AC Conductance of Transmembrane Protein Channels. The Number

Simultaneous measurements of the AC and DC conductances of α-hemolysin (αHL) ion channels and outer membrane protein F (OmpF) porins in dilute ionic...
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J. Phys. Chem. B 2007, 111, 9165-9171

9165

AC Conductance of Transmembrane Protein Channels. The Number of Ionized Residue Mobile Counterions at Infinite Dilution Eric N. Ervin,† Ryan J. White,† Treggon G. Owens,§ John M. Tang,‡ and Henry S. White*,† Department of Chemistry, UniVersity of Utah, 315 South 1400 East, Salt Lake City, Utah 84112, Electronic Bio Sciences, 5764 Pacific Center BouleVard, Suite 204, San Diego, California 92121, and Department of Molecular Biophysics and Physiology, Rush UniVersity Medical Center, 1750 West Harrison Street, Chicago, Illinois 60612 ReceiVed: March 5, 2007; In Final Form: May 6, 2007

Simultaneous measurements of the AC and DC conductances of R-hemolysin (RHL) ion channels and outer membrane protein F (OmpF) porins in dilute ionic solutions is described. AC conductance measurements were performed by applying a 10 mV rms AC voltage across a suspended planar bilayer of 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine in the absence and presence of the protein and detecting the AC current response using phase-sensitive lock-in techniques. The conductances of individual RHL channels and OmpF porins were measured in symmetric KCl solutions containing between 5 and 1000 mM KCl. The AC and DC conductances of each protein were in agreement for all solution conditions, demonstrating the reliability of the AC method in single-channel recordings. Linear plots of conductance versus bulk KCl concentration for both proteins extrapolate to significant nonzero conductances (0.150 ( 0.050 nS and 0.028 ( 0.008 nS for OmpF and RHL, respectively) at infinite KCl dilution. The infinite dilution conductances are ascribed to mobile counterions of the ionizable residues within the protein lumens. A method of analyzing the plots of conductance vs KCl concentration is introduced that allows the determination of the concentration of mobile counterions associated with ionizable groups without knowledge of either the protein geometry or the ion mobilities. At neutral pH, an equivalent of 3 mobile counterions (K+ or Cl-) is estimated to contribute to the conductivity of the RHL channel.

Introduction The use of transmembrane proteins as highly sensitive analyte-specific sensors is of great interest in the field of biotechnology and chemical sensing.1,2 In these measurements, specific interactions between a transmembrane protein, inserted in a lipid bilayer, and a target molecule are measured by the variation in the conductance of the protein. Transmembrane proteins have been used to detect a range of analytes that include small organic molecules,3 nucleic acids,4-6and monovalent cations.2 To date, the majority of protein conductance studies have been performed using direct current (DC). This method employs a constant voltage that is applied between two electrodes positioned on opposite sides of the lipid bilayer containing the protein, and the current within the protein is recorded as a function of time or slowly varying potential. Alternating current (AC) impedance analyses have been widely used to investigate the impedance of lipid bilayers deposited on metal surfaces.7-10 Recently, Wilkes et al. have employed AC lock-in amplifier techniques to measure the conductance of individual OmpF porins.11-13 There are several advantages in employing a small-signal (e.g., 10 mV rms amplitude) AC analysis of the protein’s conductance in comparison to the conventional DC measurement. First, and from a pragmatic view, the DC measurement requires nonpolarizable * To whom correspondence should be addressed. E-mail: white@chem. utah.edu. † University of Utah. § Electronic Bio Sciences. ‡ Rush University Medical Center.

electrodes (e.g., Ag/AgCl electrodes) to provide DC currents across the membrane. This experimental requirement is relaxed in the AC measurement, because charging and discharging of the electrode double layer14 of polarizable electrodes (e.g., Pt) is generally sufficient to provide the AC voltage perturbation, as in the case of classical conductance measurements in bulk solutions. In addition, by using phase-sensitive detection, AC measurements provide higher signal-to-noise ratios (SNR) and can be more effective in the presence of large noise sources than a DC measurement.15,16 AC measurements may also provide significant advantages in fundamental investigations of transmembrane proteins, a consequence of being able to use smaller electrical perturbation than those currently employed in conventional DC analyses. In the typical DC measurement, a 50-100 mV bias is applied across a bilayer that is 5 nm thick, generating a high electric field on the order of 10-20 MV/m. Electric fields of this magnitude are sufficiently large to cause electrostatic elastic deformation of the protein,17,18 influence protein-molecule binding kinetics,19,20 and greatly influence molecule and ion transport rates (due to electrophoresis and electroosmosis adjacent to and through the protein).21 Reducing the magnitude of the DC voltage is possible, but at the expense of greatly reduced SNR. Although a finite electric field across the membrane layer is required in all transmembrane conductance measurements, the low-noise AC techniques using smallamplitude signals can potentially and significantly reduce these adverse effects. In the present work, we have explored the use of AC lock-in methods, following the lead of Wilkes et al.,11-13 as a viable

10.1021/jp071785z CCC: $37.00 © 2007 American Chemical Society Published on Web 06/28/2007

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Figure 1. Schematic of bilayer chamber and instrumentation used in the dual AC/DC conductance measurements.

