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Tethered Bilayer Membranes Containing Ionic Reservoirs: Selectivity and Conductance Gowri Krishna,† Jurgen Schulte,‡ Bruce A. Cornell,† Ron J. Pace,§ and Peter D. Osman*,| AMBRI Ltd, Level 3, 126 Greville Street, Sydney 2067, Australia, Department of Applied Physics, University of Technology, P.O. Box 123, Sydney 2007, Australia, Chemistry Department, Faculty of Science, Australian National University, Canberra, ACT 0200, Australia, and Telecommunications & Industrial Physics, CSIRO, P.O. Box 76, Epping NSW 1710, Australia Received July 14, 2002. In Final Form: November 3, 2002 Ion channels, such as gramicidin A, selectively facilitate the transport of ions across biological and synthetic membranes. The conductance properties of ion channels are frequently characterized in synthetic bilayer lipid membranes (BLMs). The instability of BLMs has seriously limited the range of applications for these structures, and tethered bilayer lipid membranes (tBLMs) have addressed the problem through tethering many of the membrane components to a solid surface. In the present study, thin gold substrates have been used to tether thiol- and disulfide-terminated membrane components to form a tBLM electrode to provide a reservoir for ions. This study reports on the ion selectivity and apparent permeability of gramicidin channels in such tethered bilayer membranes. The investigations using electrical impedance spectroscopy indicated that the magnitude of ionic conductance varies substantially in reservoirs with different chemical structures. This study addressed the effect of changing ionic concentration, the effect of changing the species in the bulk solution above the membrane, and the influence of the chemical structure of the reservoir tethers. The effect of two-dimensional packing on membrane conductance was also investigated. The present observations suggested that (a) the reservoir region resistivity has a major influence on the overall conductivity of the membrane and in some instances can dominate conduction, (b) the conduction behavior is nonlinear and exhibits saturation with increasing electrolyte concentration, and (c) that ion pairing in the reduced dielectric ( ∼50) reservoir region is the likely basis for the latter effect. The inferred limiting ionic mobilities of alkali chloride species in the membrane reservoir regions were 3-4 orders of magnitude less than in aqueous solution, indicating that the reservoirs resembled hydrated polymer gels.
Introduction Membranes define cellular structures, provide physical integrity, and facilitate many aspects of cellular activity. Transport across membranes can be active or passive. Mostly, active transport occurs across membrane channels, which allows a flow of materials in specific directions and under controlled conditions. Ion channels such as gramicidin can be incorporated into synthetic membranes to mimic the functions of ion channels in cell membranes, allowing selective transport or diffusion of monovalent cations across the hydrophobic interior of the membranes. Gramicidin A (gA) is a bacterial peptide that forms dimeric channels with defined “open and closed” states. It is known to bind and conduct monovalent cations and is blocked by divalent cations. It is small and stable, making it suitable for study by a range of biophysical techniques such as NMR spectroscopy,4,5 molecular dy* Corresponding author. E-mail:
[email protected]. † AMBRI Ltd. ‡ University of Technology. § Australian National University. | CSIRO. (1) Cornell, B. A.; Braach-Maksvytis, V. L.; B. King, L. G.; Osman, P. D.; Raguse, B.; Wieczorek, L., Pace, R. J. Nature 1997, 387, 580-583 and references sited therein. (2) Krishna, G.; Schulte, J.; Cornell, B. A.; Pace, R.; Wieczorek, L.; Osman, P. D. Langmuir 2001, 17(16), 4858-4866 (3) Cornell, B. A.; Krishna, G.; Osman, P. D.; Pace, R.; Wieczorek, L. Biochem. Soc. Trans. 2001, 29, 613-617 (4) Cornell, B.; Separovic, F.; Smith, R. Biophys. J. 1992, 61, A525
namic simulations,6-8 and theoretical modeling.9 It forms one of the best-characterized ion channels14,15 used for modeling membrane transport functions. In a bilayer lipid membrane (BLM), the conducting conformation of gA is a right-handed, single-stranded, β6.3-helical membrane spanning dimer.10-13 Site-specific modifications and substitution of specific amino acids have permitted generation of models for the relationship between the structure and function of the gA channel.16-21 (5) Separovic, F.; Gehrmann, J.; Milne, T.; Cornell, B.; Lin, S. Y.; Smith, R. Biophys. J. 1994, 67, 1495. (6) Woolf, T. B.; Roux, B. Proc. Natl. Acad. Sci. U.S.A. 1994. 91, 111631-11635. (7) Roux, B. Annu. Rev. Biophys. Biomol. Struct. 1994, 23, 731-61. (8) Woolf, T. B.; Roux, B. Biophys. J. 1997, 961-981. (9) Hollerbach, U.; Chen, D. P.; Busath, D. T.; Eisenberg, B. Langmuir 2000, 16(13), 5509-5514. (10) Wallace, B. A. J. Struct. Biol. 1998, 121, 123-141. (11) Killian, J. A. Biochim. Biophys. Acta 1992, 1113, 391-425. (12) Woolley, A.; Wallace, B. A. J. Membrane Biol. 1997, 129, 109136. (13) Andersen, O.; Sawyer, D. B.; Koeppe, R. E. In Biomembrane Structure and FunctionsThe State of the Art; Academic Press: London, 1992; 227-244. (14) Cornell, B. J. Bioenerg. Biomembr. 1987, 19, 655-676 and references cited there in. (15) Urry, D. W. Proc. Natl. Acad. Sci.U.S.A. 1972, 69(6), 16101614. (16) Daumas, P.; Heitz, F.; Ranjalahy-Rasoloarijao, L.; Lazaro, R. Biochimie. 1989, 71, 77-81. (17) Koeppe, R. E., II; Andersen, O. S. In Proteins and Function; L’Italien, J. J., Ed.; Plenum Press: London, 1987; 623-628. (18) Stankovic, C. J.; Heinemann, S. H.; Schreiber, S. L. J. Am. Chem. Soc. 1990, 112, 3702-3704.
