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Nano-scale mechanics of protein and DNA assemblies
Single molecule imaging and probing by atomic force microscopy
Iwan A. T. Schaap
Nano-scale mechanics of protein and DNA assemblies
Single molecule imaging and probing by atomic force microscopy
ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus
prof.dr. T. Sminia, in het openbaar te verdedigen
ten overstaan van de promotiecommissie van de faculteit der Exacte Wetenschappen op woensdag 12 april 2006 om 15.45 uur
in het auditorium van de universiteit, De Boelelaan 1105
Iwan Alexander Taco Schaap
geboren te Delft
promotor: prof.dr. C.F. Schmidt
Contents 1 Introduction 5 2 Observation of microtubules with scanning force microscopy
in liquid 15
3 Resolving the molecular structure of microtubules under
physiological conditions with scanning force microscopy 23
4 Small versus large cantilevers for non-invasive imaging at
single protein resolution in liquids with atomic force microscopy
5 Displacements of single kinesin motors followed by atomic
force microscopy 43
6 Deformation and collapse of microtubules on the nanometer
7 Elastic response, buckling and instability of microtubules
under radial indentation 61
8 Tau protein binding forms a 1 nm thick layer along
protofilaments without affecting the radial stability of microtubules
9 Rapid chiral assembly of rigid DNA building blocks for
molecular nanofabrication 99
10 Samenvatting 109 11 List of publications 111
On the cover: A microtubule (a protein tube present in cells) one million times magnified, imaged with an atomic force microscope.
Chapter 1 5
Chapter 1 Introduction During my doctoral research I worked on several projects in which I have studied mechanical properties of biological macromolecules. Insight in the mechanics of bio-molecules, proteins and DNA, can teach us more about their function in their very complex natural environment, the cell. On the other hand, we can use the ideas offered by nature to design mechanically stable constructs from biomaterials for nanotechnological applications. Our samples are only a few nanometers in size (1 nanometer is 10-9 meter). To perform accurate mechanical measurements it is crucial to be able to image with molecular resolution in a close-to-native environment (in liquid, at room temperature). Electron microscopy, which provides molecular resolution, requires fixed and stained or frozen samples, precluding the observation of dynamic processes. Optical microscopy, especially combined with contrast enhancing techniques, like differential interference contrast (DIC) is suitable for studying biologically active specimens in liquid, but the ~200 nm resolution limit is not sufficient to resolve single proteins. By labeling the sample with fluorescent markers in single molecule fluorescence assays, nanometer displacements of single molecular motors have been resolved (1). Optical tweezers are also a powerful tool to study single bio-molecules (2). A molecule, that can be a single protein or a DNA strand, is coupled to a bead which is trapped in a focused laser beam. The displacements of the bead and the related force can be monitored with nanometer and pico-Newton accuracy (1 pico-Newton is 10-12 N). For example the step size of the motor protein kinesin has been resolved using this technique (3). Most of my experiments have been performed with an atomic force microscope (AFM). This technique, were a very fine probe is scanned over the sample, combines single molecule resolution, with the ability to work in liquids at room temperature. In addition AFM can be used as a very sensitive force transducer, to measure forces exerted by the sample or to apply forces to the sample. The achievements described in this thesis can be summarized in three points: i) We have developed the experimental procedures to study bio-molecules in a close to natural environment (in liquid at room temperature), such that the samples could be imaged with nanometer resolution without destroying them. For AFM imaging, the molecule of interest needs to be attached to a surface. Adsorption should be strong enough to hold the molecule, but not so strong that it deforms its structure. Critical for all our experiments was the force applied to the sample by the AFM probe. We applied new AFM techniques like tapping mode with small cantilevers and jumping mode and succeeded in limiting the forces to just tens of pico-Newtons. Using these techniques we have published the first high-resolution images of intact microtubules (4). These techniques can now be easily adapted to study other biological systems. ii) We have measured the mechanical response (deformation under load) of various bio-molecular assemblies: natural protein tubes (microtubules), artificial protein tubes ((5), this work was performed in a collaboration and is not expanded in this thesis), and
Chapter 1 6
artificially created DNA pyramids (tetrahedra). We applied forces up to a nano-Newton and monitored the indentation of the objects with sub-nanometer resolution. We have used analytical and finite element modeling to understand and explain this mechanical response in detail. Our experiments demonstrate the effectiveness of various strategies to engineer robust nanometer sized constructs. DNA tetrahedra use a triangulated architecture, which gives them a very high resistance against deformations. Microtubules rely on a tubular design with longitudinal reinforcements to achieve a very high axial rigidity. iii) We studied the interactions between bio-molecules like they occur in the living cell. We have investigated the morphology and mechanical consequences of tau proteins binding to microtubules. Furthermore we have studied the action of kinesin motor proteins that walk over the microtubule and are responsible for transport in the cell. Using AFM we imaged the displacements of individual motors and investigated how they move and what they do at roadblocks. Bio-molecules All the samples we have studied were made of deoxyribonucleic acid (DNA) or proteins (6). The main function of DNA is storage of the genetic code. It is a very stable molecule, which under optimal conditions can persist for millions of years (7). DNA is a helical filament of two paired chains. It is composed of only 4 different building blocks, the nucleotides (figure 1). By varying their sequence an almost infinite number of combinations can be made. In chapter 9 we have used DNA as construction material in self-assembling nanostructures. The advantage of DNA in nanotechnology is that the specific recognition between the bases makes it possible to design well-defined interactions that can result in self-assembling higher ordered structures. Only very recently we found that also in nature DNA is used as construction material to enhance the mechanical rigidity of a Parvo virus (8).
Figure 1. DNA is made of four types of nucleotides, which arepaired into a helical filament. Each nucleotide consist of a sugar-phospate unit to which one of the four bases is attached, adenine(A), cytosine (C), guanine (G) or thymine (T). Adenine pairs onlywith thymine (A-T), and guanine with cytosine (G-C). Thediameter of the helix is ~ 2 nm (image from www.welcome.ac.uk).
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Proteins consist of a sequence of twenty different amino acids, encoded by sequences of DNA (genes). The three-dimensional structure of a protein depends on its amino acid composition and can be very complicated. Proteins have many functions in the cell: they are used as building material, they form enzymes that can catalyze all kinds of chemical reactions, and some are specialized to act as little machines, for example to copy DNA or for transporting compounds through the cell. In chapter 2 to 8 we investigated microtubules (MTs), a tubular assembly of tubulin proteins (figure 2). MTs are the most rigid filaments of those forming the eukaryotic cell skeleton (6). This cytoskeleton is a highly dynamic system, enabling the cells to regulate their shape, for example during growth, locomotion or division. MTs interact with a multitude of MT associated proteins (9) in order to adjust the chemical or mechanical properties and thereby their function. Tau is one of the most abundant MT-associated proteins involved in stabilization and bundling of MT, and tau malfunctioning has been found related to many neuro-degenerative diseases (10, 11) including Alzheimer's disease. In chapter 8 we studied the morphology and mechanical consequences of tau proteins binding to MTs. MTs also facilitate intracellular transport by serving as tracks for molecular motors of the kinesin and dynein families (12). They are involved in organelle and vesicle transport, but also in the separation of chromosomes during cell division. Kinesin was found to walk in 8 nm steps (3), each powered by the hydrolysis of one ATP molecule. The exact coordination between the biochemical and the mechanical cycle of kinesin is still under debate. In chapter 5 we studied by AFM imaging the dynamic interaction between MTs and the kinesin motor-protein.
Atomic force microscopy Scanning probe microscopes scan a very sharp probe (tip) over a surface and use the tip-sample interaction to generate a topographical image. The scanning tunneling microscope (STM), invented in 1982 and awarded with the Nobel price in 1986, uses the tunneling current between the metal tip and the conductive surface as feedback signal to control the tip-sample distance (13). Since then STM has been used for imaging of conductive surfaces with single atom resolution. Based on STM the atomic force microscope (AFM) was developed by G. Binnig, C. F. Quate, and C. Gerber in 1985 (14). Instead of electrical tip-sample interaction, AFM uses the force interaction between the tip and sample as feedback signal, enabling detection of insulating surfaces. Figure 3a shows a very fine
Figure 2. MT, built from α and β tubulin proteins that form dimers. The dimers, 8 nm in length, self assemble into MTs, with a diameter of 25 nm and a length that can reach micrometers.
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probe mounted at the end of a flexible cantilever as used in AFM. The probe is scanned over the surface to map out the three-dimensional topography of a sample. The stiffness of the cantilever, and its bending measured by a reflected laserbeam, determines the force that is applied to the sample via the probe (figure 3b). AFM can be used to image surfaces at single atom resolution when operated in vacuum (15). Bio-molecules are relatively fragile, and require conditions that are close to their natural environment. With the development of new scanning techniques and the ability to operate the AFM in liquid, the AFM has been used with increasing success from the late 1980's to study biological samples (16). The AFM working modes used in biology are: contact mode, jumping mode and dynamic mode (17). In brief, in contact mode the tip is kept in mechanical contact with the surface at a constant cantilever deflection while scanning. This results in high lateral forces applied to the sample and can only be used with very stable samples, like a crystal monolayer of proteins (18). In jumping mode the tip is brought down to contact for every scan-point, to map out the topography of the sample. To minimize the lateral forces, the tip is elevated from the sample during lateral movement (19). The pulsed force mode (20) works essentially in the same way with the difference that this was originally not implemented digitally but controlled by analogue electronics. In dynamic mode or tapping mode (21, 22), the tip is oscillating at the cantilever resonance frequency with a certain free amplitude, when the tip is brought closer the surface the amplitude is reduced due to tip-sample interaction. To image a sample, the tip is brought close to the sample such that the amplitude reduces. This reduced amplitude (the set point) is kept constant by a feedback loop that controls the tip-sample distance via the z-piezo For most biological samples only dynamic mode or
Figure 3. a) Electron micrograph of an AFM cantilever (Photo from Olympus). Thecantilever has a length between 50 and 200 micrometer. A sharp probe is mounted atthe end and is used to scan the surface bound sample. b) The vertical distancebetween the sample and the probe is controlled via a piezo scanner. When the probecontacts the sample, the cantilever will bend. The amount of bending is measured viaa reflected laser beam on a photo-detector, and is used as feedback signal tomaintain the applied force constant. The force applied to the sample depends on thebending and spring-constant of the cantilever.
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jumping mode have been shown suitable, i.e. DNA molecules can be routinely imaged in liquids in both modes (23, 24). We have used the single nanometer resolution in liquids of AFM to study the topography of MTs and their interaction with tau and kinesin proteins, and to investigate the structure of artificial DNA tetrahedra. The experiments were performed both in dynamic mode and in jumping mode. We found our samples very sensitive to the forces applied, and an accurate control of the tip-sample interaction was necessary to limit the force and thereby the damage to the sample. The approaches we followed are described in detail in chapters 2 to 4. Mechanical measurements The mechanical interaction between the AFM probe and the sample has to be controlled tightly to prevent damage to the sample. However because of this tip-sample interaction the AFM can also be used as a very sensitive force transducer to perform mechanical measurements. We probed the mechanical properties of our samples by locally deforming them in 'pushing experiments'. Alternatively AFM has been used to measure mechanical properties by stretching single molecules by pulling experiments (reviewed in (25)). For our nano-indentation experiments we carefully positioned the probe above the sample and brought down the probe towards it. When the probe contacts the sample, both the sample and the cantilever will deform (figure 4a). Because we know the cantilever spring-constant, we can calculate the relation between the applied force and the indentation of the object. This procedure is explained in detail in chapter 7. Figure 4b shows an object subjected to compressive force. The relation between the applied force and the deformation of an object can be described as:
Where the force (F) per area (A) is called stress, the strain is the fractional change in length and is given by the ratio of the change in length (∆L) to the original length (L0).
Figure 4. a) AFM pushing experiment on a MT (drawing not to scale). The probelocally indents the MT, by recording the bending of the cantilever with a reflectedlaser beam we can calculate the relation between the applied force and the objectdeformation. b) Deformation of an object depends on the applied force, the objectshape and the Young's modulus.
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The relation between stress and strain is proportional and defined by the constant E, the elastic modulus of the material (the Young's modulus). The Young's modulus is thus independent of the load and object dimensions, and depends only on the material. Even though the macromolecular objects were deformed on a nanometer scale which is comparable to the size of the subunits, we found that as long as deformations are small this relation still holds. The indentation of our samples when poked with the AFM probe depends on three things: i) The material the object is made of. If this material is stiffer, the object will be more resistant against deformations. The parameter describing the material elastic properties is the Young's modulus. ii) The geometry of the object. The rod in figure 4b for example will deform less under the same force when either the radius is increased or the length is decreased. iii) The boundary conditions. How is the object supported and how is the load applied? If the load is distributed over a larger area the stress and deformation will be less. Because both the geometry of our samples and the loading conditions (the tip-sample and the sample-surface interaction) are much more complicated than the example shown in figure 4b, it was challenging to predict the relation between our sample geometry, Young's modulus and the observed sample indentation. For all our measurements we made models to simulate and understand the observed behavior from the experiments. To describe a mechanically complex experiment like the indentation of the MT, that has a corrugated surface, with a spherical probe, we used finite element methods (FEM, figure 5). With FEM an object is divided in many small regions (the finite elements). For each element the structural performance (strain and stress) is approximated and propagated to its neighboring elements. Provided that enough elements are used, the behavior of the entire structure can thus be approximated. A detailed description of the modeling procedure is given in chapter 7.
Figure 5. A MT modeled with FEM. At the left the structure is divided in manysmall elements. Right shows the computed result when a force in the form of aparabolic tip was applied.
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Outline of the thesis This thesis consists of a collection of published and submitted publications and can be divided in two parts. Chapters 2 to 5 describe the progress in the application of AFM to image MTs and MT binding proteins at single protein resolution, without damaging them. Chapters 6 to 9 describe the use of AFM as a mechanical tool to measure elastic properties by sub-nanometer indentations of bio-molecular assemblies (microtubules, DNA tetrahedra) at sub-nano-Newton forces. Part 1. In chapter 2 we show that it was possible to scan MTs by AFM without destroying them. The sample attachment to the surface in combination with the force applied by the AFM to the sample was the key to success. By operating the AFM in 'jumping mode' we carefully controlled this scan force, and we could observe MTs in different states, from flat 5 nm high layers of tubulin proteins to round 24 nm high MTs. These results opened the way to the experiments in chapters 3, 6, 7 and 8. Chapter 3 demonstrates that with this technique the MT structure could be imaged up to single protein resolution in liquid at room temperature, revealing sub-structures of the MT, the protofilaments, but also point defects in the MT lattice. To prevent damage to the MT, the applied scan-force had to be kept below 300 pN. In chapter 4 we show that by using smaller cantilevers it was also possible to scan MTs without destroying them in the more conventional 'tapping mode'. The advantage of this method is that is allows much faster image acquisition (as fast as 3 seconds per image in our setup, but in principle milliseconds are possible (26)). The drawback is that it only works with certain cantilevers (The Olympus BL150 is the only commercial available cantilever we found suitable). 'Jumping mode' is much less sensitive to the type of cantilever used, but it is slower (30 or more seconds per image) and is only implemented by one AFM manufacturer (Nanotec, Spain, but see also WITec, Germany (20)). We used the ability to work at higher frame rates described in chapter 4 in chapter 5 to study the action of kinesin motor proteins, which could be imaged with single protein resolution while they walked over MTs. We did resolve the 8 nm steps (3) and we found that the heads of individual motors used a single protofilament for processivity. When the motors were hindered by traffic jams they slowed down or even stopped during their run, they lacked the flexibility to bypass obstacles but got stalled on the same protofilament instead. Because in the cell kinesin motors will encounter many other proteins bound to the MT, this raises questions about the functionality of processive kinesin and the current kinesin models (27). Part 2. In chapter 6 we did explore the mechanical response of MTs when they were radially indented with the AFM tip using sub-nano-Newton forces. We found a linear response for small deformations and a non-linear response for larger deformations, which we attributed to the destruction of the MT. By modeling the MT as a thin-shelled tube we could couple the measured spring constant to the tube dimensions and the Young's modulus of tubulin. This research is extended in chapter 7, where we have investigated in detail the elastic behavior at small deformations (up to 3.6 nm) and the subsequent MT instabilities when higher forces (> 0.3 nN) were applied. At an indentation force of around 0.3 nN we observed an instability corresponding to a ~1 nm indentation, which could be due to partial or complete rupture of a relatively small number of tubulin-tubulin bonds. These
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indentations were reversible with hysteresis when the tip was retracted and no trace of damage was observed in subsequent high-resolution images. We modeled the results using FEM, and investigated the importance of the boundary conditions like loading the MT with a parabolic tip instead of a point force. We also modeled the effects of the protofilaments. The relatively stiff protofilaments act as axial reinforcements and play a major role in increasing the resistance of the MT against bending, but we found that they did hardly contribute to the radial stiffness. In chapter 8 we have studied the morphology and mechanical consequences of tau proteins binding to MTs. We could show that tau forms a ~1 nm thick layer around the MT and leaves the protofilament structure unaffected. Interestingly, although tau strongly affects MT kinetics, the radial mechanical strength of MTs was almost unaffected by the presence of tau. The longitudinal binding pattern of tau explains the lack of correlation between kinetics and the radial mechanical stabilization of MTs. In chapter 9 we have resolved the 3D structure of self-assembling 3 dimensional DNA structures. These tetrahedra with a size of ~7 nm were imaged using ultra sharp scanning probes with a resolution sufficient to distinguish the individual DNA ribs. Thus we confirmed that they follow their design plan and assemble in rigid 3D nanostructures. By compressing the DNA tetrahedron we have measured, for the first time, the axial compressibility of DNA and observed the buckling of the double helix under high loads.
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References 1. Yildiz, A., Forkey, J. N., McKinney, S. A., Ha, T., Goldman, Y. E., and Selvin, P.
R. Myosin V walks hand-over-hand: Single fluorophore imaging with 1.5-nm localization. (2003) Science. 300: 2061-2065.
2. Bustamante, C., Macosko, J. C., and Wuite, G. J. Grabbing the cat by the tail: manipulating molecules one by one. (2000) Nat Rev Mol Cell Biol. 1: 130-136.
3. Svoboda, K., Schmidt, C. F., Schnapp, B. J., and Block, S. M. Direct observation of kinesin stepping by optical trapping interferometry. (1993) Nature. 365: 721-727.
4. Schaap, I. A. T., de Pablo, P. J., and Schmidt, C. F. Resolving the molecular structure of microtubules under physiological conditions with scanning force microscopy. (2004) Eur Biophys J. 33: 462-467.
5. Graveland-Bikker, J. F., Schaap, I. A. T., Schmidt, C. F., and de Kruif , C. G. Structural and mechanical study of a self-assembling protein nanotube. (2006) Nano Letters. in press.
6. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P. Molecular Biology of the Cell. (2002). Garland Science, New York.
7. Cano, R. J., Poinar, H. N., Pieniazek, N. J., Acra, A., and Poinar, G. O., Jr. Amplification and sequencing of DNA from a 120-135-million-year-old weevil. (1993) Nature. 363: 536-538.
8. Carrasco, C., Carreira, A., Schaap, I. A. T., Serena, P. A., Gómez-Herrero, J., Mateu, M. G., and de Pablo, P. J. Anisotropic mechanical reinforcement of a virus by its genomic DNA. (2006) submitted.
9. Cassimeris, L., and Spittle, C. Regulation of microtubule-associated proteins. (2001) Int. Rev. Cytol. 210: 163-226.
10. Drewes, G., Ebneth, A., and Mandelkow, E. M. MAPs, MARKs and microtubule dynamics. (1998) Trends Biochem Sci. 23: 307-311.
11. Lee, V. M., Goedert, M., and Trojanowski, J. Q. Neurodegenerative tauopathies. (2001) Annu. Rev. Neurosci. 24: 1121-1159.
12. Hirokawa, N. Kinesin and dynein superfamily proteins and the mechanism of organelle transport. (1998) Science. 279: 519-526.
13. Binning, G., Rohrer, H., Gerber, C., and Weibel, E. Surface Studies by Scanning Tunneling Microscopy. (1982) Phys. Rev. Lett. 49: 57-61.
14. Binnig, G., Quate, C. F., and Gerber, C. Atomic Force Microscope. (1986) Phys. Rev. Lett. 56: 930-933.
15. Giessibl, F. J. Atomic-Resolution of the Silicon (111)-(7x7) Surface by Atomic-Force Microscopy. (1995) Science. 267: 68-71.
16. Weisenhorn, A. L., Drake, B., Prater, C. B., Gould, S. A. C., Hansma, P. K., Ohnesorge, F., Egger, M., Heyn, S. P., and Gaub, H. E. Immobilized Proteins in Buffer Imaged at Molecular Resolution by Atomic Force Microscopy. (1990) Biophys. J. 58: 1251-1258.
17. Moreno-Herrero, F., Colchero, J., Gomez-Herrero, J., and Baro, A. M. Atomic force microscopy contact, tapping, and jumping modes for imaging biological samples in liquids. (2004) Phys Rev E. 69: -.
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18. Muller, D. J., Baumeister, W., and Engel, A. Controlled unzipping of a bacterial surface layer with atomic force microscopy. (1999) P Natl Acad Sci USA. 96: 13170-13174.
19. de Pablo, P. J., Colchero, J., Gomez-Herrero, J., and Baro, A. M. Jumping mode scanning force microscopy. (1998) Appl. Phys. Lett. 73: 3300-3302.
20. RosaZeiser, A., Weilandt, E., Hild, S., and Marti, O. The simultaneous measurement of elastic, electrostatic and adhesive properties by scanning force microscopy: pulsed-force mode operation. (1997) Meas. Sci. Technol. 8: 1333-1338.
21. Martin, Y., Williams, C. C., and Wickramasinghe, H. K. Atomic Force Microscope Force Mapping and Profiling on a Sub 100-a Scale. (1987) J. Appl. Phys. 61: 4723-4729.
22. Zhong, Q., Inniss, D., Kjoller, K., and Elings, V. B. Fractured Polymer Silica Fiber Surface Studied by Tapping Mode Atomic-Force Microscopy. (1993) Surf. Sci. 290: L688-L692.
23. Moreno-Herrero, F., de Jager, M., Dekker, N. H., Kanaar, R., Wyman, C., and Dekker, C. Mesoscale conformational changes in the DNA-repair complex Rad50/Mre11/Nbs1 upon binding DNA. (2005) Nature. 437: 440-443.
24. Moreno-Herrero, F., de Pablo, P. J., Alvarez, M., Colchero, J., Gomez-Hertero, J., and Baro, A. M. Jumping mode scanning force microscopy: a suitable technique for imaging DNA in liquids. (2003) Appl Surf Sci. 210: 22-26.
25. Fisher, T. E., Marszalek, P. E., and Fernandez, J. M. Stretching single molecules into novel conformations using the atomic force microscope. (2000) Nat Struct Biol. 7: 719-724.
26. Ando, T., Kodera, N., Takai, E., Maruyama, D., Saito, K., and Toda, A. A high-speed atomic force microscope for studying biological macromolecules. (2001) P Natl Acad Sci USA. 98: 12468-12472.
27. Cross, R. A. The kinetic mechanism of kinesin. (2004) Trends Biochem Sci. 29: 301-309.
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Chapter 2 Observation of microtubules with scanning force microscopy in liquid Pedro. J. de Pablo, Iwan. A. T. Schaap, Christoph. F. Schmidt Fysica van Complexe Systemen. Divisie Natuurkunde en Sterrenkunde. Vrije Universiteit. De Boelelaan 1081, 1081 HV. Amsterdam. The Netherlands. Published in Nanotechnology 14 (2003) 143 Contribution of authors AFM experiments were performed by Pedro de Pablo and Iwan Schaap. Pedro de Pablo optimized the AFM scanning technique and Iwan Schaap performed sample purification, optimized the attachment of the microtubules and wrote software for data analysis. Abstract We present the application of scanning force microscopy using the jumping mode to investigate microtubules adsorbed to glass in air and in liquid. To fix the microtubules the glass surfaces were silanized with aminopropyl-triethoxy-silane. The observed structures ranged from disrupted microtubules in air to intact microtubules in liquid. Intact microtubules show heights between 20 and 24 nm confirming the diameter found in electron microscopy studies. The force applied by the tip was critical for the microtubule height, indicating deformation by the tip. Internal structure, corresponding to protofilaments, was found.
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1. Introduction Most eukaryotic cells contain a cytoskeleton, a polymeric internal protein framework responsible for the rigidity of the cell. In contrast to a bone skeleton, the cytoskeleton is a highly dynamic system, enabling the cells to regulate their shape, for example during cell division. Three main types of filaments are involved in forming the cytoskeleton : filamentous actin (F-actin), intermediate filaments and microtubules. Microtubules are built from heterodimers of two similar subunits, α and β tubulin (figure 1(a)). These dimers are joined end-to-end to form protofilaments. 13 parallel protofilaments (figure 1(b)) assemble into a hollow tube with a wall thickness of about 5 nm. The overall diameter is about 25 nm while the length can vary from tens of nanometres to hundreds of microns. The cytoskeleton also serves the intracellular traffic: molecular motors use the filaments as tracks to carry their load. Microtubules serve as tracks for the movement of motors of the kinesin and the dynein families. They are involved in organelle and vesicle transport, but also in the separation of chromosomes during cell division. Kinesin was found to walk in 8 nm steps , each powered by the hydrolysis of one ATP molecule. The system microtubule–kinesin can be considered as one of the smallest nanomachines. Understanding the processes driving the microtubule–kinesin system will provide a powerful tool for nanotechnology making it possible to modify or build nanomachines with kinesin features.
