Simultaneous Alternating and Direct Current Readout of Protein Ion

Anal. Chem. 2008, 80, 2069-2076

Simultaneous Alternating and Direct Current Readout of Protein Ion Channel Blocking Events Using Glass Nanopore Membranes Eric N. Ervin,†,‡ Ryuji Kawano,† Ryan J. White,†,§ and Henry S. White*,†

Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112

Alternating current (ac) phase-sensitive detection is used to measure the conductance of the ion channel r-hemolysin (rHL), while simultaneously applying a direct current (dc) bias to electrostatically control the binding affinity and kinetics of charged molecules within the protein lumen. Ion channel conductance was recorded while applying a 10-20 mV rms, 1-2 kHz bias across a single rHL protein inserted in a 1,2-diphytanoyl-sn-glycero-3-phosphocholine lipid bilayer that is suspended across the orifice (100-500 nm radius) of a glass nanopore membrane. Step changes in the ac ion channel conductance with a temporal response (t10-90) of 1.5 ms and noise amplitude of ∼2 pA were obtained using a low-noise potentiostat and a lock-in amplifier. These conditions were used to monitor the reversible and stochastic binding of heptakis-(6-O-sulfo)-β-cyclodextrin and a nine base pair DNA hairpin molecule to the ion channel. Alternating current methodology allows the binding kinetics and affinity between the protein ion channel and analyte to be investigated as a function of the dc bias, including ion channel conductance measurements in the absence of a dc bias. Stochastic single-molecule detection employing transmembrane protein channels embedded into planar lipid bilayers have applications in the medical, biotechnology, and chemical sensing fields.1 Specifically, there has recently been extensive studies in which the ion channel R-hemolysin (RHL) has been used to detect or measure the concentration of analytes ranging from metal ions to nucleotides.2-28 Protein/analyte interactions range in duration * Corresponding author. E-mail: [email protected] † University of Utah. ‡ Current address: Electronic Bio Sciences, 5754 Pacific Center Blvd. Suite 204, San Diego, CA. § Current address: Department of Chemistry and Biochemistry, University of California at Santa Barbara, Santa Barbara, CA. (1) Panchal, R. G.; Smart, M. L.; Bowser, D. N.; Williams, D. A.; Petrou, S. Curr. Pharm. Biotechnol. 2002, 3, 99-115. (2) Nakane, J.; Wiggin, M.; Marziali. A. Biophys. J. 2004, 87, 615-621. (3) Bayley, H.; Cremer, P. Nature 2001, 413, 226-230. (4) Neher, E.; Steinbach, J. H. Physiol. J. 1978, 277, 153-176. (5) Mathe, J.; Askimentiev, A.; Nelson, D. R.; Schulten, K.; Meller, A. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 12377-12382. (6) Sanchez-Quesada, J.; Ghadiri, M. R.; Bayley, H.; Braha, O. J. Am. Chem. Soc. 2000, 48, 11757-11766. (7) Jeon, T.; Malmstadt, N.; Schmidt, J. J. J. Am. Chem. Soc. 2005, 128, 4243. 10.1021/ac7021103 CCC: $40.75 Published on Web 02/23/2008

