Langmuir 2007, 23, 10581-10588
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Interpreting Ion Fluxes to Channel Arrays in Monolayers Josep Monne´,† Yolanda Dı´ez,† Jaume Puy,† Josep Galceran,*,† and Andrew Nelson‡ Departament de Quı´mica, UniVersitat de Lleida, RoVira Roure 191, 25198 Lleida, Spain, and Self Organising Molecular Systems (SOMS) Centre, UniVersity of Leeds, Leeds, United Kingdom ReceiVed May 17, 2007. In Final Form: July 20, 2007 The exponentially decaying permeability model interprets the chronoamperometric currents arising from Tl+ reduction at a Hg electrode covered with a phospholipid monolayer (DOPC) containing gramicidin monomer by combining three processes: (i) the diffusion of an ion to a membrane surface with an array of channels, (ii) the conformational dynamics of the individual channels, and (iii) the passage of the ion through the channels. The introduction of a variable permeability allows us to uncouple the diffusion from the heterogeneous processes, given that the concentration of a species at the active surface can be obtained by semi-integration of the currents. Consideration of a reverse step for the dehydration process at the mouth of the channel allows the analysis of potential steps away from diffusionlimited conditions where a Nernstian-like behavior of the relevant parameter is observed. The model has been successfully applied to data with all trans retinol or benzo-R-pyrene as additive to the phospholipid monolayer and to monolayers without any additive at all.
1. Introduction The phospholipid monolayer on a mercury electrode is a classical electrochemical system for modeling biological membrane processes.1-5 In spite of the fact that only a monolayer is being investigated, as opposed to a bilayer which forms the backbone of biological membranes, the sheer simplicity and manipulability of the model makes it a perfect vehicle for understanding the fundamental principles of biological membrane structure and function. This model system has also been shown to have a particular useful application to study the fundamental physical chemical mechanisms of ion channel function with incorporated monomolecular gramicidin in the monolayer.5-9 Since Nelson’s pioneering work, many other people (see, for instance, refs 10-13) have developed supported membrane systems with incorporated ion channels of increasing complexity. The use of permeant electroactive probes to characterize these channel systems has not been extensively used in spite of its sensitivity. This is mainly due to the lack of a model to analyze the data. There remains, therefore, a requirement for a generic analysis which can relate the currents observed in these channel arrays to channel function. In previous work,14 we have analyzed the currents and the permeation when potential steps (in diffusion-limited conditions) * Corresponding author. † Universitat de Lleida. ‡ University of Leeds. (1) Nelson, A.; Auffret, N. Mar. EnViron. Res. 1988, 24, 51-56. (2) Nelson, A.; Auffret, N. J. Electroanal. Chem. 1988, 244, 99-113. (3) Nelson, A.; Auffret, N.; Readman, J. Anal. Chim. Acta 1988, 207, 47-57. (4) Nelson, A.; Auffret, N. J. Electroanal. Chem. 1988, 248, 167-180. (5) Moncelli, M. R.; Becucci, L.; Nelson, A.; Guidelli, R. Biophys. J. 1996, 70, 2716-2726. (6) Nelson, A. Biophys. J. 2001, 80, 2694-2703. (7) Becucci, L.; Moncelli, M. R.; Guidelli, R. Biophys. J. 2002, 82, 852-864. (8) Moncelli, M. R.; Becucci, L.; Guidelli, R. Biophys. J. 1994, 66, 19691980. (9) Moncelli, M. R.; Becucci, L.; Buoninsegni, F. T.; Guidelli, R. Biophys. J. 1998, 74, 2388-2397. (10) Quist, A. P.; Chand, A.; Ramachandran, S.; Daraio, C.; Jin, S.; Lal, R. Langmuir 2007, 23, 1375-1380. (11) Terrettaz, S.; Mayer, M.; Vogel, H. Langmuir 2003, 19, 5567-5569. (12) Becucci, L.; Moncelli, M. R.; Guidelli, R. Langmuir 2003, 19, 33863392. (13) Gritsch, S.; Nollert, P.; Jahnig, F.; Sackmann, E. Langmuir 1998, 14, 3118-3125.
