Chronoamperometric Study of Tl(I) Reduction at Gramicidin-Modified

k1 + k-1 relates to the rate at which partition preceding the charge transfer is attained. ..... (31) Crow, D. R. Polarography of Metal Complexes; Aca...
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Langmuir 1999, 15, 7031-7039

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Chronoamperometric Study of Tl(I) Reduction at Gramicidin-Modified Phospholipid-Coated Mercury Electrodes Andrew Nelson* and Dan Bizzotto† Plymouth Marine Laboratory, Plymouth, PL1 2PB, U.K. Received March 10, 1999. In Final Form: May 24, 1999 An investigation into the effect of gramicidin on the kinetics of the Tl(I)/Tl(Hg) process at dioleoyl phosphatidylcholine (DOPC)- and modified-DOPC-coated electrodes has been performed using chronoamperometry and cyclic voltammetry. In this system, the Tl+ reduction mechanism resembles a CrEr type mechanism. The thermodynamic (K) and kinetic (k) parameters were measured and conform to a process whereby the Tl+ ion is complexed by the gramicidin in the monolayer. K ) k1/k-1 is a partition coefficient representing the concentration of Tl+ in the monolayer relative to the concentration of Tl+ in solution. k ) k1 + k-1 relates to the rate at which partition preceding the charge transfer is attained. The values of the rate constants are consistent with the published values of the ion entry and exit rate constants of the bimolecular gramicidin channel. Approximate coverage values of gramicidin available for Tl+ binding and transport can be calculated which are low. K decreases with increase in negative potential. K increases by a factor of 5 in layers of DOPC with PS and by a factor of between 2 and 3 in layers of DOPC with retinol. k1 increases in layers of DOPC with PS by a factor of 10.

Introduction 1

The system of phopholipid monolayer coated electrodes with incorporated gramicidin has been studied for some time.2-5 One important application has been assessing the effect of the lipid environment and lipid fixed charge on the transporting function of the gramicidin molecule.4-5 The electrochemistry has been investigated using voltammetric and potential step techniques where the electrochemical behavior of the system was shown to resemble that of a homogeneous chemical reaction preceding a reversible charge transfer.4,5 In this mechanism the ratedetermining step of the ion passing through the gramicidin-modified monolayer was considered to mimic the homogeneous chemical step.6-11 Despite the large amount of work which has been done with this system, various questions still remain. Radial diffusion processes12-17 have been considered to be unimportant in the electrochemistry * To whom correspondence should be addressed. Fax: 44-1752633102. Tel: 44-1752-633290. Email: [email protected]. † Present address: Department of Chemistry, University of British Columbia, Vancouver, BC V6T 1Z1, Canada. Phone: 604822-1306. Fax: 604-822-2847. Email: [email protected]. (1) Miller, I.R. In Topics in Bioelectrochemistry and Bioenergetics; Milazzo, G., Ed.; John Wiley and Sons: Chichester, 1981; Vol. 4, pp 161-224. (2) Nelson, A. J. Electroanal. Chem. 1991, 303, 221-236. (3) Nelson, A. J. Chem. Soc., Faraday Trans. 1993, 89, 2799-2805. (4) Nelson, A. Langmuir 1996, 12, 2058-2067. (5) Nelson, A. Langmuir 1997, 13, 5644-5651. (6) Nicholson, R. S.; Shain, I. Anal. Chem. 1964, 36, 707-723. (7) Galus, Z. Fundamentals of Electrochemical Analysis; Ellis Horwood: Chichester, 1993; pp 335-386. (8) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications; John Wiley and Sons: New York, 1980; pp 429-487. (9) Bottempelli, G.; Magno, F.; Mazzochin, G. A.; Seeber, R. Ann. Chim. 1989, 79, 103-216. (10) Saveant, J. M.; Vianello, E. Electrochim. Acta 1963, 8, 905-923. (11) Saveant, J. M.; Vianello, E. Electrochim. Acta 1967, 12, 629646. (12) Amatore, C.; Saveant, J. M.; Tessier, D. J. Electroanal. Chem. 1983, 147, 39-51. (13) Cheng, I. F.; Whitely, L. D.; Martin, C. R. Anal. Chem. 1989, 61, 762-766.

since the gramicidin concentration in the monolayer has been assumed to be high. The question remains as to whether radial diffusion processes are significant at lower gramicidin concentrations. In connection with this, some estimate of the ion conducting gramicidin concentration in the monolayer which adsorbs from solution would be useful. In addition the transport of ions through the unmodified phospholipid monolayer was always thought to be insignificant in the electrochemistry. It would be useful to distinguish between the characteristics of ion transport facilitated by the gramicidin and ionic translocation through the unmodified monolayer. Most importantly no attempt has yet been made to estimate the individual rate constants and equilibrium constant of the preceding apparent chemical step. The gramicidin molecule and its structure have been the subject of much research in the past decade. The conformation of the 15-peptide gramicidin in different environments has been relatively well characterized.18,19 Its form in solution depends very much on the solvent, and its structure in lipid bilayers is correlated with its solvent history.18,19 In its most common conducting conformation, each molecule in each monolayer of a lipid bilayer exists as a β6.3 helix, and both helices are opposed back to back to form a bimolecular channel. At one end of the gramicidin peptide chain at positions 9, 11, 13, and 15, are four tryptophan residues which through hydrogen bonding with the lipid polar groups and water stabilize the β6.3 helix in the lipid bilayer.20,21 In contrast to the well understood properties of gramicidin in lipid bilayers, there (14) Bilewicz, R.; Majda, M. J. J. Am. Chem. Soc. 1991, 113, 54645466. (15) Scharifker, B. J. J. Electroanal. Chem. 1988, 240, 61-76. (16) Scharifker, B. J. In Microelectrodes: Theory and Applications; Montenegro, M. I., Ed.; Kluwer Academic Publishers: Netherlands, 1991; pp 227-239. (17) Finklea, H. O.; Snider, D. A.; Fedyk, J.; Sabatini, E.; Gafni, Y.; Rubinstein, I. Langmuir 1993, 9, 3660-3667. (18) Killian, J. A. Biochim. Biophys. Acta 1992, 1113, 391-425. (19) Wallace, B. A. Adv. Exp. Med. Biol. 1996, 398, 607-614. (20) Wallace, B. A. Annu. Rev. Biophys. Chem. 1990, 19, 127-157. (21) Hu, W.; Lee, K. C.; Cross, T. A. Biochemistry 1993, 27, 70357047.