10.1021/la026238d CCC: $25.00 © 2003 American Chemical Society Published on Web 01/30/2003
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Figure 1. Structure of the membrane. The bilayer membrane is tethered to the gold surface with the reservoir-forming region in the middle. The tethered components include lipids spanning the full membrane (MSL4xB and MSLOH), lipids spanning half thickness (DLP), and tethered gA (TgA). These membrane components are linked to the tethering groups via tetraethylene glycol linkers, which form the reservoir. The mobile components are the phytanyl lipids, DPEPC, and GDPE, with the diffusing gramicidin (FgA) in the outer membrane leaflet.
The selectivity and transport of ions through gA have been studied experimentally with the aid of channel mutations16-21 and modeled using molecular dynamic simulations.6-8 Gramicidin channels transport monovalent cations having an unhydrated radius of less than about 2 Å, but they are impermeable to divalent cations and anions and larger cations.22,23 Divalent cations block the passage of monovalent ions,10-14 while anions do not block the gramicidin channel.24,25 Tethered Membranes. Recently we have described a novel system involving a synthetic lipid bilayer attached to a gold substrate.1-3 Figure 1 is a schematic representation of the supported membrane assembly. Polar tethering species attach the membrane to the electrode, providing a hydrophilic region between the membrane and the gold surface. This region acts as a reservoir for ions transported across the membrane.1,26,27 The reservoir exists as a gellike structure,2 which is permeable to ionic species. The (19) Jude, A. R.; Providence, L. L.; Schumutzer, S. E.; Shobana, S.; Greathouse, D. V.; Andersen, O. S.; Koeppe, R. E. Biochemistry 2001, 40(5), 1460-1472. (20) Koeppe, R. E., II; Andersen, O. S. Annu. Rev. Biophys. Biomol. Struct. 1996, 25, 231-258. (21) O’Connell, A. M.; Koeppe, R. E., II; Andersen, O. S. Science 1990, 250, 1256-1259. (22) Urban, B. W.; Hladky, S. B.; Haydon, D. A. Fed. Proc. 1978, 37(12), 2628-2632 and references therein. (23) Urban, B. W.; Hladky, S. B.; Haydon, D. A. Biochim. Biophys. Acta 1980, 602, 331-354. (24) Myers, V. B.; Haydon, D. A. Biochim. Biophys. Acta 1972, 274, 313-322. (25) Tian, F.; Cross, T. A. J. Mol. Biol. 1998, 285, 1193-2003. (26) Raguse, B.; Braach-Maksvytis, V. L. B.; Cornell, B. A.; King, L. G.; Osman, P. D.; Pace, R. J.; Wieczorek, L. Langmuir 1998, 14, 648659 and references sited therein. (27) Pace, R. J.; Braach-Maksvytis, V. M. B.; King, L. G.; Osman, P. D. J.; Raguse, B.; Wiekzorek, L.; Cornell, B. A. SPIE 1998, 3270, 5058.
electrical properties of tethered bilayer lipid membranes (tBLM) are very dependent on the properties of this reservoir region. Figure 1 shows the components of the tethered membrane and Figure 2 their chemical structure and our naming convention. Details of chemical structures and syntheses are described elsewhere.26,28-30 The tethering components forming the inner membrane leaflet include lipids spanning the full membrane (MSL4xB and MSLOH), half membrane spanning lipids (DLP), and tethered gramicidin (gAyySSbn). The tethers are made up of tetraethylene glycol units terminating in benzyl disulfide or in a sulfhydryl group at the gold surface. The small disulfide molecule MAAD (mercaptoacetic acid disulfide) at the gold surface introduces two-dimensional spacing in addition to the intrinsic spacing provided by the benzyl disulfide groups. The outer layer of the membrane is comprised of lipids spanning half the thickness of the membrane and mobile gramicidin diffusing freely. The composition of this membrane region is typically 30% glycerol diphytanyl ether (GDPE) and 70% glycerol diphytanyl ether phosphatidylcholine (DPEPC), with the proportion of gramicidin adjusted to the required level of conductance (in 8 × 10-4 mole ratio of the lipids or its multiples). The use of ester or ether chemical linkages and the introduction of spacers allow modification of the chemical nature and surface packing of the reservoir structures, as (28) Burns, C. J.; Field, L. D.; Morgan, J.; Petteys, B. J.; Prashar, J.; Ridley, D. D.; Sandanayake, S.; Vignevich, V. Aust. J. Chem. 2001, 54, 431-438. (29) Burns, C. J.; Field, L. D.; Hashimoto, K.; Petteys, B. J.; Ridley, D. D.; Rose, M. Aust. J. Chem. 1999, 52, 387-394. (30) Raguse, B.; Culshaw, P. N.; Prashar, J.; Raval, K. Tetrahedron Lett. 2000, 41, 2971-2974 and references sited therein.
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Figure 2. The membranes described in Figure 1 were prepared by combining several basic functional units. The inner layer tethering components contain a reactive group (S-S or SH) to allow chemisorption of the inner layer leaflet of the membrane to the gold surface. The tethering components include compounds 1, 2, 3 (a, b, or c), with or without spacer, and C-terminally modified gA, compound 4. The untethered components are compounds 5, 6, and 7. When assembled, a two-dimensional fluid tethered membrane with nanoscale thickness results. Species 4 and 5 pair to form conducting ion channels across this bilayer membrane.
