Electrochemical Characterization of Ferricyanide Retention by

This report describes measurement of retention of electroactive ferricyanide ... of ferricyanide permeation rate constants as a function of pH and tem...
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J. Phys. Chem. B 2002, 106, 3503-3509

3503

Electrochemical Characterization of Ferricyanide Retention by Polymerized Diacetylenic Phospholipid Vesicles Ivan Stanish,† Daniel A. Lowy,‡ Leonard M. Tender,* and Alok Singh* Center of Bio/Molecular Science and Engineering, NaVal Research Laboratory, Code 6900, Washington, DC 20375 and NoVa Research, Inc., 1900 Elkin St., Alexandria, Virginia 22308 ReceiVed: June 11, 2001; In Final Form: January 18, 2002

This report describes measurement of retention of electroactive ferricyanide (Fe(CN)63-) entrapped within structurally stable photopolymerized vesicles composed of diacetylenic lipid 1-palmitoyl-2-(tricosa-10,12diynoyl)-sn-glycero-3-phosphocholine (PC8,9PC). Vesicle size, shape, and dispersity were assessed by dynamic laser light scattering and rates of permeation of ferricyanide measured by cyclic voltammetry. Gold disk electrodes modified with 6-mercaptohexanol or 2-mercaptoethanamine (cysteamine) respond with quantitative sensitivity to extravesicular ferricyanide over a concentration range of 10 µM to 0.1 M, are insensitive to entrapped ferricyanide even at high applied oxidative potentials, and resist fouling by vesicles, vesicle fragments, or vesicle-rupturing surfactant. Quantitative changes in ferricyanide peak current over time enabled straightforward determination of ferricyanide permeation rate constants as a function of pH and temperature. At 25 °C, ferricyanide permeability increased from 1.1 × 10-12 to 2.5 × 10-12 cm/s with increasing pH from 6 to 8. At pH 7, ferricyanide permeability temperature dependency was found to fit an Arrhenius rate expression, increasing exponentially from 1.6 × 10-12 to 5.8 × 10-11 cm/s with increasing temperature from 25 to 70 °C, yielding a calculated energy barrier for permeation of 65 kJ/mol and a half-life for intravesicular ferricyanide loss as high as 2.4 weeks. Greater permeability observed at 15 °C relative to 25 °C is attributed to membrane defects present in the gel-phase. These results are consistent with diffusion of Fe(CN)63- across intact vesicle walls rather than a pore type mechanism and demonstrate the ability to tune retention of entrapped species by robust polymerized vesicles.

Introduction Vesicle entrapment of molecules has demonstrated application in drug delivery1-4 cosmetics,2,4 catalysis,5 biosensing,6 enantioselective sequestration,7,8 biomineralization,9 magnetic resonance imaging,10 toxic metal ion separation,11-13 artificial photosynthesis,14-16 modeling biomolecular structure and function,17,18 and materials processing on the submicron scale (e.g., nanoparticle synthesis19-22 and mesoporous templating23). A number of experimental methods exist to determine permeation rates of entrapped molecules across vesicle membranes that utilize fluorescent probes (e.g., carboxyfluorescein24 or hydroxyquinone sulfonic acid25), radioactive probes,26 chromophoric complexing probes,27 enzymatic probes,4 NMR line broadening probes,28,29 or ionic probes interrogated by potential30 or conductivity measurements.31,32 Owing to interest in vesicle entrapment of electroactive species for energy harvesting and energy storage applications, we were motivated to develop a method to investigate vesicle retention of entrapped electroactive probes. Reported here is direct (i.e., no preseparation steps) measurement of temperature and pH dependent permeation of electroactive ferricyanide (Fe(CN)63-) entrapped within polymerized vesicles composed of 1-palmitoyl-2-(tricosa-10,12diynoyl)-sn-glycero-3-phosphocholine lipids (PC8,9PC) (Figure 1A). Ferricyanide (a well studied electroactive probe)33 is readily detected in extravesicular solution by cyclic voltammetry at gold * To whom correspondence should be addressed. E-mail: (A. S.) [email protected], (L. T.) [email protected]. † Center of Bio/Molecular Science and Engineering. ‡ Nova Research, Inc.

