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Keywords:

  • Micropatterning;
  • plasma membrane;
  • CD4;
  • Lck;
  • single molecule microscopy;
  • equilibrium binding constant

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

Quantification of protein interactions in living cells is of key relevance for understanding cellular signaling. With current techniques, however, it is difficult to determine binding affinities and stoichiometries of protein complexes in the plasma membrane. We introduce here protein micropatterning as a convenient and versatile method for such investigations. Cells are grown on surfaces containing micropatterns of capture antibody to a bait protein, so that the bait gets rearranged in the live cell plasma membrane. Upon interaction with the bait, the fluorescent prey follows the micropatterns, which can be readout with fluorescence microscopy. In this study, we addressed the interaction between Lck and CD4, two central proteins in early T-cell signaling. Binding curves were recorded using the natural fluctuations in the Lck expression levels. Surprisingly, the binding was not saturable up to the highest Lck expression levels: on average, a single CD4 molecule recruited more than nine Lck molecules. We discuss the data in view of protein- and lipid-mediated interactions. © 2012 International Society for Advancement of Cytometry


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

Interactions of membrane proteins are crucial for the initiation of cellular signaling. Only the tight regulation of binding and unbinding events allows for controlling enzyme–substrate interactions, which ultimately lead to the triggering of cellular responses. For example, a helper T cell becomes activated upon the recognition of antigenic peptides presented via major histocompatibility complex (MHC)-II on an antigen-presenting cell (1). Besides the T cell antigen receptor complex, which directly binds the presented peptide, the coreceptor molecule CD4 plays a major role in this process. It binds MHC-II independently of the peptide load, thereby forming bi- or trimolecular junctions. CD4 is a transmembrane glycoprotein with a short cytosolic tail, to which Lck, the major src-family kinase involved in early T-cell signaling, can bind. Following the current paradigm, it is the binding of CD4 to MHC-II brings Lck close to the T cell antigen receptor complex for phosphorylation of immunoreceptor tyrosine-based activation motifs [2].

Dicysteine motifs in the polypeptide chains of both CD4 and Lck were described to mediate the direct protein interaction (3–6). We recently used a novel micropatterning method to investigate CD4–Lck interactions in vivo [7]. Besides confirming the importance of a zinc clasp structure formed by the four cysteines, we observed that also the lipid environment stabilizes the protein interaction: in particular, the off-rate was dramatically increased in case of a truncated Lck mutant that lacks membrane anchorage. We suspected that membrane rafts (8,9) may be involved in stabilizing Lck binding to CD4. Indeed, CD4 contains two palmitoylation sites, which were shown to modulate its association with detergent-resistant membranes (DRMs) (10,11). Also, Lck was found in DRMs; localization in DRMs is modulated by protein interactions via the SH3 domain [12].

In this study, we aimed at a quantitative characterization of the equilibrium binding between CD4 and Lck, using the micropatterning technique [7] in combination with single molecule tools for absolute quantification of protein densities. The micropatterning method is based on rearranging a bait protein directly in the live cell plasma membrane by growing cells on surfaces containing micropatterns of an antibait antibody. Such micropatterns can be easily produced, e.g., by soft lithography; here, we used grids with a periodicity of 6 μm. Interactions with a fluorescently labeled prey are read out via total internal reflection (TIR) fluorescence microscopy. Enrichment of the prey at bait-positive sites is a signature of the bait–prey interaction (for more information on the technique, see, e.g., Refs. 13 and 14).