The microtubule–kinesin system has been investigated mainly by three techniques: differential interference contrast optical microscopy (DIC), electron microscopy (EM) and optical tweezers. DIC is suitable for studying biologically active specimen in liquid. Microtubules generate enough contrast to be imaged, but the ≈200 nm resolution is not sufficient to visualize either microtubule protofilaments or individual kinesins, the force-generating head of which is about 10 nm in size. Nevertheless, DIC has been successful in indirectly studying the action of kinesin by observing either moving microtubules or micron-sized beads moving on immobilized microtubules . EM studies  have yielded important structural data about both kinesin and microtubules, but this technique is limited to the study of inactive (stained or frozen) samples. Optical tweezers are a powerful tool  to measure the pico-Newton forces exerted by molecular motors as well as the nm
(a) (b) (c)
Figure 1. Structure of a microtubule. In (a) α-β tubulin dimer with its dimensions isshown. In (b) and (c) the whole microtubule formed by the tubulin dimers and a cross-section are shown, respectively.
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motions generated. The step size of kinesin has been resolved using this technique . Since optical tweezers are mostly used in conjunction with DIC it is not possible to visualize the motors themselves and therefore the forces measured cannot be coupled directly to the conformational changes of kinesin. In this paper we explore the capabilities of scanning force microscopy (SFM) to study microtubules in liquids in a non-intrusive way. SFM combines the high resolution of the EM and the capability to study biologically active samples in liquids. Vater et al  showed the ability of the SFM to image microtubules in liquid using polylysine surfaces. Though no internal details of the microtubules were reported, the height of entire microtubules ranged between 10 and 19 nm. This height would correspond to a deformed microtubule. Fritz et al  reported internal structure at the end of a broken microtubule, using trimethoxy-silylpropyldiethylenetriamine coated glass to attach microtubules. Heights of about 40 nm are reported, being much higher than the expected 25 nm. Kacher et al  showed images of microtubules decorated with kinesin, though no movement of kinesin on the microtubule is reported. 2. Materials and methods 2.1. Microtubules Tubulin was purified from pig brains by two cycles of assembly and disassembly followed by chromatography on phosphocellulose . The tubulin was supplemented with 10% glycerol and 1 mM GTP, and incubated for 30 min at 35 °C. Subsequently the polymerized microtubules were 200 times diluted in Pem80 buffer (80 mM Pipes pH 6.9, 1 mM EGTA, 2 mM MgCl2) plus 10 µM taxol. The taxol-stabilized microtubules were stored dark at room temperature and used as working stock for a maximum of four days. 2.2. Sample preparation To attach microtubules (negatively charged) to the glass surfaces, cover slides were immersed in a solution of 0.1% of aminopropyl-triethoxy-silane (APS) (Sigma–Aldrich), which provides a positive surface charge. Then the glass was rinsed with water and dried in an oven at 65 °C. Afterwards a droplet of about 40 µl of taxol-stabilized microtubules was pipetted into the liquid cell. The prepared sample was incubated for 10 min at room temperature to fix the microtubules to the silanized surface. 2.3. SFM A NanotecTM SFM was operated in jumping mode (JM) (Nanotec S.A. Madrid, Spain) . In this mode a force versus distance curve is performed at each point of the image, moving the tip laterally when there is no tip–sample contact. In this way, dragging forces are avoided. Tapping mode was also used, but was found not to be convenient for the experiments because the force applied to the microtubules is not well controlled  and, as will be shown later, this is important to prevent damage to the microtubules. By using JM, the loading force on the microtubules can be precisely controlled down to a lower
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limit of about 100 pN. Olympus cantilevers with spring constants ranging between 0.05 and 0.76 N m−1 were used. 3. Results and discussion 3.1. Microtubules in air Images of microtubules were acquired in air. A droplet of microtubuli solution was pipetted on a silanized glass. After incubating for 10 min, the glass was rinsed with water and dried. The sample (figure 2) shows disrupted microtubules, most probably because they are not in their natural medium. Two different structures can be distinguished: profile 1 of figure 2 shows a height of 6.5 nm and profile 2 a height of only 3.5 nm. These two different heights were also observed in many other samples in air and probably represent two stages of microtubule disruption. The 6.5 nm probably represents a microtubule with the two walls closely squeezed. Consequently the 3.5 nm height, being half the size, represents only one wall. 3.2. Microtubules in liquid Figure 3(a) shows microtubules on glass in liquid with heights ranging from 20 to 25 nm. With respect to the expected diameter of 25 nm, it is reasonable to assume that these microtubules are intact and almost not deformed. In figure 3(bII) the horizontal derivative of the enclosed area of figure 3(bI) is shown. The derivative of the topography enhances the edges, revealing the internal structure of the microtubules. This internal structure shows four longitudinal rows in each microtubule with a spacing of about 16 nm. Those structures are very likely to represent protofilaments of the microtubules. According to figure 1(c), at least five protofilaments should be imaged by the SFM tip. However, the number and spacing of protofilaments resolved by the SFM depend on the dilation  of the image caused by the finite tip size. 3.3. Deformation of microtubules It was observed in our experiments that the set-point force used to image microtubules is critical in order to achieve good results: usually 1 nN was enough to destroy the microtubules. Depending on the applied force, microtubules behave in different ways. In figure 4 three SFM images were taken in liquid with different forces. In figure 4(d) the topographic profiles of the images are compared. Figure 4(e) shows the crosssections of a
Figure 2. Microtubules in air. The microtubulesshow heights of 3.5 nm and 6.5 nm.
Chapter 2 19
microtubule in the different states explaining the data. When forces up to about 0.5 nN were applied, microtubules showed heights between 20 and 24 nm (figures 4(a) and (d)). In this case we assume that the microtubules are at most slightly deformed (see figure 4(e)). If subsequent images were taken at the same force, the height remained constant. When the force was increased to 1 nN, microtubules showed heights of 10 nm (figures 4(b) and (d)). We assume that this situation represents a fully collapsed microtubule where the walls are touching each another (figure 4(e)). Once this degree of deformation was reached, a second image of the same microtubule, with even lower force, showed a height of 5 nm, which corresponds to the thickness of a single microtubule wall (figure 4(e)). Usually, when the force exceeded 1 nN the first scan already showed microtubules of 5 nm height. However, sometimes microtubules withstand forces up to 3 nN, showing a
0.5 nN 1 nN 3 nN
0 100 200 300
1 2 3
(a) (b) (c)
Figure 4. Three different microtubule imagestaken with jumping mode in liquid at differentforces: (a) at a force of 0.5 nN, (b) at a force of 1nN and (c) at 3 nN. The three profiles arecompared in (d). In (e) three differentconformational sections are proposed to explainthe data.
Fig. 3b I
Figure 3. Microtubules in liquid. (a) Ageneral view of a glass surfacecovered with microtubules. Theheight ranges between 20 nm and 24nm, corresponding to intact or slightlydeformed microtubules. (bII) Shows azoom of two microtubules from (bI). 4protofilaments are visible as verticalrows in each microtubule.
Chapter 2 20
height of 10 nm. Again, when the second image was taken at the same place the height of the microtubule became 5 nm. In both cases we assume that this means that the upper microtubule wall was ripped off by the tip and only the microtubule wall that was attached to the surface remained. It is interesting to compare the dried microtubules in air (figure 2) with the microtubules in liquid (figure 4). The height of a collapsed microtubule in liquid (10 nm in figure 4) was more than the height of a collapsed one in air (6.5 nm in figure 2). If both images were to represent a double-walled microtubule, this would mean either that the SFM returned different heights in air or, more likely, that denaturation and dehydration of the tubulin subunits affected the thickness of the microtubule wall. Another possibility is that the applied forces in air are higher than in liquid because of the adhesion force. The adhesion force in air stems mainly from the meniscus between tip and surface  and it increases the applied force to about 20 nN, one order of magnitude higher than the forces we used in liquid. That could result in a higher compression of the microtubules in air than in liquid. 4. Conclusions In the work presented here it is demonstrated that silanization of glass surfaces with APS is a suitable method to attach microtubules, most likely by electrostatic interaction, without deforming them. Only when operated in jumping mode in liquid, was the SFM able to image the microtubules at the expected height of about 24 nm. The all-important condition was the application of forces lower than 0.5 nN, which could only be achieved with cantilevers with a low spring constant (0.05 N m−1). When applying a higher force than 1 nN the height was reduced to 10 nm, suggesting a collapsed microtubule where the two walls, each 5 nm thick, are touching. Applying higher forces or repeated scanning of a collapsed microtubule resulted in a height of 5 nm corresponding to a single wall. For future experiments it will be interesting to more accurately map the elastic deformation of the microtubule. Once the elastic limit is known, the stiffness of the microtubule wall can be computed. Using low forces, it is also possible to distinguish the protofilaments. Although the spacing of the protofilaments is 4 nm, the dilation effect of the tip results in an apparent spacing of 20 nm. This high resolution combined with the capability to study intact microtubules demonstrates the potential of the SFM as a powerful tool to study the kinesin–microtubule system in action. Acknowledgment We acknowledge financial support of the Dutch Foundation for Fundamental Research on Matter (FOM).
Chapter 2 21
References  Berg J M, Tymoczko J L and Stryer L 2002 Biochemistry 5th edn (New York: Freeman) ch 34  Svoboda K, Schmidt C F, Schnapp B J and Block S M 1993 Nature 365 721  Vale R D, Reese T S and Sheetz M P 1985 Cell 42 39  Nogales E, Whittaker M, Milligan R A and Downing K H 1999 Cell 96 79  Bustamante C, Macosko J C and Wuite G L 2000 Nat. Rev. Mol. Cell Biol. 1 130  Vater W, Fritzsche W, Schaper A, Böhm K J, Unger E and Jovin T M 1995 J. Cell Sci. 108 1063  Fritz M, Radmacher M, Allersma M W, Cleveland J P, Stewart R J, Hansma P K and Schmidt C F 1995 SPIE 2384 150  Kacher C M, Weiss I M, Stewart R J, Schmidt C F, Hansma P K, Radmacher M and Fritz M 2000 Eur. Biophys. J. 28 611  Williams R C Jr and Lee J C 1982 Methods Enzymol. 85 376  de Pablo P J, Colchero J, Gómez-Herrero J and Baró A M 1998 Appl. Phys. Lett. 73 3300  Moreno-Herrero F, de Pablo P J, Colchero J, Gómez-Herrero J and Baró AM 2000 Surf. Sci. 453 152  Villarrubia J S 1998 J. Res. Inst. Stand. Technol. 102 425  Intermolecular and surface forces J. Israelachvili
Chapter 2 22
Chapter 3 23
Chapter 3 Resolving the molecular structure of microtubules under physiological conditions with scanning force microscopy Iwan A. T. Schaap, Pedro J. de Pablo, Christoph F. Schmidt Vrije Universiteit Amsterdam, Faculty of Sciences, Department of Physics and Astronomy, Section Physics of Complex Systems, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. Published in European Biophysics Journal 33 (2004) 462 Contribution of authors AFM experiments were performed by Iwan Schaap and Pedro de Pablo. Iwan Schaap performed sample purification and preparation. Abstract We have imaged microtubules, essential structural elements of the cytoskeleton in eukaryotic cells, in physiological conditions by scanning force microscopy. We have achieved molecular resolution without the use of cross-linking and chemical fixation methods. With tip forces below 0.3 nN, protofilaments with ~6 nm separation could be clearly distinguished. Lattice defects in the microtubule wall were directly visible, including point defects and protofilament separations. Higher tip forces destroyed the top half of the microtubules, revealing the inner surface of the substrate-attached protofilaments. Monomers could be resolved on these inner surfaces.
Chapter 3 24
Introduction The cytoskeleton of eukaryotic cells is a highly dynamic system, constantly reconstructing itself to perform complicated functions, such as cell growth, locomotion or division. Microtubules (MTs), a central component of this cytoskeleton (1), interact with a multitude of microtubule associated proteins (2) and also serve as tracks for molecular motors of the kinesin and dynein families (3). MTs are 2-dimensional tubular protein polymers and in vivo are commonly composed of 13 parallel protofilaments (4), which are connected laterally into hollow tubes. Protofilaments consist of head-to-tail joined dimers of α and β tubulin (55 kD each). The outer diameter of an MT is about 25 nm, while the length can vary from tens of nanometers to tens or even hundreds of micrometers, frequently spanning the whole cell (1). The atomic structure of tubulin has been solved by electron crystallography (5), followed by a high-resolution 3D electron microscopy (EM) reconstruction of the MT structure (6). The number of protofilaments of in vitro polymerized MTs has been found to vary between 11 and 17, depending on buffer conditions (7). Transitions have been found within individual MTs, corresponding to line defects in the MT lattice (8). It has been speculated that there might also be other types of lattice defects, such as point defects, and it has been postulated that the motor-like protein katanin, which catalyzes the break-down of MT, specifically targets such defects (9). To precisely understand the many dynamic processes that MTs are involved in, it will be crucial to be able to image with molecular resolution in physiological conditions. EM, which provides molecular resolution, requires fixed and stained or frozen samples, precluding the observation of dynamic processes. Light microscopy, on the other hand, has insufficient resolution to distinguish structures on the scale of the tubulin subunits (4 nm). To study dynamic rearrangements, interactions with motor proteins and regulatory proteins, as well as the dynamic properties of defects in the MT lattice it is necessary to merge nanometer resolution with the capability to work in a close-to-native environment at room temperature. Scanning Force Microscopy (SFM) (10) operated in buffer can meet these requirements. SFM makes use of a tip with a radius of order 10 nm to mechanically scan the sample, and thereby produces a topographical map. The sample needs to be attached to a (smooth) surface to be imaged. MTs, being hollow shell structures, are very prone to damage. Initial attempts of imaging with SFM in tapping mode were limited in resolution and struggled with the damage problem (11) or had to employ strong cross-linking by glutaraldehyde to reinforce the MTs (12). The latter method is likely to affect dynamic properties as well as interactions with other proteins. Here we show that by carefully choosing the method of surface attachment as well as the method of scanning and controlling the maximal tip force, it is possible to image MTs in buffer with single-protein resolution, without destroying or noticeably deforming them.
Chapter 3 25
Materials and Methods Sample preparation Tubulin was purified from porcine brain using standard methods (13), and polymerized at 3 mg/ml concentration by adding 10% glycerol and 1mM GTP followed by incubation at 36 ºC for 30 minutes. MTs were 200 fold diluted into PEM80 buffer (80 mM Pipes pH 6.9, 1 mM EGTA, 2 mM MgCl2) plus 10 µM paclitaxel (taxoltm) (Sigma) to prevent depolymerization. To attach the negatively charged MTs, clean glass cover slips were derivatized with a positively charged silane (14) by immersing in a 0.1 % solution of aminopropyl-triethoxy-silane (APTS, Aldrich). They were then rinsed with water and cured at 65°C. For some samples we used a 1 % solution of trimethoxysilylpropyl-diethylenetriamine (DETA, Aldrich) (15). The solution was hydrolyzed 5 minutes before immersing the cover slips for another 5 minutes, they were then rinsed with water and cured at 110°C. Imaging 40 µl of MT sample was sufficient to create a meniscus between the glass surface and the cantilever holder of the SFM (Nanotec®, Spain), submerging the sample and cantilever with tip in buffer. Soft cantilevers (OMCL-RC800PSA, Olympus Inc. Japan) with a spring constant of 0.05 N/m and a tip-radius of about 20 nm were used. Fig. 1. Sketch of the “jumping mode” scanning procedure (not to scale). A: The cantilever is drawn in two states. Black: elevated from the surface, in the position where lateral sample motion occurs. Gray: the sample has been moved upwards by the piezo until the tip-sample contact bent the cantilever to the point corresponding to the chosen set force. Cantilever deflection is measured, as common in SFM, by a laser beam, which is reflected onto a split photodiode detector. Because scanning is performed in liquid, there is no capillary tip-surface adhesion force. The arrows illustrate the vertical and horizontal motion of the sample while progressing along one scan line. B: A jump curve as displayed on the oscilloscope (averaged over tens of scan points). 1. The tip starts at a height of ~30 nm above the sample. 2. The piezo moves the sample upwards, the viscous drag on the cantilever causes a small deflection. 3. The tip contacts the sample. 4. This is the contact phase. The deflection is linear with the piezo displacement, the maximum allowed deflection is set as a parameter. Once this deflection is reached, the z-piezo position is recorded, and the piezo will retract the sample from the tip. 5. The viscous drag causes an inverted deflection on the way back. At a height of 30 nm the z-piezo movement will stop. At this point the piezo will direct the sample by a lateral displacement to the next scan point, were a new force-distance curve is performed. At each scan point only the piezo z-displacement required to reach the set force is recorded.
Chapter 3 26
Results Imaging microtubules in liquid The SFM operating method used here is “jumping mode” described elsewhere in detail (16). In this mode the SFM performs a force-distance curve at every point of a raster scan with a maximum vertical force that is set as a parameter (figure 1). For each point the vertical sample position at this set force is recorded. The tip is then elevated about 30 nm from the surface before performing the lateral motion to the next point thereby minimizing lateral drag forces on the sample. Typically we started an experiment by scanning a 3 x 3 µm area with 256 x 256 scan-points at a set force of about 100 pN. We adjusted the MT concentration by inspection of similarly prepared surfaces in a light microscope, using differential interference contrast microscopy, such that on average about 1 MT was visible in a 3 x 3 µm window. We experimented with the surface derivatization method and with sample handling (avoiding excessive shearing) until only a fraction of .10% of destroyed MTs was seen in the initial scans. MTs were typically many µm long. After selecting one MT, we zoomed in to image with higher resolution in a scan area of 500 x 500 nm. In these repeated scans at low force an occasional MT was found to disintegrate (.10% of the cases). The MT in figure 2A shows a maximum height of 23 nm, close to the 25 nm diameter observed with EM. This suggests that the tip did not indent the MT noticeably. The tip radius of about 20 nm is of the same order of magnitude as the MT diameter. This leads to exaggerated horizontal dimensions in the image, with the sides of the tip contributing to image formation, but this does not affect the measured height of the MT (17). The dilation effect is shown schematically in figure 2B, resulting here in a measured apparent MT width of 70 nm. Due to the curvature of the MT surface, the (apparent) lateral spacing between protofilaments grows from ~6 nm to ~9 nm, while the depth of the grooves between protofilaments is underreported as the tip can hardly enter them. Because the sharpest part of the tip is in contact only with the top of the MT, resolution is highest there and decreases towards the sides. In most MTs we could resolve the upper five protofilaments.
Fig. 2. Over 100 scans performed ondozens of different MTs showingprotofilaments were recorded duringmultiple sessions. Each experiment wasperformed using fresh samples and newtips. A: 3D-rendered topography map of a220 nm long MT segment on an APTSsurface, scanned with 100x100 points,applying a maximal force of 90 pN ineach point. The protofilaments runningparallel to the MT axis are clearly visible. B: Dilation effect of the tip. The graphshows the profile from A, and a tip with20 nm tip radius. Like in figure A, the zand x scale are different, therefore theinserted MT cross-section appearsdeformed.
Chapter 3 27
Effects of maximal tip force In order to probe the deformability and the destruction threshold of MTs we performed scans with increasing maximal tip forces. Scanning with forces exceeding 300 pN as well as running multiple scans with forces close to this value damaged the MTs irreversibly. Figure 3 shows that scanning with high forces tended to destroy the top halves of the MTs, whereupon the rougher inner surface of the bottom half, which was directly attached to the substrate, was imaged. Since no substantial lateral forces are exerted on the MTs while scanning in jumping mode, we suspect that the normal forces were in this case high enough to disrupt lateral and axial bonds between tubulin dimers, such that the whole top halves of the microtubules treated with such forces were disintegrated. With our cantilevers, a minimum force of 50 pN was required to overcome (thermal) noise and assure contact between the tip and the MT, a limit determined by tip and cantilever size, and detection bandwidth (18). The MTs were deformed elastically for tip forces between 50 and 300 pN. A tip force of 50 pN gave heights close to 25 nm while at forces close to 300 pN the height of the MTs was found to be about 21 nm. A systematic study of the elastic response of MTs in this geometry has been published elsewhere (19). Scanning forces around 100 pN provided good resolution without risking destruction.
Fig. 3. This image has 256 scan points per 500 nm and was processed with a derivative filter enhancing the edges. The MT attached to an APTS surface is opened intentionally by increasing the scanning force from 100 to 400 pN in the center of the image. The scanning direction was downward with horizontal scan lines. On the horizontal line where the high force was introduced a sharp horizontal cut is visible. The region where 400 pN was used is rendered in a brighter color for clarity. The inserted profiles show clearly the difference in height, 23 nm for the intact part and between 5 and 8 nm for the destroyed part, where only some remaining protofilaments can be seen. When the scanning force was reduced again to a low value, the extent to which the high force had disintegrated the MT can be seen. A few scan lines were required before an intact MT was found back.
Chapter 3 28
Single-protein resolution Figure 4A shows a high-resolution image of an opened MT showing the inner surface. The striated pattern has a 4 nm periodicity, the size of monomeric tubulin. An image of the outside of an intact MT (figure 4B) does not show the monomers in the axial direction, whereas protofilaments, i.e. gaps between monomers in the radial direction are clearly visible. Fourier transforms of the respective images (insets) confirm the monomer spacing in the inner surface by showing faint intensity at about 1/4 nm-1 (inset Fig. 4A) while no trace of a signal is seen in the Fourier transform of the image of the outer surface of the MT (inset Fig. 4B) for monomers in the axial direction.
Fig. 4. Both scans show a 100 x 100 nm region scanned with 128 x 128 points with a maximum tip force of 100 pN. A derivative filter was applied. A: Opened MT on a DETA surface showing the inner surface of the wall, the protofilaments are hardly visible, but a striated pattern is visible oriented roughly at a right angle to the MT axis. The inserted line is exactly perpendicular to the MT axis, showing the angle of the stripes. A Fast Fourier Transformed image (FFT) (inset) shows weak peaks corresponding to a periodicity of 4 nm, the size of a tubulin monomer. B: Intact MT on an APTS surface showing the outer surface imaged under similar conditions. The protofilaments are visible. Both in the topography as well as in the FFT there is no indication of the axial monomer periodicity. The protofilaments give a visible, but not very clear signature in the FFT, because only 5 are visible and their apparent spacing is not constant. C: Sketch of the axial cross-section of a protofilament based on cryo-EM results by Nogales et al. 1999. The periodicity of the monomers is much more pronounced on the inside. This is consistent with the finding that only an opened MT shows monomer periodicity in axial direction (figure 4A).
Chapter 3 29
Defects in the microtubule lattice The lateral resolution in the images was high enough to reveal lattice defects on the MTs. Figures 5A and 5B show two point defects, small holes in the MT wall. Figure 5C shows what appears to be a lateral offset in one or more protofilaments or a crack in the wall. Yet another type of defect, a split between two protofilaments, is shown in figure 5D. The split is likely related to the relatively strong bend in this MT (radius of curvature 650 nm).
Fig. 5. These images were taken with 256 scan points per 500 nm, have a derivative filter applied and were obtained on APTS surfaces. A: Point defect: One protofilament was disrupted over an apparent length of 12 nm, leaving a hole in the MT wall. The length of the defect (in combination with the dilation) suggests the absence of two tubulin dimers. The MT was scanned 3 times without observing any change, making it unlikely that scanning had induced or enhanced the defect. B: Similar point defect as in A, but now more to the side of another MT. C: One (or possibly more) protofilament(s) interrupted by a fracture after which they continue with a lateral shift. D: An MT with an unusually small radius of curvature of 650 nm, normally only seen when it is bent by an external force. An increased spacing between protofilaments at the outer side of the curve can be seen, which suggests disrupted lateral bonds. Discussion The resolution obtained with SFM depends primarily on the size of the tip, while the distance between scan points, combined with the stability of the piezo, as well as Brownian motions of both tip and sample also play a role. Axial gaps between tubulin monomers could only be detected on the MT inner wall. This is not unexpected since 3D MT reconstruction from EM data (6) show virtually no gaps between monomers in the
Chapter 3 30
axial direction on the outer protofilament surface while at the inner surface the tubulin monomers are clearly separated by a cleft (figure 4C). In the so-called B-lattice, in which form microtubules normally polymerize, lateral monomer contacts are primarily between α-α and β-β (20). Because neighboring protofilaments are staggered with a pitch of 0.92 nm, the MT helix has a rise of 3 tubulin monomers per turn. In a 13 protofilament MT, this implies an axial “seam” with α-β contacts. Evidence has been reported that growing MTs first form as flat ribbons at the growing tip and then progressively curl up to form the closed tubules (21, 22), leaving a seam with α-β contacts (23). This predicted seam was not visible in our SFM images, likely for the reason that we did not resolve differences between α and β tubulin. This is consistent with the high homology in tertiary structure found between the two types of monomers, with differences of only ~1Å (5). The split observed in figure 5D might be marking the seam, but in this case the radius of curvature of the MT was so short (650 nm) that the opening of the tube might have occurred between any pair of protofilaments in the highly strained MT. The origin of the point defects we detected might lie in the assembly process, conceivably caused by the inclusion of damaged building blocks (tubulin dimers) or by the fast growth skipping isolated sites. Defects could also be induced by external forces that exceed the elastic limits of the tube, for example by the SFM tip, or by pipetting of the MT sample before depositing it in on the substrate surface. The defect observed in fig. 5A was stable over repeated scans at low force, so that it is unlikely that it was caused by the imaging process itself. The number of defects observed so far was too small for a statistical analysis. The existence of point defects has been indirectly inferred previously in experiments with the motor-protein related protein katanin, an MT severing protein complex (24). Katanin binds the MT, and, by hydrolysis of ATP, disrupts the bonds between tubulin dimers, thereby weakening the MT’s lattice. Davis et al. (9) proposed a model, based on observations of katanin mediated severing of MTs, in which katanin binds preferentially to defects rather than to random locations. They estimated a frequency of one defect per 0.6 µm, where every postulated defect would correspond to two tubulin dimers. The fact that such defects can exist is demonstrated by our observations, although we cannot give an estimate of frequency of occurrence due to lack of statistics. Transitions in protofilament number were found to occur with a frequency of about 1 per 15-17 µm in cryo-EM studies (8, 25) under experimental conditions similar to ours (addition of paclitaxel after polymerization). This relatively infrequent occurrence might be the reason why we haven’t observed any clear examples yet. The shifted protofilament in figure 5C could be caused by a change in protofilament number. We did, however, not observe a change in width and height of the MT corresponding to an addition of one protofilament (~5 nm). It is conceivable that our imaging procedure created a bias in the sense that only the most stable MTs might have been visible at all, which are likely to be the ones with 13 protofilaments. If others, however, had been destroyed we would expect to at least see the remainders of the bottom parts of the tubes, which was not often the case. The role of paclitaxel for the mechanical properties of microtubules is not yet entirely clear. In our experiments it was used to stabilize the MTs against depolymerization at the
Chapter 3 31
low protein concentrations necessary for imaging. Because paclitaxel is a small molecule (MW = 0.85 kD) that binds to a specific location in β tubulin (26) and does not add a considerable mass, it is not expected to have major effects on the rigidity of the MT. It does, however, influence the frequency of defects. In the absence of paclitaxel Arnal and Wade (25) found a protofilament transition rate of 1 per 35 µm, increasing to 1 per 6-8 µm when paclitaxel was present during polymerization. In vivo, without paclitaxel, the formation of MTs is an easily reversible process. Although assembly and disassembly is believed to occur predominantly from the ends, it is conceivable that the lattice is more dynamic and that the MT can anneal by dynamic rearrangements of monomers or dimers. Such lattice dynamics might be measurable by the technique we have used. It is likely, however, that the relatively strong attachments needed to image the MTs would prevent some dynamic processes from occurring. We expect that the presented results, which demonstrate molecular resolution on microtubules in close to physiological conditions, will open new doors to a microscopic understanding of the many complex dynamic machineries that microtubules are involved in. Acknowledgements We thank Ken Downing for sharing his 3D MT model, Per Bullough for help with image analysis, Fred MacKintosh for helpful discussions, Johanna van Nes and René Koops for help with exploratory experiments, and financial support of the Dutch Foundation for Fundamental Research of Matter (FOM) and ALW/FOM project no. 01FB28/2.
