NANO LETTERS
Structural and Mechanical Study of a Self-Assembling Protein Nanotube
2006 Vol. 6, No. 4 616-621
J. F. Graveland-Bikker,*,† I. A. T. Schaap,‡ C. F. Schmidt,‡,§ and C. G. de Kruif†,| NIZO food research, P. O. Box 20, 6710 BA Ede, The Netherlands, Section Physics of Complex Systems, Department of Physics and Astronomy, Vrije UniVersiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands, III. Physikalisches Institut, Faculty of Physics, Georg-August-UniVersita¨t, Friedrich-Hund-Platz 1, 37077 Go¨ttingen, Germany, and Van’t Hoff Laboratory, Debye Research Institute, Utrecht UniVersity, Padualaan 8, 3584 CH Utrecht, The Netherlands Received November 9, 2005; Revised Manuscript Received January 6, 2006
ABSTRACT We report a structural characterization of self-assembling nanostructures. Using atomic force microscopy (AFM), we discovered that partially hydrolyzed r-lactalbumin organizes in a 10-start helix forming tubes with diameters of only 21 nm. We probed the mechanical strength of these nanotubes by locally indenting them with an AFM tip. To extract the material properties of the nanotubes, we modeled the experiment using finite element methods. Our study shows that artificial helical protein self-assembly can yield very stable, strong structures that can function either as a model system for artificial self-assembly or as a nanostructure with potential for practical applications.
Molecular self-assembly is a rapid and simple method for fabricating novel supramolecular architectures. Via this “bottom-up” approach, many new nanomaterials have been and will be produced.1,2 Proteins, peptides, and DNA have been used to fabricate molecular biomaterials.3 Building blocks that assemble into fibrous materials are of special interest because linear structures offer the possibility of constructing mechanically resistant materials.4 Partial hydrolysis of R-lactalbumin by a protease from Bacillus licheniformis (BLP)5 delivers such building blocks that selfassemble into filaments at neutral pH.6 Native R-lactalbumin, a 14.2-kDa whey protein, plays a crucial role in lactose synthesis7 and is high in the essential amino acid tryptophan. Nanotubes assembled from modified R-lactalbumin have a diameter of about 20 nm and a hollow core of about 8.7 nm.8 Divalent ions such as calcium were shown to trigger nanotube formation.9,10 There are naturally occurring protein nanotubes, such as tobacco mosaic virus or microtubules, with particular biological functions.11,12 Nanotubes have also been built from specially designed peptides with a limited number of amino acids, typically ranging from 2 to 10.13-15 The R-lactalbumin nanotubes we report on here are unique self-assembled structures in that they are, to the best of our knowledge, the first artificial nanotubes made of almost * Corresponding author. Current address: Center for Biomedical Engineering, Massachusetts Institute of Technology, 500 Technology Square, Cambridge, MA 02139. E-mail:
[email protected]. † NIZO food research. ‡ Vrije Universiteit Amsterdam. § Georg-August-Universita ¨ t. | Utrecht University. 10.1021/nl052205h CCC: $33.50 Published on Web 03/15/2006
© 2006 American Chemical Society
whole proteins. These nanotubes promise a variety of applications: They could serve as drug delivery devices by virtue of their cavity. Because of their linear structure, the nanotubes could also serve as an artificial fibrous scaffold to mimic natural systems.16 They could furthermore serve as templates for (in)organic nanostructures.1 We have studied R-lactalbumin nanotubes with atomic force microscopy (AFM) for two reasons. First, we wanted to image the molecular structure of the nanotubes with nanometer resolution in buffer. Second, we wanted to probe their mechanical properties, again in buffer, which is one of the first steps toward their use as structural elements for various applications.17 Nanotube Dimensions. Figure 1 shows a typical image of R-lactalbumin nanotubes adsorbed onto a glass surface and imaged by AFM. In addition, some monomers or small aggregates are visible in the background. The tubes were mostly adsorbed in a relatively straight or slightly curved conformation. Occasionally, tubes crossed each other, which resulted in a doubled height measured at the crossing points. The lengths of the tubes varied from hundreds of nanometers up to a few micrometers. The persistence length, estimated from contour lengths and end-to-end distances18 of tubes in electron micrographs, is on the order of 5 µm. This value is higher than the persistence length of DNA (50 nm), comparable to that of filamentous actin (15 µm), but not as high as that of the tube-like microtubules (1-6 mm).19 To elucidate more structural details, we performed highresolution scans of individual R-lactalbumin tubes (Figure 2A). Figure 2B shows a distribution of tube diameters
Figure 1. Overview image of R-lactalbumin nanotubes. The tubes did self-assemble after partial proteolysis of R-lactalbumin at 50 °C for 1.5 h and were stable for multiple days (see the Supporting Information). The glass surface was positively charged, using amino silane, to adsorb the tubes. Inset, upper right corner: height profile along the line indicated in the image. Inset, lower left corner: transmission electron micrograph of R-lactalbumin nanotubes prepared in the same way.