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is little known to date about the state of gramicidin in lipid monolayers.22-24 The present work is an attempt to address some of the concerns relating to the electrochemical studies of gramicidin-modified monolayers. The main objective of the work was to carry out a quantitative study of the electrochemistry of the system using potential step and accompanying voltammetric techniques. This was done to characterize in more detail the electrochemical mechanism and to study the manner in which the process depended on the gramicidin concentration in the monolayer. The aim was to extract kinetic parameters controlling the preceding chemical step and to relate these to processes associated with channel transport. Three systems were investigated in order to assess the manner in which the mechanism and the rate parameters depended on monolayer composition. These systems were dioleoyl phosphatidylcholine (DOPC), DOPC + phosphatidylserine (PS), and DOPC + 13-cis-retinol (retinol) monolayer coated electrodes. The effect of the negative charge of the PS polar group and the effect of the conjugated system of retinol on the channel transport of ions were of particular interest. The electrochemistry of the Tl+/Tl(Hg) couple was studied at lipid-coated electrodes with and without gramicidin in solution. A chronoamperometric experimental procedure was employed applying potential steps in the potential region covering the Tl+/Tl(Hg) redox process. Similar potential step experiments were also carried out on the Cd2+/Cd(Hg) process at the gramicidinmodified DOPC-coated electrode as a comparison. In previous work each potential step or voltammetric scan was applied to a newly formed monolayer.2-5 In this study the full pulsing program and cyclic voltammetry were carried out on one monolayer. This was done to enable the adsorbed monolayer and channels to fully equilibriate with the electroactive ion in solution during the experiment. Experimental Section Electrolytes were fully deaerated with special grade argon before each experiment, and a blanket of argon gas was maintained above the electrolyte during the experiment. Monolayers of DOPC (semisynthetic grade, Lipid Products, U.K.) and mixed monolayers of DOPC and PS (grade 1, bovine spinal cord, Lipid Products) and 13-cis-retinol (SIGMA Chemicals, Ltd.) were prepared as before4,5,25 by mixing DOPC and the required mole fraction of the PS and retinol in pentane and spreading respectively at the gas-water interface (area ) 28 cm2) in the electrochemical cell (volume ) 50 cm3). Such monolayers are referred to in the text as the lipid-mole fraction PS and the lipid-mole fraction retinol, respectively. The mixed layers studied were DOPC-0.12 retinol and DOPC-0.4 PS. 13-cis-Retinol was initially prepared in acetone. Monolayers at the gas-water interface were modified with gramicidin D (SIGMA) by adding volumes of 2.13 × 10-4 and 2.13 × 10-5 mol dm-3 gramicidin to the electrolyte from methanol stock solutions. The electrolyte was subsequently stirred for 5 min to allow incorporation of the gramicidin in the gas-water interface monolayer. Gramicidin D is a mixture of gramicidins A, B, and C in the approximate ratio of 72:9:19, respectively.26 A fresh mercury drop of area A ) 0.0088 cm2 was coated with the monolayer from the gas-water interface prior to each experiment. The electrolyte used was 0.1 mol dm-3 KCl prepared from precombusted KCl (BDH Chemicals Ltd). For the experiments with DOPC-0.4 PS coated electrodes, electrolytes were prepared to 0.001 mol dm-3 concentration with phosphate buffer (BDH Chemicals, Ltd.). (22) Ogoshi, S.; Mita, T. Bull. Chem. Soc. Jpn. 1997, 70, 841-846. (23) Vila, N.; Pugelli, M.; Gabrielli, G. Colloids Surf. A: Physiochem. Eng. Aspects 1996, 119, 95-104. (24) Naydenova, S.; Petrov, A. G.; Yarwood, J. Langmuir 1995, 11, 3435-3437. (25) Nelson, A.; Auffret, N.; Borlakoglu, J. Biochim. Biophys. Acta 1990, 1021, 205-216.

