Langmuir 2007, 23, 5029-5032
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Multivariate Data Analysis for Enhanced Interpretation of Electrochemical Impedance Spectra of Gramicidin-Ion Interactions in Phospholipid Monolayers Britta Lindholm-Sethson,*,† Paul Geladi,‡ Roger E. Koeppe II,§ Oskar Jonsson,| David Nilsson,| and Andrew Nelson⊥ Department of Chemistry and Centre for Biomedical Engineering and Physics, Umeå UniVersity, SE-901 87 Umea, Sweden, The Unit of Biomass Technology and Chemistry, SLU Ro¨ba¨cksdalen, P.O. Box 4097, SE - 904 03 Umeå, Sweden, Department of Biochemistry and Chemistry, UniVersity of Arkansas, FayetteVille, Arkansas 72701, UmbioAB, C/O UminoVa InnoVation AB, Box 7978, 907 19 Umeå, Sweden, and Center for Self Organising Molecular Systems, School of Chemistry, UniVersity of Leeds, LS2 9JT U.K. ReceiVed September 28, 2006. In Final Form: February 15, 2007
This article describes a multifrequency electrochemical impedance study of phospholipid monolayers on a mercury drop electrode in solutions containing electrolytes and gramicidin derivatives: gramicidin A (gA), gramicidin-BOC (g-BOC), and desformylgramicidin (g-des). The impedance spectra have been studied individually (univariate approach) and also transformed using a multivariate data reduction method (multivariate approach). It was shown that the two approaches are complementary. Thus the formation of K+-conducting channels is observed in gA only, and these channels can be distinguished from an interaction of all gramicidin derivatives with Mg2+. An unknown peptide interaction in the monolayer was observed on a slow time scale.
Introduction article1
A recent using a mercury drop electrode coated with phospholipid2,3 showed that electrochemical impedance spectroscopy could be used to characterize phospholipid gramicidin interactions. The results correlated well with conductance data, which indicated ion channel acitivity, and with data from epifluorescent microscopy of phospholipid layers at the airwater interface. The article went a considerable way toward improving the understanding of the interactions of different gramicidin derivatives with phospholipid layers but did not characterize interactions between the electrolyte cations and the gramicidin derivatives associated with the phospholipid layer. In this article, we examine the impedance data in more depth to look for ion-gramicidin interactions using multivariate analysis combined with a close inspection of the impedance spectra. The present article shows how a simple principal component analysis can guide the electrochemist to find the relevant parts of the impedance spectra where specific peptide interactions take place. This also leads to new qualitative conclusions about the interaction between lipid membrane and polypeptides as a function of time.
Electrochemical Impedance Spectroscopy. The study of the electrical properties of the monolayer/electrode system is carried out by superimposing a sinusoidal ac voltage of 5 mV rms over a dc voltage of -0.400 V versus 3.5 M KCl Ag/AgCl. Fifty frequencies between 65 000 and 0.1 Hz were spread logarithmically, and the resulting sinusoidal current was measured. The measurement at each frequency comprises an absolute impedance |Z| and a phase shift Φ. These values are converted to complex impedance through the following equation Z ) |Z|‚ejΦ ) Re Z + j Im Z ) R + jX
(1)
where Z is the complex impedance, R is the resistance, j2 ) -1, and X is the reactance. For the sake of interpretation, the complex impedance in eq 1 is often transformed to complex capacitance
C)
1 ) Re C + j Im C jωZ
(2)
Materials and Methods For experimental procedure and materials, reference is made to the previous article,1 where a more complete literature reference list is found. * To whom correspondence
[email protected]. † Umeå University. ‡ SLU Ro ¨ ba¨cksdalen. § University of Arkansas. | UmbioAB. ⊥ University of Leeds.
should
be
addressed.
