various carboxylic acid permeation studies (units 102 cm/s) Acid Formic Acetic Propionic Butyric Pentanoic Hexanoic Temperature,
C

Ref (8) Ref (4) Ref (9) Ref (16) 0.22 0.089 0.076 0.0633 20 5 2

0.0234 0.0238 0.061 0.115 0.18

0.0203 0.0028 0.0025 0.0061 0.111

25

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0.036 (0.033–0.040) 0.66 0.060 (0.057–0.063) 0.19 (0.16–0.21) 9.5 0.72 (0.69–0.75) 8.0 (6.6–9.8) 110 23.0 (17.7–33.3) 22 5 2 22 5 2

Values for this study are expressed in terms of a maximally likely value and a statistical range as described in the text.

then dipped into sulfuric acid with NoChromix for 2 h. After rinsing away the acid, the coverslips were sonicated in ultrapure water again for 30 min, and stored in methanol for later use.

GUV preparation and observation GUVs were made according to the electroformation technique of Angelova et al. (31). For the GUV used in most permeability measurements, the lipid composition was based on a 1:1:1 (molar ratio) mixture of DPPC, DOPC, and cholesterol. To visualize GUVs, TR-DPPE was added to this mixture at 0.1 wt% (relative to total lipid mass). To immobilize GUVs on the glass surface, 10 wt% biotin-DPPE was added to the lipid mixture. For cholesterol-free permeability measurements, the GUV was made from a 1:1 mixture of DPPC and DOPC, with 10 wt% biotin-DPPE added. Lipids were dissolved in chloroform and spread as a thin film on the surface of a piece of ITO-coated glass. After the solvent had evaporated and the remaining film was thoroughly dried, it was rehydrated with a buffer containing 1 mg/mL fluorescein-dextran (40 kDa), 2 mM HEPES at pH 7.0, and 200 mM sucrose. During electroformation, this buffer was heated to 37
C in a cell formed from two pieces of ITO-coated glass separated by a 1/8 inch rubber gasket. An oscillating 100 mV signal was applied at 1 Hz using an 8116A pulse/function generator (HP, Palo Alto, CA). After 4 h, the GUV suspension was removed from the cell and injected into a microfluidic channel constructed from patterned PDMS bonded to a No. 1 coverslip. There, GUVs were observed by SDCM. The channels were made from PDMS patterned via standard polymer micromolding techniques (32). The patterned PDMS and the coverslip were oxidized by corona treatment (BD-20AC, Elecro-Technic Products, Chicago, IL) to bond them irreversibly (33). The PDMS channel was a T-junction (34) configuration with two inlets and one outlet. The channel used to observe the GUV had a width of 1 mm, depth of 100 mm, and length of 1 cm. The biotin-avidin interaction was used to immobilize GUVs on the glass surface as previously described (30). Briefly, after fusing biotin-DPPEcontaining liposomes onto the glass surface, the channel was flushed with avidin solution, and then biotin-DPPE-containing GUVs were introduced. SDCM was performed using a Yokogawa (Tokyo, Japan) CSUX confocal head on a Nikon (Tokyo, Japan) TI-E inverted microscope. Illumination was provided by 50 mW solid-state lasers at 491 or 561 nm. Fluorescein-dextran (40 kDa) was excited at 491 nm, and emission was captured at 525 nm. TR-DPPE was excited at 561 nm, and emission was captured at 595 nm. Images were captured at 100 ms intervals. Constant illumination intensity, camera amplification, and 100 ms exposure time were used for all images.