Nelson and Bizzotto Each experiment consisted initially of three cyclic voltammograms (CVs) at three scan rates of 0.2, 2, and 20 V s-1. Following this, a series of potential steps were carried out. In these, the electrode was pulsed from -0.2 V to successive more negative voltages from -0.3 to -0.7 V at 0.025 V intervals. The duration of each pulse was 0.2 s. Between each pulse the electrode was held at -0.2 V for 10 s to remove all the reduced ion from the mercury. In the pulsing experiments, the current (i(t)) was recorded at a 4 kHz sampling frequency with a 2 kHz low-pass prefilter. The current transients were analyzed in two ways. First the current values at 50 ms following the initiation of the pulse were plotted versus the potential to give normalized sampled current versus potential ((i/i0) vs -E) plots. Second, the exact equation27 describing the current transient arising from a CrEr process was also applied. In this, the current transient from 2 to 200 ms was fitted to the i(t) vs t transient. A curve fitting routine in the IGOR analysis program (Wavemetrics) was used for this. Current data at shorter time scales than 2 ms were not included in the fit because of errors due to the charging current. This procedure was carried out for all current transients from potential steps between -0.5 and -0.7 V with Tl+ as the electroactive ion. Forward and back scans of potential steps were carried out on coated electrode systems in solutions of higher gramicidin concentration. Mean values of the kinetic parameters derived from the forward and back scans of potential steps were estimated, and the range of the two values is shown as an error bar in the results. After the pulsing program, three more cyclic voltammograms were recorded at the same three scan rates as at the beginning of the experiment. At the end of the experiment, a capacitance-potential curve of the coated electrode was recorded to check the integrity of the layer. In the capacity measurements, the cell was stimulated with an ac waveform (75 Hz, 0.0045 V root mean square) superimposed on a voltage ramp (scan rate (V), 5 mV s-1). The capacity was calculated from the out-of-phase and in-phase components of the current assuming a RC circuit. In the experiments, the concentration of electroactive ion in solution was 10-4 mol dm-3 added from a working solution of TlNO3 (SIGMA) or Cd(NO3)2 (BDH). All experiments with retinol were performed under dim red light because of the light sensitivity of the compounds. Experiments were carried out using a Metrohm potentiostat (E506 Polarecord) and data were recorded with a Maclab (16 bit, 100 kHz) data acquisition system. The Maclab system was also used to stimulate the cell potential. The Metrohm potentiostat in combination with a PAR 5110 lock-in amplifier was employed to check the capacitance of the coated and uncoated electrodes. All potentials in this study are quoted versus the Ag/AgCl:3.5 mol dm-3 KCl reference electrode.

Data Analysis Methods: Chronoamperometry The full equation27 describing the current (i(t))-time (t) transients arising as a result of a potential step to a one-electron reversible electrode process preceded by a homogeneous chemical reaction (CrEr) can be written:

i(t) ) [FAD1/2c0/(1 - K2)][{K(e-kt - K)/π1/2 t1/2} + eBt{[K(k + B)1/2 erf[(k + B)1/2 t1/2]] - B1/2 erf(B1/2t1/2)}] (1) In eq 1, k ) k1 + k-1 and k1 and k-1 are the forward and reverse homogeneous rate constants, respectively, of the chemical step of which K ()k1/k-1) is the equilibrium constant. k represents the rate of attainment of chemical equilibrium prior to the charge transfer.9 B ) K2k/(1 K2), D is the diffusion coefficient taken in this study as 2 × 10-5 cm2 s-1 for Tl+,28 and c0 is the bulk concentration (26) Hladky, S. B.; Haydon, D. A. Curr. Top. Membr. Transp. 1984, 21, 327-372. (27) Macdonald, D. D. Transient techniques in Electrochemistry, Plenum Press: New York, 1977; pp 96-100. (28) Kolthoff, M.; Lingane, J. J. Polarography; Interscience Publishers: New York, 1952; p 52.

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experiment.30 When applied to the gramicidin-modified coated electrode, radial diffusion processes to the individual gramicidin pores, if significant, may appear in the analysis as a chemical step preceding the electron transfer.12 Results and Data Analysis

Figure 1. Derived current values from the exact (continuous line) and approximate (dashed line) equation describing the current transient (i(t)) resulting from a CrEr electrode mechanism as a function of time (t) following a potential step. K ) 0.005, k ) 80 s-1,c0 ) 10-4 mol dm-3, D ) 10-4.7cm2 s-1, and A ) 0.0088 cm2.

of the electroactive and electroinactive oxidized species in solution taken as 10-4 mol dm-3 in these experiments. The important feature of eq 1 is that it is valid for all values of K provided k-1 > k1 and for current data obtained over all real time. The approximate equation applied to a one-electron CrEr electrode process is given by7,8

i(t) ∼ FAD1/2c0B1/2eBt erfc(B1/2t1/2)

(2)

In contrast to eq 1, eq 2 assumes that K , 1 and that the concentration of the electroactive species is effectively zero at t ) 0. Implicit in eq 2 is that a steady-state exists at t ) 0 where

i(t) ) FAD1/2c0B1/2

(3)

and the flux of the electroactive ion to the electrode surface is described by the heterogeneous rate constant7

kf ) k1(D/k)1/2

(4)

This steady state is manifest as a mutual compensation of the rates of chemical reaction and ionic diffusion within the solution bounded by a reaction layer of thickness: 7,10,11,29 µ ) D1/2/(k1 + k -1)1/2. Figure 1 shows a comparison of i(t) derived from eqs 1 and 2, where K ) 0.005 and k ) 80 s-1. This indicates that i(t) derived from eq 1 decays with time and converges with i(t) derived from eq 2 after time t ) 1/(k1 + k -1) ) τ. Since the current, i(t), derived from eq 2 has exhibited a relatively negligible decrease from t ) 0, it can be assumed that a quasi-steady-state exists at the electrode at t ) τ. Figure 1 shows therefore that the initial reaction of electroactive ion at the electrode as indicated by eq 1 leads to a quasi steady state at t ) τ. At longer time scales the current, i(t), decays due to progressive diffusional depletion in solution. Features of eqs 1 and 2 are that they have been derived assuming linear diffusion of the reacting species to a plane surface. Although used to describe electrode reactions at a spherical electrode in this work, the surface of the electrode could be assumed to be planar because of the short time scale of the (29) Albery, W. J.; Hitchman, M. L. Ring Disc Electrodes; OUP: London, 1971; p 47.