© 2008 American Chemical Society

of microseconds to tens of milliseconds and are typically measured by applying a 40-100 mV dc bias across the lipid bilayer to drive current through the protein channel. Analyte binding events are recorded as a transient decrease in channel conductance as the analyte binds to, or translocates through, the protein channel. Single ion channel recordings of protein/analyte interactions using alternating current (ac) methods, Figure 1A, offer a number of potential advantages in comparison to conventional dc measurements.29-32 First, the application of a dc bias across a lipid bilayer can alter the affinity and kinetics of analyte binding and translocation rates by a number of mechanisms. For instance, if (8) Schmidt, C.; Mayer, M.; Vogel, H. Angew. Chem., Int. Ed. 2000, 39, 31373140. (9) Braha, O.; Walker, B.; Cheley, S.; Kasianowicz, J. J.; Song, L.; Gouaux, J. E.; Bayley, H. Chem. Bio. 1997, 4, 497-503. (10) Kang, X.; Cheley, S.; Guan, X.; Bayley, H. J. Am. Chem. Soc. 2006, 128, 10684-10685. (11) Petermann, M. C.; Ziebarth, J. M.; Braha, O.; Bayley, H.; Fishman H. A.; Bloom, D. M. Biomed. Microdev. 2002, 4, 231-236. (12) Arial, Y.; Braha, O.; Bayley, H. J. Am. Chem. Soc. 2006, 128, 1705-1710. (13) Goodrich, C. P.; Kirmizialtin, S.; Huyghues-Despointes, B. M.; Zhu, A.; Scholtz, J. M.; Markoraov, D. E.; Movileanu, L. J. Phys. Chem. B 2007, 111, 3332-3335. (14) Kang, X.-f.; Cheley, S.; Rice-Ficht, A. C.; Bayley, H. J. Am. Chem. Soc. 2007, 129, 4701-4705. (15) Shim, J. W.; Gu, L. Q. Anal. Chem. 2007, 6, 2207-2213. (16) Braha, O.; Gu, L. Q.; Zhou, L.; Lu, X.; Cheley, S.; Bayley, H. Nat. Biotechnol. 2000, 18, 1005-1007. (17) Schmidt, J. J. Mater. Chem. 2005, 15, 831-840. (18) Kasianowicz, J. J. Dis. Markers 2002, 18, 185-191. (19) Nakane, J.; Akeson, M.; Marziali, A. Electrophoresis 2002, 16, 2592-2602. (20) Jung, Y.; Cheley, S.; Braha, O.; Bayley, H. Biochemistry 2005, 44, 89198929. (21) Kasianowicz, J. J.; Henrickson, S. E.; Weetall, H. H.; Robertson, B. Anal. Chem. 2001, 73, 2268-2272. (22) Gu, L. Q.; Cheley, S.; Bayley, H. Science 2001, 291, 636-640. (23) Deamer, D. W.; Branton, D. Acc. Chem. Res. 2002, 35, 817-825. (24) Kasianowicz, J. J.; Brandin, E.; Branton, D.; Deamer, D. W. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 12377-12382. (25) Astier, Y.; Braha, O.; Bayley, H. J. Am. Chem. Soc. 2006, 128, 1705-1710. (26) Kasianowicz, J. J.; Burden, D. L.; Han, L. C.; Cheley, S.; Bayley, H. Biophys. J. 1999, 76, 837-845. (27) Gu, L. Q.; Braha, O.; Conlan, S.; Cheley, S.; Bayley, H. Nature 1999, 398, 686-690. (28) Howorka, S.; Cheley, S.; Bayley, H. Nat. Biotechnol. 2001, 19, 636-639. (29) Wilk, S. J.; Petrossian, L.; Goryll, M.; Thornton, T. J.; Goodnick, S. M.; Tang, J. M.; Eisenberg, R. S. IEEE Sens. 2005, 2, 1165-1168. (30) Wilk, S. J.; Aboud, S.; Petrossian, L.; Goryll, M.; Tang, J. M.; Eisenberg, R. S.; Saraniti, M.; Goodnick, S. M.; Thornton, T. J. J. Phys.: Conf. Ser. 2006, 38, 21-24. (31) Wilk, S. J.; Petrossian, L.; Goryll, M.; Tang, J. M.; Eisenberg, R. S.; Saraniti, M.; Goodnick, S. M.; Thornton, T. J. Proc. Phys. 2006, 110, 201-204. (32) Ervin, E. N.; White, R. J.; Tang, J.; Owens, T.; White, H. S. J. Phys. Chem. B 2007, 111, 9165-9171.

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Figure 1. (A) Voltage input signal for ac ion channel conductance measurements as a function of dc bias. (B) A suspended lipid bilayer and RHL ion channel over the orifice of a GNP membrane (not drawn to scale).