The article is organized as follows: we first provide evidence in an in vitro test system that saturation binding curves can be obtained, yielding the dissociation constant KD. As test system, we chose the interaction between a primary antibody on the surface and a fluorescent secondary antibody in solution. Next, we studied the interaction between CD4 and a fusion protein of Lck with monomeric green fluorescent protein (Lck–mGFP) in living T24 cells. Here, we exploited the natural fluctuations of Lck–mGFP expression levels between cells to record the binding curve. The CD4–Lck interaction, however, was not saturable up to the highest expression levels, precluding a direct determination of equilibrium binding constants. Surprisingly, absolute quantification of the surface densities by single molecule microscopy revealed the recruitment of ∼9.2 Lck–mGFP molecules per CD4 molecule, further confirming that, in addition to the direct binding motifs on the polypeptide chains, interaction mechanisms based on the local environment are also involved.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

Reagents

Phosphate buffered saline (PBS) was purchased from PAA-Laboratories, Austria. The isotype control monoclonal antibody (mAb) PPV-04 conjugated with fluorophore AF647, the CD4 mAbs (clone MEM-115 conjugated with AF647 and unlabeled clone MEM-241), were purchased from EXBIO Praha, Czech Republic. The mAb against GFP was from Novus Biologicals, CO (clone 9F9.F9), fluorescein isothiocyanate (FITC)-labeled chicken-anti-mouse IgG was from BioFX Laboratories. Streptavidin (#S-0677) and polybrene were purchased from Sigma-Aldrich, and bovine serum albumin (BSA) from Roth, Germany.

Microcontact Printing

Epoxy-functionalized glass coverslips and poly-di-methyl-siloxane (PDMS) stamps were provided by CBL GmbH, Austria [13]. The micropatterning for the in vitro experiments was performed as described elsewhere (7,13,14). For the in vitro experiments, the biotinylated mouse IgG was diluted in 10-fold access of biotinylated BSA; thereby, low amounts of fluorescent prey (FITC anti-mouse IgG) were sufficient to record the saturation curves. For the experiments on cells, the antibodies were directly stamped onto the epoxy-coated glass coverslips: the PDMS stamps were rinsed with 100% ethanol and double-distilled water (ddH2O) and dried under a stream of nitrogen. While the stamps were incubated with 50 μg/mL antibody in PBS for 3–5 min, epoxy coverslips were washed like the PDMS stamps before. Subsequent to incubation, the PDMS stamps were intensely rinsed with PBS and ddH2O and dried with N2. Immediately after drying, the stamps were placed onto the epoxy coverslips upside down and incubated for 30 min. The patterned field was marked on the opposite side of the coverslip and, after removal of the stamp, sealed with a silicone incubation chamber (Secure-Seal hybridization chambers; Sigma-Aldrich). No further passivation was required in the live cell experiments. All incubations were done at room temperature.

Cell Culture

The human embryonic kidney cell line HEK293T was grown in DMEM (Invitrogen) supplemented with 100 μg/mL penicillin and 100 μg/mL streptomycin (Invitrogen), 2 mM l-glutamine (Invitrogen), and 10% heat-inactivated fetal calf serum from Sigma-Aldrich. The human bladder carcinoma cells T24 (DSMZ # ACC 310) were cultured in RPMI 1640 medium (PAA-Laboratories) containing 10% fetal calf serum (PAA-Laboratories). All cells were grown in a humidified atmosphere at 37°C and 5% CO2.

For the micropatterning analysis, the T24 cells were grown to a confluency of around 70% and harvested by treatment with trypsin/EDTA (PAA-Laboratories). Then, they were seeded onto the micropatterned surfaces and incubated in the Secure-Seal hybridization chambers for 1 h under the growing conditions described above.

Virus Production and Gene Overexpression

Retroviral particles expressing CD4-yellow fluorescent protein (YFP), wild type CD4 or Lck-GFP were produced in HEK293T cells as described previously (7,15,16). Supernatants were harvested and filtered, and T24 cells were infected with either CD4-YFP retrovirus or a combination of CD4 and LCK-GFP retrovirus. Infection was performed at 60% confluency in the presence of 5 μg/mL polybrene for 24 h. Three days after infection, expression of transduced genes was detected.

Microscopy

In vitro experiments were performed under epi-illumination on a home-built microscopy system designed for large area readout at single molecule sensitivity [17]. The system is based on a Zeiss Axiovert 200/M microscope equipped with a Zeiss α-Fluar 100× objective (NA = 1.45). We used a 488-nm Argon Ion laser (Innova, Coherent) for illumination and a back-illuminated CCD camera (NTE/CCD 1340/100-EMB; Roper Scientific) for detection. Scanning was performed in time delay and integration mode [17].