Parts a and b of Figure 2 show plots of the current (i(t)), sampled after 50 ms, versus the voltage (-E) for successive concentrations of gramicidin in solution. These results were derived from potential step current transients. Immediately evident is the reduction wave of Tl+ in the region of the redox potential of the Tl(I)/Tl(Hg) process. This current increases in height with increase of gramicidin in solution. Significant also is the decrease in Tl+ reduction current at potentials more negative than the limiting current region. In contrast the Cd2+ ion is not reduced in the potential domain of the redox process. If this reduction wave of Tl+ is compared with the diffusionlimited wave at an uncoated electrode (Figure 2b), it bears resemblance to a kinetically limited reduction wave in polarography arising from a CrEr process.31,32 Parts a and b of Figure 2 also show that an increased reduction current of Cd2+ and Tl+ is evident at potentials more negative than -0.7 V corresponding to the onset of the lipid phase transition. This rise in reduction currents at potentials more negative than -0.7 V is shifted to more positive potential values when the DOPC monolayer is modified with gramicidin. Figure 2c displays capacity versus potential (C vs -E) plots of the coated electrodes. The C vs -E plots of the gramicidin-modified DOPC-coated electrode are similar to those of a pure DOPC monolayer coated electrode. The onset of the lipid phase transition is shown very clearly as an increase in the capacity value at potentials more negative than -0.8 V (Figure 2c). The capacity-potential curve of the gramicidin-modified DOPC monolayer shows that the gramicidin marginally shifts the onset of the phase transition of DOPC to more positive potential values. Figure 3 shows tables of CVs carried out at the gramicidin-modified DOPC-coated electrode system. Here it can be seen that the reduction current decreases with decrease of gramicidin in the monolayer although the potential of the reduction current wave remains constant. This peak becomes increasingly sigmoidal in shape at high scan rates and also when the experiments are carried out with lower gramicidin in solution. It is observed also that the potential of the oxidation peak shifts to more negative potentials with a decreasing concentration of gramicidin in the monolayer. The same peak potential shifts to more negative potentials with increase in scan rate (V) by about 0.03 V per decade of V. When the gramicidin concentration in the electrolyte is lowered to 6.36 nmol dm-3, the oxidation current is sigmoidal in shape at the highest scan rate of 20 V s-1. The data from the experiments are characteristic as shown previously2-5 of a reversible reduction preceded by a reversible chemical reaction (CrEr)6-11 and a reversible oxidation followed by a reversible chemical reaction (ErCr).6-9 Figure 4 shows examples of fits of the exact CrEr equation to the current transients from potential step experiments carried out at the gramicidin-modified DOPCcoated electrode. The fit to the analytically derived (30) Oldham, K. B.; Myland, J. C. Fundamentals of Electrochemical Science; Academic Press: San Diego, CA, 1994; p 431. (31) Crow, D. R. Polarography of Metal Complexes; Academic Press: London, 1969; pp 112-158. (32) Koryta, J. Adv. Electrochem. Electrochem. Eng. 1967, 6, 289327.

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electrodes. In addition, the presence of PS in the DOPC monolayer increases the value of k1 by a factor of almost 10. Figures 5 and 6 show that the value of k1 is dependent on the concentration of gramicidin in solution. This is in contrast to the value of k-1 which shows a smaller dependence on gramicidin concentration. Discussion

Figure 2. Normalized current-potential (i/i0 vs -E) plots for the reduction of Cd2+ (a) and Tl+ (b) at 10-4 mol dm-3 concentration in 0.1 mol dm-3 KCl on a Hg electrode (0) and on an electrode covered by DOPC at a 50 ms second sampling time (O, 2, ], b). Gramicidin concentration in electrolyte: 0 (O), 6.01 (2), 11.93 (]), and 23.77 (b) nmol dm-3. (c) Capacitance-potential (C vs -E) plots of DOPC-coated mercury electrodes: in 0.1 mol dm-3 KCl (solid line) and in solution containing 12.7 nmol dm-3 of gramicidin (dotted line).

transients is good for all experiments. Figure 5 displays the relation of the individual values of K, k1, and k-1 derived from the CrEr equation with increase in negative potential at the coated electrode systems. In the highest concentrations of gramicidin in solution, K shows a decrease with an increase in negative potential. Figure 6 displays the values of K, k1, and k-1 at a potential of -0.55 V derived from the experiments with the three different monolayer systems. The value of K is increased by a factor of 5 at DOPC with added 0.4 PS coated electrodes and by a factor of between 2 and 3 at DOPC with added 0.12 retinol coated