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18. Gittes, F., and C. F. Schmidt. 1998. Thermal noise limitations on micromechanical experiments. Eur. Biophys. J. Biophys. Lett. 27:75-81.
19. de Pablo, P. J., I. A. T. Schaap, F. C. MacKintosh, and C. F. Schmidt. 2003. Deformation and collapse of microtubules on the nanometer scale. Phys. Rev. Lett. 91:-.
20. Mandelkow, E. M., R. Schultheiss, R. Rapp, M. Muller, and E. Mandelkow. 1986. On the surface lattice of microtubules: helix starts, protofilament number, seam, and handedness. J. Cell. Biol. 102:1067-1073.
21. Kirschner, M. W., L. S. Honig, and R. C. Williams. 1975. Quantitative electron microscopy of microtubule assembly in vitro. J. Mol. Biol. 99:263-276.
22. Simon, J. R., and E. D. Salmon. 1990. The structure of microtubule ends during the elongation and shortening phases of dynamic instability examined by negative-stain electron microscopy. J. Cell. Sci. 96:571-582.
23. Kikkawa, M., T. Ishikawa, T. Nakata, T. Wakabayashi, and N. Hirokawa. 1994. Direct visualization of the microtubule lattice seam both in vitro and in vivo. J. Cell. Biol. 127:1965-1971.
24. McNally, F. J., and R. D. Vale. 1993. Identification of katanin, an ATPase that severs and disassembles stable microtubules. Cell 75:419-429.
25. Arnal, I., and R. H. Wade. 1995. How does taxol stabilize microtubules? Curr. Biol. 5:900-908.
26. Snyder, J. P., J. H. Nettles, B. Cornett, K. H. Downing, and E. Nogales. 2001. The binding conformation of Taxol in beta-tubulin: a model based on electron crystallographic density. Proc. Natl. Acad. Sci. USA 98:5312-5306.
Chapter 3 34
Chapter 4 35
Chapter 4 Small versus large cantilevers for non-invasive imaging at single-protein resolution in liquids with atomic force microscopy Carolina Carrasco1, Iwan A. T. Schaap2, Christoph F. Schmidt2, Julio Gómez-Herrero1, Pedro J. de Pablo1
1 Departamento de Física de la Materia Condensada. Universidad Autónoma de Madrid,
28049 Madrid, Spain. 2 Physics of Complex Systems, Department of Physics and Astronomy, Vrije Universiteit
Amsterdam, The Netherlands. Contribution of authors This work was initiated by the idea of Pedro de Pablo to operate the small Olympus biolevers in tapping mode and Iwan Schaap proposing to compare the behavior of both cantilevers using microtubules as a force sensor. Carolina Carrasco and Iwan Schaap performed the experiments with microtubules in Amsterdam. Control experiments were performed by Carolina Carrasco in Madrid. Abstract For the successful application of atomic force microscopy to study biological samples it is critical to limit the force exerted by the scan probe. We compared the potential of two cantilevers whose main difference is the size. Both cantilevers were operated in dynamic mode to image microtubules in liquids. While with the small cantilevers it was possible to find a range of conditions for stable non-destructive imaging, the large cantilevers did not allow stable and non-destructive imaging. The performance of both cantilevers is discussed in the light of their different physical properties.
Chapter 4 36
The application of Atomic Force Microscopy (AFM) 1 to study biological systems is a field in continuous expansion 2. It allows experiments under biologically relevant conditions (in liquid at room temperature) on the mechanical and structural properties of bio-molecules, interacting proteins and DNA at single protein level 3. AFM uses a sharp tip, mounted at the end of a flexible cantilever, to mechanically scan the sample. If the tip-sample interaction is not accurately controlled this can easily lead to disruption of the fragile bio-molecules. The AFM working modes used in biology are: contact mode, jumping mode and dynamic mode 4. In brief, in contact mode the tip is kept in mechanical contact with the surface at a constant cantilever deflection while scanning. This results in high lateral forces applied to the sample and can only be used with very stable samples, like a crystal monolayer of proteins 7. In jumping mode the tip is brought down to contact for every scan-point, to map out the topography of the sample. To minimize the lateral forces, the tip is elevated from the sample during lateral movement 5. In dynamic mode or tapping mode 6 the tip is oscillating at the cantilever resonance frequency with a certain free amplitude, when the tip is brought closer the surface the amplitude is reduced due to tip-sample interaction. To image a sample, the tip is brought close to the sample such that the amplitude reduces. This reduced amplitude (the set point) is kept constant by a feedback loop that controls the tip-sample distance via the z-piezo. For most biological samples only dynamic mode or jumping mode have been shown suitable, i.e. DNA molecules can be routinely imaged in liquids in both modes 8. The fabrication of very small cantilevers (2 µm ×10 µm) is a milestone in the application of dynamic mode in liquids 9. Combined with advanced AFMs, they permit very fast imaging of several frames per second 10 which allowed visualization of protein dynamics 11. Also it demonstrated that even fragile samples like microtubules could be scanned in a non-destructive way 12, albeit not at single protein resolution yet. We tested the effect of the cantilever dimensions on their performance in acoustic dynamic mode. As test sample and force sensor we choose microtubules whose mechanical response and fragility was characterized in previous experiments 13. Microtubules, 25 nm diameter protein tubes, are a central component of the cytoskeleton 14 giving shape to the cell. Microtubules have been recently imaged with AFM in liquids using jumping mode 15, obtaining for the first time clear single protein resolution on undamaged samples. However, even in jumping mode, where microtubules were imaged with forces slightly below 100 pN, not more than ~10 images of the same microtubule could be obtained without destruction. Due to their hollow geometry microtubules are very sensitive to radial indentations 13. Forces on the order of 100 pN are enough to cause substantial indentations (k ~ 0.07 N/m) 16. Table 1: Cantilever properties length x width x
thickness (µm) k (N/m) f0 air
(KHz) f0 liquid (KHz)
Q factor liquid
Biolever (SL) 60 x 30 x 0.18 ~0.03 ~37 ~9 ~3.5 OMCL800PSA (CL) 200 x 20 x 0.8 ~0.05 ~18 ~4.5 ~2
Chapter 4 37
Table 1 summarizes the relevant parameters of both cantilevers tested. While the surface area of the small cantilever (SL)17 is more than two times smaller than that of the conventional cantilever (CL)18, its spring constant remained comparable due to the reduced thickness. Microtubules were adsorbed on silanized glass surfaces 15 and scanned in liquid 19. Images were taken in dynamic mode by oscillating the cantilevers with a dither piezo at resonance. Figure 1 shows microtubules imaged with both types of cantilevers. With the SL the axial rows of tubulin proteins, the protofilaments, were clearly resolved, and the height was 25 nm (figure 1a). With the CL the microtubules showed a reduced height of only 4 nm, corresponding to a protein monolayer 15 thus showing a destroyed microtubule (figure 1b). In all cases we optimized the image conditions to the best of our knowledge. With Olympus TR400 cantilevers (100 µm long triangular cantilevers with a spring constant of 0.08 N/m) we obtained similar results as in figure 1b (results not shown). In jumping mode we could image intact microtubules with all three cantilevers. To understand the difference in performance we plotted the cantilever amplitude and average normal force as function of the z-piezo position (which controls the tip-sample distance). This is shown in figure 2 for both the SL and CL. Their free amplitudes were set at 17 nm and the measured amplitude (dotted lines) remained constant until the point where the interaction between the tip and surface appeared (z=0 nm), then the amplitude decreased linearly with the distance. When the distance between the cantilever and sample was further reduced the amplitude reached again a constant level. Now the tip was in permanent contact with the sample, but since the cantilever was still driven by the dither piezo, an apparent residual amplitude remained because the cantilever deflection was measured by a reflected laser beam focused at some distance from the tip. The average force exerted by the tip on the sample (solid lines) is a product of the cantilever spring constant and the average cantilever deflection. The average force on the sample was zero
Figure 1. Scan results with different cantilevers operated in dynamic mode. a: Two parallel microtubules scanned with the SL. The profile shows the 25nm height, the protofilaments are clearly visible and the microtubule is notdamaged. b: A microtubule scanned with the CL. The profile shows areduced height, this microtubule is clearly flattened.
Chapter 4 38
when the tip was far away, but started to increase when the tip-sample interaction appeared (at z=0). This increase in average force became linear with z when the tip got in permanent contact with the sample, this is when the amplitude reached a constant level. To obtain images of soft samples the set point amplitude was chosen close to the free amplitude to minimize the average force. We used a set point indicated with arrows in figure 2. This set point corresponded to an average force of 70 pN for both cantilevers (mind that with the SL we could easily go to lower forces, but with the CL not). In both cases this was below the critical force at which microtubules collapse (300 pN). With the SL it was possible to image the microtubule several times before disrupting it, with the CL the microtubules got destroyed immediately. Even though the average force was much lower than the microtubule critical force, we succeeded only with the SL to image intact microtubules.
Figure 2. Dynamic mode in liquids for both cantilevers. Black represents the SL and grey the CL. The left scale and the dotted lines show theamplitude, when the cantilever is far from the surface this amplitude is constant at 17 nm.When the z-piezo extends the tip-sample distance decreases, and at z=0 the amplitudestarts to decrease linear with z. Then at a further reduction of the tip-sample distance theamplitude reaches a constant level, the tip is now in permanent contact with the sample.Because the cantilever is still driven by the dither piezo, there is still an apparent residualamplitude. The right scale and the solid lines show the average force exerted by the tip to the sample.The average force starts to increase when the tip starts to interact with the sample at z=0,when the tip is in permanent contact the relation between z and the average force becomeslinear. The arrow indicates the set point amplitude we used for our first test, for bothcantilevers chosen such that we applied an average force of 70 pN.
-10 0 10 20 300
average force (pN)
Chapter 4 39
To test whether the microtubules could be imaged undamaged with the CL at a lower average force we reduced the free amplitude. Figure 3 shows the lowest free amplitude (4 nm) that still permitted stable imaging (discussed below). At this amplitude we achieved an average force of 30 pN but even at this low force only a couple of scan lines could be taken before the microtubule got destroyed. A further reduction of the free amplitude and thereby the average force was not possible. Figure 2 showed that there was a residual amplitude when the tip was in permanent contact with the surface. Since we used acoustic oscillation, the cantilever still oscillated via the dither piezo movement when the tip touched the surface 20. For both cantilevers this residual amplitude was a constant fraction of the free amplitude (see figures 2 and 3). But while for the SL the residual amplitude was ∼15% of the free amplitude, for the CL the residual amplitude was as high as ~60%. The lower limit for the free amplitude that could still be used for stable imaging was set by the noise on the cantilever amplitude signal and the absolute difference between the free and the residual amplitude. From the CL behavior at small amplitudes (grey dotted line in figure 3) it is obvious that the feedback can only work properly if the difference between the free and the residual amplitude is larger than the noise of the cantilever amplitude signal. Figure 3 also shows the SL operated at a reduced free amplitude. The low average force (20 pN) made it possible to scan the microtubule for at least 80 times without destroying it (figure 4).
Figure 3. Dynamic mode in liquids at low amplitude/force conditions. Black represents the SL and grey the CL. The left scale and the dotted linesshow the amplitude. For the CL this was the lowest amplitude that still allowedfor stable imaging. The right scale and the solid lines show the average forceexerted by the tip to the sample. For the CL this was 30 pN. For the SL thesettings are shown we used to obtain the results in figure 4. The average forcewas 20 pN.
-5 0 5 100
average force (pN)
Chapter 4 40
With this study we clearly showed the importance of selecting the right cantilever in combination with the AFM operating mode used. When working in jumping mode, several types of cantilevers could be used to obtain stable images from intact microtubules, showing that the applied forces are well controlled and can be kept under 300 pN at all times. In dynamic mode the used cantilever was very critical. Only one type of the three we tested, the SL, permitted scanning of undamaged microtubules. To date, the SL is the smallest cantilever commercially available and probably the only cantilever suitable for scanning intact microtubules in dynamic mode. The question how exactly the cantilever geometry is related to its performance is not answered yet. It is clear that the noise plays an important role. In our experiments the lower limit on the average force was set by the noise on the cantilever amplitude signal and the absolute difference between the free and the residual amplitude. The noise on the cantilever signal depend on its surface area and spring constant, the SL has the clear advantage of a much smaller surface area compared to CL but with an comparable spring constant, in figures 2 and 3 this is reflected in a lower noise on the amplitude signal for the SL. The amplitude can also be electronically filtered to reduce the noise, but this would probably restrict the maximum scan speed. To improve performance the residual amplitude could be lowered as this would allow a lower free amplitude which in turn will result in a lower average force. The ratio between the free and the residual amplitude is coupled to the cantilever geometry and the size and position of the laserspot that picks up the deflection signal 22. Alternative forms of dynamic mode, like magnetic driven cantilever oscillations 23 might also reduce the residual amplitude. An intriguing question that emerged from our results is: although we achieved similar average forces for both tested cantilevers, only with the SL we could scan intact microtubules. This implies that the peak forces are much higher for the CL than for the SL at similar average forces. To test this, amplitude versus z-piezo curves should be recorded with a sufficient sample rate to investigate the individual oscillation cycles to measure the peak forces. Preliminary experiments in our laboratories confirmed that at similar average
frame 1 frame 80
Figure 4. Microtubule scanned with the SL using thesettings from figure 3. The 1st and 80th frame obtained at anaverage force of 20 pN during 18 minutes at 64 x 64 pixelsshow that scanning did not induce any damage.
Chapter 4 41
forces, the maximum applied force per cycle was for the CL indeed much higher (more than twofold) than for the SL. A major advantage of reducing the size of AFM cantilevers is the increase in resonance frequencies that in turn permits higher frame rates in liquids 10. Combined with the reduction of the tip-sample interaction in dynamic mode, the use and development of smaller cantilevers will be essential for the application of AFM to study dynamic biological samples in a non-intrusive way.
Chapter 4 42
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12 T. Ando, N. Kodera, Y. Naito, T. Kinoshita, K. Furuta, and Y. Y. Toyoshima, Chemphyschem 4 (11), 1196-1202 (2003).
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14 B. Alberts, J. Lewis, M. Raff, K. Roberts, and P Walter, Molecular biology of the cell. (Garland, New York, (2002)).
15 I. A. T. Schaap, P. J. de Pablo, and C. F. Schmidt, European Biophysics Journal with Biophysics Letters 33 (5), 462-467 (2004).
16 I. A. T. Schaap, C. Carrasco, P. J. De Pablo, and C. F. Schmidt, Submitted (2005). 17 www.olympus.com, BL-RC150VB. 18 www.olympus.com, OMCL - RC800PSA. 19 www.nanotec.es. 20 D. Bonnell, Scanning Tunneling Microscopy and related techniques. (Wiley VCH,
2003). 21 S. J. O'Shea and M. E. Welland, Langmuir 14 (15), 4186-4197 (1998). 22 T.E. Schäffer, Nanotechnology 16, 664-670 (2005) 23 C. Rankl, V. Pastushenko, F. Kienberger, C. M. Stroh, and P. Hinterdorfer,
Ultramicroscopy 100 (3-4), 301-308 (2004).
Chapter 5 43
Chapter 5 Displacements of single kinesin motors followed by atomic force microscopy. Iwan A. T. Schaapa, Carolina Carrascob, Pedro J. de Pablob, Christoph F. Schmidta a Department of Physics and Astronomy, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands. b Departamento de Física de la Materia Condensada C-III, Universidad Autónoma de Madrid, 28049 Madrid Contribution of authors Initial experiments showing kinesin bound to MTs were performed in 2003 by Iwan Schaap and Pedro de Pablo and repeated in 2004 by Iwan Schaap and Carolina Carrasco in Amsterdam. Only with the application of tapping mode with biolevers (chapter 4) it became possible to see kinesin in action. The AFM experiments described in this work were performed by Iwan Schaap and Carolina Carrasco in 2005, sample optimization and preparation was performed by Iwan Schaap. Abstract In eukaryotic cells active intracellular transport is essential. On the one hand to control highly coordinated events like the separation of chromosomes during cell division. On the other hand to drive transport over distances that cannot be covered anymore by diffusion, like the transport in axons. In both cases motor proteins from the kinesin family that walk over microtubules are responsible Upon binding the microtubule, processive motors of the kinesin-1 family can take multiple steps and can travel hundreds of nanometers before releasing. The coordination between the two heads of kinesin during motility is still under debate 1. We have used atomic force microscopy to image the displacements of single processive kinesin motors at nanometer resolution and showed that the individual heads used a single protofilament during their walk. Under crowded conditions, we found that kinesin was easily hindered by the presence of other motors, they lacked the flexibility to bypass obstacles but slowed down or got stalled on the same protofilament instead. Because in the cell kinesin will encounter many other proteins bound to the microtubule, this raises questions how in vivo congestions on the microtubule are avoided.
Chapter 5 44
Introduction Kinesin is a dimeric motor that is composed of two homologue proteins, each consisting of a globular head and a long stalk. Dimerization takes place by formation of a coiled coil by the two stalks, the heads contains the microtubule (MT) binding domain and the ATP binding pocket, the stalk is responsible for cargo binding. Upon binding to the MT, processive motors of the kinesin-1 family can take multiple steps of 8 nm powered by the hydrolysis of ATP and can travel hundreds of nanometers before releasing 2. MTs are the largest of the filaments that make up the cytoskeleton, a framework that gives structure and shape to the cell. The MT outer diameter is about 25 nm, while their length can reach many micrometers. MTs are composed of 13 parallel protofilaments, which are connected laterally into hollow tubes. These protofilaments, that run parallel with the MT axis, consist of head-to-tail joined dimers of α and β tubulin 3. We have combined several recent advances in atomic force microscopy (AFM) to visualize individual kinesin motors on MTs without having to attach markers to the sample. The use of an AFM probe to scan a sample implies mechanical interaction with the sample. For bare MTs we have previously found that their destruction could be prevented by carefully limiting the applied scan forces 4. Here we operated the AFM in tapping mode using relatively small cantilevers, this enabled us to limit the average scan force to 20 pN while maintaining single protein resolution at sub-minute frame rates 5. For our experiments we used truncated Neurospora crassa kinesin (Nkin, a kind gift from Günther Wöhlke), a member of the kinesin-1 family 6. This construct has been show to form processive dimeric motors 7. Although at saturating levels of ATP, Nkin is about 3 times faster than human kinesin-1, its Michaelis-Menten constant is an order of magnitude higher 8. This makes it easier to tune the speed of Nkin at low concentrations of ATP as used in our experiments.
Chapter 5 45
Results First we tested whether the forces applied during scanning did not disturb the binding of kinesin to the microtubule and if the spatial resolution was sufficient to distinguish the individual kinesin heads. After attaching the MTs to a silanized glass surface 4, we washed the sample with 20 µg/ml casein to prevent unspecific binding of kinesin to the surface. When, in presence of 0.3 mM AMP-PNP (a non-hydrolysable ATP analogue), kinesin was added in equimolar ratios to the tubulin dimers, the height of the MTs increased from 25.9 ± 1.5 nm (avg. ± sd, 31 MTs measured) to 30.4 ± 1.7 nm (11 MTs measured, see also chapter 8). This increase, caused by the decoration of the exposed side of the MTs, was therefore due to one layer of motor proteins. Besides the 4.5 nm increase in height, a typical globular pattern with an 8 nm axial periodicity was visible (figure 1a). Using slightly lower kinesin concentrations resulted in a more sparsely decorated MT where isolated motors became visible (figure 1b). We did not found evidence for something else than a random binding pattern to the MT surface. Figures 1b and 1c show individual motors with its two heads bound parallel to the MT axis. The average spacing of the heads of individual motors was 8 nm, and their height was 3.5 nm. A small reduction compared to the fully decorated MTs, perhaps explained by the short stalk that has more space to fold sideways when the MT surface was not fully decorated. By keeping the average scan force below 30 pN we could scan the decorated MTs for tens of scans without removing or displacing the kinesin.
Figure 1. Characterization of kinesin bound to MTs by AFM. Images were recorded in presence of 0.3 mM AMP-PNP, at low ATP concentrations we obtained comparable images. a) MT decorated with kinesin (we added between one and two motors per tubulin dimer), the upper 3 protofilaments clearly show the individual kinesin heads, the FFT (inset) shows an axial periodicity of 8 nm. b) When kinesin was added at medium concentrations (less then one motor per tubulin dimer), individual motors could be clearly distinguished. The 3D rendered image shows that the heads always appeared in pairs of two parallel to the MT axis. c) At lower kinesin concentrations (one motor per ten or more tubulin dimers) isolated motors could be seen, again with the heads bound parallel to the MT axis. The inset graph gives the average topography of 17 kinesin molecules, the clearly visible interhead spacing was 8 nm, the height 3.5 nm.
a b c
Chapter 5 46
To follow the walk of single kinesin motors we have used the potential of AFM to follow protein dynamics at single protein resolution. For these experiments the samples were prepared as described at figure 1c. Then the sample was washed with 5 sample volumes of buffer and ATP was added at a concentration of 0.25-2 µM. For some samples (including the sample shown in figures 2a-d) no AMP-PNP was used, but kinesin was added directly in presence of 0.5 µM ATP to a sample with immobilized MTs. At low scan speeds we imaged single motors that appeared and disappeared in sequential frames, indicating that kinesin was mobile but ran too fast to capture it in sequential frames. To increase the temporal resolution we increased the scan frequency and reduced the scan area. In our AFM setup (Nanotec, Madrid, Spain) this permitted frame rates up to 1 frame per 3 seconds, which was sufficient to follow kinesin at low ATP concentrations. However most movies were recorded at lower scan rates to obtain a higher resolution. A sequence of frames in figure 2 shows the motility of 3 motors in 2 samples. In each frame the heads were bound in line with a single protofilament. In the subsequent frames the motors stayed on that same protofilament. The speeds we found in different experiments ranged from 2 to 9 nm/s, a variation consistent with the expected exponential distribution of step intervals at limiting ATP concentrations 9. Figure 3 shows all the displacements we imaged at single protein resolution. The displacements could be fitted very well on an 8 nm grid, consistent with the tubulin dimer periodicity and established values for the step size of kinesin 2,3. Kinesin motility could also be observed by repeatedly scanning the same line across a MT, thus imaging only an area of ~200 x 2 nm. This allowed a higher temporal resolution, but at the cost of spatial information. We observed kinesin running through the scanned line, which gave a temporary increase in height of ~3 nm over the width of one pf (data not shown).
Figure 2. Single kinesin motors moved over the MT. a-d) Four frames acquired each in 30 seconds show single kinesin motors that walked over the MT at an average speed of 3 nm/s at 0.5 µM ATP. Frame a shows 2 kinesins, indicated with arrows. Frame b shows that both motors have moved downward (from the leading kinesin only the last head is still visible). In frame c the second kinesin has moved further down. Frame d shows that also the second kinesin has disappeared. e-f) Two frames from another sample show an upward displacement of 16 nm. The two kinesin heads are clearly visible. The position of the arrow is fixed in both frames.
a b c d
Chapter 5 47
Figure 3. The displacements of kinesin showed a periodicity of 8 nm. a) The graph shows 28 displacements we found in a total of 12 movies, recorded with different samples. Each movie comprised 2 to 4 frames. Each curve represents a profile taken over the protofilament with kinesin bound. On the x-axis the axial displacement of kinesin compared to the first or previous frame is shown. Most displacement distances were observed more than once, in that case the curves were averaged. For clarity the curves are plotted with a vertical offset. b) After deduction of the 8 nm periodicity, the average from the curves in a) is plotted. The two heads spaced 8 nm apart can be clearly distinguished.