are applied to a system where the phospholipid monolayer contained monomolecular gramicidin channels. The use of additives on such systems is a typical experimental procedure to understand the effect of drugs, anaesthetics, or other bioactive compounds on the properties of biological membranes. It is known that hydrophobic bioactive compounds influence gramicidin activity in phospholipid membranes, because of their interaction with the peptide and/or the lipid monolayer structure, affecting the stability and the ion transport characteristics of gramicidin leading to changes in the permeability of the membrane.15 In the present work, we extend, in a more quantitative way, the study carried out previously6 considering the impact of additives all trans retinol and benzo-R-pyrene (polyconjugated systems) on the permeability of gramicidin-modified phospholipid monolayers to Tl+. We have used retinol because of its significant biological function and its presence in biological membranes,16 and we have used benzo-R-pyrene to look at the effects of a potential pollutant17 on ion channel function, so that the system could be used in later applications as a sensor if there is a response. Mechanistically, the effect of both retinol and benzo-R-pyrene could be of interest because retinol is polyconjugated and benzoR-pyrene is polyaromatic, and thus, the molecules have the potential to interact with the aromatic tryptophan residues of gramicidin and affect its structure and ion channel function. We also refine the EDP (exponentially decaying permeability) model14 to improve the fitting of currents and permeability at some potentials with experimental values obtained when these additives are used. The refinement tackles an important factor. Previously, the application of the EDP was restricted to potentials defining the limiting current region of Tl+ reduction. This is somewhat restrictive, since the permeability of the gramicidin modified monolayer at less negative potentials approaching the PZC of mercury is also of interest. We describe how this is done in this paper by introducing an additional treatment which includes the redox behavior of Tl+/Tl(Hg) and allows the estimation of the (14) Monne´, J.; Galceran, J.; Puy, J.; Nelson, A. Langmuir 2003, 19, 46944700. (15) Suchyna, T. M.; Tape, S. E.; Koeppe, R. E.; Andersen, O. S.; Sachs, F.; Gottlieb, P. A. Nature 2004, 430, 235-240. (16) N’soukpoe-Kossi, C. N.; Sedaghat-Herati, R.; Ragi, C.; Hotchandani, S.; Tajmir-Riahi, H. A. Int. J. Biol. Macromol. 2007, 40, 484-490. (17) Thiele-Bruhn, S.; Brummer, G. W. Plant Soil 2005, 275, 31-42.
10.1021/la701447g CCC: $37.00 © 2007 American Chemical Society Published on Web 09/18/2007
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Figure 1. Outline representing the diffusion of Tl+ ions (red circles), their occupation of the gramicidin channels (green cylinders) and their arrival at the mercury electrode. Not correctly oriented gramicidin channels cannot contribute to the passage of ions. The solution-side surface of the phospholipids layer corresponds to the plane x ) 0 in the three-dimensional real system. In the model, x is the only relevant spatial coordinate.
parameters characterizing the permeability of the monolayer from potentials of about -0.375 V vs Ag/AgCl. This treatment also introduces an extra parameter k-2, which characterizes the transport of Tl+ from the gramicidin pore into solution. Although the model has been checked with experimental data of a relatively simple channel array in a phospholipid monolayer, it can be used to analyze the data obtained from more complex channel systems. 2. Experimental System Our modeled system consists of a phospholipid monolayer of dioleoyl phosphatidylcholine (DOPC) covering a mercury drop with ionic channels of gramicidin acting as a permeant path across the monolayer (see Figure 1). A metal ion (Tl+) in the solution is reduced at the mercury electrode when a potential step is applied during 40 ms, and we measure the obtained currents as a response function. Experiments were carried out as described in the following: 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. Working solutions of all-trans retinol and benzo-R-pyrene (SIGMA Chemicals Ltd) were initially prepared in acetone. Monolayers of DOPC (Semi-synthetic grade, Lipid Products, U.K.) and mixed monolayers of DOPC and all-trans retinol and benzo-R-pyrene were prepared as before18 by mixing DOPC and the required mole fraction of the compound in pentane and spreading the mixture at the gas-water interface (area ) 28 cm2) in the electrochemical cell (volume ) 50 cm3). The composition of the monolayers is referred to in the text as the molar fraction of the additive. Monolayers at the gas-water interface were modified with gramicidin D (SIGMA Chemicals Ltd) by adding 3 µL of 2.13 × 10-4 mol L-1 gramicidin in methanol stock solution to the electrolyte.19 Ten minutes were allowed to enable incorporation of the added gramicidin into 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.20,21 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 (18) Nelson, A.; Auffret, N.; Borlakoglu, J. Biochim. Biophys. Acta 1990, 1021, 205-216. (19) Nelson, A.; Bizzotto, D. Langmuir 1999, 15, 7031-7039. (20) Hladky, S. B.; Haydon, D. A. Curr. Top. Membr. Transport 1984, 21, 327-372. (21) Broniatowski, M.; Suarez, M. N.; Romeu, N. V.; Dynarowicz-Latka, P. J. Phys. Chem. B 2006, 110, 19450-19455.