Ervin et al. the unfiltered AC current (iac) from the potentiostat was returned to the lock-in amplifier, analyzed by phase-sensitive detection and synchronously filtered. Dual AC/DC conductance measurements were performed by superimposing a DC bias from the potentiostat onto the AC signal. The DC current required to maintain the DC bias was passed through a built-in 3 kHz threepole Bessel filter. The time constant of the lock-in was set to 10 µs. Both AC and DC signals were recorded simultaneously at a rate of 10 Hz by collecting 10 000 samples/s and averaging 1000 samples/pt using in-house LabVIEW (National Instruments) written programs. Results

means to measure the conductivity of transmembrane proteins supported in a lipid bilayer. The specific goals of this work are (i) to characterize the influence of the membrane reactance (associated with capacitive charging of the bilayer) on protein conductance measurements, (ii) to explore the similarities or differences in the AC and DC conductivities, and (iii) to use the AC analysis to determine the limiting conductances of transmembrane proteins at infinite electrolyte dilution. Two wellstudied transmembrane proteins, OmpF and RHL, have been used in these investigations because their DC conductances are well established and serve as benchmarks for AC analyses. Materials and Methods Chemicals and Materials. KCl (Mallinckrodt), K2HPO4‚ 3H2O (Mallinckrodt), and KH2PO4 (Mallinckrodt) were used as received. All solutions were prepared using H2O of resistivity greater than 18 MΩ‚cm from a Barnstead E-pure water purification system. 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) (Avanti) obtained in chloroform was dried under a nitrogen stream and diluted to a concentration of 10 mg/mL in decane (Aldrich). OmpF porin (1 µg/mL) was obtained in 1.0% n-octylpolyoxyethylene, 1 M KCl, buffered at pH 7.4 with 10 mM potassium phosphate buffer (PPB) as a generous gift from Rush University Medical Center. RHL (Aldrich) was used as received and diluted to 3 µg/mL in 1 M KCl, 10 mM PPB (pH ) 7.4). Conductance Measurements. A schematic diagram of the bilayer chamber and instrumentation for dual AC/DC conductance measurements is shown in Figure 1. The bilayer chamber and cup (both made from Delrin, a hydrophobic acetal resin) were purchased from Warner Instruments (Hamden, CT). The cup and bilayer chamber form a two-compartment cell, separated by a cylindrical hole with a length of 250 µm and a diameter of 150 µm. POPC bilayers were formed across the hole using a painting method.22,40 First, an ∼2 µL solution of POPC in decane was spread around the hole to prime the surface for painting the bilayer. This solution was allowed to dry for ∼10 min. The cup was inserted into the bilayer chamber, which was mounted above a stir plate. Two Ag/AgCl electrodes (Bioanalytical Systems, Inc.) were inserted into the individual cell compartments, each filled with electrolyte solution to equal heights to minimize hydrostatic pressure across the membrane. A second ∼2 µL volume of POPC dissolved in decane was then spread over the surface near the hole, and a fine gel-loading pipet tip was employed to paint the POPC lipid across the hole. The AC conductance across the lipid bilayer was measured by applying a 10 mV rms signal (Vin) between the two Ag/ AgCl electrodes from a digital lock-in amplifier (R810, Stanford Research Systems) interfaced to a potentiostat (Dagan ChemClamp voltammeter/amperometer). A voltage proportional to