To mimic a crowded environment for kinesin on the MT, we have added kinesin to the MT sample at a saturating concentration of multiple motors per tubulin dimer, and we imaged kinesin landing on the MT. Figure 4 shows such an experiment where after ~2 minutes the first motors landed on the MT and ran away immediately (probably in downward direction). But when more motors landed, they were slowed down by crowding. Empty gaps in the partially decorated MT show that there was still motility, as the gaps regularly changed place. Often the gaps spanned only 8 nm, the space for a single head, thus making it unlikely that the gaps were caused by the release of a single motor, which would leave a 16 nm gap. The same figure also shows a defect in the MT, the motors tended to stop at the topside of this defect and stayed there. Similar behavior was observed in other experiments, indicating that kinesin kept sticking for minutes in front of defects before releasing.
0 16 32 48 64 80 96 112
displacement in nm
-8 0 8 160
axial distance in nm
Chapter 5 48
Figure 4. Kinesin was slowed down by traffic jams and stopped by defects in the MT lattice. Shown are 7 frames acquired each in 10.5 seconds from a 60 frame movie (the frame numbers are indicated). This movie was recorded directly after kinesin was added to the buffer in presence of 0.5 µM ATP. 9) The undecorated MT shows a defect visible as a disruption in the MT surface (indicated by the white arrowhead). In the following frames, the arrowhead is laid over the defect. In the next frames (not shown) motors appeared and disappeared, probably because their speed was too high to capture in sequential frames. 23, 24) Two individual motors (indicated by circles), of which the upper one took one step downward. 36) Above the defect, motors appeared (indicated by the white line), they remained visible in the next frames. At the downstream side of the defect, the MT remained undecorated in the following frames. This might suggest that kinesin could not pass the lattice defect but got stopped upstream. 43-45) The 8 nm gaps between the motors are mobile (one gap, indicated by circles, moved upward from 43 to 44) suggesting that the rows of motors did still slowly proceed downward.
23 24 36
43 44 45
Chapter 5 49
Discussion Our observations in presence of AMP-PNP showed individual kinesin motors with its heads 8 nm spaced apart bound to a single protofilament. Such a binding orientation was suggested for dimeric kinesins from electron microscopy experiments 10. In our experiments we found a clear relation between the kinesin : tubulin ratio and the degree of MT decoration, that ranged from fully decorated MTs to the visibility of isolated motors. The predominant spacing of the kinesin heads was 8 nm, but occasionally we also observed a spacing of 16 nm leaving a 8 nm gap between the heads (Figs. 1a, 1b and 4), also reported by 10. The number of heads enclosing these 8 nm gaps was mostly even, indicating that multiple motors at both sides of the gap were bound with both heads. This suggests that not single motors with their heads spaced 16 nm apart were responsible for the gaps. Likely the gaps were caused by a not continuous decoration of the MT by kinesin. Although we resolved kinesin displacements in multiples of 8 nm, the scan speed did not permit us to resolve each step of the individual motors when they walked over the MT. Ando 11 showed that by using very small cantilevers with a high resonance frequency a scan rate of multiple frames per second was achieved, but did not succeed yet in convincingly resolving kinesin walking over the MT. Higher scan rates would enable to follow kinesin steps step by step, but will increase the tip-sample interaction and make an accurate control of the applied force more difficult. In our experiments the scanned area of a MT often got damaged after ~100 images. For optimal results the frame rate should be set roughly equal to the stepping frequency of kinesin. When single motors in presence of low ATP concentrations were followed during their walk, their topology appeared identical to that of the AMP-PNP fixed motors. At low ATP concentrations we could follow runs up to 96 nm, a distance limited by the scanned area and the frame rate rather than by the run length of the motor. The intervals of displacement showed a clear 8 nm periodicity. We showed that kinesin followed accurately the protofilament axis (as shown in gliding assays by Ray et al. 12) and used a single protofilament for processivity. The tendency of kinesin to follow a single protofilament and the disability to step sideward may partly explain why it got relatively easily trapped by traffic jams and defects. A mechanism to avoid the accumulation of motors on the MT would be the unbinding of kinesin, triggered by a roadblock. Rosenfeld 13 speculated an increased release rate when the trailing head meets an obstacle during its forward step, which could facilitate sidesteps. Recently the detachment rate of rat kinesin-1 was measured when hindered by mutated kinesin monomers that were used as roadblocks 14. This work showed that kinesin is expected to detach rapidly when running into a roadblock. Recent work by Seitz and Surrey 15, showed the opposite and confirmed (at high ATP concentrations for drosophila kinesin-1) our findings (obtained with fungal kinesin-1) that kinesin preferred to wait instead of to unbind when it meets a roadblock on the microtubule. Further experiments will be required to find out if this contradiction depends on the experimental procedures or perhaps by the different behavior of the various members of the kinesin-1 family 7. By mutating kinesin Hurd and Saxton 16 were able to induce congestion of the fast axonal transport by the accumulation of organelles. Many neurogenerative diseases have been found related with proteins interacting with motor activity 17, induction of blockades could
Chapter 5 50
a possible mechanism. Yet, the observed stalling of healthy kinesin-1 at MT lattice defects and traffic jams is remarkable and controversial. For intracellular transport this would mean that the MTs have to be relatively clean to guaranty a free passage for kinesin. Competing motors or other microtubule binding proteins 18, would act as roadblocks and cause congestions. We expect that the development and application of AFM will provide more insight by visualizing the dynamic protein behavior under crowded conditions at a single protein resolution.
Chapter 5 51
Methods Sample preparation Taxol stabilized microtubules were diluted to 7.5 µg/ml in buffer (80 mM Pipes pH 6.9, 1 mM EGTA, 2 mM MgCl2) plus 8 µM taxol. To attach the negatively charged MTs, clean glass cover slips were silanized with positively charged trimethoxysilylpropyl-diethylenetriamine (Aldrich) as described in chapter 3. 20 µl of sample was allowed to incubate for 10 minutes. To prevent kinesin from unspecific binding to the surface, we washed the sample with 20 µg/ml casein in buffer (cleaned by ultra centrifugation for 1 hour at 120.000 g) plus taxol. Before imaging 20 µl buffer plus taxol was added resulting in a total sample volume of 40 µl. For imaging kinesin bound to the MT, we added kinesin, in presence of 0.3 mM AMP-PNP, at concentrations given in figure 1. For the single kinesin motility assays as in figure 2, we first added kinesin in presence of 0.3 mM AMP-PNP. The sample was then washed with 5 volumes of buffer plus taxol before 0.5-2 µM ATP was added. An alternative procedure was adding the kinesin in presence of 0.5 µM ATP, thereby avoiding the addition of AMP-PNP. This alternative procedure was less successful, often no kinesin motors could be found on the MT. For the experiments with kinesin under crowded conditions, the microtubule sample was prepared as described, and we added kinesin at saturating concentrations of multiple motors (2 to 4) per tubulin dimer. Kinesin was added in presence of 0.5-2 µM ATP. Motor proteins For imaging kinesin motors we tested several constructs and found motors with truncated stalks giving best results, probably because of the absence of a long dangling stalk. For the experiments described here we used a truncated form of the Neurospora crassa kinesin, a member of the kinesin-1 family (a kind gift from Günther Wöhlke), this construct has been show to form dimeric motors and maintained its processivity7. AFM The AFM (Nanotec, Madrid, Spain) was operated in buffer at room temperature in tappingmode. We used 30 x 50 µm BL150 (Olympus, Japan) cantilevers in tappingmode around a frequency of 8 KHz, at a maximum scanspeed of 4 µm per seconds. This allowed aquisition times of 3 seconds for a 150 nm x 150 nm area scanned with 64 scanlines. However most movies were recorded at lower scan rates and more scan lines in favor of a higher resolution. This technique is characterized in chapter 4.
Chapter 5 52
References 1 C. L. Asbury, Curr Opin Cell Biol 17 (1), 89 (2005). 2 K. Svoboda, C. F. Schmidt, B. J. Schnapp et al., Nature 365 (6448), 721 (1993). 3 E. Nogales, M. Whittaker, R. A. Milligan et al., Cell 96 (1), 79 (1999). 4 I. A.T. Schaap, P. J. de Pablo, and C. F. Schmidt, Eur Biophys J 33 (5), 462
(2004). 5 C. Carrasco, I. A.T. Schaap, C. F. Schmidt et al., manuscript in preparation. 6 C. J. Lawrence, R. K. Dawe, K. R. Christie et al., J. Cell. Biol. 167 (1), 19 (2004). 7 A. Kallipolitou, D. Deluca, U. Majdic et al., in Embo J (2001), Vol. 20, pp. 6226. 8 G. Steinberg and M. Schliwa, J Biol Chem 271 (13), 7516 (1996). 9 M. J. Schnitzer and S. M. Block, Nature 388 (6640), 386 (1997). 10 G. Skiniotis, T. Surrey, S. Altmann et al., Embo J 22 (7), 1518 (2003). 11 T. Ando, N. Kodera, Y. Naito et al., Chemphyschem 4 (11), 1196 (2003). 12 S. Ray, E. Meyhofer, R. A. Milligan et al., J. Cell. Biol. 121 (5), 1083 (1993). 13 S. S. Rosenfeld, P. M. Fordyce, G. M. Jefferson et al., J Biol Chem 278 (20),
18550 (2003). 14 I. M. Crevel, M. Nyitrai, M. C. Alonso et al., Embo J 23 (1), 23 (2004). 15 A. Seitz and T. Surrey, Embo J 25 (2), 267 (2006). 16 D. D. Hurd and W. M. Saxton, Genetics 144 (3), 1075 (1996). 17 S. Gunawardena and L. S. Goldstein, J Neurobiol 58 (2), 258 (2004). 18 J. C. Bulinski, T. E. McGraw, D. Gruber et al., J. Cell. Sci. 110 ( Pt 24), 3055
(1997); A. Ebneth, R. Godemann, K. Stamer et al., J. Cell. Biol. 143 (3), 777 (1998).
Chapter 6 53
Chapter 6 Deformation and collapse of microtubules on the nanometer scale Pedro J. de Pablo, Iwan A. T. Schaap, Frederick C. MacKintosh, Christoph F. Schmidt Division of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands Published in Physical Review Letters 91-9 (2003) 098101 Contribution of authors AFM experiments were performed by Pedro de Pablo and Iwan Schaap. Pedro de Pablo performed most data analysis. Iwan Schaap performed sample purification and preparation, wrote software for calculating the indentation curves form the force vs. distance curves and performed the finite element simulations. Fred MacKintosh performed the analytical calculations. Abstract We probe the local mechanical properties of microtubules at the nanometer scale by radial indentation with a scanning force microscope tip. We find a linear elastic regime that can be described by both thin-shell theory and finite element methods, in which microtubules are modeled as hollow tubes. We also find a non-linear regime and catastrophic collapse of the microtubules under large loads. The main physics of protein shells at the nanometer scale shows simultaneously aspects of continuum elasticity in their linear response, as well as molecular graininess in their non-linear behavior.
Chapter 6 54
Microtubules (MT) are among the principal components of the cytoskeleton, the dynamic structural framework of cells. . MTs are cylindrical shells of about 25 nm diameter, formed by a regular helical lattice of α-β tubulin dimers, non-covalently joined by protein-protein bonds. Alternatively one can view MTs as constructed of 13 parallel protofilaments joined laterally. Their length can vary from tens of nanometers to hundreds of microns. The mechanical properties of MTs play a crucial role in processes such as intracellular transport and cell division. MT elastic properties have been studied previously by observing the thermal fluctuations of MT shape , by actively bending the MT with optical tweezers , and by observing bending against membranes or hard surfaces . Bending experiments typically probe length scales much greater than the size of the protein subunits. At this micrometer (i.e., cellular) scale, the bending of MTs is well described by the continuum mechanics of elastic rods [5, 6], although there remains considerable uncertainty over the value of the bending rigidity. MTs have also been modeled as elastic shells before to study GHz acoustic excitations . Here, we probe the mechanics of single MTs locally by radial indentation with a Scanning Force Microscope (SFM) tip, directly observing their local, tube-like structure. SFM has been used in the past to attempt to image MTs and to measure their mechanical properties . These experiments, however, probed only bending modes of MTs. Using the Hertz model (valid only for solid bodies), Vinckier et al.  found an apparent Young’s modulus (extrapolated to zero glutaraldehyde concentration) of about 3 MPa, which is substantially smaller than what we find by taking into account the tube-like structure of MTs. Thus, in prior MT experiments it has not been possible to probe their hollow structure. Furthermore, it was previously found that MTs were too fragile to withstand the interaction with the tip and they had to be strongly cross-linked with glutaraldehyde. Here we were able to image and manipulate microtubules without chemical cross-linking. Tubulin was purified from porcine brain following established recipes . MTs were polymerized, diluted in presence of taxol  to avoid their depolymerization , and attached to glass coated with aminopropyl-triethoxy-silane as described before . To image MTs in buffer, the SFM (NanotecTM) was operated in Jumping Mode . We used cantilevers with a spring constant of 0.05 N/m and a tip-radius of about 20 nm (OMCL-TR-400PSA, Olympus. Japan). The minimal loading force (50 pN) is given by the thermal noise of the cantilever . Fig. 1a shows a typical MT imaged with SFM at a maximal force of 50 pN. The measured height of around 25 nm (fig. 1b) matches with the 25 nm diameter observed in EM studies . In order to investigate the mechanical properties of MTs, the tip was positioned on top of a single MT as judged from a directly preceding image, and several force vs. distance curves (FZ) (black curves in fig. 1c) were performed at the same spot at a constant sampling rate and constant velocity. At a maximum force of ∼1 nN the number of FZs, which can be performed at one spot until the MT is destroyed (fig. 1b) was up to ∼5. Once the contact between MT and tip is established (see arrow fig. 1c), the FZ curve is linear up to a certain critical force. At a force that varies between repeated attempts and between different microtubules over a range from ~300 pN to ~500 pN (inset of fig. 1c), the FZ curves showed catastrophic discontinuities. In control experiments we found no evidence of measurable adhesion forces between tip and microtubules (data not shown).
Chapter 6 55
We will first focus on the quantitative interpretation of the linear elastic regime. The cantilever deflection (vertical axis in fig 1c) is related to the force exerted by the tip via the known cantilever stiffness of 0.05 N/m. The signal reporting the cantilever deflection is calibrated by performing an FZ on glass (gray curve in fig.1c). The indentation depth ∆z (fig. 1c) is calculated from the z-difference between MT and glass curves at a given force. A number of averaged indentation curves in the linear regime from 5 MTs and a linear regression are shown in fig. 2a, demonstrating a linear elastic regime up to an indentation of ∼4 nm. The effective spring constant is k = 0.100 ± 0.005 N/m (s.e.m.). Indentation of a semi-infinite solid object is commonly described by the Hertz model , which due to geometry, has no linear-response. The geometry in our case is different, and the Hertz model is not applicable because the MT is a hollow cylindrical shell that can bend, buckle, and collapse, which a solid object cannot do. In the present case a linear dependence of the force on the indentation depth is expected for deformations of the order of the shell thickness [5, 18]. The linear elastic deformation of curved shells in general involves coupling of out-of-plane bending with in-plane compression [5, 18]. An exceptional case is that of a hollow cylinder that can flatten under a extended radial load, by bending without compression. For a uniform cylindrical shell of thickness t this deformation is governed by a bending modulus given by ( )[ ]23 112/ νκ −= Et , where ν is the Poisson ratio and E is the Young’s modulus . Apart from a geometric prefactor of order unity, ( )2/ Rd measures the
Figure 1. (a) shows a typical SFM image of a MT before performing a set ofFZs. In (b) a hole can be observed at the spot of the microtubule where theFZs where performed. (d) shows a typical set of FZ performed on a MT. Theinset shows a histogram of the force where the non-linear regime begins. Apeak is found at 400 pN.
Chapter 6 56
deviation of the local curvature away from the equilibrium cylindrical shape (radius R), where d is the indentation depth. The bending energy therefore scales as ( ) RRdEt 223 / per unit length of the tube.
As the cylinder becomes longer the total bending energy, assuming homogeneous flattening, grows without limit. Under a point load, the cylinder will therefore return to its undistorted shape at a certain distance from the point of loading. For long, thin-walled cylinders (i.e., to leading order in t/R) the zone of deformation extends a distance R>l along the axis from the point of force application, as can be quantitatively determined from the analytic solution (fig. 2b). In a scaling approach, we can illustrate the essential physics and estimate the relevant length scales by minimizing the total elastic energy associated with the deformation. Given a non-uniform indentation along the cylinder axis, there is a longitudinal, in-plane displacement u along the axis of the cylinder that is proportional to the indentation d, but also must decrease with increasing R/l . In fact, analytic results  show that l/Rdu ≈ , and hence the strain is of order 2/ lRd . This results in an approximate, combined elastic energy
( ) ( ) lll RRdEtRRdEtU tot22223 // += . (1)
0.00 0.05 0.101.365
1.2 1.6 2.0 2.4 2.8
0 1 2 3
0.094 N/m 0.116 0.106 0.093 0.094
Figure 2 (a) shows the indentation of 5 microtubules in the linearregime, with their calculated spring constants. Inset of (a) showsthe cross section of a microtubule based on electron microscopydata . In (b) the prefactor for k ∝ Et5/2/R3/2 is plotted vs. t/R.The gray line represents the effective deformed length l. Both ofthem are plotted from the analytical solution for a symmetricallydeformed tube, as sketched. (c) shows the Young’s Modulus vs.the effective wall thickness t using equation (3).
Chapter 6 57
Minimization of Utot leads to tRR /≈l . Thus, the dominant or softest mode of deformation of the cylinder surface extends along the axis far away from the point of force application. The local flattening of the cylinder extends thus roughly tRR / along the axis and R in the other direction. We expect from this result that our experiments will not be very sensitive to the SFM tip radius, so long as it is comparable to the MT radius. Since Utot is harmonic in the indentation d, we obtain an effective spring constant given by
2/32/5 / REt , apart from a prefactor of order unity. From the complete analytic solution obtained within the classical theory of shells [18, 19], we calculate that the spring constant
Sk for the case of equal and opposite point forces f is about 2/32/5 /37.1/ REtdfkS ≅= (2)
to within 1% over the range 1.0/002.0 << Rt (fig. 2b). This does not exactly correspond to the experimental situation where the tip applies a force f from one side while the MT is supported by a flat surface from the other side, and where the observed change in height ∆z (inset of fig. 2c) is an apparent change in diameter of the cylinder. The deformations and forces are computed for finite-length cylindrical sections in the correct experimental geometry using finite element methods (CADRE, cadrepro4.2TM). The model based on a 3D tube consisting of 12609 plates, each of which is treated within a thin shell approximation with a poisson ratio of 0.3. For small displacements we confirm the scaling behavior of equation (2) up to about 1.0/ ≈Rt , (appropriate for MTs), but with a somewhat different prefactor,
2/32/5 /18.1/ REtzfkS ≅∆= . (3) This corresponds to a stiffer spring, taking into account the fact that the height change ∆z should be compared with 2d. It is interesting to consider the corresponding expression for spherical surfaces , where REtkS /2≈ . The effective spring constant for the indentation of cylinders is weaker by a factor of 1/ <Rt , because of the ability of the cylinder to flatten without much in-plane compression. The additional rigidity of spherical surfaces is related to a classical theorem due to Jellett  that says that closed spherical (or more generally, ellipsoidal) surfaces are completely rigid if they are inextensible. We now explore the implications of the model for our experimental data. We expect that the indentation response reveals a different aspect of microtubule mechanics from prior bending experiments. Microtubules are rather structured and far from being homogeneous shells. The structure of MTs is known to atomic resolution from electron microscopy (inset fig. 2a). One evident feature is the existence of deep grooves between the protofilaments, while the inside surface as well as the top of an individual protofilament are rather flat . Given this complex structure, it is clear that indenting experiments are testing very different properties than bending experiments. Flexural rigidity is determined by the full thickness of the protofilament and the overall tube diameter, while indentation is primarily sensitive to the thin bridges between the protofilaments where the strain will be concentrated. In order to compare our results to bending experiments we estimate an effective Young’s modulus of the microtubule wall from our data. To apply our model, we have to assume an effective wall thickness somewhere between the radially averaged wall thickness and the thickness of the bridges between the protofilaments (inset of fig. 2a). In fig. 2c the Young’s Modulus, calculated from the experimental spring constant k using
Chapter 6 58
expression (3), is plotted vs. the assumed effective wall thickness running from 1.1 nm to 2.7 nm and was found to be ~1 Gpa. In order to refine our result, we carried out a finite element calculation for a cylindrical tube reinforced with longitudinal beams, mimicking the protofilaments , and introducing anisotropy in a homogeneous tube. Using the experimental k = 0.1 N/m, the calculation results in a Young’s Modulus of about ~0.8 GPa. This value correspond to an effective wall thickness of ~1.6 nm (close to the 1.1 nm bridge thickness shown in fig. 2a) in the homogenous tube model (fig. 2c). This confirms that the bridges dominate the elastic response. Even though we examine a different mode of deformation and do so at the nanometer scale, the Young’s modulus we derive, given the known geometry of the MT, is consistent with the results from prior bending experiments .
In the following we discuss the non-linear regime of the measured elastic response (fig. 1d). The sudden decrease of force is likely caused by either one of two processes: slipping off of the tip from the MT onto the glass substrate or MT collapse. The force necessary to make the tip slip is difficult to estimate since it would depend on the exact position of the tip over the MT and on the attachment of the MT to the substrate. The vertical distance moved should in that case, however, account for the full diameter of the MT. For a collapsed MT, in contrast, some material would be present between the tip and the glass. The inset of fig. 3 shows a typical indentation curve. Given the variation in these individual indentation curves, we also show an indentation histogram of 23 such curves on 5 different MTs (all at the same approach velocity and sampling rate). This histogram demonstrates a clear pattern of stages in the indentation. The peak (i) represents the linear regime of indentation. Since the distance moved between the point of first contact and the peak (ii) is ∼15 nm, which is about the inner diameter of a MT (fig. 2a), the peak (ii) most likely reflects a collapsed double layer of tubulin between the tip and glass. We also
-35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
-30 -15 0 15∆Z (nm)
Figure 3. The indentation curve of a single FZ is plotted inthe inset, showing two jumps. The MT is indented forpositive values of the axis x. The histogram of 23indentation curves performed on 5 MTs is showing 4different peaks, corresponding to the different deformationstates of the MT.
Chapter 6 59
expect to see two other possible indentations: (1) corresponding to a single layer of tubulin, and (2) to bare glass. There is evidence for these in the peaks on the right of the histogram (iii and iv). No indentations beyond 25 nm from contact were observed. In the histogram is evident that the full indentation of 25 nm was rarely seen, indicating that slip off or complete break-through were rare. In conclusion, we have used the nanometer sized SFM tip to indent microtubules, and found a linear elastic response with an apparent spring constant k = 0.1 N/m up to a deformation of about 4 nm, comparable to the shell thickness22. The elastic response is well described by models of the MTs as isotropic cylindrical shells made from a homogeneous material. Taking into account the deeply grooved structure of MTs, we estimate a Young’s modulus of 0.8 GPa. Characteristically for cylindrical shells and in contrast with spherical shells, these microtubules are expected to flatten under a point load over a large length of order tRR / , which is large compared with the cylinder radius of order 10 nm. Indentation probes locally the protein structure of MTs in a very different way from bending experiments. Radial indentation is very sensitive to the circumferential corrugations of the shell, and therefore complements bending experiments that mainly depend on axial structure formed by the protofilaments. While we have here focused on the physical properties of MTs, we are also strongly interested in the biological functional implications of these material properties. The forces needed to deform locally MTs are only about an order of magnitude larger than the force a single motor protein can exert, and are thus in the range of biologically relevant forces. Interestingly, the radial stiffness of MTs will also be a sensitive function of the binding of microtubule associated proteins, particularly the ones that bind in the grooves between the protofilaments . We acknowledge fruitful discussions with D. Schaap, J. van Mameren, E. Peterman, G. Sgalari and T. Smith, and financial support of the Dutch Foundation for Fundamental Research of Matter (FOM) and ALW/FOM project no. 01FB28/2.
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References  M. Schliwa, The Cytoskeleton: an introductory survey (Springer Verlag, New
York, 1986); S. Inoue and E. D. Salmon, Mol. Biol. Cell 6, 1619 (1995); D. Boal, Mechanics of the cell (Cambridge University Press, 2002); B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Molecular Biology of the Cell (Garland Science, New York, 2002).
 F. Gittes, B. Mickey, J. Nettleton, and J. Howard, J Cell Biol 120, 923 (1993).  H. Felgner, R. Frank, and M. Schliwa, J Cell Sci 109, 509 (1996).  M. Elbaum, D. K. Fygenson, and A. Libchaber, Phys. Rev. Lett. 76, 4078 (1996);
M. Dogterom and B. Yurke, Science 278, 856 (1997).  L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon Press, 1986).  J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer,
Sunderland, 2001).  Y. M. Sirenko, M. A. Stroscio, and K. W. Kim, Phys. Rev. E 53, 1003 (1996).  A. Kis, S. Kasas, B. Babic, A. J. Kulik, W. Benoit, G. A. D. Briggs, C.
Schonenberger, S. Catsicas, and L. Forro, Phys. Rev. Lett. 89, 248101 (2002).  A. Vinckier, C. Dumortier, Y. Engelborghs, and L. Hellemans, J. Vac. Sci.