Monne´ et al. was 0.1 mol L-1 KCl prepared from pre-combusted salts (BDH Chemicals Ltd.). The experiments consisted of a series of potential steps applied to the monolayer. In these, the electrode was pulsed from -0.2 V to successively more negative voltages from -0.3 to -0.7 V at 0.025 V intervals. The duration of each pulse was 0.04 s. Between each pulse, the electrode was held at -0.2 V for at least 10 s to remove the reduced Thallium from the mercury. In the pulsing experiments, the current (I(t)) was recorded at a 40 kHz sampling frequency with a 20 kHz low-pass pre-filter. Forward and back scans of potential steps were carried out on 2-3 replicate coated electrode systems, and results were termed a, b, and c, respectively. Mean values of the current and the kinetic parameters were derived from the forward scans of potential steps. The range of results of the replicate experiments is displayed as error bars. In the experiments, the concentration of electroactive ion in solution was 10-4 M added from a working solution of TlNO3 (Sigma Chemicals Ltd.). Experiments with all-trans retinol were performed under dim red light because of the light sensitivity of the compound. Measurements 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 (A and D Instruments Ltd.) was also used to stimulate the cell potential. All potentials in this study are quoted versus the Ag/AgCl:3.5 M KCl reference electrode. For experiments with each of the additives, from the measured current, we have subtracted the corresponding capacitive current, which we have obtained by measuring the current in the system with the additive in the phospholipid layer but without Tl+ in solution. With benzo-R-pyrene, only the blank corresponding to a concentration of 6% of additive was available. We have used this blank with all other benzo-R-pyrene concentrations and supposed a small impact on the respective currents, which is reasonable as we have observed a small change for blanks at different concentrations of all-trans retinol.
3. Exponentially Decaying Permeability Model with Reverse Step 3.1. Basic Principles. The EDP model stems from a series of assumptions regarding mass transport in solution, channel activity, and translocation. The transport of the electroactive permeant species M toward the electrode surface from the bulk solution is assumed to be described by planar diffusion
∂cM(x,t) ∂2cM(x,t) ) DM ∂t ∂x2
(1)
where DM is the diffusion coefficient of such species. The origin of the coordinates of the one-dimensional approach corresponds to the monolayer-solution interface (see Figure 1), and a mean field approach is considered. This means that the permeant ion concentration at any x (including x ) 0) and the conducting sites on the monolayer are uniformly spread. When semi-infinite diffusion and an initial homogeneous profile are assumed, it can be shown14,22 that there is a relationship between flux and concentration of electroactive species at x ) 0 on the solution/monolayer surface
c/M - cM(0,t) )
xDM t
∫0
[
]
∂cM(x,t) ∂x
xπ(t - τ)
x)0
dτ
(2)
In absence of adsorption and accumulation of Tl+ in the monolayer (which is reasonable as extensively discussed in refs 7, 14, and (22) Oldham, K. B.; Myland, J. C. Fundamentals of Electrochemical Science; Academic Press: San Diego, CA, 1994.
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22-26), the measured current can be obtained from the incoming flux of M at x ) 0
[
I(t) ) nFADM
]
∂cM(x,t) ∂x
(3)
x)0
By combination of eqs 2 and 3, the average concentration of M at the lipid surface, cM(0,t), can be obtained from the measured currents. The definition of the local permeability14 as the ratio between the flux and the concentration at the monolayer-solution interface has proved to be useful to uncouple diffusion from the translocation process just with the nonadsorption assumption
P(t) ≡
[
DM
]
∂cM(x,t) ∂x cM(0,t)
x)0
(4)
The combination of the three last equations leads to an expression to compute either the intensity current (I) from a given permeability or vice versa
[
P(t) nFAc/M -
1
xπDM
I(τ)dτ
∫0t x
t-τ
]
) I(t)
(5)
k2
followed by a reversible electron transfer. The reaction scheme for such a system can be described by k-2
electron transfer
M0 (in Hg) {\} M (channel) {\ } M (at x ) 0) (8) k 2
3.2. EDP without Reverse Step. In a first approximation,14 we assumed a first-order kinetic process for the conversion from the conducting form of gramicidin (Gr*) to the nonconducting form, with constants k+ for activation and k- for deactivation, as had been suggested elsewhere.6 On the other hand, we assumed a first-order heterogeneous kinetics for the passage across the channel with a global rate constant k2 (mainly related to dehydration7), corresponding to the scheme
cM (0,t) 98 cM0 (in Hg)
Figure 2. Plots of the experimental current (oscillating thin line) and the fittings corresponding to the standard EDP model (dashed line) and refined EDP model (solid thick line). E ) -0.4 V, c/M ) 0.1 mol‚m-3. Concentration of gramicidin: 12.7 nM.