in our previous study of the dielectric properties of reservoir species.2 Four analogues of sulfur-tetraethylene glycol tethers were compared. Here we examine the extent to which ionic mobility in these reservoir systems influence the overall conductive response of the gramicidin channels incorporated in the bilayer. Ion Conductance in Tethered Membranes with gA Channels. In BLM bounded at both interfaces by an
infinite reservoir, the ionic flow is generally dominated by the characteristics of the ion channel. The gramicidin conductance is dependent on the dimerization constant and on the species and concentration of ions in the bathing solution. It is conceivable that the flow of ions through any channel is governed by factors such as (i) restrictions to the flow of ions to and from the channel mouth, (iii) depletion of ions near the channel mouth, (iii) the binding
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of ions near the channel mouth, (iv) the transport mechanism of the ion across the channel, and (v) changes to channel configuration by the membrane environment. In the tBLM used here, tethered gA molecules (Figure 1) associate reversibly with mobile gA molecules to form a continuous path for ions to traverse the hydrophobic interior of the membrane. Net ion flow is driven by an externally applied potential between the gold electrode and a counter-reference electrode in the bathing solution. The mobility and density of the ions within the reservoir will limit the ion flux through the gramicidin channel if ionic diffusion in the reservoir region is sufficiently restricted. The tBLM incorporating gA channels thus provides a system for interpreting the behavior of ionic reservoirs as reflected in gross conductance behavior of the membrane/ion channel complex. Gramicidins functionalized at the C-terminus are used in these investigations. It is known that transport function is preserved in C-terminally functionalized gA channels, while N-terminal modifications alter channel conduction drastically.34 In particular, high-resolution NMR investigations of analogues of the compounds used in these investigations show that channel function36 and peptide helical configuration are preserved.35 Reservoir Influence on Membrane Conduction. When fully hydrated, the reservoirs tested here are estimated to be approximately 4 nm thick.1,26 Thus, the ions flow into a region that is in close proximity to the gold surface. This region is also packed with the chains of the reservoir tethers, resulting in a potential modification of the properties from that of a bulk electrolyte solution. Three reservoir chemistries were compared where the lipid composition was the same, while the polar tethers that form the reservoir were different. The nonpolar region of the membrane inner leaflet comprises a mix of phytanyl and methylene chains, which are covalently coupled via the polar linker (reservoir chain) to the disulfide attachment groups. In tethered membranes containing gramicidin, the properties of the reservoir between the membrane and the gold electrode are observed to have a strong influence in modulating the apparent conductivity of membranes incorporating gramicidin.2 In this work, we present a systematic study of this effect for a range of reservoir types and monovalent cationic species transported by gA. Previously, we reported on the interfacial capacitance2 in these tethered membranes and demonstrated that the tBLM interfacial capacitance could be separated into two components, the diffuse and the Helmholtz capacitances. In this paper, we interpret the observed, macroscopic conduction in the tBLM using a distributed network model of the membrane-reservoir system. This allowed the ionic conductivity of the reservoir regions to be inferred as a function of reservoir electrolyte concentration. This latter was then compared quantitatively with the predicted dependence given by the Onsager theory of dilute electrolytes37,38 and a semiphenomenological approach involving ion pairing. The ion channel selectivity and conduc(31) Jain, M. The Biomolecular Lipid Membrane; Van Norstrand Reinhold Company: New York, 1972; Chapter 4. (32) Coster, H. G. L.; Smith, J. R. Biochim. Biophys. Acta 1974, 373, 151-164. (33) Woodhouse, W.; King, L. G.; Wieczorek, L.; Cornell, B. A. Faraday Discuss. 1998, 111, 247-258. (34) Seoh, S.; Busath, D. D. Biophys. J. 1993, 65, 1817-1827. (35) Separovic, F.; Barker, S.; Delahunty, M.; Smith, R. Biochim. Biophys. Acta 1999, 1416, 48-56. (36) Suarez, E.; De, E.; Molle, G.; Lazaro, R.; Viallefont, P. J. Pept. Sci. 1998, 4, 371-377. (37) Davies, C. W. Electrochemistry; George Newnes Ltd.: 1967; Chapter 3.
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tance properties in the tBLM were compared with observations in conventional BLM. Materials and Methods Tethered Reservoirs. The instrumentation and measurement techniques developed by Cornell et al. were used in all these investigations.1 The method for tethering reservoir species was the same as that described earlier.2,3,26 Four types of test membranes were compared. In membranes the predominant species was the double length phytanyl lipid (Figure 2, compounds 3a-c). The first type of tBLM was the spaced succinate membrane, where the reservoir chains incorporate two succinate groups (Figure 2, compound 3a). Spacing on the substrate was introduced with the inclusion of 50 mol % MAAD. The same type of reservoir, without additional two-dimensional spacing, was the second type of test membrane. Membranes comprising lipid reservoirs without succinate groups and ether linkages (Figure 2, compound 3b) form the third test group. The incorporation of an 11-carbon methylene chain to the tethering end of the reservoirs (Figure 2, compound 3c) gave the fourth variable for the test membranes. These are referred to as (1) Succinate + Spacer, (2) Succinate, (3) All-ether, and (4) C-11 membranes, respectively. The structures of the membrane forming compounds are shown in Figure 2. Membrane Preparation. All membrane components were synthesized according to the methods of Burns et al.28,29 and Raguse et al.26,30 The tethering components of the tBLM were codissolved in high-purity ethanol.2 Glass microscope slides were coated with a 100 nm evaporated gold layer bonded by a 50 nm Cr layer to a glass substrate and immediately dipped in the membrane tethering layer solution for 1 h to tether the monolayer, rinsed in ethanol, and stored at 4 °C until tested. The mobile lipid leaflet (outer layer) was then formed from a solution of GDPE, DPEPC, and gramicidin-biotin (gA5xB) in ethanol, following the method of Cornell et al.1,3 Electrodes with tethered membranes were assembled into sensor arrays,2 each possessing 16 independent 4 mm diameter test wells. Rinsing the test wells containing membrane-forming solutions with high purity water assembled the membranes. Stock solutions of AR-grade LiCl, NaCl, KCl, CsCl, and NH4Cl (2 M) were prepared and diluted with freshly collected Milli-Q water to give solutions in the range of 1, 5, 10, 50, 100, 500, and 1000 mM. Impedance Measurements. The impedance spectrum was obtained by sweeping an applied ac potential from 1 to 1000 Hz, superimposed on a dc offset.1-3,26 A three-terminal excitation is employed with a Au working electrode, a Ag/AgCl reference, and a Pt counter electrode. The results reported here are based on fitting the simple network model31-33 to a plot of frequency versus impedance.2 The impedance spectra of the test membranes were recorded with 30, 50, and 70 mV ac and bias voltages of -300, 0, and +300 mV dc for each concentration of test electrolyte. As noted earlier,2 the membrane impedance properties are independent of ac excitation voltage in the above range, while the bias voltage effect saturates above ∼+200 mV dc (depending on reservoir type). The data reported here are for 50 mV ac excitation and +300 mV dc bias. The measurements were repeated after replacing the water with electrolyte solution in the test cells starting with the lowest ionic concentration and each successive concentration thereafter. Impedance spectra of the membranes were recorded with 1, 5, 10, 50, 100, 500, and 1000 mM concentrations for each test electrolyte for the four test membranes referred to as succinate + spacer, succinate, all-ether, and C-11. Model for Membrane ConductionsThe Distributed Network Model. A model has been developed to describe the electrical response of gramicidin channels operating independently in a sensor membrane containing an ionic reservoir, as used here. The gA channels are distributed randomly in two dimensions within the membrane plane and the ion flux through these is effectively in series with the redistributive flows throughout the membrane space. For gA densities less than 109 (38) Antropov, L. I. Theoretical Electrochemistry; Mir publishers: Moscow, 1972; Chapter 5.