As discussed in the Introduction, a motivation for using a small AC signal (e.g., 10 mV rms) to measure channel conductance is to avoid the potential adverse effects that a larger DC bias can have on the measurement and interpretation of analyte binding kinetics in sensor applications. AC measurements may also offer higher sensitivity and faster time resolution in single-channel recordings. Because our current goal is to develop the AC methodology and to investigate the conductance of transmembrane proteins in very dilute (low salt concentration) solutions, we first present a brief description of the frequency response of the AC signal of supported lipid bilayers. Specifically, we demonstrate that the conductance of the protein can be directly obtained from the step changes in AC current upon protein insertion, even when these conductances are comparable in magnitude to the frequency-dependent reactance associated with the bilayer capacitance. Next, the AC and DC conductances (G, Ω-1) of OmpF and RHL in symmetric KCl solutions ranging in concentration from 5 to 1000 mM are reported. Here, plots of G versus the bulk KCl concentration, Cbulk, exhibit significant nonzero intercepts, corresponding to the infinite dilution conductance of the proteins. These results are in good agreement with the work done by Green et al. and Banach et al., in which surface charge influences the conductance of protein channels.23,24 In the Discussion Section, a method of analyzing the G vs Cbulk plots is introduced that allows the determination of the concentration and number of mobile counterions associated with ionized protein residues without knowledge of either the protein geometry or the ion mobilities. AC Frequency Response of the Bilayer Membrane. The impedance (Z) of the lipid bilayer is expressed as the parallel combination of the membrane resistance, Rm, and the frequencydependent reactance ((2πfCm)-1), the latter associated with membrane capacitance, Cm.

Z-1 ) Rm-1 + 2πfCm

(1)

In eq 1, f is the frequency of the applied small-amplitude AC voltage. For POPC bilayers suspended across the 150-µmdiameter aperture of the Delrin cup, Rm is ∼100 GΩ (or larger) and Cm ∼ 40 pF, consistent with values reported by other laboratories.27,35 In the experiments reported herein, Rm and Cm are evaluated for each bilayer film from the current-voltage response to a linear voltage ramp (10-100 mV/s) applied between the two Ag/AgCl electrodes (data not shown). For values of f > 1 Hz, the capacitive reactance of the POPC bilayer is comparable to or significantly smaller than the membrane resistance (i.e., (2πfCm)-1 e Rm). Thus, the AC current measured in the absence of a high-conductance channel contains a significant (or dominant) component from the bilayer capacitance. For instance, at f ) 10 Hz, the reactance, (2πfCm)-1, of a 40 pF membrane is 0.4 GΩ, corresponding to 0.4% of Rm

AC Conductance of Transmembrane Protein Channels (∼100 GΩ)). Thus, the observed AC current in the absence of an RHL channel or OmpF porin is dominated by the membrane reactance. This point is of critical importance in the analysis of bilayer and protein AC conductance measurements and is explored in more depth in the following paragraphs. Equation 1 also describes the membrane impedance after a pore or channel inserts into the bilayer membrane. In this case, Rm is associated with the channel resistance, which is ∼1 GΩ for RHL and ∼0.25 GΩ for OmpF in 1 M KCl solutions. Thus, following protein insertion, the capacitive reactance (2πfCm)-1 is comparable to Rm, and both the ion flux through the channel or pore and the membrane charging contribute significantly to the observed impedance in the AC measurement. (Formally, “admittance” should be used in place of “conductance and susceptance” in describing the AC response; by using only the real component of the AC response and for simplicity in comparing the experimental AC and DC responses, the term “conductance” will be used hereafter for both responses.) For example, at f ) 10 Hz, the observed AC conductance across a 40 pF bilayer containing one RHL results from the ion flux through the channel (representing ∼29% of the total conductance, eq 1) and charging of the bilayer membrane (71%). At higher frequencies, a larger fraction of the AC conductance is associated with the membrane capacitance. Equation 1 predicts that Z ) Rm as f f 0 and Z ) (2πfCm)-1 as f f ∞. For the POPC bilayer (Cm ∼ 40 pF and Rm∼100 GΩ), the transition frequency between these limiting behaviors occurs at 0.04 Hz () (2πRmCm)-1). Thus, for all practical frequencies required for reasonable data acquisition rates (e.g., >1 Hz), the AC response contains a significant conductance from the membrane capacitance. The significant contribution of the membrane charging current makes the interpretation of the AC measurement slightly more complicated than the analogous DC measurement. In the DC measurement, the observed change in conductance upon insertion of protein is due solely to the change in Rm. Since Rm decreases from ∼100 GΩ to ∼1 GΩ upon protein insertion, the observed steplike increase in conductance appears above a near-zero conductance background. For instance, for a 100 mV DC voltage, the DC current increase from ∼1 to ∼100 pA upon insertion of RHL in a 1 M KCl solution (vide infra). In the AC measurement at 10 Hz, the membrane reactance of 0.4 GΩ for a 40 pF bilayer is already smaller than the 1 GΩ resistive pathway offered by the protein. Thus, the steplike change in iac upon protein insertion is observed above the significant background current from the lipid bilayer. For a 10 Hz, 10 mV rms AC voltage, iac increases from 25.0 to 35.0 pA upon protein insertion, corresponding to a 40% increase above the background. Although the large background signal is undesirable, the steplike change in conductance in the AC measurement is still exactly proportional to the conductance of the protein. In the previous example, the 10 pA increase in (from 25.0-35.0 pA) is readily measured with lock-in amplifier techniques and used to compute the (correct) value of the protein resistance (10 mV/ 10 pA ) 1 GΩ). In practice, the analyses are greatly simplified by recording only the real component of the AC current, iac (0°). Because Rm and the membrane reactance are in parallel, iac (0°) is given by Ohm’s law, iac (0°) ) Vac/Rm and, ideally, does not contain any interfering baseline (i.e., the current measured when only a bilayer is present) contributions from the membrane reactance. Thus, assuming that there are no inherent differences in the AC and DC conductances of a protein, the experimental traces of G vs t in a 1 M KCl solution