the analyte is an ionic species, the binding affinity is inherently a function of the dc bias, due to spatial variation in the electrochemical potential of the analyte ion as it moves within the electric field applied across the channel.33,34 Even for neutral analytes, a dc bias results in electroosmosis through the ion channel and electrostatic deformation of the protein channel, potentially introducing artifacts in the ion channel recording.35,36 While a finite electric field across the membrane layer is required in all nanopore measurements, the use of a low amplitude (e.g., 10 mV rms) ac signal allows the protein/analyte interaction to be measured in the absence of large dc fields, thereby reducing the effects of electroosmosis, electrophoresis, and protein deformation. In addition to this fundamental advantage, ac methods allow the use of capacitive coupling at the electrode/ electrolyte interfaces to drive ion fluxes in the channel, eliminating faradaic reactions for signal translation. This is potentially important in cases where variation in electrolyte concentration or hydrogen/oxygen evolution would interfere in microfluidic channels. Finally, in principle, combining ac conductance measurements with phase-sensitive-detection (PSD) allows ion channel recordings in the presence of high background noise sources.37,38 In pursuing the development of ac ion channel recordings, a key issue is the ability to simultaneously maintain both high signalto-noise ratio (SNR) and adequate time resolution. In phasesensitive detection experiments, the SNR is largely determined by the bandwidth or time constant (TC) of the low-pass filter of the lock-in amplifier, where TC ) 1/(2πf-3dB) and f-3dB is the -3dB or “breakpoint” frequency. TCs of 1.0 s and 1.0 ms correspond, (33) Gu, L.; Cheley, S.; Bayley, H. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 15498-15503. (34) Gu, L.; Cheley, S.; Bayley, H. J. Gen. Physiol. 2001, 118, 481-493. (35) Aksimentiev, A.; Schulten, K. Biophys. J. 2005, 88, 3745-3761. (36) Krasilnikov, V. O.; Merzlyak, P. G.; Yuldasheva, L. N.; Capistrano, M. F. Eur. Biophys. J. 2005, 34, 997-1006. (37) Davies, E. R. Electronics, Noise, and Signal Recovery; Academic Press: London, U.K., 1993. (38) Horowitz, P.; Winfield, H. The Art of Electronics, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1989.

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respectively, to f-3dB ) 0.16 and 160 Hz. Increasing the TC decreases the bandwidth of the measurement and thus a larger SNR is obtained. However, the improvement in SNR is at the expense of the time resolution of the measurement.39 A sufficiently small TC must be used in order to accurately measure rapid changes in current, such as those produced from an analyte binding and unbinding to a protein pore. In practice, an intermediate TC is needed to maximize the SNR while still providing adequate time resolution. Alternating current/PSD-based ion channel recordings are reported herein using glass nanopore (GNP) membranes as a support for suspended lipid bilayers.40 GNP membranes comprise a single conical-shaped pore (10-500 nm radius orifice) embedded in a thin (∼50 µm) glass membrane at the end of a glass capillary, shown in Figure 1B. As demonstrated in a recent report describing dc-based ion channel recordings, the GNP membrane with a 100300 nm orifice is particularly well suited as a support structure for suspended lipid bilayer and ion channel measurements.40 The GNP offers several critical advantages over conventional planar lipid bilayer experiments using larger orifices (∼30-100 µm diameter) in polymer-based membranes, e.g., Teflon, including excellent mechanical and electrical stability of the bilayer. Continuous ion channel recordings of single-molecule detection for >400 h have been achieved with the GNP membranes.40 Alternating current/PSD measurements of the interaction of two charged molecules (heptakis-(6-O-sulfo)-β-cyclodextrin (s7βCD), z ) -7, and a 9 base-pair DNA hairpin molecule, z ) -22) with a single wild-type R-hemolysin (RHL) protein channel are reported herein. The binding interactions of these ions with RHL have been previously investigated using dc methods47,50 and are used as benchmarks in pursuit of developing ac ion channel recording methods. In addition to describing the ac/PSD ion channel recording method, we demonstrate that the binding kinetics and affinity in ion channel recordings can be measured at zero dc bias. To the best of our knowledge, these results correspond to the first direct electrical measurements of single protein/analyte interactions in the absence of a constant driving force. (39) Model SR830 DSP Lock-In Amplifier manual, Stanford Research Systems: Sunnyvale, CA, 1993. (40) White, R. J.; Ervin, E. N.; Yang, T.; Chen, X.; Daniel, S.; Cremer, P. S.; White, H. S. J. Am. Chem. Soc. 2007, 129, 11766-11775. (41) White, R.; Zhang, B.; Daniels, S.; Tang, J. M.; Ervin, E. N.; Cremer, P. S.; White, H. S. Langmuir 2006, 22, 10777-10783. (42) Zhang, G.; Galusha, J.; Shiozawa, P. G.; Wang, G.; Bergren, A. J.; Jones, R. M.; White, R. J.; Ervin, E. N.; Cauley, C. C.; White, H. S. Anal. Chem. 2007, 79, 4778-4787. (43) Wayment, J. R.; Harris, J. M. Anal. Chem. 2006, 78, 7841-7849. (44) Alvarez, O. How to Set Up a Bilayer System. In Ion Channel Reconstitution; Miller, C., Ed.; Platinum Press: New York, 1986; pp 115-130. (45) Blair, D. P.; Sydenham, P. H. J. Phys. E.: Sci. Instrum. 1975, 621-627. (46) Mayer, M.; Kreibel, J. K.; Tosteson, M. T.; Whitesides, G. M. Biophys. J. 2003, 85, 2684-2695. (47) Gu, L.; Serra, M. D.; Vincent, J. B.; Vigh, G. S.; Cheley, S.; Braha, O.; Bayley, H. Proc. Natl. Aacd. Sci. U.S.A. 2000, 97, 3959-3964. (48) Norton, J. D.; White, H. S.; Felberg, S. W. J. Phys. Chem. 1990, 94, 67726780. (49) Vercoutere, W.; Winters-Hilt, S.; Olsen, H.; Deamer, D.; Haussler, D.; Akeson, M. Nat. Biotechnol. 2001, 19, 248-252. (50) Vercoutere, W. A.; Winters-Hilt, S.; DeGuzman, V. S.; Deamer, D.; Ridino, S. E.; Rodgers, J. T.; Olsen, H. E.; Marziali, A.; Akeson, A. Nucleic Acids Res. 2003, 31, 1311-1318.

