Interactions between synaptic vesicle fusion proteins explored by atomic force microscopy
Abstract
Measuring the biophysical properties of macromolecular complexes at work is a major challenge of modern biology. The protein complex composed of vesicle-associated membrane protein 2, synaptosomal-associated protein of 25 kDa, and syntaxin 1 [soluble N-ethyl-maleimide-sensitive factor attachment protein receptor (SNARE) complex] is essential for docking and fusion of neurotransmitter-filled synaptic vesicles with the presynaptic membrane. To better understand the fusion mechanisms, we reconstituted the synaptic SNARE complex in the imaging chamber of an atomic force microscope and measured the interaction forces between its components. Each protein was tested against the two others, taken either individually or as binary complexes. This approach allowed us to determine specific interaction forces and dissociation kinetics of the SNAREs and led us to propose a sequence of interactions. A theoretical model based on our measurements suggests that a minimum of four complexes is probably necessary for fusion to occur. We also showed that the regulatory protein neuronal Sec1 injected into the atomic force microscope chamber prevented the complex formation. Finally, we measured the effect of tetanus toxin protease on the SNARE complex and its activity by on-line registration during tetanus toxin injection. These experiments provide a basis for the functional study of protein microdomains and also suggest opportunities for sensitive screening of drugs that can modulate protein–protein interactions.
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Exocytosis is the process in which an intracellular membrane-bound vesicle fuses with the plasma membrane, leading to the release of the vesicle content into the extracellular space. One of the most extensively studied forms of exocytosis is the chemical synaptic transmission used by nervous system cells to communicate. A better understanding of this mechanism is a key to understanding synaptic transmission and synaptic plasticity, learning, and memory.
The current hypothesis suggests soluble N-ethyl-maleimide-sensitive factor attachment protein receptor (SNARE) proteins are mediators of membrane fusion (1–4). In this model, vesicle-associated membrane protein 2 (VAMP 2) is located on the vesicle membrane whereas syntaxin 1 and synaptosomal-associated protein of 25 kDa (SNAP-25) reside in the target membrane (Fig. 1A). Before the fusion process, these proteins assemble into a highly thermostable ternary complex (5–7), which consists of a coiled-coil bundle of four α-helices (one from syntaxin 1, one from VAMP 2, and two from SNAP-25) bound in a parallel alignment (8–10). Whether the SNARE complex triggers fusion directly or indirectly is still controversial (11). The “zipper” model proposes that the complex zips from the membrane distal amino termini to the proximal carboxyl termini, thus bringing the vesicle and the membrane in a close configuration that might induce fusion (4, 10). The sequence of steps leading to fusion is still not clear. The SNARE complex could exist in a partially zipped conformation (12) and complete zippering would then be triggered by a Ca2+-dependent mechanism, leading to fusion (4).
Fig. 1.
The neuronal Sec1 (nSec1) protein could regulate the interaction of syntaxin 1 with its binding partners (13). nSec1 binds syntaxin 1 in a closed conformation (14) and prevents its binding with SNAP-25 or VAMP 2 (15). In addition, the complexes syntaxin 1–nSec1 and syntaxin 1–SNAP-25 have been shown to be mutually exclusive (15).
Tetanus and botulinum toxins prevent neurotransmission by specific proteolysis of one of the synaptic SNAREs (16). Tetanus toxin (TeTx) blocks neurotransmitter release at inhibitory neurons in the spinal cord. TeTx is composed of a light chain responsible for proteolytic cleavage of VAMP 2 (17, 18) and a heavy chain, which binds to neurons (16).
To directly measure interaction forces between SNARE proteins, we used an atomic force microscope (AFM). This instrument was primarily designed to make atomic-resolution images (19), but it recently appeared to be a very useful tool for measuring molecular interactions (20–23). This type of measurement is accomplished by binding one molecular species onto a very small tip, mounted at the end of a cantilever, and a second one on a flat surface, such as mica or gold. By periodically approaching and retracting this tip to and off the substrate, bonds between the two molecules are alternately created and disrupted (Fig. 1B a–c). Monitoring cantilever deflections during such an approach-retraction cycle provides a typical force-distance curve (Fig. 1B). A bond breaking between two proteins gives a characteristic signal (Fig. 1B, arrow), called hereafter one event that permits us to calculate the required force to unbind the proteins. Analysis of force curves recorded for many approach-retraction cycles results in a force histogram, which allows calculation of the mean interaction force. This methodology has been successfully applied to measure interaction forces between several different proteins (24–26).