Acid transport experiments Cleaning of glass coverslips The No. 1 glass coverslips (microscope coverslips with a thickness of ~140 mm) were first sonicated in ultrapure water at 80
C for 30 min, and

Primary acid transport experiments were performed on a single GUV composed of DPPC, DOPC, cholesterol, TR-DPPE, and biotin-DPPE and bound to the bottom of a microfluidic channel. The two inlet channels were used to inject 200 mM glucose buffered either with 2 mM HEPES Biophysical Journal 101(3) 700–708

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at pH 7.04 or an acid-containing 2 mM HEPES buffer at pH 6.45. Solutions were injected into either inlet using a syringe pump. The linear flow velocity in the observation channel was 15 mm/s. The solutions injected into the channel also contained 0.05 mg/mL fluorescein-dextran to facilitate visualization of the acid concentration external to the GUV. In a permeation experiment, an acid solution was pumped into the channel from one of the two inlets as images were recorded. The pH 7.04 glucose solution containing 0.05 mg/mL fluorescein-dextran was then pumped into the channel from the second inlet to flush away the acid solution and remove the acid that had been transported into the GUV. A syringe containing a different acid solution was then connected to the first inlet and this new acid was injected into the channel. This process was repeated for all acids analyzed.

Image analysis Images were analyzed using ImageJ (freely available from the National Institutes of Health; http://rsbweb.nih.gov/ij/) and MATLAB (The MathWorks, Natick, MA). To correct for illumination heterogeneity, the images were flat-fielded pixel-by-pixel in reference to an image of an empty (no GUVs) field at the same fluorophore concentration (30). For each vesicle permeation experiment, the acid solution pH and camera settings were the same. In each image, the fluorescence intensities of six 2–3 mm diameter circles were measured in the interior of the GUV. The mean of these measurements was used as the internal intensity. The standard deviations of the internal fluorescence measurements were propagated as errors throughout the data analysis. For analyses in which the full diffusion profile of an acid was investigated, profiles were based on fluorescence intensities measured along lines drawn through the GUV center. The complete methodology for converting these intensity measurements to concentration profiles is included in the Supporting Material.

Correlating fluorescence intensity to acid concentration Fluorescein is a pH-sensitive dye, and can therefore be used to determine solution pH based on fluorescence intensity. We carefully established relationships between fluorescence intensity, solution pH, and acid concentration. Carboxylic acids were titrated into 200 mM glucose, 2 mM HEPES, pH 7.04 buffer solution to measure how the solution pH changed with acid concentration. Solution pH was measured using a Beckman F340 pH/Temp meter (Brea, CA). To test how the fluorescence intensity changes with pH, acids were titrated into a 1 mL cuvette containing 200 mM glucose buffered with 0.1 mg/mL fluorescein-dextran (40 kDa) and 2 mM HEPES at pH 7.04. Fluorescence was measured using a Shimadzu RF-5301PC spectrofluorophotometer (Kyoto, Japan).

Finite difference modeling A one-dimensional finite difference model was implemented based on Fick’s second law:

vci v2 c i ¼ : vt vx2

(1)

To simplify the calculation process, dimensionless variables were used in the calculation, where ci is the concentration of species i (acid anion A or protonated acid HA), D is the diffusion coefficient of the acid in water, t is dimensionless time, equal to TD/r2, with T as dimensional time, r is the GUV radius, and x is the dimensionless distance from the bulk exterior boundary, equal to X/r, with X as the dimensional distance. At initial conditions (t ¼ 0), concentration was assumed to be zero everywhere. The boundary condition at the vesicle exterior was a time-varying concentration Biophysical Journal 101(3) 700–708

as measured experimentally. A no-flux boundary condition was used at the GUV center. At the membrane, flux was based on the concentration gradient across the membrane as

dc ¼ Pðco;mem  ci;mem Þ; dt

(2)

where P is the dimensionless membrane permeability, equal to 3 Pr/D, where P is the true membrane permeability, and co,mem and ci,mem are external and internal concentration adjacent to the membrane. As carboxylic acids are weak acids, both charged and uncharged species coexist in solution. Only the uncharged species can permeate the lipid membrane. The concentration ratio of charged and uncharged species at each point in the model was based on pH and literature values of pKa (8). In the finite difference model, spatial and time derivatives were discretized with time and space steps dT and dX. In the model dT was set as 5  106 s; dX was set as 105 cm. The model and fitting routine were run in MATLAB.