Technol. B 14, 1427 (1996).  R. C. Williams, Jr. and J. C. Lee, Methods Enzymol 85, 376 (1982).  The role of taxol in the mechanical properties of MT remains unclear, with prior
experiments showing both increased and decreased rigidity. (B. Mickey and J. Howard, J. Cell Biol. 130, 909 (1995); 
 I. Arnal and R. H. Wade, Curr Biol 5, 900 (1995).  P. J. de Pablo, I. A. T. Schaap, and C. F. Schmidt, Nanotechnology 14, 143 (2003).  F. Moreno-Herrero, P. J. de Pablo, R. Fernandez-Sanchez, J. Colchero, J. Gomez-
Herrero, and A. M. Baro, Appl. Phys. Lett. 81, 2620 (2002).  F. Gittes and C. F. Schmidt, Eur. Biophys. J. Biophys. Lett. 27, 75 (1998).  D. Chretien and R. H. Wade, Biol Cell 71, 161 (1991).  K. L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge,
2001).  F. Niordson, Shell Theory (North Holland, New York, 1985).  I. A. T. Schaap, P. J. de Pablo, F. C. MacKintosh, and C. F. Schmidt, submitted.  J. H. Jellett, Roy. Irish Acad. trans. 22, 343 (1855).  H. Li, D. J. DeRosier, W. V. Nicholson, E. Nogales, and K. H. Downing, Structure
(Camb) 10, 1317 (2002); K. H. Downing, Private communication.  A linear response has also been shown to be possible for the indentation of
bacteria, due primarily to turgor pressure (M. Arnoldi, M. Fritz, E. Bauerlein, M. Radmacher, E. Sackmann, and A. Boulbitch, Phys. Rev. E 62, 1034 (2000)).
 H. Felgner, R. Frank, J. Biernat, E. M. Mandelkow, E. Mandelkow, B. Ludin, A. Matus, and M. Schliwa, J. Cell Biol. 138, 1067 (1997).
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Chapter 7 Elastic response, buckling and instability of microtubules under radial indentation Iwan A.T. Schaap#, Carolina Carrasco§, Pedro J. de Pablo§, Frederick C. MacKintosh#, Christoph F. Schmidt#
# Vrije Universiteit Amsterdam, Department of Physics and Astronomy, Amsterdam, The Netherlands.
§ Departamento de Física de la Materia Condensada C-III Universidad Autónoma de Madrid, 28049 Madrid
This work is submitted for publication Contribution of authors AFM experiments were performed by Iwan Schaap, Carolina Carrasco and Pedro de Pablo. Iwan Schaap performed sample purification and preparation, data analysis and finite element simulations. Fred MacKintosh performed the analytical calculations. Abstract We have tested the mechanical properties of single microtubules by lateral indentation with the tip of an atomic force microscope. Indentations up to ~ 3.6 nm, i.e. 15 % of the microtubule diameter resulted in an approximately linear elastic response, and indentations were reversible without hysteresis. At an indentation force of around 0.3 nN we observed an instability corresponding to a ~ 1 nm indentation step in the taxol-stabilized microtubules, which could be due to partial or complete rupture of a relatively small number of lateral or axial tubulin-tubulin bonds. These indentations were reversible with hysteresis when the tip was retracted and no trace of damage was observed in subsequent high-resolution images. Higher forces caused substantial damage to the microtubules, which either led to depolymerization or, occasionally, to slowly reannealing holes in the microtubule wall. We have modeled the experimental results using finite element methods and find that the simple assumption of a homogeneous isotropic material, albeit structured with the characteristic protofilament corrugations, is sufficient to explain the linear elastic response of microtubules.
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INTRODUCTION Microtubules In most eukaryotic cells a combination of three types of protein filaments: F-actin, microtubules (MTs) and intermediate filaments and their accessory proteins make up a three-dimensional polymer network, the cytoskeleton. The cytoskeleton acts as a mechanical framework for the cell, providing rigidity and shape. It is involved in many complex active cellular tasks such as motility, growth and mitosis/meiosis (1). The polymeric construction materials of the cytoskeleton differ in many ways from common technical polymers; for one, most are 'semi-flexible' or rather rigid as single filaments. Considerable progress has been made in understanding the relationship between molecular and collective structure and function (2). Basic to understanding the whole cytoskeleton is the understanding of the individual filaments. MTs are the most rigid of the cytoskeletal filaments and have the most complex structure. Their outer diameter is about 25 nm, while length can vary from tens of nanometers to tens or even hundreds of micrometers, frequently spanning the whole cell (1). In vivo MTs are composed of 13 parallel protofilaments (3), which are connected laterally into hollow tubes (Fig. 1a). The number of protofilaments of in vitro polymerized MTs has been found to vary between 11 and 17, depending on buffer conditions (4). Protofilaments consist of head-to-tail connected dimers of α and β tubulin (55 kD each). The atomic structure of tubulin has been solved by electron crystallography (5), and the whole MT structure has subsequently been reconstructed by electron microscopy (6). Resistance to bending is clearly an important property of microtubules in many of their functions. During mitosis MTs form the mitotic spindle. Many single cellular eukaryotic organisms and also many cells of higher eukaryotes (such as sperm cells or lung epithelial cells) possess cilia or flagella, specialized bundles of microtubules, to propel themselves or to pump fluid. Microtubules also form the core of neuronal axons. Mechanical measurements The bending stiffness of MTs has been measured both passively by analyzing thermal fluctuations in shape and actively using optical tweezers, for an overview see (7). Published values for the flexural rigidity range all the way from 1*10-24 to 32*10-24 Nm2. Complementary to bending of MTs it is possible to explore how they respond under a very different force, namely one leading to a radial indentation. We have recently tested MT elasticity by indentation with Atomic Force Microscopy (AFM) and have modeled the tubes with a thin-shell finite element model (8). In this paper we describe in more detail the linear elastic response of microtubules tested in the same way. We demonstrate that the results can be very well described using macroscopic continuum mechanics. We have extended the finite-element modeling beyond thin-shell dynamics to explore buckling and to explain the effect of the protofilaments as axial reinforcements. We furthermore control for the effect of the finite AFM tip size. At higher forces we have observed instabilities and breakage events of the microtubule wall in the experiments, likely representing either bond rearrangements or breakage of a few protein bonds, which were remarkably reversible as long as the damage was limited.
Chapter 7 63
METHODS Sample preparation Tubulin was purified from porcine brain using standard methods (9), and polymerized at 3 mg/ml concentration by adding 10 % glycerol and 1mM GTP followed by incubation at 36 ºC for 30 minutes. MTs were diluted to 10 µg/ml in buffer (80 mM Pipes pH 6.9, 1 mM EGTA, 2 mM MgCl2, 10 µM paclitaxel (Sigma)). To immobilize the negatively charged MTs on a surface, clean glass cover slips were derivatized with a positively charged silane by immersing in a 0.1 % solution of aminopropyl-triethoxy-silane (APTS, Aldrich) or trimethoxysilylpropyl-diethylenetriamine (DETA, Aldrich). They were then rinsed with water and dried at respectively 65°C or 110°C.
0 5 010 15
Figure 1 a) Sketch of the experiment (not to scale): the MT is build from tubulin proteins arranged ina tube. The AFM tip mounted on a cantilever deforms the MT locally. b) Typical force vs.indentation curves: black is the pushing curve, gray the retraction curve. The left curveshows that the MT deformed linearly and reversibly for forces up to 0.3 nN. The inset scanshows a MT after the pushing experiment. For the middle curve more force was applied.The MT collapsed and the backward curve shows that the deformation is irreversible. Theinset image shows the damaged MT afterward. The right curve was performed on glass.
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20 µl of MT sample were incubated for 10 minutes on the silanized surface. The sample was then washed with multiple volumes of buffer to remove the unbound MTs, and mounted on the AFM, without letting the sample dry out. All experiments were performed at room temperature. AFM imaging To minimize damage induced by scanning, we operated the AFM in “jumping mode” (10), which we found suitable for obtaining single protein resolution in liquid while maintaining the structural integrity of the MTs (11). In this mode the AFM performs a force-distance curve (FZ) at every point of a raster scan with a maximum vertical force that is set as a parameter. For each point the vertical sample position at this set force is recorded. The tip is then elevated about 30 nm from the surface before performing the lateral motion to the next point thereby minimizing lateral drag forces on the sample. Force vs. distance curves First we imaged an intact MT in a scan area of ~ 150 x 150 nm2. While recording the next image, an FZ curve was performed in the center of the MT, which was located from a preceding scanline. To perform an FZ curve, the scanner piezo stopped x-y scanning and performed a ramp in the z direction starting from a pre-defined distance. Force corresponds to the deflection of the cantilever, which is detected by a reflected laser beam on a split photo detector and is recorded as function of the z motion. Diode signals (in Volts) were converted to absolute deflection (in nm) using an FZ curve on the glass substrate (using the fact that the glass is incompressible). This deflection signal is converted to force via the known cantilever stiffness. Typically we started an FZ curve with the tip 30 nm elevated above the MT, and used a z displacement between 35 and 70 nm. Every FZ curve was sampled with 3000-10000 sample-points at 15 KHz, every point of the plotted curves was averaged from ~ 30 sample points. Varying the approach speed from 30 to 160 nm/s did not result in differences in elastic behavior or breakage events. Force vs. indentation curves When performing an FZ curve on top of a MT, the cantilever and the MT can be regarded as two springs in series (Eq. 1):
+= , (1)
which gives for kMT
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This assumes that both springs are linear. In that case the MT spring constant kMT can be simply calculated by filling in kms and the known spring constant for the cantilever kcl in Eq. 2. If the measured response is not linear, i.e. kms is not a constant, a data analysis program can be used to subtract the cantilever deflection from every measured data point. Stiffness maps To visualize the stiffness distribution during imaging in jumping mode a development version of the WSxM scanning software was used (Nanotec, Madrid, Spain), see also (12). For each scanpoint an FZ curve (~ 40 nm in 10 ms), is performed with the force limited to ~ 100 pN to prevent damage. A linear fit is performed to the contact part of the retraction curves (the region for fitting is selected by the user), normally sampled with ~ 10 points counted from the point of maximum cantilever deflection and its slope is stored. The acquisition of every xy-coordinate, for which both the height as slope are stored, takes ~ 20 ms. Afterwards the spring constant can be calculated as shown before. Cantilevers To test the independence of the results of the type of cantilevers used for the experiment, we used two different rectangular cantilevers from Olympus, RC800PSA (200x20 µm, 0.05 N/m) and BL-RC150VB (60x30 µm, 0.03 N/m). Of most cantilevers batches we calibrated a few using Saders method (13), else we used the stiffness values given by Olympus. Finite element modeling For finite element modeling we used FEMLAB 3.1i (Comsol, Zoetermeer, Netherlands) following the manufacturer's instructions and examples for the methods we used. Some models were made from thin shells, where compression in the normal direction of the plate is ignored and buckling does not occur. In addition we made thick-shell models from 3D-“brick elements” without these limitations. To simulate contact with a parabolic shaped AFM tip, we used a contact-penalty stiffness method. Non-linear springs connected the tip with the tube surface, during periods of non-contact they have a very low stiffness and do not contribute to the deformation. When the gap between the tip and tube closes the spring becomes very stiff and the tube gets indented. By integrating the vertical component of load over the total contact area, the force is obtained (the horizontal components cancel out due to symmetry). Models where solved using the parametric nonlinear solver, where the parameter solved for is the stepwise lowering of the tip on the tube. To reduce computing time, the model was reduced to a quarter tube taking advantage of symmetry. For the thin-shell models the computation time took up to a few hours, whereas the brick models required 1 to 4 days per model on a 2.4 GHz PC with 1 GB of RAM.
Chapter 7 66
RESULTS Linear response The mechanical response of an object to an external force depends on both geometry and the material properties of the object. The elastic behavior we measured for MTs is determined by their tubular shape and by the elastic properties of the tube wall material, the tubulin proteins. For a macroscopic cylindrical shell made from a homogeneous isotropic material and subjected to a point load, a linear elastic response is expected for deformations on the order of the shell thickness. In general there is also a viscous component of the response, but for the compression rates used here the viscous drag forces against the fluid are negligible. Fig. 1b shows that MTs, although they are only 25 nm in diameter, responded like macroscopic tubes for forces up to ~ 0.3 nN, which corresponded to a 15 % deformation. The response was linear and reversible. Only at higher forces sudden steps in the indentation were seen, and the deformation was no longer reversible. To determine the reproducibility of the linear elastic part of the deformation, we recorded over 100 force vs. distance (FZ) curves during multiple experiments and used 2 different types of cantilevers (Fig. 2). Although the cantilevers had different dimensions and spring constants, the values found for the MT response were independent of the cantilevers. To quantify the
0 20 40 60 80 100 1200.0
springconstant critical force
distance from end in nm
springconstant from FEMsimulation 0
critical force in pN
0.00 0.02 0.04 0.06 0.08 0.10 0.120
MT springconstant in N/m
0.03 N/m cantilever 0.05 N/m cantilever
Figure 3 Indentation experiments were performed close to a previously cut end of a MT (see inset). The graph shows spring constants (normalized to values obtained on the same MT far from the cut) and the force at which the MT collapsed. At distances larger than ~ 50 nm no effect was measurable, at lower distances the MTs rigidity seemed affected. The curve gives the spring constant predicted by FEM, using the thin-shell model, which also shows that end effects occurred only at distances less than ~ 50 nm.
Figure 2 Microtubule spring constants measuredusing two different types of cantilevers(0.03 N/m, n=57 and 0.05 N/m, n=50). The14 experiments were performed on twodifferent AFMs, each time using newcantilevers and samples. The Gaussian fit(performed on the cumulative histogram)gives 0.074 N/m ± 17 % (avg ± sd).
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spring constant, a fit was performed to the linear part of the deformation resulting in a value of 0.074 N/m ± 17 % (avg ± sd). The average standard deviation found in the individual experiments (set of measurements performed with the same cantilever) was 13 %, showing that variations in the cantilever spring constant contribute roughly equally to the observed variation. The remaining variation can include boundary conditions (MT attachment), the fitting procedure, but also (local) differences in MT elasticity. Several EM studies (14, 15) have reported transitions in the number of protofilaments with a frequency of about one per 15-17 µm, which should give a variation in MT diameter and a clear difference in stiffness. In the 100s of µm MTs scanned we never found clear evidence for a variation in the protofilament number, which should show as a combination of a changed height and stiffness and protofilaments showing an angle with the MT axis. It is expected that the deformed region of a tube under a point load will extend to both sides in axial direction for several tens of nanometers (8). We confirmed this estimate by finite element modeling (see below). This implies that the end of a MT should appear softer. To probe this, we cut MTs (by scanning at high force > 0.3 nN) and obtained FZ curves close to the cut ends. Fig. 3 shows that, in agreement with the modeling, this effect is not seen until ~ 50 nm distance from the end. Experimentally it was difficult to probe closer to the end. To check for more local variations in the stiffness on the MT surface, we recorded stiffness maps (see methods). In Fig. 4 such a stiffness map shows a fairly homogenous distribution of the MT stiffness over its surface. The stiffness in the center and up to a few nm to each side was constant and than decreased slightly towards its sides. This behavior was qualitatively reproduced in finite element modeling with a finite tip size and involves contact with the side of the tip and lateral deformation, the response to which in turn depends on not well-controlled surface attachment conditions (data not shown). Thus, overall, the probed elasticity is relatively insensitive to the exact location and does not rely on nm accurate positioning of the probe exactly on the center of the tubes. The
Figure 4 a) MT topography b) simultaneously acquired stiffness map, thedarker colors represent softer regions. The MT was clearly softerthan the background and the stiffness on the MT washomogeneously distributed over its surface. Towards the sides thestiffness was slightly reduced. Also the MT appeared stiffer whenprobed between the protofilaments, as indicated by the lines.
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stiffness map in Fig. 4 shows also an axial pattern representing the protofilaments. When overlaying the stiffness maps with the simultaneously recorded topography images, it becomes evident that the stiffness is slightly higher when probed between 2 protofilaments than when probed on top of one protofilament, which we discuss in the modeling section. The observed difference in stiffness (~ 10 %) is close to the noise in the measurements so it does not show in the histogram of Fig. 2. Non-linear response An ideal thin-walled tube shows a linear response to an indentation depth on the scale of the wall thickness. For larger indentation buckling occurs accompanied by an inversion of curvature from convex to concave in the radial direction (16). Note that, in contrast to spherical shells, curvature in the axial direction will immediately be concave. In our experiments the situation will be modified in several ways, (i) thermal fluctuation of the cantilever (rms deflection of the tip ~ 0.5 nm) will cause a smooth transition to contact, (ii) insertion of the tip into the finite thickness wall (Hertzian contact, (17)), will cause a gradual stiffening on a scale of in our case not more than ~ 1 nm. Over this distance the compression of the wall dominates the total indentation. (iii) The finite tip size causes an increasing contact area and becomes strongly noticeable at large indentations where it tends to cancel the effects of buckling. Fig. 1b shows that the measured response remained very close to linear up to deformations of ~ 3.6 nm and exhibited no clear signs of non-linearities before collapse. Collapse of the tubes is expected when the stress exceeds the ultimate strength of the material. For the MT this happened at tip forces higher than ~ 0.3 nN where the deformation became clearly non-linear and irreversible. The breakage itself was most likely caused by the rupture of protein bonds between the tubulin subunits.
-10 -5 0 5 10 15
indentation [nm]0 5 10 15 20 25
indentation [nm]Figure 5 a) 24 indentation curves, from 5 different experiments. The curves are shifted such that thefirst steps superimpose. At an average force of 0.27 nN a stepwise indentation of 1 nm isclearly visible after which the deformation continues with a comparable slope. Then, at anaverage force of 0.35 nN, a sequence of multiple steps is seen, the collapse of the MT. b) Individual curves on different MTs from different experiments, the grey curves show thatthe backward curves are almost identical to the forward, only that the backward jumpsoccurred at a lower force of 0.21 nN on average.
Chapter 7 69
In order to investigate the events near collapse we limited the applied force to 0.3-0.4 nN and then sampled with high temporal resolution. This surprisingly revealed an instability resulting in a well-defined ~ 1 nm step of the tip at 0.27 nN ± 30 % (avg ± sd) preceding the catastrophic collapse of the MTs (Fig. 5a). In Fig. 5b we applied just enough force to see the step but to avoid the collapse of the MT. These force indentation curves show that the step was reversible, the retraction curves show the backward steps occurring at a slightly lower force of 0.21 nN ± 20 %. Subsequent imaging did not reveal any damage in the MTs. In most cases we could perform multiple of such curves on a single location without seeing damage in the images afterwards, suggesting a self-healing mechanism. In a few occasions we even found that this self-repairing mechanism was not limited to the small initial instability. Fig. 6 shows an experiment where substantial collapse was seen in the indentation curve. The image made directly afterwards shows the damage as a hole in the MT, 2 protofilaments were clearly disrupted. Subsequent imaging showed that the hole was slowly reannealing. The experimental conditions were such that there was no free tubulin in solution. Therefore the self-repairing likely depended on the reconnection of the disrupted protein bonds.
-5 0 5 100.0
a b c d
Figure 6 Self healing MT. a) The curve shows the force indentation preceding image b where thetip indented the MT by 10 nm. The sequence of images b, c, d) show that the MT closedover a period of 4 minutes (the fuzziness in the middle image is caused by the tip beingalmost out of contact, as a result of the low scan forces). Fiducial marks (highlighted inthe background) were used to compensate for sample drift. No free tubulin was presentin the solution such that the re-annealing must be due to reconnecting tubulin bonds.
Chapter 7 70
Modeling In order to quantitatively relate our measured force vs. indentation curves to the material parameters of the protein assembly making up the MTs, we have used a combination of complementary analytic and computational simulation methods. We begin in both cases by modeling MTs as homogeneous elastic shells with dimensions (e.g., inner and outer radii) based on an axial projection of the electron density map of MTs (kindly provided by K. Downing, see also Fig. 9). Using finite element methods (FEM), this model has also been extended to account for the most prominent inhomogeneities in the MT structure, namely the longitudinal, rib-like structures of the protofilaments. The elastic response of a MT to an AFM tip depends not only on the local elastic properties and geometry of the MT but also on the boundary conditions. For instance, the force-indentation relationship is expected to depend sensitively to the proximity of the probe tip to MT ends. For simplicity, we begin with the response of a long MT, for which end effects are not important. Thus, we model the MT as a cylinder that is uniform along its axis.
Figure 7 Comparison of the scaling behavior of the analytical model and the FEM calculations. a) Dependence of tube's spring constant on t/R. The black curve shows the analyticalcalculated function F, this function varies as (t/R)5/2 with a prefactor C = 1.38 (inset) towithin less than 2 % for t/R < 0.1. The FEM calculations for a symmetrically-loaded tubeare shown as circles, and the FEM calculations for the tube that was loaded form the topand supported at the bottom over its whole length as triangles. Scaling behavior for allmodels is identical, only the prefactors depend on the boundary conditions. b) Dependence of the deformed axial length on t/R. The black curve shows the analyticalresult. The prefactor was about ~ 0.7 (see inset). The FEM calculations for asymmetrically-loaded tube is shown as circles and for a top-loaded tube as triangles.Scaling behavior for all models is identical, only the prefactors depend on the boundaryconditions. For the top-loaded tube we found a prefactor of 1.2. The square symbol givesthe deformed length from the MT with protofilaments (where we used 1.1 nm for t, seealso Fig. 9), it shows that the presence of protofilaments do not cause a substantial shiftin l/R.
10 0.01 0.10.00.40.81.2
analytical, symmetrical load FEM, symmetrical load FEM, top load FEM, top load with protofilaments
Chapter 7 71
For the same boundary conditions, probe tip shape, and geometry of an elastic cylinder, the linear force-indentation relationship, i.e., effective spring constant k, must be proportional to the Young’s modulus E of the material. On dimensional grounds we can expect that the spring constant for indenting a homogeneous cylindrical shell of thickness t and radius R with a point-like probe tip must be of the form )/(** RtFREk = , where F is a dimensionless function of t/R. In the limit of a thin shell (R >> t), we can ignore compression in the tube wall in its normal direction, and the tube deformation is characterized entirely by bending and in-plane compression and shear. In this limit, we previously found that
2/32/5 // RCEtzfk ≅∆= , (3) where the prefactor C depends on the particular boundary conditions and only weakly on t/R. For equal and opposite point forces, this can be calculated analytically (8) based on the methods of thin-shell elasticity theory (18). The results of the calculation agree with our FEM results. There are two principal results of the theoretical analysis. First, the dependence of the spring constant on tube geometry is given in Eq. 3. We demonstrate these results in Fig. 7a where we show the function F/(E*R) defined above. We see that this function varies as (t/R)5/2 with a prefactor C = 1.38 (fig 7a, inset) to within less than 2 % over for t/R < 0.1 (for Poisson ratio 0.3). Second, the characteristic axial length of deformation is identified as:
2/1)/( tRR≈l (4) away from the point force. In Fig. 7b we compare the deformation length l obtained from both methods. In the case of the analytic calculation, this length is determined from the axial decay length of the most extended mode of deformation (found to decay exponentially in the axial direction). For the FEM results, this is determined by an exponential fit of the deformation profile (using the form l/xe− where x is the axial distance from point of indentation). We find that 2/1)/(7.0 tRR≅l to within 10 % over the range 0.005 < t/R < 0.1. Although the above results were calculated for opposing point forces, we find from our FEM analysis that the scaling relationships above for both k and l hold for different boundary conditions. In the same thin-shell limit, using FEM for a long tube composed of thin plates (8) subjected to a radially applied point force from the top and supported over its whole length by a flat substrate, we find a prefactor C = 1.2. Thin-shell, radially indented by tips of varying radius Because the axial deformed length exceeds the AFM tip radius (~ 20 nm), and because for small indentations the cross-sectional shape of the tube remains convex, the assumption of a point load seems justified for small indentations. This is not necessarily true for large indentations. To investigate the effects of a more realistic load distribution, we modeled the indentation of the tube with a parabolic tip. Thin-shell FEM gives a non-linear response because the contact area will increase with indentation. Fig. 8a shows the calculated force vs. indentation curves for different tip sizes. They show the expected non-linearity: the spring constant increases with the indentation, and this effect is stronger for bigger tips. For deformations up to 4 nm (the measured indentations before collapse), this effect is less than 10 percent. In any case, this tip effect is expected to occur after buckling
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occurs, i.e. after the inversion of radial curvature under the tip. Buckling, however, is not captured by our thin-shell FEM model due to the way it is constructed, so that the result is only qualitatively valid in the sense that the force vs. indentation curves will shift upwards at indentations larger than ~ 4 nm with increasing tip size. Thick-wall model MTs do have a wall thickness that is not negligible compared to their radius (t/R ~ 0.2). Therefore thick-shell FEM seems a more appropriate approach. Thick-shell FEM also accounts for buckling. We created a series of models composed of 3-dimensional brick elements. We expect two effects: First, the total response should be softer than predicted by thin-shell modeling because of compression of the tube wall. Second, buckling will result in softening at larger indentations. Due to the compressible nature of the tube wall, indentation with a very localized force resulted in numerical instabilities. Therefore we only simulated parabolic tips with a tip radius larger 5 nm. Fig. 8b gives the force vs. indentation curves for different wall thicknesses and tip radii. At small indentations the response is indeed softer than that calculated by the thin-shell model for the same wall thickness and Young's modulus. The discrepancy is stronger for thicker walls and sharper tips. The flattening of the curves (buckling) occurs at an indentation about equal to the wall thickness as expected, and the transition region is
0 1 2 3 4 50
indentation in nm
shell, 5 nm tip 2 nm wall, 20 nm tip 2 nm wall, 5 nm tip 1 nm wall, 20 nm tip 1 nm wall, 5 nm tip 0.5 nm wall, 20 nm tip 0.5 nm wall, 5 nm tip
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indentation in nm
60nm tipradius 20nm tipradius 5nm tipradius pointforce
Figure 8 Effects of the finite tip size and wall thickness on the tube response. The tubes, with a 10nm radius, were loaded from the top and supported over their whole length at the bottom. a) Thin-shell model: effect of tip radius on the response of a tube with a wall thickness of1.6 nm and a Young's modulus of 0.6 GPa. At indentations up to 4 nm with realistic tipsizes up to 40 nm the effects are small, at most 10 %. At larger deformations the effects ofthe tip size become evident. b) Thick-shell model: dependence of the response on the wall thickness. The Young'smodulus was calculated using equation 3. The tube softens (buckles) at smalldeformations. This effect is most obvious for the thinnest wall. The critical indentation forbuckling scales with the wall thickness. Indenting with a bigger tip radius partly masks thiseffect. This masking is stronger for bigger wall thicknesses.