State of Gramicidin in the Monolayer. The results in parts a and b of Figure 2 show that in the region of the redox potentials of the Tl(I)/Tl(Hg) and Cd(II)/Cd(Hg) processes only Tl+ passes across the gramicidin-modified monolayer. This evidence indicates that the Tl+ ions are being transported through the gramicidin channel lumen since it is well established that divalent ions are not conducted by gramicidin channels.33 Figure 2c shows that at potentials more positive than -0.7 V the gramicidinmodified layer remains in an organized state. This is commensurate with previous studies on DOPC and gramicidin-modified DOPC monolayers.34 The results therefore indicate that at potentials more positive than -0.7 V, the channel-mediated translocation of Tl+ is the most significant factor controlling its electrochemical behavior. At more negative potentials, the phospholipid monolayer undergoes a phase transition whereby it becomes nonselectively permeable to ions due to an increasing number of defects35 being formed. In parts a and b of Figure 2 it can be seen that the presence of gramicidin in DOPC monolayers increases the nonselective permeability of the monolayers to ions at potentials more negative than -0.7 V. This is due to the influence of the gramicidin in the monolayer on the formation of defects at the onset of the lipid phase transition. This effect is evident in Figure 2c as a capacitance increase at potentials more positive than -0.8 V. The correlation between the increase in the capacitance and the nonselective ionic permeability of spread and adsorbed lipid monolayers was seen first by Miller and collaborators.36,37 The results in Figure 2 support the notion that the gramicidin molecule as the β6.3 helix form is the conducting species in phospholipid monolayers. While there is no direct evidence concerning the orientation of the helix in lipid monolayers, intuitive reasoning suggests that the β6.3 helix is oriented in the monolayer in the same way as in half a bilayer. This supposition is based on the known orientation of lipid monolayers on mercury and the forces which facilitate this. Recent experimental evidence showed that the shift in the potential of zero charge (PZC) due to DOPC transfer to mercury (0.435 V) was in agreement with the surface potential (0.450 V) of condensed phosphatidylcholine (PC) monolayers at the gas-water interface.35 This finding indicates that lipid monolayers at the mercury-water interface are oriented in a manner similar to lipid monolayers at the gas-water interface with the polar heads in the aqueous phase. Indeed, previous calculations have predicted that the lipid molecules within a phospholipid monolayer on mercury should be oriented with their tails toward the mercury and their heads toward the aqueous phase between potentials -0.2 to -0.8V.38 This configuration is energetically driven since (33) Hille, B. Ionic Channels of Excitable Membranes; Sinauer Associates: Sunderland, MA, 1984; pp 291-314. (34) Rueda, M.; Navarro, I.; Ramirez, G,; Prieto, F.; Nelson, A. J. Electroanal. Chem. 1998, 454, 155-160. (35) Bizzotto, D.; Nelson, A. Langmuir 1998, 14, 6269-6273. (36) Miller, I. R.; Blank, M. J. Colloid Interface Sci. 1968, 26, 34-40. (37) Pagano, R. E.; Miller, I. R. J. Colloid Interface Sci. 1973, 45, 126-137. (38) Leermakers, F. A. M.; Nelson, A. J. Electroanal. Chem. 1990, 278, 53-72.

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Figure 3. Cyclic voltammograms of 10-4 mol dm-3 Tl+ in 0.1 mol dm-3 KCl at DOPC-coated electrodes. Scan rate and gramicidin concentration in the electrolyte in nmol dm-3 (in top left-hand corner of each CV) are indicated.

Figure 4. Fits of the experimental current-time ((i(t))-(t)) transients (dashed line) to the analytically derived current (solid line) from the exact equation characterizing a CrEr mechanism. Inset of (b) shows in addition the current (stippled line) derived from the approximate form of the equation characterizing a CrEr mechanism using the same values of K and k. Experiments carried out at DOPC-coated electrodes in 0.1 mol dm-3 KCl with 10-4 mol dm-3 Tl+ and with 12.7 (a), 6.36 (b), 3.18 (c), and 1.27 (d) nmol dm-3 gramicidin following a potential step from -0.2 to -0.55V.

the mercury surface is relatively nonpolar and nonpolarizing within this potential region. It is proposed that the orientation of the gramicidin β6.3 helix within the lipid monolayer is facilitated in the same way as that of the lipid. The tryptophan residues on the gramicidin molecule

are polar and polarizable18-21 so they would much prefer to associate with the polar heads of the lipid than sit next to the mercury. Model. The fits of the data to the exact form of the CrEr equation in Figure 4 might arise from the significance of

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Figure 5. Estimated values of K, k1 and k-1 from potential step experiments at DOPC (a), DOPC-0.4PS (in pH 7 electrolyte with 0.001 mol dm-3 phosphate buffer) (b), and DOPC-0.12 retinol (c) coated electrodes in 0.1 mol dm-3 KCl with 10-4 mol dm-3 Tl+ and with 12.7 (2), 6.36 (0), 3.18 (9), 1.27 (O), 0.636 (4), and 0.318 (b) nmol dm-3 gramicidin. Potential stepped from -0.2 V. Values of K, k1, and k-1 plotted versus the potential (-E) of the step.

radial diffusion processes to the individual gramicidin pores within the time scale of the experiment.12 If this is the case, then k-1 should equal D/0.36r2 ) 5.5 × 1011 s-1,12 where r is the radius of the gramicidin channel which is 2 × 10-8 cm.26 The observed value of k-1 of 40 to 120 s-1 (Figure 6) is very much below this value. This indicates that other models must be sought to explain the results in this study. A mechanism is therefore proposed which is based on the fact that the Tl+ ion forms stable complexes with the gramicidin channel in phospholipid bilayers.39-44 In this model, Tl+ in solution undergoes a reaction with the gramicidin channel in the phospholipid monolayer to form a complexed species. This complex is electroactive since the Tl+ ion diffuses within the channel to undergo reversible charge transfer at the electrode surface. The mechanism can be depicted as shown in Scheme 1. Scheme 1

In the context of Scheme 1, the value of K derived from the CrEr equation represents a partition coefficient of Tl+ in the monolayer relative to Tl+ in solution and can be (39) Henze, R.; Neher, E.; Trapane, T. L.; Urry, D. W. J. Membr. Biol. 1982, 64, 233-239. (40) Urry, D. W.; Trapane, T. L.; Venkatachalam, C. M.; Prasad, K. U. Can. J. Chem. 1985, 63, 1976-1981. (41) Hinton, J. F.; Koeppe, R. E. II; Shungu, D.; Whaley, W. L.; Paczkowski, J. A.; Millet, F. S. Biophys. J. 1986, 49, 571-577. (42) Hinton, J. F.; Whaley, W. L.; Shungu, D.; Koeppe, R. E., II; Millet, F. S. Biophys. J. 1986, 50, 539-544.