Figure 2. (a) High-resolution image showing the right-handed helix. The inset, a 2D Fourier transformation, shows the helical periodicity. (b) Distribution of the measured heights of the tubes. The average is 20.9 ( 0.3 nm (mean ( sem, n ) 42).
measured from the heights of 42 different tubes. The average height was 20.9 ( 0.3 nm (mean ( sem). The average apparent width of the tubes was 54 nm. This value is an overestimation of the diameter, due to lateral dilation caused Nano Lett., Vol. 6, No. 4, 2006
by the tips with a nominal tip radius of 20 nm and is consistent with an actual width of about 20 nm. Using the relation Rt ) W2nt/16Rnt, where Rt is the tip radius, Wnt is the measured tube width, and Rnt is the tube radius (see the Supporting Information), we can calculate an exact actual tip radius based on the measured tube heights, which are unaffected by tip size. The average tip radius for the different experiments was calculated to be 17.6 ( 1.0 nm (mean ( sem, n ) 10), consistent with the nominal tip radius specified by the manufacturer. Helical Structure. In high-resolution scans, the protein tubes displayed a right-handed helical pattern, clearly visible in Figure 2A. To determine the pitch (axial rise per helical turn) of the helix, we need to take into account the geometrical distortions caused by scanning with a conical tip of finite radius. Scanning with an infinitely sharp tip would produce a 2D projection of the helix, that is, a sinusoidal curve: y ) Rnt sin(2πx/P), Where P is the pitch and Rnt is the nanotube radius. A finite-sized tip will still produce an approximately sinusoidal image of the helix. This is evident if one approximates the tip as a sphere: while “rolling” around the helix, the center of the sphere would move on a helix with a sinusoidal projection with a larger amplitude but the same period: y ) (Rnt + Rt) sin(2πx/P), where Rt is the tip radius. The actual image would be a truncated sinusoidal if the tip radius exceeds the tube radius. The coordinate system was aligned such that x is parallel and y is normal to the tube axis. This sine curve was overlaid on the image, and its periodicity was fitted by eye to the helical pattern (Figure 2A). The periodicities found gave a pitch of 105.3 ( 4.8 nm (mean ( sem, n ) 10) measured for different tubes in separate experiments. For a tube diameter of 20.9 ( 0.3 nm, this results in a pitch angle of 58 ( 1°. Using Fourier-transformed images of the helical structure, the distance between the helix strands was found to be 5.4 ( 0.2 nm (mean ( sem, n ) 10). This gives an interstrand spacing in the axial direction of 5.4 nm/cos 58° ) 10.3 nm. Together with the 105 nm pitch, this implies a 10-start helix. The measured depth of the grooves between the helical strands was about 0.6 nm, but the actual groove is likely to be deeper because the relatively large tip cannot completely enter the narrow groove. Nanotube Rigidity. The elastic properties of the tubes were determined by local radial indentation of individual tubes with the AFM tip while recording the force as a function of indentation depth.20 The tip was positioned exactly on top of a single tube, which was located by performing line scans at right angles to the tube just before indentation. Figure 3A depicts several force-versus-indentation curves (FZ curves) illustrating the typical responses. While the tip approached the tube, no force was measured (horizontal part of the curves). When the tip reached the top of the tube, indentation started, and the slope of the curves changed abruptly. The contact point could be defined to within less than 1 nm. For the first 5 nm of indentation, the response in force was linear with indentation depth. In repeated experiments this initial force response was linear up to an indentation of 5.6 ( 0.6 nm (mean ( sem, n ) 617
Figure 3. Indentation of R-lactalbumin nanotubes by an AFM tip. For all experiments we used Olympus RC800PSA (200 × 20 µm, 0.05 N/m) cantilevers. (a) Typical indentation curves up to high forces (linear and nonlinear regime), including one retraction curve (grey line). All five curves were from different tubes and in each case the first high force indentation on this tube. (b) Five successive low-force indentations on the same spot of one tube remaining within the reversible elastic regime (black, approach; gray, retraction curves).