(6)
Combining the gramicidin interconversion model with the firstorder heterogeneous kinetic model one obtains the functionality
P(t) ) k2[Gr*] ) k2[Gr*]∞ + (k2[Gr*]0 - k2[Gr*]∞)e-kΣt ) P∞ + P∆e-kΣt (7) for the permeability. The exponentially decay functionality for the permeability is the origin of the name EDP model. Semi-integration of experimental currents (see eq 5) allows us to obtain the experimental permeability and fit the found permeability to the EDP functionality (see eq 7) to retrieve the corresponding parameters P∞, P∆, and kΣ. In a second phase, once the values of these parameters are known, the numerical solution of the integral eq 5 allows us to obtain the current at any time and compare it with the original experimental value. The EDP model has proved to be useful for the most negative potentials but exhibits some limitations such as the lack of fitting for more positive potentials (see Figure 2). So, an improved EDP model that takes into account the well documented reverse step for the hydration of the Tl+ at the channel crossing7 has been developed. 3.3. EDP with Reverse Step or Refined EDP. We now refine the scheme given in eq 6 to include the reverse step for the dehydration, with a rate constant k-2, of the ionic species Tl+ (23) Oldham, K. B. Anal. Chem. 1986, 58, 2296-2300. (24) Oldham, K. B. J. Appl. Electrochem. 1991, 21, 1068-1072. (25) Mahon, P. J.; Oldham, K. B. Electrochim. Acta. 2001, 46, 953-965. (26) Hepel, M. J. Electroanal. Chem. 2001, 509, 90-106.
Balancing the fluxes leaving the solution, crossing the channels and entering the amalgam, one can write
DM
( ) ∂cM ∂x
x)0
) k2cM(0,t)Gr* - k-2cM(channel) ) DM0
( ) ∂cM0 ∂x
x)-L
(9)
in the same coordinate system described in Figure 1. k-2 (in m s-1) is a heterogeneous first-order rate constant, whereas k2 (in m4 mol-1 s-1) is a second-order rate constant. Notice that the rate of outflow from a channel only depends on the concentration of metal in the channel cM(channel) and does not involve the concentration of gramicidin explicitly (although, implicitly, the amount of metal in the channel at a given time will depend on the number of active gramicidin channels which have been occupied). Dividing eq 9 by cM(0,t) and using P(t) given by eq 7, one obtains
cM(channel) I(t) ) P∞ + P∆e-kΣt - k-2 nFAcM(0,t) cM(0,t)
(10)
Now, we assume Nernstian equilibrium across the mercury surface, so that, using the coefficient Y27
Y)
cM0(-L,t) cM(channel)
{
) exp -
nF (E - E0) RT
}
(11)
where L stands for the lipid monolayer thickness and cM0(-L,t) stands for the concentration of Tl° just at the inner side of the mercury surface. Thus, eq 10 can be written
k-2 cM0(-L,t) I(t) ) P∞ + P∆e-kΣt ) Y cM(0,t) nFAcM(0,t) cM0(-L,t) (12) P∞ + P∆e-kΣt - k3 cM(0,t)
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Figure 3. Plots of experimental permeability (oscillating line) and the fitting corresponding to the standard EDP model (thin dashed line) and refined EDP model (thick solid line) for permeability. Parameters as in Figure 2. Values of the parameters obtained are (i) with standard EDP model: P∞ ) 3.77 × 10-5 m s-1, P∆ ) 2.93 × 10-5 m s-1 and kΣ ) 177.27 s-1; (ii) with refined EDP model: P∞ ) 5.78 × 10-5 m s-1,P∆ ) 3.18 × 10-5 m s-1, kΣ ) 1053.74 s-1 and k3 ) 1.11 × 10-4 m s-1.