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Figure 2. In-phase AC response (iac (0°)) across a POPC bilayer as a function of frequency (a) between 0 and 500 Hz. The gray diamonds were obtained in response to a 10 mV rms, applied between two Ag/ AgCl electrodes separated by a POPC bilayer in a 1 M KCl, 10 mM PPB (pH 7.4) solution. The solid line in (a) represents iac (0°) of the equivalent electric circuit shown in (b). The lipid bilayer is represented by a parallel RmCm combination (Rm ) 100 GΩ and Cm ) 40 pF), and C1 (25 pF) and R1 (1 MΩ) are associated with the current-to-voltage converter. Rs is the sense resistor (1 Ω) used to compute iac (0°) in equivalent circuit.

should exactly track the DC G vs t traces, with step changes in G observed above a near-zero baseline for both measurements. This expectation is experimentally observed (vide infra). Figure 2A shows a plot of iac (0°) response to a 10 mV rms signal across a POPC bilayer membrane (without protein) for 0 < f < 500 Hz. For an ideal parallel RmCm circuit, iac (0°) should be independent of f and equal to a value computed by Ohm’s law, iac (0°) ) Vac/Rm. This is clearly not observed in the data of Figure 2A, which shows a pronounced upward curvature over the entire frequency range. This nonideal behavior is due to the input impedance of the i/V converter of the potentiostat, which is modeled as a parallel combination of resistor and capacitor. The latter elements have values on the order of 25 pF and 1 MΩ, respectively. An equivalent circuit that captures the essential features of the frequency response is shown in Figure 2B, where R1 and C1 represent the input resistance and capacitance of the potentiostat and Rs ()1 Ω) is used to compute the simulated current in the circuit. The frequency response of the equivalent circuit was computed using the electrical circuit simulator, SwCADIII, and is shown as the solid line in Figure 2A. The agreement between the experimental and simulated frequency response is quite reasonable and can be improved by slight adjustments to the values of Rm, Cm, R1, and C1. Since the values used for the instrumental C1 (25 pF) and R1 (1 MΩ) elements are only approximately known, a refined fitting to the data is not warranted. Although iac (0°) contains a reactive component due the instrumental and other stray impedances, the absolute value of iac (0°) is small at frequencies below 10 Hz. For the data in Figure 2A, iac (0°) ) 0.6 pA at 10 Hz, which is less than 1% of the corresponding value expected upon insertion of a 1 GΩ RHL channel (∼100 pA) in a 1 M KCl solution. However, for