10), or about 25% deformation. The linear response confirmed that the tubes were hollow because for a solid cylinder the expected response is nonlinear with a local stiffness increasing with indentation depth due to tip-sample geometry,21 even if the tube material has a linear elastic response for the deformation amplitudes involved. Beyond an indentation depth of about 6 nm, the response became nonlinear with the curves leveling off. This is the opposite behavior from that of a solid cylinder and implies buckling, or breakage of the tubes. At even higher forces, the curves increased in slope again and approached a vertical line, which was caused by the tip reaching the (incompressible) glass surface. Figure 3A shows total indentations between 18 and 22 nm, which corresponded to the heights of these particular nanotubes. The retraction curve followed a different path, indicating that the deformation was largely not elastic for such indentations. Small Deformations - Young’s Modulus. To investigate whether the linear part of the response was reversible, we performed repeated force-indentation curves with a limited force on the same spot. Such a sequence of five curves is shown in Figure 3B (including approach and retraction curves). It demonstrates, first, that there was no detectable hysteresis (at an approach and retraction speed of 100 nm/ s). This implies that the response of the tubes at this deformation rate was purely elastic with a negligible viscous component. Second, the data show that repeated response curves were virtually identical upon repeated (small) indentations. The reversibility probably lasts for the whole linear regime (up to 5.6 ( 0.6 nm indentation). Averaging the results from indentations of 18 tubes in different experiments, an average spring constant of 0.058 ( 0.014 N/m (mean ( sem) was obtained (for a distribution of the nanotubes’ spring constants see the histogram in the Supporting Information Figure 2). Furthermore, the spring constant was shown to be independent of the rate of indentation between 37 and 150 nm/s. The variation in elastic response when measured on a single tube was considerably less (Figure 3B). The variation in the elastic responses of different tubes (24%) could be due to a slight 618
variation in wall thickness or tube diameter, defects in the structure, or errors in the calibration of the cantilever stiffness. The measured spring constant of the tubes is determined by both their material properties and their geometry. Using a model with simplifying assumptions, one can calculate a Young’s modulus to characterize the tube material. Indentation of (semi-infinite) solid objects is commonly described by the Hertz model,21 which predicts a nonlinear response for purely geometrical reasons. For hollow cylinders, such as the R-lactalbumin tubes, the Hertz model is not appropriate. As long as the indentation remains on the order of the shell thickness, the force is expected to rise linearly with indentation depth. A model for an asymmetrically loaded hollow cylinder is described by De Pablo et al.22 The relation between the Young’s modulus and the spring constant, derived using both thin-shell theory and finite element methods (FEM), is: E = (kR3/2)/(1.18t5/2), where E is the Young’s modulus, k is the spring constant, R is the radius, and t is the wall thickness of the tube (SI units). This model assumes a hollow cylinder of homogeneous material with the tip force applied as a point force. The latter assumption is not as restrictive as it may appear because the deformation of the tube extends over tens of nanometers, larger than the tip radius.22 For spherical shells the assumption of a point force has been shown not to affect the results.23,24 The assumption of a thin shell, where no compression in the normal direction is allowed, might be restrictive, however, because the wall thickness of the R-lactalbumin nanotubes is not small compared to the tube radius. We compared the results of the thin-wall model with finite element modeling of a thick-walled tube (see Supporting Information). Tubes were modeled with a radius of 7.5 nm, and the wall thickness was varied to simulate a range of effective wall thicknesess. Figure 4a shows the resulting indentation curves where the Young’s modulus was chosen for each wall thickness such that the curve was as close as possible to the measured average stiffness of 0.058 N/m. Figure 4b shows both the results of the thin-shell model and the results for thick-walled tubes in FEM. Compared to the thick-wall model, the thinshell model clearly underestimated the Young’s modulus. The assumption of homogeneity is likely an oversimplification because the tubes consist of relatively large protein building blocks and show a rather corrugated surface in the scans. The effective wall thickness may well be less than 6 nm because the grooves between the helix strands are likely to be a few nanometers deep. The monomers will probably have a smaller contact area than a 6 nm wall thickness would suggest. A reasonable estimation of the effective wall thickness of 3 nm, which is the size of one monomer, gives a Young’s modulus of 0.1 GPa for a thick-walled tube in Figure 4b. Large Deformations. Indentations beyond the linear regime resulted in damage to the tube wall, or even in obvious tube breakage. Figure 3A shows the forces required to indent the tubes beyond 5 nm. The slope of the curves decreased beyond this point, which can be explained by damage or buckling of the tube wall, resulting in less rapidly Nano Lett., Vol. 6, No. 4, 2006
Figure 5. Severe indentation led to damage of R-lactalbumin nanotubes: (a) Nanotube before indentation; the arrow indicates the spot of indentation. (b) The nanotube has been broken by the indentation, as is clear from the cleft. The indentation curve in the inset shows a plateau at about 0.4 nN. (c) The tip perforated the tube wall, resulting in a hole. (d) A fragment of the tube (100 nm) was cut out after an indentation at the upper fracture.