expressed as

K ) [Tl+(Gram)mon]/[Tl+]

(5)

where [Tl+(Gram)mon] is the volume concentration of the channel-Tl+ complex in the lipid monolayer and [Tl+] is the concentration of Tl+ in solution. k1 is a pseudo-firstorder rate constant dependent on the volume concentration of unbound gramicidin in the monolayer ([Grammon]). This is consistent with the experimental observations (Figure 6). On the other hand, k-1, is a first-order rate constant relating to the channel-Tl+ complex dissociation and therefore should be independent of [Grammon]. In fact, although k-1 is less dependent on [Grammon] than k1, it is not entirely independent (see Figures 5 and 6). Gramicidin-Tl+ Interaction. A more accurate understanding of the rate constants in terms of Scheme 1 can be obtained if they are interpreted in terms of the classical CrEr mechanism6-11 and the molecular rate constants of the gramicidin channel interaction with ions. By analogy with the CrEr mechanism, when the ion in the channel-modified monolayer and solution thickness δ, defined as (D/(k1 + k-1))1/2, is removed by reduction, a quasi-steady-state ensues after time, τ (see Figure 4b). In this quasi-steady state, a mutual compensation of the channel exchanges of ions and ionic diffusion processes within the solution layer, δ, takes place. The rate constants, which describe the interaction of the ion with the monomolecular gramicidin channel in a (43) Hinton, J. F.; Fernandez, J. Q.; Shungu, D.; Whaley, W. L.; Koeppe, R. E., II; Millet, F. S. Biophys. J. 1988, 54, 527-533. (44) Jing, N.; Prasad, K. U.; Urry, D. W. Biochim. Biophys. Acta 1995, 1238, 1-11.

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Figure 7. Values of log k1′ (filled symbols) and log k-1′ (open symbols) calculated as described in the text from values of k1 and k-1, respectively estimated from potential step (-0.2 to -0.55 V) experiments at DOPC (9,0), DOPC-0.4 PS (in pH 7 electrolyte with 0.001 mol dm-3 phosphate buffer) (2,4) and DOPC-0.12 retinol (b,O) coated electrodes in 0.1 mol dm-3 KCl with 10-4 mol dm-3 Tl+ plotted versus the gramicidin concentration in solution.

the exchange of ions in to and out of the channel-modified monolayer can be written in terms of k1′ and k-1′ respectively as:

kinhet[Grammon] ) kin[Grammon](1.3 × 10-7 cm) ) k1′(1.3 × 10-7 cm) (7) kouthet ) k-1′(1.3 × 10-7 cm) Figure 6. Estimated values of K, log k1, and log k-1 from potential step experiments at DOPC (2), DOPC-0.4 PS (in pH 7 electrolyte with 0.001 mol dm-3 phosphate buffer) (b), and DOPC-0.12 retinol (0) coated electrodes in electrolyte 0.1 mol dm-3 KCl with 10-4 mol dm-3 Tl+ and added gramicidin. K, log k1, and log k-1 are plotted versus the gramicidin concentration in solution. Potential step from -0.2 to -0.55 V.

water-lipid monolayer two-phase system, are heterogeneous. These constants relate to the partition of the ion into the channel from solution, and the partition of the ion into the solution from the channel and can be termed kinhet and kouthet, respectively. If these constants are divided by the length of the channel (1.3 × 10-7 cm26), one obtains the molecular second-order channel entry rate constant, kin, and the molecular first-order channel exit rate constant, k-1′. Thus 1/k-1′ is the lifetime of the ion in the monomolecular channel on mercury at equilibrium with the solution. kin and k-1′ can be compared with the gramicidin channel rate constants quoted in the literature which represent the transport of the ion in to and out of the channel, respectively, in terms of the molecular dimensions of the channel.26,45-50 A pseudo-first-order rate constant k1′ can be defined in terms of kin as

k1′ ) kin [Grammon]

(8)

In contrast to k1′ and k-1′, the first-order rate constants k1 and k -1 characterize ionic translocation processes in a volume of solution enclosed by the layer, δ, which are in steady state and equal to the rates of partition of ions in to and out of the channels, respectively. As a result, the sum of the heterogeneous rate constants describing the exchange of ions in to and out of the channels can be expressed as D/δ or D1/2(k1 + k-1)1/2. The heterogeneous rate constants relating to the ionic exchanges in to and out of the channel-modified monolayer are proportional to D/δ by the factors (k1/(k1 + k-1)) and (k-1/(k1 + k-1)) and can be written

kinhet[Grammon] ) (k1/(k1 + k-1)) (D1/2 (k1 + k-1)1/2) ) k1D1/2/(k1 + k-1)1/2 (9) kouthet ) k-1D1/2/(k1 + k-1)1/2

(10)

Equation 9 is equivalent to eq 4 associated with the CrEr mechanism. A combination of eqs 7 and 8 with eqs 9 and 10 respectively, gives

k1D1/2/(k1 + k-1)1/2 ) k1′(1.3 × 10-7 cm)

(11)

(6)

k-1D1/2/(k1 + k-1)1/2 ) k-1′(1.3 × 10-7 cm) (12)

As a result, the heterogeneous rate constants relating to

Accordingly, the molecular entry and exit rate constants for Tl+ in to and from the gramicidin-modified monolayer, k1′ and k-1′, can be calculated from k1 and k-1, respectively. Plots of k1′ and k-1′ for DOPC-coated electrodes versus the gramicidin concentration in solution are displayed in Figure 7. The relative independence of k-1′ from [Grammon]

(45) Urban, B. W.; Hladky, S. B.; Haydon, D. A. Biochim. Biophys. Acta 1980, 602, 331-354. (46) Finkelstein, A.; Andersen, O. S. J. Membr. Biol. 1981, 59, 155171. (47) Urry, D. W.; Venkatachalam, C. M.; Spisni, A.; Bradley, R. J.; Trapane, T. L.; Prasad, K. U. J. Membr. Biol. 1980, 55, 29-51. (48) Jordan, P. C. J. Membr. Biol. 1984, 78, 91-102. (49) Jordan, P. C. Biophys. J. 1984, 45, 1091-1100.