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Figure 3. The cell model. A regular hexagonal array of cylindrical cells used to model a random distribution of irregular membrane patches each containing a single conducting channel. The cell radius, Rcell, is defined by the mean two-dimensional channel densities. A conducting channel is located at the center of each cell and by symmetry there is no net ion flow across the cell boundaries. The electrical response of each cell is identical and modeled by a finite element analysis assuming linear (Ohmic, etc.) behavior of the membrane, channel, and reservoir components. Because Rcell . d (the reservoir thickness), only radial ion flux from the (point) channel at the cell center is considered and the radial symmetry makes the problem essentially one-dimensional (annular elements; see the text).
Figure 4. Equivalent circuit model of the electrical network representing a single cell within the hexagonal array of Figure 3. For each annular element (i) in the cell, the reservoir capacitance (Helmholtz plus diffuse) (CTi) and membrane admittance (combination of GmI and CmI) scale with element area (see ref 2), while the reservoir resistance (Ri) is determined by eq 1. channels/cm2 (as employed here), the mean channel in-plane spacing is approximately 300 nm, about 100 times larger than the reservoir thickness. We assumed that reservoir ionic relaxation along directions normal to the substrate plane is “instantaneous”, in comparison to the time scale of relaxation in directions within the plane. The reservoir is thus effectively a two-dimensional capacitive and conductive system, which contains randomly distributed Ohmic connections through the membrane to the external bulk solution. Even this system is difficult to model if the ion channels are randomly distributed. However, we observed only the macroscopic electrical behavior of the membrane system with a defined average channel density. During the testing of this model, we made two simplifying assumptions, which appear to be physically reasonable and permit quantitative modeling of the membrane response: (1) The ac driving frequencies (1-1000 Hz) are sufficiently low that diffusive relaxation effects on the ion movements in the reservoir may be ignored; i.e., the reservoir acts like a simple homogeneous Ohmic medium. (2) A ‘cell model’ of the channel distribution is adequate to interpret the bulk electrical response; i.e., the channels are assumed to be uniformly distributed in a quasihexagonal array,
with one channel located at the center of each cell. Cell size is then determined simply by the mean channel density in two dimensions. A cell is created for each conducting channel, which just contacts adjoining cells (see Figures 3 and 4). By symmetry there should be no current flow across all boundaries, so cells may be regarded as independent. In a finite element approximation, each cell is divided into 10 annular regions with equivalent circuit, as shown. This number of elements has been found adequate to simulate limiting continuum behavior. The inner radius of an annular region is i∆r, where i ) 0-10 and the annulus width is ∆r (∆r ) Rcell/10). The total resistance (Ri) from the inner to outer annulus surface is (i g 1)
Ri )
F∆r 2πd∆ri
) (F/d)(1/2πi)
(1)
where F is the reservoir specific resistivity and d the reservoir thickness (∼40 Å). The quantity [F/d] is included as the reservoir impedance value. For 0.1 M NaCl in water and d ) ∼40 Å, [F/d]
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is less than 109 Ω (F for 0.1 M saline is approximately 102 Ω cm53). The shunting gold surface (Helmholtz + diffuse) and membrane impedances of the annular elements (Figure 4) similarly scale with annulus area in the expected manner (see also ref 2). Modeling results suggested that [F/d] for the reservoir is approximately 1012-1013 Ω. The response scaled with the number of ion channels but was much less sensitive to channel resistance. Thus, changes in the conductivity of the membrane depend principally on changes to the number density of the channels or on the conductivity of the reservoir but not on the conductivity of the gA channels themselves. For example, a decade change in channel density (units of channels cm-2) gives a decade change in the apparent Ohmic response (impedance at phase minimum) of the membrane. This was also seen in the phase profiles. Using the same parameter values, the effect of increasing channel resistivity by a factor of 10 (from 1 × 1011 to 1012 Ω) was hardly detectable in the overall membrane conductivity response for the network model. However, calculated network model response to a change in reservoir resistivity from 1013 Ω (∼Succinate) to 1012 Ω (∼All-ether) showed that the apparent Ohmic response of the membrane decreased also by almost precisely a factor of 10, although the true channel conductance was the same in both cases. Ionic Mobility from Experimental Data. To determine ionic mobility, the bulk membrane conductance (G) was obtained by fitting the impedance and phase data to the RC network model (shown in Figure 5) for each test concentration.2 The conductance at infinite electrolyte dilution was derived, by extrapolating the linear part of the titration plot to zero concentration (G0). It was assumed that the conductance should be null when no electrolytes are present in the bathing solution. A residual conduction existed that was different from that of well-insulated membranes without ion channels. Conductance due to the test ions is then
ionic conductance and using the above treatment to derive an ionic mobility Λexp, which is normalized by the limiting mobility Λ0exp
G1 ) G - G0
Λres ) Λexp/Λ0exp
(2)
From G1, the reservoir model allows determination of a value of F-1, the reservoir specific conductance to be determined, given the known channel density. Then the ionic mobility54 in the reservoir, Λexp, is found as
Λexp ) F-1/Cres
Figure 5. Conduction for membranes incorporating different concentrations of outer and inner layer gramicidin (data points). Superimposed on the experimental data are traces determined from the dimerization model of the association of the inner and outer layer gramicidins (see eq 11). The lines are the best global fit, using the parameter values for the gramicidin association (Km), deposition partitioning (Kdep), and apparent channel conductance given in the text. Data were collected with an external electrolyte, NaCl at 100 mM, in the All-ether reservoir system.