For experiments on live cells, a second home-built system was used, also based on a Zeiss Axiovert 200 microscope. Illumination of the samples was done in objective-type TIR configuration via a Zeiss 100× NA = 1.46 α Plan–Apochromat objective. The 488-nm and 514-nm emission of an Ar+ laser (Spectra Physics) were used to image Lck-GFP and CD4-YFP, respectively. After appropriate filtering, the fluorescence signal was recorded via a liquid nitrogen-cooled Micro Max 1300-PB CCD camera (Roper Scientific).

Flow Cytometry

The cells were detached using 1.5 mM EDTA in PBS. For cell surface labeling, 2 × 105 cells were incubated with 5 μg/mL of the respective mAb in PBS/1% BSA/0.02% NaN3 for 20 min on ice. The stained cells were measured by using an LSRII or FACSCalibur flow cytometer (Becton Dickinson). The LSRII was equipped with a 488-nm and a 633-nm laser and with emission filters 530/30 or 660/20 and the FACSCalibur with the 488-nm and 635-nm lasers and the emission filters 530/30 and 661/16. Data analysis was done with the FlowJo (TreeStar) software.

Data Analysis

Images of the patterns were first segmented by using an automated gridding algorithm, which separates the images in squares of 6 μm, each containing one circular spot of 3 μm diameter. Next, the high signal F+ was calculated as mean fluorescence from the central region of the spot; the low signal F was determined from an area along the border separating adjacent features with a thickness of 1 μm (Fig. 1D).

image

Figure 1. (A) Schematic drawing of the assay to measure dissociation constants in vitro. A passivating grid of BSA was printed onto an epoxy-coated class coverslip, backfilled with streptavidin, and functionalized with biotinylated mouse-mAbs as bait. The binding of FITC-labeled anti-mouse IgG as prey was measured. (B) Standard-epi-fluorescence image of a subregion of a scanned chip after incubation with 70 nM anti-mouse IgG. (C) Fluorescence intensity profile along the dashed blue line in (B). The spots can be easily discriminated over a constant background of approximately 4500 counts, which is caused by excitation of unbound fluorescent prey in solution. (D) Zoom of the red dashed square in (B), specifying the calculation of F+ and F: The high signal F+ was determined as the central circular 1 μm2 region (indicated by the yellow shaded area) of a spot. The low signal F was calculated from a 1-μm thick area at the border between adjacent features (indicated by the red-shaded area). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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To quantify the number of secondary antibody molecules in the in vitro assay, FITC anti-mouse IgG was immobilized on a glass surface at a density sufficiently low to see well-separated single molecule signals. To quantify the number of CD4-YFP and Lck-mGFP molecules in the live cell experiments, the cells were photobleached until a very low density of fluorescent molecules remained, so that again single well-separated signals were observable. The single molecule signals were then fitted by a two-dimensional Gaussian function, the volume of which gives the single molecule brightness Bsm.

For the in vitro experiments, we accounted for the fact that the mAbs were labeled stochastically on reactive lysines, so that the number of dye molecules per mAb was not fixed but statistically distributed; in particular, a significant fraction of mAb (1-ηbright) can be expected to carry no fluorophore. We assumed a Poissonian distribution, which describes mAb labeling reasonably well [18]. The labeling degree of FITC mAbs was determined via UV-VIS spectroscopy, yielding 0.42 FITC molecules per mAb. We thus expect 28% single- and 6% double-labeled proteins; 66% of the proteins are estimated to be not visible under these conditions. In the live cell experiments, we accounted for molecular dark states of the fluorescent proteins by dividing the surface densities with the fraction of bright molecules [88% and 75% for GFP and YFP, respectively (19,20)]. In both cases, the number of proteins was determined from the ensemble brightness Be by

  • display math(1)