Chapter 7 73
extended with increasing wall thickness. As shown in Fig. 8a, the finite tip size causes an upward shift in the curves, which partially compensates for the effect of buckling. At higher wall thicknesses the tip size has more of an effect because the deformed length decreases (Eq. 4) so that the tip-tube contact area is larger. Protofilaments Modeling the MTs as smooth homogenous tubes ignores an important structural feature of the MTs. MTs are assembled from linear protofilaments and show deep axial grooves on the outside while the inside is relatively smooth. Nevertheless, the initial modeling of the MTs as unstructured shells is not as unrealistic as it may seem because most of the strain is localized to the bridges between the protofilaments, and the homogenous model uses an effective wall thickness close to that of the bridges. To approximate reality better, we composed a model that includes the protofilaments as axial ribs, with dimensions based on an axial projection of the electron density map of MTs (kindly provided by K. Downing). This model consists of a core tube on which the protofilaments are mounted as external ribs. In Fig. 9 the model and the response curves calculated with it are shown. The force vs. indentation curves look very similar to those of the thick-walled tubes. Again the tip radius had hardly any effect on the deformation at small indentations.
0 1 2 3 40
indentation in nm
20 nm tip between pf 40 nm tip between pf
20 nm tip on pf 40 nm tip on pf
Figure 9 MT model including the protofilaments. The Young's moduluswas set to 0.6 GPa. The behavior was very similar to that of thethick-walled tubes. The graph shows the difference in responsebetween pushing on top of the pf or between two (by rotating themodel), the difference is ~ 13 % and was also visible in ourexperiments (Fig. 4).
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DISCUSSION Still under the assumption of a homogeneous material, we can compare finite element modeling with the indentation data while varying the Young’s modulus of the material to fit the data. Using the most realistic model including protofilaments we find the best fit with a Young’s modulus of 0.6 GPa. But even the very simplified thin-shell model describing a MT as a smooth homogenous tube, ignoring tip size and buckling, gives very similar numbers when one uses a value of t close to that of the 1.1 nm thickness of the inter-protofilament bonds. When we fixed the inner radius of the tube to 8.4 nm (inset Fig. 9) and the Young's modulus at 0.6 GPa, we found an effective wall thickness of 1.54 nm. For comparison, an effective Young’s modulus can also be calculated from MT bending experiments. Values reported for the flexural rigidity range from 1*10-24 to 32*10-24 Nm2, with most measurements leaning towards the high end of this range (7). To extract the Young's modulus E from the flexural rigidity EI, the moment of inertia I for the cross-section of the tube needs to be known. This can be numerically calculated from the EM cross section we also used for the model in Fig. 9, and gives 2.7*10-32 m4. This in turn, predicts Young's moduli between 0.04 and 1.2 GPa from the bending experiments. Considering that the most reported values are at the high end of the range, this agrees very well with the value we found from indenting the MT. This result is remarkable since the response to deformation in the two geometries, axial bending and radial indentation is dominated by different parts of the microtubule structure. In bending experiments the flexural rigidity is dominated by the protofilaments, whereas for indenting experiments most strain is localized in the thin connections between the protofilaments. Given the similar values obtained for E, this suggests that the material properties of tubulin do not vary considerably between the centers of the protofilaments and the bond region in between them. This finding is in contrast to results from osmotic compression of microtubules where the authors report evidence for orders of magnitude more compliant material between the protofilaments (19). Compression experiments of microtubules have been performed before by AFM on MTs covalently cross-linked with glutaraldehyde (20). The observed stiffness was strongly affected by the cross-linking and imaging without cross-linking was not possible. Only recent progress in AFM methods in particular “jumping mode” in liquid (11, 21) or “tapping mode” in liquid using very small cantilevers (22) has made it possible to scan the fragile microtubules without destroying them and has made it thereby possible to study the elastic properties without chemical cross-linking. Without any stabilization, however, MTs depolymerize spontaneously. Therefore we used taxol-stabilized MTs. The effect of taxol on bending rigidity has been controversial (23-25). Taxol, binding close to the lateral β-tubulin contacts, has been proposed to stabilize these lateral contacts. Alternatively, or perhaps in addition, it may hold the protofilaments in a straight stable confirmation (26). Taxol is a small molecule, and thus, although it binds close to the lateral bonds, it is not expected to add much to the mass density, which could affect the response to indentation. In the stiffness maps (Fig. 4) the protofilaments appeared softer than the gaps between them. This seems at first glance counterintuitive with the protofilaments being the thickest part of the tube wall. The phenomenon is, however, consistent with the description we
Chapter 7 75
have developed so far, and is also reproduced by modeling. When pushing between the protofilaments with a 20 nm radius tip, the load gets distributed over two protofilaments, and the apparent stiffness of the tube is slightly higher than when pushing exactly on one protofilament. Furthermore the observed boundary effects when pushing close to the MT ends or towards the sides are confirmed by our finite element models (data not shown). For larger indentations we found as expected non-linear behavior. Non-linearity due to geometry, i.e. buckling of the tube wall gave a gentle change in slope in the FEM results which was more or less compensated by the finite size of the tip which causes the load to be spread laterally over the tube. Modeling also showed that buckling gets less pronounced for higher wall thickness, or in the presence of protofilaments. When we included the protofilaments in the finite element model, we saw that the tip only contacted the ridges of the upper, or the upper two, protofilaments, getting less embedded in the tube wall than is the case for the homogenous tube models. This resulted in a larger degree of independence of the tip radius. For large deformations (5.5 nm for a 20 nm tip, pushing on top of a single protofilament), the tip started to contact the neighboring protofilaments as well, which resulted in a stiffening of the response. In the actual experiments, however, the MT collapsed before that point was reached. Besides the geometrical non-linearities there was clear evidence of structural transitions or damage to the MTs as described above. After irreversible failure one could usually see the damage to the MTs in images taken after the pushing experiments. This damage usually involved removal of parts of the top protofilaments, which implies breakage of tubulin bonds in and between the upper protofilaments. Given that MTs are inherently instable, it was not surprising that they mostly kept disintegrating under repeated imaging after this type of damage. The small and reversible step in indentation we found preceding the full collapse ( Fig. 5), was likely caused by only a partial rearrangement of bonds or a limited opening of bonds. From finite element modeling we know that buckling of the tube wall will not show such sudden transitions. The weakest connections in the MT structure (27) seem to be the ones between the protofilaments. This is also confirmed by the different ways tubulin can organize in (rings, sheets, MTs with different protofilament numbers, double walled MTs, and more) (28). We can estimate the energy dissipation involved in the observed instability in the MT wall from the area under the force vs. indentation curve highlighted in Fig. 10. This area represents the difference in work between deforming a MT without and with the change causing the instability. Given that the 1 nm step occurs on average at ~ 0.27 nN, this gives 1.35*10-19 J (32.8 kBT) for the energy necessary to cause the change. One can speculate on different scenarios that could explain the observed reversible 1 nm step: i) The weakest connections, the lateral bonds between the protofilaments give way and the MT splits open like a zipper. After the load is released they re-anneal. The observation of a well defined 1 nm step, followed by further sudden steps at higher loads, argues against this scenario. It would be difficult to understand why the unzippering process does not continue smoothly. ii) The MT lattice might have alternative bi-stable confirmations. Recently it has been shown (29) that for sheets with an inverted radius of curvature (GMPCPP ribbons) protofilaments arrange in pairs with the lateral bonds between protofilaments exhibiting two different and alternating conformations. Within a pair the lateral bonds are
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indistinguishable from those of an intact MT and the protofilaments have the usual inward curvature, whereas between the pairs the bonds are rearranged and curvature is inverted. One could speculate that such an instability might occur in our experiments over the deformed length of the MT, a limited distance on the order of 100-200 nm (where curvature is inverted). Using the work calculated from the data, this gives an energy of ~ 2 kBT per pair of tubulin dimers that have their conformation flipped if one line of bonds is involved, 1/nth of this value if n protofilament pairs are flipped. This energy is less than that of a single lateral dimer bond (see below), which is consistent. iii) The 1 nm step is caused by total disruption of tubulin-tubulin bonds. It has been estimated by modeling that the lateral bonds (3.2-5.7 kBT) between dimers are ~ 5.2 x weaker than the axial bonds (18.5-27.8 kBT) (30). This is supported by EM reconstructions of MTs that show much thinner lateral than axial connections (27) and by the way MTs shorten with the protofilaments fraying out at the depolymerizing ends, showing that the lateral bonds dissociate before the axial bonds (31). Pushing one tubulin dimer out of the microtubule lattice would involve disruption of 1 axial bond and 2 lateral dimer bonds, leaving the dimer retained on one (axial side). Such a mode of rupture is consistent with Fig. 7, where a strong indentation caused the (in this case reversible) disruption of 2 parallel axial bonds. Rapidly reannealing damage would of course have disappeared before the first image was recorded after producing damage. Using the ratio of 5.2, we get 18.5 kBT for the axial bond and 3.6 kBT for the lateral bonds between dimers from our data. These experimentally derived values are upper limits as they were obtained by assuming a minimum disruption of bonds, but they do agree remarkably well with the previously calculated values for binding energies (30). In vivo, MTs are decorated with a multitude of accessory proteins (MAPs) (32). Many of these might have as yet unknown mechanical functions. One prediction can be made from our results: when an accessory protein binds on the ridges of the protofilaments as, for
Figure 10 Force indentation curve showing the 1 nm step. Theshaded part indicates the work needed for theobserved instability. The work was measured by thedifference between the measured force indentationcurve and backwards extrapolated from the curvesection after the step. This gives 1.35*10-19 J (32.8kBT).
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example, predicted for tau (33), the resistance against compression will hardly change, whereas the flexural rigidity would likely increase. This has been observed for tau (23, 34). To make MTs rigid against radial compression, the proteins should fill up the grooves between the protofilaments. The AFM indentation experiments we have presented here access a mode of deformation of microtubules that is different from bending experiments. The focus is on different parts of the microtubule structure, the grooves between the protofilaments, and the deformation is localized on the scale of about 100 nm. We expect that this will enable further research into local variations of microtubule mechanics under various circumstances and into the local mechanical effects of microtubule binding proteins. Acknowledgements
We thank Ken Downing for providing the electron density map of the MT cross-section and Julio Gómez-Herrero for useful discussions about the AFM experiments. This work was supported by the Dutch Foundation for Fundamental Research on Matter (FOM). Carolina Carrasco was supported by the by the Ministerio de Ciencia y Tecnología through project MAT2001-0664 and by the access to research infrastructures activity in the sixth framework programme of the EU (contract RII3-CT-2003-506350, Laserlab Europe).
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Molecular Biology of the Cell. Garland Science, New York. 2. Gardel, M. L., J. H. Shin, F. C. MacKintosh, L. Mahadevan, P. Matsudaira, and D.
A. Weitz. 2004. Elastic Behavior of cross-linked and bundled actin networks. Science 304:1301-1305.
3. Tilney, L. G., J. Bryan, D. J. Bush, K. Fujiwara, M. S. Mooseker, D. B. Murphy, and D. H. Snyder. 1973. Microtubules: evidence for 13 protofilaments. J. Cell. Biol. 59:267-275.
4. Pierson, G. B., P. R. Burton, and R. H. Himes. 1978. Alterations in number of protofilaments in microtubules assembled in vitro. J. Cell. Biol. 76:223-228.
5. Nogales, E., S. G. Wolf, and K. H. Downing. 1998. Structure of the alpha beta tubulin dimer by electron crystallography. Nature 391:199-203.
6. Nogales, E., M. Whittaker, R. A. Milligan, and K. H. Downing. 1999. High-resolution model of the microtubule. Cell 96:79-88.
7. Vanburen, V., L. Cassimeris, and D. J. Odde. 2005. A Mechanochemical Model of Microtubule Structure and Self-Assembly Kinetics. Biophys. J.
8. de Pablo, P. J., I. A. T. Schaap, F. C. MacKintosh, and C. F. Schmidt. 2003. Deformation and collapse of microtubules on the nanometer scale. Phys. Rev. Lett. 91
9. Williams, R. C., Jr., and J. C. Lee. 1982. Preparation of tubulin from brain. Methods Enzymol. 85:376-385.
10. de Pablo, P. J., J. Colchero, J. Gomez-Herrero, and A. M. Baro. 1998. Jumping mode scanning force microscopy. Appl. Phys. Lett. 73:3300-3302.
11. Schaap, I. A. T., P. J. de Pablo, and C. F. Schmidt. 2004. Resolving the molecular structure of microtubules under physiological conditions with scanning force microscopy. Eur Biophys J 33:462-467.
12. A-Hassan, E., W. F. Heinz, M. D. Antonik, N. P. D'Costa, S. Nageswaran, C. A. Schoenenberger, and J. H. Hoh. 1998. Relative microelastic mapping of living cells by atomic force microscopy. Biophys. J. 74:1564-1578.
13. Sader, J. E., J. W. M. Chon, and P. Mulvaney. 1999. Calibration of rectangular atomic force microscope cantilevers. Rev Sci Instrum 70:3967-3969.
14. Chretien, D., F. Metoz, F. Verde, E. Karsenti, and R. H. Wade. 1992. Lattice defects in microtubules: protofilament numbers vary within individual microtubules. J. Cell. Biol. 117:1031-1040.
15. Arnal, I., and R. H. Wade. 1995. How does taxol stabilize microtubules? Curr. Biol. 5:900-908.
16. Landau, L. D., and E. M. Lifshitz. 1986. Theory of Elasticity. Pergamon Press, New York.
17. Johnson, K. L. 2001. Contact Mechanics. Cambridge University Press, Cambridge. 18. Niordson, F. 1985. Shell Theory. North-Holland, New York.
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19. Needleman, D. J., M. A. Ojeda-Lopez, U. Raviv, K. Ewert, J. B. Jones, H. P. Miller, L. Wilson, and C. R. Safinya. 2004. Synchrotron X-ray diffraction study of microtubules buckling and bundling under osmotic stress: A probe of interprotofilament interactions. Phys. Rev. Lett. 93:-.
20. Vinckier, A., C. Dumortier, Y. Engelborghs, and L. Hellemans. 1996. Dynamical and mechanical study of immobilized microtubules with atomic force microscopy. J. Vac. Sci. Technol. B 14:1427-1431.
21. Moreno-Herrero, F., P. J. de Pablo, M. Alvarez, J. Colchero, J. Gomez-Hertero, and A. M. Baro. 2003. Jumping mode scanning force microscopy: a suitable technique for imaging DNA in liquids. Appl Surf Sci 210:22-26.
22. Ando, T., N. Kodera, Y. Naito, T. Kinoshita, K. Furuta, and Y. Y. Toyoshima. 2003. A high-speed atomic force microscope for studying biological macromolecules in action. Chemphyschem 4:1196-1202.
23. Mickey, B., and J. Howard. 1995. Rigidity of microtubules is increased by stabilizing agents. J. Cell. Biol. 130:909-917.
24. Venier, P., A. C. Maggs, M. F. Carlier, and D. Pantaloni. 1994. Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations. J Biol Chem 269:13353-13360.
25. Felgner, H., R. Frank, and M. Schliwa. 1996. Flexural rigidity of microtubules measured with the use of optical tweezers. J. Cell. Sci. 109:509-516.
26. Amos, L. A., and J. Lowe. 1999. How Taxol stabilises microtubule structure. Chem Biol 6:R65-69.
27. Li, H., D. J. DeRosier, W. V. Nicholson, E. Nogales, and K. H. Downing. 2002. Microtubule structure at 8 A resolution. Structure (Camb) 10:1317-1328.
28. Unger, E., K. J. Bohm, and W. Vater. 1990. Structural diversity and dynamics of microtubules and polymorphic tubulin assemblies. Electron Microsc Rev 3:355-395.
29. Wang, H. W., and E. Nogales. 2005. Nucleotide-dependent bending flexibility of tubulin regulates microtubule assembly. Nature 435:911-915.
30. VanBuren, V., D. J. Odde, and L. Cassimeris. 2002. Estimates of lateral and longitudinal bond energies within the microtubule lattice. Proc. Natl. Acad. Sci. USA 99:6035-6040.
31. Tran, P. T., P. Joshi, and E. D. Salmon. 1997. How tubulin subunits are lost from the shortening ends of microtubules. J Struct Biol 118:107-118.
32. Cassimeris, L., and C. Spittle. 2001. Regulation of microtubule-associated proteins. Int. Rev. Cytol. 210:163-226.
33. Al-Bassam, J., R. S. Ozer, D. Safer, S. Halpain, and R. A. Milligan. 2002. MAP2 and tau bind longitudinally along the outer ridges of microtubule protofilaments. J. Cell. Biol. 157:1187-1196.
34. Felgner, H., R. Frank, J. Biernat, E. M. Mandelkow, E. Mandelkow, B. Ludin, A. Matus, and M. Schliwa. 1997. Domains of neuronal microtubule-associated proteins and flexural rigidity of microtubules. J. Cell. Biol. 138:1067-1075.
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Chapter 8 Tau protein binding forms a 1 nm thick layer along protofilaments without affecting the radial stability of microtubules Iwan A.T. Schaap1, Bernd Hoffmann2, Carolina Carrasco3, Rudolf Merkel2, Christoph F. Schmidt1
1 Section Physics of Complex Systems, Department of Physics and Astronomy, Vrije
Universiteit Amsterdam, The Netherlands 2 Institute of Thin Films and Interfaces, ISG4: Biological Layers, Research Center Jülich
GmbH, 52425 Jülich, Germany 3 Departamento de Física de la Materia Condensada C-III, Universidad Autónoma de
Madrid, 28049 Madrid Contribution of authors Iwan Schaap and Carolina Carrasco performed the AFM experiments. Tau purification and biochemical experiments with tau were performed by Bernd Hoffmann. Iwan Schaap performed the finite element simulations. Abstract Tau is one of the most abundant microtubule-associated proteins involved in kinetical stabilization and bundling of axonal microtubules. Although intense research has revealed much about tau function and its involvement in Alzheimer’s disease during the past years, it still remains unclear how exactly tau binds on MTs and if the kinetic stabilization of MTs by tau is accompanied, at least in part, by a mechanical reinforcement of MTs. In this paper we have used atomic force microscopy to elucidate both aspects by visualizing and mechanically analyzing microtubules in the presence of native tau isoforms. We could show that tau at saturating concentrations forms a 1 nm thick layer around the microtubule, but leaves the protofilament structure well visible. The latter observation argues for tau binding mainly along and not across the protofilaments. Although tau strongly affects MT kinetics, the radial mechanical strength of microtubules was almost unaffected by tau, consistent with tau binding along the tops of the protofilaments. Finite-element calculations confirmed our findings.
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Introduction Tau proteins form a family consisting of several isoforms generated by alternative splicing in the mammalian central nervous system. All tau isoforms are expressed mainly in axons and bind to microtubules (MTs) with three or four MT binding sites at their C-terminal ends. Besides their functions in MT stabilization and in establishing cell polarity (1) tau isoforms can also aggregate into pathologically relevant “paired helical filaments” that are the hallmarks of Alzheimer’s disease and other neurodegenerative diseases (2). Malfunction of tau in neurons appears to be intimately related to its interactions with MTs. The interaction itself is regulated by tau phoshorylation at multiple sites, but only an ill-coordinated phosphorylation finally results in tau aggregation (for reviews see (3,4)). Tau function for neuronal development, its aggregation to paired helical filaments, and the overall important regulation of tau binding via phosphorylation have been mainly analyzed for human tau isoforms. Additionally, same results have been found for other mammalian organisms as pig (5), rat, mouse and guinea pig (6). Tau is a natively unfolded protein that does not have a well-defined 3D shape as shown by structural, spectroscopic and biochemical experiments (7). The absence of compact folding is due to its strongly hydrophilic amino acid composition (8) and makes tau one of the most soluble proteins known. The unfolded character of tau has precluded a detailed structural analysis so far. Protein cross-linking studies suggested preferential regions of interaction with tubulin (9,10) but these could not be interpreted in terms of a specific pattern of folding on the MT surface. Several studies using different electron microscopy techniques showed that tau is located on the outside of MTs (11,12) but no structural information on the MT binding regions of tau could be observed. Recent cryo-EM studies of unstained vitrified specimens, followed by image reconstruction led to somewhat contradictory conclusions concerning tau binding. Al-Bassam et al. (13) proposed tau binding parallel with the outer protofilament rim, whereas Kar et al. (14) suggested a partial tau localization to the inner MT surface. In the most recent experiments tau binding to MTs was visualized using metal shadowing freeze-dried MTs and tubulin sheets decorated with tau. The results showed tau binding along protofilaments but also a lateral cross-linking between them (15). These and other studies (16,17) agreed that tau binds tightly to MTs (for human full length tau (htau40) a Kd of below 1 µM was found) and that it lowers the critical concentration for MT assembly substantially. Tau mainly prevents catastrophes and reduces the rate of depolymerization to less than 0.1 µm/min compared to a rate exceeding 10 µm/min without tau (18,19). In this paper we have addressed two basic questions: Where do mammalian tau isoforms bind to the MT and how does such tau binding affect the mechanical rigidity of the MTs. For the experiments we have used the complete set of tau isoforms isolated from pig brain to simulate physiological conditions of binding to MTs. Such a tissue-purified pool of tau isoforms has the advantage of containing all natural post-translational modifications such as phosphorylations compared to tau proteins expressed in E. coli. For the analysis of tau binding to MTs we have used atomic force microscopy (AFM). This technique has allowed us to image MTs with single-protein resolution in a close-to-native environment at room temperature (20), thus avoiding difficulties in structure preservation due to sample fixation. In addition, we have used the AFM tip as a force transducer to probe the mechanical response of single tau-decorated Mts by local
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indentation. In contrast to flexural rigidity measurements, indentation experiments measure the radial elasticity of the MTs which is dominated by the inter-protofilament bonds (21). We performed similar experiments with a protein that binds in a well-known geometry to MTs, namely a truncated form of a kinesin-1 (Nkin) from N. crassa which binds to the outer ridge of MT protofilaments (22).
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Materials and Methods Protein purifications Tubulin and microtubule-associated proteins (MAPs) were purified from pig brain by cycles of assembly and disassembly in vitro according to Williams and Lee (23). Partially purified tubulin and MAPs were solubilized in PM buffer (100 mM Pipes, pH 6.9, 2 mM EGTA, 1 mM MgSO4, 2 mM DTT) and separated from each other by ion-exchange chromatography using P11-phosphocellulose. Pure tubulin without affinity to P11 phosphocellulose was pooled and diluted down to a concentration of 3 mg/ml and stored at -80°C after addition of GTP to a final concentration of 1 mM. MAP separation was performed by DEAE phosphocellulose chromatography. After MT and MAP binding to DEAE phosphocellulose, proteins were sequentially eluted in a gradient of KCl ranging from 0 to 0.8 M KCl. Fractions were analyzed by silver staining and tau western blot. Unspecific protein bands and KCl in tau fractions were diminished by size fractionation in a Sephadex-200 column and a subsequent centrifugation in centricon columns with a 30 kDa cut-off. Tau protein was stored in aliquots at -80°C. The purity of proteins was tested by Western blotting and silver stain experiments after SDS-page. Alkaline-phosphatase-coupled secondary antibodies were used for protein detection. The Nkin kinesin from Neurospora crassa (a kind gift from Günther Wöhlke, Munich) we used was truncated at amino acid 433 as described elsewhere (24,25). Protein concentrations were determined by Bradford assay. Microtubule polymerisation and protein binding For MAP-free microtubule polymerization 10 µl of tubulin (3 µg/µl) were incubated for 30 min at 37°C in PEM-80 buffer (80 mM Pipes, pH 6.8, 2 mM MgCl2, 1 mM EGTA). The resulting microtubules were diluted 1:20 in PEM-80 buffer containing 7 µM paclitaxel. To reduce background artefacts during AFM analysis, PEM-80 buffer had been centrifuged for 2 h at 100.000 g before addition of paclitaxel. Diluted microtubules were stored at room temperature and used as stock solution with a concentration of 0.15 mg/ml polymerized tubulin for subsequent experiments. For each AFM experiment the MTs were diluted to 7.5 µg/ml in dilution buffer. For the experiments with tau, tau was added to MTs in solution and allowed to bind for 30 minutes at 37°C. For the experiments with kinesin, 20 µl of the diluted MTs were first incubated on the surface before 1 µl kinesin (0.5 mg/ml) and 1 µl Adenosine 5′-(β,γ-imido)triphosphate (AMP-PNP, 1 mM) was added. Immuno labelling experiments Microtubules from the stock solution were diluted to a final concentration of 7.5 µg/ml in paclitaxel-containing PEM-80 buffer and incubated without or with tau protein in ratios of 10:1 to 1:1 (tubulin:tau) for 30 min at 37°C. Tau-decorated MTs were pelleted by centrifugation at 20.000 g for 15 min and washed once with PEM-80+paclitaxel buffer. Incubations with tau antibody (ab8739, Abcam) and a secondary antibody fused to Cy3 were performed at 37°C for 30 min each. After each antibody incubation, repeated washing cycles were performed with PEM-80+paclitaxel buffer. As a control, MTs were visualized with a rat anti-tubulin antibody (clone YL1/2, Chemicon). Fluorescence
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analysis of bound tau was performed on a Zeiss Axiovert 200 microscope equipped with a TRITC filter set and an ORCA-ER digital CCD camera. Atomic force microscopy We operated the AFM (Nanotec, Madrid, Spain) in 'jumping mode' (26) which we found suitable for obtaining single protein resolution in buffer at room temperature while preserving the structural integrity of the MTs. We used Olympus cantilevers (RC800PSA, 200x20 µm) with a tip-radius of ~20 nm and spring constants, calibrated using Saders method (27), of around 0.06 N/m. AFM samples were prepared as described elsewhere (20). Briefly, 20 µl samples of MTs were incubated for 30 minutes on a silanized glass surface, and washed with dilution buffer. From topographical scans performed at the lowest possible scan force (<0.1 nN), we measured the average heights of the MTs. The height information of each scan point was plotted into a histogram and by measuring the distance between the maxima in the histograms representing the glass surface and the top of the MT respectively, we obtained the average height. The z-piezo was calibrated using a 26 nm grid (TGZ01, Mikromasch, Estonia). The mechanical response of the MTs was measured by performing force-versus-distance curves on top of individual MTs and on the glass surface. The difference between these curves, after superimposing the contact points, gave the indentation of the MT as a function of tip force. All AFM experiments were performed in buffer at 22 ºC. Finite element simulations For finite element modelling we used FEMLAB 3.1i (Comsol, Zoetermeer, Netherlands) following the manufacturers instructions and examples for the used methods. Models were constructed from 3D brick elements and were based on the cross sections shown in Figure 6, which were extruded in axial direction. The model size was reduced to a quarter tube taking advantage of symmetry (~50000 elements) The computing time was 1-4 days per model on a 2.4 GHz PC with 1 GB of RAM. To simulate contact with a parabolic AFM tip we used a contact-penalty stiffness method. Non-linear springs connected the tip with the tube surface. During periods of non-contact they have a very low stiffness and do not contribute to the deformation. When the gap between the tip and tube closes, the spring becomes very stiff and the tube gets indented. By integrating the vertical component of load over the total contact area, the force is obtained (the horizontal components cancel out due to symmetry). Models were solved using the parametric nonlinear solver, where the parameter solved for is the stepwise lowering of the tip on the tube.