Figure 5. Evolution of fitted P∞ with potential. Other parameters as in Figure 2. (a) Gramicidin without additive; (b) Different amounts of added all trans retinol; (c) Different amounts of added benzoR-pyrene. Markers for concentrations of additive in (b) and (c) as in Figure 4.
by a numerical fitting procedure if we have the values of cM0(-L,t) and cM(0,t). These values have been calculated as follows: Figure 4. Values of the experimental currents at 20 ms since the application of the potential step at DOPC-coated electrodes. Panel a with added all trans retinol and panel b with added benzo-Rpyrene at concentrations: 1.2% (×), 2.4% (4), 6% (]), and 12.7% (O). The marker solid square (joined with dashed line) stands for the experiments without additive. Other parameters as in Figure 2.
(i) cM(0,t) ) c/M -
I(τ)
1 nFAxDMπ
∫0t x
t-τ
dτ
(14)
obtained by combining eqs 2 and 3.
where
k3 ≡
k-2 Y
(13)
So, from the experimental currents, we can find the value of the parameters P∞, P∆, and kΣ and k3 (for a given applied potential) (27) Galceran, J.; Companys, E.; Puy, J.; Cecı´lia, J.; Garce´s, J. L. J. Electroanal. Chem. 2004, 566, 95-109.
(ii) cM0( - L,t) is found from equations for the electric charge transferred Q(t). Its value can be expressed as
Q(t) ) nFADM0
∫0t
( ) ∂cM0 ∂x
x)-L
dτ
(15)
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Figure 6. Plot of the variation of kΣ vs E (error bars embrace three replicates) with no additive to the lipidic layer. Parameters as in Figure 2.
and from the Duhamel relationship28
∫0
t
(
)
∂ci(x,τ) ∂x
x)0
dτ )
-1
∫0
t
xπDi
ci(0,τ) - c/i
xt - τ
dτ
(16)
one can write
Q(t) )
∫0t I(τ) dτ ) nFA
x
DM0 π
∫0t
cM0(-L,τ)
xt - τ
dτ (17)
A FORTRAN program allows to compute the numerical integral of the current and solve the integral eq 17 to obtain the value of cM0(-L,t). Once the values of P∞, P∆, and kΣ and k3 are available, one can simulate the expected values for the current by combining eqs 12 and 14 to yield
(
I(t) 1 ) c/M nFA nFAxDMπ
I(τ)
∫0t x
t-τ
)
dτ (P∞ + P∆e-kΣt) k3cM0 (-L,t) (18)
and compare with the experimental ones. Figure 2 shows the fitting of the experimental currents with the EDP and the refined EDP models at a potential (E ) -0.4 V) far away from diffusionlimited conditions. The refined EDP model exhibits a better agreement with experimental currents than the old model, and the same can be observed with the recovered permeability (see Figure 3). The incorporation of just one more parameter, k3, to the first model improves the fitting of currents and permeability where the old model showed more difficulties. Notice that, according to its definition in eq 13, two physical processes are embedded in k3: (i) the reverse step of hydration and (ii) the reversible electron transfer. The introduction of this new parameter allows a fine-tuning of the fitting with a slight impact on the values of P∞ and P∆, retrieved by the original EDP model (see parameters recovered by each model in caption of Figure 3). Another effect of the introduction of k3 in the model is that the expected permeability does not tend asymptotically to P∞ for very long times (as in the original EDP model), consistently with the observed experimental decreasing values. (28) Cecı´lia, J.; Galceran, J.; Salvador, J.; Puy, J.; Mas, F. Int. J. Quantum Chem. 1994, 51, 357-367.
Figure 7. Plot of the values of ln(k3) vs E for a solution: (a) without any additive (3 replicates); (b) with different amounts of all trans retinol added and (c) with different amounts of benzo-R-pyrene. Rest of parameters as in Figure 2. The added straight lines fit a region of quasi-Nernstian behavior: (a and c) fitting of averages of all series; (b) fitting of lowest and largest concentration of additive. Markers for concentrations of additive in (b and c) as in Figure 4.
4. Results and Discussion In this section, we analyze the trends of the parameters retrieved by the refined EDP model. 4.1. Impact of the Potential Step. Markers solid square in Figure 4 show that, when no additive (neither retinol nor benzoR-pyrene) is present, the current increases as the potential becomes more negative until it reaches a maximum and then decreases slightly, as already reported previously.6,7 This behavior suggests two regions or regimes: one range of potentials with increasing currents (-0.375 to -0.5 V) and another range (E < -0.5 V) where the current reaches a plateau which can be related to the mercury surface acting as a sink (given that for Thallium E0 t -0.420 V vs Ag|AgCl) and any further change on the currents could be adscribed to changes in the conducting gramicidin
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Figure 8. Plots for currents (oscillating lines) and their simulated values (continuous lines) for the system with 12.7 nM gramicidin: without any additive (lowest line), 6% of added benzo-R-pyrene (middle line) and 6% of all trans retinol (upper line). Applied potential: -0.6 V. Rest of parameters as in Figure 2.