electrodes modified with 6-mercaptohexanol or 2-mercaptoethanamine. While ferri-/ferrocyanide (Fe(CN)63-/4-) voltammetry is well behaved at bare gold electrodes, the modified gold electrodes are far more stable with respect to adsorption of potentially fouling adsorbates (i.e., vesicles, vesicle fragments, surfactants) while preserving quantitative sensitivity to extravesicular Fe(CN)63- over a wide concentration range. These electrodes are also insensitive to Fe(CN)63- entrapped inside vesicles allowing sensitive quantification of permeated ferricyanide in extravesicular sample volumes. This study constitutes the first report characterizing vesicle retention properties by direct electrochemical measurement of the permeation rate of a vesicle-entrapped electroactive probe. Experimental Section Reagents. The following reagents were purchased from Aldrich unless stated otherwise and were used as received: potassium ferricyanide (99.99+%), sulfuric acid (98% w/w), hydrogen peroxide (30% w/w), sodium hydroxide (99.99%), sodium dihydrogen phosphate (99%), sodium sulfate (99.9%), 1-palmitoyl-2-(tricosa-10,12-diynoyl)-sn-glycero-3-phosphocholine lipids (PC8,9PC, Avanti Lipids, Alabaster, AL), Amberlite IRA, a strongly basic anion-exchange resin (Sigma), ultrapure n-octyl-β-D-glucopyranoside (OG, Biosynth A.-G., Switzerland), 2-mercaptoethanamine (2-MEA, 98%), and 6-mercaptohexanol (6-MCH, 97%). Sulfate-phosphate buffers (SPB) were prepared with deionized water (DIW, 18 MΩ-cm, Milli-Q Millipore, Bedford, MA). Vesicle Formation and Characterization. Dried lipids (60 mg) were added to 3 mL of 100 mM potassium ferricyanide in

10.1021/jp012208s CCC: $22.00 © 2002 American Chemical Society Published on Web 03/08/2002

3504 J. Phys. Chem. B, Vol. 106, No. 13, 2002

Stanish et al. TABLE 1: Vesicle Properties measured values AVg DVes (nm)

95% confidence interval (nm)

Dia σVes (nm)

CVes (mg/mL)a

208

200-216

43

14.3

calculated

valuesb

NVes (#/mL)

AVes (cm /mL)

i (µL/mL) VVes

Disp MolFe(CN) (mol/mL) 6

1.31 × 1013

1.71×104

55.2

5.52 × 10-6

2

Denotes total dry vesicle weight per mL dispersion. b Normalized to vesicle dispersion volume. a

Figure 1. A schematic representation of polymerized PC8,9PC vesicles encapsulating ferricyanide with chemical structure of PC8,9PC lipid (A) and TEM image of a vesicle sample (B).

DIW. After incubation at 50 °C for 2 h, vesicles were extruded 10 times at 50 °C through 0.2 µm Nucleopore filters (Corning) using a Lipex extruder (Lipex Biomembranes Inc., Vancouver, BC) producing a translucent, monodisperse suspension of large unilamellar28 vesicles (LUVs ca. 200 nm diameter). Extravesicular ferricyanide was removed by anion exchange chromatography (12 cm column height) using 0.1 M NaCl as the mobile phase. Eluted vesicles were cooled to 7 °C for 15 min, then photopolymerized by irradiation at 254 nm for 15 min using a Rayonet Photochemical reactor equipped with sixteen 75 W Hg lamps (South New England Ultraviolet Co., Hamden, CT). Aliquots (1 mL) of vesicle suspension were dried and weighed. Mass of dry vesicles (typically 15 mg/mL) was calculated by subtracting the mass of encapsulated ferricyanide and external buffer from the total dispersion mass. Vesicle size was characterized by dynamic laser light scattering using a Coulter Model N4MD sub-micron particle analyzer (Hialeah, FL) whereby the instrument software computes the average vesicle diameter at a confidence interval of 95% and the vesicle size standard deviation assuming a Gaussian distribution. Based on mass balance for a monodisperse vesicle population tot tot i i tot CVesDisp VVesDisp ) NVesCFeCN VVes + CoBuffer(VVesDisp o memb memb o 3 ) + NVesVVes /V ˜ lipid where VVes ≡ 4/3π{(RVes ) NVesVVes o - tmemb)3} and V ˜ lipid ≡ VlipidNAV/MWlipid (1) (RVes