(3)
where Cres is the true total concentration of ions in the reservoir (see ref 2). According to Antropov,38 a plot of the ionic mobility against the square root of true ionic concentration (reservoir) allows the limiting mobility at zero concentration to be obtained by extrapolation. The experimental relative mobility (RM) of the reservoir is then obtained by taking the ratio of the observed (39) Ito, K.; Ono, H. Electrochim. Acta 1997, 43, 1247-1252. (40) Kim, J. S.; Kim, S. H. Solid State Ionics 1999, 124, 91-99. (41) Ono, H.; Ito, K. Polymer 1995, 36(4), 891-893. (42) Balabai. N.; Waldeck, D. H. J. Phys. Chem. (B) 1997, 101, 23392347. (43) Mafe, S.; Ramirez, P.; Tanioka, A.; Pellicer, J. J. Phys. Chem. (B) 1997, 101, 1851-1856. (44) Finkelstein. A.; Andersen, A. J. Membr. Biol. 1981, 59, 1551171. (45) Schonknecht, G.; Althoff, G.; Junge, W. J. Membr. Biol. 1992, 126, 265-275. (46) Roux, B.; Karplus, M. Biophys. J. 1991, 59, 961-81. (47) Badia, A.; Lennox, R. B.; Reven, L. Acc. Chem. Res. 2000, 33, 475-8. (48) Ullman, A. Chem. Rev. 1996, 96, 1533-1554. (49) Clegg, J. S. Am. J. Physiol. 1984, 246, R133-R151. (50) Pauser, S.; Zschunke, A.; Khuen, A.; Keller, K. Magn. Reson. Imaging 1995, 13(2), 269-276. (51) Osman, P.; Braach-Maksvytis, V.; Cornell, B.; King, L.; Pace, R.; Raguse, B.; Wieczorek, L. Biophys. J. 1997, 72, A397. (52) Aylward, G. H.; Findlay, T. J. V. SI Chemical Data; John Wiley & Sons: New York, 1974; pp 125. (53) Vanysek, P. In Handbook of Chemistry and Physics; Lide, D. R., Eds.; CRC Press LLC: Boca Raton, 2002; 5-94. (54) Atkins, P. W. Physical Chemistry; Oxford University Press: Oxford, 1990; pp 750.
(4)
(see eq 8). Modeling Relative Mobility. (a) Onsager Model. Onsager’s treatment provides a well-known basis for calculating the mobility of ions in very dilute solution.37,38 The present data are compared with the prediction of this theory (eqs 5-8) for the concentration dependence of ionic mobility, with respect to mobility at limiting dilution in the reservoir region, referred to as the relative mobility of the ions (RM). The Onsager approach uses a Debye-Huckel model of ionic distribution to determine the concentration dependence of mobility of the individual ions. In effect, a particular ion is likely to be surrounded by ions of opposite charge moving in the opposing direction, consequently reducing the mobility of the reference ion. Ionic mobility37 is then predicted to behave as
Λi ) Λ0 - S[(Ci)1/2]
(5)
where Λi is the mobility of the ion at concentration Ci, Λ0 is the mobility at limiting infinite dilution, and S is a constant referred to as the Onsager slope.37 As concentration increases, the interactions between ions increase with consequent reduction in the mobility. The Onsager slope, S, is then calculated from
S)
[
(2.801 × 106)Z1‚Z2‚qΛ0 3/2
1/2
(T) ‚(1 + q )
+
]
41.25(Z1 + Z2) η(T)1/2
(
‚
)
Z1 + Z2 2
1/2
(6)
where
q)
Z1‚Z2 Λ1 + Λ2 ‚ Z1 + Z2 Z2‚Λ1 + Z1‚Λ2
is the dielectric value of the solvent medium (tethered reservoir
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region), Z1 and Z2 are the valencies of the charge-bearing cation and anion, respectively (both 1 in this case) Λ1 and Λ2 are the limiting mobilities of the cation and anion, η is the solvent medium viscosity, and T is the temperature. In eq 6, the first term is described as a correction for decreases in conductivity due to the relaxation effect in aqueous solutions of electrolytes and the second term as addressing electrophoretic effects.37,38 For a monovalent system, the equation simplifies further and q ) 0.5. The reservoir resistivity was derived by fitting membrane data to a distributed network model, as discussed above. Comparison with known values for saline53 suggests an effective viscosity on the order of 102 P in the reservoir, which reduces the electrophoretic term in eq 6 to a negligible value. This second term can then be ignored so that S has one major component addressing the charge cloud effects. The Onsager slope S can thus be represented by
S)
[
]
(2.801 × 106)Z1‚Z2‚qΛ0 (T)3/2‚(1 + q1/2)
(7)
Substituting S in eq 5 and taking the ratio of ionic mobilities, the expression for relative mobility (RM) is compared with eq 4.
[
]
Λi 8.2 × 105(Ci)1/2 ) 1Λ0 (3/2)(T3/2)
(8)
(b) Ion Pairing Model. It is well-known that the Onsager model fails quantitatively in a number of instances. A simple relevant model, due to Bjerrum,37,38 is often employed. This assumes that ions of opposite charge may interact with sufficient strength (relative to thermal energy, kT) such that effectively “ion pairs” form in solution, which carry diminished (or zero) effective net charge. This reduces bulk conduction in the solution. Such an effect is particularly significant in cases where the solvent bulk dielectric is significantly below that of water.42,43 In its most elementary form, the treatment assumes that the intrinsic mobility of free ions is constant (equal to its limiting dilution value) and the bulk conduction is due to the concentration of such species, with the ion pairs (if neutral) not contributing. For monovalent ions associating as ion pairs, C+ + C- T C+C-, the association constant, Kass, is then
Kass )
[C+C-] [C+][C-]
(9)
Then with the above assumption of concentration-independent mobility
ΛCi/Λ0 ) [Ci+]/[Ci] )
(1 + 4Kass[Ci])1/2 - 1 2Kass[Ci]
(10)
where [Ci] is the total concentration of cation or anion species (paired and free) in the solution. These two models will be used to interpret the experimental conductance data in terms of the ionic mobility within the reservoir region.