Recent studies have shown that the unbinding forces measured by AFM linearly depend on the logarithm of the applied loading rate (27–30), which, according to Arrhenius' law (31), reflects the influence of thermal fluctuations on the dissociation process. This linear dependence allows us to explore the energy landscape of a receptor–ligand complex by estimating the corresponding potential barrier widths (28, 31) and their related dissociation rates (28–30). If only one potential barrier exists, the dissociation rate extrapolated under zero force coincides with the natural off-rate, koff (29).
In this study we measured by AFM the interaction forces between pairs of the SNAREs syntaxin 1, SNAP-25, and VAMP 2, and interaction forces between all three SNAREs. Moreover, we measured the effects of nSec1 and TeTx on these interactions. These experiments yield insight into SNAREs kinetics and provide a basis for exploring complex biochemical pathways by AFM.
Materials and Methods
Proteins Expression and Purification. GST-tagged recombinant SNARE proteins SNAP-25' VAMP 2, and nSec1 were expressed in bacteria (32, 33). Plasmids were kindly provided by R. Scheller (Genetech, South San Francisco). They were purified by glutathione-agarose affinity chromatography. Proteins were eluted with 10 mM glutathione in 50 mM Tris·HCl, pH 8. Keeping the GST tag on the proteins decreases the possibility that crosslinking occurs in binding regions of the SNAREs and, in consequence, inactivates them. His-tagged syntaxin 1A was expressed in bacteria from a pQE9 plasmid (Qiagen, Basel) containing the syntaxin 1A cDNA (without the coding region of the C-terminal transmembrane region). It was purified on Ni2+-agarose and eluted with imidazole. Recombinant TeTx light chain was prepared as described (34). TeTx was inactivated by incubation at 100°C for 15 min.
Sample Preparation for AFM Study. The substrate consisted of a freshly cleaved mica sheet functionalyzed by aminopropyltriethoxysilan (35). Proteins (200–300 ng/μl) were crosslinked to it by using glutaraldehyde (0.5%, 15-min incubation). This method had been verified to keep proteins functionality intact (36, 37). The AFM tip was washed in a detergent solution and immersed in glutaraldehyde (0.5%, 15 min), and proteins (200–300 ng/μl) were finally attached by a 15-min incubation. For successive protein deposition on mica, a first type of protein was normally crosslinked and rinsed with Tris-buffered saline (TBS). Then a second protein was deposited on the surface (15 min) and finally rinsed with TBS. Premixed binary complexes were obtained by mixing two proteins in equal concentrations (overnight at 4°C) before crosslinking to mica with glutaraldehyde.
AFM Measurements and Data Processing. Experiments were performed at room temperature on a Nanoscope III (Digital Instruments, Santa Barbara, CA) with force volume mode operating in liquid. Unless specified, measurements were done in TBS buffer with a constant retraction speed of 355 nm/s. We used Digital Instruments AFM cantilevers (nominal spring constant 0.06 N/m) calibrated as described (38). Force curves were analyzed off-line by a fuzzy logic algorithm developed in our laboratory (39), to discriminate true events from false events. Each experiment was independently done at least three times. Loading rate-dependent experiments were performed by varying the retraction velocity from 20 nm/s to 5,000 nm/s. The loading rate was determined by the slope on the force curve before an unbinding event (28, 29).
Results
Interaction Between SNARE Proteins. The direct interaction forces between synaptic SNARE proteins have so far never been determined. Here we used AFM to analyze these forces. To test whether recombinant syntaxin 1, SNAP-25, or VAMP 2 specifically bound in our AFM chamber, we first measured interactions in a “one-to-one” configuration (one protein on the substrate and one protein on the tip). When the two proteins interacted specifically, a clear interaction peak appeared on the force histogram, as it was the case for syntaxin 1 (on the tip) and SNAP-25 (on the mica, Fig. 1C), providing the mean interaction force. In contrast, a nonspecific interaction showed only a few dispersed background events without a clear interaction peak, as we measured in experiments between syntaxin 1 and the unrelated control protein GST (Fig. 1D). We found that each of the three SNAREs interacted specifically with the others. As mean interaction forces, for a constant retraction speed of 355 nm/s, we measured 115 ± 6 pN with VAMP 2 on the tip and syntaxin 1 on the mica (Fig. 2C), 172 ± 6 pN with VAMP 2 on the tip and SNAP-25 on the mica (Fig. 2B), and, as the strongest interaction, 265 ± 4 pN when syntaxin 1 was on the tip and SNAP-25 on the mica (Fig. 2 A, P < 0.001). For each of the three tested proteins, we performed control experiments with one SNARE on the tip and GST on the mica. All of these experiments resulted in typical force histograms of nonspecific interaction (Fig. 1D).