E-mail:
(1) Whitehouse, C.; Gidalevitz, D.; Cahuzac, M.; Koeppe, R. E., II; Nelson, A. Langmuir 2004, 20, 9291-9298. (2) Pagano, R. E.; Miller, I. R. J. Colloid Interface Sci. 1973, 45, 126-137. (3) Nelson, A.; Benton, A. J. Electroanal. Chem. 1986, 202, 253-270.
where ω is the angle frequency (2πf) and C is the complex capacitance. Re C is the real capacitance and is related to the dielectric constant of the capacitor medium. Im C is the imaginary capacitance and is related to dielectric loss due to ionic conduction. The preferred transformation in this article is the one leading to complex capacitance because the dielectric properties of the monolayer are investigated. Multivariate Methods. Complex impedance is measured at the 50 frequencies to form a spectrum. This spectrum is a vector of 50 complex numbers or a vector of 100 numbers of which 50 are real and 50 are imaginary. When all spectra for all I experiments are collected, they form a data matrix X. In this form, they allow multivariate analysis, which is a data reduction technique. A simple
10.1021/la062850j CCC: $37.00 © 2007 American Chemical Society Published on Web 03/27/2007
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Table 1. Experiments concentration
lipida
electrolyteb
0 0 0 130 130 130 130 130 130 130 130 130
pspc dopc dopc dopc pspc dopc dopc pspc dopc dopc pspc dopc
K K Mg K K Mg K K Mg K K Mg
peptidec
replicatesd
gA gA gA boc boc boc des des des
3 6 7 6 6 8 6 6 6 6 5 6
a DOPC or DOPC-0.3PS monolayers. b Electrolyte: 0.1 M KCl or 0.05 M Mg(NO3)2. c Gramicidin A, desformyl gramicidin, or BOCgramicidin. d Number of consecutive recordings performed in an 8 to 9 min interval.
but powerful method of analyzing X is principal component analysis.4 X ) TP′ + E
(3)
X: data matrix (I × K), often pretreated T: score matrix (I × A) P: loading matrix (K × A) E: residual (I × K) By making TP′ large enough in the sum of squares sense and making E small enough, nearly all of the meaningful variation in the data is concentrated in TP′, hence data reduction has happened. The scores in T and the loadings in P in eq 3 can be used to make plots called score and loading plots. These plots can be used to detect outliers and groupings in the data and to seek an understanding of why these occur. In the present article, the data form a 71 × 100 matrix. The 71 objects are the experiments as explained in Table 1. Replicate measurements were made on the same solution without removing it from the measurement cell. They were made in sequence and therefore give a time evolution of the solution/membrane combination. The 100 variables are 50 real and 50 imaginary capacitances. The data were pretreated by mean centering and scaling to unit variance for each variable. Principal component analysis, PCA, was used to calculate three principal components, which explain 79, 13, and 3.5% of the total sum of squares, respectively. Calculations were made in Evince (Umbio AB, Umeå, Sweden).
Results Objective Overview of Impedance Data with Principal Component Analyses. Multivariate results in this article are given for the data analysis of the whole data matrix only. The 71 × 100 capacitance matrix was mean-centered and scaled to unit standard deviation for each frequency. Principal component analysis, PCA, was used to extract two components that explain 79 and 13%; see Figure 1. The score plot in Figure 1 summarizes the main features of the present system and gives a good overview of the data, which would be difficult when comparing individual impedance spectra. It is evident that the measurements in 0.05 M Mg(NO3)2 form one separate group and the measurements in 0.1 M KCl form another. A line is drawn in Figure 1 to discriminate between the Mg and K samples. It is also seen that 130 nM samples differ from 0 nM samples. The cyan circles on and above the zero line are all Mg(NO3)2 whereas the ones below this line are KCl, so for the 0 nM samples the separation is also (4) Jackson, J. E. A User’s Guide to Principal Components; Wiley: New York, 1991.
Figure 1. Score plot of the 71 × 100 data matrix, as in Table 1, containing the first and second PCA scores. Cyan circle, zero gramicidin concentration, x ) Mg/DOPC; triangle, K/DOPC; square, K/PS-DOPC. Red, BOC-gram; green, des-gram; and blue, gA. The arrows show the time evolution of the membranes. A line indicates the separation of Mg (above line) and K (below line) spectra.