Results (a) Effect of Gramicidin Concentration on Membrane Conduction. The conductance of the membrane systems varied monotonically with the concentrations of the membrane outer (TgA) and inner layer (FgA) gramicidins, as expected. It was assumed that the mole fractions of incorporated membrane outer layer components are essentially the same as those in the alcohol-based solutions used to form the outer layer leaflet by rapid dilution. Although this is a plausible assumption, direct experimental confirmation of it has been difficult. The very low levels (0.6 fM) of gA present in the functioning sensor membrane under normal operating conditions are below those available to chemical measurement ion channel
concentration. For the membrane inner layer gA components covalently attached to the gold surface through a tether, the concentration of incorporated species increased with the concentration of TgA in the membrane inner layer alcoholic incubation medium, as seen in Figure 5. However, the relative concentrations of deposited species may be different than those within the incubation solutions, due to the complex and poorly understood nature of the gold-sulfur attachment process.47,48 For low relative concentrations of the gA components, we have assumed that the deposited surface concentrations should be proportional to the corresponding mole ratios in the deposition solutions. With these conservative assumptions it was possible to fit a simple bimolecular model to the outer and inner layer gramicidin titration data (Figure 5). The fitting parameters were the conducting dimer formation equilibrium constant, 1/Km, the apparent dimer conductivity, FGA (under the given ionic conditions), and the partition coefficient, Kdep, relating the relative concentrations of deposited to solution tethering gA species. Km is then the dimerization association constant, in units of mole fraction. The mole fraction concentrations of the conducting dimer (D), membrane outer layer gramicidin (FgA), and the membrane inner layer gramicidin (TgA) are then related by
[D] )
[TgA]([FgA] - [D]) Km + [FgA] - [D]
(11)
The best-fit parameter values for Km and Kdep were 2.0 × 10-5 and 0.15, respectively, in the all-ether membrane system. These are presumed to hold for all ionic concentrations and all membrane systems studied. The Kdep value suggested that deposition of the TgA species from the alcohol solution is less favored relative to the other membrane inner layer components (principally DLP). An alternative explanation, that a fraction of the inserted gA species is inactive, cannot be excluded but is regarded as less likely, since this fraction would need to be independent of the tethered gA concentration over a considerable range. In Figure 5, the TgA concentrations are the values inferred from the Kdep ratio. The apparent channel conductivity consistent with the data in Figure 5 is ∼1.5 × 10-12 S, approximately 7 times less than that of the native gA dimer in a BLM in contact with bulk ionic solution (see below). (b) Effect of Ionic Media on Membrane Conduction. The bathing solutions ranged in concentration from 1 mM to 1 M (1, 5, 10, 50, 100, 500, and 1000 mM) for each ionic species. The observed membrane conductance increased with the concentration of the bathing solution up to approximately 100 mM concentration in the bulk solution. At concentrations greater than 100 mM, the rate of change of conduction with electrolyte concentration was slower in all reservoir systems and appeared to saturate in all cases except the C-11 system. In the latter case, although the ionic conduction was relatively low compared to the All-ether reservoir system, it continued to increase linearly with ionic concentration of the bathing solution over the full range studied. Figure 6A-D illustrates the dependence of the membrane conductance on the bathing solution ionic concentration for the four reservoir systems and range of ionic species studied here (all chloride salts). Beyond ∼100 mM external electrolyte concentration, all the monovalent cations exhibited saturating or more weakly increasing conductance response (C-11, All-ether reservoirs). Figure
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Figure 6. (A-D) Comparison of the conductance in the tBLM systems for different monovalent electrolyte species. Graphs on the left (A, C) plot the conductance in membranes with spacer molecules. Those to the right (B, D) are membranes with no additional spacers to modify the two-dimensional packing at the gold surface. The magnitude of conduction in the test membranes varied substantially with reservoir and ion type. The All-ether DLP-containing membranes showed greatest overall conduction. (E) Differences in the magnitude of measured conductance (presented as admittance) at three excitation voltages (30, 50, 70 mV ac). External electrolyte, NaCl.
6E shows the conductance response over the full concentration range studied for each reservoir type, with Na+ as the external cation and a range of ac excitation voltages. In an earlier study,2 we modeled the diffuse capacitance of the four different membrane types and inferred an effective dielectric constant for the reservoir medium of each membrane. From this we were able to estimate a distribution constant for partitioning of the ionic species between the bulk solution and membrane reservoir. Although this treatment was not rigorous, a consistent interpretation was possible, with the inferred values of
the reservoir dielectric constants being in the range of 45-54. The Succinate reservoir possessed the lowest value of 45, with the other three reservoirs falling within the range of 52-54. Figure 7A,B shows the conductivity as a function of the derived ionic concentration in the reservoirs. The initial slopes in Figure 7A are then a measure of the intrinsic ionic mobilities (at infinite dilution) within the reservoir regions for each membrane type. The Allether reservoir has a much higher ionic mobility than the other three, this being the principal reason for the much higher apparent channel conductivity observed for this
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Figure 7. Ionic conductance for Na+ in the four reservoir systems with respect to calculated concentration in the reservoir region (A) linear and (B) log-log plot. The concentration in the reservoir was derived by taking into account the inferred dielectric nature of each of these reservoirs (see ref 2). This “true” concentration in each reservoir is significantly less than the external bulk solution, due to unfavorable ion partitioning into the lower dielectric reservoir regions (cf. Figure 6). The dashed line in Figure 7B has a slope of 0.50.
Figure 8. Relative mobility of Na ions inferred experimentally (data points) for the four reservoir systems, as a function of [reservoir electrolyte concentration]1/2. The predicted theoretical behavior (unbroken lines) from the Onsager model (eqs 5-8), using the respective reservoir dielectric constants previously determined2 is also shown. The broken lines are the best fits of the ion pairing model (eqs 9, 10). In each case, the values of the experimentally determined limiting mobility (Λ0exp), the reservoir dielectric (r), and the fitted ion pairing association constant (Kass) are listed in Table 1.