and from measuring vesicle outer diameter, vesicle wall thickness,34,35 and phosphatidylcholine lipid volume,35 vesicle number concentration, surface area, encapsulated volume, and

molecular weight (typically 3 × 108 Da) were calculated. Terms in eq 1 are defined as follows: total concentration of the vesicle tot ), total volume of the vesicle dispersion dispersion (CVesDisp tot aliquot (VVesDisp), number of vesicles in dispersion aliquot (NVes), intravesicular ferricyanide concentration (CiFeCN), intrai ), concentration of extravesicular buffer vesicular volume (VVes o o (CBuffer), vesicle volume (VVes ), vesicle membrane volume memb ˜ lipid), outer vesicle radius (VVes ), specific lipid volume (V o ), membrane thickness (tmemb), lipid volume (Vlipid), (RVes Avogadro’s number (NAV), and lipid molecular weight (MWlipid). Electron transmission microscopy (Zeiss EM-10, Germany) was used to measure vesicle size and shape of unstained vesicle samples (Figure 1B). Resultant vesicle properties are listed in Table 1. Electrode Modification. Gold disk electrodes (0.03 cm2 geometric area, Bioanalytical Systems, BAS, Lafayette, ID) were polished with alumina (BAS polishing kit), thoroughly rinsed with DIW, sonicated in DIW at 100 W for 5 min, and then heated at 81 °C in piranha solution (H2SO4:H2O2, 3:1 v/v) for 20 min. These clean electrodes were rinsed, sonicated again for 10 min, and then activated electrochemically in 0.1 M aqueous H2SO4 by consecutive voltammetric scans from 0.0 to 1.5 V vs Ag/AgCl, sat. KCl, at the sweep rate of 0.1 V s-1. Electrodes were coated with a short-chain monolayer by immersion in 50 mM 2-MEA in ethanol or 1 mM 6-MCH in deionized water for 12 h at 4 °C. Electrode modification is evidenced by expected decrease in charging current of a modified relative to a bare Au electrode, observed by cyclic voltammetry. Electrochemical Measurements. Electrochemical measurements were performed with a CV-50W voltammetric analyzer (BAS) equipped with a model C3 cell stand (BAS) and a divided glass microcell (BAS). A 2-MEA or 6-MCH modified gold electrode, a Pt-coated Nb wire (BAS), and a Ag/AgCl, sat. KCl electrode (BAS) served as the working, counter, and reference electrodes, respectively. The supporting electrolyte, sodium phosphate buffer (SPB), consisted of 100 mM Na2SO4 adjusted to the desired pH with 10 mM of mono- and disodium phosphate. Cyclic voltammograms were recorded without degassing in the potential range of -0.1 to +0.4 V vs Ag/AgCl, sat. KCl at the sweep rate of 0.1 V s-1. Constant temperature was achieved with a water-jacketed glass cell and a heating bath (Model RTE-111, Neslab Instruments, Inc., Newington, NH) Determination of percent vesicle entrapped ferricyanide permeated into extravesicular volumes of samples maintained at a specified pH and temperature was conducted in the following manner: aliquots (0.1-0.2 mL) of freshly desalted polymerized vesicles encapsulating 0.1 M ferricyanide were diluted with buffer (1:1 v/v) at specified pH and temperature (dilution does not affect pH). At designated intervals following dilution, three cyclic voltammograms were acquired at 2-MEA

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Figure 3. Cyclic voltammetry at pH 7 and 25 °C of ferricyanide at a 2-MEA modified gold electrode in solution containing freshly prepared vesicles entrapping ferricyanide (0 h), after 44 and 128 h, and after addition of vesicle rupturing surfactant (details in text).