(50) Jordan, P. C. Biophys. J. 1984, 45, 1101-1107.

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Nelson and Bizzotto

is thus in accordance with it being representative of the channel-Tl+ dissociation depicted in Scheme 1. The binding constant (βTl(Gram)′) for the ion in the monomolecular channel may be written in terms of k1′ and k-1′ for a water-lipid monolayer system and assuming concentrations to equal activities as

βTl(Gram)′ ) kin/k-1′ ) k1′/(k-1′[Grammon]) ) [Tl(Gram) mon]/[Tl+] [Grammon] (13) In the context of this study and by comparing eqs 5 and 13

k1′/k-1′ ) K

(14)

The stability constant of Tl+-bimolecular channel complexes in phospholipid bilayers (βTl(Gram)′′) has been characterized, and generally values are reported from 500900 mol-1 dm3 40,41 for singly occupied bimolecular channels. It has been proposed that in the structure of the Tl+-bimolecular channel complex, the ion is bound in the region bounded by the tryptophan residues close to the lipid-water interface.19 An assumption is made in this study that the form and binding constants of the Tl+bimolecular channel complex are similar to those of the Tl+-monomolecular channel complex, that is, βTl(Gram)′ ∼ βTl(Gram)′′. It is possible to compare the values of k1′ and k-1′ with the literature estimates of the Tl+ ion bimolecular channel entry and exit rate constants respectively and the equilibrium constant, βTl(Gram)′′, of the bimolecular gramicidin channel-Tl+ complex. The values of k-1′ of 2.2 × 105 to 3.8 × 105 s-1 are similar to some published values of the Tl+ ion exit rate constant from singly occupied bimolecular gramicidin channels (2.5 × 105 s-1)26 but are higher than other quoted values of 6.3 × 104 s-1.45 Generally, the exit rate constants of other univalent ions from the singly occupied bimolecular gramicidin channel are within an order of magnitude of 2.5 × 105 s-1.46,47 As shown in eq 13, the second-order ion channel entry rate constant (kin) can be calculated from k-1′ and βTl(Gram)′. Using the value of 500 mol-1 dm3 for βTl(Gram)′ as an upper estimate for the Tl+ interaction with the monomolecular gramicidin channel within DOPC on mercury, calculated values of kin are between 1.4 × 108 and 1.8 × 108 mol-1 dm3 s-1. These values are a factor of ∼3-4 less than the value of kin measured by Urban et al.45 for Tl+ entry into the bimolecular gramicidin channel (5 × 108 mol-1 dm3 s-1) and a factor of ∼8-10 less than the diffusionally controlled channel entry rate constant26,33 of 2πrDN ) 1.5 × 109 mol-1 dm3 s-1 where N is Avogadro’s number. A value of [Grammon] can be calculated from eqs 5 and 13 by dividing K by βTl(Gram)′ which is again assumed to be 500 mol-1 dm3 as an upper estimate. For DOPC monolayers, [Grammon] is found to vary from 3.1 × 10-4 to 4.6 × 10-5 mol dm-3 depending on the solution gramicidin concentration. [Grammon] can be more conveniently expressed as a surface concentration of unbound gramicidin cGram(mon) in the phospholipid layer of thickness1 1.3 × 10-7 cm as varying from 3.8 × 10-14 to 5.8 × 10-15 mol cm-2. If all the gramicidin from 50 cm3 of a 12.7 nmol dm-3 solution enters a lipid monolayer of 28 cm2 area at the gas-water interface, a surface concentration of 2.3 × 10-11 mol cm-2 gramicidin in the lipid will ensue. This is 600 times higher than the 3.8 × 10-14 mol cm-2 of unbound gramicidin in the lipid estimated in this study. This is not unreasonable since a larger proportion of the gramicidin in the lipid will be complexed by the electrolyte potassium