Saturation curves were analyzed by fitting the data with the Langmuir equation

  • display math(2)

using a two-parametric nonlinear fit (Matlab, Math Works). L is the concentration of free fluorescent ligand molecules. For analysis of the in vitro experiments, L is given by the applied IgG concentration. For live cell experiments, F- was used as a measure of L. Rmax and KD are the fit parameters, where Rmax is the surface density of immobilized antibodies and KD the equilibrium dissociation constant. The confidence contours in Figure 2B were obtained by bootstrapping. Briefly, 104 iterations of the fit were run on virtual data sets generated by distributing each data point according to its standard deviation and mean value assuming a Gaussian distribution.

image

Figure 2. (A) Saturation binding curve of FITC-anti-mouse IgG to mouse mAbs recorded on the micropatterned surfaces. Full circles represent the mean of three independent experiments on different chips (the star indicates the experiment shown in Fig. 1). Data were fitted by the Langmuir equation (solid line), yielding as best fit KD = 3.5 nM and Rmax = 166 molecules/μm2. (B) Confidence intervals for the fit parameters Rmax and KD. A clear correlation can be seen: for example, a higher KD = 6 nM, in combination with a higher Rmax = 180 molecules/μm2, would also agree with the data (white triangle; the according Langmuir curve is shown as dotted-dashed line in (A). The corresponding Langmuir curve to the white circle is shown as dashed line).

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Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

In the first approach, we show here that the micropatterning technique allows for recording binding curves and for determination of equilibrium binding constants KD, even under highly unfavorable conditions of high unspecific background. We chose here a mouse IgG as bait and a FITC-labeled anti-mouse IgG as prey. The bait was arranged in periodic 3-μm spots with a distance of 3 μm and detected with the fluorescent prey. Figure 1 shows data obtained after incubation with 70 nM anti-mouse IgG: The spots (signal F+) can be easily discriminated over a constant, rather high, background (F). F is caused by the residual excitation of unbound fluorescent prey in solution, F+ is the sum of F and specific contributions; we, therefore, calculated the specific signal as F+-F. Figure 1D depicts our criterion for determination of F+ and F.

For this particular concentration, the background contributed substantially to the overall signal. Technically, it would have been possible to reduce F by reverting to TIR illumination; yet, we wanted to demonstrate the feasibility of the method even under rather straightforward microscopy conditions. Full binding curves of the fluorescent prey to the surface-bound bait were recorded on individual chips by sequential incubation of the micropatterns with increasing concentrations of FITC anti-mouse IgG. Figure 2A shows the average of three independent experiments. On the y-axis, we provided here the specific signal F+-F in absolute units of bound molecules per square micrometer using Eq.  (1). The data were fitted by the Langmuir equation [Eq.  (2)]. We also visualized the confidence intervals of the fit in Figure 2B. A KD of 3.5 nM was estimated, which is a reasonable value for secondary antibody binding [21]. The high correlation of KD and Rmax in Figure 2B is noteworthy: it means that the data can also be described by a higher KD if the maximum value Rmax was chosen higher and vice versa. To indicate the confidence boundaries, we also plotted the respective Langmuir curves in A as dashed and dashed-dotted lines (corresponding to the position of the triangle and the circle in B, respectively).

We next attempted to quantify interactions in the living cell. As bait and prey, we selected the membrane-anchored proteins CD4 and Lck, respectively, which were also used in our previous micropatterning studies [7]. First, we characterized the quality of the bait micropatterns induced by CD4 mAb (Fig. 3A). From the brightness of the signals within CD4-YFP positive regions, we calculated the CD4-YFP surface density by comparison with its single molecule brightness, yielding on average 515 ± 25 molecules/μm2.

image

Figure 3. Schematic drawing of the assay to study CD4-lck binding in living cells and representative images. As a substrate, we used 3-μm spots of anti-CD4 IgG at a distance of 3 μm. Cells expressing CD4-YFP (A) and CD4/Lck-mGFP (B) were seeded on the patterns. DIC and TIR images of single cells are shown. Essentially, all CD4-YFP was arranged according to the mAb patterns (A). The Lck-mGFP was substantially enriched at the CD4-positive areas, yet a slight unbound fraction in between the patterns can be observed (B). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