Figure 2. Cyclic voltammetry at pH 7 and 25 °C of 30.7 mM ferricyanide in the presence of 100 mg/mL octylglucoside detergent and PC8,9PC vesicles measured using a bare (A), 2-MEA modified (B), and 6-MCH modified (C) gold electrode.

or 6-MCH modified gold electrodes. Normalization of the (steady-state) ferricyanide oxidation peak current of a given aliquot to the oxidation peak current of the same aliquot following addition of 50 µL of 500 mg/mL OG to rupture vesicles (additional volume accounted for) yielded percent entrapped ferricyanide permeated into extravesicular sample volume. For these electrode systems, it was found that the dimensionless ratio of the Fe(CN)63- concentrations is independent of the chemical modification of the electrode. These electrodes produced stable results relative to bare Au electrodes, and behaved as true ferricyanide probes (i.e., as sensors that otherwise do not significantly perturb the system). Ferricyanide oxidation peak current at the modified gold electrodes is linearly dependent on extravesicular ferricyanide concentration.39 Dynamic laser light scattering of each aliquot confirmed that vesicle structure remained intact. Results and Discussion Ferricyanide Voltammetry at Modified Electrodes. Figure 2 compares cyclic voltammetry of ferricyanide at a freshly cleaned bare gold electrode (Figure 2A), a 2-MEA modified gold electrode (Figure 2B), and a 6-MCH modified gold electrode (Figure 2C) recorded in buffer (SPB, pH 7, 25 °C) with PC8,9PC vesicles encapsulating 0.1 M Fe(CN)63- ruptured

by addition of 100 mg/mL OG. All three electrodes demonstrate quasi-reversible ferricyanide voltammetry (i.e., greater than 60 mV peak separation), low peak current, and large peak width.37 Most important with respect to the work described here, ferricyanide voltammetry in the presence of intact vesicles (see below) or ruptured vesicles with surfactant is highly reproducible at the modified electrodes while not reproducible at bare gold electrodes. We attribute the stable, quasi-reversible behavior of the modified electrodes to the monolayer films on the electrode surfaces which inhibit adsorption of intact vesicles, ruptured vesicles, or surfactant and which kinetically suppress electron transfer by decreasing (but not blocking) ferricyanide-electrode coupling.38 This assumption is supported by insensitivity of ferricyanide voltammetry of the modified electrodes to addition of vesicles or surfactant. Although quasi-reversible, the ferricyanide peak currents at the modified electrodes scale linearly with ferricyanide concentration, allowing quantification of ferricyanide concentration in solutions containing intact and surfactant ruptured vesicles.37 Electrochemistry of Entrapped and Extravesicular Ferricyanide. Figure 3 illustrates a number of phenomena pertaining to ferricyanide retention by polymerized PC8,9PC vesicles observed by ferricyanide cyclic voltammetry at 2-MEA modified electrodes. The innermost (solid) curve is an overlay of three cyclic voltammograms recorded in the following solutions: i) buffer (SPB, pH 7, 25 °C) emphasizing a well-formed monolayer with double-layer capacitance of 48.5 µF/cm2,38 ii) buffer containing polymerized PC8,9PC vesicles, and iii) buffer containing freshly prepared PC8,9PC vesicles encapsulating 0.1 M ferricyanide. Consistency among the three voltammograms indicates lack of electrochemical interference from buffer and vesicles, near complete removal of extravesicular ferricyanide, and electrochemical isolation of entrapped ferricyanide even at highly oxidative potentials relative to the ferricyanide oxidation potential. The outermost voltammogram (labeled “Total [Fe(CN)6]”) was recorded after addition of concentrated detergent (final cell concentration 100 mg/mL OG) to rupture partially polymerized vesicles. Note that here and throughout the text rupture signifies the structural transformation from vesicles to micelles with a concomitant release of total entrapped ferricyanide. Ancillary voltammetric experiments (not shown) demonstrated that addition of detergent did not affect voltammetry. The intermediate voltammograms (labeled “44 h” and “128 h”) illustrate monitoring of time elapsed permeation of ferricyanide

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Figure 4. Rate of release in the linear regime (short time) of vesicle entrapped ferricyanide normalized to the maximum concentration based on the external volume at pH 7 and 25 °C. The data were numerically fitted (dashed line) using eq 6.