membrane type. The log-log plot in Figure 7B shows that the conductivity exhibits approximately a power law dependence on reservoir ionic concentration, which is similar for all four reservoir systems. The slope, ∼0.5, is consistent with an ion-pairing model of the ionic mobility, discussed below. (c) Ionic Mobility in the Reservoir. The observed relative mobilities of Na+ ions in the various membrane reservoirs (data points) are shown in Figure 8A-D. The limiting mobility, Λ0exp, in each case is shown in Table 1. These were determined from the respective membrane
responses using the distributed network model, the inferred ion partitioning into the reservoirs,2 and the derived membrane channel densities, as determined above. In each graph, the unbroken line shows the relative conductance of NaCl in the reservoir media predicted by the Onsager model, using the earlier inferred values of the effective dielectric constants.2 The broken line shows the corresponding behavior predicted by the ion pairing model (eq 10), using the best fit values for the pairing constant, Kass, as listed in Table 1. The dependence of relative mobility or conductivity on concentration ap-
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Table 1. Ionic Mobility and the Nature of the Reservoirsa
membrane
expl limiting mobility, Λ0exp (mS m2 mol-1)
reservoir dielectric, r
ion-pairing constant, kass (M-1)
succinate + spacer succinate all-ether C-11 DLP
0.0027 0.0027 0.0117 0.0014
54 45 52.5 52
80 800 70 150
Limiting mobility of Na+ in the four reservoir systems was calculated from experimental data using eq 8. The association constant was the best fit value for each reservoir. The limiting mobility of Na+ in the Succinate and the Succinate + Spacer was the same, but the ion-pairing phenomenon was increased in the (unspaced) succinate reservoir. The All-ether reservoir appeared to impose the least restriction on ionic mobility in the reservoir, consistent with the high level of conductance observed in these reservoirs (cf. Figure 6). The limiting mobility in the C-11 system was lowest in this series of measurements.
peared to be similar for all the ionic species investigated. The reduction in mobility as concentration increased was greater than could be modeled with the Onsager equation, but the ion pairing model gave reasonable quantitative fits in all cases. This was consistent with observations in other solvent systems (see Discussion). Experimental data, with 100 mM Na in the bulk bathing solution, for each reservoir was used to calculate limiting mobility (Λ0exp). The best-fit value for reservoir conductivity was derived from the distributed network model using membrane data and applied to eq 8 to calculate the Λ0 for Na in each reservoir (Table 1). The Λ0exp values derived from experimental data are smaller than the corresponding value for NaCl in water (∼12 mS m2 mol-1 52), indicating that the effective viscosity in the reservoir regions is more typical of a hydrated gel or concentrated polymer solution than an “aqueous” compartment. Even for the most conductive reservoir type (All-ether), the overall membrane response is dominated by the reservoir properties and barely reflects the intrinsic channel conductance behavior under any of the conditions examined here. Discussion The ion conduction of gramicidin channels has been widely studied in artificial lipid membranes and the estimates reported for monomer-dimer equilibrium. Using sodium as a model, the activity was shown to follow Michaelis-Menton behavior with a single channel conductance of 14.6 pS and a binding affinity constant for Na+ of 310 mM.44 The reported dimerization equilibrium constants range between 1011 and 1014 cm2 mol-1 (i.e. Km ∼ 6 × 1012 to 6 × 109 molecules cm-2). This was observed to be dependent on the composition of the lipid membranes. In thylakoid membranes, the dimerization constant for gramicidin was larger (times 10) than the reported values in phosphatidylcholine bilayer membranes.45 Woodhouse et al. report Km values of the order of 6 × 109 molecules cm-2 for tBLM33 (∼3 × 10-5 mole fraction units), similar to that reported here and typical of values seen in C16 phytanyl chain lipids. An important conclusion from modeling the observed membrane conductivity response is that the reservoir properties dominate and limit the membrane conductance. The intrinsic gA conductances, as would be seen in patch clamping or BLM experiment, are obscured, because they are in series with the poor conduction of the reservoir space. The distributed network model showed that the total Ohmic electrical response of the membrane, although
proportional to the density of conducting channels, was independent of the gramicidin channel conduction properties. Interestingly, the supported membrane system may actually resemble “nature” more closely in this regard than the conventional experimental environments used to study channel properties. The protein/solute etc. levels inside living cells are very high, with all water being in effect “bound”.49,50 The effective viscosities (∼100 P or more) and resulting ionic mobilities may approach those observed in the reservoir systems studied here. The ionic conductivities varied between the membrane systems studied, and the order of selectivity was somewhat different from that observed for gramicidin A in a conventional BLM. This presumably reflects the differing conductivity responses of the reservoirs to the range of monovalent cations tested. Of the four reservoir types, the All-ether and C-11 membranes had cation selectivity profiles closer to those of gA in a BLM with preference for larger ions.25 The results of these investigations can be considered in terms of the following factors: (i) the two-dimensional packing density of the reservoir components; (ii) the chemical nature of the tethers effect on the ionic conduction and selectivity of the membrane; (iii) the response of membrane conduction to increasing bulk ionic concentration showing saturation behavior similar to that reported for electrolytes in nonaqueous solvents and conducting polymer matrixes. (a) Effect of Spacer Groups. Including the spacer species in Succinate membranes allows examination of packing constraints on membrane conduction. The conduction in the unspaced Succinate system was taken as unit conduction for each ionic species. The magnitude of conduction in the spaced membranes was expressed as multiples of the conduction observed in the unspaced system for each ionic species compared. The maximum conductance range across all ions varies between 2- and 3-fold at 1 M concentration in the bulk solution, for the spaced and unspaced Succinate reservoir types (Figure 6A-D). The selectivity range declined somewhat as the ionic concentration increased. The spacer induced conduction enhancement for the ion species (1 M bulk) was reflected in the following sequence: Cs (2.8) > K (2.7) > Na (2.2) > Li (2.04). The use of spacers improved the magnitude of the membrane conduction for a given external salt concentration, but the Λ0exp data from Figure 8 show that, somewhat surprisingly, the actual ionic mobility in the reservoir was not significantly altered (at least for Na+ in the Succinate systems examined). This effect was only weakly dependent on the ion type (i.e. averages ∼2.5 times here), as seen above. (b) Chemical Structure of the Reservoir. The succinate membrane and the all-ether membrane are structurally similar and had no additional spacers. They represented the two performance extremes of the membrane systems examined and differ in the chemical nature of the linkers, with the succinate linkers having four additional carbonyl groups along the polyether reservoir chains (Figure 3). Again, expressing the conduction in All-ether membranes for each ionic species as a multiple of the corresponding conduction observed in succinate membranes, the ratio of the conduction (1 M) of the two reservoirs is in the following order: NH4 (42) > Cs (23) > Na (14) > K (13) > Li (4). Ignoring the closeness in the responses of Na+ and K+ ions, this follows the selectivity series of gA in a free BLM14,25 and appears to be inversely proportional to the hydrated radii of the metal ions. In this investigation we have used biotinylated gA. We