Fig. 2.
We then analyzed whether the presence of the third SNARE alters the one-to-one interaction forces. For this one-to-two configuration (an assembly of two of the proteins on the mica and the third protein on the tip), we studied two types of assemblies: (i) the two proteins on the mica side were deposited successively (see Materials and Methods and Fig. 2 D and E) and (ii) the two proteins on the mica were premixed before deposition (see Materials and Methods and Fig. 2 F–H). Compared with the one-to-one interaction force with VAMP 2 on the tip and syntaxin 1 on the mica (115 ± 6 pN, Fig. 2C), the interaction force increased to 226 ± 7 pN when VAMP 2 was on the tip and SNAP-25 was deposited on the mica before syntaxin 1 (Fig. 2E). A similar phenomenon was observed for the VAMP 2–SNAP-25 interaction: presence of the third protein (i.e., syntaxin 1) increased the VAMP 2–SNAP-25 interaction from 172 ± 6 to 244 ± 2 pN (Fig. 2 B and D). The strongest among all interactions in the one-to-two configurations was achieved with VAMP 2 on the tip and a complex of premixed syntaxin 1 and SNAP-25 on the mica substrate. In this case the interaction force reached 279 ± 3 pN (Fig. 2F, P < 0.001).
These results showed that in the AFM chamber each of the three SNAREs interacted specifically with the others. In addition, the interaction forces were significantly higher when the three proteins of the complex were present compared with the one-to-one configurations.
Loading Rate Dependence of the Unbinding Force and Dissociation Rate Estimation. To deeper analyze the mechanisms of the SNARE complex dissociation in our experimental set-up, we measured the dependence of the unbinding force on the applied loading rate for the binary interaction syntaxin 1–SNAP-25 and the interaction of VAMP 2 with a premixed complex of syntaxin 1 and SNAP-25. By modulating the tip retraction velocity, a wide range of different loading rates varying from 200 to 80,000 pN/s was applied. The unbinding force was found to depend linearly on the logarithm of the applied loading rate, as shown in Fig. 3A for the interaction of syntaxin 1 with SNAP-25 and in Fig. 3B for the interaction of VAMP 2 with a premixed complex of syntaxin 1 and SNAP-25. Only one slope was observed for this logarithmic dependence, showing that the same potential barrier was dominating the dissociation for all of the applied loading rates. Fitting a natural logarithm to our data permitted us to measure the corresponding potential barrier widths (31). These were estimated to be 3.6 ± 0.6 Å for syntaxin 1–SNAP-25 and 4.5 ± 0.7 Å for VAMP 2 versus a premixed syntaxin 1 and SNAP-25 binary complex. Extrapolating the loading rate at zero force allowed an estimation of the dissociation rate for the given potential barrier (28–30). We obtained a dissociation rate of ≈3 × 10–7 s–1 for the interaction syntaxin 1–SNAP-25 and ≈2 × 10–10 s–1 for VAMP 2 against a binary complex of syntaxin 1 and SNAP-25.
Fig. 3.
Estimation of the Number of Complexes Necessary to Dock One Vesicle. The knowledge about interaction forces of the SNAREs allowed us to estimate the number of complexes necessary to hold a vesicle close to the presynaptic membrane. The binding energy n·Vb(z) provided by a number n of complexes had to withstand the electrostatic repulsion Vel(z) exerted by the presynaptic membrane on the vesicle. Thus, the total energy of a vesicle standing at a distance z from the presynpatic membrane was given by V(z) = n·Vb(z) + Vel(z). Therefore, the number of complexes necessary to dock one vesicle could be calculated as the minimum value of n that led to a total potential yielding a stable bound state. As we considered only a bound or unbound state for the vesicle, we model Vb(z) by a simple slope (critical force of 200–300 pN, unbinding distance of 20 nm, see Supporting Text, which is published as supporting information on the PNAS web site, www.pnas.org). The electrostatic potential was described analytically by the Poisson–Boltzmann equation and diminished by a screening effect caused by charged ions present in cytoplasm. Here, we considered two extreme cases, one with a cytoplasm containing positive ions only (0.15 M) and one with equal concentration of positive and negative ions (0.15 M) (see Supporting Text for detailed calculations). The first situation yielded a weaker screening than the latter and showed that a minimum of seven complexes would be required to maintain a vesicle at 18 nm from the membrane (Fig. 4A). To reduce this distance to 11 nm, 11 complexes would be necessary. On the opposite, considering a situation with equal concentrations of positive and negative ions showed that one complex could maintain a vesicle at 5 nm from the membrane (Fig. 4B).