from intact vesicles (confirmed by dynamic laser light scattering) using cyclic voltammetry. Normalization of the “44 h” and “128 h” oxidation peak currents by oxidative peak currents of each sample after addition of concentrated detergent indicated 7.0% and 22.4% permeation of entrapped ferricyanide after 44 and 128 h, respectively. Ferricyanide concentration following vesicle rupture (labeled “Total [Fe(CN)6]” in Figure 3) is 2.5 mM based on oxidation peak current,36 which agrees well with calculated Disp /VReserVoir ∼ 2.2 estimates from Table 1 (i.e., VVesAddedMolFe(CN) 6 mM). Measurement of Permeation Rate of Entrapped Ferricyanide. Assuming that diffusion of ferricyanide through vesicle membranes is rate limiting and reversible, Fick’s first law of diffusion39 (eq 2) can be applied to describe the net flux of entrapped ferricyanide permeating into the extravesicular volume (JFeCN (t) [mole/cm2-s]) as a function of a permeation rate constant (PFeCN [cm/s]) and the intra- and extravesicular ferricyanide concentrations (CiFeCN (t) [mole/cm3] and CoFeCN (t) [mole/cm3]). i o JFeCN ) PFeCN(CFeCN (t) - CFeCN (t))

(2)

The rate of change of the inner and outer vesicle ferricyanide concentrations due to ferricyanide permeation is defined by eqs 3a and 3b as and i dCFeCN ) -JFeCNAVes Vi dt

Vo

o dCFeCN ) JFeCNAVes dt

(3a)

(3b)

where Aves [cm2], Vi [cm3], and Vo [cm3] correspond to the average vesicle area at the bilayer midplane, and the inner and outer vesicle volumes, respectively. A more convenient relationship between intra- and extravesicular ferricyanide concentration (eq 4) can be derived by integration of eqs 3a and 3b i o i o (0) + VoCFeCN (0) ) ViCFeCN (t) + VoCFeCN (t) (4) ViCFeCN

where CiFeCN(0) [mole/cm3] and CoFeCN(0) [mole/cm3] correspond to the initial inner and outer vesicle ferricyanide

concentrations, respectively. Combining eqs 2-4 enables expression of PFeCN (eq 5) in terms of experimentally measurable CoFeCN(t)

PFeCN )

(

)(

o dCFeCN (t) Vo Vo i o / CFeCN (0) + CFeCN (0) i + dt AVes V

( ))

o CFeCN (t) 1 +

Vo Vi

(5)

Figure 4 depicts dependency of experimentally measured percent entrapped ferricyanide permeated into extravesicular volume at pH 7 and 25 °C vs time during the initial 24 h period following vesicle formation. Average vesicle size (measured periodically ex situ) remained constant at 208 nm (σ ) 43 nm) following a decrease from 226 nm (σ ) 39 nm) within the first 2 h, which we attribute to osmosis. In the case of measuring CoFeCN(t) during the time period immediately following vesicle formation in which inner and outer vesicle ferricyanide concentrations have not appreciably changed from their initial values (see Figure 4), eq 5 can be approximated by

PFeCN )

1 i CFeCN

o (t) Vo dCFeCN dt AVes (0)

(6)

o (t)/dt ) Equation 6 is consistent with Figure 4 (i.e., dCFeCN constant), providing a straightforward measure of PFeCN. In the o (t) during a later time period, the inner case of measuring CFeCN o (t)/ and outer ferricyanide concentrations converge and dCFeCN dt tends toward zero, requiring numerical fitting of experimental data to eq 5 (nonlinear least-squares, Mathematica 3.0) to obtain PFeCN. For example, at 0.14 fractional loss of entrapped ferricyanide, the permeability coefficient calculated using eq 6 has about 5% error relative to eq 5. Permeability of Ferricyanide as a Function of pH and Temperature. Ferricyanide permeability across polymerized PC8,9PC vesicles was measured using 6-MCH modified Au electrodes (Figures 5 and 6) and tabulated (Table 2 ) as a function of pH and temperature. Table 2 also reports ferricyanide fluxes (moles/cm2-s) and transport velocities (M/s) in the linear (short time) transport regime. With respect to pH at 25 °C (Figure 5), the permeability of entrapped ferricyanide exhibits

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J. Phys. Chem. B, Vol. 106, No. 13, 2002 3507

Figure 5. Rate of release of vesicle entrapped ferricyanide normalized to the maximum concentration based on the external volume at 25 °C for pH 6 (0), 7 ((), and 8 (×). The data were numerically fitted (solid line) using eq 5.