9168 J. Phys. Chem. B, Vol. 111, No. 30, 2007 measurements in less concentrated solution, the channel resistance increases significantly, and the nonideal reactance associated with the instrument impedance introduces a significant contribution to the iac (0°), even at low frequencies. For example, when the KCl concentration is lowered from 1 M to 10 mM, resulting in an ∼100-fold decrease in RHL channel conductance, the expected increase in iac (0°) upon protein insertion is only ∼1 pA, comparable to the 0.6 pA baseline current due to the nonideal reactance. The experimentally measured values of iac (0°) and G presented below are entirely consistent with these predictions. The key points of the above analysis are (i) the bilayer can be reasonably modeled as a parallel RmCm component; (ii) the AC conductance is readily understood in terms of the equivalent circuit of the measurement system; (iii) in the absence of a highconductance RHL channel or OmpF porin, the AC current contains a significant contribution from capacitive charging of the bilayer membrane; (iv) in concentrated electrolyte solutions, the real component of the AC current, iac (0°), at low frequencies is proportional (to within 1%) to the conductance of the protein; and (v) in dilute solutions, the baseline nonideal reactive component of iac (0°) (and thus G) must be subtracted from the observed values to obtain the correct protein conductance. Thus, as long as the step changes in current associated with the protein are measurable above the noise, the background iac does not present any additional challenges in analysis of the protein conductance. Specifically, the protein conductance computed from the AC signal above the finite background is performed in an identical manner to that of the conventional DC measurement. This conclusion is expected to include situations in which the protein conductance varies in response to binding to solution analytes. rHL Conductance. RHL is an ion channel secreted from Staphylococcus aureus. The protein comprises seven identical polypeptides (293 residues) that form a mushroom-shaped pore. The protein measures ∼10 nm in length.25 The cap region is ∼5.0 nm long and ∼10 nm in diameter and sits above the lipid bilayer. An ∼5.0-nm-long, β-barrel region (∼2 nm opening diameter) extends through the lipid bilayer.26 RHL can transport molecules up to 2 kDa across the lipid bilayer.27 The pore is known to be slightly anion-selective and contains a 1.4-nmdiameter constriction at the top of the β-barrel region, about halfway down the lumen of the pore.28 The constriction region contains seven negative glutamic acids above seven positive lysines.3,29 The DC conductance of RHL has been extensively investigated.2-6 Figure 3 shows representative AC (black) and DC (gray) G vs t traces, acquired simultaneously, showing the insertion of two RHL channels. A 10 mV rms, 10 Hz signal is superimposed on a -50 mV DC bias between the two Ag/AgCl electrodes in a 1.0 M KCl, 10 mM PPB (pH ) 7.4) solution. At t ) 0 s, only the POPC bilayer is present with a measured AC and DC conductance of ∼0.010 nS. At t ) 68 s, a single RHL channel inserts into the bilayer, creating a conductive pathway across the bilayer with G ∼ 0.9 nS, in good agreement with the value of ∼ 1 nS reported in the literature.2,5 At t ) 108 s, a second RHL inserts into the bilayer, and the conductance jumps to ∼1.7 nS. The AC and DC conductances of RHL 1 M KCl, 10 mM PPB (pH 7.4) measured in at least seven different experiments using different bilayers and proteins were determined to be 0.95 ( 0.08 nS and 0.89 ( 0.09 nS, respectively. As discussed above, the AC and DC G vs t traces for RHL in 1 M KCl are expected to be nearly identical, with near-zero baseline values. This prediction is confirmed by the results

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Figure 3. Simultaneous AC/DC measurements of the protein conductance as a function of time, showing the insertion of two RHL channels. The gray trace represents the DC response (Vdc ) -50 mV), and the black trace represents the AC response (Vac ) 10 mV rms at 10 Hz). The data were acquired in a 1 M KCl, 10 mM PPB (pH 7.4) solution.

Figure 4. Simultaneous AC/DC measurements of the protein conductance as a function of time before and after insertion of RHL in (a) 100 mM and (b) 20 mM KCl solutions. The gray trace represents the DC response (Vdc ) -50 mV), and the black trace represents the AC response (Vac ) 10 mV rms at 10 Hz).

shown in Figure 3. At lower KCl concentrations, the G vs t traces from both the DC and AC measurements exhibit significant baselines prior to protein insertion. Figure 4 shows G vs t traces for RHL measured in 100 mM and 20 mM KCl solutions. As expected, the baseline conductance value increases with decreasing electrolyte concentration and represents a significant fraction of the total conductance at the lower concentrations. The larger baseline conductance observed in the AC measurement is due to the capacitive charging of the bilayer and the nonideal instrumental reactances, as described above. However, in both the AC and DC measured traces of G vs t, the protein conductance is simply proportional to the change in current as the protein inserts into the bilayer, which is readily measured above the baseline value. Figure 5 shows a plot of G vs Cbulk for KCl concentration ranging from 10 to 100 mM KCl. Conductance values are

AC Conductance of Transmembrane Protein Channels

Figure 5. Conductance of RHL as a function of bulk KCl concentration (Cbulk). The gray squares and black triangles represent, respectively, the DC (Vdc ) -50 mV) and AC measurements (Vac ) 10 mV rms at 10 Hz). The dashed line represents a fit of the data using eq 4 (see text).