Determining permeability Finite difference models were run at a series of permeabilities using the measured external concentration, pKa, and diffusivity for each acid. The model results in the vesicle interior were compared with experimental data at the permeabilities to obtain a c2 value (Eq. 3).

c2 ¼

X ðci  mi Þ2 s2i

;

(3)

where ci are the experimental concentrations, mi are the model concentrations, and si are the standard deviations of the experimental data, summed over all data points. As described below, slow-permeating acids could be fit on the basis of a single uniform interior acid concentration, whereas fastpermeating acids required an explicit fit of the entire concentration profile interior to the membrane. The c2 statistic describes the differences between the model results and experimental data, weighted by the error of the experimental data. Smaller c2 values represent a better fitting result. The best-fit permeability P is at the minimum c2 value. Reported ranges of P are based on those permeabilities that produced a c2 corresponding to a p-value of 0.1 or greater (see Supporting Material).

RESULTS AND DISCUSSION Acid transport into a single GUV In each experiment, images were captured at a constant rate as acid solution was injected into the microfluidic channel. A typical time series of images demonstrating acid permeation into a GUV is shown in Fig. 1 a. This time series shows that internal fluorescence intensity gradually decreased as acid permeated into the GUV. Once fluorescence intensity inside the GUV equilibrated to a constant level, neutral buffer solution was pumped into the channel to flush away the acid solution. Images captured as acid subsequently diffused out of the GUV are shown in Fig. 1 b. During the process of acid efflux, the internal fluorescence intensity of the GUV gradually increased, eventually recovering its initial level. This demonstrates that the fluorescence decrease upon exposure of the GUV to acid solution was caused by acid permeation rather than photobleaching or fluorophore leakage.

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of buffer exchange. To account for the effect of buffer exchange rates on the transmembrane transport process, acid concentration outside of the vesicle was measured as a function of time. Both the neutral buffer solution and the acid solution contained fluorescein-dextran at ~1/10 the concentration of that inside the GUV. The fluorescence intensity exterior to the vesicle was converted to solution pH and acid concentration. The solid and dot-dashed lines in Fig. 2 show how the solution pH changes inside and outside the GUV with time as it is exposed to various acid solutions. It is immediately obvious from these data that as the acyl chain length of the acid increases, the rate of transport also increases. Formic acid has the lowest permeability; hexanoic acid has the highest permeability. In other words, carboxylic acid permeability increases monotonically with lipophilicity. To establish the pH values shown on the y axis of Fig. 2, an empirical relationship between fluorescent intensity and pH was established for each acid. The pH/intensity data, as well as the empirical fit that was used to determine pH in the transport experiments, are shown in Fig. 3 a. The empirical relationship between relative intensity (I) and pH shown here is

FIGURE 1 Time series of SDCM images showing the fluorescence intensity (ex 491 nm, em 525 nm) change when acetic acid is transported (a) into and (b) out of a GUV. Scale bar is 20 mm.

To guarantee accurate measurements, the pH gradient and flow rate were optimized. The pH gradient must be sufficiently large to visualize, but an excessively large pH gradient results in transport too fast to capture with SDCM. Similarly, the microfluidic flow must be sufficiently fast to allow for rapid buffer exchange, but excessive flow rates result in vesicle motion that make the observations impossible. After several trials, a pH gradient from 6.45 (exterior) to 7.04 (interior) was selected. This relatively small pH gradient also eliminates diffusion potential barriers to transport, leaving the membrane itself as the sole barrier (35). A linear flow rate of 15 mm/s was found to be optimal (see the Supporting Material). Even at these fast buffer exchange rates, some acids were found to diffuse into the GUV at a timescale similar to that a

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FIGURE 2 Solution pH change inside and outside the GUV with time for six carboxylic acids. The solid line and the dot-dashed line represent the pH change inside and outside GUV. The dashed lines are finite difference modeling fitting results. (a) Formic acid, (b) acetic acid, (c) propionic acid, (d) butyric acid, (e) pentanoic acid, and (f) hexanoic acid. Biophysical Journal 101(3) 700–708