Figure 7. Thermal dependence from 25 °C to 72 °C of initial ferricyanide permeability across polymerized PC8,9PC vesicle membranes at pH 7.

Figure 6. Rate of release of vesicle entrapped ferricyanide normalized to the maximum concentration based on the external volume at pH 7 for temperatures 15 °C (0), 25 °C (dashed line, refer to Figure 4 for extended sampling times), 45 °C ()), And 72 °C (4). The data were numerically fitted (dashed and solid lines) using eq 5.

TABLE 2: Rate of Fe(CN)6 Release as a Function of pH and Temperaturea 25 °C 6 PFe(CN) o

pH

(cm/s)

1.1 × 10-12 1.6 × 10-12 2.5 × 10-12

6 7 8

6 JFe(CN) o

(mol/cm2-s)

1.1 × 10-16 1.6 × 10-16 2.5 × 10-16

6 νFe(CN) o

(M/s)

1.3 × 10-9 1.9 × 10-9 2.9 × 10-9

pH 7 T (°C) 15 25 45 72 a

6 PFe(CN) o

(cm/s)

2.0 × 10-12 1.6 × 10-12 1.3 × 10-11 5.8 × 10-11

6 JFe(CN) (mol/cm2-s) o

6 νFe(CN) (M/s) o

2.0 × 10-16 1.6 × 10-16 1.3 × 10-15 5.8 × 10-15

2.4 × 10-9 1.9 × 10-9 1.5 × 10-8 6.9 × 10-8

( 5% relative error for values.

pH7 pH8 the following trend: PpH6 FeCN < PFeCN < PFeCN. The basis for this trend cannot be explained by chemical events such as lipid oxidation or hydrolysis. Lipid oxidation is expected to occur at nearly equal rates since oxygen concentration is approximately the same at each pH.40,41 Furthermore, oxidation of various unsaturated lipids near pH 7 occurs on order of days, beyond the time scale of the short-term experiments described here.40,41 Likewise, hydrolysis of unsaturated lipids near pH 7 occurs on order of days.42,43 Therefore, pH dependent transport of ferricyanide across PC8,9PC vesicle membranes is most likely attributable to the relevant system-dependent parameters for passive transport (discussed in more detail below). With respect to temperature at pH 7, the permeability of entrapped ferricya15°C 45°C nide exhibits the following trend: P25°C FeCN < PFeCN < PFeCN < 72°C PFeCN (see Figure 6). This general trend of increasing ferricya-

nide permeability with increasing temperature is expected since ferricyanide permeation across lipid membranes is a thermally activated process. However, the anomalous behavior of P25°C FeCN < P15°C FeCN may be due to reorganization of monomeric and oligomeric lipids within the vesicle membrane, resulting in membrane defects that occur below the melting temperature of monomeric PC8,9PC (e.g., 23 °C44).45 Passive Transport of Ferricyanide across Polymerized PC8,9PC Vesicle Membranes. Equation 7, based upon onedimensional diffusion of solute across a membrane taking into account a Boltzmann distribution in solute molecule energy,46 provides a figure of merit (i.e., the temperature coefficient, Q1039) for delineation of active vs passive transport based on temperature and transport energy.