Figure 4. (a) Simulated deformation of a thick-walled tube. The tube radius was kept constant at 7.5 nm, while the wall thickness (t) was varied. The Young’s modulus (E) was chosen such that the deformation up to 4 nm could be fitted with 0.058 N/m. Despite the expected nonlinearities (tip shape effect, buckling of the thick wall), the effective response curve is close to linear, but the actual curve shape depends on the wall thickness. (b) Deformation of a thick-walled tube compared to a thin-walled tube. The Young’s modulus to get a spring constant of 0.058 N/m is calculated with the thin-shell model from ref 22 (shown in black). The results from the thick-wall FEM computations are shown in red. At increasing wall thickness (and thus the ratio t/R), the thin-shell model underestimates the Young’s modulus increasingly. At 2 nm wall thickness the difference is a factor of 1.45, whereas at 6 nm it increased to 1.83. The inset shows a 3 nm thick-walled tube indented by a parabolic tip with a 20 nm radius; the colors indicate the stress.
increasing resistance upon further deformation. Figure 5 correlates an indentation curve showing a clear nonlinearity with damage to the tube imaged right after the indentation. In cases where the FZ curve contained obvious changes in slope or a plateau, breakage of the tubes was often observed as exemplified in Figure 5. Here a tube was imaged before and after indentation. There is a clear fracture line visible across the tube after the severe indentation; the applied force at the slope change was about 0.4 nN, which is a typical Nano Lett., Vol. 6, No. 4, 2006
force at which significant deviations from linearity were observed in the FZ curves. The type of damage seen after high-force indentation varied. Sometimes severe indentation only caused a hole in the tube, see Figure 5C. In several cases the images before and after indentation were identical. It is unlikely that the tube was not damaged at all, so either the wall was damaged, but not visibly, or the tube selfrepaired within the time between indentation and imaging. Figure 5D is an image of a completely broken tube; in this case a section of about 100 nm was excised from the tube. Conspicuously, the tubes always broke roughly along the direction of the threads of the helical structure on top of the tube. This indicates that the interactions between helix threads are weaker than the interactions within a thread. We have characterized self-assembling R-lactalbumin nanotubes both structurally and mechanically. The outer diameter of 20.9 nm we observed by AFM for the R-lactalbumin nanotube is in good agreement with the diameter obtained from TEM (Figure 1 inset, estimated diameter of about 20 nm9 and small-angle X-ray scattering (SAXS) experiments on the same tubes: 19.9 nm.8 The self-assembly of the hydrolyzed R-lactalbumin molecules occurred in a right-handed helical fashion. Figure 6 depicts a 3D model of the R-lactalbumin nanotube based on the observed data. It is not possible to directly determine the inner diameter of the R-lactalbumin nanotubes by AFM measurements. Previous SAXS experiments gave an inner diameter of about 8.7 nm.8 A cavity of 8.7 nm implies a wall thickness of about 6 nm. This is more than the size of a monomer (3 nm), so the wall probably consists of dimers, as was also suggested on the basis of the SAXS results. If the nanotubes were assumed to be constructed of stacked rings, then a cross-sectional view would show a ring containing 10 dimers assembled radially around the hollow core. Because a pitch of 105 nm implies about 35 stacked rings in the longitudinal direction (105 nm/3 619
Figure 6. Model of R-lactalbumin nanotube as a 10-start righthanded helix with outer diameter 21 nm, inner diameter 8.7 nm, pitch 105 nm, pitch angle 58°, and inter-strand spacing 5.4 nm.