seen, indicating an ion-lipid interaction in the absence of peptide. The measurements in Mg(NO3)2 all cluster together very well. Two types of lipid monolayers were prepared on the mercury drop: pure DOPC (i.e., dioleoyl phosphatidyl choline) and DOPC0.3PS (i.e., 30% DOPS, dioleoyl phosphatidyl serine). When looking only at the measurements in 0.1 M KCl, the scores from the DOPC-0.3PS monolayer are more spread out than at the pure DOPC monolayer, and the derivatives are clearly separated from each other, which is not the case for the pure DOPC monolayer. A clear time dependence is seen for all three gA derivatives in DOPC-0.3PS. Other time dependencies could be seen, but they are of the same order of magnitude as the measurement variation. An exception is the case of gA interaction at a DOPC monolayer in 0.05 M Mg(NO3)2, where a reversed time dependence is seen; however, it is not marked in the plot. Further analysis of these data by PCA is possible, but these results are not mentioned here. However, in a recent publication it was demonstrated how complex numbers from electrochemical impedance spectroscopy can be used in chemometrics not only to obtain complex number scores and loadings but also to concentrate the information in fewer components.5 Direct Analysis of Impedance Data. Gramicidin DeriVatiVe Interaction at DOPC and the DOPC-0.3PS Monolayer in 0.1 M KCl. In Figure 2a,b, the data are displayed from measurements after 50 min of exposure to a 130 nM peptide solution in 0.1 M KCl. As already reported, the overall extent of interaction is smaller at a pure DOPC monolayer than at a mixed layer. Without peptide in solution, both monolayers show simple capacitance behavior manifested by a dielectric loss peak at 30 kHz and a corresponding increase in Re C in the same frequency regime. At lower frequencies, Re C assumes a constant value of 1.8 µF/cm2, and Im C is zero. As gA is added to solution, two additional processes due to the peptide interaction are seen. First, a relaxation has developed in a frequency regime that in the sixth scan (i.e., after 50 min) (5) Geladi, P.; Nelson, A.; Lindholm-Sethson, B. Anal. Chim. Acta., in press, 2007, doi:10.1016/j.aca.2007.01.037. (6) Hinton, J. F.; Fernandez, J. Q.; Shungu, D. C.; Millett, F. S. Biophys. J. 1989, 55, 327-330.
Gramicidin-Ion Interactions in Monolayers
Figure 2. . Complex capacitance after 50 min of exposure to a 130 nM peptide solution in 0.1 M KCl. gA (9 and 0), des-gram ([ and ]), and BOC-gram (b and O), where Re C is represented by solid symbols and Im C is represented by open symbols. No peptide in solution (+). (a) DOPC monolayer and (b) mixed monolayer; 70:30 DOPC/DOPS.
occurs at 1400-6 Hz for both types of monolayers. The characteristic frequency for this process is estimated to increase slightly with time from 100 to 170 Hz. Second, at low frequencies a third relaxation process is seen as a sharp rise in the imaginary capacitance. In the case of g-BOC and g-des interactions with the two types of monolayers, only one relaxation process in addition to the RC element is clearly observed at low frequency (i.e., the lowfrequency tail). It is very significant that the median-frequency relaxation observed with gA in solution is not present. Peptide Interaction with a DOPC Monolayer in 0.10 M KCl and 0.05 M Mg(NO3)2. In Figure 3a,b, a comparison is made between the first and final scans with 130 nM gA in 0.1 M KCl and 0.05 M Mg(NO3)2. The imaginary and real parts of the complex capacitance are displayed as a function of frequency. With gA and K+ in solution, there is a dramatic increase in the real part of the capacitance with time. This is due to an increase both in the zero-frequency capacitance of the layer1 leading to an increase in the diameter of the RC semicircle and in the median relaxation around 160 Hz. These interactions increase with time, which is clearly observed in Figure 3b. This
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Figure 3. . Results from measurements with 130 nM gA in solution. (a) Real part of the complex capacitance and (b) imaginary part of the complex capacitance. Measurements performed in 0.05 M Mg(NO3)2: after 6 min (O) and after 70 min (b). Measurements performed in 0.10 M KCl: after 6 min (0) and after 50 min (9). No peptide in solution (+).