EXPERIMENTAL SECTION Reagents and Protein. KCl, K2HPO4‚3H2O, and KH2PO4 (all from Mallinckrodt) were used as received. Acetonitrile (J. T. Baker) was stored over 3 Å molecular sieves. Wild-type R-hemolysin, (RHL) (lyophilized powder, monomer, Sigma-Aldrich), heptakis-(6-O-sulfo)-β-cyclodextrin (s7βCD) (Aldrich), and singlestranded DNA (5′-GTTCGAAACGTTTTCGTTCGAAC-3′) (SigmaGenosys) were used as received and diluted in 1.0 M KCl, 10 mM potassium phosphate buffer (PPB) (pH ) 7.4). All solutions were prepared using H2O from a Barnstead E-pure water purification system. 1,2-Diphytanoyl-sn-glycero-3-phosphocholine (DPhPC) (Avanti) was obtained in chloroform, dried under a nitrogen stream, and diluted to a concentration of 10 mg/mL in decane (Aldrich). Ag/AgCl electrodes were prepared by oxidizing a 0.25 mm radius Ag wire in a saturated FeCl3 (Matheson Coleman & Bell) solution for ∼60 s. Glass Nanopore Membranes. The fabrication of glass nanopore (GNP) membranes employed for ion channel recordings has previously been detailed.41,42 Briefly, GNP membranes are fabricated by first sealing the end (∼25-75 µm) of an electrochemically sharpened Pt wire into the end of a heated soda-lime glass capillary (Dagan Corporation SB16 capillaries, 1.65 mm o.d., 0.75 mm i.d.; softening point 700 °C; manufacturer provided composition, 67.7% SiO2, 2.8% BaO, 15.6% Na2O, 5.6% CaO, 4% MgO, 1.5% B, and 0.6% K2O%) using a H2 torch. The end of the glass capillary is polished after cooling, while monitoring the conductivity between the sealed Pt and the polishing surface, until a Pt disk of desired size is exposed.42 The Pt disk is then electrochemically etched in a 20% CaCl2 solution to create a shallow nanopore in the insulating glass. The remaining Pt is then pulled from the glass leaving a single conical-shaped pore in a thin glass membrane. Full details of the fabrication process are presented in ref 42. Prior to application as a structural support in ion channel recordings, the GNP membrane is chemically modified with 3-cyanopropyldimethylchlorosilane (Gelest, Inc.), yielding a monolayer that exposes a terminal -CN group to the solution. This surface modification produces a surface of intermediate hydrophobicity, allowing deposition of a lipid monolayer in a tailsdown configuration on the glass membrane, as previously demonstrated by fluorescence microscopy and vibrational sum frequency spectroscopy.40 The -CN functionality has sufficient hydrophilic character to allow aqueous solutions to wet small glass nanopores. After the deposition of the silane monolayer on the interior and exterior surfaces of the GNP membrane, a lipid/ decane solution (10 mg/mL) is painted across the exterior surface of the GNP as described below, resulting in the spontaneous formation of a lipid monolayer on the glass surfaces and a lipid bilayer suspended across the GNP orifice, Figure 1B.40 The suspended bilayer above the opening of the nanopore is mechanically robust and has been demonstrated to be well suited for ion channel recordings.40 The -CN terminated silane monolayer also prevents protein absorption on the glass surface, as reported earlier by Wayment and Harris.43 Alternating Current rHL Recordings. A schematic diagram of the GNP membrane and instrumentation for ac/dc conductance measurements is shown in Figure 2. Following surface modification with 3-cyanopropyldimethylchlorosilane, the glass capillary