nm), the orientation of the adjacent ring should have an angular offset around the tube axis of about 10° (360° divided by 35 rings). When 10 dimers are stacked around a hollow core, then the interstrand spacing on the outside of the tube would be 2πRnt/10. This is about 6 nm, which agrees well with the observed 5.4 nm spacing. Intermediate states of tube assembly were not observed, so the nanotubes appear to be built by one-by-one assembly of either monomers or dimers. Helical assembly is a common feature in nature, seen with DNA, F-actin, or TMV. If monomers are capable of forming linear polymers, then they will in general stack with some twist angle which results in a helix. TMV is built up of one-by-one assembled monomers in a one-start helix.11 The HIV-Rev protein tubes are made up of Rev dimers, arranged in a six-start helix.25 Although we could determine dimensions and important structural features of the R-lactalbumin tubes, higher-resolution AFM or electron microscopy 3D reconstruction would be necessary to give a more detailed model on the molecular level. To estimate the Young’s modulus of the R-lactalbumin nanotubes, we applied a thick-walled finite element model, where the effects of a finite wall thickness are included. This more appropriate model gave results clearly different from the thin-shell model, resulting in a 40 to 80% higher Young’s modulus for values of t from 1.5 to 6 nm. How meaningful the calculated Young’s modulus for the R-lactalbumin nanotubes is depends on the suitability of the homogeneous model we used to calculate the modulus from the measured spring constants and on the accuracy of the effective wall thickness estimation. Compared with Young’s moduli of other (biological) structures, the R-lactalbumin nanotubes are clearly stiffer than whole living cells, which have Young’s moduli typically in the range of 10-4 to 10-2 MPa;26 or myofibrils and casein micelles, which both have typical moduli of 10-1 MPa.27,28 This is not unexpected because all those are composites with only a limited volume fraction of protein material. However, R-lactalbumin nanotube walls seem slightly softer than microtubule walls, with a Young’s modulus of 0.6 GPa;29 or bacteriophage capsids, 1.8 GPa.30 Nonproteinaceous tubes, such as carbon nanotubes, are significantly stiffer: their Young’s modulus can be as high as 1 TPa.17,31 Surprising is the apparent contradiction between the relative short persistence length of about 5 µm estimated from TEM and the tube-like design of the R-lactalbumin tubes. Microtubules, having comparable dimensions, show persis620
tence lengths 2-3 orders of magnitude higher. This might be caused by weak contacts between the successive turns of the helix. Such a tube could be considered as a relatively thin-walled tube reinforced with stiff helical ribs. Analogous to a shower hose or a phone cord, this design results in a very flexible tube while maintaining a high resistance against radial indentations. In conclusion, this study shows that artificial helical protein self-assembly can yield stable, relatively strong structures that can function either as a model system for artificial selfassembly or as a nanostructure with the potential for practical applications. Acknowledgment. We thank the Dutch Ministry of Economic Affairs through Innovative Research Program Industrial Proteins, Friesland Foods Domo, AVEBE, NIVE, and the Dutch Foundation for Fundamental Research of Matter (FOM) for financial support. Supporting Information Available: Detailed methods section, tip-sample dilation, histogram of the nanotube stiffness, and the results of the persistence length measurements. This material is available free of charge via the Internet at http://pubs.acs.org. Abbreviations AFM TEM BLP DETA FZ curve FEM