Fig. 4.
Additional Analysis Providing Indirect Strong Control Data and Information on AFM Capabilities. To gain further insights into the fusion mechanism and gather additional data supporting the reliability of our findings, two additional experiments were performed. In the first series, we included nSec1 in our model. In the second series, we included the TeTx protease. nSec1 is known to prevent synaptic SNARE complex formation when bound to syntaxin 1 (15). To study the role of nSec1 in the synaptic SNARE complex formation with AFM, we first measured the nSec1 interaction with syntaxin 1, SNAP-25, or premixed syntaxin 1–SNAP-25. nSec1 strongly interacted with syntaxin 1 alone (Fig. 5A) but not with SNAP-25 (Fig. 5B) or syntaxin 1 premixed with SNAP-25 (Fig. 5C).
Fig. 5.
Then we tested nSec1 effects on the SNARE complex formation. The experiment started by recording 1,600 force curves of the interaction between VAMP 2 (on the tip) and a premixed syntaxin 1–SNAP-25 binary complex (on the mica). We then stopped data acquisition and exchanged the TBS buffer in the chamber by TBS containing 40 ng/μl nSec1. After a 15-min incubation at room temperature, we recorded again 1,600 force curves and then compared the number of events detected before and after nSec1 injection. In this configuration (VAMP 2 on the tip, syntaxin 1–SNAP-25 premixed complex on the mica), addition of nSec1 did not significantly alter the number of events (Fig. 5Da) and interaction force remained constant (data not shown). In contrast, in an experiment in which syntaxin 1 was on the tip and SNAP-25 on the mica, addition of nSec1 induced a 60% decrease in event numbers (Fig. 5Db).
These results showed that nSec1 interacted specifically with syntaxin 1 and prevented its binding to SNAP-25. In contrast, nSec1 seemed to have no effect on the SNARE complex formation when syntaxin 1 was already bound to SNAP-25.
TeTx is known to prevent neurotransmision by cleaving VAMP 2 (17). We recorded 1,600 force curves in TBS buffer with VAMP 2 on the tip and a premixed syntaxin 1–SNAP-25 binary complex on the mica (Fig. 6A). Then we exchanged the buffer with TBS containing 200 nM TeTx light chain, followed by incubation for 30 min at 37°C. Finally we recorded 1,600 force curves again (Fig. 6B). The number of events drastically decreased to <50% of the original value preceding TeTx injection (Fig. 6Cb).
Fig. 6.
To confirm that this effect was caused by the proteolytic activity of TeTx, we did two control experiments. First, we repeated the experiment as above, but with the injection of a deactivated TeTx (heated 15 min at 100°C). As expected, we did not measure any significant change in event numbers (Fig. 6Cc) or in the interaction forces (data not shown). Second, we tested the effects of TeTx on the binary interaction of syntaxin 1 (on the tip) and SNAP-25 (on the mica). The number of events measured before and after TeTx introduction were similar (Fig. 6Ca) and interaction forces remained constant (data not shown).
Finally, we recorded on-line the interaction between VAMP 2 (on the tip) and a syntaxin 1–SNAP-25 premixed complex (on the mica), during the injection of TeTx in the AFM chamber. The number of events per fixed time interval (131 s) decreased in an exponential way (Fig. 6D, ▴). In contrast, in a control experiment in the absence of TeTx, the number of events per time interval remained stable over time (Fig. 6D, ▪). These results clearly suggested that cleavage of VAMP 2 by TeTx prevented the SNARE complex formation. In addition, they showed that AFM is able to follow on-line an enzymatic action.