Figure 2. Schematic of the GNP membrane and instrumentation used in the ac conductance measurements.

is filled with an electrolyte solution. An Ag/AgCl electrode is placed inside the glass capillary, and the capillary is inserted into a pipet holder (Dagan) that is connected to a 5 mL gastight syringe (Hamilton) and a pressure gauge (Mabis Healthcare Inc.). The syringe and pressure gauge are used to control the pressure across the suspended bilayer during ion channel recordings. The glass capillary is inserted into a small (∼1 mL volume) home-built cell containing a second Ag/AgCl electrode. The cell is filled with electrolyte solution, forming a two-compartment cell separated by the orifice of the GNP membrane. Lipid bilayers were formed across the GNP orifice using the painting method44 by first gently spreading ∼1 µL of 10 mg/mL DPhPC lipid/decane solution across the GNP membrane surface using a 200 µL round gel-loading pipet tip (Fisherbrand). A clean pipet tip is then lightly dragged across the GNP orifice, creating a bilayer. Successful bilayer formation is indicated by the formation of a 70-100 GΩ seal, as measured in the 1.0 M KCl PPB solution.40 Solution containing the RHL monomer was added to either the internal GNP membrane electrolyte solution or to the external cell electrolyte solution, as indicated later in describing specific experiments. In all experiments reported within, s7βCD and RHL were added, respectively, to the solutions on opposite sides of the bilayer, since s7βCD binds to the RHL channel from the trans protein side.48 The DNA hairpin molecule and RHL were added to the same electrolyte solution as the hairpin enters RHL from the cis protein side.50 The pressure control and monitoring system described above allows a transmembrane pressure to be applied to control protein activity in the suspended bilayer, as previously described.40 Briefly, a small positive pressure (>20 mmHg) inside the capillary, relative to the exterior solution, is required for spontaneous insertion of RHL into the lipid bilayer. Larger pressures result in an increased rate of protein insertion. Spontaneous deactivation of protein in the lipid bilayer occurs when the pressure is reduced below 20 mmHg. In the experiments reported herein, an initial pressure between 80 and 120 mmHg was applied to induce insertion of a single RHL channel. The pressure was then immediately reduced to ∼20 mmHg in order to maintain a single protein channel in the bilayer while ensuring that no further insertions occurred. Analytical Chemistry, Vol. 80, No. 6, March 15, 2008