Figure 9. Plots for the permeability: measured (oscillating lines) and their recovered values (from the fitted parameters; continuous lines) for the system with 12.7 nM gramicidin: without any additive (lowest lines), 6% of benzo-R-pyrene added (middle lines) and 6% of all trans retinol (upper lines). Applied potential: -0.6 V. Other parameters as in Figure 2.
channels. Similar behaviors are observed when different amounts of additive are incorporated to the lipidic layer (see section 4.2) In Figure 5a, we can observe that the parameter P∞, computed with the refined EDP model from the currents in a system without additive, essentially follows the general trend of the currents (as shown in Figure 4): P∞ increases from E ) -0.375 to -0.5 V, and then remains practically constant. These observed trends in the plots of the current and P∞ versus the potential suggest that the maximum permeability of the gramicidin channel occurs at applied potentials about 0.10 to 0.15 V negative of the point of zero charge (PZC) of mercury and decreases at more positive or negative potentials. According to the model P∞ ) k2[Gr*]∞, so a variation in permeability can be ascribed to a variation in the active gramicidin concentration in the layer and/or to a variation in the facility in the passage of the ions. The negative position of the potential for the maximum conductivity with respect to the PZC potential could indicate that other effects can be involved in the passage of the ion Tl+ through the pore such as competition between the electrolyte ion K+ and Tl+ for entering into the channel and the dependence of these phenomena on the potential. Further work is necessary to establish this. For kΣ, however, a very slight increase of its value with more negative potentials can be observed (see Figure 6), indicating a faster attainment of the equilibrium between the gramidicin forms.
Figure 10. Plot of the retrieved values of P∆ vs E. Parameters as in Figure 2. (a) Gramicidin without additive; (b) Different amounts of added all trans retinol; (c) Different amounts of added benzoR-pyrene. Markers for concentrations of additive in (b and c) as in Figure 4.
If we plot ln(k3) versus the potential, see Figure 7a, two different zones of potentials can be observed. First, in the range from -0.375 to -0.475 V, coinciding with the range of potentials with increasing currents of Figure 4, we see a linear behavior with a slope around -26.3 V-1. If we had a perfect Nernstian behavior, the negative slope should correspond to the value of -nF/RT, i.e., -38.9 V-1, for a system with one exchanged electron (like Tl+|Tl0) because manipulation of the definition of k3 and use of eq 11 leads to
ln k3 ) ln
k-2 nF ) C1 + E Y RT
(19)
In our plot an almost Nernstian behavior appears, given that a straight line with a negative slope fits the points. One speculation on the origin of the discrepancy in the slope values is that the value of cM(channel) is just an average of the concentrations
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Table 1. Values of Recovered Constants for the Different Additive Concentrations at -0.4 V P∞ / (m s-1) no additive 1.2% 2.4% 6% 12%
P∆ / (m s-1)
6.55 × ( 0.59 × 10 retinol benzopyrene 6.90 × 10-5 ( 6.51 × 10-5 ( 6.30 × 10-6 1.36 × 10-5 8.88 × 10-5 ( 4.50 × 10-5 ( 1.43 × 10-5 1.30 × 10-6 1.34 × 10-4 ( 9.24 × 10-5 ( 2.67 × 10-5 1.07 × 10-5 2.11 × 10-4 ( 4.44 × 10-5 ( 2.40 × 10-6 1.98 × 10-5 10-5
-5
4.00 × 10 ( 0.67 × 10 retinol benzopyrene 6.64 × 10-5 ( 2.84 × 10-5 ( 5.50 × 10-6 4.00 × 10-6 8.04 × 10-5 ( 2.25 × 10-5 ( 1.17 × 10-5 1.60 × 10-7 7.26 × 10-5 ( 5.66 × 10-5 ( 1.32 × 10-5 3.2 × 10-6 7.70 × 10-5 ( 3.64 × 10-5 ( 1.60 × 10-6 1.00 × 10-6 -5
inside the monolayer and does not correspond exactly to the concentration in direct contact with the Hg. In the second region, for more negative potentials, current is diffusion limited and the value of the parameter k3 has a small influence on the fitting of experimental currents and permeability. As seen in Figure 7, a kind of constant residual value (ln(k3) ≈ -11) is recorded by the fitting code. 4.2. Impact of Added All Trans Retinol and Benzo-R-pyrene. 