calculated using Ohm’s Law, which assumes linear i-V curves. As previously reported, transmembrane proteins (RHL and OmpF) exhibit current rectification,30-32 that increases roughly in inverse proportion to electrolyte concentration. In our experiments, nonlinear i-V curves were observed across both RHL and OmpF at KCl concentrations below 100 mM. However, the DC conductance measured at negative potentials (-100 or -50 mV) is only slightly smaller (within 20%) than that at positive potentials. Since the standard deviations in the slope and intercept of conductivity vs concentration curves encompass this deviation, the smaller error due to current rectification is ignored. Below 10 mM KCl, the conductance associated with the protein could not be measured due to the measurement noise. The linear dependence of conductivity on concentration extends up to 1.0 M KCl. The intercept and slope of this line are 0.028 (( 0.008) nS and 0.85 (( 0.09) nS/M-1, respectively. OmpF Conductance. OmpF is a porin found in the outer membrane of Escherichia coli. These proteins consist of three identical polypeptides (340 residues) that combine to form three 16-stranded β-barrels that extend through a lipid bilayer.33,34 The protein is ∼4.0 nm long and contains three distinct waterfilled channels that are ∼1.2 nm in diameter.35 Each channel can transport molecules up to 600 Da.36 The pore is known to be slightly cation-selective37and contains a constriction zone halfway down the lumen of each channel. The oval-shaped constriction zone (∼0.7 × 1.1 nm) contains three positively charged arginines on one side and negatively charged aspartate and glutamate on the other side.38-40 OmpF is well-known for its distinctive voltage gating characteristics in which each trimer can independently open and close.41 Figure 6 shows representative AC (black) and DC (gray) G vs t traces showing the insertion and subsequent voltage gating of two OmpF porins. In this experiment, a 10 mV rms, 10 Hz signal was superimposed on a -100 mV DC bias across a POPC bilayer in a 1.0 M KCl, 10 mM PPB (pH 7.4) solution. At t ) 0 s, only the bilayer is present, and the AC and DC conductances are ∼0.010 nS. At t ) 58 s, one OmpF porin inserts into the bilayer with all channels open, yielding a conductance of ∼3.9 nS, in good agreement with the value of 4.2 ( 0.12 nS reported in the literature.40 At t ) 90 s, a single channel closes, yielding g ∼ 2.8 nS and at t ) 125 s, a second OmpF porin inserts into the lipid bilayer. This insertion is followed by the additional closing of three single channels (out of the six total channels comprising the two OmpF porins). As is clearly apparent in

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Figure 6. Simultaneous AC/DC measurements of the conductance as a function of time, showing the insertion and subsequent voltage gating of two OmpF porins. The gray trace represents the DC response (Vdc ) -100 mV), and the black trace represents the AC response (Vac ) 10 mV rms at 10 Hz). The data were acquired in a 1 M KCl, 10 mM PPB (pH 7.4) solution.

Figure 7. Conductance of OmpF as a function of bulk KCl concentration (Cbulk). The gray squares and black triangles represent, respectively, the DC (Vdc ) -100 mV) and AC measurements (Vac ) 10 mV rms at 10 Hz). OmpF conductances correspond to the protein with all three channels open. AC/DC data where acquired simultaneously in symmetrical KCl solutions. The solid line is simply to guide the eye.

Figure 6, the AC and DC conductances of the proteins track each other very well in 1 M KCl solutions. The AC and DC conductances of the OmpF trimer in at least five different experiments using different proteins and bilayers were determined to be 3.8 ( 0.2 nS and 4.1 ( 0.2 nS, respectively, in 1 M KCl, 10 mM PPB (pH 7.4). Figure 7 shows the AC (black triangles) and DC (gray squares) conductances of the OmpF trimer as a function of bulk electrolyte concentration, Cbulk, from 5 mM to 100 mM KCl. Each point represents a minimum of three different experiments using different bilayers and proteins. Similar to the results in the 1 M KCl solution, the agreement between DC and AC conductances is reasonable over the entire concentration range. Below 5 mM, the conductance jump associated with protein insertion could not be measured because the increase in conductance was within the noise of the measurement. The linear dependence of conductivity on concentration extends up to 1.0 M KCl. The intercept and slope of this line are 0.15 (( 0.05) nS and 5.4 (( 1.3) nS/M-1, respectively. Discussion Protein Conductance at Infinite Dilution. Figures 5 and 7 show that the conductances of both OmpF porins and RHL channels extrapolate to nonzero values as the concentration of KCl approaches zero. The extrapolated values of G are significant, representing ∼20% of the values in 0.1 M KCl

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solutions. The infinite dilution conductances of the protein channels result from mobile electrolyte counterions associated with the ionizable residues of the protein.23,24,42,43 Thus, the total conductance of the channel, in the presence of solutions containing KCl, arises from the residue counterions plus those additional K+ and Cl- that reversibly partition between the bulk solution and interior of the protein. Partitioning of ions between the bulk solution and channel interior is clearly evident by the linear increase in conductance with increasing bulk KCl concentration (Cbulk), employing the implicit assumption that the channel conductance is proportional to the total charge carrier concentration inside the protein and that the mobilities of the ions are relatively concentrationindependent. Brownian dynamics simulations have shown that the number of K+ and Cl- ions inside RHL normalized to the bulk KCl concentration is approximately constant (∼22.9 K+ and 23.2 Cl-/Cbulk) for Cbulk between 0.4 and 2.0 M.44 Ignoring the slight difference in the numbers of K+ and Cl- ions and using the reported interior volume of 56 nm3 for RHL,45 the partition coefficient of KCl between the bulk solution and interior of the protein, κKCl ) Cp/Cbulk, is computed to be to 0.68. Thus, the concentration of KCl in the interior solution of the protein is ∼68% of the bulk solution value for Cbulk between 0.4 and 2.0 M. At lower Cbulk, between 0.1 and 0.4 M, the Brownian dynamics simulations show a slight nonuniform increase in the numbers of K+ and Cl- ions inside the channel relative to the bulk KCl concentration, a consequence of the number of ions being determined by the number of ionized residues and, thus, independent of Cbulk. The conductance of a channel is given by