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The ac conductance of the lipid bilayer and protein were measured by applying a 10-20 mV rms, 1-2 kHz signal (Vac) from a lock-in amplifier (R810, Stanford Research Systems) between the two Ag/AgCl electrodes using a potentiostat (Dagan Chem-Clamp voltammeter/amperometer). A dc voltage from the potentiostat was superimposed on the ac signal. The ac current (iac) response was measured by PSD. The output dc voltage of the lock-in amplifier (proportional to iac) was sampled at a rate of 5 kHz, directly out of the lock-in amplifier using an in-house LabVIEW (National Instruments) written program. All electrical potentials are referenced to the Ag/AgCl electrode in the internal solution of the glass capillary. Data analysis was performed using Origin 7.5 (OriginLab). Experiments were conducted at 22 ( 3 °C. RESULTS AND DISCUSSION Phase-sensitive detection is commonly used to recover signals buried in noise.45 This reports describes the use of PSD to measure stochastic binding events of small molecules to a single protein ion channel in a suspended lipid bilayer. Thus, for introductory purposes, the PSD technique is briefly described below. In the PSD measurement, an externally generated ac voltage (Vac rms at frequency f) is used to drive current, iac, through the ion channel embedded in the lipid bilayer, using a potentiostat and two Ag/AgCl electrodes to couple the ionic and electronic currents. A voltage proportional to iac, generated at the currentto-voltage converter of the potentiostat, is multiplied by Vac to generate a sinusoidal voltage at frequency 2f, offset by a dc amplitude that is proportional to both the magnitude of iac and the phase angle between Vac and iac. This resulting signal is then passed through the internal low-pass filter (LPF) of the lock-in amplifier in order to remove the associated ac component, leaving only the dc signal. The magnitude of the output dc signal is proportional to iac and is the parameter recorded in the ac ion channel measurements reported below. The LPF time constant (TC), which is adjustable on commercial lock-in amplifiers, sets the degree of output smoothing or the magnitude of noise that is passed through the filter. Noise is defined as the magnitude (peak-to-peak) of variations in the output dc voltage of the lock-in amplifier, typically associated with background signals (e.g., 60 Hz) and thermal noise. Increasing TC effectively decreases the LPF cutoff frequency, producing better filtering and a smoother signal. Decreasing TC increases the LPF cutoff frequency, resulting in higher noise. To simultaneously obtain a low-noise signal and the required time resolution (which depends on the frequency of ion channel binding events), the TC of the LPF is adjusted during the measurement. Typically, a LPF requires a time equal to ∼5 times the cell time constant, RC (R ) resistance and C ) capacitance), for the current to rise from an initial value to a final value.39 For simplicity, time resolution is defined herein as the time required for the lock-in amplifier output signal to rise from 10 to 90% of the final value in current (t10-90),46 in response to a change in the system conductance (e.g., as an RHL channel inserts into the lipid bilayer). In practice, an intermediate TC is needed to keep the output noise to a minimum while still offering adequate time resolution. The insertion of a single RHL channel into a lipid bilayer suspended over a GNP membrane (160 nm-radius orifice) is 2072 Analytical Chemistry, Vol. 80, No. 6, March 15, 2008

Figure 3. Simultaneous measurement of ac/dc conductance showing the insertion of a single RHL channel into a DPhPC bilayer suspended over a 160 nm radius orifice GNP membrane. The gray trace represents the dc (Vdc ) 50 mV) response while the black trace represents the ac (Vac ) 10 mV rms at 1.0 kHz) response. The background conductance of the ac trace (∼10 nS), originating from the capacitive susceptance of the GNP/lipid bilayer, has been subtracted from the G-t trace. The data were obtained in a 1.0 M KCl, 10 mM PPB (pH 7.4) solution. The internal solution of the GNP capillary contained 1 µM RHL.

demonstrated in the conductance vs time (G vs t) trace shown in Figure 3. Here, a 10 mV rms, 1.0 kHz ac signal is superimposed on a 50 mV dc bias between two Ag/AgCl electrodes in a 1.0 M KCl, 10 mM PPB (pH 7.4) solution. At t ) 0, only a suspended lipid bilayer is present, and there is essentially no dc current (bilayer resistance ∼100 GΩ), corresponding to Gdc ∼ 0. The ac current, however, contains a significant electrical susceptance contribution from capacitive GNP membrane/bilayer charging (∼114 pA) even prior to RHL insertion.32 The effective conductance associated with this charging current has been subtracted from the data shown in Figure 3 for a quantitative comparison of the change in dc and ac conductance upon RHL insertion. At ∼18 s, a single RHL inserts into the bilayer, producing a conductive pathway for ions across the bilayer. In both the ac and dc G-t plots, the change in conductance corresponds to ∼0.90 nS, in good agreement with the reported conductance literature value for RHL of ∼1 nS.3 The data shown in Figure 3 were obtained using a TC of 1 ms and sampled at a rate of 10 000 samples/s. The data were then averaged (1000 samples/pt) in order to decrease the measurement noise. This averaging technique results in a t10-90 of ∼0.1 s that is not a function of TC. Long-time averaging techniques are a simple means to decrease the noise of the measurement and are adequate for measuring long-lived current changes, where the current response simply changes from one stable state to another, Figure 3, and temporal resolution is not a primary concern. However, short-lived events that are well below the time resolution of the measurement are not seen as they are averaged out. For faster measurements, such as that needed to detect binding events between protein pores and analyte molecules or the translocation of an analyte, which occur in the microsecond to millisecond time