Q10 )

xT + 10 -Ea10 exp RT(T + 10) xT

(7)

Here, R, T, and Ea represent the ideal gas constant, temperature, and the minimum kinetic energy required to diffuse across the vesicle membrane, respectively. Values of Q10 close to 1.0 are characteristic of passive processes, although a considerably large Q10 of 1.3 has been reported for molecules with molecular weights ranging from 10 to 1000 g/mol in water (at 20 °C) having an energy barrier to transport from 10 to 17 kJ/mol.47 For the polymerized PC8,9PC vesicles investigated here, the energy barrier for ferricyanide permeability is calculated using the following Arrhenius-type expression (eq 8), Ea)0 exp PFeCN ) PFeCN

( ) -Ea RT

(8)

where PFeCN, R, T, and Ea, are defined as before, and PEa)0 FeCN represents the ferricyanide permeability rate constant at zero energy barrier. The natural log of experimentally measured ferricyanide permeation rate constants at pH 7 as a function of inverse temperature between 25 °C and 72 °C (Figure 7) is linear and yields by fit to eq 8, Ea ) 65 kJ/mol (regression error of less than 0.01) and PEa)0 FeCN ) 0.417 cm/s. Inserting the calculated energy barrier into eq 7 for 20 °C yields Q10 ) 2.3. These values compare well with reported data for charged solutes (i.e., Q10 ) 2.01, Ea ) ∼50 kJ/mol)47 and for potassium ions (i.e., Q10 ) 2.3, Ea ) ∼60 kJ/mol)47 passively crossing artificial and natural membranes. Large Q10 values are not surprising, since

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membranes do provide an appreciable barrier to charged solute transport. Although a more reliable criterion for determining the ion transport process is the Ussing-Toerell equation,48 additional evidence supporting passive ferricyanide transport across polymerized PC8,9PC vesicle membranes is provided by observing similar magnitudes in ferricyanide permeabilities (1.6 × 10-12 - 5.8 × 10-11 cm/s, ionic radii ) 3.6 Å)49 to other anions such as Cl- (7 × 10-12 - 7 × 10-13 cm/s,50 ionic radii ) 1.67)51 and Br- (2 × 10-11 cm/s,50 ionic radii ) 1.82 Å)51 and by virtue of the experimental design (i.e., no “shuttling” agents introduced into the membrane). Two common explanations exist in the literature for describing the mechanism of passive ionic transport across membranes: the pore mechanism52 and the solubility-diffusion mechanism.52 Based on size (ionic radii ) 3.6 Å), charge (-3), and lipid length (PC8,9PC hydrophobic tail length of 23 carbons), ferricyanide permeation does not appear to follow a pore-type process. As a point of reference, the transition from a pore to solubility-diffusion mechanism for hydrated potassium ion (ionic radii ) 3.31 Å) permeation is near 17 carbons in tail length for unsaturated phosphatidylcholine lipids.52 For protons (H3O+ with ionic radii ) 1.1 Å), this transition occurs for unsaturated phosphatidylcholine lipids near 21 carbons in tail length.52 A pH dependent, proton-hydroxyl permeability (on the order of 10-4 cm/s) observed in vesicle membranes was attributed to a mechanism similar to that found in water and ice, whereby protons/hydroxyls are transferred across the bilayer by rearrangement of hydrogen bonds.53 Therefore, charge compensation (i.e., counterion transport) presumably by hydroxide ions for the efflux of ferricyanide is not expected to be rate limiting. From arguments above, ferricyanide permeability is likely to be rate limiting and appears to follow a solubility-diffusion mechanism, where for the simplest case, eq 939,54 applies.

PFeCN )

s DFeCNKFeCN lmemb

(9)