atomic force microscopy/-scope transmission electron microscopy Bacillus licheniformis protease N1-[3-(trimethoxysilyl)propyl]diethylenetriamine force versus distance curve finite element modeling
References (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)
Bittner, A. M. Naturwissenschaften 2005, 92, 51-64. Zhang, S. Nat. Biotechnol. 2003, 21, 1171-1178. Seeman, N. C. Chem. Biol. 2003, 10, 1151-1159. Viney, C. Curr. Opin. Solid State Mater. Sci. 2004, 8, 95-101. Breddam, K.; Meldal, M. J. Eur. Biochem. 1992, 31, 103-107. Ipsen, R.; Otte, J.; Qvist, K. B. J. Dairy Res. 2001, 68, 277-286. Brew, K.; Grobler, J. A. In AdVanced Dairy Chemistry - Vol. 1: Proteins; Fox, P. F., Ed.; Elsevier Science Publishers LTD: Essex, 1992. Graveland-Bikker, J. F.; Fritz, G.; Glatter, O.; de Kruif, C. G. J. Appl. Crystallogr., in press, 2006. Graveland-Bikker, J. F.; Ipsen, R.; Otte, J.; De Kruif, C. G. Langmuir 2004, 20, 6841-6846. Graveland-Bikker, J. F.; de Kruif, C. G., submitted for publication. Klug, A. Philos. Trans.: Biol. Sci. 1999, 354, 531-535. Alberts, B.; Johnson, A.; Lewis, J.; Raff, M.; Roberts, K.; Walter, P. Molecular Biology of the Cell, 4th ed.; Garland Science: New York, 2002. Reches, M.; Gazit, E. Science 2003, 300, 625-627. Khazanovich, N.; Granja, J. R.; McRee, D. E.; Milligan, R. A.; Ghadiri, M. R. J. Am. Chem. Soc. 1994, 116, 6011-6012. Zhang, S. G.; Marini, D. M.; Hwang, W.; Santoso, S. Curr. Opin. Chem. Biol. 2002, 6, 865-871. Ryadnov, M. G.; Woolfson, D. N. J. Am. Chem. Soc. 2004, 126, 7454-7455. Salvetat, J.-P.; Bonard, J.-M.; Thomson, N. H.; Kulik, A. J.; Forro, L.; Benoit, W.; Zupperoli, L. Appl. Phys. A 1999, 69, 255-260. Dame, R. T.; van Mameren, J.; Luijsterburg, M. S.; Mysiak, M. E.; Janicijevic, A.; Pazdzior, G.; van der Vliet, P. C.; Wyman, C.; Wuite, G. J. L. Nucleic Acids Res. 2005, 55, e68. Howard, J. Mechanics of Motor Proteins and the Cytoskeleton; Sinauer Associates, Inc.: Sunderland, MA, 2001. Vinckier, A.; Dumortier, C.; Engelborghs, Y.; Hellemans, L. J. Vac. Sci. Technol., B 1996, 14, 1427-1431.
Nano Lett., Vol. 6, No. 4, 2006
(21) Johnson, K. L. Contact Mechanics; Cambridge University Press: Cambridge, 2001. (22) de Pablo, P. J.; Schaap, I. A. T.; MacKintosh, F. C.; Schmidt, C. F. Phys. ReV. Lett. 2003, 91, 98-101. (23) Heuvingh, J.; Zappa, M.; Fery, A. Langmuir 2005, 21, 3165-3171. (24) Nolte, A. J.; Rubner, M. F.; Cohen, R. E. Macromolecules 2005, 38, 5367-5370. (25) Watts, N. R.; Misra, M.; Wingfield, P. T.; Stahl, S. J.; Cheng, N.; Trus, B. L.; Steven, A. C. J. Struct. Biol. 1998, 121, 41-52. (26) Radmacher, M. Methods Cell Biol. 2002, 68, 67-90. (27) Nyland, L. R.; Maughan, D. W. Biophys. J. 2000, 78, 1490-1497.
Nano Lett., Vol. 6, No. 4, 2006
(28) Uricanu, V. I.; Duits, M. H. G.; Mellema, J. Langmuir 2004, 20, 5079-5090. (29) Schaap, I. A. T.; Carrasco, C.; de Pablo, P. J.; MacKintosh, F. C.; Schmidt, C. F., submitted for publication. (30) Ivanovska, I. L.; de Pablo, P. J.; Ibarra, B.; Sgalari, G.; MacKintosh, F. C.; Carrascosa, J. L.; Schmidt, C. F.; Wuite, G. J. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 7600-7605. (31) Palaci, I.; Fedrigo, S.; Brune, H.; Klinke, C.; Chen, M.; Riedo, E. Phys. ReV. Lett. 2005, 94, 175502.
NL052205H
621