Table 1. Time Resolution (t10-90) and Measurement Noise as a Function of the Lock-In Amplifier Time Constant (TC)a

a

TC (ms)

t10-90 (ms)

noise (pA)

100 10 1 0.3 0.03

510 ( 30 48 ( 2 5.0 ( 0.3 1.6 ( 0.2 NA

1.0 ( 0.1 1.0 ( 0.2 1.5 ( 0.2 6(1 NA

All measurements made with Vac ) 10 mV rms at 1 kHz.

Table 2. Bilayer Current and Measurement Noise as a Function of the Input Reference Frequency (f)a f (kHz)

iac (pA)

noise (pA)

0.5 1.0 2.0 5.0 10.0

40 ( 10 110 ( 10 420 ( 8 750 ( 10 890 ( 10

25 ( 3 6(1 2.0 ( 0.2 2.0 ( 0.1 2.0 ( 0.1

a All measurements made using a low-pass filter time constant (TC) of 0.3 ms.

intervals, such long-time averaging analysis cannot be employed. In these cases, the time resolution and noise associated with the ac measurement are determined by the input signal frequency and the TC of the lock-in amplifier, as discussed above. Table 1 lists the t10-90 and noise values associated with iac measured across a lipid bilayer suspended over the 120 nm radius orifice of a GNP membrane, as a function of the TC of the LPF (0.03-100 ms). These data were acquired at a sampling rate of 5 kHz without averaging. Here, t10-90 was measured from changes in current as an RHL channel inserted into the lipid bilayer (data not shown). In all cases, t10-90 was measured to be equal to ∼5 times the TC. As TC is decreased (effectively increasing the bandwidth of the measurement), the cutoff frequency of the LPF is increased and more noise is passed at the output of the lock-in amplifier. At a TC of 0.03 ms, the noise of the system is so high that it overloaded the lock-in amplifier and a t10-90 was not available (NA). Table 2 lists the ac current level and associated noise from a lipid bilayer (in the absence of the ion channel) suspended over the 120 nm radius orifice of a GNP membrane as the signal frequency (f) is increased from 0.5 to 10 kHz, while maintaining a constant TC (0.3 ms). The ac current response associated with the suspended lipid bilayer increases in proportion to f as expected,32 since the capacitive susceptance of the GNP membrane and lipid bilayer is proportional to f. Also, the data in Table 2 shows that the noise associated with the measurement decreases from ∼25 pA at 0.5 kHz to ∼2 pA at ∼2 kHz. The noise decreases with increasing frequency because as f is increased, the bandwidth of the measurement effectively shifts away from the major interfering source of noise, i.e., 60 Hz. The key points from above are (i) smaller TCs of the LPF result in increased time-resolution at the expense of increased noise and (ii) because smaller TCs are associated with increased bandwidth, the input f must be shifted away from any interfering signals in order to decrease the measurement noise. A current limitation to

Figure 4. Alternating current as a function of time showing multiple blocking events of an RHL channel by s7βCD. The ion channel was inserted in a DPhPC bilayer suspended over the orifice (320 nm radius) of a GNP membrane. The current response was measured using a 10 mV rms, 1 kHz ac signal superimposed on the -25 mV dc bias (TC ) 10 ms). The data were recorded in a 1.0 M KCl, 10 mM PPB (pH ) 7.4). The external solution contained ∼1 µM RHL, while the internal solution of the GNP capillary contained 50 µM s7βCD.

the ac/PSD method for measuring binding events occurring in RHL is that as f is increased, the capacitive current of the system also increases, eventually overloading the lock-in amplifier. With our current instrumentation, we are limited to low input frequencies (