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relationships are shown in Fig. 3 b for each acid. Note that in the experimental pH range (6.4–7.0) the acids all behave similarly in this buffer. In the finite difference model described below, acid concentration was based on the empirical fit of a fifth-order polynomial to these data (shown as the solid line in Fig. 3 b). Determining permeability To determine precise permeability values, it is necessary to fit these data to a transport model. The slow-permeating acids (formic and acetic) are transported into the GUV at a much slower timescale than that at which the acid solution is injected into the channel. The more quickly permeating acids, however, such as pentanoic acid and hexanoic acid, are transported into the GUV at a timescale similar to that at which injection into the microchannel occurs. This means that to quantify permeability of these acids, we must account for the change in external concentration. To accomplish this, we used a simple one-dimensional finite difference model in which one boundary condition was set by the experimentally measured external concentration. This model was based on Fick’s second law of diffusion and membrane flux theory. The GUV was modeled as Biophysical Journal 101(3) 700–708

a spherically symmetric structure, allowing for a model in one spatial dimension. Model parameters—GUV diameter, acid diffusivities, acid pKa-values, and distance of measured external concentration from the bilayer—were taken from experimental conditions or literature values. The external boundary condition was set using fluorescence data measured at 1.5 radii from the GUV center. Fig. 4 shows how this model is able to account for the transport behavior of the system, including the finite speed of buffer exchange. This figure shows the modeled change of concentration interior and exterior to the GUV with time for two different acid species. The permeabilities used here for each acid are based on the results shown in Fig. 2. The permeation of acetic acid (total duration 63.0 s) is much slower than that of hexanoic acid (total duration 2.5 s). For acetic acid the membrane permeation represents the main transport resistance; nearly all the concentration gradient occurs at the membrane. On the other hand, diffusive resistance outside of the membrane represents a significant barrier for hexanoic acid. A significant concentration gradient extends into the bulk solution. To fit the model and obtain permeability values for slowpermeating acids, with concentration profiles such as that in Fig. 4 a, a single uniform interior concentration was used at each experimental time point. For acids that permeated the membrane more quickly, producing profiles like that shown in Fig. 4 b (this represents butyric, pentanoic, and hexanoic acids), the entire interior concentration profile was fit at each time point. Concentration profile data, along with a best-fit model, are shown in Fig. 4 c. Details on data processing to produce concentration profiles are included in the Supporting Material. Another important factor that the model takes into consideration is the protonated/deprotonated state of the acids. Uncharged species HA and charged species A and Hþ coexist in solution. Previous studies show only uncharged molecular species can penetrate through lipid membranes (36). Protons, however, are so small that they can also penetrate lipid membranes at an appreciable rate (37). In our experiment, the acids were dissolved in 2 mM HEPES buffer solution at no more than 0.27 mM. Even if all of the acid molecules were dissociated, the buffer can accept all dissociated protons, guaranteeing that there is no proton permeation through the lipid membrane in the experiment. The model calculated the concentrations of the protonated and deprotonated species according to local solution pH and acid pKa. Both species were allowed to diffuse, but only the protonated species could permeate the lipid membrane. Finite difference models were run at a series of permeabilities using the measured external concentration, pKa, and diffusivity for each acid. The model results in the vesicle interior were compared with experimental data at the permeabilities to obtain a c2 value (Eq. 3). Results of fitting experimental data to the model are shown in Fig. 2. The solid line shows the measured pH at the GUV center.

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One parameter in the model is the diffusivity of each acid species in water. We obtained these diffusivity values from the literature rather than measuring them directly. We probed the sensitivity of our model fitting results to diffusivity and found that it was relatively insensitive except in the case of hexanoic acid. For hexanoic acid, the diffusivity used here establishes a lower limit for the permeability. If the actual diffusivity is smaller, it would imply a greater hexanoic acid permeability.