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Results We purified tubulin and MAPs from pig brain and used ion exchange chromatography and size fractionation columns in order to obtain highly purified tau protein (Fig. 1A). The comparison of tau protein present in crude brain extract and after purification revealed that six distinct tau isoforms could be isolated with molecular weights between 45 and 65 kDa (Fig. 1A). Two additional bands of lower molecular weight were tau degradation product as shown by western blot analysis (Fig. 1B). Although the tau isoforms bound to MTs during MT assembly and disassembly cycles in the earlier during purification, it could not be excluded that tau isoforms had lost their binding activity as pure proteins. Therefore we incubated MAP-free MTs with purified tau and analyzed for complex formation in immuno-labelling experiments. At stoichiometric ratios of 1:1 to 1:3 (tau:tubulin), we observed strong tau binding to microtubules (Fig. 2A and B). At ratios of 1:10 and below, the fluorescent antibody decoration of the microtubules became speckled and finally strongly diminished. Under these conditions we controled that pure MTs remained permanently detectable with tubulin specific antibodies (Fig. 2C). Since immuno-labelling experiments resulted in strong bundling of MTs in the presence of tau, we additionally analyzed tau covered MTs using DIC microscopy. Here, a few MT-bundles were detected (Fig. 2D and 2E) as described in the literature (28), but insufficient amounts to argue that strong bundling was caused mainly by tau and not by the antibodies used for labelling. The weak ability of tau to bundle MTs was also confirmed by transmission electron microscopy (data not shown). Despite MT bundling, the strong fluorescence signal indicated a complete MT coverage with tau. These control experiments suggest that the structural and mechanical effects on MTs described below were exclusively caused by the binding of purified tau.
Figure 1. Purity of tau. Tau proteins of pig brain were isolated using ion exchange and size chromatographic techniques as described in Material and Methods. Tau isoforms were separated in SDS-page chromatography and analyzed for purity by silver stain (A) and western blot analysis (B). The size of marker proteins is given in kDa on the right. Black lines between A and B indicate tau protein bands present in both experiments and proof the purity of isolated tau used for the experiments described here.
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Figure 2. Tau binding to microtubules. Tau protein was incubated with MTs in a 1:1 (A) and 1:3 (B) ratio (tau:tubulin) and fluorescently labelled with anti-tau antibodies. MT-tau aggregates were diluted 1:400 and analyzed. As control MTs without tau were labelled with a MT specific antibody (C). Note that fluorescent signals do not represent single microtubules but bundles fused by antibody interaction. Bundling of MTs was analyzed in the absence of antibodies in DIC microscopy. MTs were incubated with tau in a 3:1 ratio (tau:tubulin) bundling is indicated by arrows (D). MTs incubated with tau in a 1:1 ratio (E) or without tau (F) did not show bundling. Scale bars represent 10 µm.
0 18 20 22 24 26 28 30 32 340
height in nm
undecorated MTs MT + tau MT + kinesin
Figure 3. Height distribution of MTs. Undecorated MTs show an average diameter of 25.9 nm at a loading force of <10 nN. When MTs are pre-incubated with tau the height increased by 2.2 nm. Kinesin added 4.5 nm to the MT height. Note that the 2.2 nm are caused by tau binding all around MTs while kinesin is bound to MTs just on one site because in this case MTs were attached to the surface before addition of kinesin.
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Figure 4. AFM analyses of MTs. A) MT without tau showing clearly the protofilaments. B) For MTs with tau (ratio of 1:1), the protofilaments remain visible. The height increased by 2 nm (see Table 1). Inset, loose fibers with a height of ~ 0.5 nm could occasionally be seen. C) At higher tau : tubulin ratios additional aggregates with heights from 3-10 nm were found (the bottom figure is at a reduced magnification). D) MTs decorated with kinesin gave a very distinctive pattern, and an increase in height of 4 nm. Note that in this case MTs were attached to the surface before kinesin was added. Therefore, kinesin is bound only to the exposed MT sides. The height of MTs incubated with tau at a molar ratio of 1:1 (tau:tubulin, 26 measurements in 5 experiments with different samples) was compared to the height of MTs without tau (51 measurements in 12 experiments). The MT height increased from 25.9 ± 1.5 nm (avg. ± s.d.) to 28.1 ± 2.0 nm, an increase of 8.5 % (Fig. 3 and Table 1). All MTs tested showed the same increase in height over their whole scanned length. Figure 4B shows the effects of tau bound to MTs at a ratio of 1:1 (tau:tubulin). As for MTs without tau (Fig. 4A), protofilaments remained visible indicating that tau does not fill or span the grooves. At lower ratios of tau to tubulin (1:20 - 1:3) fibrous structures could occasionally be observed on top of MTs, although not fixed but rather mobile in repetitive scans (Fig. 4B, arrows in zoomed images). They appeared to be tens of nm long but their height was only on the order of 0.5 nm, at the limit of the AFM resolution in liquid. The measured height might be an underestimate of the actual thickness due to the mobility of the fibers. At increased tau concentrations (3:1 and higher) fuzzy patches could be seen. Unlike the fibers, they were fixed in place showing heights ranging from 3 to 10 nm (Fig.
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4C). The increase in height by 2 nm is consistent with the fluorescent labelling experiments and is strong evidence for tau binding to the outside of the MTs. The clearly visible and unaffected protofilament structure after tau binding argues for a tau-MT interaction along the outer ridge of the protofilaments and not in the grooves between protofilaments. Tight binding of tau to MTs is expected to affect the mechanical rigidity of the MTs. The exact binding geometry of tau on MTs is not known. Different binding modes will affect the elastic response of MTs to particular deformations in different ways. Binding along and on top of the protofilaments would primarily increase rigidity against bending deformations. Depending on the location of tau binding sites there is the possibility of tau spanning the protofilamental structure, either on the outside of the MTs or possibly the inside (14). This should have a strong effect on the mechanical behaviour of MTs when deformed radially. In our experiments we have probed the radial indentation of the MTs, a mode of deformation dominated by the rather weak lateral bonds (compared to the axial bonds) between the protofilaments (21). In earlier experiments the linear response of undecorated MTs to indentation with the tip of an AFM could be fitted with a simple Hooke’s law with a spring constant of 0.074 N/m (21). In the presence of saturating concentrations of tau we here found that the response of MTs to indentation was again linear with the force, and we obtained a spring constant of 0.077 N/m (Table 1). The small (4 %) difference to the earlier results lies within the standard deviation and is therefore not significant. Spring constants for tau covered MTs were highly reproducible as shown in the indentation curves (Fig. 5A). The forces at which tau-decorated MTs irreversibly collapsed were in the range of 0.4 to 0.5 nN, slightly higher than the 0.35 nN reported for undecorated MTs (29). The fact that the elastic response was qualitatively (linearity) and quantitatively indistinguishable from that of undecorated MTs (Fig. 5B) while the diameters were clearly larger is compelling evidence for the fact that tau does not bind with any major part of its mass between protofilaments, but that at least its bound sections mainly align with the tops of the protofilaments. Table 1. Height and spring constants for undecorated MTs and MTs decorated with tau or kinesin. Standard deviation is given as s.d. height ± s.d. spring constant ± s.d. undecorated MT
25.9 ± 1.5 nm 51 scans on 31 MTs
0.074 ± 0.014 N/m 107 measurements on 25 MTs
MT + tau 1:1 ratio
28.1 ± 2.0 nm 26 scans on 7 MTs
0.077 ± 0.006 N/m 11 measurements on 4 MTs
MT + Kinesin 1:1 ratio
30.4 ± 1.7 nm 23 scans on 11 MTs
~0.08 N/m Not constant, see Fig. 5 6 measurements on 5 MTs
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-10 -5 0 5 10 15 200.0
-5 0 50.0
-5 0 50.0
indentation in nm
Figure 5. Mechanical response was probed for decorated and undecorated MTs. For comparison the computed behavior of the model with tau (black line from figure 6) was added to each plot. (A) 6 indentation curves from 3 experiments on tau decorated MTs. Deformation is approximately linear for the first 4 nm. At forces between 0.4 and 0.5 nN the MTs collapsed. The probed stiffness is almost similar to that of undecorated MTs, the critical force under which they collapse is slightly higher (B) Typical indentation curves on undecorated MT (see also (29)) (C) 6 curves performed on kinesin decorated MTs, and the model from figure 6 (black line). The average stiffness (obtained by a linear fit to the indentation up to 0.3 nN) does not differ much from undecorated or tau decorated MTs. But the stiffness is no longer constant. Instead it increases with indentation depth. To verify our approach we probed MTs decorated with the kinesin motor protein Nkin. The binding of Nkin is well described, Several crystal structures of kinesins as well as their binding site to MTs are known (22,30-32). Kinesins bind to the ridge of protofilaments, with a distinct binding site close to the small groove formed at the interface of α- and β-tubulin. Thus kinesin is not expected to cause a stiffening of the MTs against radial indentation. At the ratio of 1:1 (Nkin:tubulin), Nkin was able to cover the whole surface of MTs (Fig. 4D). Kinesin binding resulted in a very distinct binding pattern and an increase in height by 4.5 nm per side (Fig. 3 and Table 1). There is a change in the shape of the indentation curves. Upon initial contact the decorated MTs appeared soft, while they stiffened (the slope increased) with higher forces (Fig. 5C). The indentation curves no longer begin linearly. A linear fit to the first 0.3 nN results in an
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average spring constant of 0.08 N/m. This again very slight increase in radial stiffness by 8 % (Table 1), shows clearly that even the addition of a thick layer of material to the MT exterior does not automatically lead to a proportional increase in MT stiffness against radial indentation. We created a set of finite element models to interpret the measured response characteristics and to evaluate possible binding patterns of tau in terms of their expected effect on the mechanical behaviour of the MTs. The 3D models, based on the MT structure derived from electron microscopy (33), simplified as described in (21), approximate the MT as a cylindrically symmetric tube with protofilaments as external axial reinforcements. In the calculations the model was radially compressed by a parabolic tip with a 20 nm radius to simulate indention with the AFM tip. Tau was added either as a 1 nm diameter solid ridge on top of the protofilaments or as 0.5 nm thick layer between the protofilaments (see Fig. 6 for dimensions of the models). The graph in figure 6 shows a strong increase in stiffness if tau is bound between the protofilaments, whereas if tau is added on top of the protofilaments, it adds very little to the stiffness. The increase of stiffness in the former case is about 60% over the undecorated MTs, which is far beyond the error margins of our experiment. The lack of an effect in the latter case is understandable because the response to a radial tube deformation is dominated by the weakest part of the tube, which are the thin connecting bridges between the protofilaments. The inset in Figure 6 confirms that the strain in an indented model MT is concentrated between the protofilaments.
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Figure 6. Finite element simulations upon tau binding. On top the cross-sections of the models with their dimensions in nm are given. Left, MT in the absence of tau. Center, tau is added as a 0.5 nm thick layer between the protofilaments. Right, tau is added as 1 nm thick filaments on the ridges of the protofilaments. For all models the elastic modulus of the added material was set 0.6 GPa, which is equally to that of MT. The graph shows the computed deformation of the tube when indented with a parabolic tip with a 20 nm radius. The addition of tau as 1 nm filaments on top of the protofilaments adds very little to the probed stiffness, but when tau is added as a 0.5 nm layer between the protofilaments, the stiffness increases by more than 60%. The inset shows the MT with tau on top of the protofilaments. The strain (indicated by brighter colors) is concentrated at the loading point and between the protofilaments.
no tau tau between pf tau
0 1 2 3 40
indentation in nm
tau between protofilaments tau on top protofilaments no tau
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Discussion We purified tau proteins and microtubules from adult pig brain. Because tau and tubulin are strongly conserved proteins, we expect that the pig proteins used here are a good general model system. Since it is unknown if specific tau isoforms behave differently in decorating the MT they might thereby affect MT stiffness also differently. To circumvent this problem, we chose to work with the complete set of tau isoforms simultaneously. By using tissue-purified tau containing multiple isoforms and resembling the natural pool of tau isoforms in the cell, we staid very close to the natural conditions with respect to isoform composition and post-translational modifications. The MTs incubated with tau showed a by about 2 nm increased diameter, suggesting decoaration of the MT by tau. The observed increase in MT diameter could also be explained by a tau-induced, increase in average protofilament number. Such an effect has been described for taxotere or GMP-CPP (34). An 8.5 % increase in diameter (14 instead of 13 protofilaments) should, for geometrical reasons, reduce the MT spring constant by 11.5 % percent using (29):
2/32/5 /*2.1 REtkmt = , Eq. 1 where k is the MT spring constant, t the effective wall thickness, E the Young’s modulus of the wall material and R the tube radius. This was not observed, but a stiffening effect of tau binding in the grooves could potentially have exactly canceled the geometric softening. We believe that this explanation is unlikely, because, first, we did not polymerize MTs in the presence of tau, but instead stabilized MTs with paclitaxel before the addition of tau. Second and more convincingly, we did only see straight protofilaments in our images, and no evidence for a helical twist that would be expected for an increased protofilament number (34). At high ratios of tau:tubulin we observed fuzzy patches of 3 to 10 nm thickness on the microtubules (fig. 4c). These are likely caused by either multilayer attachment of tau to the MTs or by tau proteins that cannot bind anymore over their whole length to the MTs. Such a mode of incomplete binding would provide a mechanism for MT bundling or cross-linking. DIC microscopy showed only bundling at high concentration of tau. The fact that the surface of the MTs in these patches appeared less well defined or soft (as shown by the response in indentation experiments, data not shown) is consistent with the largely unfolded structure of tau (7). One of the main motivations for our study was to explore the correlation between the binding geometry of microtubule associated proteins and the mechanical properties of microtubules. The binding pattern of tau is controversial. It’s strongly hydrophilic and largely unfolded character makes it difficult to image and characterize by electron microscopy. Some experiments have suggested that tau binds partially inside MTs in a radial fashion (14) whereas on the outside a part of the molecule is believed to bind along the protofilament (13). Recent EM results with metal-shadowed freeze-dried MTs (15) suggest an increase in density along the outer ridges of protofilaments by EM reconstruction, but no signs of tau binding to the MT inside. One reason for these conflicting observations could be different experimental procedures. Tau localization inside MTs was shown for MTs co-polymerized with tau, in the absence of paclitaxel, but
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with GMP-CPP and TMAO (14). The absence of paclitaxel, however, did not cause binding to the MT interior in the experiments of ref. (15). Our results are consistent with tau binding mainly along the outer ridges of the protofilaments. The increase in diameter discussed above would not be measurable if tau were either bound in the grooves between the protofilaments or on the inside. The clear visibility of the grooves argues against binding of any substantial fraction of the protein in the grooves. Most importantly, the fact that the rigidity against indentation is unaffected by tau binding while there is clear evidence of tau decoration makes it unlikely that much of the tau protein is located between protofilaments, or bound radially on the inside of the MT. Both, tau binding inside MTs in a protofilament-crossing manner and localization in the grooves on the outside would strongly affect indentation stiffness, as it would have to substantially increase the effective wall thickness. For undecorated MTs this effective wall thickness is only about 1.5 nm (21), so that even a small amount of additional material would make a difference, given the almost cubic dependence of the stiffness on wall thickness (Eq. 1). We prepared our MTs with paclitaxel and tau was added after polymerization. This procedure might preclude certain MT-tau interactions. It should be instructive to compare the elastic response of microtubules to indentation to their response to bending. This flexural rigidity is expected to be sensitive to other geometrical features of the microtubules, in particular it should not be sensitive to the thickness of the bridges between the protofilaments, but much more to their diameter. Unfortunately, there is still considerable disagreement in the literature about the exact value of the MT flexural rigidity (35), and the situation might be more complicated than the bending of a homogeneous tube. Mickey and Howard (19) found only a slight increase in the flexural rigidity of MTs stabilized with tau. In contrast, Felgner et al. (36) found a more than twofold increase for several tau-constructs. When MTs were stabilized with a mixture of MT associated proteins they were found to have a 6 to 16 times increased stiffness (37,38). The point that the binding of proteins to the protofilament ridges does not change the response of MTs to indentation much is confirmed by the experiments with kinesin. Nkin is known to bind to the ridges (22,30-32). The Nkin-decorated MTs showed an increase in wall thickness of 4.5 nm (table 1). EM reconstructions have shown that one bound head increases the MT radius by about 4 nm (39), consistent with the increase in radius we have observed. As expected, despite the increased outer diameter, the Nkin decorated MTs show an average stiffness (≤ 0.3 nN) comparable to that of undecorated MTs, confirming that the effective wall thickness, i.e. the thickness of the bridges, did not increase. If the layer of motor proteins were to fill the grooves between protofilaments and create a smooth tube, one can estimate a wall thickness of 4 nm (similar to the thickness of a protofilament), with an inner tube radius of 8.4 nm and a Young's modulus of 0.6 GPa (21). From Eq. 1 we then expect a major increase in the spring constant from 0.074 to 0.7 N/m. While MTs, undecorated or decorated with tau, responded approximately linearly to indentation, the indentation curves performed on Nkin decorated MTs are not linear near the contact point. The MTs initially appear softer, but stiffen up at increasing force. This phenomenon is understandable when one considers the relatively thick decorated protofilaments the tip interacts with (pf + Nkin > 8 nm). The initial deformation is thus better described by the Hertz model of indenting a semi-infinite solid (40), which
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gives a characteristic non-linear response, and is expected to be dominated by compression within the wall itself (41). After this initial embedding of the tip in the wall, the response of the Nkin decorated MT will again be determined by the thinnest parts of the tube cross-section, the lateral bonds between the protofilaments. At higher indentation depths, when the MT surface bends inward, the Nkin heads might touch each other. This possibly explains the increased stiffness at indentations of more than 3 nm (Fig. 3c). It is intriguing to speculate if mechanical stabilization is correlated with kinetic stabilization. Microtubules exhibit dynamic instability, i.e. they are by construction on the verge of instability. The energy driving depolymerization is believed to be stored elastically in the tubulin dimers which are thought to have a tendency to curve outwards when GTP is hydrolyzed to GDP on the β-subunit (42,43). A correlation between MT binding and kinetic MT stabilization is described for many MT binding proteins, measured as an increased level of nucleation, a reduction of catastrophe events and/or a reduction of depolymerization (44-47). The exact mechanisms how MAPs kinetically stabilize MTs are not well understood. Given the model of the outwards curved protofilaments, it seems likely that the correlation between mechanical response and kinetics is also complex. Binding on the ridge could prevent the curving, while binding in the grooves could prevent the splaying apart of protofilaments. In any case, given the physiological importance of dynamic instability, it is likely that the function of MAP-generated changes in MT mechanics are mainly regulating this instability rather than e.g. stiffening the microtubule for structural purposes. The latter could be much more efficiently achieved by bundling of MTs. On the other hand, the fact that motors and also tau do not bind in the grooves might serve to maintain the dynamic instabilty. In conclusion our experiments have shown that AFM is a useful tool to characterize tau and possibly other MAP binding to MTs. Measuring the response to indentation and possibly also to bending can shed light on binding geometries and makes it possible to correlate mechanical properties with chemical properties and function. Acknowledgment We thank Sabine Dieluweit for TEM analysis of MTs and MT/Tau samples, Günther Wöhlke for providing us with Nkin, Fred MacKintosh and Pedro de Pablo for helpful discussions and Pedro de Pablo also for help with the exploratory tau binding experiments. This work was supported by the Dutch Foundation for Research on Matter (FOM).
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Chapter 9 Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication Russell P. Goodman,1 Iwan A. T. Schaap,2 Catherine F. Tardin,2 Christoph M. Erben,1 Richard M. Berry,1 Christoph F. Schmidt,2 Andrew J. Turberfield1
1 Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road,
Oxford OX1 3PU, UK. 2 Department of Physics and Astronomy, de Boelelaan 1081, Vrije Universiteit, 1081 HV,
Amsterdam, The Netherlands. Published in Science 310 (2005) 1661 Contribution of authors DNA tetrahedron design and biochemical experiments were performed by Russell Goodman, Richard Berry, Christoph Erben and Andrew Turberfield from the Oxford University. Iwan Schaap and Catherine Tardin performed the AFM experiments, and their analysis in Amsterdam. Abstract Practical components for 3D molecular nanofabrication must be simple to produce, stereopure, rigid and adaptable. We report a family of DNA tetrahedra, less than 10 nanometers in size, that can self-assemble in seconds with near-quantitative yield of one diastereomer. They can be connected by programmable DNA linkers. Their triangulated architecture confers structural stability; by compressing a DNA tetrahedron with an atomic force microscope, we have measured the axial compressibility of DNA and observed the buckling of the double helix under high loads.
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Three-dimensional (3D) construction by self-assembly requires rigid building blocks such as tetrahedra. DNA is an ideal material for nanofabrication of rigid structures because assembly can be controlled by base-pairing (1) and is relatively inexpensive and simple to execute (2). However, DNA nanofabrication presents the problem of avoiding unwanted by-products. It is often possible to ensure that the target structure is the one that creates the largest number of Watson-Crick base pairs and is therefore the most stable product. Usually, however, there are many other possible structures that are only slightly less stable: if all component oligonucleotides are simply mixed without precaution, the yield of the target structure can be extremely low and disordered, polymeric structures can form instead. Successful strategies for the synthesis of 2D periodic structures involve a hierarchy of interactions in which pre-formed building blocks are linked by weaker interactions to form an array (3-5), but 3D construction is much less well developed. Polyhedral DNA nanostructures with the connectivities of a cube (6) and of truncated and regular octahedra (7,8) have been made, each using a different synthetic strategy. Trisoligonucleotidyls, three oligonucleotides connected by a trifunctional linker (9), have also been reported to form tetrahedral (10). The cube (6) was assembled in solution by ligation of 10 oligonucleotides, in three stages with intermediate purification steps, with 1% yield. The solid-support synthesis of the truncated octahedron (7) allowed greater control of the assembly process: two halves of an edge could only be joined by ligation after a deprotection step in which a restriction endonuclease was used to cleave two precursor hairpin loops to create overlapping sticky ends. This synthesis, starting with 48 oligonucleotides, took approximately two worker-years; yield was less than 1%. Both the cube and truncated octahedron were covalently closed catenanes that could not be disassembled without breaking covalent bonds: in designing the octahedron (8) this robust design principal was sacrificed to permit assembly by folding. The principal component of the octahedron, a 1.7 kb oligonucleotide synthesized using 64 synthetic oligonucleotides and amplified by cloning, was designed to have branched secondary structure: the octahedron was formed when branches folded and were bound together by intramolecular paranemic interactions (11). The junctions that form the vertices of these 3D nanostructures are flexible. DNA nanostructures with triangulated architectures may be capable of resisting deformation, but their mechanical properties have not been measured. Rigidity is not enough to ensure that a DNA polyhedron has a robust and well-defined structure; it is also necessary to select one of the two possible diastereomers (enatiomers with respect to the identities of their vertices) that satisfy the pattern of connectivity imposed by the design of hybridization interactions. Discrimination between diastereomers of DNA polyhedra has yet to be demonstrated, and the stereoselectivity of the syntheses described above is unknown. We have synthesized a family of DNA tetrahedra that have been designed to self-assemble in a single step in only a few seconds. A single diastereomer can be synthesized with yields as high as 95%. We demonstrate their versatility as building blocks for 3D nanofabrication by assembling one regular and nine different irregular tetrahedra and by connecting them with programmable DNA linkers. We then use Atomic Force Microscopy (AFM) to image the tertiary structure of individual tetrahedra and to
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demonstrate their rigidity, which we exploit to measure the response of DNA to axial compression.