ion.39-44 In addition an equally large fraction may be present in other conformations not amenable to the complexation and transport of univalent ions.18,19 One can estimate from the gramicidin surface concentration as before3 a fraction of electrode area exposed to the solution through the channel pores, (1 - θ), of 2.9 × 10-5 to 4.4 × 10-6. These values of (1 - θ) are the lowest estimate depending on the assumed upper limit value of βTl(Gram)′. The observation of sigmoid oxidation peaks in the CV s at the highest scan rate carried out in solutions of low gramicidin concentration (Figure 3) is indicative that radial diffusion processes may be significant under these conditions. This is consistent with the low (1 - θ) values on the coated electrode and the very short experimental time scales.12 The decrease of K (see Figure 5) with increase in negative potential in experiments in the highest solution gramicidin concentration shows that the increase in negative potential is influencing the partition of Tl+ into the monolayer. This is reflected in the decrease in the Tl+ reduction current with increase in negative potential shown in Figure 2b and appears like the double-layer influence on the kinetics of a preceding chemical reaction in the CrEr mechanism.51-53 A comparison of the values of K, k1, and k-1 derived from experiments carried out at the three different monolayer systems is interesting (see Figure 6). The DOPC-0.4 PS and DOPC-0.12 retinol monolayer coated electrode systems exhibit higher values of K than the DOPC monolayer coated electrode systems. This represents an influence of PS and retinol on the partition coefficient of Tl+ in the monolayer. An increase in the concentration of ion conducting gramicidin in the monolayer and/or an increase in the interaction between the ion and the gramicidin would achieve this. The latter effect might arise from the long-range interactions between the negative charge on PS and between the delocalized electrons on the retinol and the Tl+ ion.54 This would further stabilize the Tl+ ion in the gramicidin channel and increase βTl(Gram)′. Studies are underway investigating these problems. The influence of PS on the k1 and k-1 value is also instructive. This indicates how PS through its negative charge increases the kinetics of the Tl+ entry into and exit from the pore. Such influences of negative charge on the channel transport kinetics have been previously predicted.55,56 Conclusions 1. Gramicidin channels in phospholipid monolayers transport Tl+ ions but not Cd2+ ions at potentials more positive than -0.7 V. In this case the electrochemical reduction of Tl+ resembles a CrEr process. An increase in gramicidin in the monolayer increases the permeability of the layer to Tl+ and Cd2+ ions at more negative potentials approaching the onset of the first phase transition. 2. The thermodynamic (K ) k1/k-1) and kinetic (k ) k1 + k-1) parameters conform to a mechanism whereby the Tl+ ion is complexed by the gramicidin channel in the monolayer. Thus K is a monolayer/solution partition coefficient for Tl+ and k represents the rate at which the partition prior to the charge transfer is attained. A firstorder channel exit rate constant, k-1′, of 2.2 × 105 to 3.8 (51) Matsuda, H. J. Phys. Chem. 1960, 34, 336. -339. (52) Parsons, R. Adv. Electrochem. Electrochem. Eng. 1961, 1, 1-64. (53) Delahay, P. Double Layer and Electrode Kinetics; WileyInterscience: New York, 1965. (54) Kumpf, R. A.; Dougherty, D. A. Science 1993, 261, 1708-1710. (55) Jordan, P. C. Biophys. J. 1987, 51, 297-311. (56) Jordan, P. C.; Bacquet, R. J.; McCammon, J. A.; Tran, P. Biophys. J. 1989, 55, 1041-1052.

Tl(I) Reduction at Coated Electrodes

× 105 s-1 is estimated. The second-order channel entry rate constant in DOPC layers, kin, can be calculated as between 1.4 × 108 and 1.8 × 108 mol-1 dm3 s-1. Coverage values of unbound gramicidin in the monolayer are estimated which are low. Both kin and the gramicidin coverage were estimated assuming that the value of the stability constant of the Tl+-bimolecular gramicidin channel complex in bilayers is similar to that of the Tl+monomolecular gramicidin channel complex in lipid monolayers on mercury. 3. K decreases with increase in negative potential. K increases by a factor of 5 in layers of DOPC with PS and by a factor of between 2 and 3 in layers of DOPC with retinol. k1 increases in layers of DOPC with PS by a factor of 10. Glossary A, area of electrode B ) K2k/(1 - K2) C, differential capacity cGram(mon), surface concentration of conducting gramicidin in monolayer c0, bulk concentration of electroactive and electroinactive ion D, diffusion coefficient of electroactive and electroinactive ion E, applied potential vs Ag/AgCl:3.5 mol dm-3 KCl F, Faraday’s constant [Grammon], volume concentration of conducting (unbound) gramicidin in monolayer i(t), current transient in response to voltage pulse i/i0, ratio of sampled current at coated electrode to that at uncoated electrode K ) k1/k-1 k ) k1 + k-1 k1, forward rate constant of chemical reaction preceding rapid electron transfer k-1, reverse rate constant of chemical reaction preceding rapid electron transfer k1′, molecular pseudo-first-order rate constant of Tl+ partition from solution to gramicidin-modified monolayer k-1′, molecular first-order rate constant of Tl+ partition from gramicidin-modified monolayer to solution kin, second-order rate constant of Tl+ partition into gramicidin channel from solution kinhet, heterogeneous rate constant of Tl+ partition from solution to gramicidin channel

Langmuir, Vol. 15, No. 20, 1999 7039 kouthet, heterogeneous rate constant of Tl+ partition from gramicidin channel to solution N, Avogadro’s number r, internal radius of gramicidin channel t, time [Tl+(Gram)mon], volume concentration of gramicidin channel-Tl+ complex in monolayer [Tl+], concentration of Tl+ in solution V, scan rate in cyclic voltammetry Greek Symbols βTl(Gram)′, stability constant of monomolecular gramicidin channel-Tl+ complex βTl(Gram)′′, stability constant of bimolecular gramicidin channel-Tl+ complex δ, quasi-steady-state diffusion layer thickness µ, reaction layer associated with the CrEr mechanism τ, relaxation time to quasi-steady state of current in response to voltage pulse (1 - θ), fraction of electrode area exposed to solution through the channel pores Abbreviations ac, alternating current CrEr, reversible chemical reaction preceding rapid electron transfer CV, cyclic voltammogram DOPC, dioleoyl phosphatidylcholine ErCr, reversible chemical reaction following a rapid electron transfer PC, phosphatidylcholine PS, phosphatidylserine PZC, potential of zero charge RC, resistance-capacitance retinol, 13-cis-retinol

Acknowledgment. This work was supported by a Ministry of Defence/DERA (U.K.) grant “Phospholipid layers” D/ACSA/R/3/10/4/3/20. D.B. acknowledges support from NSERC (Canada) in the form of a PDF and from the Marine Biological Association of the U.K. (MBA) for a bursary. Thanks to Manuela Rueda, Herman van Leeuwen, and Frans Leermakers for very helpful comments and discussion throughout this work. LA990287H