G ) F(Vp/dp2)(Σ|zi|Ciµi)

(2)

where µi, Ci and zi represent the mobility, concentration, and charge, respectively, of the ith mobile species. F is Faraday’s constant, and Vp and dp are the volume and length, respectively, of the channel. The linearity and nonzero intercepts of the plots of G vs Cbulk suggest that eq 2 may be expanded into separate terms for the counterion conductance and the conductance due to additional K+ and Cl- that partition into the lumen from the bulk solution. In doing so, we assume the number of counterions is independent of Cbulk, whereas the number of additional ions that partition into the lumen is determined by κKCl ) Cp/Cbulk. This assumption allows eq 2 to be written explicitly in terms of the individual contributions of the counterions, K+ and Clconductances.

G ) F(Vp/dp2)(Σ|zci|Cciµci + |zCl|κKClCbulkµCl + |zK|κKClCbulkµK) (3) Equation 3 can be simplified by the reasonable assumption that the identity of all counterions correspond to either K+ or Cl-, since the latter two species are present in essentially infinite solution, and by noting that µCl(7.9 × 10-4 cm2 s-1 V-1) ∼ µK(7.6 × 10-4 cm2 s-1 V-1)() µKCl) and that |zK| ) |zCl| ) 1.

G ) F(Vp/dp2)(CciµKCl + 2κKClCbulkµKCl)

(4)

Equation 4 indicates that a plot of G vs Cbulk should be linear with a slope (S) ) F(Vp/dp2)(2κKClµKCl) and an intercept (I) ) F(Vp/dp2)(|zci|Cciµci). The ratio of the measured intercept and slope, I/S,

I/S ) (Cci/2κKCl)

(5)

can be thus be used to determine the concentration of counterions associated with the ionized residues. From the plot of G vs Cbulk in Figure 5 for RHL, I ) 0.028 ( 0.008 nS and S ) 0.85 ( 0.09 nS/M-1. Using κKCl ) 0.68 (vide supra) yields Cci ) 0.045 ( 0.012 M for residue counterions that contribute to the channel conductance. From this value and using Vp ) 56 nm3 for RHL, the number of mobile counterions, Np, inside the lumen is readily computed from the expression Np ) (2 ions/molecule)(Cci)(Avogadro’s number)(Vp)) and found equal to 3.0 ( 1.0. Using the experimentally determined value of Cci, eq 4 was fit to the G vs Cbulk data in Figure 5 (dashed line). A value of µci ∼ 1.2 × 10-4 cm2 s-1 V-1 was assumed, along with the literature values of κKCl, Vp, and dp noted above, yielding an excellent fit of the eq 4 to the plot of G vs Cbulk. The value of 1.2 × 10-4 cm2 s-1 V-1 is a factor of 7 smaller than the mobilities of K+ and Cl- in bulk solution (µ ∼ 7.7 × 10-4 cm2 s-1 V-1). However, previous computer simulations suggest that the mobility of ions within the protein lumen is lower than that in bulk solution.44 Aksimentiev and Schulten recently reported that electrophoretic mobility of K+ ions in RHL is ∼7-20 times smaller than in bulk solution.17 Thus, the smaller value of µci used to fit eq 4 to the data seems quite reasonable. Analogously, from the plot of G vs Cbulk in Figure 4 for OmpF, I ) 0.15 ( 0.05 nS and S ) 5.4 ( 1.3 nS/M-1. Although the linearity of the plot in Figure 7 suggests that κKCl for OmpF is relatively constant, we are not aware of reported values of κKCl for OmpF and at this time cannot extract values of Cci or Np. The I/S ratio for OmpF (0.029 ( 0.009 M) corresponds to κKClCci ) 0.057 ( 0.018 M, from which Np can be determined in the future when κKCl is known. Np ∼ 3 for RHL indicates that approximately three mobile counterions inside the lumen contribute to the conductance of this protein. It is remarkable that of the 14 potentially ionized residues within the “constriction region”, only a few have mobile counterions associated with them, the remainder of which must form salt bridges. The chemical identity (K+ or Cl-) and their association with specific ionized residues cannot be ascertained from the conductance data presented here. Of fundamental significance to the implementation of protein based biosensors, however, is the finding that a small number of residue counterions provide sufficient conductance to allow sensing applications in very low ionic strength solutions. The conductances of RHL and OmpF measured at the lowest bulk KCl concentration employed in this study (5 mM in Figure 5 and 10 mM in Figure 7) are primarily due to the residue counterion conductance rather than the conductances arising from K+ or Cl- that enters the channel from the bulk solution. This suggests that these proteins can be used in dilute ionic solutions, expanding their applications in sensing applications. The finite intercept of the G vs Cbulk plots also suggests that the protein conductance should level off and remain constant at sufficiently small values of Cbulk. The concentration at which this occurs corresponds to the situation in which K+ and Clentering the pore no longer significantly contribute to the pore conductance. This limiting behavior has been recently observed in synthetic nanopores in glass, where the counterion conductance associated with the fixed glass surface charge becomes the dominant contributor to ion flow.46-48 Presently, in our experiments, the significant uncertainty in values of G (see error bars in Figures 5 and 7) prevents observation of the leveling off of the conductance. However, the bulk KCl concentration at which the leveling off will occur can be anticipated by assuming that the conductance will be dominated by residue