Discussion
The development of new technologies allows the exploration of biophysical properties of macromolecular complexes at work and following biological processes at the molecular level (40). In the present study, we have used AFM to measure the interaction forces within a complex made of three proteins. Moreover a fourth protein has been added, either to modulate the binding of the proteins (nSec1) or proteolyse one of the proteins (TeTx). Initial experiments deal with the three SNARE proteins (syntaxin 1, SNAP-25, and VAMP 2) and an extensive series of controls. These results reveal specific interactions between the SNAREs with unbinding forces among the highest recorded so far between proteins by AFM (22, 24, 36). This finding may reflect the very high stability of the SNARE complex, which resists SDS denaturation and heating at 90°C (5–7). In addition, we show that the interaction forces measured in the presence of the three proteins are higher compared with those measured with two SNAREs only. The interaction force measured between VAMP 2 and a syntaxin 1–SNAP-25 premixed complex (279 pN) increases compared with the one-to-one interactions VAMP 2–syntaxin 1 (115 pN) or VAMP 2–SNAP-25 (172 pN). This finding suggests that the affinity of VAMP 2 for syntaxin 1 and SNAP-25 depends on whether the two latter proteins interact with each other. If syntaxin 1 and SNAP-25 are premixed in a test tube before their deposition on mica, they can freely bind to each other before strongly interacting with VAMP 2 attached on the tip (279 pN). The lower forces recorded when syntaxin 1 is deposited after or before SNAP-25 (226 and 244 pN, respectively) certainly indicates that the SNAP-25–syntaxin 1 complex cannot form in an optimal way because of the particular deposition sequence.
Because the SNARE complex formation involves three different proteins, one can speculate that the first interaction to take place is the strongest among the one-to-one interactions, i.e., syntaxin 1–SNAP-25. This first event would then be followed by the interaction with VAMP 2. Consistent with this finding, the interaction force measured between VAMP 2 and the syntaxin 1–SNAP-25 premixed complex is the strongest interaction among all of the configurations tested. This sequence for the SNARE complex formation, which we propose here, is consistent with crystallographic and kinetic data recently published (9, 14, 41).
To deeper understand the mechanisms related to the SNARE complex dissociation, we have measured the dependence of the unbinding forces on the loading rate logarithm. A clear linear dependence is shown for the interaction of syntaxin 1 with SNAP-25 and of VAMP 2 with a premixed complex of syntaxin 1 and SNAP-25 (Fig. 3), reflecting that only one potential barrier is prevalent for the measurements at the applied loading rate. The corresponding dissociation rates are very slow (3 × 10–7 s–1 and 2 × 10–10 s–1, respectively) compared with values measured by the same technique for other biomolecular interactions [0.004–0.06 s–1 for antibody–antigen interactions (29), 0.4–1.6 s–1 for sugar–receptor complexes (28), 0.002 s–1 for P-selectin (30)]. Nevertheless, a dissociation rate of ≈5 × 10–7 s–1 for the syntaxin 1–SNAP-25 interaction has been extrapolated from experiments in solution applying denaturants conditions (41). Because this value is in good agreement with our result, it suggests that the unbinding forces, which we measured here, are determined by the same energy barrier that is prevalent for spontaneous dissociation in solution.
Crystallographic and kinetic data (9, 14, 41) and the present study show that the binary complex syntaxin 1–SNAP-25 is a major intermediate state in the SNARE complex formation. Assuming that the SNARE complex dissociation in vitro passes by this intermediate state, two reactions would dominate the dissociation kinetics: the unbinding of VAMP 2 from the syntaxin 1–SNAP-25 binary complex and the dissociation of this binary complex. The SNARE complex dissociation rate could therefore be estimated by multiplying the dissociation rate of these two reactions, which have been measured by AFM. This would result in a value of ≈6 × 10–17 s–1, corresponding to a half-life time of almost one billion years, which agrees with recent published data (41). This extremely slow rate shows that once the SNARE complex is formed in vitro it does not dissociate within a biological relevant time. Therefore, the presence of the ATPase N-ethyl-maleimide-sensitive factor and the adaptor protein α-SNAP, which assist in dissociation of the SNARE complex after fusion and prior recycling (1, 42), is absolutely necessary for correct in vivo function of the SNAREs.