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The experiments determining acid permeability were performed in a single vesicle for all acids, eliminating much of the possible experimental variability. To test the reproducibility of this method across different vesicles, the permeability of acetic acid was measured in 10 GUVs with varying diameters. These diameters were uniformly distributed in the range from 18.1 to 31.3 mm. Each permeation process was observed twice. The standard deviation of the measured permeability over these experiments was 0.015  102 cm/s.

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FIGURE 4 Modeled concentration profiles of (a) acetic acid and (b) hexanoic acid. The GUV membrane is at 6.25 mm. The GUV center is at 19 mm. The origin of the x axis represents the position where the external fluorescence intensity was measured. Each line represents the concentration distribution across the GUV membrane at one time step. As time goes on, the concentration increases from the bottom to the top. For acetic acid, the total model duration shown is 63.0 s, with a time step of 4.5 s. For hexanoic acid, these values are 2.5 s and 0.157 s. (c) Best fit of the model to experimental concentration profiles in the GUV interior for hexanoic acid at the initial time, final time, and three time steps during the permeation process.

The dashed fitting line represents the model results at this point in the vesicle at the permeability that corresponds to the minimum c2 value. We also constructed a finite difference model in which buffer equilibrium and diffusion were handled explicitly; we found that an explicit inclusion of the buffer species introduced no significant change to the best-fit permeability across the range of measured permeabilities (see Supporting Material).

Controlling for membrane lipid composition Lipid compositions similar to the one used here are known to exhibit liquid ordered-liquid disordered phase separation, with a typical transition temperature at 29
C (38). Although the results described previously were obtained with a vesicle showing no apparent phase separation, we also repeated the experiment at temperatures spanning this miscibility transition temperature to probe whether potential unobservable phase separation has an effect on weak acid transport. Permeation of acetic acid was observed in a GUV at 27 and 32
C. The difference (~6% faster at the higher temperature) was within the measurement error, indicating that any effect introduced by phase separation is too small to resolve by this technique, and an insignificant effect in terms of comparing permeabilities across acid species (see Supporting Material for detailed results). We also considered the effect that the inclusion of cholesterol had on membrane permeability. It has been reported that lipid membranes with cholesterol have permeabilities 5–10 times smaller than cholesterol-free membranes (39–42). In this work, we focus on cholesterol-containing membranes because slower permeabilities allow for more precise permeability measurements and because cholesterol-containing membranes more closely resemble membranes of biomedical interest. To examine how our technique captures the difference between cholesterol-containing and cholesterol-free membranes, we repeated a set of our experiments in a cholesterol free-GUV composed of DPPC, DOPC, and biotin-DPPE. The permeation processes for formic, acetic, and propionic acid were studied (Fig. 5). The permeabilities Biophysical Journal 101(3) 700–708

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for these acids were measured as 0.37  102 cm/s, 0.43  102 cm/s, and 1.0  102 cm/s. The permeabilities are ~5– 10 times larger than in a cholesterol-containing membrane. As with cholesterol-containing membranes, acid permeability increases as alkyl chain length increases.

To consider the effects of the presence of a flow stream and the anisotropic convective environment around a vesicle tethered to one wall of a channel, we put together a 3D finite element simulation comparing the situations of permeation of acid into a vesicle freely suspended in static solution, a vesicle suspended in a flow stream, and a vesicle anchored to a channel wall in a flow stream (see the Supporting Material). Examining the complete range of permeabilities we observed here, we found that the expected measured permeability in these three configurations would differ by no more that 4%.