4.2.1. Impact on the Current, P and P∞. In Figure 4a we can see that the presence of all trans retinol induces higher currents than when it is absent, and currents increase with increasing all trans retinol concentrations. With added benzo-R-pyrene (see Figure 4b), we find an irregular behavior for the variation of the current with the concentration of additive which could be due to the uncertainty of the data. In any case, addition of all trans retinol produces larger values of current than addition of benzo-R-pyrene, for similar concentrations of both additives. This fact suggests that the addition of all trans retinol stabilizes the gramicidin channels, and thus, the current decay is slower and less pronounced, so that more channels remain conducting. In this respect, all trans retinol shows more efficiency than benzo-Rpyrene.6 Additions of concentrations greater than 6% of benzo-R-pyrene lead to a decrease of the current indicating a lowering in the activity of the conducting channels. Such an effect is not surprising in view of the larger size of the planar benzo-R-pyrene which might readily interfere with the conducting properties of the channel. Perhaps the irregular behavior of benzo-R-pyrene could be due to the use of blanks that do not correspond at these benzoR-pyrene concentrations for which we had supposed small influence. Similar results (i.e., permeability increasing in the order: no additive < benzo-R-pyrene < all trans retinol) can be observed when we plot the permeability and current evolution for the different additives (Figure 8 and 9). Both figures show a very good agreement between experimental and modeled (with the refined EDP) currents and permeabilities. This behavior of the permeability can be expressed in terms of the parameters involved. Thus, in Figure 5b, we can see that as the concentration of all trans retinol increases P∞ also increases; so there are less conducting channels that have been deactivated. On the other hand, in Figure 5c, a similar irregular behavior as occurred with currents (Figure 4b) with increasing additions of benzo-R-pyrene can be observed, indicating that I and P∞ follow the same trend. In any case, it seems that those amounts of added all trans retinol change the permeability of the pores but do not modify the self-assembly of the phospholipid monolayer or that of the channels, whereas the addition of benzo-R-pyrene can be seen as more agressive. All trans retinol increases the gramicidin permeability since it stabilizes the channel by decreasing the rate of channel
-5
kΣ / (s-1)
k3/(m s-1)
1159.73 ( 115.02 retinol benzopyrene 924.56 ( 634.27 ( 50.37 117.82 1098.90 ( 428.02 ( 168.37 4.50 520.47 ( 394.02 ( 71.07 33.15 362.41 ( 187.94 ( 24.64 2.86
1.36 × 10-4 ( 0.22 × 10-4 retinol benzopyrene 1.41 × 10-4 ( 1.35 × 10-4 ( 1.20 × 10-5 1.50 × 10-5 1.93 × 10-4 ( 9.55 × 10-5 ( 3.50 × 10-5 1.26 × 10-5 2.99 × 10-4 ( 1.76 × 10-4 ( 4.90 × 10-5 3.50 × 10-5 4.22 × 10-4 ( 6.75 × 10-5 ( 1.00 × 10-6 1.55 × 10-6
transformation to the nonconducting form. This effect can be explained on the molecular scale through the π electrons of the polyconjugated retinol interacting with the four aromatic tryptophan residues at the channel mouth. The effect of benzo-Rpyrene is rather more complex. Similar to all trans retinol, it decreases the rate of channel transformation to the nonconducting form by interacting with the four aromatic tryptophan residues29 at the gramicidin. On the other hand, there is no marked increase in the permeability of the channel. Indeed, in some cases a decrease in permeability is noted. 4.2.2. Impact on P∆. P∆ (with or without additive) shows a similar behavior to P∞ in its variation with respect to the applied potential (see Figure 10). Two potential regions appear: one, between -0.35 and -0.55 V, where P∆ increases steadily (see Table 1), and a second region, of more negative potentials, where P∆ decreases, reproducing the general behavior of currents and P∞. With added all trans retinol, the general trend seen with P∞ is observed again: with increasing additions of the retinol, the observed P∆ values increase, and they are always higher than without additive (see Figure 10b). On the other hand, when benzoR-pyrene is added (see Figure 10c), it seems that small concentrations of additive yield P∆ values smaller than those without additive, and that large concentrations of benzo-R-pyrene yield larger P∆ values, but still lower values than the P∆ values obtained when the same amount of all trans retinol was added. 