The SNARE complex in vivo could exist in a partially zipped conformation (12). However, the complex formed in vitro certainly reflects a fully zipped complex (4). Because our kinetic results agree with values obtained in vitro (41), the SNARE complex that we formed here probably represents a full zippering. Nevertheless, we cannot exclude that the particular configuration of AFM measurements (cytosolic domain of VAMP 2 firmly attached to the tip and SNAP-25 and cytosolic domain of syntaxin 1 attached to the mica) might interfere with a complete zippering.
Our force measurements on the SNAREs permit us to estimate the number of complexes necessary to dock one vesicle. We have developed a theoretical model based on our data and analyzed two situations. Within a cytoplasm containing positive ions only, a minimum of seven complexes would be required, but in a cytoplasm with equal concentrations of positive and negative ions, only one complex would be necessary. Typical mammalian neurons contain both negative and positive ions with a predominance of K+. Therefore, physiological conditions must be an intermediate case between the two considered here and are probably better modeled with the positive ions situation. In any case, this study shows that one complex alone cannot dock one vesicle and probably a minimum of four or five complexes might be necessary to keep a vesicle close to the presynaptic membrane. This finding agrees with the generally believed idea that multiple SNARE complexes are necessary for fusion to occur (5, 43, 44). In addition, our model suggests that docking might begin with the formation of one SNARE complex, followed by the binding of other complexes, which would bring the vesicle and the membrane closer, as suggested in Fig. 4.
To provide further insight on the fusion mechanism, gather additional control data, and collect further evidence about AFM abilities, we have explored the SNARE complex interactions with nSec1 and TeTx. Our experiments show that nSec1 strongly interacts with syntaxin 1 alone (Fig. 5A), but does not interact with a premixed syntaxin 1–SNAP-25 complex (Fig. 5C), in agreement with previously published data (15). Similarly, we show that nSec1 injected into the AFM chamber significantly diminishes syntaxin 1–SNAP-25 interaction (Fig. 5Da). Assuming that nSec1 in solution interacts with syntaxin 1 on the tip, we conclude that syntaxin 1, bound to nSec1, cannot interact with SNAP-25 any more, which is consistent with recently published work (15). On the contrary, when the syntaxin 1–SNAP-25 complex is already formed, nSec1 injection does not change the interaction of VAMP 2 with the binary complex (Fig. 5Db). Therefore, we speculate that nSec1 prevents SNARE complex formation by binding to syntaxin 1, but does not have any effect when syntaxin 1 is already bound to SNAP-25.
Finally, our results demonstrate that TeTx has no effect on the syntaxin 1–SNAP-25 interaction (Fig. 6Ca), but strongly interferes with the binding of VAMP 2 to the two other proteins (Fig. 6 B and Cb). These results are consistent with published data showing that TeTx prevents SNARE complex formation by cleaving VAMP 2 (17). Upon injection of TeTx in the AFM chamber, the number of events recorded between VAMP 2 and the SNAP-25–syntaxin 1 premixed complex diminishes exponentially as a function of time (Fig. 6D), as one could expect in any enzymatic reaction.
Taken together, our data clearly show that AFM can be applied to explore not only one-to-one protein interactions but also complex systems involving several proteins studied within static or dynamic conditions. The data emphasize the extreme stability of the synaptic SNARE complex and therefore the necessity for the presence of additional “modulatory” proteins within living cells. In addition, the fact that a theoretical model based on our measurements allows us to predict that a minimum of four complexes might be necessary for fusion to occur opens opportunities for dissecting the final steps involved in the fusion event. We further anticipate that AFM studies will soon permit the dynamic investigation of signaling macromolecular domains in cell-free and intact cell systems.
Note
Abbreviations: SNARE, soluble N-ethyl-maleimide-sensitive factor attachment protein receptor; VAMP 2, vesicle-associated membrane protein 2; SNAP-25, synaptosomal-associated protein of 25 kDa; nSec1, neuronal Sec1; TeTx, tetanus toxin; AFM, atomic force microscope; TBS, Tris-buffered saline.
Acknowledgments
We thank Dr. T. Coppola for his useful comments. This work was supported by Swiss National Science Foundation Grants NB 31-00052587.97 and 2000-065160.01.
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Copyright © 2003, The National Academy of Sciences.
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Received: January 22, 2003
Published online: July 9, 2003
Published in issue: July 22, 2003
Acknowledgments
We thank Dr. T. Coppola for his useful comments. This work was supported by Swiss National Science Foundation Grants NB 31-00052587.97 and 2000-065160.01.
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