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observed no significant difference between biotinylated gA in BLMs or tBLMs, thus allowing us to compare the results in tBLM with that reported for gA in free BLM.51 The performance differential showed much greater variation with ionic species than was the case above with spacer group introduction. This presumably reflects the capacity of the cations to specifically interact with polar carbonyl oxygens, as is believed to occur during ion passage through the conducting gA.46 Such polar interactions would be expected to impede ion mobility. (c) Conduction Saturation Behavior. The reservoir regions of the tethered membranes appeared to have high effective viscosities and moderately polar character. The apparent dielectric strengths, ∼ 50, are midway between those of water (80) and a polar alcohol like MeOH (32) and comparable to that of DMSO (47). The ionic mobilities inferred from the electrical response modeling were strongly concentration dependent, as seen in Figure 8. This dependence was much stronger than that predicted by the Onsager “ion atmosphere” approach, using the above values of the dielectric strengths deduced from the ion partitioning.2 Although these latter are model-dependent values, their magnitudes appear reasonable and internally consistent (as shown below). It is well-established43 that “small” ions in reduced dielectric media are liable to associate with sufficient strength to form effective “ion pairs”. A recent study42 of electrolyte-solvent-induced rotational friction on anionic dye molecules in both water and DMSO solutions found that ion-pairing effects were pronounced in the latter case and could quantitatively explain the solute concentration dependence of the rotational correlation times. Figure 8 shows that this is also the case here, with the inferred pairing association constants exhibiting an inverse correlation with the reservoir dielectric strength, as expected. The magnitudes of the Kass values, ∼70-800 M-1 for NaCl, were somewhat larger than for simple monovalent salts in a comparable dielectric strength solvent (DMSO, ) 47, Kass ∼ 20 M-1 for NaNO3) but of a generally similar order. Ion pairing is then the most likely explanation of the apparent “saturation” behavior of the membrane conduction response with increasing electrolyte concentration. At external electrolyte concentrations above ∼200 mM, most of the ions partitioning into the membrane reservoir regions are “locked up” in nonconducting pairs. A similar effect is seen in poly(ethylene oxide)-carboxylic acid alkali salt conducting polymers,41 which although anhydrous, resemble our reservoir regions chemically. These exhibit ionic conductivities in the range 10-4-10-6 S cm-1, similar to the ∼10-5-10-6 S cm-1 for our reservoir regions under typical operating conditions (i.e. ∼50 mM internal electrolyte concentration). The bulk conductivity of the polymer systems increases initially with the concentration of ionic species and then plateaus and in some instances drops with further increase in the total ion concentration similar to our observations. We have characterized tethered membrane reservoirs for use in practical applications. The four reservoirs provide researchers an opportunity to select the most suitable reservoir for a specific application. In our laboratories we found the higher conductivity of the Allether reservoir to be advantageous in improving the dynamic range of detection while developing immunoassays for sensing thyroid stimulating hormone. These reservoir-containing membranes may also be used with
Krishna et al.
other small ion channels such as free gramicidin or alamethicin, which will be the subject of a separate paper. Conclusion Ion conductance and selectivity were investigated in tethered bilayer membranes. A simple network model was found applicable, in which each gramicidin may be regarded as having its own reservoir domain, in electrical isolation from other channels and domains. The correspondence of the model with experimental data suggested that in tBLMs membrane conduction is determined principally by the number density of channels and much less by channel resistivity. This model was used to fit data and to extract reservoir resistivity values, which were found to be comparable to those of similar conducting polymers,39-41 under similar conditions and polar nonaqueous solutions. Below 100 mM, the conductance in tBLM increased rapidly in proportion to the bulk electrolyte concentrations and more gradually at higher concentrations. In addition, the conduction behavior could reach a state of saturation, dependent on the chemical nature of the reservoir. The probable basis of this effect is ion pairing in the reduced dielectric medium of the reservoir. Overall conduction in a tBLM was dominated by the reservoir behavior and was lower by an order of magnitude or more than would be expected for a BLM of similar gA channel density. The flow of ions was highest in membranes where tethering chains were formed with tetraethylene glycol groups with ether type linkages. Provision of two-dimensional spacing improved membrane conduction, by increasing ionic partitioning into the reservoir The ion selectivity in tBLMs was different from that reported for free BLM containing gA channels. The selectivity behavior could be altered to more closely resemble conventional BLM by replacing the ester type linkers with ether linkers. The presence of an 11-carbon passivation layer between the gold and the tethered reservoir, in addition, resulted in the ion selectivity being closest to that in a free BLM. Acknowledgment. The original research work was undertaken at the Cooperative Research Centre for Molecular Engineering and Technology. The authors acknowledge the support provided by peers, co-workers, and the Management of AMBRI Ltd in completing this work. The special chemicals synthesized by the Chemistry Group associated with the CRC program and AMBRI Ltd are appreciated. Nomenclature BLM ) Bilayer lipid membrane tBLM ) Tethered bilayer lipid membrane Ci ) Concentration of electrolyte Cm) Membrane capacitance Cres ) Ionic concentration in the reservoir DLP ) Double length phytanol (the first layer leaflet of the membrane attached to the reservoir chain) DPEPC ) Glycerol diphytanyl ether phosphatidylcholine (second layer lipid component of the membrane) r ) Dielectric constant of reservoir w ) Dielectric constant for aqueous buffer Λ ) Mobility Λexp ) Experimental ion mobility Λ0 ) Limiting mobility η ) Solvent medium viscosity gA ) Gramicidin A (used as tethered and free components) TgA ) Tethered gramicidin FgA ) Untethered/free/mobile gramicidin
tBLMs Containing Ionic Reservoirs GDPE ) Glycerol diphytanyl ether (second layer lipid component of the membrane) Gm ) Membrane conductance Km ) Dimerization association constant Kdep ) Partition coefficient MSL ) Membrane spanning lipid
Langmuir, Vol. 19, No. 6, 2003 2305 S ) Onsager slope T ) Temperature (297 K) Z ) Valency LA026238D