AC Conductance of Transmembrane Protein Channels counterions when these counterions represent >90% of the total number of mobile ions in the channel. The measured residue counterion concentration of 45 mM in RHL, coupled with the partition coefficient, κKCl, of ∼0.68, yields an anticipated value of Cbulk ∼6 mM. Below this value, the conductance is expected to level off and be dominated (>90%) by the residue counterions. High-precision, low-noise measurements should allow this region to be explored in the future. As a final note, the contribution to the protein conductance arising from the dissociation of H2O is clearly negligible in the neutral pH solutions. Even after accounting for any reasonable perturbation of the dissociation equilibrium of H2O within the protein interior, the concentrations of H+ and OH- (on the order of 10-7 M) are orders of magnitude smaller than that of the counterion concentrations at infinite dilution (10-3 - 10-2 M). Conclusion In agreement with the recent reports of Wilkes et al.,11-13 our results demonstrate that AC phase-sensitive measurements are effective in measuring the conductivity of transmembrane protein pores. With the appropriate choice of frequency, the conductance of a transmembrane protein can be directly computed from the in-phase component of iac. This application is potentially useful in the field of biosensors, in which protein pores are used as stochastic sensors for various analytes.2 For instance, a small-amplitude AC measurement in the absence of a DC voltage can be used to limit the effects of electroosmosis and electrophoresis on the binding kinetics between a membrane channel and analyte. Thus, stochastic counting rates can potentially be explored without interferences from DC biases. We have measured the limiting conductances of OmpF and RHL at infinite ion dilution. The infinite dilution conductances of these proteins are significant, contributing ∼20% to the total conductance in a 0.1 M KCl solution. Methodology has been introduced that allows the concentration of residue counterions to be determined from conductance plots without a priori knowledge of the protein geometry or ion mobilities within the channel. This method should be generally useful for investigating the infinite dilution conductance of other transmembrane channels. Acknowledgment. This research was supported by the Defense Advanced Research Project Agency. References and Notes (1) Panchal, R. G.; Smart, M. L.; Bowser, D. N.; Williams, D. A.; Petrou. Curr. Pharm. Biotechnol. 2002, 3, 99-115. (2) Bayley, H.; Cremer, P. Nature 2001, 413, 226-230. (3) Gu, L.; Braha, O.; Conlan, S.; Cheley, S.; Bayley, H. Nature 1999, 398, 686-690. (4) Nakane, J.; Wiggin, M.; Marziali, A. Biophys. J. 2004, 87, 615621. (5) Deamer, D. W.; Branton, D. Acc. Chem. Res. 2002, 35, 817-825. (6) Howorka, S.; Cheley, S.; Bayley, H. Na. Biotechnol. 2001, 19, 636639. (7) Romer, W.; Steinem, C. Biophys. J. 2004, 86, 955-965. (8) Terrettaz, S.; Vogel, H. Surf. Sci. Nanotechnol. 2005, 3, 203-206. (9) Drexler, J.; Steinem, C. J. J. Phys. Chem. B 2003, 107, 1124511254. (10) Becucci, L.; Monicelli, M. R.; Guidelli, R. Langmuir 2006, 22, 1341-1346.

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