Figure 1. DNA tetrahedra. (A) Design of a DNA tetrahedron formed by annealing four oligonucleotides. Complementary subsequences hybridize to form each edge are identified by color. (B) Two views of a space-filling representation of a 3×20/3×30-bp tetrahedron. The backbone of each oligonucleotide is indicated by a single color. (C) AFM image showing several tetrahedra on a mica surface. (D) AFM images, recorded with ultrasharp tips, of four tetrahedral; the three upper edges are resolved. The DNA tetrahedron is designed to be mechanically robust; it consists of rigid triangles of DNA helices covalently joined at the vertices (Fig. 1A) (12). The four component oligonucleotides each run round one face and hybridize to form the double-helical edges. Four edges contain nicks, i.e. breaks in the DNA backbone, where the 5′ and 3′ ends of an oligonucleotide meet. At each vertex, adjacent edges are attached through single, unpaired ‘hinge’ bases. In contrast to the challenging syntheses of DNA cubes (6) and octahedra (7, 8), the synthesis of tetrahedra is extremely simple: all four oligonucleotides are combined in equimolar quantities in hybridization buffer at 95°C then cooled to 4°C in 30 s (13). Tetrahedra form with ~95% yield and migrate as single bands on a nondenaturing electrophoresis gel (Fig. S1) (13). A covalently closed catenane may be produced by enzymatic ligation of the four nicks in the DNA backbone. We believe that the designed hierarchy of interactions between oligonucleotides contributes to the high efficiency of this one-step synthesis. We expect hybridization between oligonucleotides 1 and 2, and also 3 and 4, to form the stable, unnicked edges B and E (Fig 1A) to occur first as the solution temperature falls. Other edges can then form cooperatively; once the formation of any other edge has linked these pairs to form a four-strand complex, all further hybridization interactions required to complete the tetrahedron are intramolecular and
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therefore expected to be faster than competing intermolecular interactions that would form larger complexes. The positions of the nicks are such that none of these intramolecular interactions is substantially hindered by bonds already formed. The tetrahedra imaged by AFM in Fig. 1, C and D, were designed to have three 30-basepair (bp) edges meeting at one vertex and three 20-bp edges bounding the opposite face (a molecular model is shown in Fig. 1B). They are expected to bind to a surface in one of two orientations, with heights of ~10.5 nm if resting on the small face and ~7.5 nm if resting on any of the other three faces. Figure 1C, recorded with a tip 20 nm in radius, shows several objects with heights consistent with the two orientations. Figure 1D shows high-resolution images, obtained using ultrasharp tips with radii of only 2 to 3 nm, which resolve the three upper edges of individual tetrahedra.
Figure 2. Topological and structural analysis of a 20 bp regular tetrahedron. (A and B) Denaturing gels showing products of all possible combinations of ligated and unligated nicks. Control lanes contain oligonucleotides of the same length as the four components of the tetrahedron: linear (lanes A1 and B1), circular (lanes A2 and B2), double (lanes A3 and B3) and triple (lane B4) linked circles. (C) Fully ligated tetrahedron (lane 1) after gel purification (lane 2) and Exo III digestion (lane 3). (D and E) Edge digestions of a fully ligated tetrahedron on a native gel. (D) Lanes 1 to 6: single cuts; lane 7: uncut tetrahedron. (E) Lanes 2 to 16, double cuts; lanes 1 and 17: uncut tetrahedron. Lane M, 50 bp ladder. See (13) for synthesis of markers and for keys to ligated oligonucleotides and edge-cutting enzymes.
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To confirm that our constructs had the topology of a tetrahedron, we used selective enzymatic ligation and digestion. Incubation with T4 DNA ligase leads to ligation (covalent closure) of the nicks where the 5′ and 3′ ends of an oligonucleotide are held together in the middle of an edge, but only if the 5′ end is prepared with a terminal phosphate group. Sixteen regular 20-bp tetrahedra were formed with every combination of ligated and unligated nicks. In the denaturing gels shown in Fig. 2, A to C, linear oligonucleotides dissociated and only circular, catenated oligonucleotides were constrained to migrate together. According to the design, each ligation should produce a circular oligonucleotide and all circles produced by multiple ligations should be catenated with a linking number corresponding to the number of complete helical turns in each edge – in this case two. The expected bands appeared when one, two, three, and four oligonucleotides were ligated (products of failed ligation were also observed). Digestion with exonuclease III, which can hydrolyze duplex DNA from a free 3′ end, confirmed that they contained circular oligonucleotides (Fig 2C, lane 3). The topology of the corresponding single-, double-, triple- and quadruple-linked circles can be described using Conway’s notation (14) as (∞), (-4), (4,4,4) and (6**188.8.131.52.13.4) respectively (Fig. S2) (13). These results are consistent with the topology of the designed structure. Because each edge of the tetrahedron has a different base sequence, sequence-specific enzymatic digestion can be used to provide further confirmation of the tetrahedron’s tertiary structure. Each edge was designed to contain a different restriction sequence that may be digested (cut) by one of six restriction endonucleases. The effects of edge digestion on a fully ligated tetrahedron are shown using native gels in Fig. 2, D and E. None of the six possible single edge cuts, not even the blunt cut produced by Alu I (lane 1), had a measurable effect on the tetrahedron’s mobility (Fig. 2D): we conclude that the tetrahedron’s tertiary structure is particularly stable. The products of each of the 15 possible double-edge digests are shown in Fig. 2E. Three of the cuts created a band with lower mobility than the uncut band; the remaining 12 cut bands had higher mobility. The two groups correspond to two distinct ways of cutting the tetrahedron twice: higher mobility bands were created by cuts on adjacent edges and lower mobility bands by cuts on opposite edges, confirming the designed relations between edges. Our assembly method is extremely flexible. Figure 3A shows two series of tetrahedra made with four 20-bp edges, a fifth edge of 20 or 10 bp, respectively; and a sixth edge, opposite the fifth, that varied in length between 10 and 30 bp. Each synthesis resulted in a single-band product whose mobility decreased with increasing edge length. We can also adapt the design to introduce nicks into all six edges (Fig. S3) (13); single-stranded overhangs at these nicks could be used to create sticky ends to join tetrahedra to make 3D structures. We have investigated an alternative linking strategy based on the incorporation of a single-stranded gap in a tetrahedron edge (Fig. 3B); oligonucleotides containing two subsequences, each capable of hybridizing in a gap, can be used to link tetrahedra in a programmable manner. A linking strand containing two identical subsequences joins pre-formed tetrahedra to create homodimers as expected (Fig. 3B, lanes 2 and 4) (Fig. S4) (13). We have also used linkers incorporating two different binding sequences to create heterodimers (Fig. S5) (13).
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Dimer formation was used to investigate the stereoselectivity of the synthesis. The gapped edge is not free to rotate: the position of the gap along the edge determines the azimuthal position of the free end of the hybridized linker, and thus whether it can reach and hybridize with another tetrahedron. Two gap positions were designed, one for each of the two strands forming the edge, such that the linking strand would project away from the centre of one diastereomer but into the centre of the other (Fig. 3B, outer panels). In the latter configuration, the linker is expected to be inaccessible. Controls with gaps translated by five bases (half a helical turn) were designed to have the opposite linker orientation. The results of linking experiments for a tetrahedron with 5×20/1×30-bp edges (Fig. 3B) are consistent with the presence of a large excess of the diastereomer in which the major groove of each helix faces inward at each vertex, indicating a significant difference between the formation rates or stabilities of the two possible diastereomers. Stereoselective synthesis, in combination with structural rigidity, ensures that the relative coordinates of any part of the structure can be defined with near-atomic accuracy, an essential property of a nanostructure to be used as a building block for molecular nanofabrication. We use these structurally braced tetrahedra to investigate the behavior of DNA under compression. Although DNA under tension has been widely studied (15-18), DNA strands of micrometer length buckle at extremely low forces. Measurement of the response of DNA to large compressive loads could help resolve the current controversy over the nature of structural changes associated with rare large-angle deformations of the double helix (19, 20). To measure the mechanical response of a single tetrahedron directly, we used an AFM tip as a sensitive force transducer. The tip was centered over a tetrahedron located in imaging mode and was then moved toward the surface while recording force. Compression curves for seven distinct 3×20/3×30-bp tetrahedra, as imaged in Fig. 1, are shown in Fig. 4. For forces up to ~100 pN, the response was approximately linear and reversible (Fig. 4, inset) with an average force constant of 0.18(±0.07) Nm-1. At higher forces, the response was nonlinear and varied from tetrahedron to tetrahedron; tetrahedra generally softened suddenly and deformed irreversibly at a load between 70 and 200 pN.
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Figure 3. Versatility and stereoselectivity of tetrahedron synthesis. (A) Tetrahedra with five 20-bp edges and one edge of 10 bp (lane 1), 15 bp (lane 2), 20 bp (lane 3), 25 bp (lane 4), or 30 bp (lane 5). Tetrahedra with four 20-bp edges, one 10-bp edge and an opposite edge of 10 bp (lane 6), 15 bp (lane 7), 20 bp (lane 8), 25 bp (lane 9), or 30 bp (lane 10). For both series the tetrahedra in the first and last lanes are illustrated by 3D models; the edge that is varied is marked with an arrow. (B) Linking experiments demonstrating stereoselectivity. A linking strand may join two 5×20/1×30-bp tetrahedra by hybridizing in 10-bp single-stranded gaps in both long edges. There are two possible diastereomers of a DNA tetrahedron. Four gap positions, two in each strand forming the edge, were designed such that the linker would emerge on the outside of one diastereomer, accessible for further hybridization (left panel), and on the inside of the other, hindering further hybridization (right panel). A strong dimer band is observed in only the two cases consistent with the presence of diastereomer, in which the major groove of each helix faces inwards at the vertices. See (13) for detailed information on structures. Lane M, 50-bp ladder.
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To model the compressibility of a DNA tetrahedron, we treat its edges as elastic rods pinned (freely hinged) at the vertices. The calculated response of a 3×20/3×30-bp tetrahedron to a compressive load applied between the top vertex and the surface supporting the bottom face is approximately the same for both orientations and is dominated by axial compression of the upstanding edges. The calculated force–displacement (F-d) curve is approximately linear up to a critical load at which the tetrahedron buckles. The boundary conditions at the bottom face have a small effect on the response: if the bottom vertices are not fixed but allowed to slide on the surface then the bottom edges stretch and the overall stiffness of the construct is reduced by ~3% and ~13% for the tall and short orientations of the tetrahedron, respectively. From the gradient of the linear part of the measured F-d curve, we infer an elastic modulus of Kc = 0.7(±0.3) nN for one DNA double helix in compression. In the linear response regime, elastic moduli measured by extension and compression should be equal: our value for Kc is near that of the elastic modulus of DNA in tension Ke ~ 1.1 nN, obtained by fitting the force-extension curves of DNA duplexes (17, 18). Our direct measurement of the axial elastic response of DNA in compression was made possible by the braced structure of the tetrahedron that enabled a short DNA helix to bear a compressive load without bending or tilting.
Figure 4. Compression of single DNA tetrahedra. Compression curves show linear elastic response up to a load of 0.1 nN. At higher forces, most tetrahedra deform irreversibly. Offsets were adjusted to overlap the linear parts of the seven curves. Inset: Reversibility of the elastic response of a typical tetrahedron. We may use our measured elastic modulus to estimate the load at which we would expect the edges of a tetrahedron to buckle. If a DNA duplex is modeled as a uniform cylinder of radius r = 1 nm (21), then the critical compressive force in an edge at which we would expect Euler instability is Fc = π2r2K/(2υl)2, where K is the elastic modulus, l is the edge length, and υ is a numerical factor that depends on the boundary conditions at the vertices. If the vertices are pinned, then υ = 1; if the orientations of the edges at the vertices are fixed, then υ = ½. The corresponding AFM tip loads lie in the range from 50 to 300 pN, which is consistent with the range of loads at which tetrahedra were observed to soften suddenly. Our observations of the failure of tetrahedra under high load can thus be
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explained on the basis of the traditional model of uniform DNA bending (20); this result is consistent with our interpretation that the linear part of the F-d curve is caused by pure axial compression of the tetrahedron’s upstanding edges before buckling occurs. The structural changes associated with DNA bending are the subject of controversy: suggestions that sharp bends due to local melting or kinking (22) are observed in DNA cyclization experiments (19, 23, 24) are countered by measurements that indicate that the probability of such kinks is very low (20). Extended observation of tetrahedra under compression may be a useful method to investigate the energy and sequence-dependence of inhomogeneous bending and of the effects of compressive strain on DNA-protein interactions.
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References and Notes 1. N. C. Seeman, Nature 421, 427 (2003). 2. Commercial oligonucleotide synthesis costs ~50¢ per base for several nanomoles and, at its simplest, fabrication requires only mixing of aqueous solutions. 3. E. Winfree, F. R. Liu, L. A. Wenzler, N. C. Seeman, Nature 394, 539 (1998). 4. J. Malo, J. C. Mitchell, C. Vénien-Bryan, J. R. Harris, H. Wille, D. J. Sherratt, A. J. Turberfield, Angew. Chem. Int. Ed. 44, 3057 (2005). 5. H. Yan, S. H. Park, G. Finkelstein, J. H. Reif, T. H. LaBean, Science 301, 1882 (2003). 6. J. H. Chen, N. C. Seeman, Nature 350, 631 (1991). 7. Y. W. Zhang, N. C. Seeman, J. Am. Chem. Soc. 116, 1661 (1994). 8. W. M. Shih, J. D. Quispe, G. F. Joyce, Nature 427, 618 (2004). 9. M. Scheffler, A. Dorenbeck, S. Jordan, M. Wüstefeld, G. von Kiedrowski, Angew. Chem. Soc. 116, 1661 (1994) 10. A. Dorenbeck, thesis, Ruhr-Universität Bochum (2000). 11. X. Zhang, H. Yan, Z. Y. Shen, N. C. Seeman, J. Am. Chem. Soc. 124, 12940 (2002). 12. In a preliminary communication (25), we introduced a tetrahedral nanostructure with nicks positioned such that helices could separate and unwind at the vertices: this construct was not expected to resist deformation. 13. See supporting material on Science Online 14. J. H. Conway in Computation Problems in Abstract Algebra, J. Leech, Ed. (Pergamon Press, Oxford, England, 1970). 15. C. Bustamante, J. F. Marko, E. D. Siggia, S. Smith, Science 265, 1599 (1994). 16. S. B. Smith, Y. J. Cui, C. Bustamante, Science 271, 795 (1996). 17. M. D. Wang, H. Yin, R. Landick, J. Gelles, S. M. Block, Biophys. J. 72, 1335 (1997). 18. C. G. Baumann, S. B. Smith, V. A. Bloomfield, C. Bustamante, Proc. Natl. Acad. Sci. U.S.A. 94, 6185 (1997). 19. T. E. Cloutier, J. Widom, Proc. Natl. Acad. Sci. U.S.A. 102, 3645 (2005). 20. Q. Du, C. Smith, N. Shiffeldrim, M. Vologodskaia, A. Vologodskii, Proc. Natl. Acad. Sci. U.S.A. 102, 5397 (2005). 21. M. E. Hogan, R. H. Austin, Nature 329, 263 (1987). 22. F. H. C. Crick, A. Klug, Nature 255, 530 (1975). 23. J. Yan, J. F. Marko, Phys. Rev. Lett 93, 108108 (2004). 24. P. A. Wiggins, R. Phillips, P. C. Nelson, Phys. Rev. E. 71, 021909 (2005). 25. R. P. Goodman, R. M. Berry, A. J. Turberfield, Chem. Commun. 1372 (2004) Acknowledgements We thank J. Johannes for advice on the topology of circular catenanes. Supported by the UK Bionanotechnology and Biological Sciences Research Council, Engineering and Physical Sciences Research Council, Medical Research Council, and Ministry of Defence (through the UK Bionanotechnology Interdisciplinary Research Collaboration); the Oxford life Sciences Interface Doctoral Training Centre; the Rhodes Trust; the Natural Sciences and Engineering Research Council of Canada; and the Dutch Foundation for Fundamental Research on Matter (FOM).
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Chapter 10 Samenvatting Nano-mechanica van eiwit en DNA structuren Het zichtbaar maken en het betasten van moleculen met atomic force microscopie Dit proefschrift bestaat uit een collectie van artikelen waarvan een deel reeds gepubliceerd is en de rest nog gepubliceerd zal worden in wetenschappelijke tijdschriften. De objecten die ik heb onderzocht zijn gemaakt van DNA of eiwitten. Hoewel DNA in levende organismen meestal voor de opslag van erfelijke eigenschappen dient, hebben wij het gebruikt als constructiemateriaal om er kleine bouwsteentjes van te maken. Eiwitten hebben vele functies in de cel, ze worden gebruikt als bouwmateriaal, ze vormen enzymen die chemische reacties reguleren, en sommige werken als motoreiwitten en hebben een transportfunctie in de cel. In hoofdstukken 2 tot en met 8 hebben we microtubuli onderzocht, dit zijn buisvormige eiwitstructuren die stevigheid aan de cel geven, ze fungeren als celskelet. Een microtubule bestaat uit tubuline eiwitten die in lengterichting met elkaar binden en zo lange filamenten vormen, de protofilamenten. Dertien van deze protofilamenten binden zijdelings met elkaar en sluiten zich tot een buis, de microtubule. Microtubuli kunnen micrometers lang zijn maar hun diameter is slechts 25 nanometer (1 nanometer is 10-9 meter). Om op deze schaal nauwkeurige metingen te kunnen doen is het essentieel om een microscoop te gebruiken met een nanometer resolutie, die ook gebruikt kan worden onder omstandigheden die lijken op die in de cel (waterig, bij kamertemperatuur). Voor al het onderzoek heb ik een atomic force microscoop gebruikt. Dit type microscoop gebruikt een heel fijn naaldje om het object af te tasten, vervolgens wordt deze informatie vertaald naar een driedimensionaal beeld. Juist omdat het object mechanisch wordt afgetast is het belangrijk om dit met een heel lage kracht te doen zodat de DNA of eiwit structuren niet beschadigen. In hoofdstuk 2 tot en met 5 wordt gedemonstreerd dat het mogelijk is om microtubuli met een atomic force microscoop zichtbaar te maken zonder ze te slopen. Het was belangrijk om ze goed aan het oppervlak vast te maken en om de scankracht beneden de 300 picoNewton te houden (1 picoNewton is 10-12 Newton). Onder deze condities was de resolutie hoog genoeg om de individuele eiwitten van 4 nanometer elk te kunnen onderscheiden. De mogelijkheid om met deze resolutie onder relatief natuurlijke omstandigheden te werken hebben we gebruikt om de interactie tussen microtubuli en andere eiwitten te bestuderen. In hoofdstuk 8 wordt een onderzoek aan het tau eitwit beschreven. Tau komt veel in zenuwcellen voor en zorgt voor stabilisatie en bundeling van microtubuli. Veel neuropatische aandoeningen (bijvoorbeeld de ziekte van Alzheimer) zijn gerelateerd aan defecten aan het tau eiwit. Hoe tau precies aan microtubuli bindt, en wat het effect is op de mechanische eigenschappen van microtubuli, is nog niet bekend. Uit mijn onderzoek blijkt dat tau een 1 nanometer dikke laag om de microtubule vormt, deze laag is niet homogeen maar bindt alleen aan de buitenkant van de protofilamenten. Ondanks de toegenomen diameter neemt de (radiale) stijfheid van de
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microtubule nauwelijks toe door de tau binding. In hoofstuk 5 wordt onderzoek aan het motoreiwit kinesine beschreven. Kinesine motoreiwitten binden ook aan microtubuli, maar kunnen zich door ATP (brandstof) te hydroliseren voortbewegen langs de microtubule. Kinesine motoreiwitten zijn verantwoordelijk voor het transport van materialen in de cel. Door microtubuli en kinesine met de atomic force microscoop zichtbaar te maken, konden we kinesine zien ‘lopen’ over de microtubule met stappen van 8 nanometer. Ook zagen we dat kinesine maar op 1 protofilament liep en niet zomaar een stap opzij kon doen. Wanneer er veel kinesine op de microtubule was dan veroorzaakte dit dan ook opstoppingen op de microtubule. In extreme gevallen stopte kinesine zelfs om te wachten op de voorliggers. In de cel zijn er naast kinesine veel andere eiwitten die ook aan de microtubule binden. Ons onderzoek roept nieuwe vragen op over het natuurlijke gedrag van kinesine, bijvoorbeeld hoe worden opstoppingen op microtubuli voorkomen in de cel? In de hoofdstukken 6 tot en met 9 hebben we de atomic force microscoop gebruikt als instrument om mechanische eigenschappen te meten. De scherpe naald van de microscoop werd gebruikt om objecten in te duwen om zo hun elasticiteit te bepalen. In hoofdstuk 6 en 7 worden de mechanische eigenschappen van microtubuli beschreven. Bij het induwen gedroeg de microtubule zich elastisch tot indrukkingen van 3.6 nm. Bij grotere vervormingen trad er meestal onherstelbare schade op, waarschijnlijk omdat de afzonderlijke tubuline eiwitten dan uit hun verband geduwd werden. In sommige gevallen was het mogelijk om een gat in de microtubule te duwen, dat zich naar verloop van tijd weer sloot, een zelf-reparerend mechanisme. Door gebruik te maken van de eindige elementen methode (een numerieke methode uit de constructie- en bouwwereld die onder andere gebruikt wordt om het mechanisch gedrag van gebouwen, bruggen en vliegtuigen te berekenen) heb ik de experimenten gesimuleerd, om op deze manier de verbanden te berekenen tussen de vorm van de microtubule, het materiaal waarvan deze gemaakt is en de gemeten elasticiteit. In hoofdstuk 9 hebben we driedimensionale structuren onderzocht die zichzelf assembleren uit DNA fragmenten. Eerst hebben we deze 7 nanometer hoge DNA tetraëders zichtbaar gemaakt door gebruik te maken van extra scherpe scan naalden. Door vervolgens de tetraëders in te drukken konden we de vervorming meten. Hieruit hebben we de elasticiteit van DNA bepaald onder samendrukking in de lengterichting, en laten zien dat DNA gebruikt kan worden om er stevige bouwstenen van te maken. De technieken, die voor het onderzoek beschreven in dit proefschrift zijn ontwikkeld, om met een atomic force microscoop bio-moleculen zichtbaar te maken zonder ze te beschadigen, kunnen nu relatief eenvoudig aangepast worden om andere biologische systemen te onderzoeken. Met de opgedane kennis over de mechanische eigenschappen van bio-moleculen, eiwitten en DNA, hebben we een beter inzicht gekregen in hun functie in hun natuurlijke omgeving, de cel. Voor microtubuli bijvoorbeeld, fungeren de protofilamenten als verstevigingsribben in de lengterichting. Hierdoor krijgt de microtubule een grotere stijfheid in de lengterichting. Deze ideeën uit de natuur kunnen we ook toepassen om van bio-materialen stabiele zichzelf assemblerende structuren te ontwerpen voor toepassingen in de nanotechnologie.
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List of publications Publications in academic journals P.J. de Pablo, I.A.T. Schaap and C.F. Schmidt Observations of microtubules with scanning force microscopy in liquid Nanotechnology 14 (2003) 143 P.J. de Pablo, I.A.T. Schaap, F.C MacKintosh and C.F. Schmidt Deformation and collapse of microtubules on the nanometer scale Physical Review Letters 91-9 (2003) 098101 D.D. Addie, I.A.T. Schaap, L. Nicolson and O. Jarrett Persistence and transmission of natural type I feline corona virus infection Journal of General Virology 84 (2003) 2735 I.A.T. Schaap, P.J. de Pablo and C.F. Schmidt Resolving the molecular structure of microtubules under physiological conditions with scanning force microscopy European Biophysics Journal 33 (2004) 462 R.P. Goodman, I A.T. Schaap, C.F. Tardin, C.M. Erben, R.M. Berry, C.F. Schmidt and A.J. Turberfield Rapid Chiral Assembly of Rigid DNA Building Blocks for Molecular Nanofabrication Science 310 (2005) 1661 J.F. Graveland-Bikker, I.A.T. Schaap, C.F. Schmidt and C.G. de Kruif Structural insight in an artificial self-assembling protein nanotube Nano Letters (2006) in press
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Publications in preparation I.A.T. Schaap, C. Carrasco, P.J. de Pablo, F.C MacKintosh and C.F. Schmidt Elastic response, buckling and instability of microtubules under radial indentation (in preparation) I.A.T. Schaap, B. Hoffmann, C. Carrasco, R. Merkel and C.F. Schmidt Tau protein binding forms a 1 nm thick layer along protofilaments without affecting the radial stability of microtubules (in preparation) C. Carrasco, A. Carreira, I. A. T. Schaap, P. A. Serena, J. Gómez-Herrero, M. G. Mateu and P. J. de Pablo Anisotropic mechanical reinforcement of a virus by its genomic DNA (in preparation) C. Carrasco, I.A.T. Schaap, C. F. Schmidt, J. Gómez-Herrero and P. J. de Pablo Small versus large cantilevers for non-invasive imaging at single-protein resolution in liquids with atomic force microscopy (in preparation) I.A.T. Schaap, C. Carrasco, P.J. de Pablo, and C.F. Schmidt Displacements of single kinesin motors followed by atomic force microscopy (in preparation)