In eq 9, DFeCN (cm2/s), KFeCNs, and lmemb (cm) signify the effective diffusion constant of ferricyanide, the membrane partition coefficient of ferricyanide, and the membrane thickness, respectively. The physicochemical significance for each term is elaborated in the literature.52 To calculate the ferricyanide partition coefficient (∼10-14), an estimate for the diffusion coefficient across lipid membranes may be approximated by using the Stokes-Einstein equation (i.e., DFeCN ) RT/ 6πηRFeCN31,56) to be 5.5 × 10-6 cm2/s, the membrane length known from X-ray and light scattering studies to be ∼ 4 nm,34,35 and the permeability coefficient taken from Table 2 to be ∼10-12 cm/s. A partition coefficient of 10-14 seems somewhat low as compared to values tabulated in the literature.55 A more detailed description for the passive transport of ions across membranes incorporates interfacial resistances into the transport model,50 a key phenomenon for charged solute transport. In our system, the observed pH dependence on ferricyanide permeability (see Figure 5) is likely accounted by a diffusion-solubility effect. Perhaps, at higher pHs (buffered by 10 mM phosphate) the rate of anion exchange between hydroxide ions and ferricyanide at the outer vesicle membrane/aqueous interface increases. Alternatively, changes in pH could affect the chemical environment of the vesicle membrane, which would kinetically influence ferricyanide permeation. The effect of pH on ferricyanide permeability for the model described by eq 9 could contribute to an altered “lumped” property in KFeCNs or DFeCN. By combing eqs 2 and 3a and integrating under the assumption of no initial extravesicular ferricyanide, the half-life, τ1/2,

for the intravesicular loss of ferricyanide becomes i τ1/2 ) 0.693(RVes /3PFeCN)

(10)

i denotes the inner vesicle radius. For our system at where RVes pH 7 and 25 °C, τ1/2 is 2.4 weeks. This is a remarkable value for the entrapment and retention of negatively charged solutes within vesicles. We attribute a large τ1/2 value to the enhanced structural stability of PC8,9PC vesicle membranes imposed by polymerization and the presumed ability of polymerized membranes to drastically retard movement of charged solutes. As an illustration of the physical difference in media between homogeneous solutions and lipid bilayers, the diffusion coefficient of ferricyanide in water56 (at 25 °C) is 0.98 × 10-5 cm2/s as opposed to 5.5 × 10-6 cm2/s estimated above for vesicle membranes. Relative to homogeneous aqueous media, the observed decrease in solute permeability within natural and artificial vesicle membranes is known to depend strongly on solute molecular weight. The mass dependence of solute diffusion in homogeneous media is proportional to (molecular weight)-1/2 or (molecular weight)-1/3 54 whereas that for nonelectrolyte diffusion across egg lecithin vesicle membranes is proportional to (molecular weight)-1/4.2 54 and that of natural cell membranes can be as high as (molecular weight)-1/6.0.54 Exploiting the strong permeability dependence on solute molecular weight is possible for our vesicle system in addition to altering the frictional properties imposed by the polymerized membrane network. Eventually, we plan to not only further stabilize vesicle membranes through extensive polymerization but to fabricate “molecular sieving-type” vesicle membranes that prevent transport of charged species based on molecular size.

Conclusion Cyclic voltammetry of ferricyanide in extravesicular sample volumes utilizing 6-mercaptohexanol or 2-mercaptoethanamine modified gold electrodes enabled detailed measurement of pH and temperature-dependent permeability of ferricyanide across photopolymerized PC8,9PC vesicle membranes. At 25 °C, ferricyanide permeability increased from 1.1 × 10-12 to 2.5 × 10-12 cm/s with increasing pH from 6 to 8. At pH 7, the ferricyanide permeability-temperature dependency was investigated and found to fit an Arrhenius rate expression, increasing exponentially from 1.6 × 10-12 to 5.8 × 10-11 cm/s with increasing temperature from 25 to 72 °C, yielding a calculated energy barrier for permeation of 65 kJ/mol. Greater permeability observed at 15 °C relative to 25 °C is attributed to membrane defects present in the gel-phase. These results in conjunction with the relevant physicochemical properties of ferricyanide and PC8,9PC membranes for transport support the diffusion of Fe(CN)63- across intact vesicle walls rather than by a pore type mechanism. At pH 7 and 25 °C, a remarkably large half-life of 2.4 weeks was calculated for the retention of Fe(CN)63- within polymerized PC8,9PC vesicles. This investigation represents the first electrochemical characterization of anomaly lengthy retention of electroactive species entrapped within stable polymerizable vesicles. Aside from fluorescent probes and selective metal ion sensors, the electrochemical method reported provides a convenient and sensitive probe for detecting electroactive species down to 10 µM, beyond typical sub-millimolar limits of detection using ultraviolet-visible, nuclear magnetic resonance, or conductometric spectroscopy.

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