is observed only with potassium ions in solution and not in presence of Mg2+ (i.e., in the absence of K+). Interestingly, in 0.05 M Mg(NO3)2 a significant relaxation at around 40 Hz is clearly visible that is not observed in 0.1 M KCl. This specific gA interaction that solely occurs in the presence of divalent cations decreases with time, as can be seen in Figure 3a,b. With g-BOC and g-des in 0.05 M Mg(NO3)2, the impedance spectra are almost time-independent and are very similar to those obtained in 0.1 M KCl. Moreover, the magnitudes are not as large as in the case of gA in solution yet are larger than those obtained with no peptide in solution. Nevertheless, in 0.05 M Mg(NO3)2 a minor relaxation at around 40 Hz is observed with all derivatives, similar to the gA case, but is not present in 0.1 M KCl. With g-BOC in solution, this relaxation increases slightly with time whereas in the case of g-des the interaction hardly changed with time. This medianfrequency relaxation at 40 Hz is not observed with magnesium in solution at a pure DOPC monolayer. A general observation is that the low-frequency dielectric loss tail is the same size for g-des and gA but only half the size for g-BOC irrespective of the type of electrolyte.
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Discussion
of g-BOC, it was only half the size. The molecular explanation for this difference when comparing g-BOC to gA or g-des remains enigmatic because molecular motions (e.g., rotation and wobbling of the peptide) are much faster than the time regime of the lowfrequency tail. Subtle differences in lipid-peptide clustering or microdomain formation could conceivably be responsible for the observed behavior.
Four important points will be discussed on the basis of the results from a close inspection of the PCA score plot and the impedance spectra. First, there is a significant difference between the measurements performed in KCl and Mg(NO3)2, as seen in the second component. This is explained by the observed development of the 40 Hz relaxation that is specific to peptide-Mg2+ interaction and seems to decrease with time. A similar behavior is found for the two derivatives but is smaller in size. These observations can also be perceived in the score plot but are not highlighted there. More measurements are needed to clarify this further. Second, when only the measurements in 0.1 M KCl are considered, the PCA score plot clearly indicates that all three gramicidin derivatives interact to a larger extent with the mixed monolayer than with the pure DOPC monolayer, which is also observed in Figure 2a,b. Moreover, in the case of the mixed monolayer the three different gramicidin derivatives are clearly separated from each other, whereas they are not when measured at the pure DOPC monolayer. These findings emphasize that the membrane itself in these experiments serves as a sensitive membrane sensor and that a careful choice of the lipid layer composition can be important in the development of membranebased sensors. Third and also considering only measurements in 0.1 M KCl, it is seen that the largest interaction is always observed with gA in K+ solution after prolonged exposure to the solution, regardless of the choice of monolayer, as is seen in Figure 1. This is a clear indication that the potassium ion interacts strongly with the monolayer-bound gA and that the interaction increases with the time of exposure. The magnitude of the interaction increases with time, as does the characteristic frequency (from 70 to 160 Hz). Because this is observed only with gA and potassium in solution, it is concluded that this interaction is related to ion channel activity. This was verified in the previous article with an electroactive probe.1 Fourth, in both electrolytes the rise of the low-frequency dielectric loss tail was the same size for gA and g-des. In the case
Summary First, it is clearly demonstrated that PCA score plots are useful in obtaining an objective overview of the various interactions in a complex system (Figure 1). Not only does the PCA score plot give an indication of whether there are specific interactions that cause grouping(s) in the data but it also reveals the time dependence of an interaction process and the relative size. Second, it is seen that the features in the impedance spectra with the peptide in solution can be identified as specific dielectric relaxations at the lipid monolayer: •At high frequencies, a process related to the Maxwell-Wagner relaxation is observed that is also related to the charge-storing capacitance of the interface. As the peptide is incorporated into the layer, this high-frequency capacitance increases. •At median frequencies, ionic movement can be observed. In this case and in the presence of potassium, it is interpreted as ion channel activity with native gramicidin. With magnesium in solution, a relaxation is also observed at 40 Hz that is probably related to protein folding to accommodate the Mg ion, which can bind5 to gramicidin peptides but is not transported. •At low frequencies, a dielectric loss tail is observed, reflecting an unknown molecular interaction on a slow time scale. Acknowledgment. We thank Dr. Conor Whitehouse for performing the experiments, and we acknowledge the sixth framework project BBMO and EPSRC grant no. GR/R67/439/ 01 is for financial support. LA062850J