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For the interaction analysis, we used a cell line stably expressing unlabelled CD4 and Lck-mGFP and seeded the cells on surfaces containing micropatterned CD4 mAb; the unlabelled CD4 was chosen to eliminate potential influences of the fluorescent protein to the interaction. We found strong rearrangement of Lck-mGFP to the CD4-positive regions, consistent with our previous observations [7] (Fig. 3B). Our idea was now to use the variations in the expression levels of Lck-mGFP between individual cells for recording a binding curve.

Figure 4A shows the specific Lck-mGFP signal in CD4-positive regions (F+-F) as a function of the unspecific signal (F) for each detected spot. We took here F as a measure of the Lck-mGFP surface density. Previous studies showed that essentially all Lck molecules were membrane anchored (7,16), so that potential contributions from the cytosol could be neglected here. Interestingly, the curve did not show any tendency of leveling off, indicating that the Lck concentration was not sufficient to saturate the binding to CD4. In order to get a better understanding of the interaction mechanism, we quantified the concentrations. The brightness of Lck-mGFP spots was again determined by comparison with the brightness of single mGFP molecules. The CD4 density was estimated from the data obtained on CD4-YFP spots upon correction of the reduced expression level in the double-transduced cells; a correction coefficient of 2.32 was obtained via flow cytometry (see Fig. 5). To our surprise, the surface density of the specifically enriched Lck-mGFP was on average approximately ninefold higher than the surface density of CD4 in the spots (compare dashed lines in Fig. 4A). In Figure 4B, we plotted the probability distributions for the surface density of all observed CD4 spots and compared it with the specific Lck-mGFP signal. Only upon multiplying the CD4 concentration with a factor of 9.2, the two curves could be overlayed. Therefore, on average 9.2, Lck-mGFP molecules are recruited by a single CD4 molecule.

image

Figure 4. (A) Binding curve for Lck-mGFP. We analyzed 159 spots recorded on 56 cells and plotted the specific Lck signal against the unspecific signal (open circles). For better visualization, we grouped the data in sets of 20 data points and plotted the mean (full circles) and standard error of the mean (error bars). In contrast to the in vitro experiment, the data do not show any tendency of saturation. We further included the average surface density of Lck (1930 molecules/μm2) and the estimated surface density of CD4 (220 molecules/μm2). (B) Cumulative density function (cdf) of the specific Lck signal (full line) and of the CD4 signal (dashed line). Multiplying the CD4 signal by a factor of 9.2 yielded the best overlay of the curves (dotted line).

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image

Figure 5. Surface expression levels of CD4 in T24 transductants. T24 cells were transduced with either CD4-YFP alone or a combination of wild-type CD4 and Lck-mGFP. Cell surface expression of CD4 was visualized by using mAb MEM-115 conjugated with AF647. The fluorescence intensities (FIs) of the Lck-mGFP construct versus the CD4 mAb (A) or the CD4-YFP construct versus the CD4 mAb (B) are shown in the two-dimensional dot plot diagrams. Gates were set for double positive populations. (C) The CD4 surface stainings of the gated populations in (A) and (B) are displayed in the single-parameter histogram. Stainings of isotype control mAbs were included. Mean fluorescence intensities (MFIs) were calculated by the FlowJo software to estimate the relative CD4 surface expression levels of the cells in the two experiments. In the table, we show the MFI values, the ratio of the MFI value from the cells in gate of (B) over those in gate of (A), and the average ratio that was taken for further calculations.