Controlling for vesicle immobilization To minimize tension imposed on the membrane by immobilization, we used a biotin-DPPE-based immobilization system that allows for significant molecular flexibility. On the basis of 3D reconstructions of vesicle confocal images, we estimate that the tension in an immobilized GUV membrane is ~7.5 times greater than that in a free-floating GUV (see Supporting Material). This compares to a burst tension that is over 10,000 times that of the tension in a free-floating GUV (43). We repeated the acetic acid transport experiment using a GUV with lower (5 wt%) membrane biotin-DPPE concentrations to demonstrate that the effect of attachment tension on membrane transport was minimal. The permeability is 0.067  102 cm/s, compared to the 0.060  102 cm/s permeability measured at 10 wt% biotin-DPPE. This difference is insignificant in terms of making comparisons between the transport rates of the various acids. TABLE 2

Comparison to Overton’s rule Permeabilities from various carboxylic acid permeation studies including this one are listed in Table 1. From acetic acid to butyric acid the permeabilities are in the same range as other results. For pentanoic acid and hexanoic acid, the permeabilities are higher than most other studies. Permeabilities increase with acyl chain length of the acid molecules: an agreement with Overton’s rule. The octanol/water and hexadecane/water partition coefficients of these six acids are listed in Table 2. This table also reports theoretical permeabilities P as calculated according to the partition-diffusion theory: P ¼ KD/l, where D is the

Comparison of Overton’s rule to experimental results, normalized to formic acid Ratio Koct/water

Formic acid Acetic acid Propionic acid Butyric acid Pentanoic acid Hexanoic acid

0.29* 0.49* 1.8* 6.2* 18.1* 76y

*From Wolosin et al. (4). y From Walter et al. (3). z From Potts et al. (44). x From Bidstrup et al. (45). { From Walter et al. (46). k From Grime et al. (8). **From Saracino et al. (47). Biophysical Journal 101(3) 700–708

4

Khex/water (10 ) y

1.1 5.3y 23y 87y 490z 1400y

5

D (10

2

cm /s) x

1.516 1.271x 1.009x 0.918x 0.817x 0.784x

pKa {

3.75 4.76k 4.87** 4.83k 4.83k 4.85k

P ¼ KoctD/l

P ¼ KhexD/l

Pexp

1 1.4 4.1 12.9 33.6 135.5

1 4.0 14.0 47.9 240.1 658.2

1 1.7 5.3 20.0 222.2 638.9

Imaging Molecular Transport across Lipid

707

diffusivity of the molecule in the membrane, K is the oil/ water partition coefficient, and l is the membrane thickness. That the measured permeabilities are consistent with the change in oil/water partition coefficients demonstrates that Overton’s rule applies for this system. Fig. 6 shows trends in permeability for the series of acids studied here in terms of both acyl chain length and partition coefficient.

Confocal microscopy was used to image the transport of carboxylic acids with different lengths of carbon chains into a single GUV. By observing the change in intensity from a pH-sensitive fluorophore encapsulated inside the GUV, it was possible to directly observe the transport process. This technique combines rapid buffer exchange in a microfluidic device with high-speed confocal microscopy to accurately observe rapid transmembrane transport processes. All experiments were performed in a single GUV, eliminating any experimental variation caused by vesicle polydispersity or lack of uniformity in the membrane formation protocol. Although even a glance at the data reveals a clear monotonic trend relating acid length to permeability, a finite difference model can be fitted to the experimental data to obtain precise permeability values. The clear adherence to −0.5

10

log (P(cm/s))

−1.5 −2 −2.5 −3 −3.5 0

1

2

3

4

5

6

7

Acyl tail length −0.5

Koct

log10(P(cm/s))

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−3 −3.5

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−1

b

SUPPORTING MATERIAL Additional text with equations, 13 figures, two tables, and references are available at http://www.biophysj.org/biophysj/supplemental/S00063495(11)00774-0.

CONCLUSIONS

a

Overton’s rule observed here contrasts other recent results. This technique promises to be useful in understanding with greater detail how the molecular properties of druglike molecules determine their transport behavior into cells.

−4

−3

−2

−1

0

1

2

log K 10

FIGURE 6 Trends in permeabilities of a homologous series of carboxylic acids. (a) P versus acyl chain length. (b) P versus octanol/water, hexadecane/water partition coefficient, K (log10 scale).

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