4.2.3. Impact on kΣ. kΣ decreases when adding all trans retinol or benzo-R-pyrene (see Figure 11). This decrease does not follow a linear trend with the concentration of additive, but the decrease is more significant at lower concentrations. The decrease, from a common value without additive, is larger for benzo-R-pyrene than for all trans retinol at low concentrations, which could be related to some clustering of benzo-R-pyrene around gramicidin channels (a clustering of pyrene has been observed in phospholipid bilayers30-32). For larger concentrations of additive, kΣ tends to similar values for both additives. 4.2.4. Impact on k3. As we can see in Figure 7b, in the quasiNernstian region of potentials, two practically parallel straight lines represent the evolution of ln(k3) with the potential for the most diluted and the most concentrated all trans retinol addition. Both lines exhibit almost the same value for the slope (around -26 V-1), which, added to the gramicidin-only slope (around -26 V-1 in Figure 7a) and to the benzo-R-pyrene slope (-22 (29) Andersen, O. S.; Koeppe, R. E.; Roux, B. IEEE T. Nanobiosci. 2005, 4, 10-20. (30) Engelke, M.; Behmann, T.; Ojeda, F.; Diehl, H. A. Chem. Phys. Lipids 1994, 72, 35-40. (31) Engelke, M.; Klockmann, H. C.; Diehl, H. A. Spectrochim. Acta A 1996, 52, 85-91. (32) Engelke, M.; Bojarski, P.; Diehl, H. A.; Kubicki, A. J. Membr. Biol. 1996, 153, 117-123.
10588 Langmuir, Vol. 23, No. 21, 2007
Figure 11. Evolution of kΣ with the added concentration of all trans retinol (open diamond) and benzo-R-pyrene (full diamond) for E ) -0.500 V.
V-1 in Figure 7c), reflects that the concentration of additive has little impact on the (de)hydration and reversible electron-transfer steps.
Conclusions The concept of a variable permeability allows us to uncouple diffusion from the translocation process and can be applied to any array of ion channels in a supported monolayer or bilayer membrane where a redox probe is being used to investigate their function. The simple EDP model reasonably describes the overall behavior of the permeability in terms of a decay of the gramicidin active channels. The slightly decreasing currents and permeabilities at long times appeared among the limitations of the simple model. An improved version of the EDP model, taking into account a reverse step for the hydration step, allows an improved fitting of the data and the processing of fluxes at potentials not necessarily corresponding to diffusion-limited conditions. The new parameter k3 follows a quasi-Nernstian dependence with the potential at more positive potentials than those characteristic of diffusionlimited conditions.
Monne´ et al.
The analyzed additives have a molecular structure that can interact with the tryptophan residues of the gramicidin located at the mouth of the channel, resulting in a modification of the permeability of the channels. The addition of all trans retinol or benzo-R-pyrene to the monolayer slows down the decay of the permeability and increases the intensity current with respect to the nonmodified monolayer, the former compound being more effective than benzo-R-pyrene in stabilizing the open channels. The stabilization of the channels by the additives can be tentatively ascribed to molecular interactions with gramicidin slowing down the rate of the conversion to the nonconducting form of gramicidin. Starting from a common value when no additive is present, P∞ increases and kΣ decreases with increasing concentrations of additive. This variation is nonlinear with increase in the additive concentration (see Figure 11), which could arise from a clustering of the compound around the channel. Regarding the effect of the potential on the parameters, we can see that for a given additive concentration, increasing values of currents and permeabilities are observed between potentials of -0.35 and -0.5 V. For more negative potentials, currents and permeabilities decrease. This could suggest a decrease in the stability of the channels for these values and/or a competition of Tl+ with other cations (i.e., K+) or other conformational/ permeability effects. A slight dependence of kΣ and P∞ on the potential can be observed. k3 shows a different behavior at potentials more positive than -0.5 V (quasi-Nernstian) than at very negative potentials (practically unaltered). Acknowledgment. The authors gratefully acknowledge support of this research by BBMO #005199 FP6-2003-LifeSciHealth-Specific Action Support, by the Spanish Ministry of Education and Science (Projects CTQ2006-14385 and CTM200613583), and from the “Comissionat d’Universitats i Recerca de la Generalitat de Catalunya”. LA701447G