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Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

We described here the application of protein micropatterning for analysis of binding processes in equilibrium. In the first part of this paper, we showed the proof-of-principle on an in vitro test system. The specific detection of binding reactions on surfaces via fluorescence microscopy was boosted by the availability of TIR excitation [22] and refined since [23], as the evanescent field allows for selective excitation of the receptor-bound fluorescent ligand even in the presence of free ligand in solution. Still, control experiments need to be performed without receptor to determine the residual background of unbound fluorescent ligand. In contrast, on the micropatterned surfaces described here, the receptor-functionalized area and the receptor-free control area are juxtaposed on the same parts of the chip, so that a single experimental run is sufficient for recording the full saturation curve. In addition, the chips can be readout with standard fluorescence microscopy without the need for TIR excitation: even at high background signal from the unbound fluorescent ligand, the difference signal due to bound ligand can be easily distinguished. Similar approaches were followed by Piehler and coworkers [24], who used micropatterned surfaces for the analysis of single molecule binding kinetics.

The situation gets more challenging when it comes to analysis of protein interactions in living cells. The most common technology is Förster resonance energy transfer, in which bait and prey have to be labeled with fluorophores of overlapping emission and absorption spectra; when bait and prey interact, the two fluorophores come sufficiently close so that excitation energy of the donor gets transferred to the acceptor. Obtaining qualitative information with Förster resonance energy transfer is rather straightforward; however, quantification of the binding affinities and complex sizes is difficult or even impossible (25,26). A clearer picture can be obtained from single molecule data, where the proteins of interest are tracked and their collisions, bindings, and unbindings are followed and quantified (27–30). Yet, such experiments and the data analysis are demanding; for example, substantial underlabeling is typically required—since at standard concentrations, the single molecule signals would overlap—which renders quantitative analysis difficult.

We have introduced the micropatterning technique as a rather simple alternative to existing approaches [7]. Here, we used it for a more detailed characterization of the interaction between CD4 and Lck. The surprising observation that each CD4 molecule recruits on average 9.2 Lck molecules could be rationalized by the following explanations:

Lck may be preclustered. Indications for Lck homo-association arose from crystallographic studies on Lck SH3-SH2 domains, where the SH2 domain of one protein was found to bind to the SH3 domain of the second protein and vice versa, creating a “head to tail” interaction of two molecules [31]. Notably, the authors could not detect any interaction in solution and, therefore, speculated that the membrane environment may facilitate the dimerization. Interaction between isolated SH2 and SH3 domains was also shown biochemically [32], and zinc-dependent homodimerization was reported for Lck SH3-domains in solution [33]. Moreover, glutathione S-transferase-pull down assays revealed association of SH2-SH3 domains with endogenous full-length Lck from Jurkat T cell lysates [34]. Finally, using single molecule brightness analysis, we reported the homo-association of fluorescent Lck in the plasma membrane of living T24 cells [7]. Yet, up to now, there was no evidence for cluster sizes larger than dimers, so that Lck homo-association alone most likely does not account for the pronounced recruitment found in this study.

CD4 may be embedded in a membrane environment, which favors Lck partitioning. One could envision that a few Lck molecules—in our study, nine molecules—are associated with the CD4 lipid environment. Indeed, in our previous study, we found the recruitment of Lck-N10-mGFP to CD4 micropatterns [7]. Lck-N10 is a truncation mutant consisting only of the first 10 N-terminal amino acids, which constitute essentially the Lck membrane anchor but is devoid of any protein interaction motifs. We concluded that the membrane environment is involved in the interaction process. This was further confirmed by the reduction of the Lck-CD4 interaction in case of using the nonpalmitoylated CD4 mutant CD4-C396S-C399S as bait. Moreover, we observed strong interaction when we used endogenous CD59 as bait and measured the recruitment of putative raft markers including various GPI-GFP constructs [35]. Taken together, the micropatterning approach allows for quantification of different protein interaction mechanisms, as demonstrated here for direct binding and for indirect associations.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

This work was supported by the GEN-AU Project of the Austrian Federal Ministry for Science and Research and the Austrian Science Fund Projects Y250-B03 and I301-B12. Stefan Sunzenauer is recipient of a DOC-fellowship of the Austrian Academy of Sciences at the Institute of Biophysics.

Literature Cited

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results
  6. Discussion
  7. Acknowledgments
  8. Literature Cited
  9. Supporting Information

Additional Supporting Information may be found in the online version of this article.

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